Interval Monte Carlo Simulation Research Articles

Real-world engineering problems: Two surrogate methods for robust vibration control of moving mass-beam coupling systems with epistemic uncertainty

The dynamic responses and the vibration control of the moving mass-beam coupling systems are one of the real-world problems in engineering fields including vehicle-bridge coupling systems and missile-gun systems. There are many uncertainty factors in the real-world engineering applications. Analyzing the effects of uncertainty on the state trajectory of the system is significant to realize the safe operation of the system. This paper develops two surrogate methods to research the evidence-theory-based robust adaptive fuzzy sliding mode control (ET-RAFSMC) of the moving mass-beam coupling systems. For the first approach, the active learning Kriging (ALK) is combined with the ET-RAFSMC to perform the evidence response analysis through an interval Monte Carlo simulation, and then a Karush-Kuhn-Tucker condition is utilized to alleviate the burden of searching the extreme responses. The other surrogate method is the Lobatto polynomial function, which integrates with a spare sampling method for improving the computational efficiency and accuracy when running the extreme value analysis of the ET-RAFSMC. The accuracy and the efficiency of the proposed methods are studied by comparing with Monte Carlo simulations as well as Legendre expansion model. Finally, the performance of the ET-RAFSMC is studied through comparing with the traditional sliding mode control.

A bounding-limit-state-surface-based active learning Kriging method for hybrid reliability analysis under random and probability-box variables

Abstract This paper presents a new method for efficient hybrid reliability analysis under both random and probability-box variables. Due to the existence of probability-box variables, the failure probability yielded by hybrid reliability analysis is an interval value. In practical engineering, numerical models are becoming more and more time-consuming, which promotes that metamodel-assisted reliability analysis methods gain considerable attention. The failure probability in hybrid reliability analysis under both random and probability-box variables can be calculated by transforming the original uncertainty space into the standard normal space. Then a limit-state band with two bounding limit-state surfaces is generated in the standard normal space. In this paper, it is determined that the lower and upper bounds of failure probability can be accurately estimated based on a Kriging metamodel as it can well describe the two bounding limit-state surfaces. Then, a new active learning strategy based on bounding limit-state surface is proposed to sequentially update Kriging metamodel by adding new update points in the vicinity of the bounding limit-state surfaces into design of experiments. Meanwhile, two error measurement functions are presented to terminate the update process by calculating the metamodel error. Combining the bounding-limit-state-surface-based active learning Kriging with interval Monte Carlo simulation, a new method for hybrid reliability analysis under both random and probability-box variables is developed. In this method, the lower and upper bounds of failure probability are estimated by interval Monte Carlo simulation based on the built Kriging metamodel. The proposed method is tested by six examples. Its comparison with some existing reliability analysis methods is provided. The high accuracy and efficiency of the proposed method are validated by comparative results.

Oparta na teorii entropii niezawodnościowa optymalizacja konstrukcji dla zmiennych rozmytych i przedziałowych

Reliability-based design optimization under fuzzy and interval variables is important in engineering practice. The interval Monte Carlo simulation (IMCS), extremum method, and saddlepoint approximation (SPA) can be used for reliability optimization issues contain only interval variables. Thus, how to deal with the fuzzy variables is critical for system reliability analysis and optimization design. The α-level cut method can be applied to deal with fuzzy variables but it is complex and computationally expensive. Therefore, an equivalent conversion method based on entropy theory is proposed in this paper, which can convert the fuzzy variables to the normal random variables to avoid the complex integral process. According to the equivalent conversion method, the entropybased sequential optimization and reliability assessment (E-SORA) is developed in combination with the worst case analysis (WCA) for reliability-based design optimization under fuzzy and interval variables. A numerical example about the reliability design of the crank-link mechanism under fuzzy and interval variables is solved by the E-SORA, double-loops method, and α-level cut algorithm, respectively, is used to demonstrate the accuracy and efficiency, and the results show that the proposed method is feasible for reliability-based design optimization under fuzzy and interval variables

A Novel Reliability Analysis Method for Turbine Discs with the Mixture of Fuzzy and Probability-Box Variables

Abstract Fuzzy and probability-box (p-box) variables exit widely in aerospace engineering. To evaluate the reliability of turbine discs under the mixture of these two types of variables and guarantee safety, the critical point lies in how to deal with the fuzzy variables. In this paper, a novel method based on equivalent transformation of entropy and saddlepoint approximation (SPA) is proposed to estimate the reliability of turbine discs with the mixture of fuzzy and p-box variables. The advantage of the proposed method is that it can transform fuzzy variables whose memberships are non-normal into normal random variables through entropy invariability; meanwhile, using the SPA, the required sample size and corresponding computational cost decreases greatly. An example is used to illustrate the proposed method and a comparison is also made with the interval Monte Carlo simulation (IMCS). The results indicate that the proposed method is promising and has higher efficiency with almost the same accuracy.

Generalized reliability analysis of structues based on interval finite element

Relative to the special structure reliability theory only considering randomness, the advanced theory is called generalized reliability which considers randomness, fuzziness and unascertainty at the same time. This theory was first proposed by Wang GuangYuan academician in 1980s. In this thesis, some research results of the team of authors are introduced. Fuzziness is considered by the fuzzy mathematics and unascertainty is reckoned with the interval mathematics. First, some basic conceptions of interval math and interval finite element are introduced. Then generalized reliability analysis methods of three kinds of uncertainty conditions are discussed with the tool of interval finite element. In the first condition, both randomness and unascertainty are considered and the parameters of the random variables are interval variables. The second condition is that randomness and fuzziness are separated. The basic variables are random and the failure criterion is fuzzy. Randomness and fuzziness are coupling in the third condition. The parameters of the random variables are fuzzy numbers to reflect fuzziness. Finally, authors propose and develop the generalized reliability analysis methods of this three cases using the interval Monte Carlo Simulation (IntMCS) and the interval First Order Reliability Method (IntFORM). By means of a plane truss example, the applicability and effectiveness of these methods are shown. After a series of research, some conclusions can be summarized. The IntFORM proposed in this thesis has enough computational accuracy and more computational efficiency than IntMCS. Therefore, this method can be used in the reliability analysis of large-scale structures.

Structural reliability analysis under evidence theory using the active learning kriging model

ABSTRACTStructural reliability analysis under evidence theory is investigated. It is rigorously proved that a surrogate model providing only correct sign prediction of the performance function can meet the accuracy requirement of evidence-theory-based reliability analysis. Accordingly, a method based on the active learning kriging model which only correctly predicts the sign of the performance function is proposed. Interval Monte Carlo simulation and a modified optimization method based on Karush–Kuhn–Tucker conditions are introduced to make the method more efficient in estimating the bounds of failure probability based on the kriging model. Four examples are investigated to demonstrate the efficiency and accuracy of the proposed method.

Hybrid reliability analysis with both random and probability-box variables

Hybrid reliability analysis (HRA) with both aleatory and epistemic uncertainties is investigated in this paper. The aleatory uncertainties are described by random variables, and the epistemic uncertainties are described by a probability-box (p-box) model. Although tremendous efforts have been devoted to propagating random or p-box uncertainties, much less attention has been paid to analyzing the hybrid reliability with both of them. For HRA, optimization-based Interval Monte Carlo Simulation (OIMCS) is available to estimate the bounds of failure probability, but it requires enormous computational performance. A new method combining the Kriging model with OIMCS is proposed in this paper. When constructing the Kriging model, we only locally approximate the performance function in the region where the sign is prone to be wrongly predicted. It is based on the idea that a surrogate model only exactly predicting the sign of performance function could satisfy the demand of accuracy for HRA. Then OIMCS can be effectively performed based on the Kriging model. Three numerical examples and an engineering application are investigated to demonstrate the performance of the proposed method.

Saddlepoint approximation-based reliability analysis method for structural systems with parameter uncertainties

Due to epistemic uncertainty, precisely determining parameters of all distribution is impossible in engineering practice. In this article, a novel reliability analysis method based on the saddlepoint approximation is proposed for structural systems with parameter uncertainties. The proposed method includes four main steps: (1) sampling for random and probability-box variables, (2) approximating the cumulant generating functions for systems under the best and worst cases, (3) calculating saddlepoints for the best and worst cases, and (4) calculating the lower and upper bounds of the probability of failure. The proposed method is effective because it does not require a large sample size or solving complicated integrals. Furthermore, the proposed method provides results that have the same accuracy as the existing interval Monte Carlo simulation method, but with significantly reduced computational effort. The effectiveness of the proposed method is demonstrated with three examples that are compared against with the interval Monte Carlo simulation method.

Reliability Assessment with Fuzzy Random Variables Using Interval Monte Carlo Simulation

AbstractIn this work structural reliability assessment is presented for structures with uncertain loads and material properties. Uncertain variables are modeled as fuzzy random variables and Interval Monte Carlo Simulation along with interval finite element method is used to evaluate failure probability. Interval Monte Carlo is compared with existing search algorithms used in the reliability assessment of fuzzy random structural systems for both efficiency and accuracy. The genetic algorithm as one of the well developed approaches is selected for comparison. Fuzzy randomness is used as a model for handling both aleatory and epistemic uncertainties. Fuzzy quantities are calculated using the α‐cut approach. In the case of Interval Monte Carlo, bounds on response quantities are obtained for each α‐cut using only one run of interval finite element method, however genetic approach requires performing Monte Carlo Simulation for each of the considered different possible combinations within the search domain (α‐cut) and running finite element for each of the Monte Carlo realizations. In the presented examples both load and material uncertainties are considered. Numerical results show the computational efficiency of the Interval Monte Carlo approach and its superiority to the alternative search approaches such as optimization and genetic algorithms. In addition, results show how that Interval Monte Carlo approach provides guaranteed and sharp enclosure to the system solution.

Models and considerations for parallel implementation of Monte Carlo simulation methods for power system reliability evaluation

This paper proposes three topologies for parallelizing the fixed interval Monte Carlo simulation for reliability evaluation of interconnected power systems. The important issue of random number generation for parallel algorithms is also explored in detail. Several studies have been conducted to gain insight into the quantitative and performance results. Extensions of the proposed topologies and random number generation schemes to other simulation techniques are also discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>