Reliability Calculations with the Stochastic Finite Element

PREFACE

There are two kinds of uncertainties, fussiness and randomness in engineering problems. Several researchers in China and abroad pay attention to the influence of random factors on the structure. In machinery, dam, construction, earthquake and other fields, random factors do have a great impact on the structure. The spatial variability of structural material properties is studied as a random process by many scholars. With the deepening of human understanding, it is not practical to ignore the design of randomness.

In the first chapter, the fuzzy reliability of a single component maintenance system and the repairable series system are studied. Two fuzzy methods for reliability allocation are proposed. The second chapter discusses the reliability of the rigid rotor balance. Based on the sensitivity analysis, a Monte Carlo simulation for the reliability calculation of gears is proposed. Based on the sensitivity analysis, an optimization method for reliability calculation is proposed. The reliability calculation of spring is studied by using the HL-RF method. In the third chapter, optimization design-based HL-RF and IS for the gearbox are proposed. A multi-objective reliability-based fuzzy optimization design for gear box is proposed.

The fourth chapter proposes an improved method of perturbation stochastic finite element to save computational time. In the fifth chapter, differential equations are transformed into linear equations by the Wilson q method. Linear equations are solved by the Successive Over Relaxation method. Anew method of calculating dynamic reliability using the Neumann stochastic finite element is proposed. The sixth chapter discusses the design model of the gearbox established by using the stochastic finite element method. A new method of stochastic finite element for vibration is also proposed. In the last chapter, four stochastic finite element methods are proposed to calculate nonlinear vibration.

Wenhui Mo

School of Mechanical Engineering

Hubei University of Automotive Technology

China

Fuzzy Reliability

Abstract

Considering the influence of fuzzy factors, the fuzzy reliability of single component maintenance system and the repairable series system is studied.

Two fuzzy methods for reliability allocation are proposed: One uses the second-order fuzzy comprehensive evaluation method, and the other one uses the fuzzy optimization method.

Keywords: Fuzzy reliability, Fuzzy optimization method, Repairable series system, Reliability allocation, Second-order fuzzy comprehensive evaluation method, Single component maintenance system.

INTRODUCTION

There is no absolute clear boundary between normal and abnormal operation (failure) of the system, but it is often a form of transition through an intermediary - work with failure, so it is a fuzzy concept. Zadeh LA, an American fuzzy mathematician, uses the degree of membership to describe the intermediary transition of differences, which is a description of fuzziness in precise mathematical language.

The fuzzy reliability analysis in the posits reliability theory is defined precisely and a general approach by a system of functional equations is proposed [1]. A fuzzy fault-tree based reliability analysis of an optimally planned transmission system is presented [2]. An attempt has been made to present a new approach for the stability analysis of slopes incorporating fuzzy uncertainty [3]. Fuzzy numbers are used to define an equivalence class of probability distributions compatible with available data and corresponding upper and lower cumulative density functions [4]. The most relevant parameters are identified by means of different sensitivity analysis techniques. Then, fuzzy models are devised which efficiently do the required mapping between the system outputs and the identified relevant inputs [5]. A new fuzzy multi-objective optimization method is introduced, and it is used for the optimization decision making of the series and complex system reliability with two goals [6]. An approach to fuzzy rule base design using a tabu search algorithm (TSA) for nonlinear system modeling is presented [7]. A new modelling approach for determining the reliability and availability of a production system is proposed by considering all the components of the system and their hierarchy in the system structure [8]. A new algorithm has been introduced to build the membership function and non-membership function of the fuzzy reliability of a system having components following different types of intuitionistic fuzzy failure rates [9]. A fuzzy-based reliability approach is presented to check the basic events of system fault trees, the failure precise probability distributions of which is not available [10]. Some recent results on the application of the fuzzy Bayes methodology for the analysis of imprecise reliability data are proposed [11]. New means for predicting time to failure of the components, using a calibration regression method for measuring the error prediction in the extrapolation process are proposed [12]. A road-map has been provided to assess the reliability indices of repairable systems with uncertain limits [13]. This paper introduces evidence variables and fuzzy variables simultaneously to describe the uncertain epistemic parameters and a novel dual-stage reliability analysis framework