Reliability Calculations with the Stochastic Finite Element - Wenhui Mo - E-Book

Reliability Calculations with the Stochastic Finite Element E-Book

Wenhui Mo

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Beschreibung

Reliability Calculations with the Stochastic Finite Element presents different methods of reliability analysis for systems. Chapters explain methods used to analyze a number of systems such as single component maintenance system, repairable series system, rigid rotor balance, spring mechanics, gearbox design and optimization, and nonlinear vibration. The author proposes several established and new methods to solve reliability problems which are based on fuzzy systems, sensitivity analysis, Monte Carlo simulation, HL-RF methods, differential equations, and stochastic finite element processing, to name a few.
This handbook is a useful update on reliability analysis for mechanical engineers and technical apprentices.

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Seitenzahl: 92

Veröffentlichungsjahr: 2020

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Table of Contents
Welcome
Table of Content
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Usage Rules:
Disclaimer:
Limitation of Liability:
General:
PREFACE
Fuzzy Reliability
Abstract
INTRODUCTION
FUZZY RELIABILITY OF SINGLE COMPONENT MAINTENANCE SYSTEM
Transition Fuzzy Probability
Fuzzy Validity of the System
Fuzzy Reliability of the System
Example
Fuzzy Reliability of Repairable Series System
State and Membership Degree
Repairable Series System with the Same n Components
Repairable Series System with Different n Components
Fuzzy Comprehensive Evaluation Method of Reliability Distribution
Fuzzy Comprehensive Evaluation of Subsystem
Series System
Parallel System
Fuzzy Method of Reliability Distribution
Fuzzy Optimization Method
Series System
Parallel System
Hybrid System
Fuzzy Optimization Method for Series System
CONCLUDING REMARKS
CONSENT FOR PUBLICATION
CONFLICT OF INTEREST
ACKNOWLEDGEMENTS
REFERENCES
Reliability Calculation
Abstract
INSTRUCTION
RELIABILITY OF RIGID ROTOR BALANCE
RELIABILITY CALCULATION OF STATIC BALANCE
RELIABILITY CALCULATION OF DYNAMIC BALANCE
MONTE CARLO SIMULATION OF GEAR RELIABILITY CALCULATION
RELIABILITY CALCULATION BASED ON SENSITIVITY ANALYSIS
THE RELIABILITY OF SPRING
CONCLUDING REMARKS
CONSENT FOR PUBLICATION
CONFLICT OF INTEREST
ACKNOWLEDGEMENTS
REFERENCES
Reliability-Based Optimization Design
Abstract
INTRODUCTION
RELIABILITY-BASED OPTIMIZATION DESIGN USING HL-RF
The Importance Sampling-Based Optimization Design for the Gearbox
Multi-Objective Reliability-Based Fuzzy Optimization Design for the Gearbox
CONCLUDING REMARKS
CONSENT FOR PUBLICATION
CONFLICT OF INTEREST
ACKNOWLEDGEMENTS
REFERENCES
Perturbation Stochastic Finite Element of Mechanical Vibration
Abstract
INTRODUCTION
PERTURBATION STOCHASTIC FINITE ELEMENT OF MECHANICAL VIBRATION
AN IMPROVED METHOD OF PERTURBATION STOCHASTIC FINITE ELEMENT
CONCLUDING REMARKS
CONSENT FOR PUBLICATION
CONFLICT OF INTEREST
ACKNOWLEDGEMENTS
REFERENCES
Stochastic Finite Element Method of Dynamic Reliability
Abstract
INTRODUCTION
DYNAMIC RELIABILITY OF STRUCTURE USING THE SUCCESSIVE OVER RELAXATION METHOD
DYNAMIC RELIABILITY OF STRUCTURE USING NEUMANN STOCHASTIC FINITE ELEMENT
CONCLUDING REMARKS
CONSENT FOR PUBLICATION
CONFLICT OF INTEREST
ACKNOWLEDGEMENTS
REFERENCES
Optimization Design of Stochastic Finite Element
Abstract
INTRODUCTION
OPTIMIZATION MODEL
Calculation of Mean and Variance of Dynamic Stress
Comparison of Design Parameters
CONCLUDING REMARKS
CONSENT FOR PUBLICATION
CONFLICT OF INTEREST
ACKNOWLEDGEMENTS
REFERENCES
Stochastic Finite Element for Nonlinear Vibration
Abstract
INSTRUCTION
TAYLOR EXPANSION METHOD
Perturbation Technology
Newton Method
The Homotopy Perturbation Method
CONCLUDING REMARKS
CONSENT FOR PUBLICATION
CONFLICT OF INTEREST
ACKNOWLEDGEMENTS
REFERENCES
Reliability Calculations with the Stochastic Finite Element Authored byWenhui Mo School of Mechanical Engineering Hubei University of Automotive Technology

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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