Structural reliability analysis based on improved wolf pack algorithm AK-SS

The paper presents a hybrid active-learning approach for structural reliability analysis via adaptive Kriging surrogate models. The quasi first-order reliability method is first proposed for characteristic truncation point of a structural performance function. This is used to define a truncation boundary via the joint probability distribution function of input random variables. To reduce simulation time for new training samples, a U-function based criterion is further implemented to refine the candidate sample set. Since the reliability-based expected improvement function and U functions are combined together to evaluate new training samples, it finalizes a hybrid active-learning Kriging (HALK) to develop adaptive surrogate models for the structural reliability analysis. Several numerical examples are presented to demonstrate potential applications of the proposed HALK algorithm. Compared to benchmark results provided by the brutal force Monte-Carlo simulation method, the effectiveness of the HALK approach has been justified by dealing with various structural reliability problems.

Application of spherical subset simulation method and auxiliary domain method on a benchmark reliability study

In this paper, a Back Propagation (BP) neural network prediction method based on improved wolf swarm algorithm (IWPA) is proposed to study students' academic early warning. The improved wolf pack algorithm has strong search ability, excellent solution ability and fast convergence speed. It can optimize the initial weight and threshold of BP neural network and improve the nonlinear fitting ability of prediction model. The simulation results illustrates that the prediction algorithm has better effectiveness in optimizing accuracy and improving convergence speed in student academic precaution based on UCI data set.

Assessing small failure probabilities by AK–SS: An active learning method combining Kriging and Subset Simulation

Bounds-based structure reliability analysis of bogie frame under variable load cases

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.

Bayesian inference with Subset Simulation: Strategies and improvements

Markov Chain Monte Carlo simulation has received considerable attention within the past decade as reportedly one of the most powerful techniques for the first passage probability estimation of dynamic systems. A very popular method in this direction capable of estimating probability of rare events with low computation cost is the subset simulation (SS). The idea of the method is to break a rare event into a sequence of more probable events which are easy to be estimated based on the conditional simulation techniques. Recently, two algorithms have been proposed in order to increase the efficiency of the method by modifying the conditional sampler. In this paper, applicability of the original SS is compared to the recently introduced modifications of the method on a wind turbine model. The model incorporates a PID pitch controller which aims at keeping the rotational speed of the wind turbine rotor equal to its nominal value. Finally Monte Carlo simulations are performed which allow assessment of the accuracy of the first passage probability estimation by the SS methods.

Modified subset simulation method for reliability analysis of structural systems

Heliostats represent the most important maintenance cost in the solar power tower plant. The aim of this work is to provide a failure probability analysis for heliostat design in order to minimize this maintenance cost. Based on mechanics of material study and wind aerodynamic analysis, a performance function, with five random variables, has been developed wherein the random variables are: wind speed, inside and outside pedestal diameters, pedestal yield stress and mirror mass. Four main methods have been proposed: first order reliability method, second order reliability method, Monte Carlo (MC) method and subset simulation (SS) method. The variation of failure probability with the variation of pedestal wall thickness and wind speed, for different outside diameters and heliostat azimuth and elevation angles, has been simulated. The results show that SS is more efficient and accurate for small failure probabilities; however, MC is more accurate for high failure probabilities.

Structural reliability is an engineering method that focuses on the calculation and prediction of the probability of failure for a structural system. Structural reliability is used by many pipeline operators to assess the probability of failure, and these probability of failure estimates are then used to manage safety, environmental, and operational risks for threats such as corrosion, cracking, and third-party damage. In the structural reliability approach, the probability of failure is obtained from a multi-dimensional integral, for which the solution is commonly estimated numerically using Direct Monte Carlo (DMC) simulation. DMC is straight-forward and robust but requires a significant amount of computational effort to estimate small probabilities, which are typical of threats to pipeline integrity. Subset Simulation is an approach that improves on the efficiency issues of DMC by representing the rare event probability as the product of a number of more frequent events, which are each estimated separately. Previous work published at IPC in 2020 by Bandstra and Fraser [1] showed very close agreement between DMC and Subset Simulation for a single defect reference case with a single limit state. This study extends that initial work by applying Subset Simulation to various failure models for a variety of pipeline defects. Subset Simulation is applied to the CSA corrosion model, PRCI MAT-8 crack model, and the EPRG dent failure model, and the performance is evaluated by comparing the results to DMC. For each of these comparisons, simulations are performed across a large-scale grid of validation cases that consider a range of pipeline and defect sizes. An approach that utilizes Subset Simulation to handle multiple limit states is also presented and applied for relevant failure models and the results are evaluated against DMC.

• An active learning Kriging methodology for Bayesian updating is presented. • The BUS method recasts the updating problem into an equivalent reliability problem, solved with a Kriging metamodel. • A multi-fidelity approach is employed in the active learning Kriging model, where models of different accuracy are adopted. • Multi-fidelity Bayesian optimization is used for calculating the constant c of the BUS method. • An improved version of the Quantified Active learning Subset Simulation method is proposed to define the posterior samples. The paper presents a multi-fidelity framework for efficient Bayesian updating using active learning Kriging models. The updating problem is solved as an equivalent probabilistic problem using the Bayesian updating with Structural reliability (BUS) method. The proposed approach leverages an ensemble surrogate modeling strategy that combines two Kriging models of multiple fidelities, thereby enhancing predictive capacity while reducing computational cost by exploiting information from models of different fidelity levels. A key contribution is the integration of multi-fidelity Bayesian optimization in order to determine the optimal BUS constant, ensuring accurate transformation of the posterior into a reliability problem. Furthermore, an improved version of the Quantified Active Learning Subset Simulation (qAK-SuS) method, previously proposed by the authors, is proposed in order to efficiently estimate small failure probabilities and obtain the posterior distribution. The proposed framework, called qAK-BUS, offers a robust solution for Bayesian inference in engineering systems by smartly balancing model fidelity, prediction variance, and learning efficiency. Three numerical examples and an engineering application that involves the updating of a reinforced concrete bridge are examined for demonstrating and validating the proposed framework.

Deep reinforcement learning-based sampling method for structural reliability assessment

The paper presents a semi-empirical based response surface approach for structural reliability analysis of steel plates with non-uniform corrosion represented by random fields. The approach consists of using a semi-empirical design equation as simplified response surface model, which is then calibrated iteratively by means of the results of non-linear finite element analyses at the design points calculated by the First Order Reliability Method. This technique has been successfully applied to problems formulated in terms of discrete random variables and is now applied to problems involving spatial variability of structural parameters represented by random fields. The approach is first illustrated with an example of the ultimate strength of plates with random imperfections and material properties and then applied to plates with random fields of corrosion discretized using the Expansion Optimal Linear Estimation method. The results obtained by the semi-empirical based response surface approach and by coupling directly the First Order Reliability Method and the finite element code are compared.

A New Approach for Structural Reliability Analysis of Offshore Drilling Riser System