Classification Approach for Reliability Analysis with Stochastic Finite-Element Modeling (original) (raw)

Efficient structural reliability analysis based on adaptive Bayesian support vector regression

Computer Methods in Applied Mechanics and Engineering, 2021

To reduce the computational burden for structural reliability analysis involving complex numerical models, many adaptive algorithms based on surrogate models have been developed. Among the various surrogate models, the support vector machine for regression (SVR) which is derived from statistical learning theory has demonstrated superior performance to handle nonlinear problems and to avoid overfitting with excellent generalization. Therefore, to take the advantage of the desirable features of SVR, an Adaptive algorithm based on the Bayesian SVR model (ABSVR) is proposed in this study. In ABSVR, a new learning function is devised for the effective selection of informative sample points following the concept of the penalty function method in optimization. To improve the uniformity of sample points in the design of experiments (DoE), a distance constraint term is added to the learning function. Besides, an adaptive sampling region scheme is employed to filter out samples with weak probability density to further enhance the efficiency of the proposed algorithm. Moreover, a hybrid stopping criterion based on the error-based stopping criterion using the bootstrap confidence estimation is developed to terminate the active learning process to ensure that the learning algorithm stops at an appropriate stage. The proposed ABSVR is easy to implement since no embedded optimization algorithm nor iso-probabilistic transformation is required. The performance of ABSVR is evaluated using six numerical examples featuring different complexity, and the results demonstrate the superior performance of ABSVR for structural reliability analysis in terms of accuracy and efficiency. c

An optimization method for learning statistical classifiers in structural reliability

Probabilistic Engineering Mechanics, 2010

Monte Carlo simulation is a general and robust method for structural reliability analysis, affected by the serious efficiency problem consisting in the need of computing the limit state function a very large number of times. In order to reduce this computational effort the use of several kinds of solver surrogates has been proposed in the recent past. Proposals include the Response Surface Method (RSM), Neural Networks (NN), Support Vector Machines (SVM) and several other methods developed in the burgeoning field of Statistical Learning (SL). Many of these techniques can be employed either for function approximation (regression approach) or for pattern recognition (classification approach). This paper concerns the use of these devices for discriminating samples into safe and failure classes using the classification approach, because it constitutes the core of Monte Carlo simulation as applied to reliability analysis as such. Due to the flexibility of most SL methods, a critical step in their use is the generation of the learning population, as it affects the generalization capacity of the surrogate. To this end it is first demonstrated that the optimal population from the information viewpoint lies around in the vicinity of the limit state function. Next, an optimization method assuring a small as well as highly informative learning population is proposed on this basis. It consists in generating a small initial quasi-random population using Sobol sequence for triggering a Particle Swarm Optimization (PSO) performed over an iteration-dependent cost function defined in terms of the limit state function. The method is evaluated using SVM classifiers, but it can be readily applied also to other statistical classification techniques because the distinctive feature of the SVM, i.e. the margin band, is not actively used in the algorithm. The results show that the method yields results for the probability of failure that are in very close agreement with Monte Carlo simulation performed on the original limit state function and requiring a small number of learning samples.

Comparative study of computational methods of structural reliability assessment

Safety is an essential requirement of a structural system. Reliability is an additional tool of growing importance in engineering, as it allows us to quantify uncertainties in the design. Thus, reliability assists us in making more suitable decisions regarding the safety of a structure. The present work compares and analyzes structural reliability methods applied to various examples of limit state functions. These methods are essential tools for this analysis because they identify and quantify uncertainties in random variables, allowing the evaluation of the probability of failure of the structure. Structural reliability methods were programmed and simulated in the Python language. The performance of these methods was analyzed through examples of linear, nonlinear, implicit, and explicit limit state functions. The results indicate that the simulation of Monte de Carlo brute force (MCBF) and importance sampling (MCAI) proved to be quite efficient for the examples studied in this work, with values equal to or very close to the reference values from the literature. The First Order and Second Moment Method (FOSM) presented limitations in some examples when the basic random variables do not have a normal distribution and the limit state function is nonlinear. The first-order reliability method (FORM) employs a failure surface linearization, which does not work well for highly nonlinear problems. The second-order reliability method (SORM) has improved the FORM results by including additional information about the curvature of the limit state function.

Structural System Reliability Prediction Using Multi-Point Approximations for Design

2000

In most engineering problems, there is more than one limit-state function describing the system response requirements. For example, in a complex structure, the stresses in each of the members can be posed as limit-state functions along with the displacements and the natural frequencies. There are no criteria to distinguish one limit-state over the other in order to convert the system reliability problem into component reliability. Therefore in dealing with multiple limit-states there exist design points that are common to two or more of the limit-states. These intersection points have a great influence on the failure probability of the system when the intersection points are near the most probable failure points (MPP). Accurate determination of the intersection points of the limit-states is almost impossible. For the determination of these intersection points, a first-order approximation is usually constructed at each of the MPP's, and the intersection of these approximate functions is considered as the common point on the limitstates. For problems with high non-linearity and a large number of non-normal random variables the above procedure would result in gross errors. The first-order approximations of the limit-states at the MPP are invalid in most cases. An accurate way of defining highly non-linear functions is presented using a new class of approximations. In this paper, a methodology for dealing with multiple limit-states as in system reliability is discussed. This methodology is used in conjunction with the Monte Carlo simulation to estimate the structural failure probability. Furthermore, two numerical examples are presented to show the applicability of the proposed method.

Probabilistic Computational Methods in Structural Failure Analysis

Probabilistic methods are used in engineering where a computational model contains random variables. Each random variable in the probabilistic calculations contains uncertainties. Typical sources of uncertainties are properties of the material and production and/or assembly inaccuracies in the geometry or the environment where the structure should be located. The paper is focused on methods for the calculations of failure probabilities in structural failure and reliability analysis with special attention on newly developed probabilistic method: Direct Optimized Probabilistic Calculation (DOProC), which is highly efficient in terms of calculation time and the accuracy of the solution. The novelty of the proposed method lies in an optimized numerical integration that does not require any simulation technique. The algorithm has been implemented in mentioned software applications, and has been used several times in probabilistic tasks and probabilistic reliability assessments.

Structural reliability and stochastic finite element methods

Engineering Computations, 2018

Purpose This paper aims to provide a comprehensive review of uncertainty quantification methods supported by evidence-based comparison studies. Uncertainties are widely encountered in engineering practice, arising from such diverse sources as heterogeneity of materials, variability in measurement, lack of data and ambiguity in knowledge. Academia and industries have long been researching for uncertainty quantification (UQ) methods to quantitatively account for the effects of various input uncertainties on the system response. Despite the rich literature of relevant research, UQ is not an easy subject for novice researchers/practitioners, where many different methods and techniques coexist with inconsistent input/output requirements and analysis schemes. Design/methodology/approach This confusing status significantly hampers the research progress and practical application of UQ methods in engineering. In the context of engineering analysis, the research efforts of UQ are most focused...

STRUCTURAL RELIABILITY ASSESSMENT WITH STOCHASTIC PARAMETERS

The performance of a structure [23] is assessed by its safety [1], serviceability [1] and economy [1]. Since we do not know the exact details of loads [4] acting on a structure at any time, there is always some uncertainty about the total loads on structure. Thus random variables (means stochastic variable) of loads and other parameters are the main criteria of design variables [18]. They vary with space and time. The input variables is never certain and complete. The safety factor provided in the existing codes and standers primarily based on practice, judgment and experience, may not be adequate and economical. Using the techniques presented earlier, we can design or analyze individual members in the contest of structural reliability [2][3][22][24]. However we are not examined how the system performs [23] or how to calculate the reliability of the structure as a whole.

RELIABILITY ANALYSIS OF STRUCTURES USING STOCHASTIC FINITE ELEMENT METHOD

Author of the monograph, Juraj Králik, has been working at the Department of Structural Mechanics as assistant since September 1, 1976 and as associate professor since January 18, 1988. During the years 2000 - 2006 he was the head of Department. He holds lectures in two study programs: Engineering Structures and Transport Structures; and Civil Engineering and Architecture. He teaches the following subjects: Mechanics of Structures and Materials, Seismic Enginering and Computer Design, Risk Engineering, Safety and Reliability of Buildings. His regular students and doctoral students have won several prizes in the student research competitions at the Faculty. He has been implementing advanced computer programs and methods in teaching and research at the Department, being himself an author of more than 100 programs of the static and dynamic applications. He is guarantor of using the licensed software systems ANSYS and MathCAD at the Department and Faculty, too. As the co-guarantor, he has established the doctoral study program “Applied Mechanics”. During the years 2000-2006, in cooperation with the Slovak Chamber of the Civil Engineers he was the supervisor of seven volumes of the postgraduate study course „Aeroelasticity and Seismicity“, and the chairman of seven volumes of the International Conference „New Trends in the Statics and Dynamics of Buildings“. His results were presented in more than 300 papers in conference proceedings and journals, 10 papers are indexed in prestigious database „Web of Science“. Three papers were published in the currented international journals „Mathematics and Computers in Simulation” (1999), „Control and Cybernetics” (2006) and “Engineering Structures” (2009). 17 research and grant projects were managed by him. His works were cited in more than 200 papers in scientific and special publications. As the reputable scientific personality he was the member of the scientific committees of several international conferences abroad. In the year 1989 he was appointed an expert of the safety and reliability of nuclear power plants in Slovakia. He cooperated at the analysis of the seismic resistance of the nuclear power plant buildings and their safety under impact of explosion, missile and container drop. More than 100 expertises were realized by him in the field of the safety and reliability of the NPP buildings in Slovakia. Some of his research and expert works were awarded by significant institutions. The most significant is the honorable award of the Czech Engineering Academy for the paper „Probability Analysis of Reinforced Concrete Structure Failure of Nuclear Power Plants Due to Loss of Coolant Accident “ published in the journal „ENGINEERING MECHANICS“ in 2006.

Numerical Approximation of Structural Reliability Analysis Methods

International Journal of Innovation and Applied Studies, 2017

We know that with the reliability structure, modeling is based on a deterministic physical system: the latter extract degradation mechanisms. Thus, mechanisms taken into account are crack propagations and are defects from thermal or vibratory fatigue, corrosion or erosion etc... The structure is submitted to some loadings in its environment; this, defines a finite number of modes of degradation. We can envision envisage two possible outcomes: failure or success. Therefore, we could consider the failure probability deterministic or probabilistic. According to the probabilistic approach, the risk will be evaluated without probability of failure. It is understood that this evaluation represents the entire problem of this work. In our study, we are going to be examining the development of two methods of structural reliability, which are the first order and second order: That is why we are going to use FORM and SORM method alongside with the Monte Carlo simulation, which are so effective...