UDDS-DNN: Uncertainty and Distance-Driven Sequential Sampling Deep Neural Network Method for Structural Reliability Analysis

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.

Surrogate modeling immersed probability density evolution method for structural reliability analysis in high dimensions

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.

A new bivariate dimension reduction method for efficient structural reliability analysis

Efficient response surface method for high-dimensional structural reliability analysis

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 possibility of applying the measure of information uncertainty (entropy) in structural reliability analysis of electricity distribution networks is assessed. The essential factors influencing the process of reliability analysis and related to the presence of information uncertainty are highlighted. The peculiarities of reliability analysis in network designing and operation, when it is required to estimate the state of elements and choose the efficient structure of a network are considered. The opportunities and limitations in the application of existing methods of structural reliability analysis are evaluated; it proves the importance of information uncertainty measurement. The conceptual apparatus of entropy includes the mathematical procedure of its calculation. Fail-safe operation probability and probability of network element failure are taken as reliability index. The mathematical expressions proposed for calculating entropy are applicable when there are two independently functioning network elements, each of which will be able to be in one of two states with a fraction of probability: operable and non-operable. The obtained results allowed identifying the more reliable elements/objects. The application of the proposed mathematical procedure allows to compare network elements with each other through the value of entropy and to choose the most reliable ones. Thus, the proposed solution is a preliminary step in the uncertainty removal task.

In the reliability analysis of safety critical complex engineering structures, a very large number of the system parameters can be considered as random variables. The difficulty in computing the failure probability using the classical first- and second-order reliability methods (FORM and SORM) increases rapidly with the number of variables or ‘dimension’. There are mainly two reasons behind this. The first is the increase in computational time with the increase in the number of random variables. In principle, this problem can be handled with superior computational tools. The second reason, which is perhaps more fundamental, is that there are some conceptual difficulties typically associated with high dimensions. This means that even when one manages to carry out the necessary computations, the application of existing FORM and SORM may still lead to incorrect results in high dimensions. This paper is aimed at addressing this issue. Based on the asymptotic distribution of quadratic form in Gaussian random variables, two formulations for the case when the number of random variables n →∞ is provided. The first is called ‘strict asymptotic formulation’ and the second is called ‘weak asymptotic formulation’. Both approximations result in simple closed-form expressions for the probability of failure of an engineering structure. The proposed asymptotic approximations are compared with existing approximations and Monte Carlo simulations using numerical examples.

A response-surface-based structural reliability analysis method by using non-probability convex model

A stress-strength interference model in its interval form, with uncertain quantities of structures described by interval numbers, is used for reliability analysis. Such structural reliability analysis problem is called structural interval reliability analysis. A discrete possibility degree method for structural interval reliability is proposed. By comparing equally-spaced-points of structural interval stress value and structural interval strength value, a partition for comparison relations (big, equal or small) between interval stress and interval strength is built. Based on this partition, new concepts for interval reliability analysis are defined, such as structural safety possibility degree and structural failure possibility degree, etc. By one simple example, the feasibility and effectiveness of discrete possibility degree method for structural interval reliability are demonstrated.

An optimization method for learning statistical classifiers in structural reliability

Tongwamen Bridge is a critical link between Dongmen Island and the land in Shipu town, Zhejiang province, China. It is a 238 m span, half-through, concrete-filled steel tubular (CFST) X-type arch bridge. The width of the deck is only 10 m, yielding a width-to-span ratio of 1/23.8. The plane truss type section rib was adopted, which made of two CFST chords and web member system. The lateral stability is the key issue to this bridge. However, the existing researches on Tongwamen Bridge's lateral stability are all the deterministic structural analysis. In this paper, a new strategy for positioning sampling points of the response surface method (RSM), based on the composite method combining RSM with geometric method for structural reliability analysis, is employed to obtain the reliability index of lateral stability. In addition the correlated parameters were discussed in detail to find the major factors. According to the analysis results, increasing the stiff of lateral braces between the arch ribs and setting the proper inward-incline degree of the arch rib can enhance obviously the reliability of lateral stability. Moreover, the deck action of non-orienting force is less than the two factors above. The calculated results indicate that the arch ribs are safe enough to keep excellent stability, and it provides the foundation that the plane truss rib would be a competitive solution for a long-span, narrow, CFST arch bridge.

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.

The hypercone method for structural reliability analysis: Its theoretical principles

An adaptive β-shell active learning Kriging method for structural reliability analysis