Data-Model Fusion Methods and Applications Toward Smart Manufacturing and Digital Engineering

Engineering ›› 2025, Vol. 55 ›› Issue (12) : 36 -50. DOI: 10.1016/j.eng.2024.12.034

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2024-02-08	2024-12-12	2025-12-27
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2025-04-22	2024-11-29

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Abstract

As pivotal supporting technologies for smart manufacturing and digital engineering, model-based and data-driven methods have been widely applied in many industrial fields, such as product design, process monitoring, and smart maintenance. While promising, both methods have issues that need to be addressed. For example, model-based methods are limited by low computational accuracy and a high computational burden, and data-driven methods always suffer from poor interpretability and redundant features. To address these issues, the concept of data-model fusion (DMF) emerges as a promising solution. DMF involves integrating model-based methods with data-driven methods by incorporating big data into model-based methods or embedding relevant domain knowledge into data-driven methods. Despite growing efforts in the field of DMF, a unanimous definition of DMF remains elusive, and a general framework of DMF has been rarely discussed. This paper aims to address this gap by providing a thorough overview and categorization of both data-driven methods and model-based methods. Subsequently, this paper also presents the definition and categorization of DMF and discusses the general framework of DMF. Moreover, the primary seven applications of DMF are reviewed within the context of smart manufacturing and digital engineering. Finally, this paper directs the future directions of DMF.

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Data-model fusion / Model-based methods / Data-driven methods / Smart manufacturing / Digital engineering

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Fei Tao, Yilin Li, Yupeng Wei, Chenyuan Zhang, Ying Zuo. Data-Model Fusion Methods and Applications Toward Smart Manufacturing and Digital Engineering. Engineering, 2025, 55(12): 36-50 DOI:10.1016/j.eng.2024.12.034

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1. Introduction

Over the past few years, the rapid advancement of information technology has significantly accelerated the intelligent and digital transformation in manufacturing. Numerous manufactural enterprises have embraced this transformation by capitalizing on emerging technologies, such as the Internet of Things [1], digital twin [2], and cloud computing [3]. As the representative paradigms of this transformation, smart manufacturing and digital engineering have been unprecedentedly employed across diverse industrial fields. On the one hand, smart manufacturing represents a revolutionary manufacturing paradigm wherein manufacturing machines are interconnected through wireless networks, monitored by sensors, and governed by advanced computational intelligence to enhance product quality and system productivity, and reduce costs. Digital engineering, on the other hand, refers to a new paradigm, which aims at the construction of digital counterparts of real-world products, systems, or processes for a more effective insight, management, and optimization of manufacturing systems and processes [4].

As pivotal supporting technologies for smart manufacturing and digital engineering, cyber-physical systems and cloud computing have been widely adopted in manufacturing to collect unprecedentedly large volumes of industrial data and obtain relevant domain knowledge throughout the entire lifecycle of a product. To effectively utilize these industrial data and domain knowledge, advanced analytical methods have been investigated to transform them into insightful and valuable information to enable a more effective decision-making process. These advanced analytical methods can be typically classified as three groups: model-based methods, data-driven methods, and hybrid methods that integrate model-based and data-driven methods, which are also known as data-model fusion (DMF).

Model-based methods refer to mathematical methods grounded in system behaviors derived from physical laws or prior domain knowledge [5]. Model-based methods have been adopted in numerous fields, such as process design [6], fault detection [7], damage identification [8], and remaining useful life prediction [9]. Data-driven methods rely on data analysis to extract meaningful insights, patterns, and knowledge, without necessarily requiring prior domain knowledge or explicit mathematical models based on physical laws [10]. Data-driven methods are also applied in numerous fields, such as defect inspection [11], fault diagnosis [12], maintenance decision [13], quality control [14], and scheduling optimization [15]. While the effectiveness of model-based methods and data-driven methods has been demonstrated in many applications of smart manufacturing and digital engineering, both of them have issues that need to be addressed. For example, model-based methods are highly dependent on assumptions or domain knowledge that may not be existent or precise, resulting in reduced reliability and precision. Data-driven methods typically require a significant amount of data that may be difficult to obtain, and are mostly black-box methods that lack interpretability.

As an answer to the aforementioned issues, DMF was presented to seamlessly integrate model-based methods and data-driven methods to overcome the drawbacks of both methods in a unified manner. Despite an increasing research effort has been made around DMF, a unanimous definition remains elusive [16], [17], [18], [19], [20] and a conceptual framework of DMF is rarely discussed. For example, some scholars define DMF as the pattern that incorporates prior knowledge into machine learning [19], [21], while other scholars believe that the recently emerging scheme termed physics-informed machine learning, which applies machine learning methods to build the solver of a differential equation, belongs to DMF [20], [22], [23], [24].

To fill these gaps, this work provides the state-of-the-art review of DMF by systematically screening related articles reported in the existing literature. Table 1 summarizes the review methodology, including the database, article type, time period, language, searching strings, and screening criteria. Due to the lack of unanimity in the initial appearance of DMF, this work focuses on relevant papers from the Web of Science Core Collection over the past five years. To ensure completeness, this work screened the retrieved papers in three steps. First, this work obtained related articles by searching for the topic “data-model fusion.” Second, this work meticulously reviewed the contents of abstract, introduction, and conclusions of each paper to evaluate the correlation between its research topic and DMF. An iterative process was followed to produce a comprehensive list of search strings for DMF, as listed in Table 1. Third, the authors repeatedly searched for these strings in the context of smart manufacturing and digital engineering. By evaluating the correlation between the retrieved papers and the research topic, irrelevant papers were excluded. Following these steps, a list of high-frequency terminologies related to DMF was obtained, as shown in Fig. 1.

By comprehensively reviewing well-selected articles from various databases and synthesizing diverse perspectives, this paper aims to answer seven questions regarding DMF: ➀ What is the categorization and composition of model-based and data-driven methods? ➁ What is the fusion strategy of model-based and data-driven methods? ➂ How to categorize DMF? ➃ What is the conceptual framework of DMF? ➄ How can DMF be implemented? ➅ In which industrial fields has DMF been applied? ➆ What is the future direction of DMF? The remainder of this paper is organized as follows: 2 Overview of model-based methods, 3 Overview of data-driven methods summarize the categorizations of model-based methods and data-driven methods, respectively. Section 4 provides a generic framework of DMF. Section 5 presents a conceptual framework of DMF. Section 6 reviews the industrial applications of DMF in the context of smart manufacturing and digital engineering. Section 7 discusses the challenges faced by DMF and prospective directions for its development. Finally, Section 8 summarizes the primary contributions and conclusions of this paper.

2. Overview of model-based methods

As essential tools for exploring scientific theory and engineering practice, model-based methods have been widely applied in numerous industrial fields. However, the classification of model-based methods remains inconsistent. For example, some studies consider physical law-based methods as the primary type of model-based methods, while others view state estimation models, such as Kalman filters and particle filters, as the primary branch of model-based methods [25], [26]. To deal with such an inconsistency, this section systematically reviews the state-of-the-art model-based methods [5], [27] and classifies them into empirical, analytical, and numerical categories based on problem complexity and the ability to obtain closed-form solutions. Empirical model-based methods are suitable for less complex and more intuitive solutions, while analytical and numerical methods are used for more complex problems. Moreover, analytical methods can provide closed-form solutions, whereas numerical methods typically offer only approximate solutions. The detailed classification of model-based methods and their related models are presented in Table 2 [5], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], and these methods are further illustrated in 2.1 Empirical model-based methods, 2.2 Analytical model-based methods, 2.3 Numerical model-based methods.

2.1. Empirical model-based methods

The empirical model-based methods rely on observations and real-world data rather than theoretical or abstract principles [5]. These methods serve as approximate representations to illustrate the relationships between independent and dependent variables [28], making them integral to smart manufacturing and digital engineering, particularly in areas such as manufacturing process modeling [29] and optimization [30].

Fig. 2(a) presents the generic framework for empirical model-based methods. The causal relationships between independent and dependent variables are first initialized to formulate an appropriate model assumption, which may involve polynomial, exponential, or logarithmic models. Following this, experimental data are collected for both independent and dependent variables, and a parameter estimation method is selected to estimate the parameters of the presumed empirical model. These parameter estimation methods include least squares-based methods and interpolation-based methods, all of which aim to minimize the deviation between observed and predicted dependent variables. Once the model is built, the observed independent variables are input into the model to inform decision-making processes. As shown in Table 2, empirical model-based methods can be further categorized into linear or nonlinear types, depending on whether the fitted empirical models are linear or nonlinear.

2.2. Analytical model-based methods

Analytical model-based methods utilize mathematical equations to provide closed-form solutions that describe system behaviors and assess performance [31], [32]. In the realm of smart manufacturing and digital engineering, these methods leverage physical laws, dynamics, or mechanical mechanisms to enable decision-making throughout the entire product life cycle [33], [34], [35], including improving manufacturing processes [36] and enhancing precision [37].

As illustrated in Fig. 2(b), in the generic framework of analytical model-based methods, the formulation of an analytical model is initiated to incorporate relevant domain knowledge such as physical laws and probabilistic correlations. This knowledge is also applied to determine certain ascertainable parameters within the analytical model. For parameters that cannot be predetermined, experimental data are used to estimate them through parameter estimation methods, such as least-squares estimation, maximum likelihood estimation [50], the expectation-maximization algorithm [51], Bayesian estimation [52], and covariance matrix estimation [53]. Once all parameters are determined, the observed independent variables are fed into the analytical model to compute closed-form solutions using methods such as belief propagation [54], variable elimination [55], Monte Carlo methods [56], expectation propagation [57], and variational inference [58].

Analytical model-based methods can be further classified as two groups: non-probabilistic and probabilistic analytical model-based methods, based on whether the uncertainty and randomness of experimental data are taken into account [38], [39], [40]. Non-probabilistic analytical model-based methods mainly rely on physical theories or first principles to construct physics-based models that yield analytical solutions [59]. These models enable the computation of analytical solutions for dependent variables based on manually predetermined parameters and parameters estimated by analyzing extensive experimental data. Probabilistic analytical model-based methods consider the uncertainty and randomness of variables and the causal relationships between random variables in a unified manner [60], [61]. Some of the probabilistic and non-probabilistic analytical models are listed in Table 2.

2.3. Numerical model-based methods

Numerical model-based methods compute the solutions of a significant number of mathematical equations to search for an approximate solution to a complicated physical problem [41]. In the context of smart manufacturing, numerical model-based methods enable the digitalization of manufacturing systems and have been employed in many industrial applications throughout the entire product lifecycle [62], such as product design and development [42], [44] and process simulation [45], [46], [48].

The generic framework of numerical model-based methods is illustrated in Fig. 2(c). To initiate the process, a numerical model assumption is formulated as the integration of both related domain knowledge and a presumed empirical model. For example, a numerical model assumption could be a solvable empirical representation, which is often expressed as a weighted sum of analytically solvable models, to address complex or insolvable problems. Subsequently, for parameterization of the numerical model assumption, the manual determination of parameters, constraint relations, and boundary conditions is conducted under the guidance of relevant domain knowledge. The inclusion of constraint relations and boundary conditions serves the purpose of ensuring the numerical solutions align with the correct solution spaces as much as possible. Lastly, numerical computation methods are employed to provide an approximate solution, where these methods include a series of techniques designed to realize the approximation process of optimal numerical solutions with high precision.

Numerical model-based methods can be categorized as meshing and meshless numerical models based upon the requirement for discretized solution domains [47], [49]. Meshing numerical model-based methods focus on computing numerical solutions within discretized solution domains to compute the solution of a numerical model. Depending on whether the discretized solution domains to be analyzed are internal or peripheral, the meshing numerical model-based methods can be further classified. Meshing numerical model-based methods for internal domains include the finite element method [63], finite differential method [64], finite volume method [65], and so on. The primary meshing numerical model-based method for boundary domains is the boundary element method [66]. While the efficiency of meshing numerical model-based methods has been demonstrated, they face limitations in handling materials with complex structures due to the substantial costs associated with adjusting or inspecting meshes [67]. As a complement, meshless numerical model-based methods eliminate the need for discretizing the solution domain. These methods facilitate the analysis of interactions between adjacent nodes to compute numerical solutions. Numerical computation methods for meshless numerical models include element-free Galerkin [68], smoothed particle hydrodynamics [69], and SPG [70]. Meshless numerical model-based methods have shown efficiency in solving challenging problems. However, they still present challenges such as significant computational burdens and the requirement for substantial programming efforts.

3. Overview of data-driven methods

Over the past few decades, the rapid advancement of information and communication technologies, including Internet of Things, cloud computing, and artificial intelligence, has significantly accelerated the acquisition, transmission, storage, and utilization of big data [71]. To effectively deal with this big data, data-driven methods are increasingly employed. Data-driven methods rely on data analysis techniques to extract potential features and reveal hidden patterns within big data to enable correlation analysis and decision-making across diverse engineering applications [72].

Although numerous efforts have been made toward the evolution of data-driven methods, the classification of data-driven methods remains inconsistent. For example, the predominant view among scholars was that machine learning plays a critical role in these methods [73], [74], [75], [76], [77], whereas some researchers believed that data processing, feature extraction, and statistical analysis were the integral parts of data-driven methods [78], [79]. To deal with such inconsistency, this work classifies data-driven methods into two main groups: statistical analysis methods and machine learning methods, considering the era of wide adoption of machine learning and the complexity of the problem to be analyzed [80]. Statistical analysis methods are typically employed before machine learning methods to solve fewer complex problems, while machine learning methods are adopted to handle more complex problems. Statistical analysis methods are further classified based on the specific target of the statistical analysis, and machine learning methods are further categorized based on the depth of their network structures [75], [81]. More details can be found in Table 3 [82], [83], [84], [85], [86], [87], [88], [89], [90], [91], [92], [93], [94], [95], [96], [97], [98], [99]. The compositions and applying procedures of statistical analysis methods and machine learning methods are illustrated in 3.1 Statistical analysis methods, 3.2 Machine learning methods, respectively.

3.1. Statistical analysis methods

Statistical analysis methods are essential tools for collecting, organizing, and analyzing data, and they were widely adopted prior to the widespread use of machine learning methods. These methods can be further classified as descriptive and inferential statistical analysis methods [100]. The composition and procedures of descriptive and inferential statistical analysis methods are illustrated in 3.1.1 Descriptive statistical analysis methods, 3.1.2 Inferential statistical analysis methods, respectively.

3.1.1. Descriptive statistical analysis methods

Descriptive statistical analysis methods seek to summarize statistical features and analyze correlations within samples [82], [83]. The descriptive statistical analysis methods are applied for evaluating performance of manufacturing process [84], [85], [86].

Regarding the type of analysis results, descriptive statistical analysis methods can be categorized into statistical feature analysis methods [101] and correlation analysis methods [102], as presented in Fig. 3(a). Statistical feature analysis methods aim to visualize the statistical features of samples using various statistical tools. These methods can display multiple statistical features such as median, range, percentiles, deviation, variance, and standard deviation. Correlation analysis methods aim to reveal hidden correlations such as trends, clustering, and feature significance within data.

Regarding the number of random variables to be considered, descriptive statistical analysis methods can be further classified as univariate and multivariate methods [103]. Univariate descriptive statistical methods primarily utilize statistical tools to reveal the evolutionary trend of univariate random variables. These methods include frequency tabulation, pie charts, and autoregressive models. Univariate analysis serves as the foundation of multivariate descriptive statistical analysis. The objective of multivariate analysis is to outline the statistical features of multivariate samples and reveal the interactions among multiple variables [104]. Typical multivariate methods include frequency crosstabulation, scatter diagrams, radar maps, Pearson correlation [105], nonlinear regression [106], and logistic regression [107].

3.1.2. Inferential statistical analysis methods

Inferential statistical analysis methods are employed to infer parameters and correlations of product lifecycle data through the examination of statistical characteristics [87]. In smart manufacturing and digital engineering, inferential statistical analysis methods also play an essential role in the evaluation of manufacturing accuracy [88], [89], capacity [90], and profit [91], [108].

The procedures of inferential statistical analysis primarily include random sampling and inference [87]. Random samples are initially sampled from data population by using specific sampling techniques, including simple random sampling, systematic sampling, stratified sampling, and cluster sampling. Subsequently, significant parameters of product lifecycle data are inferred through either parameter estimation or hypothesis testing. In parameter estimation, statistical features of random samples are utilized to estimate the parameters of the population. In hypothesis testing, hypotheses concerning parameters are formulated, and random samples are then employed to determine whether the null hypotheses should be accepted or rejected.

Inferential statistical analysis methods can be classified as parametric and non-parametric inferential statistical analyses [109], as presented in Fig. 3(a). The prerequisite for parametric inferential statistical analysis methods is the assumption that a random variable is continuous and follows a specific probability distribution. For example, the prerequisite of student’s t-test is that a random variable follows a normal distribution [110]. However, in most cases, the probability distribution of a random variable is not always available. To address this issue, non-parametric inferential statistical analysis methods can be employed as they are not reliant on the assumption of a specific probability distribution for a random variable. As a result, non-parametric inferential statistical analysis methods have a broader application field compared to parametric inference. Typical non-parametric inferential statistical analysis methods include the Friedman test [111], Kruskal-Wallis H test [112], Mann-Whitney U test [113], and Shapiro-Wilk test [114].

3.2. Machine learning methods

While the capabilities of descriptive or inferential statistical analysis have been demonstrated, these methods are not effective in either feature extraction or pattern recognition. Machine learning methods enable the construction of shallow or deep nonlinear mapping architectures to extract features and recognize hidden patterns from product lifecycle data [115], [116], [117]. These methods can be further grouped into shallow machine learning methods and deep learning methods, as illustrated in 3.2.1 Shallow machine learning methods, 3.2.2 Deep learning methods, respectively.

3.2.1. Shallow machine learning methods

Shallow machine learning methods mainly use classical machine learning methods to construct a shallow nonlinear mapping architecture to identify hidden correlation within product lifecycle data [66], [67], [68]. In smart manufacturing and digital engineering, shallow machine learning methods can be used across diverse applications, such as process optimization [92], fault diagnosis [93], and process condition monitoring [94].

The generic framework of shallow machine learning methods includes feature extraction, feature selection, model fitting and testing, and decision-making, as shown in Fig. 3(b). First, feature extraction identifies essential features that preserve critical information within product lifecycle data. Second, feature selection aims to choose an optimal subset of extracted features to avoid redundant information and reduce the feature dimensionality. Third, the selected features are fed into a shallow network architecture to perform model fitting and testing [118], [119]. Lastly, a machine learning model is gained and adopted to recognize hidden correlation and enable decision-making [120], [121].

Based upon whether shallow machine learning methods are supervised, they can be further classified as supervised, semi-supervised, and unsupervised shallow machine learning methods. Supervised shallow machine learning methods, such as support vector machine (SVM) and multilayer perceptron (MLP), are typically viewed as decision-making algorithms that map data to labels [122]. Semi-supervised shallow machine learning methods leverage labeled samples to infer the characteristics of unlabeled samples [123]. Unsupervised shallow machine learning methods explore data structure and decrease data dimensionality to extract or select features [124]. While various shallow machine learning methods can facilitate feature extraction and analysis, it is important to note that manual feature extraction demands extensive domain knowledge. Therefore, adopting an end-to-end approach without the need for extracting features manually becomes necessary.

3.2.2. Deep learning methods

The outcome of employing deep learning methods is an end-to-end deep neural network, such as convolutional neural network (CNN), graph convolutional networks (GCN), or long short-term memory (LSTM), which extracts high-dimensional features and reveals hidden patterns within product lifecycle data [95]. In the context of smart manufacturing and digital engineering, deep learning methods can facilitate the analysis of large-scale industrial data and key feature recognition in diverse industrial domains, such as defect detection [96], anomaly detection [97], reliability analysis [98], and fault diagnosis [99].

The flow diagram of deep learning methods is presented in Fig. 3(c), including network construction, hyperparameter setup, model training and testing, and decision-making. First, a deep network structure is designed based on the characteristics of product lifecycle data that is to be analyzed [125]. Second, the deep learning network is parameterized through hyperparameter settings, parameter learning, and hyperparameter tuning. Third, raw data are divided into training samples and test samples, where the training samples are used to train the deep neural network based on the backpropagation algorithm, while test samples are employed to evaluate the performance of the deep neural networks [126]. Lastly, the trained deep neural network is utilized for various decision-making processes in smart manufacturing.

Similar to shallow machine learning methods, deep learning methods can also be classified as unsupervised, semi-supervised, and supervised deep learning methods, based on whether they are supervised. Unsupervised deep learning methods aim to learn the deep representation of unlabeled samples, promoting the exploration of meaningful patterns in data without labels [127], [128]. Semi-supervised deep learning methods aim to utilize both labeled and unlabeled samples by building generative models or pretraining deep learning neural networks [129], [130]. Supervised deep learning methods rely on labeled samples to establish the mapping between inputs and outputs [131], [132]. In comparison with statistical analysis methods and shallow machine learning, which depend on only a few nonlinear or linear functions for pattern recognition, deep learning methods are known for their greater capability in pattern recognition by stacking extensive nonlinear mapping layers. However, the stacked nonlinear mapping layers make deep learning methods difficult to interpret the internal computational mechanisms, which affects the interpretability of the decision-making.

4. DMF methods

The effectiveness of both model-based and data-driven methods has been demonstrated across various fields in smart manufacturing and digital engineering. However, each method presents its own set of challenges that must be addressed.

As outlined in Section 2, model-based methods can be broadly classified as empirical, analytical, and numerical methods, each of which faces limitations in practical application. As an example, empirical model-based methods may be too simplified to capture all the correlations or principles within a complex physical system, leading to suboptimal performance. Analytical model-based methods heavily depend on domain-specific knowledge which may not always be available or might not accurately reflect the true behaviors of complex systems. Furthermore, numerical model-based methods often involve complex high-order models that are computationally intensive, resulting in increased costs and reduced efficiency.

Similarly, data-driven methods also encounter significant challenges. These methods rely heavily on large volumes of data, which may not always be accessible. In addition, data-driven methods, particularly deep learning methods, are often criticized for their lack of interpretability. This “black-box” nature can severely undermine the trustworthiness of these methods.

To address the issues of both model-based and data-driven methods, numerous efforts have been made to fuse model-based and data-driven methods, such a fusion is also known as DMF [133], [134], [135], [136]. These efforts are summarized in Table 4 [17], [18], [19], [20], [133], [137], [138], [139], which presents terminologies and explanations reported in the existing literature. Despite these considerable efforts, the definition of DMF remains inconsistent, and generic frameworks for its implementation are rarely discussed. To fill these gaps, this section offers a clear definition and categorization of DMF within the context of smart manufacturing and digital engineering. Furthermore, it details the general procedures and frameworks associated with different categories of DMF methods.

4.1. Definitions of DMF

DMF represents a hybrid approach that integrates model-based and data-driven methods by leveraging domain knowledge and product lifecycle data in a synchronized manner. DMF aims to achieve several key objectives: ➀ reducing the data dependency when using data-driven methods, ➁ alleviating the knowledge reliance when applying model-based methods, ➂ enhancing the interpretability of data-driven methods, and ➃ enabling the decision-making of both model-based and data-driven methods.

In this work, we classify DMF as four distinct groups based on the fusion level: data-level, feature-level, method-level, and decision-level DMF. Each of these levels is discussed in detail in the subsequent sections.

4.2. Data-level DMF: a sequential fusion approach

Data-level DMF integrates model-based and data-driven methods sequentially; this approach either utilizes model-based methods to generate or enhance data, or employs data to infer domain knowledge that informs model-based methods [140], [141], [142], [143], [144]. Data-level DMF is typically employed in two circumstances: ➀ When precise prior domain knowledge is available, but data are scarce or unavailable, and ➁ when data are sufficient, but prior domain knowledge is unreliable or unavailable. Thus, data-level DMF reduces the data-driven methods’ dependency on data and the model-based methods’ reliance on domain knowledge.

As mentioned earlier, data-level DMF connects model-based methods with data-driven methods sequentially. Therefore, data-level DMF can be also referred to as sequential DMF. Depending on the order in which both methods are connected, data-level DMF can be classified into two types: ➀ model-based methods-enhanced data generation, and ➁ data-driven methods-enhanced knowledge inference. The generic frameworks of both types are presented in Fig. 4. In the framework of model-based methods-enhanced data generation, relevant domain knowledge is initially used to construct simulation or optimization models. Simulation models enable the generation of simulation samples to address data scarcity, while optimization models enhance data to improve decision-making performance of data-driven methods. In contrast, data-driven methods-enhanced knowledge inference begins with applying data-driven methods to infer temporarily varying parameters or reveal unknown physical mechanisms. These inferred parameters or mechanisms are then integrated into model-based methods to assist in the decision-making process.

4.3. Feature-level DMF: an embedded fusion approach

Feature-level DMF integrates model-based and data-driven methods in a cohesive manner, where each approach enhances the other. Specifically, model-based methods are employed to augment the automated features extracted by data-driven methods, while data-driven methods are used to enrich the physics-based features provided by model-based approaches [145], [146], [147], [148], [149]. This type of DMF is particularly valuable when both data and domain knowledge are accessible. It offers two key advantages: ➀ model-based methods can imbue automated features with physical meaning or enhance their utility, and ➁ automated features derived from data-driven methods can enrich model-based features to improve decision-making performance.

As aforementioned, feature-level DMF involves the integration of model-based and data-driven methods in a nested manner, often with one approach embedded within the other. Consequently, this form of DMF can be also referred to as embedded DMF. Depending on the patterns of embedding, embedded DMF can be classified into two main types: model-based methods embedded within data-driven methods, and data-driven methods embedded within model-based methods. The general frameworks for both types of embedded DMF are illustrated in Fig. 4. In the case where model-based methods are embedded within data-driven methods, data are first processed by data-driven methods to extract automated features. Concurrently, model-based methods are applied to impart physical meaning to these features or to extract the most valuable information from them. The resulting enhanced or fused features are then used in data-driven methods for subsequent decision-making. Conversely, when data-driven methods are embedded within model-based methods, domain knowledge is used to develop model-based methods for extracting physics-based features. Data are then introduced into data-driven methods at appropriate intervals to derive automated features across various domains, such as time and frequency domains. These automated and physics-based features are combined or concatenated and subsequently used in model-based methods for decision-making.

4.4. Method-level DMF: an interacted fusion approach

Method-level DMF integrates model-based methods with data-driven methods in an interactive manner. For example, model-based methods contribute to constructing partial or complete loss functions for data-driven methods. Such an integration becomes particularly relevant to circumstances where either data alone is available while model-based mechanisms are insufficient, or both data and domain knowledge are available but insufficient [140], [150], [151], [152], [153], [154]. Method-level DMF can enhance the interpretability of data-driven methods and compensate for the incomplete physical mechanisms of model-based methods.

As previously noted, method-level DMF wherein model-based methods help define the partial or complete loss functions for data-driven methods refers to as an interactive approach between model-based and data-driven methods. Both methods are interconnected through parameters that are trained and updated during both forward and backward propagation. Consequently, method-level DMF can be also referred to as interactive DMF. Method-level DMF primarily includes two primary categories: physics-guided neural networks (PGNN) [155] and physics-informed neural networks (PINN) [156], [157], [158]. The general frameworks for PGNN and PINN are illustrated in Fig. 4. In a PGNN framework, during feedforward propagation, product lifecycle data are input into data-driven methods to estimate parameters for model-based methods. These estimated parameters are then used in model-based methods to make initial decisions. These decisions, along with the expected targets, contribute to the calculation of physical losses. During backpropagation, these physical losses are employed to update the parameters within the data-driven methods. In contrast, a PINN framework disposes product lifecycle data through data-driven methods during feedforward propagation to generate outputs. These outputs are used to formulate data loss and serve as parameters for model-based methods to create physical loss. The final loss is derived from the integration of these two losses, which is then used to update the parameters within the data-driven methods during backpropagation.

4.5. Decision-level DMF: a parallel fusion approach

As illustrated in Fig. 4, decision-level DMF arranges model-based and data-driven methods within a parallel framework, where each method independently generates decisions that are subsequently combined to derive a final outcome [159], [160], [161]. Such an approach enhances the decision-making by leveraging the unique strengths of both methods. In practice, decision-level DMF is employed when both data and knowledge are available; however, relying on a single method alone may result in suboptimal performance. Consequently, decision-level DMF significantly improves the decision-making by effectively merging the results from both model-based and data-driven methods.

As previously mentioned, decision-level DMF involves the parallel fusion of model-based and data-driven methods, where both methods independently obtain decisions. This parallel processing approach is also referred to as parallel DMF. Decision-level DMF can be further classified based on the methods used for decision fusion: weighted sum-enabled and error compensation-enabled. Weighted sum-enabled decision-level DMF focuses on assigning optimized weights to the decisions generated by the model-based and data-driven methods to enhance overall decision-making performance. On the other hand, error compensation-enabled decision-level DMF utilizes one method to make an initial decision and then employs the other method to predict and compensate the computational errors of the initial decision, so that the performance of decision-making can be enhanced.

5. Conceptual framework of DMF

The advantages of employing DMF have garnered significant attention from both academia and industry, and numerous studies have been conducted on introducing different levels of DMF. However, a comprehensive conceptual framework of DMF is rarely discussed in the existing literature. To fill this gap, this section introduces a generic conceptual framework for DMF, referred to as Model_DMF, where all essential elements associated with DMF are included. The framework consists of five primary elements: data-driven methods, model-based methods, fusion strategies, services, and connections, as illustrated in Fig. 5. The purpose of this framework is to integrate all essential elements within DMF and clearly define the objectives and constraints involved in deploying DMF.

All five elements involved in DMF can be mathematically represented as Eq. (1), where Dd refers to a set of data-driven methods, Mb represents a set of model-based methods, Fs denotes a set of fusion strategies, and Ss refers to services. Cn represents the connections among model-based methods, data-driven methods, fusion strategies, and services.

(1)

Model DMF = {Dd, Mb, Fs, Ss, Cn}

Dd includes three groups of data-driven methods, which can be mathematically represented by Eq. (2), where St refers to statistical analysis methods, Ml denotes shallow machine learning methods, and Dl represents deep learning methods.

(2)

Dd = {St, Ml, Dl}

Mb involves three types of model-based methods, which are mathematically represented in Eq. (3). Em refers to empirical model-based methods. An represents analytical model-based methods. Nu represents numerical model-based methods.

(3)

Mb = {Em, An, Nu}

Fs incorporates four levels of data-model fusion strategies, which can be expressed as in Eq. (4), where Df, Ff, Mf, and Sf refer to data-level, feature-level, method-level, and decision-level fusion strategies, respectively.

(4)

Fs = {Df, Ff, Mf, Sf}

Ss involves three primary elements, as written in Eq. (5), where Kn refers to relevant domain knowledge, Da represents data, and De pertains to demands or decision-making within the context of smart manufacturing and digital engineering.

(5)

Ss = {Kn, Da, De}

Cn involves all connections, which can be mathematically written as Eq. (6). In Eq. (6), Cn_DF is the connection between Dd and Fs; Cn_MF refers to the connection between Mb and Fs; Cn_DF and Cn_MF support the realization of DMF. Cn_SD represents the connection between Ss and Dd, and this connection aims to transfer data to data-driven methods and obtain some decision-making or supports from Dd; Cn_SM refers to the connection between Ss and Mb, and this connection aims to transfer domain knowledge to model-based methods and provide the decision-making of model-based methods for Ss; Cn_SF refers to the connection between Ss and Fs where Ss supports Fs in domain knowledge and data while Fs provides DMF-based decision-making for Ss; and Cn_DM refers to the connection between Dd and Mb.

(6)

Cn = {Cn_DF, Cn_MF, Cn_SD, Cn_SM, Cn_SF, Cn_DM}

The objective function of the proposed generic conceptual framework of DMF can be mathematically written as Eq. (7), where S(∙) represents the selection function and Cn(∙) represents the integration of Dd, Mb, and Fs. This objective involves identifying the most effective model-based methods, data-driven methods, and fusion strategies to meet the specified requirements. These requirements are defined as the integrated function of data-driven methods, model-based methods, and fusion strategies. Moreover, the selection of data-driven and model-based methods is constrained by the data availability and the extent of domain knowledge, respectively.

(7)$\begin{array}{l} \arg \max \mathrm{De}:=\{\mathrm{Dd}, \mathrm{Mb}, \mathrm{Fs}: S(\mathrm{Dd}) \in \mathrm{Da}, S(\mathrm{Mb}) \in \mathrm{Kn}\} \\ \text { Dd, Mb, Fs } \\ \text { De }:=\mathrm{Cn}(\mathrm{Dd}, \mathrm{Mb}, \mathrm{Fs}) \end{array}$

6. Industrial applications of DMF

This section explores the industrial applications of DMF across the various stages of product lifecycle, including product design, manufacturing, experimentation, testing, and verification (ETV), and maintenance. These applications and their specific objectives are illustrated in Fig. 6, with further details provided in the subsections below.

6.1. DMF in the product design

Traditional product design has predominantly relied on numerical simulations to optimize the design process and enhance production efficiency while minimizing downtime and costs. However, constructing high-fidelity models for these simulations can be computationally expensive. DMF offers a more cost-effective alternative for enabling product design across various dimensions, such as topology, form, and thermal design.

For example, in heat exchanger topology design, DMF has been employed to create a global optimization framework based on a response surface surrogate model to reduce computational costs significantly [162]. Similarly, in the form design of a destroyer-type vessel, DMF established a surrogate model to streamline the design space to achieve cost-effective global form optimization of the hull [163]. In addition, in satellite thermal design, DMF integrated a first-principles-based loss function with a neural network surrogate model to balance prediction accuracy and training costs [164].

6.2. DMF in the product manufacturing

In manufacturing, DMF is primarily applied to process control, which involves monitoring and optimizing production processes to enhance efficiency, flexibility, and productivity. Traditionally, this control was conducted by using both model-based and data-driven methods. However, model-based methods often resulted in complex and high-order ordinary differential equations, making them less suitable for real-time applications [165]. Data-driven methods, while effective for real-time analysis, depend heavily on large volumes of training data, which may not always be available.

DMF addresses these limitations by leveraging numerical simulation data sets to train a deep neural network, constrained by first principles, as a surrogate model [166]. This approach reduces the dependency on extensive process data by allowing the surrogate model to approximate correlations between process parameters and relevant physical variables. Furthermore, DMF integrates simulation data with real-world data collected during the manufacturing process to train the neural network for quality parameter control [167], reducing the need for high-quality and high-volume training samples.

6.3. DMF in the product maintenance

Smart maintenance, which involves fault diagnostics and remaining useful life prediction of equipment, relies on analyzing condition monitoring data from industrial sensor networks to inform maintenance decisions [10]. Both model-based and data-driven methods are integral to this process, but each has its limitations [23]. Model-based methods may produce inaccurate predictions due to dynamic working conditions of equipment, while data-driven methods can lack interpretability and may conflict with fundamental physical principles [168].

DMF addresses these challenges of individual method by concurrently leveraging model-based and data-driven methods. DMF began with the employment of machine learning to predict health conditions and iteratively calibrate model-based parameters for higher prediction accuracy [169], [170], [160]. In addition, DMF enhances the interpretability of data-driven methods by incorporating domain knowledge; such an incorporation could be achieved through the creation of physically meaningful features, the design of interpretable deep learning architectures, or the utilization of physics-informed loss functions [171], [172], [173].

6.4. DMF in the product ETV

As industries undergo digital transformation, ETV is shifting from physical environments to digital space. Digital ETV focuses on assessing the status of products and manufacturing systems in a digital space, and ensures the correctness of manufacturing schemes to support further process optimization [174], [175], [176].

Traditional digital ETV relies heavily on numerical simulations, which can be computationally expensive due to the plenty of process parameters to be solved. DMF mitigates this challenge by reducing the number of parameters through the utilization of surrogate model and hybrid model [166]. For example, a deep neural network-based surrogate model, trained on reduced data sets from numerical simulations, can approximate the correlation between essential process parameters and relevant physical variables, so that the computational process can be simplified. Moreover, DMF enabled the development of hybrid models that combined machine learning algorithms with analytical models to directly predict specific process parameters to further reduce computational complexity in digital ETV [177], [178].

7. Future directions of DMF

This section explores the future directions of DMF centering on three aspects: multi-disciplinary theories guiding DMF, emerging technologies supporting DMF, and potential applications of DMF.

7.1. Digitization theories guiding DMF

As aforementioned, DMF integrate both model-based and data-driven methods, and DMF is inherently multi-disciplinary. The effectiveness of DMF closely aligns with the availability of models and data in industrial scenario. To enhance the capabilities of DMF, the adoption of relevant digital theories such as digital engineering and digital twins are essential. For example, digital engineering enables the creation of a comprehensive information space that includes all relevant data and models for DMF, so that the available applications can be broadened [4]. In addition, digital twins can also assist in DMF. Digital twins are characterized by the real-time interaction between physical and digital worlds. Digital twins can provide a dynamic platform where real-time data from the physical system can be continuously integrated with physics-based models, enabling iterative interaction, enhanced accuracy, and more informed decision-making through the seamless combination of both approaches [179], [180].

7.2. Emerging technologies supporting DMF

The implementation and utilization of DMF in the context of smart manufacturing and digital engineering also heavily rely on emerging technologies, such as large language models and cloud-edge-end collaboration. The substantial computational cost associated with training and fine-tuning large-scale deep neural networks poses a significant challenge for DMF. Large language models composed by numerous deep learning networks offer a solution by enabling DMF across various analytical tasks [181]. By re-pretraining and instruction tuning these networks with domain-specific knowledge, they can be adapted for industrial-scale models, so that the computational burden can be significantly reduced. Moreover, the efficient application of DMF was often hindered by the inflexible allocation of computational tasks and resources [182]. Cloud-edge-end collaboration addresses this issue by distributing computational tasks across the cloud data center, edge servers, and terminal equipment. In this manner, more data analysis and more secured data transmission can be achieved.

7.3. Further applications of DMF

While DMF has already been applied in various industrial sectors, there remains significant potential for its application in other industrial areas, such as manufacturing service collaboration and virtual testing. Manufacturing service collaboration relies on complex network models to elucidate the complex relationships between service nodes, thereby facilitating the cooperation among manufacturing enterprises [183]. DMF can enhance manufacturing service collaboration by eliminating redundant nodes and updating causal relationships within these network models to significantly improve the efficiency of collaboration. In addition, virtual testing, which is often constrained by the high costs associated with constructing and computing high-order numerical models, reaps the benefits from DMF. By adopting data-driven methods to establish surrogate models, DMF can simplify these complex numerical models to reduce the computational costs associated with virtual testing in manufacturing systems [184].

8. Conclusions and future works

The increasing demand for interpretable, rapid, and transparent decision-making has driven the integration of model-based and data-driven methods across various applications. As a hybrid paradigm that fuses both approaches, DMF has garnered significant attention from both industry and academia. This paper provides a comprehensive overview of the current state-of-the-art DMF research and its applications through the examination of more than 150 articles. The primary contributions of this paper are outlined as follows:

(1) A thorough overview of both model-based and data-driven methods within the realms of smart manufacturing and digital engineering is presented, and the classifications and generic frameworks for both methods are introduced respectively.

(2) A definition of DMF is provided by examining relevant terminologies. Based on this definition, DMF is classified as four levels: data-level, feature-level, method-level, and decision-level.

(3) A generic conceptual framework of DMF is proposed to illustrate all necessary elements within DMF and clarify the objective of performing DMF.

(4) The primary industrial applications of DMF are introduced by spanning design, manufacturing, maintenance, and ETV, along with insights into future developments and promising application areas.

Despite the rapid growth of DMF, several pressing issues need to be addressed to enhance its viability in practice. For example, a generic paradigm is needed to guide manufacturing enterprises in implementing and applying DMF more effectively. In addition, a more systematic integration of data and models throughout the entire lifecycle of a product is essential to enable more intelligent decision-making in manufacturing systems. In future work, we will focus on addressing these critical issues.

CRediT authorship contribution statement

Fei Tao: Writing - review & editing, Writing - original draft, Supervision, Investigation, Conceptualization. Yilin Li: Writing - original draft, Investigation. Yupeng Wei: Writing - review & editing, Visualization. Chenyuan Zhang: Writing - review & editing. Ying Zuo: Writing - review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grants (52275471 and 52120105008), the Beijing Outstanding Young Scientist Program, and the New Cornerstone Science Foundation through the XPLORER PRIZE.

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Park S, Changgyun K, Youm S. Establishment of an IoT-based smart factory and data analysis model for the quality management of SMEs die-casting companies in Korea. Int J Distrib Sens Netw 2019; 15(10):15501477198.

[2]	Khalid S, Song J, Azad MM, Elahi MU, Lee J, Jo SH, et al. A comprehensive review of emerging trends in aircraft structural prognostics and health management. Mathematics 2023; 11(18):3837.

[3]	Chen Y. Integrated and intelligent manufacturing: perspectives and enablers. Engineering 2017; 3(5):588-95.

[4]	Tao F, Ma X, Liu W, Zhang C. Digital engineering: state-of-the-art and perspectives. Digit Eng 2024;1:100007.

[5]	Chen Z. Understanding of the modeling method in additive manufacturing. IOP Conf Ser Mater Sci Eng 2020;711:012017.

[6]	Gernaey KV, Gani R. A model-based systems approach to pharmaceutical product-process design and analysis. Chem Eng Sci 2010; 65(21):5757-69.

[7]	Ortiz J, Carrasco RA. Model-based fault detection and diagnosis in ALMA subsystems. In: Proceedings of the SPIE 9910, Observatory Operations: Strategies, Processes, and Systems, VI; 2016 Jun 26-Jul 1; Edinburgh, UK. Bellingham: SPIE Digital Library; 2016. p. 919-29.

[8]	Zhang F, Yu H, Wang J. A novel damage identification method for flue gas turbine blades based on tip timing. ISA Trans 2023;135:537-50.

[9]	Lei Y, Li N, Gontarz S, Lin J, Radkowski S, Dybala J. A model-based method for remaining useful life prediction of machinery. IEEE Trans Reliab 2016; 65 (3):1314-26.

[10]	Zhang W, Yang D, Wang H. Data-driven methods for predictive maintenance of industrial equipment: a survey. IEEE Syst J 2019; 13(3):2213-27.

[11]	Weimer D, Scholz-Reiter B, Shpitalni M. Design of deep convolutional neural network architectures for automated feature extraction in industrial inspection. CIRP Ann 2016; 65(1):417-20.

[12]	Janssens O, Slavkovikj V, Vervisch B, Stockman K, Loccufier M, Verstockt S, et al. Convolutional neural network based fault detection for rotating machinery. J Sound Vibrat 2016;377:331-45.

[13]	Liu C, Zhu H, Tang D, Nie Q, Zhou T, Wang L, et al. Probing an intelligent predictive maintenance approach with deep learning and augmented reality for machine tools in IoT-enabled manufacturing. Robot Comput-Integr Manuf 2022;77:102357.

[14]	Ke C, Zhang M, Zuo Y, Xiang F, Zhang D, Tao F. Data-driven real-time control method for process equipment in flow shop towards product quality improvement. Procedia CIRP 2022;107:908-13.

[15]	Ding K, Lei J, Chan F, Hui J, Zhang F, Wang Y. Hidden Markov model-based autonomous manufacturing task orchestration in smart shop floors. Robot Comput-Integr Manuf 2020;61:101845.

[16]	Wang J, Li Y, Gao RX, Zhang F. Hybrid physics-based and data-driven models for smart manufacturing: modelling, simulation, and explainability. J Manuf Syst 2022;63:381-91.

[17]	Karniadakis GE, Kevrekidis IG, Lu L, Perdikaris P, Wang S, Yang L. Physics- informed machine learning. Nat Rev Phys 2021; 3(6):422-40.

[18]	Azodi CB, Tang J, Shiu SH. Opening the black box: interpretable machine learning for geneticists. Trends Genet 2020; 36(6):442-55.

[19]	Farbiz F, Habibullah MS, Hamadicharef B, Maszczyk T, Aggarwal S. Knowledge-embedded machine learning and its applications in smart manufacturing. J Intell Manuf 2023; 34(7):2889-906.

[20]	Rai SahuCK R. Driven by data or derived through physics? A review of hybrid physics guided machine learning techniques with cyber-physical system (CPS) focus. IEEE Access 2020;8:71050-73.

[21]	von Rueden L, Mayer S, Beckh K, Georgiev B, Giesselbach S, Heese R, et al. Informed machine learning—a taxonomy and survey of integrating prior knowledge into learning systems. IEEE Trans Knowl Data Eng 2021; 35 (1):614-33.

[22]	Guo S, Agarwal M, Cooper C, Tian Q, Gao RX, Guo W, et al. Machine learning for metal additive manufacturing: towards a physics-informed data-driven paradigm. J Manuf Syst 2022;62:145-63.

[23]	Hagmeyer S, Zeiler P, Huber MF. On the integration of fundamental knowledge about degradation processes into data-driven diagnostics and prognostics using theory-guided data science. PHM Society Eur Conf 2022; 7 (1):156-65.

[24]	Karimpouli S, Tahmasebi P. Physics informed machine learning: seismic wave equation. Geosci Front 2020; 11(6):1993-2001.

[25]	Jin XB, Robert Jeremiah RJ, Su TL, Bai YT, Kong JL. The new trend of state estimation: from model-driven to hybrid-driven methods. Sensors 2021; 21 (6):2085.

[26]	Venkatasubramanian V, Rengaswamy R, Yin K, Kavuri SN. A review of process fault detection and diagnosis: part I: quantitative model-based methods. Comput Chem Eng 2003; 27(3):293-311.

[27]	Bikas H, Stavropoulos P, Chryssolouris G. Additive manufacturing methods and modelling approaches: a critical review. Int J Adv Manuf Technol 2016; 83 (1-4):389-405.

[28]	Duan Z, Li C, Ding W, Zhang Y, Yang M, Gao T, et al. Milling force model for aviation aluminum alloy: academic insight and perspective analysis. Chin J Mech Eng 2021; 34(1):18-35.

[29]	Burek J, Plodzien M, Zylka L, Sulkowicz P. High-performance end milling of aluminum alloy: influence of different serrated cutting edge tool shapes on the cutting force. Adv Prod Eng Manag 2019; 14(4):494-506.

[30]	Fuh KH, Hwang RM. A predicted milling force model for high-speed end milling operation. Int J Mach Tools Manuf 1997; 37(7):969-79.

[31]	Anderson Jr CE. Analytical models for penetration mechanics: a review. Int J Impact Eng 2017;108:3-26.

[32]	Buzacott JA, Yao DD. Flexible manufacturing systems: a review of analytical models. Manage Sci 1986; 32(7):890-905.

[33]	Lahiff C, Gordon S, Phelan P. PCBN tool wear modes and mechanisms in finish hard turning. Robot Comput-Integr Manuf 2007; 23(6):638-44.

[34]	Grzesik W. Wear development on wiper Al₂O₃-TiC mixed ceramic tools in hard machining of high strength steel. Wear 2009; 266(9- 10):1021-8.

[35]	Moufki A, Molinari A, Dudzinski D, Molinari A, Dudzinski D. Modelling of orthogonal cutting with a temperature dependent friction law. J Mech Phys Solids 1998; 46(10):2103-38.

[36]	Jing X, Lv R, Chen Y, Tian Y, Li H. Modelling and experimental analysis of the effects of run out, minimum chip thickness and elastic recovery on the cutting force in micro-end-milling. Int J Mech Sci 2020;176:105540.

[37]	Jin X, Altintas Y. Slip-line field model of micro-cutting process with round tool edge effect. J Mater Process Technol 2011; 211(3):339-55.

[38]	Ray D, Ramirez-Marquez J. A framework for probabilistic model-based engineering and data synthesis. Reliab Eng Syst Saf 2020;193:106679.

[39]	Huang L, Ruan S, Xing Y, Feng M. A review of uncertainty quantification in medical image analysis: probabilistic and non-probabilistic methods. Med Image Anal 2024;97:103223.

[40]	Drugowitsch J, Pouget A. Probabilistic vs. non-probabilistic approaches to the neurobiology of perceptual decision-making. Curr Opin Neurobiol 2012; 22 (6):963-9.

[41]	Argyropoulos CD, Markatos NC. Recent advances on the numerical modelling of turbulent flows. Appl Math Model 2015; 39(2):693-732.

[42]	Altaf MS, Bouferguene A, Liu H, Al-Hussein M, Yu H. Integrated production planning and control system for a panelized home prefabrication facility using simulation and RFID. Autom Construct 2018;85:369-83.

[43]	Zhang L, Zhou L, Ren L, Laili Y. Modeling and simulation in intelligent manufacturing. Comput Ind 2019;112:103123.

[44]	Yan S, Zhou Z, Dinavahi V. Large-scale nonlinear device-level power electronic circuit simulation on massively parallel graphics processing architectures. IEEE Trans Power Electron 2017; 33(6):4660-78.

[45]	Xiang L, Pan T, Yu Z, Zheng W. Two kinds of lathe improvement techniques based on Ansys simulation analysis. IOP Conf Ser Mater Sci Eng 2018;382:032058.

[46]	Otten D, Weber TA, Arent JC. Manufacturing process simulation—on its way to industrial application. Int J Aviat Aeronaut Aerosp 2018; 5(2):1217.

[47]	Chenot JL, Bay F. An overview of numerical modelling techniques. J Mater Process Technol 1998;80-81:8-15.

[48]	Kutin A, Dolgov V, Podkidyshev A, Kabanov A. Simulation modeling of assembly processes in digital manufacturing. Procedia CIRP 2018;67:470-5.

[49]	Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P. Meshless methods: an overview and recent developments. Comput Methods Appl Mech Eng 1996; 139(1-4):3-47.

[50]	Myung IJ. Tutorial on maximum likelihood estimation. J Math Psychol 2003; 47(1):90-100.

[51]	Do CB, Batzoglou S. What is the expectation maximization algorithm? Nat Biotechnol 2008; 26(8):897-9.

[52]	Voršilák M, Kolář M, Čmelo I, Svozil D. SYBA: Bayesian estimation of synthetic accessibility of organic compounds. J Cheminform 2020; 12(1):35.

[53]	Hoffbeck JP, Landgrebe DA. Covariance matrix estimation and classification with limited training data. IEEE Trans Pattern Anal Mach Intell 1996; 18 (7):763-7.

[54]	Felzenszwalb PF, Huttenlocher DP. Efficient belief propagation for early vision. Int J Comput Vis 2006; 70(1):41-54.

[55]	Chandru V. Variable elimination in linear constraints. Comput J 1993; 36 (5):463-72.

[56]	Kroese DP, Brereton T, Taimre T, Botev ZI. Why the Monte Carlo method is so important today. Wiley Interdiscip Rev Comput Stat 2014; 6(6):386-92.

[57]	Sammaknejad N, Zhao Y, Huang B. A review of the expectation maximization algorithm in data-driven process identification. J Process Contr 2019;73:123-36.

[58]	Blei DM, Kucukelbir A, McAuliffe JD. Variational inference: a review for statisticians. J Am Stat Assoc 2017; 112(518):859-77.

[59]	Chen XY, Fan JP, Bian XY. Theoretical analysis of non-probabilistic reliability based on interval model. Acta Mech Solida Sin 2017; 30(6):638-46. Chinese.

[60]	Lei Y, Li N, Lin J. A new method based on stochastic process models for machine remaining useful life prediction. IEEE Trans Instrum Meas 2016; 65 (12):2671-84.

[61]	Larrañaga P, Karshenas H, Bielza C, Santana R. A review on probabilistic graphical models in evolutionary computation. J Heuristics 2012; 18 (5):795-819.

[62]	Zhang FL, Ni JT, Zhang LB, Chen YS, Wang JJ. Bop shear force evaluation under complex scenarios. Petrol Sci 2023; 20(4):2442-51.

[63]	Kim JW, Sul SH, Choi JB. Development of user customized smart keyboard using smart product design-finite element analysis process in the internet of things. ISA Trans 2018;81:231-43.

[64]	Patidar KC. On the use of nonstandard finite difference methods. J Diff Equ Appl 2005; 11(8):735-58.

[65]	Lian Y, Gan Z, Yu C, Kats D, Liu WK, Wagner GJ. A cellular automaton finite volume method for microstructure evolution during additive manufacturing. Mater Des 2019;169:107672.

[66]	Chen L, Lu C, Lian H, Liu Z, Zhao W, Li S, et al. Acoustic topology optimization of sound absorbing materials directly from subdivision surfaces with isogeometric boundary element methods. Comput Methods Appl Mech Eng 2020;362:112806.

[67]	Kirkup S. The boundary element method in acoustics: a survey. Appl Sci 2019; 9(8):1642.

[68]	Tey WY, Asako Y, Ng KC, Lam WH. A review on development and applications of element-free Galerkin methods in computational fluid dynamics. Int J Comput Methods Eng Sci Mech 2020; 21(5):252-75.

[69]	Monaghan JJ. Smoothed particle hydrodynamics and its diverse applications. Annu Rev Fluid Mech 2012; 44(1):323-46.

[70]	Wu CT, Wu Y, Crawford JE, Magallanes JM. Three-dimensional concrete impact and penetration simulations using the smoothed particle Galerkin method. Int J Impact Eng 2017;106:1-17.

[71]	Diez-Olivan A, Del Ser J, Galar D, Sierra B. Data fusion and machine learning for industrial prognosis: trends and perspectives towards Industry 4.0. Inf Fusion 2019;50:92-111.

[72]	Donoho D. 50 years of data science. J Comput Graph Stat 2017; 26(4):745-66.

[73]	Azimi M, Eslamlou AD, Pekcan G. Data-driven structural health monitoring and damage detection through deep learning: state-of-the-art review. Sensors 2020; 20(10):2778.

[74]

Eleftheriadis P, Giazitzis S, Ozmalatyalilar C, Leva S, Zich R.An overview of data-driven methods for the state of health estimation. In:Proceedings of the 2023 IEEE International Conference on Environment and Electrical Engineering and 2023 IEEE Industrial and Commercial Power Systems Europe (EEEIC/I&CPS Europe); 2023 Jun 6-9; Madrid, Spain. Piscataway: IEEE; 2023. p. 1-6.

[75]	Xu Y, Zhou Y, Sekula P, Ding L. Machine learning in construction: from shallow to deep learning. Dev Built Environ 2021;6:100045.

[76]	Xu N, Xie Yu, Liu Q, Yue F, Zhao D. A data-driven approach to state of health estimation and prediction for a lithium-ion battery pack of electric buses based on real-world data. Sensors 2022; 22(15):5762.

[77]	El-Brawany MA, Adel Ibrahim D, Elminir HK, Elattar HM, Ramadan EA. Artificial intelligence-based data-driven prognostics in industry: a survey. Comput Ind Eng 2023;184:109605.

[78]	Chen Z, O’Neill Z, Wen J, Pradhan O, Yang T, Lu X, et al. A review of data-driven fault detection and diagnostics for building HVAC systems. Appl Energy 2023;339:121030.

[79]	Tibaduiza DA, Torres-Arredondo MA, Mujica LE, Rodellar J, Fritzen CP. A study of two unsupervised data driven statistical methodologies for detecting and classifying damages in structural health monitoring. Mech Syst Signal Process 2013; 41(1-2):467-84.

[80]	Malhotra R. Comparative analysis of statistical and machine learning methods for predicting faulty modules. Appl Soft Comput 2014;21:286-97.

[81]	Stapor K, Stapor K. Descriptive and inferential statistics. In: StaporK,editor. Introduction to probabilistic and statistical methods with examples in R. Berlin: Springer Nature; 2020. p. 63-131.

[82]	Nick TG. Descriptive statistics. In: AmbrosiusWT,editor. Topics in biostatistics. Berlin: Springer Nature; 2007. p. 33-52.

[83]	Dong Y. Descriptive statistics and its applications. Highl Sci Eng Technol 2023;47:16-23.

[84]	Nethmini LDP, Ismail MBM. Descriptive statistics of employee performance in Brandix company. Int J Glob Bus Manag Res 2019; 8(1):51-7.

[85]	Lee KS, Nor NM, Ismail F.Industry 4.0 and lean manufacturing practices: an approach to enhance operational performance in Singapore’s manufacturing sector. Res Manag Technol Bus 2021; 2(1):456-72.

[86]	Oroye OA, Sylvester BO, Farayibi PK. Total productive maintenance and companies performance: a case study of fast moving consumer goods companies. J System Manage Ind 2022; 6(1):23-32.

[87]	Marshall G, Jonker L. An introduction to inferential statistics: a review and practical guide. Radiography 2011; 17(1):e1-6.

[88]	Anderson JC, Schroeder RG, Cleveland G. The process of manufacturing strategy: some empirical observations and conclusions. Int J Oper Prod Manage 1991; 11(3):86-110.

[89]	Shabbir MS, Wisdom O. The relationship between corporate social responsibility, environmental investments and financial performance: evidence from manufacturing companies. Environ Sci Pollut Res Int 2020; 27(32):39946-57.

[90]	Hsu BM, Shu MH. Fuzzy inference to assess manufacturing process capability with imprecise data. Eur J Oper Res 2008; 186(2):652-70.

[91]	Oyedokun GE, Tomomewo AO, Ajao OS. Cost control and profitability of selected manufacturing companies in Nigeria. J Account Strateg Finance 2019; 2(1):14-33.

[92]	Zhu K, Fuh JYH, Lin X. Metal-based additive manufacturing condition monitoring: a review on machine learning based approaches. IEEE/ASME Trans Mechatron 2021; 27(5):2495-510.

[93]	Cen J, Yang Z, Liu X, Xiong J, Chen H. A review of data-driven machinery fault diagnosis using machine learning algorithms. J Vib Eng Technol 2022; 10 (7):2481-507.

[94]	Manno A, Martelli E, Amaldi E. A shallow neural network approach for the short-term forecast of hourly energy consumption. Energies 2022; 15(3):958.

[95]	Ekins S, Puhl AC, Zorn KM, Lane TR, Russo DP, Klein JJ, et al. Exploiting machine learning for end-to-end drug discovery and development. Nat Mater 2019; 18(5):435-41.

[96]	Jia Z, Wang M, Zhao S. A review of deep learning-based approaches for defect detection in smart manufacturing. J Opt 2024; 53(2):1345-51.

[97]	Wang Y, Han X, Lu L, Chen Y, Ouyang M. Sensitivity of fractional-order recurrent neural network with encoded physics-informed battery knowledge. Fractal and Fractional 2022; 6(11):640.

[98]	Ciccarelli M, Corradini F, Germani M, Menchi G, Mostarda L, Papetti A, et al. Spectre: a deep learning network for posture recognition in manufacturing. J Intell Manuf 2023; 34(8):3469-81.

[99]	Zhu Z, Lei Y, Qi G, Chai Y, Mazur N, An Y, et al. A review of the application of deep learning in intelligent fault diagnosis of rotating machinery. Measurement 2023;206:112346.

[100]

Ali Z, Bhaskar SB. Basic statistical tools in research and data analysis. Indian J Anaesth 2016; 60(9):662-9.

[101]

Marshall G, Jonker L. An introduction to descriptive statistics: a review and practical guide. Radiography 2010; 16(4):e1-7.

[102]

Spriestersbach A, Röhrig B, Du Prel JB, Gerhold-Ay A, Blettner M. Descriptive statistics: the specification of statistical measures and their presentation in tables and graphs. Part 7 of a series on evaluation of scientific publications. Dtsch Arztebl Int 2009; 106(36):578.

[103]

Saccenti E, Hoefsloot HCJ, Smilde AK, Westerhuis JA, Hendriks MMWB. Reflections on univariate and multivariate analysis of metabolomics data. Metabolomics 2014; 10(3):361-74.

[104]

Yun YH, Li HD, Deng BC, Cao DS. An overview of variable selection methods in multivariate analysis of near-infrared spectra. Trends Analyt Chem 2019;113:102-15.

[105]

Sedgwick P. Pearson’s correlation coefficient. BMJ 2012;345:e4483.

[106]

Gallant. Nonlinear regression. Am Stat 1975; 29(2):73-81.

[107]

Yu J, Liu J. Lrprob control chart based on logistic regression for monitoring mean shifts of auto-correlated manufacturing processes. Int J Prod Res 2011; 49(8):2301-26.

[108]

Yusof ZM, Misiran M, Harun NH. Job satisfaction among employees in a manufacturing company in north Malaysia. Asian J Appl Sci 2014; 2 (01):79-87.

[109]

Mishra P, Pandey CM, Singh U, Keshri A, Sabaretnam M. Selection of appropriate statistical methods for data analysis. Ann Card Anaesth 2019; 22(3):297-301.

[110]

Mishra P, Singh U, Pandey CM, Mishra P, Pandey G. Application of Student’s t- test, analysis of variance, and covariance. Ann Card Anaesth 2019; 22 (4):407-11.

[111]

Chatfield M, Mander A. The Skillings-Mack test (Friedman test when there are missing data). Stata J 2009; 9(2):299-305.

[112]

Chien CF, Wang WC, Cheng JC. Data mining for yield enhancement in semiconductor manufacturing and an empirical study. Expert Syst Appl 2007; 33(1):192-8.

[113]

Kamis AS, Ahmad Fuad AF, Ashaari A, Mohd Noor CW. Development of wop mathematical model for efficient course alteration: LNG tanker manoeuvring analysis and Mann-Whitney U test. Ocean Eng 2021;239:109768.

[114]

Razali NM, Wah YB. Power comparisons of Shapiro-Wilk, Kolmogorov- Smirnov, Lilliefors and Anderson-Darling tests. J Stat Modeling Anal 2011; 2 (1):21-33.

[115]

Wang Z, Hong T, Piette MA. Building thermal load prediction through shallow machine learning and deep learning. Appl Energy 2020;263:114683.

[116]

Humeau-Heurtier A. Texture feature extraction methods: a survey. IEEE Access 2019;7:8975-9000.

[117]

Li JD, Cheng K, Wang S, Morstatter F, Trevino RP, Tang J, et al. Feature selection: a data perspective. ACM Comput Surv 2017;50(6):1-45.big data. IEEE Access 2020;8:54776-88.

[118]

Zebari R, Abdulazeez A, Zeebaree D, Zebari D, Saeed J. A comprehensive review of dimensionality reduction techniques for feature selection and feature extraction. J Appl Sci Technol Trends 2020; 1(1):56-70.

[119]

Shang C, You F. Data analytics and machine learning for smart process manufacturing: recent advances and perspectives in the big data era. Engineering 2019; 5(6):1010-6.

[120]

Xu K, Li Y, Liu C, Liu X, Hao X, Gao J, et al. Advanced data collection and analysis in data-driven manufacturing process. Chin J Mech Eng 2020; 33 (1):43.

[121]

Rigatti SJ. Random forest. J Insur Med 2017; 47(1):31-9.

[122]

Lunga D, Prasad S, Crawford MM, Ersoy O. Manifold-learning-based feature extraction for classification of hyperspectral data: a review of advances in manifold learning. IEEE Signal Process Mag 2013; 31(1):55-66.

[123]

Belkina AC, Ciccolella CO, Anno R, Halpert R, Spidlen J, Snyder-Cappione JE. Automated optimized parameters for T-distributed stochastic neighbor embedding improve visualization and analysis of large datasets. Nat Commun 2019; 10(1):5415.

[124]

Ramachandram D, Taylor GW. Deep multimodal learning: a survey on recent advances and trends. IEEE Signal Process Mag 2017; 34(6):96-108.

[125]

Hoang DT, Kang HJ. A survey on deep learning based bearing fault diagnosis. Neurocomputing 2019;335:327-35.

[126]

Liou CY, Cheng WC, Liou JW, Liou DR. Autoencoder for words. Neurocomputing 2014;139:84-96.

[127]

Jadhav B, Barnabas V, Sayyed M. Artificial intelligence-centric applications in data privacy and cybersecurity for human resource systems. In: KhangK, editor. AI-oriented competency framework for talent management in the digital economy:models, technologies, applications, and implementation. Raton: CRC Press; 2024. p. 339-52.

[128]

Salakhutdinov R. Learning deep generative models. Annu Rev Stat Appl 2015; 2(1):361-85.

[129]

Chen T, Kornblith S, Swersky K, Norouzi M, Hinton G. Big self-supervised models are strong semi-supervised learners. Adv Neural Inf Process Syst 2020;33:22243-55.

[130]

Hewamalage H, Bergmeir C, Bandara K. Recurrent neural networks for time series forecasting: current status and future directions. Int J Forecast 2021; 37 (1):388-427.

[131]

Van Houdt G, Mosquera C, Nápoles G. A review on the long short-term memory model. Artif Intell Rev 2020; 53(8):5929-55.

[132]

Karpatne A, Atluri G, Faghmous JH, Steinbach M, Banerjee A, Ganguly A, et al. Theory-guided data science: a new paradigm for scientific discovery from data. IEEE Trans Knowl Data Eng 2017; 29(10):2318-31.

[133]

Vadyala SR, Betgeri SN, Matthews JC, Matthews E. A review of physics-based machine learning in civil engineering. Result Eng 2022;13:100316.

[134]

Xu Y, Kohtz S, Boakye J, Gardoni P, Wang P. Physics-informed machine learning for reliability and systems safety applications: state of the art and challenges. Reliab Eng Syst Saf 2023;230:108900.

[135]

Provancher J, Collette M, Reese M. A generic framework for data model fusion. Report. Honolulu: Martin Defense Group; 2022.

[136]

Liu D, Wang Y. A dual-dimer method for training physics-constrained neural networks with minimax architecture. Neural Netw 2021;136:112-25.

[137]

Guo R, Huang T, Li M, Zhang H, Eldar YC. Physics-embedded machine learning for electromagnetic data imaging: examining three types of data-driven imaging methods. IEEE Signal Process Mag 2023; 40(2):18-31.

[138]

He H, Jin S, Wen CK, Gao F, Li GY, Xu Z. Model-driven deep learning for physical layer communications. IEEE Wirel Commun 2019; 26(5):77-83.

[139]

Yuan Z, Chen L, Liu G, Shao W, Zhang Y, Yang W. Physics-based Bayesian linear regression model for predicting length of mixed oil. Geo Sci Eng 2023;223:211466.

[140]

Kim J, Luettgen C, Paynabar K, Boukouvala F. Physics-based penalization for hyperparameter estimation in gaussian process regression. Comput Chem Eng 2023;178:108320.

[141]

Kannapinn M, Pham MK, Schäfer M. Physics-based digital twins for autonomous thermal food processing: efficient, non-intrusive reduced- order modeling. Innov Food Sci Emerg Technol 2022;81:103143.

[142]

Benner P, Goyal P, Kramer B, Peherstorfer B, Willcox K. Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms. Comput Methods Appl Mech Eng 2020;372:113433.

[143]

McAllister CD, Altuntas B, Frank M, Potoradi J. Implementation of response surface methodology using variance reduction techniques in semiconductor manufacturing. In:Proceeding of the 2001 Winter Simulation Conference (Cat. No.01CH37304); 2001 Dec 9-12; Arlington, VA, USA. Piscataway: IEEE; 2001. p. 1225-30.

[144]

Du Y, Lu X, Wang S, Du L, Wang Y, Leao B, et al. Physics-based feature extraction from bulk time-series PMU datasets for event detection. In: Proceeding of the 2021 IEEE Power & Energy Society General Meeting (PESGM); 2021 Jul 25-29; Washington, DC, USA. Piscataway: IEEE; 2021. p. 1-5.

[145]

Jin X, Zhang X, Cheng X, Jiang G, Masisi L, Huang W. A physics-based and data-driven feature extraction model for blades icing detection of wind turbines. IEEE Sens J 2023; 23(4):3944-54.

[146]

Mohamad TH, Abbasi A, Kappaganthu K, Nataraj C. On extraction, ranking and selection of data-driven and physics-informed features for bearing fault diagnostics. Knowl Base Syst 2023;276:110744.

[147]

Wang S, Wang H, Perdikaris P. On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics- informed neural networks. Comput Methods Appl Mech Eng 2021;384:113938.

[148]

Lu Y, Li Q, Liang SY. Physics-based intelligent prognosis for rolling bearing with fault feature extraction. Int J Adv Manuf Technol 2018; 97(1- 4):611-20.

[149]

Bünning F, Huber B, Schalbetter A, Aboudonia A, Hudoba de Badyn M, Heer P, et al. Physics-informed linear regression is competitive with two machine learning methods in residential building MPC. Appl Energy 2022;310:118491.

[150]

Li Y, Wang J, Huang Z, Gao RX. Physics-informed meta learning for machining tool wear prediction. J Manuf Syst 2022;62:17-27.

[151]

Brito LC, Susto GA, Brito JN, Duarte MAV. An explainable artificial intelligence approach for unsupervised fault detection and diagnosis in rotating machinery. Mech Syst Signal Process 2022;163:108105.

[152]

Yucesan YA, Viana FAC. A physics-informed neural network for wind turbine main bearing fatigue. Int J Progn Health Manag 2020; 11(1):17.

[153]

Ostad Ali Akbari V, Kuffa M, Wegener K. Physics-informed Bayesian machine learning for probabilistic inference and refinement of milling stability predictions. CIRO J Manuf Sci Technol 2023;45:225-39.

[154]

Wang J, Li Y, Zhao R, Gao RX. Physics guided neural network for machining tool wear prediction. J Manuf Syst 2020;57:298-310.

[155]

Liu S, Kappes BB, Amin-ahmadi B, Benafan O, Zhang X, Stebner AP. Physics- informed machine learning for composition-process-property design: shape memory alloy demonstration. Appl Mater Today 2021;22:100898.

[156]

Zhang XC, Gong JG, Xuan FZ. A physics-informed neural network for creep- fatigue life prediction of components at elevated temperatures. Eng Fract Mech 2021;258:108130.

[157]

Lu H, Pavan Nemani V, Barzegar V, Allen C, Hu C, Laflamme S, et al. A physics- informed feature weighting method for bearing fault diagnostics. Mech Syst Signal Process 2023;191:110171.

[158]

Goebel K, Eklund N, Bonanni P.Fusing competing prediction algorithms for prognostics. In: Proceedings of the 2006 IEEE Aerospace Conference; 2006 Mar 04-11; Big Sky, MT, USA. Piscataway: IEEE; 2006. p. 1-10.

[159]

Arias Chao M, Kulkarni C, Goebel K, Fink O. Fusing physics-based and deep learning models for prognostics. Reliab Eng Syst Saf 2022;217:107961.

[160]

Goebel K, Eklund N.Prognostic fusion for uncertainty reduction. In:Proceedings of the AIAA infotech@Aerospace 2007 Conference and Exhibit; 2007 May 7-10; Rohnert Park, CA, USA. Reston: American Institute of Aeronautics and Astronauticsp (AIAA); 2007. p. 2843.

[161]

Hankins SN, Fertig III RS. Design of heat exchangers via a bioinspired topology optimization framework with physics-informed underlying fields. Struct Multidiscipl Optim 2023; 66(7):157.

[162]

Serani A, Stern F, Campana EF, Diez M. Hull-form stochastic optimization via computational-cost reduction methods. Eng Comput 2022; 38(Suppl 3):2245-69.

[163]

Popov E, Archibald R, Hiscox B, Sobes V. Artificial intelligence-driven thermal design for additively manufactured reactor cores. Nucl Eng Des 2022;395:111862.

[164]

Bambach M, Fügenschuh A, Buhl J, Jensch F, Schmidt J. Mathematical modeling and optimization for powder-based additive manufacturing. Procedia Manuf 2020;47:1159-63.

[165]

Tanaka H, Nagai H. Thermal surrogate model for spacecraft systems using physics-informed machine learning with POD data reduction. Int J Heat Mass Transf 2023;213:124336.

[166]

Mozaffar M, Liao S, Xie X, Saha S, Park C, Cao J, et al. Mechanistic artificial intelligence (mechanistic-AI) for modeling, design, and control of advanced manufacturing processes: current state and perspectives. J Mater Process Technol 2022;302:117485.

[167]

Sideris I, Crivelli F, Bambach M. GPyro: uncertainty-aware temperature predictions for additive manufacturing. J Intell Manuf 2023; 34 (1):243-59.

[168]

Wang H, Li B, Xuan FZ. A dimensionally augmented and physics-informed machine learning for quality prediction of additively manufactured high- entropy alloy. J Mater Process Technol 2022;307:117637.

[169]

Ghosh D, Moreira J, Mhaskar P. Model predictive control embedding a parallel hybrid modeling strategy. Ind Eng Chem Res 2021; 60(6):2547-62.

[170]

Eker ÖF, Camci F, Jennions IK. Physics-based prognostic modelling of filter clogging phenomena. Mech Syst Signal Process 2016;75:395-412.

[171]

Wang J, Liang Y, Zheng Y, Gao RX, Zhang F. An integrated fault diagnosis and prognosis approach for predictive maintenance of wind turbine bearing with limited samples. Renew Energy 2020;145:642-50.

[172]

Luo W, Hu T, Ye Y, Zhang C, Wei Y. A hybrid predictive maintenance approach for CNC machine tool driven by digital twin. Robot Comput-Integr Manuf 2020;65:101974.

[173]

Maheshwari S, Shetty S, Ratnakar R, Sanyal S. Role of computational science in materials and systems design for sustainable energy applications: an industry perspective. J Indian Inst Sci 2022; 102(1):11-37.

[174]

Hu Z, Mahadevan S. Uncertainty quantification and management in additive manufacturing: current status, needs, and opportunities. Int J Adv Manuf Technol 2017; 93(5-8):2855-74.

[175]

Nath P, Olson JD, Mahadevan S, Lee YTT. Optimization of fused filament fabrication process parameters under uncertainty to maximize part geometry accuracy. Addit Manuf 2020;35:101331.

[176]

Tao F, Qi Q, Liu A, Kusiak A. Data-driven smart manufacturing. J Manuf Syst 2018;48:157-69.

[177]

Soundararajan B, Sofia D, Barletta D, Poletto M. Review on modeling techniques for powder bed fusion processes based on physical principles. Addit Manuf 2021;47:102336.

[178]

Wang J, Ye L, Gao RX, Li C, Zhang L. Digital twin for rotating machinery fault diagnosis in smart manufacturing. Int J Prod Res 2019; 57 (12):3920-34.

[179]

Tao F, Qi Q. Make more digital twins. Nature 2019; 573(7775): 490-1.

[180]

Kasneci E, Seßler K, Küchemann S, Bannert M, Dementieva D, Fischer F, et al. ChatGPT for good? On opportunities and challenges of large language models for education. Learn Individ Differ 2023;103:102274.

[181]

Kong X, Wu Y, Wang H, Xia F. Edge computing for internet of everything: a survey. IEEE Int Things J 2022; 9(23):23472-85.

[182]

Zhang Y, Cheng Y, Zheng H, Tao F. Long-/short-term preference based dynamic pricing and manufacturing service collaboration optimization. IEEE Trans Industr Inform 2022; 18(12):8948-56.

[183]

Phuyal S, Bista D, Bista R. Challenges, opportunities and future directions of smart manufacturing: a state of art review. Sustain Futures 2020;2:100023.

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