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Uncertainty propagation analysis by an extended sparse grid technique

X. Y. JIA, C. JIANG, C. M. FU, B. Y. NI, C. S. WANG, M. H. PING

《机械工程前沿（英文）》 2019年第14卷第1期页码 33-46 doi: 10.1007/s11465-018-0514-x

摘要： In this paper, an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle, aiming at improving the solving accuracy of the high-order moments and hence the fitting accuracy of the probability density function (PDF) of the system response. The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysis. Moreover, assisted by the Rosenblatt transformation, the various types of extended integration points are transformed into the extended Gauss-Hermite integration points, which makes the method suitable for any type of continuous distribution. Subsequently, within the sparse grid numerical integration framework, the statistical moments of the system response are obtained based on the transformed points. Furthermore, based on the maximum entropy principle, the obtained first four-order statistical moments are used to fit the PDF of the system response. Finally, three numerical examples are investigated to demonstrate the effectiveness of the proposed method, which includes two mathematical problems with explicit expressions and an engineering application with a black-box model.

关键词： uncertainty propagation analysis extended sparse grid maximum entropy principle extended Gauss integration Rosenblatt transformation high-order moments analysis

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Uncertainty propagation in dynamics of composite plates: A semi-analytical non-sampling-based approach

Mahdi FAKOOR, Hadi PARVIZ

《结构与土木工程前沿（英文）》 2020年第14卷第6期页码 1359-1371 doi: 10.1007/s11709-020-0658-8

摘要： In this study, the influences of spatially varying stochastic properties on free vibration analysis of composite plates were investigated via development of a new approach named the deterministic-stochastic Galerkin-based semi-analytical method. The material properties including tensile modulus, shear modulus, and density of the plate were assumed to be spatially varying and uncertain. Gaussian fields with first-order Markov kernels were utilized to define the aforementioned material properties. The stochastic fields were decomposed via application of the Karhunen-Loeve theorem. A first-order shear deformation theory was assumed, following which the displacement field was defined using admissible trigonometric modes to derive the potential and kinetic energies. The stochastic equations of motion of the plate were obtained using the variational principle. The deterministic-stochastic Galerkin-based method was utilized to find the probability space of natural frequencies, and the corresponding mode shapes of the plate were determined using a polynomial chaos approach. The proposed method significantly reduced the size of the mathematical models of the structure, which is very useful for enhancing the computational efficiency of stochastic simulations. The methodology was verified using a stochastic finite element method and the available results in literature. The sensitivity of natural frequencies and corresponding mode shapes due to the uncertainty of material properties was investigated, and the results indicated that the higher-order modes are more sensitive to uncertainty propagation in spatially varying properties.

关键词： composite plate spatially varying stochastic properties Galerkin method polynomial chaos approach semi-analytical approach

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Uncertainty assessment in hydro-mechanical-coupled analysis of saturated porous medium applying fuzzy

Farhoud KALATEH, Farideh HOSSEINEJAD

《结构与土木工程前沿（英文）》 2020年第14卷第2期页码 387-410 doi: 10.1007/s11709-019-0601-z

摘要： The purpose of the present study was to develop a fuzzy finite element method, for uncertainty quantification of saturated soil properties on dynamic response of porous media, and also to discrete the coupled dynamic equations known as - hydro-mechanical equations. Input parameters included fuzzy numbers of Poisson’s ratio, Young’s modulus, and permeability coefficient as uncertain material of soil properties. Triangular membership functions were applied to obtain the intervals of input parameters in five membership grades, followed up by a minute examination of the effects of input parameters uncertainty on dynamic behavior of porous media. Calculations were for the optimized combinations of upper and lower bounds of input parameters to reveal soil response including displacement and pore water pressure via fuzzy numbers. Fuzzy analysis procedure was verified, and several numerical examples were analyzed by the developed method, including a dynamic analysis of elastic soil column and elastic foundation under ramp loading. Results indicated that the range of calculated displacements and pore pressure were dependent upon the number of fuzzy parameters and uncertainty of parameters within equations. Moreover, it was revealed that for the input variations looser sands were more sensitive than dense ones.

关键词： fuzzy finite element method saturated soil hydro-mechanical coupled equations coupled analysis uncertainty analysis

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Inverse uncertainty characteristics of pollution source identification for river chemical spill incidentsby stochastic analysis

Jiping Jiang, Feng Han, Yi Zheng, Nannan Wang, Yixing Yuan

《环境科学与工程前沿（英文）》 2018年第12卷第5期 doi: 10.1007/s11783-018-1081-4

摘要：

Uncertainty rules of pollution source inversion are revealed by stochastic analysis

A release load is most easily inversed and source locations own largest uncertainty

Instantaneous spill assumption has much less uncertainty than continuous spill

The estimated release locations and times negatively deviate from real values

The new findings improve monitoring network design and emergency response to spills

关键词： River chemical spills Emergency response Pollution source inversion Inverse uncertainty analysis Regional Sensitivity Analysis method (RSA) Monte Carlo analysis toolbox (MCAT)

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Probabilistic seismic response and uncertainty analysis of continuous bridges under near-fault ground

Hai-Bin MA, Wei-Dong ZHUO, Davide LAVORATO, Camillo NUTI, Gabriele FIORENTINO, Giuseppe Carlo MARANO, Rita GRECO, Bruno BRISEGHELLA

《结构与土木工程前沿（英文）》 2019年第13卷第6期页码 1510-1519 doi: 10.1007/s11709-019-0577-8

摘要： Performance-based seismic design can generate predictable structure damage result with given seismic hazard. However, there are multiple sources of uncertainties in the seismic design process that can affect desired performance predictability. This paper mainly focuses on the effects of near-fault pulse-like ground motions and the uncertainties in bridge modeling on the seismic demands of regular continuous highway bridges. By modeling a regular continuous bridge with OpenSees software, a series of nonlinear dynamic time-history analysis of the bridge at three different site conditions under near-fault pulse-like ground motions are carried out. The relationships between different Intensity Measure (IM) parameters and the Engineering Demand Parameter (EDP) are discussed. After selecting the peak ground acceleration as the most correlated IM parameter and the drift ratio of the bridge column as the EDP parameter, a probabilistic seismic demand model is developed for near-fault earthquake ground motions for 3 different site conditions. On this basis, the uncertainty analysis is conducted with the key sources of uncertainty during the finite element modeling. All the results are quantified by the “swing” base on the specific distribution range of each uncertainty parameter both in near-fault and far-fault cases. All the ground motions are selected from PEER database, while the bridge case study is a typical regular highway bridge designed in accordance with the Chinese Guidelines for Seismic Design of Highway Bridges. The results show that PGA is a proper IM parameter for setting up a linear probabilistic seismic demand model; damping ratio, pier diameter and concrete strength are the main uncertainty parameters during bridge modeling, which should be considered both in near-fault and far-fault ground motion cases.

关键词： continuous bridge probabilistic seismic demand model Intensity Measure near-fault uncertainty

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An integrated optimization and simulation approach for air pollution control under uncertainty in open-pit

Zunaira Asif, Zhi Chen

《环境科学与工程前沿（英文）》 2019年第13卷第5期 doi: 10.1007/s11783-019-1156-x

摘要： Air Pollution Control model is developed for open-pit metal mines. Model will aid decision makers to select a cost-effective solution. Open-pit metal mines contribute toward air pollution and without effective control techniques manifests the risk of violation of environmental guidelines. This paper establishes a stochastic approach to conceptualize the air pollution control model to attain a sustainable solution. The model is formulated for decision makers to select the least costly treatment method using linear programming with a defined objective function and multi-constraints. Furthermore, an integrated fuzzy based risk assessment approach is applied to examine uncertainties and evaluate an ambient air quality systematically. The applicability of the optimized model is explored through an open-pit metal mine case study, in North America. This method also incorporates the meteorological data as input to accommodate the local conditions. The uncertainties in the inputs, and predicted concentration are accomplished by probabilistic analysis using Monte Carlo simulation method. The output results are obtained to select the cost-effective pollution control technologies for PM2.5, PM10, NOx, SO2 and greenhouse gases. The risk level is divided into three types (loose, medium and strict) using a triangular fuzzy membership approach based on different environmental guidelines. Fuzzy logic is then used to identify environmental risk through stochastic simulated cumulative distribution functions of pollutant concentration. Thus, an integrated modeling approach can be used as a decision tool for decision makers to select the cost-effective technology to control air pollution.

关键词： Air pollution Decision analysis Linear programming Mining Optimization Fuzzy Monte Carlo

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Jack up reliability analysis: An overview

Ahmad IDRIS, Indra Sati Hamonangan HARAHAP, Montasir Osman Ahmed ALI

《结构与土木工程前沿（英文）》 2018年第12卷第4期页码 504-514 doi: 10.1007/s11709-017-0443-5

摘要： Jack up is a mobile unit used for oil and gas exploration and production in offshore fields. On demand, the unit is moved and installed in a given location and used for a period up to 12 months before being un-installed and moved to another location. Due to its mobility and re-usability, when the unit is offered for use in a given offshore location, its suitability in terms of safe operation is evaluated in accordance with the guidelines of Site Specific Assessment (SSA) of jack up. When the unit failed safety assessment criteria, the guideline recommended that it is re-assessed by increasing the complexity of the assumptions and methods used. Reliability analysis theories are one of the frameworks recommended for the safety assessment of the units. With recent developments in uncertainty and reliability analysis of structures subject to stochastic excitation, this study aims at providing a review on the past developments in jack up reliability analysis and to identify possible future directions. The results from literature reviewed shows that failure probabilities vary significantly with analysis method used. In addition, from the variants of reliability analysis approach, the method of time dependent reliability for dynamic structures subject to stochastic excitation have not been implemented on jack ups. Consequently, suggestions were made on the areas that need further examination for improvement of the efficiency in safety assessment of the units using reliability theories.

关键词： jack up reliability analysis uncertainty analysis review of jack up

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Seismic performance of viaducts with probabilistic method

ZHU Xi, WANG Jianmin

《结构与土木工程前沿（英文）》 2007年第1卷第3期页码 267-273 doi: 10.1007/s11709-007-0034-y

摘要： Due to the uncertainty of both ground motions and structural capacity, it is necessary to consider the seismic performance of viaduct structures using the probabilistic method. The risk is quantified by a procedure on the basis of a numerical determination of the fragility curves. A group of ground motions, Large Magnitude-Short Distance Bin (LMSR-N), selected specially due to its response spectra, is accorded well with the corresponding spectra of the Chinese code for seismic design. The characteristic values of the curvature ductility factors for the serviceability and the damage control limit states are obtained, and two equations for estimating the characteristic values of the curvature ductility factors are developed through regression analysis. Then, the serviceability and damage control limit states were proposed. Three damage states were constituted according the results of the experiment by Pacific Earthquake Engineering Research (PEER) Center. The analytical fragility curves were obtained specifically, using both Capacity Spectrum Method (CSM) (non-linear static) analysis and Ineremental Dynamic Method (IDM) (non-linear dynamic) analysis, respectively, in this paper. The structural fragility curves developed by CSM method can help make the structural analysis simple and quick, avoiding the implementation of the dynamic response history analysis (RHA). Although the dynamic RHA requires a lot of complicated analysis for the structure, the results from RHA are reliable and accurate. Fragility curves are powerful tools for use in performance-based seismic bridge design.

关键词： uncertainty Earthquake Engineering regression analysis accurate fragility

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A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture

Yongchang CAI, Hehua ZHU, Xiaoying ZHUANG

《结构与土木工程前沿（英文）》 2013年第7卷第4期页码 369-378 doi: 10.1007/s11709-013-0222-x

摘要： In the framework of finite element meshes, a novel continuous/discontinuous deformation analysis (CDDA) method is proposed in this paper for modeling of crack problems. In the present CDDA, simple polynomial interpolations are defined at the deformable block elements, and a link element is employed to connect the adjacent block elements. The CDDA is particularly suitable for modeling the fracture propagation because the switch from continuous deformation analysis to discontinuous deformation analysis is natural and convenient without additional procedures. The SIFs (stress intensity factors) for various types of cracks, such as kinked cracks or curved cracks, can be easily computed in the CDDA by using the virtual crack extension technique (VCET). Both the formulation and implementation of the VCET in CDDA are simple and straightforward. Numerical examples indicate that the present CDDA can obtain high accuracy in SIF results with simple polynomial interpolations and insensitive to mesh sizes, and can automatically simulate the crack propagation without degrading accuracy.

关键词： fracture crack propagation deformable block continuous/discontinuous deformation analysis (CDDA)

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Uncertainty analysis on aquatic environmental impacts of urban land use change

ZHOU Jiquan, LIU Yi, CHEN Jining, YU Fanxian

《环境科学与工程前沿（英文）》 2008年第2卷第4期页码 494-504 doi: 10.1007/s11783-008-0072-2

摘要： Uncertainties hamper the implementation of strategic environmental assessment (SEA). In order to quantitatively characterize the uncertainties of environmental impacts, this paper develops an integrated methodology through uncertainty analysis on land use change, which combines the scenario analysis approach, stochastic simulation technique, and statistics. Dalian city in China was taken as a case study in the present work. The results predict that the Fuzhou River poses the highest environmental pollution risk with a probability of 89.63% for COD in 2020. Furthermore, the Biliu River, Fuzhou River, Zhuang River, and Dasha River have 100% probabilities for NH-N. NH-N is a more critical pollutant than COD for all rivers. For COD, industry is the critical pollution source for all rivers except the Zhuang River. For NH-N, agriculture is the critical pollution source for the Biliu River, Yingna River, and Dasha River, sewage for the Fuzhou River and Zhuang River, and industry for the Dengsha River. This methodology can provide useful information, such as environmental risk, environmental pressure, and extremely environmental impact, especially under considerations of uncertainties. It can also help to ascertain the significance of each pollution source and its priority for control in urban planning.

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Risk analysis methods of the water resources system under uncertainty

Zeying GUI,Chenglong ZHANG,Mo Li,Ping GUO

《农业科学与工程前沿（英文）》 2015年第2卷第3期页码 205-215 doi: 10.15302/J-FASE-2015073

摘要： The main characteristic of the water resources system (WRS) is its great complexity and uncertainty, which makes it highly desirable to carry out a risk analysis of the WRS. The natural environmental, social economic conditions as well as limitations of human cognitive ability are possible sources of the uncertainties that need to be taken into account in the risk analysis process. In this paper the inherent stochastic uncertainty and cognitive subjective uncertainty of the WRS are discussed first, from both objective and subjective perspectives. Then the quantitative characterization methods of risk analysis are introduced, including three criteria (reliability, resiliency and vulnerability) and five basic optimization models (the expected risk value model, conditional value at risk model, chance-constrained risk model, minimizing probability of risk events model, and the multi-objective optimization model). Finally, this paper focuses on the various methods of risk analysis under uncertainty, which are summarized as random, fuzzy and mixed methods. A more comprehensive risk analysis methodology for the WRS is proposed based on the comparison of the advantages, disadvantages and applicable conditions of these three methods. This paper provides a decision support of risk analysis for researchers, policy makers and stakeholders of the WRS.

关键词： water resources system evaluation criterion optimization model risk analysis method uncertainty

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Crack propagation with different radius local random damage based on peridynamic theory

《结构与土木工程前沿（英文）》 2021年第15卷第5期页码 1238-1248 doi: 10.1007/s11709-021-0695-y

摘要： Drawing from the advantages of Classical Mechanics, the peridynamic theory can clarify the crack propagation mechanism by an integral solution without initially setting the factitious crack and crack path. This study implements the peridynamic theory by subjecting bilateral notch cracked specimens to the conditions of no local damage, small radius local damage, and large radius local damage. Moreover, to study the effects of local stochastic damage with different radii on the crack propagation path and Y-direction displacement, a comparison and contact methodology was adopted, in which the crack propagation paths under uniaxial tension and displacement in the Y-direction were compared and analyzed. This method can be applied to steel structures under similar local random damage conditions.

关键词： peridynamics stochastic damage bilateral notch crack

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Lamb wave propagation modeling for structure health monitoring

Xiaoyue ZHANG, Shenfang YUAN, Tong HAO

《机械工程前沿（英文）》 2009年第4卷第3期页码 326-331 doi: 10.1007/s11465-009-0045-6

摘要： This study aims to model the propagation of Lamb waves used in structure health monitoring. A number of different numerical computational techniques have been developed for wave propagation studies. The local interaction simulation approach, used for modeling sharp interfaces and discontinuities in complex media (LISA/SIM theory), has been effectively applied to numerical simulations of elastic wave interaction. This modeling is based on the local interaction simulation approach theory and is finally accomplished through the finite elements software Ansys11. In this paper, the Lamb waves propagating characteristics and the LISA/SIM theory are introduced. The finite difference equations describing wave propagation used in the LISA/SIM theory are obtained. Then, an anisotropic metallic plate model is modeled and a simulating Lamb waves signal is loaded on. Finally, the Lamb waves propagation modeling is implemented.

关键词： Lamb wave modeling LISA/SIM theory finite difference equation finite element

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New computational treatment of optical wave propagation in lossywaveguides

Jian-xin ZHU,Guan-jie WANG

《信息与电子工程前沿（英文）》 2015年第16卷第8期页码 646-653 doi: 10.1631/FITEE.1400406

摘要： In this paper, the optical wave propagation in lossy waveguides is described by the Helmholtz equation with the complex refractive-index, and the Chebyshev pseudospectral method is used to discretize the transverse operator of the equation. Meanwhile, an operator marching method, a one-way re-formulation based on the Dirichletto-Neumann (DtN) map, is improved to solve the equation. Numerical examples show that our treatment is more efficient.

关键词： Adjoint operator Orthogonal Chebyshev Pseudospectral method Dirichlet-to-Neumann map

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Modeling the impact of uncertainty in emissions trading markets with bankable permits

Yongliang ZHANG, Bing ZHANG, Jun BI, Pan HE

《环境科学与工程前沿（英文）》 2013年第7卷第2期页码 231-241 doi: 10.1007/s11783-012-0431-x

摘要： The various forms of uncertainty that firms may face in bankable emission permit trading markets will affect firms’ decision making as well as their market performance. This research explores the effect of increased uncertainty over future input costs and output prices on the temporal distribution of emission. In a dynamic programming setting, the permit price is a convex function of stochastic prices of coal and electricity. Increased uncertainty about future market conditions increases the expected permit price and causes a risk neutral firm to reduce ex ante emissions in order to smooth out marginal abatement costs over time. Finally, safety valves, both low-side and high-side, are suggested to reduce the impact of uncertainty in bankable emission trading markets.

关键词： uncertainty bankable emission trading market performance