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General expression for linear and nonlinear time series models

Ren HUANG, Feiyun XU, Ruwen CHEN

《机械工程前沿（英文）》 2009年第4卷第1期页码 15-24 doi: 10.1007/s11465-009-0015-z

摘要： The typical time series models such as ARMA, AR, and MA are founded on the normality and stationarity of a system and expressed by a linear difference equation; therefore, they are strictly limited to the linear system. However, some nonlinear factors are within the practical system; thus, it is difficult to fit the model for real systems with the above models. This paper proposes a general expression for linear and nonlinear auto-regressive time series models (GNAR). With the gradient optimization method and modified AIC information criteria integrated with the prediction error, the parameter estimation and order determination are achieved. The model simulation and experiments show that the GNAR model can accurately approximate to the dynamic characteristics of the most nonlinear models applied in academics and engineering. The modeling and prediction accuracy of the GNAR model is superior to the classical time series models. The proposed GNAR model is flexible and effective.

关键词： linear and nonlinear autoregressive model system identification time series analysis

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Computation and investigation of mode characteristics in nonlinear system with tuned/mistuned contact

Houxin SHE, Chaofeng LI, Qiansheng TANG, Hui MA, Bangchun WEN

《机械工程前沿（英文）》 2020年第15卷第1期页码 133-150 doi: 10.1007/s11465-019-0557-7

摘要： This study derived a novel computation algorithm for a mechanical system with multiple friction contact interfaces that is well-suited to the investigation of nonlinear mode characteristic of a coupling system. The procedure uses the incremental harmonic balance method to obtain the nonlinear parameters of the contact interface. Thereafter, the computed nonlinear parameters are applied to rebuild the matrices of the coupling system, which can be easily solved to calculate the nonlinear mode characteristics by standard iterative solvers. Lastly, the derived method is applied to a cycle symmetry system, which represents a shaft–disk–blade system subjected to dry friction. Moreover, this study analyzed the effects of the tuned and mistuned contact features on the nonlinear mode characteristics. Numerical results prove that the proposed method is particularly suitable for the study of nonlinear characteristics in such nonlinear systems.

关键词： coupling vibration nonlinear mode original algorithm contact interface

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An integrated approach for machine-learning-based system identification of dynamical systems under control: application towards the model predictive control of a highly nonlinear reactor system

《化学科学与工程前沿（英文）》 2022年第16卷第2期页码 237-250 doi: 10.1007/s11705-021-2058-6

摘要： Advanced model-based control strategies, e.g., model predictive control, can offer superior control of key process variables for multiple-input multiple-output systems. The quality of the system model is critical to controller performance and should adequately describe the process dynamics across its operating range while remaining amenable to fast optimization. This work articulates an integrated system identification procedure for deriving black-box nonlinear continuous-time multiple-input multiple-output system models for nonlinear model predictive control. To showcase this approach, five candidate models for polynomial and interaction features of both output and manipulated variables were trained on simulated data and integrated into a nonlinear model predictive controller for a highly nonlinear continuous stirred tank reactor system. This procedure successfully identified system models that enabled effective control in both servo and regulator problems across wider operating ranges. These controllers also had reasonable per-iteration times of ca. 0.1 s. This demonstration of how such system models could be identified for nonlinear model predictive control without prior knowledge of system dynamics opens further possibilities for direct data-driven methodologies for model-based control which, in the face of process uncertainties or modelling limitations, allow rapid and stable control over wider operating ranges.

关键词： nonlinear model predictive control black-box modeling continuous-time system identification machine learning industrial applications of process control

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Model-based nonlinear control of hydraulic servo systems: Challenges, developments and perspectives

Jianyong YAO

《机械工程前沿（英文）》 2018年第13卷第2期页码 179-210 doi: 10.1007/s11465-018-0464-3

摘要：

Hydraulic servo system plays a significant role in industries, and usually acts as a core point in control and power transmission. Although linear theory-based control methods have been well established, advanced controller design methods for hydraulic servo system to achieve high performance is still an unending pursuit along with the development of modern industry. Essential nonlinearity is a unique feature and makes model-based nonlinear control more attractive, due to benefit from prior knowledge of the servo valve controlled hydraulic system. In this paper, a discussion for challenges in model-based nonlinear control, latest developments and brief perspectives of hydraulic servo systems are presented: Modelling uncertainty in hydraulic system is a major challenge, which includes parametric uncertainty and time-varying disturbance; some specific requirements also arise ad hoc difficulties such as nonlinear friction during low velocity tracking, severe disturbance, periodic disturbance, etc.; to handle various challenges, nonlinear solutions including parameter adaptation, nonlinear robust control, state and disturbance observation, backstepping design and so on, are proposed and integrated, theoretical analysis and lots of applications reveal their powerful capability to solve pertinent problems; and at the end, some perspectives and associated research topics (measurement noise, constraints, inner valve dynamics, input nonlinearity, etc.) in nonlinear hydraulic servo control are briefly explored and discussed.

关键词： hydraulic servo system adaptive control robust control nonlinear friction disturbance compensation repetitive control noise alleviation constraint control

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Analysis of stability and nonlinear response of rotor system with elliptical sliding bearing supports

LU Yanjun, LIU Heng, YU Lie, LI Qi, JIANG Ming, ZHANG Zhiyu

《机械工程前沿（英文）》 2007年第2卷第1期页码 37-45 doi: 10.1007/s11465-007-0006-x

摘要： Based on the variational constraint approach, the variational form of Reynolds equation in hydrodynamic lubrication is revised continuously to satisfy certain constraints in the cavitation zone of oil film field. According to the physical characteristic of oil film, an eight-node isoparametric finite element method is used to convert the revised variational form of Reynolds equation to a discrete form of finite dimensional algebraic variational equation. By this approach, a perturbance equation can be obtained directly on the finite element equation. Consequently, nonlinear oil film forces and their Jacobian matrices are calculated simultaneously, and compatible accuracy is obtained without increasing the computational costs. A method, which is a combination of predictor corrector mechanism and Newton Raphson method, is presented to calculate equilibrium position and critical speed corresponding to Hopf bifurcation point of bearing-rotor system, as by-product dynamic coefficients of bearing are obtained. The timescale, i.e., the unknown whirling period of Hopf bifurcation solution of bearing-rotor system is drawn into the iterative process using Poincar?Newton Floquet method. The stability of the Hopf bifurcation solution can be detected when estimating Hopf bifurcation solution and its periods. The nonlinear unbalanced periodic responses of the system are obtained by using PNF method and path-following technique. The local stability and bifurcation behaviors of periodic motions are analyzed by Floquet theory. Chaotic motions are analyzed by Lyapunov exponents. The numerical results revealed the rich and complex nonlinear behavior of the system, such as periodic, quasiperiodic, jumped solution, chaos, and coexistence of multisolution, and so on.

关键词： computational corrector mechanism predictor corrector multisolution quasiperiodic

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一类非仿射离散非线性系统的直接自适应模糊滑模控制 Article

Xiao-yu ZHANG

《信息与电子工程前沿（英文）》 2016年第17卷第12期页码 1331-1343 doi: 10.1631/FITEE.1500318

摘要：为了获得自适应特性及消除滑模控制抖振，通过使用一个动态模糊逻辑系统（Dynamic fuzzy logical system, DFLS）实现等价控制。DFLS的参数实行在线自调节。

关键词：非线性系统；离散系统；动态模糊逻辑系统；直接自适应；滑模控制

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reference tracking control design for a class of nonlinear systems with time-varying delays

Mei-qin LIU,Hai-yang CHEN,Sen-lin ZHANG

《信息与电子工程前沿（英文）》 2015年第16卷第9期页码 759-768 doi: 10.1631/FITEE.1500053

摘要： This paper investigates the trajectory tracking control for a class of nonlinear systems with timevarying delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. A unified model consisting of a linear delayed dynamic system and a bounded static nonlinear operator is introduced, which covers most of the nonlinear systems with bounded nonlinear terms, such as the one-link robotic manipulator, chaotic systems, complex networks, the continuous stirred tank reactor (CSTR), and the standard genetic regulatory network (SGRN). First, the definition of the tracking control is given. Second, the performance analysis of the closed-loop system including this unified model, reference model, and state feedback controller is presented. Then criteria on the tracking controller design are derived in terms of LMIs such that the output of the closed-loop system tracks the given reference signal in the sense. The reference model adopted here is modified to be more flexible. A scaling factor is introduced to deal with the disturbance such that the control precision is improved. Finally, a CSTR system is provided to demonstrate the effectiveness of the established control laws.

关键词： H∞ reference tracking Nonlinear system State feedback control Time-varying delays Unified model

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基于知识的多变量非线性系统变结构解耦控制

涂承媛,曾衍钧

《中国工程科学》 2001年第3卷第10期页码 48-52

摘要：

文章提出了一种基于知识的变结构解耦控制策略，并用于多变量非线性系统的控制，避免了传统解耦控制所必须的建模过程，特别是避免了相应的大量复杂的矩阵运算。阐述了其控制知识库中的一些模块，给出了其算法要点。提出的策略成功地用于一个3×3强耦合系统一三绕组加热标准温度源的恒温控制，得到了温度稳定性和温度均匀性都优于1℃的效果，这是传统方法用于该系统所无法实现的。

关键词：多变量非线性系统解耦控制基于知识的变结构解耦

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电力系统低频振荡中的非线性奇异现象

马景兰,王伟,万京生,张永丽

《中国工程科学》 2009年第11卷第8期页码 93-96

摘要：

低频振荡是影响电力系统稳定运行的一个重要方面。阐述了低频振荡产生的机理和分析方法，利用Hopf分歧理论，针对一个四阶模型的单机无穷大系统，分析了在临界点附近时可能出现的非线性奇异现象。研究表明：由于分歧的存在，导致系统稳定性在临界点附近出现奇异，从而影响了电力系统的稳定域。

关键词：低频振荡分歧理论非线性奇异

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Numerical analysis of vehicle-bridge coupling vibration concerning nonlinear stress-dependent damping

Pengfei LI; Jinquan ZHANG; Shengqi MEI; Zhenhua DONG; Yan MAO

《结构与土木工程前沿（英文）》 2022年第16卷第2期页码 239-249 doi: 10.1007/s11709-021-0804-y

摘要： Damping is known to have a considerable influence on the dynamic behavior of bridges. The fixed damping ratios recommended in design codes do not necessarily represent the complicated damping characteristics of bridge structures. This study investigated the application of stress-dependent damping associated with vehicle-bridge coupling vibration and based on that investigation proposed the stress-dependent damping ratio. The results of the investigation show that the stress-dependent damping ratio is significantly different from the constant damping ratio (5%) defined in the standard specification. When vehicles travel at speeds of 30, 60, and 90, the damping ratios of the bridge model are 3.656%, 3.658%, and 3.671%, respectively. The peak accelerations using the regular damping ratio are 18.9%, 21.3%, and 14.5% of the stress-dependent damping ratio, respectively. When the vehicle load on the bridge is doubled, the peak acceleration of the mid-span node increases by 5.4 times, and the stress-related damping ratio increases by 2.1%. A corrugated steel-web bridge is being used as a case study, and the vibration response of the bridge is compared with the measured results. The acceleration response of the bridge which was calculated using the stress-dependent damping ratio is significantly closer to the measured acceleration response than that using the regular damping ratio.

关键词： vehicle-bridge vibration system dynamic analysis stress-dependent damping energy dissipation

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Nonlinear analysis of pre-tensioned glass wall facade by stability function with initial imperfection

Siu-Lai CHAN, Yaopeng LIU, Andy LEE,

《结构与土木工程前沿（英文）》 2010年第4卷第3期页码 376-382 doi: 10.1007/s11709-010-0086-2

摘要： Pre-tensioned high strength trusses using alloy steel bar are widely used as glass wall supporting systems because of the high degree of transparency. The breakage of glass panes in this type of system occurs occasionally, likely to be due to error in design and analysis in addition to other factors like glass impurity and stress concentration around opening in a spider system. Most design does not consider the flexibility of supports from finite stiffness of supporting steel or reinforced concrete beams. The resistance of lateral wind pressure of the system makes use of high tension force coupled with the large deflection effect, both of which are affected by many parameters not generally considered in conventional structures. In the design, one must therefore give a careful consideration on various effects, such as support settlement due to live loads and material creep, temperature change, pre-tension force, and wind pressure. It is not uncommon to see many similar glass wall systems fail in the wind load test chambers under a design wind speed. This paper presents a rigorous analysis and design of this type of structural systems used in a project in Hong Kong, China. The stability function with initial curvature is used in place of the cubic function, which is only accurate for linear analysis. The considerations and analysis techniques are believed to be of value to engineers involved in the design of the structural systems behaving nonlinearly.

关键词： tension system glass wall nonlinear analysis pre-tensioning second-order analysis

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非线性科学及其在医学中的应用

涂承媛,曾衍钧

《中国工程科学》 2003年第5卷第8期页码 45-49

摘要：

简要介绍了非线性科学中的分形维方法和信息熵方法及其用于房颤信息的处理和分析，计算了未房颤时P波的及房颤时f波的格子维和信息熵，特别是，比较了未房颤时和发生房颤时的相关计算结果的显著差别，从而很容易判断是否发生了房颤。

关键词：复杂大系统非线性分形理论分形维信息熵（Shannom熵）房颤

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New nonlinear stiffness actuator with predefined torque‒deflection profile

《机械工程前沿（英文）》 2023年第18卷第1期 doi: 10.1007/s11465-022-0721-3

摘要： A nonlinear stiffness actuator (NSA) could achieve high torque/force resolution in low stiffness range and high bandwidth in high stiffness range, both of which are beneficial for physical interaction between a robot and the environment. Currently, most of NSAs are complex and hardly used for engineering. In this paper, oriented to engineering applications, a new simple NSA was proposed, mainly including leaf springs and especially designed cams, which could perform a predefined relationship between torque and deflection. The new NSA has a compact structure, and it is lightweight, both of which are also beneficial for its practical application. An analytical methodology that maps the predefined relationship between torque and deflection to the profile of the cam was developed. The optimal parameters of the structure were given by analyzing the weight of the NSA and the mechanic characteristic of the leaf spring. Though sliding friction force is inevitable because no rollers were used in the cam-based mechanism, the sliding displacement between the cam and the leaf spring is very small, and consumption of sliding friction force is very low. Simulations of different torque‒deflection profiles were carried out to verify the accuracy and applicability of performing predefined torque‒deflection profiles. Three kinds of prototype experiments, including verification experiment of the predefined torque‒deflection profile, torque tracking experiment, and position tracking experiment under different loads, were conducted. The results prove the accuracy of performing the predefined torque‒deflection profile, the tracking performance, and the interactive performance of the new NSA.

关键词： compliant actuator nonlinear stiffness actuator nonlinear spring predefined torque−deflection profile

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Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes

M.R. AKBARI,D.D. GANJI,A.R. AHMADI,Sayyid H. Hashemi KACHAPI

《机械工程前沿（英文）》 2014年第9卷第1期页码 58-70 doi: 10.1007/s11465-014-0289-7

摘要：

In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.

关键词： Algebraic Method (AGM) tower crane oscillating system angular frequency

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Mean wind load induced incompatibility in nonlinear aeroelastic simulations of bridge spans

Zhitian ZHANG

《结构与土木工程前沿（英文）》 2019年第13卷第3期页码 605-617 doi: 10.1007/s11709-018-0499-x

摘要： Mean wind response induced incompatibility and nonlinearity in bridge aerodynamics is discussed, where the mean wind and aeroelastic loads are applied simultaneously in time domain. A kind of incompatibility is found during the simultaneous simulation of the mean wind and aeroelastic loads, which leads to incorrect mean wind structural responses. It is found that the mathematic expectations (or limiting characteristics) of the aeroelastic models are fundamental to this kind of incompatibility. In this paper, two aeroelastic models are presented and discussed, one of indicial-function-denoted (IF-denoted) and another of rational-function-denoted (RF-denoted). It is shown that, in cases of low wind speeds, the IF-denoted model reflects correctly the mean wind load properties, and results in correct mean structural responses; in contrast, the RF-denoted model leads to incorrect mean responses due to its nonphysical mean properties. At very high wind speeds, however, even the IF-denoted model can lead to significant deviation from the correct response due to steady aerodynamic nonlinearity. To solve the incompatibility at high wind speeds, a methodology of subtraction of pseudo-steady effects from the aeroelastic model is put forward in this work. Finally, with the method presented, aeroelastic nonlinearity resulted from the mean wind response is investigated at both moderate and high wind speeds.

关键词： bridge aerodynamics nonlinear aeroelastic model Pseudo-steady mean wind loads

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标题作者时间类型操作

General expression for linear and nonlinear time series models

Ren HUANG, Feiyun XU, Ruwen CHEN

期刊论文

Computation and investigation of mode characteristics in nonlinear system with tuned/mistuned contact

Houxin SHE, Chaofeng LI, Qiansheng TANG, Hui MA, Bangchun WEN

期刊论文

An integrated approach for machine-learning-based system identification of dynamical systems under control: application towards the model predictive control of a highly nonlinear reactor system

期刊论文

Model-based nonlinear control of hydraulic servo systems: Challenges, developments and perspectives

Jianyong YAO

期刊论文

Analysis of stability and nonlinear response of rotor system with elliptical sliding bearing supports

LU Yanjun, LIU Heng, YU Lie, LI Qi, JIANG Ming, ZHANG Zhiyu

期刊论文

一类非仿射离散非线性系统的直接自适应模糊滑模控制

Xiao-yu ZHANG

期刊论文

reference tracking control design for a class of nonlinear systems with time-varying delays

Mei-qin LIU,Hai-yang CHEN,Sen-lin ZHANG