A Hybrid Method for Structural System Reliability‐Based Design Optimization and its Application to Trusses

Most research studies on structural optimum design have focused on single‐objective optimization of deterministic structures, while little study has been carried out to address multi‐objective optimization of random structures. Statistical parameters and redundancy allocation problems should be considered in structural optimization. In order to address these problems, this paper presents a hybrid method for structural system reliability‐based design optimization (SRBDO) and applies it to trusses. The hybrid method integrates the concepts of the finite element method, radial basis function (RBF) neural networks, and genetic algorithms. The finite element method was used to compute structural responses under random loads. The RBF neural networks were employed to approximate structural responses for the purpose of replacing the structural limit state functions. The system reliabilities were calculated by Monte Carlo simulation method together with the trained RBF neural networks. The optimal parameters were obtained by genetic algorithms, where the system reliabilities were converted into penalty functions in order to address the constrained optimization. The hybrid method applied to trusses was demonstrated by two examples which were a typical 10‐bar truss and a steel truss girder structure. Detailed discussions and parameter analysis for the failure sequences such as web‐bucking failure and beam‐bending failure in the SRBDO were given. This hybrid method provides a new idea for SRBDO of trusses. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive resonance theory-based neural algorithms for manufacturing process quality control

The demand for quality products in industry is continuously increasing. To produce products with consistent quality, manufacturing systems need to be closely monitored for any unnatural deviation in the state of the process. Neural networks are potential tools that can be used to improve the analysis of manufacturing processes. Indeed, neural networks have been applied successfully for detecting groups of predictable unnatural patterns in the quality measurements of manufacturing processes. The feasibility of using Adaptive Resonance Theory (ART) to implement an automatic on-line quality control method is investigated. The aim is to analyse the performance of the ART neural network as a means for recognizing any structural change in the state of the process when predictable unnatural patterns are not available for training. To reach such a goal, a simplified ART neural algorithm is discussed then studied by means of extensive Monte Carlo simulation. Comparisons between the performances of the proposed neural approach and those of well-known SPC charts are also presented. Results prove that the proposed neural network is a useful alternative to the existing control schemes.     

Reliability analysis of structures using neural network method

In order to predict the failure probability of a complicated structure, the structural responses usually need to be estimated by a numerical procedure, such as finite element method. To reduce the computational effort required for reliability analysis, response surface method could be used. However the conventional response surface method is still time consuming especially when the number of random variables is large. In this paper, an artificial neural network (ANN)-based response surface method is proposed. In this method, the relation between the random variables (input) and structural responses is established using ANN models. ANN model is then connected to a reliability method, such as first order and second moment (FORM), or Monte Carlo simulation method (MCS), to predict the failure probability. The proposed method is applied to four examples to validate its accuracy and efficiency. The obtained results show that the ANN-based response surface method is more efficient and accurate than the conventional response surface method.     

The use of Monte Carlo techniques in statistical finite element methods for the determination of the structural behaviour of composite materials structural components

The main purpose of this paper is to develop an alternative approach to the classical deterministic design to account for uncertainties encountered during design, construction and lifetime of structures. This approach is based on the use of statistical tools in material characterisation and structural design by means of the finite element method combined with Monte Carlo techniques. In the first instance, the mechanical behaviour of different materials, including composite materials, is characterised by means of stochastic tools. A procedure based on the combination of various methods for estimating distribution parameters has been set up to ensure correct estimation. The second part of the paper focuses on the finite element modelling of structures combined with Monte Carlo simulation to deal with the stochastic aspects of the input parameters (material properties, structure geometry and loading conditions) and determine the probability distribution characterising the structural response.     

Reliability analysis of laminated composite structures using finite elements and neural networks

Saving of computer processing time on the reliability analysis of laminated composite structures using artificial neural networks is the main objective of this work. This subject is particularly important when the reliability index is a constraint in the optimization of structural performance, because the task of looking for an optimum structural design demands also a very high processing time. Reliability methods, such as Standard Monte Carlo (SMC), Monte Carlo with Importance Sampling (MC–IS), First Order Reliability Method (FORM) and FORM with Multiple Check Points (FORM–MCPs) are used to compare the solution and the processing time when the Finite Element Method (FEM) is employed and when the finite element analysis (FEA) is substituted by trained artificial neural networks (ANNs). Two ANN are used here: the Multilayer Perceptron Network (MPN) and the Radial Basis Network (RBN). Several examples are presented, including a shell with geometrically non-linear behavior, which shows the advantages using this methodology.     

基于频率和阻尼分析的含分层损伤复合材料层合板的损伤诊断

提出了一种基于动力有限元分析和神经网络相结合的含分层损伤层合板的诊断方法。采用作者发展的含分层损伤层合板的动力有限元分析模型和方法,计算了具有不同分层长度损伤层合板的频率和模态阻尼值,以此建立样本库。应用反向传播BP神经网络训练和形成网络。典型含层间分层损伤层合板的仿真结果表明,采用对损伤变化较为灵敏的高阶模态阻尼作为网络的输入参数进行分层损伤诊断比常用的模态频率更为合理。本文中提出的是一种用于层合板的分层损伤诊断的有效和经济的方法。      

Probabilistic analysis of concrete cracking using neural networks and random fields

In this paper an algorithm for the probabilistic analysis of concrete structures is proposed which considers material uncertainties and failure due to cracking. The fluctuations of the material parameters are modeled by means of random fields and the cracking process is represented by a discrete approach using a coupled meshless and finite element discretization. In order to analyze the complex behavior of these nonlinear systems with low numerical costs a neural network approximation of the performance functions is realized. As neural network input parameters the important random variables of the random field in the uncorrelated Gaussian space are used and the output values are the interesting response quantities such as deformation and load capacities. The neural network approximation is based on a stochastic training which uses wide spanned Latin hypercube sampling to generate the training samples. This ensures a high quality approximation over the whole domain investigated, even in regions with very small probability.     

基于二项级数近似的结构概率分析

结构稳健优化设计中,一个关键的环节是分析结构响应量的概率特性,即计算响应的均值和方差。常用的方法主要有泰勒级数法、蒙特卡洛法以及数值积分法等。其中泰勒级数法精度较差,不适用于参数方差较大的随机结构,而蒙特卡洛法和高斯积分法计算量又过大。为了提高结构稳健性分析的计算效率,将结构位移的二项级数近似技术引入到高斯积分方法之中,提出一种结构位移均值及方差的计算方法。同时,用伴随向量法推导了相关的灵敏度计算公式。通过一个算例与已有的方法进行了比较,表明该方法较大程度上减少了高斯积分法的计算量,而与泰勒级数法相比,该方法又具有较高的计算精度,并且其灵敏度计算不再需要重分析,计算量较少。     

Application of BPANN and regression for prediction of bowing defect in roll-forming of symmetric channel section

In this paper both back-propagation artificial neural network (BPANN) and regression analysis are employed to predict the maximum downward deflection of the exit profile in roll-forming of symmetric channel section. To prepare a training set for BPANN, some finite element simulations were carried out. Sheet thickness, flange width, fold angle and friction coefficient were used as the input data and the maximum downward deflection as the specified output used in the training of neural network. As a result of the specified parameters, the program will be able to estimate the maximum downward deflection of the exit profile for any new given condition. Comparing FEA and BPANN results, an acceptable correlation was found.     

Failure probability estimation of steam turbine blades by enhanced Monte Carlo Method

Steam turbines are designed to work in stable operating conditions, including speed and load, to avoid mechanical stress variations. However, sometimes failures occur in the turbine components. The components having major breakdowns for fracture, an average of 75%, are the blades of the Low Pressure (LP) stage steam turbine. These blades produce around 10% of the output power turbines and 15% in some applications of combined cycle; generally longs, with a relatively low stiffness and such blades may present problems of high stress due to centrifugal forces. In this work probabilistic design procedure was applied to the group of ten blades of the LP stage steam turbine of 110 MW, in order to compute the stress changes and reliability due to variations in: damping, natural frequencies, vibration magnitude and density. The computed vibration stresses were analyzed by applying probability distributions and statistical parameters of input and output to compute the useful life. Monte Carlo technique and stochastic finite element method (SFEM) were applied. The results show that the Monte Carlo technique and SFEM are a good approach to estimate the useful life and reliability design of those blades.     

基于改进混沌粒子群的混合神经网络和蒙特卡洛法的结构随机灵敏度分析方法

针对不确定性参数对结构力学性能的随机影响,该文利用混合神经网络良好的小样本学习和泛化能力构建结构响应复杂的函数关系,采用改进的混沌粒子群算法优化网络寻址结构。结合蒙特卡洛法对结构进行随机性分析,并根据该文提出的新的灵敏度度量参数计算随机变量的全局灵敏度系数。通过数学算例和工程算例验证了所提方法的可行性,且结构响应的概率分布曲线也可以真实的反应实际情况。同时,利用该文所提出的随机灵敏度计算方法可以更好的反应各随机变量对结构响应的相关性和敏感性。     

基于神经网络方法的框架结构损伤检测的试验研究

首先建立了三层试验框架结构的有限元模型，利用未损伤状态的动态测量数据，采用神经网络方法分步对原结构的有限元模型进行了修正。然后，依据修正的有限元模型，运用神经网络方法对各种实际损伤状况进行了损伤诊断。比较了仅以三阶频率作为神经网络输入向量和三阶频率及一阶振型组合作为网络输入向量对网络训练和损伤检测结果的影响。研究表明，神经网络的输入数据越充分，网络训练的收敛速度越快；利用三阶固有频率能够对该模型结构的各种损伤进行诊断，获得满意层问刚度识别的结果。     

Identification of Materials Properties with the Help of Miniature Shear Punch Test Using Finite Element Method and Neural Networks

This paper describes an approach to identify the mechanical properties i.e. fracture and yield strength of steels. The study involves the FE simulation of shear punch test for various miniature specimens thickness ranging from 0.20mm to 0.80mm for four different steels using ABAQUS code. The experimental method of the miniature shear punch test is used to determine the material response under quasi-static loading. The load vs. displacement curves obtained from the FE simulation miniature disk specimens are compared with the experimental data obtained and found in good agreement. The resulting data from the load vs. displacement diagrams of different steels specimens are used to train the neural networks to predict the properties of materials i.e. fracture and yield strength. Two different feed forward neural networks have been created and trained in order to predict the Fracture toughness and yield strength values of different steels. L-M algorithm has been used in the networks to form an output function corresponding to the input vectors used in the network. The trained network provides the output values i.e., fracture toughness and yield strength of unknown input values, which are within in the range of data that is used for the training of network.     

基于瞬时最优控制神经网络的建筑结构主动控制研究

改进一种基于瞬时最优控制的神经网络训练算法。本方法以瞬间最优控制价值函数最小化为训练目标,考虑了地震输入的能量,利用最速下降梯度法计算权值的改变量,并对敏感度矩阵进行近似处理,可解决神经网络控制中神经网络控制器难以获得的训练输入/输出样本对的难题。该方法适合多输入/多输出结构体系,整个推导过程都是针对此体系进行的。文中通过对一个三层框架结构体系进行有效的仿真计算,说明了算法的有效性。     

Variance decomposition-based sensitivity analysis via neural networks

This paper illustrates a method for efficiently performing multiparametric sensitivity analyses of the reliability model of a given system. These analyses are of great importance for the identification of critical components in highly hazardous plants, such as the nuclear or chemical ones, thus providing significant insights for their risk-based design and management. The technique used to quantify the importance of a component parameter with respect to the system model is based on a classical decomposition of the variance. When the model of the system is realistically complicated (e.g. by aging, stand-by, maintenance, etc.), its analytical evaluation soon becomes impractical and one is better off resorting to Monte Carlo simulation techniques which, however, could be computationally burdensome. Therefore, since the variance decomposition method requires a large number of system evaluations, each one to be performed by Monte Carlo, the need arises for possibly substituting the Monte Carlo simulation model with a fast, approximated, algorithm. Here we investigate an approach which makes use of neural networks appropriately trained on the results of a Monte Carlo system reliability/availability evaluation to quickly provide with reasonable approximation, the values of the quantities of interest for the sensitivity analyses. The work was a joint effort between the Department of Nuclear Engineering of the Polytechnic of Milan, Italy, and the Institute for Systems, Informatics and Safety, Nuclear Safety Unit of the Joint Research Centre in Ispra, Italy which sponsored the project.     

Non-Gaussian simulation of local material properties based on a moving-window technique

In this paper, a moving-window micromechanics technique, Monte Carlo simulation, and finite element analysis are used to assess the effects of microstructural randomness on the local stress response of composite materials. The randomly varying elastic properties are characterized in terms of a field of local effective elastic constitutive matrices using a moving-window technique based on a finite element model of a given digitized composite material microstructure. Once the fields are generated, estimates of the random properties are obtained for use as input to a simulation algorithm that was developed to retain spectral, correlation, and non-Gaussian probabilistic characteristics. Rapidly generated Monte Carlo simulations of the constitutive matrix fields are used in a finite element analysis to create a series of local stress fields associated with the random material sample under uniaxial tension. This series allows estimation of the statistical variability in the local stress response for the random composite. The identification of localized extreme stress deviations from those of the aggregate or effective properties approach highlight the importance of modeling the stochastic variability of the microstructure.     

Evaluation of neural network models with generalized sensitivity analysis

A sensitivity analysis method for discovering characteristic features of the input data using neural network classification models has been devised. The sensitivity is the gradient of the neural network model response function, and because neural network models are nonlinear, the gradient depends on the point where it is evaluated. Two criteria are used for measuring the sensitivity. The first criterion calculates the sensitivity or gradient of the neural network output with respect to the average of the objects that comprise each class. The second criterion measures the average sensitivity of the class objects. The sensitivity analysis was applied to temperature-constrained cascade correlation network models and evaluated with sets of synthetic data and experimental mobility spectra. The neural network models were built using temperature-constrained cascade correlation networks (TCCCNs). A weight constraint was devised for the output units of the network models. This method implements weight decay with conjugate gradient training and yields more sensitive neural network models. Temperature-constrained hidden units furnish more sensitive network models than networks without constraints. By comparing the sensitivities of the class mean input and the mean sensitivity for all the inputs of a class, the individual input variables may be assessed for linearity. If these two sensitivities for an input variable differ by a constant factor, then that variable is modeled by a simple linear relationship. If the two sensitivities vary by a nonconstant scale factor, then the variable is modeled by higher order functions in the network. The sensitivity method was used to diagnose errors in the training data, and the test for linearity indicated a TCCCN architecture that had better predictability.     

3-D Spectral Stochastic Finite Element Method in Electromagnetism

Spectral stochastic finite element method (SSFEM), used in mechanics to take into account random aspects of input data, has been implemented, as an extended version, in the 3-D finite element method (FEM) software CARMEL dedicated to electromagnetic field computation. As a test case, this approach has been applied to a 3-D electrostatic problem and successfully validated by comparing with the Monte Carlo simulation method involving usual "deterministic" CARMEL resolutions     

Stochastic analysis on flexural behavior of reinforced concrete beams based on piecewise response surface scheme

To save the computational efforts of Monte Carlo simulation together with nonlinear finite element method, the analysis framework combining the response surface method and Monte Carlo simulation is usually adopted to investigate the stochastic nonlinear behavior of structures. It is found that the traditional response surface method could not describe stochastic behavior of cracked concrete beams. In order to overcome the discontinuity caused by cracking nonlinearity, a scheme by introducing a piecewise response surface is proposed in this paper. This scheme is evaluated by the stochastic analysis of several concrete beams. The comparison between the proposed method and some traditional methods, including Monte Carlo simulation and Monte Carlo simulation with traditional response surface, shows that the proposed method could well depict the stochastic behavior of concrete beams. Finally, the probability density evolution of concrete beams from short-term deflection to a long-term deflection is analyzed.     

用BP神经网络诊断结构破损

提出了一种基于BP神经网络的结构破损诊断方法,该方法以结构残余力向量作为破损诊断的网络输入。对网络训练样本采用广义空间格点法进行了变换,从而较好地解决了由于系统响应样本在数据空间分布不均对网络收敛速度及网络诊断精度的影响问题。应用实例表明,本文方法能准确诊断结构破损位置与严重程度,是一种有效的结构破损诊断方法。