Time-varying response surface method for high-temperature structural reliability analysis

Reliability is a critical indicator for evaluating the safety and performance of mechanical structures. Surrogate models are widely employed in reliability analysis to reduce computational costs; however, their accuracy strongly depends on the quality of training samples. This paper proposes an uncertainty and distance-driven sequential sampling deep neural network method (UDDS-DNN) for structural reliability analysis. First, initial training samples were generated from the Monte Carlo population (MCP) using the Minimax sampling strategy. This ensured global coverage of the random variable space. Then, the predictive uncertainty of the DNN was quantified using the Jackknife-based method. The estimated uncertainty, inter-sample distance, and probabilistic characteristics of the input random variables were considered. The adaptive learning function was constructed to guide sequential sample enrichment. The proposed method was validated through two numerical examples and three engineering case studies. Results demonstrated that UDDS-DNN achieves high accuracy and computational efficiency in multivariate, nonlinear, and complex structural reliability problems. The method provided an effective solution for reliability analysis of complex structures using DNN-based sequential sampling.

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.

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.

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.

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.

Many factors influence structural reliability in practice engineering. Some factors can be measured to obtain lots of data, but others are difficult to acquire statistical data. In view of this situation, a new structural reliability analysis method is proposed using chance theory, which is composed of probability theory and uncertainty theory and can reflect random uncertainty and cognitive uncertainty simultaneously. The performance function of a structural mechanical element is defined, and when it is a random uncertain variable, the chance distribution is established. Then the calculated method of failure measures and reliability measures for the structural mechanical element is put forward. Furthermore, considering the series system and parallel system, the performance function of the structural system is proposed, and the calculated method of failure measure is determined by theoretical proof. The results can provide a new approach to analyzing structural reliability under the uncertain circumstance of lack of statistical data.

Matrix description of differential relations of moment functions in structural reliability sensitivity analysis

This paper discusses the effects of corrosion and slamming on Floating Production Storage and Offloading (FPSO) structures in the North Sea by using a time variant structural reliability based approach. An FPSO structure currently in operation in the North Sea is analysed, an analytical approach is suggested and used to determine the Ultimate Strength of the FPSO structure and compared with other published methods. A non-linear corrosion method is then used to determine the effect of corrosion on the ultimate strength and subsequently in the reliability of the structure. Slamming loads on the midship section of the FPSO are calculated using closed form expressions. The effect of slamming and green water load on the overall vertical bending moment applied on the structure is combined with the vertical wave bending and still water loads using the Ferry Borges- Castanheta method and the SRSS rule, to provide the distribution and variation of a loading component for structural reliability analysis to be performed. Time variant reliability analysis using Monte Carlo Simulation is then used to determine reliability indices and probabilities of failure for the structural system analysed on a component level.

Efficient response surface method for high-dimensional structural reliability analysis

In common structural design, random variables, such as material strength or loads, are represented by fixed numbers defined in design codes. This is also referred to as deterministic design. Addressing the random character of these variables directly, the probabilistic design procedure allows the determination of the probability of exceeding a defined limit state. This probability is referred to as failure probability. From there, the structural reliability, representing the survival probability, can be determined. Structural reliability thus is a property of a structure or structural member, depending on the relevant limit states, failure modes and basic variables. This is the basis for the determination of partial safety factors which are, for sake of a simpler design, applied within deterministic design procedures. In addition to the basic variables in terms of material and loads, further basic variables representing the structural model have to be considered. These depend strongly on the experience of the design engineer and the level of detailing of the model. However, in the clear majority of cases [1] failure does not occur due to unexpectedly high or low values of loads or material strength. The most common reasons for failure are human errors in design and execution. This paper will provide practical examples of original designs affected by human error and will assess the impact on structural reliability.

An optimization method for learning statistical classifiers in structural reliability

Numerical integration in affine space to compute structural system reliability

Material characteristics, environmental conditions and loading characteristics under the time domain features shall be taken into consideration so as to effectively evaluate the reliability of ship grillage structure. Moreover, the method of time-variant reliability serves as an effective approach to solve the problem. In the paper, based on the loading environmental features of ships during the enlistment, research has been conducted on the changing of material geometrical and mechanical characteristics with time under the corrosive action. Furthermore, on the basis of time-variant theory, the timevariant model of section modulus as well as bending strength concerning the ship grillage structure has been established, thus generating a time-variant reliability analysis method integrated with out-crossing rate and First Order Second Moment(FOSM) method. Besides, the paper analyzes the time consecutiveness of ship grillage structure reliability based on the time-variant reliability cases of certain ship grillage structure under the corrosion environment while the failure probability of the ship during the enlistment has been accurately predicted.

During the long-term service periods of Prestressed Concrete(PC) continuous girder bridges, structural time-varying reliability will degrade due to cyclic creep induced by dynamic vehicle loading, which increases the risk of structural failure. This paper provided a time-varying reliability prediction method for the prestressed concrete continuous T-girder bridge considering random vehicle load information and cyclic creep information. Firstly, the random vehicle load information is simulated with Monte Carlo random simulation method and MATLAB software based on the monitored data obtained from weigh-in-motion (WIM) system. Then, the concrete shrinkage strain model, concrete static creep strain model, concrete cyclic creep strain model and the overall strain model are respectively provided by combining the CEB-FIP model with concrete cyclic creep theory. Finally, by using a numerical model of prestressed concrete bridge, a time-variant reliability analyzing approach of prestressed concrete T-girder bridge considering the limit state of load carrying capacity and the limit state of serviceability is investigated in detail by integrating the random vehicle loading information with the concrete cyclic creep information.

Based on material taught at the University of California, Berkeley, this textbook offers a modern, rigorous and comprehensive treatment of the methods of structural and system reliability analysis. It covers the first- and second-order reliability methods for components and systems, simulation methods, time- and space-variant reliability, and Bayesian parameter estimation and reliability updating. It also presents more advanced, state-of-the-art topics such as finite-element reliability methods, stochastic structural dynamics, reliability-based optimal design, and Bayesian networks. A wealth of well-designed examples connect theory with practice, with simple examples demonstrating mathematical concepts and larger examples demonstrating their applications. End-of-chapter homework problems are included throughout. Including all necessary background material from probability theory, and accompanied online by a solutions manual and PowerPoint slides for instructors, this is the ideal text for senior undergraduate and graduate students taking courses on structural and system reliability in departments of civil, environmental and mechanical engineering.