A generalized moving least square–based response surface method for efficient reliability analysis of structure

PurposeBecause of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit state function (LSF), the approximate accuracy of the failure probability mainly depends on the design point, and the result is that the response surface function composed of initial experimental points rarely fits the LSF exactly. The inaccurate design points usually cause some errors in the traditional RSM. The purpose of this paper is to present a hybrid method combining adaptive moving experimental points strategy and RSM, describing a new response surface using downhill simplex algorithm (DSA-RSM).Design/methodology/approachIn DSA-RSM, the operation mechanism principle of the basic DSA, in which local descending vectors are automatically generated, was studied. Then, the search strategy of the basic DSA was changed and the RSM approximate model was reconstructed by combining the direct search advantage of DSA with the reliability mechanism of response surface analysis.FindingsThe computational power of the proposed method is demonstrated by solving four structural reliability problems, including the actual engineering problem of a car collision. Compared to specific structural reliability analysis methods, the approach of modified DSA interpolation response surface for structural reliability has a good convergent capability and computational accuracy.Originality/valueThis paper proposes a new RSM technology based on proxy model to complete the reliability analysis. The originality of this paper is to present an improved RSM that adjusts the position of the experimental points judiciously by using the DSA principle to make the fitted response surface closer to the actual limit state surface.

The seismic reliability analysis of complex structure is carried out based on the response surface method and finite element method. Firstly, the appropriate design points are selected based on the mean values and standard deviations of the basic random variables. Secondly, the finite element method is employed to obtain the values of the limit state function of the complex structure. Thirdly, with selected design points and the obtained values of the limit state function of the complex structure, a polynomial function is constructed to approximate the original implicit limit state function. Then, with the established explicit polynomial limit state function and available methods of structural reliability analysis, the seismic reliability of the complex structure is estimated. Numerical analyses show that the established method is simple to use for the evaluation of the reliability analysis of complex structure.

Efficient response surface method for high-dimensional structural reliability analysis

In order to evaluate the failure probability of a complicated structure, the structural responses usually need to be estimated by some numerical analysis methods such as finite element method (FEM). The response surface method (RSM) can be used to reduce the computational effort required for reliability analysis when the performance functions are implicit. However, the conventional RSM is time-consuming or cumbersome if the number of random variables is large. This paper proposes a Legendre orthogonal neural network (LONN)-based RSM to estimate the structural reliability. In this method, the relationship between the random variables and structural responses is established by a LONN model. Then the LONN model is connected to a reliability analysis method, i.e. first-order reliability methods (FORM) to calculate the failure probability of the structure. Numerical examples show that the proposed approach is applicable to structural reliability analysis, as well as the structure with implicit performance functions.

A new bivariate dimension reduction method for efficient structural reliability analysis

An optimization method for learning statistical classifiers in structural reliability

Monte Carlo Simulation and Response Surface Method are two very powerful reliability analysis methods. Normally, in the reliability analysis of complex structures, the limit state function often can not be expressed in a closed-form. Usually, the codes for probabilistic analysis need to be combined with finite element models. ANSYS Probabilistic Design System (PDS) has provided a package to conduct probabilistic analysis automatically. This paper is going to compare the performance of these methods through an easy engineering problem in ANSYS. The results are going to be derived to show the feature of applying the corresponding reliability methods.

Fuzzy reliability analysis can be implemented using two discrete optimization maps in the processes of reliability and fuzzy analysis. Actually, the efficiency and robustness of the iterative reliability methods are two main factors in the fuzzy-based reliability analysis due to the huge computational burdens and unstable results. In the structural fuzzy reliability analysis, the first-order reliability method (FORM) using discrete nonlinear map can provide a C membership function. In this paper, a discrete nonlinear conjugate map is proposed using a relaxed-finite step size method for fuzzy structural reliability analysis, namely Fuzzy conjugate relaxed-finite step size method fuzzy CRS. A discrete conjugate map is stabilized using two adaptive factors to compute the relaxed factor and step size in FORM. The framework of the proposed fuzzy structural reliability method is established using two linked iterative discrete maps as an outer loop, which constructs the membership function of the response using alpha level set optimization based on genetic operator, and the inner loop, implemented for reliability analysis using proposed conjugate relaxed-finite step size method. The fuzzy CRS and fuzzy HL-RF methods are compared to evaluate the membership functions of five structural problems with highly nonlinear limit state functions. Results demonstrated that the fuzzy CRS method is computationally more efficient and is strongly more robust than the HL-RF for fuzzy-based reliability analysis of the nonlinear structural reliability problems.

Approximation methods such as response surface method and artificial neural network (ANN) method are widely used to alleviate the computation costs in structural reliability analysis. However most of the ANN methods proposed in the literature suffer various drawbacks such as poor choice of parameter setting, poor generalization and local minimum. In this study, a support vector machine-based radial basis function (RBF) network method is proposed, in which the improved RBF model is used to approximate the limit state function and then is connected to a reliability method to estimate failure probability. Since the learning algorithm of RBF network is replaced by the support vector algorithm, the advantage of the latter, such as good generalization ability and global optimization are propagated to the former, thus the inherent drawback of RBF network can be defeated. Numerical examples are given to demonstrate the applicability of the improved RBF network method in structural reliability analysis, as well as to illustrate the validity and effectiveness of the proposed method.

In this paper, a new method is developed that can be applied efficiently in reliability analysis and design verification of structures under random vibration. This method is based on singular value decomposition of modal coordinates cross covariance matrix. Computational algorithm and relative flow chart for this method is developed and compatible reliability criterion with this algorithm has been extracted. In order to results verification, we use Miles relation and Monte Carlo simulation -that are two well known methods in reliability analysis- and all of these methods are applied to a simple finite element model. Results show that new algorithm is more efficient for reliability analysis of structures under random vibration.

A new unequal-weighted sampling method for efficient reliability analysis

The limit state function (LSF) is implicit to many structure reliability analysis problems, which may make some classical reliability method complicated to be applied. One of the surrogate methods-support vector classification (SVC) was applied in the structural reliability analysis herein which has not been applied to structure reliability analysis until recent years. Then the advanced first order second moment method (AFOSM) can be applied. The expressions of structure system reliability sensitivity to basic variable were deduced. The flow of how to call the SVC program was presented. An example was shown to compare the SVC based method with some other classical reliability analysis methods. The results are accurately accepted and the advantages of SVC are analyzed.

Operators wish to understand the condition of their pipelines to manage ongoing integrity. Information on the condition of the pipeline along its entire length can be obtained using in-line inspection (ILI). However, some pipelines cannot be internally inspected due, for example, to tee connections, tight bends, low flow or to a lack of launcher and receiver facilities. The condition of these ‘unpiggable’ lines can sometimes be largely unknown. To aid the understating of the pipeline condition without ILI data, operators will often rely on alternative sources of information, such as localised external inspections, model predictions and company and individual experience. However, there may be significant uncertainty associated with these alternative data sources when using them to assess the condition of the entire pipeline. This uncertainty may be understood by applying a probabilistic approach to the assessment of pipeline integrity using structural reliability analysis (SRA) methods. An SRA approach applies probabilistic input parameters to a failure prediction model for a defined limit state function. Previous IPC papers[1,2,3] have presented guidance on probabilistic assessments to model pipeline failure. Recommended probability distributions are presented which account for uncertainties associated with line pipe properties, defect sizing and the error associated with the predicted failure model. However, there is little published guidance readily available on recommended defect characteristic distributions specific to internal corrosion features. Parameter distributions are recommended for defect sizing based on empirical data, which are mainly used for external corrosion features. In this paper, a case study is used to present a practical application of an SRA methodology for assessment of pipeline integrity with respect to internal corrosion. Discussion is presented on alternative sources of information for the assessment when ILI data is unavailable, including targeted external inspections of unpiggable lines and data sets from comparable piggable lines. Probability distributions are derived from the available inspection data for the internal corrosion feature size and corrosion rate input parameters to the SRA. Probabilistic analysis is used to account for the expected population of unknown features in the uninspected parts of the pipelines. The expected feature size, corrosion rate and feature density calculated are used in the SRA to estimate the total probability of failure due to internal corrosion over time for the entire length of the pipeline. Recommendations are provided on the application of an SRA methodology to assess pipeline failure due to internal corrosion.

Monte-Carlo Simulation (MCS) is a powerful tool in solving reliability problems. However, it is time-consuming use for the complex structural engineering problems. Another commonly used method, First-Order Second Moment Method (FOSM) usually requires the values and derivatives of limit state function. This paper presents two types of Least Square Support Vector Machine (LS-SVM) based reliability analysis methods, i.e. LS-SVM-based MCS and LS-SVM-based FOSM. In the first method, LS-SVM is adopted to replace the limit state function and enhance the efficiency of computing. In the second method, LS-SVM is adopted to approximate the limit state function and its partial derivatives which FOSM requires. Thus, based on the LS-SVM, both methods are substantially improved in efficiency. To assess the validity of this methodology, three structural examples are studied and discussed. The results prove that the LS-SVM based new methods are effective in structural reliability analysis problems involving the implicit limit state function.

A hybrid relaxed first-order reliability method for efficient structural reliability analysis