Reliability Analysis Of Mechanical Components Based On Most Probable Point Perturbation Method

In practical engineering problems, the theories of the design and analysis of structures are always established on the basis of the definite mathematics models. However, there are always uncertain factors in the structural engineering practices extensively, such as the inaccuracy of the measurement, the complexity of the structures or errors in manufacture, etc. When the structures are large and complex, the combination of the uncertainty can have some effect on the systems. It'll be much more accordant to consider uncertain factors in the systems design. Therefore, it is necessary to design and analyze the structures with uncertain models directly. The research on reliability of the uncertain systems is very important for design purposes. The reliability analysis of structures can help the designer to establish acceptable tolerances on structures and govern the fluctuations of the system parameters for safe operations. In a word, based on the reliability analysis of structures the reasonable structures and optimization of system design could be designed with enough reliability and little cost.Parameter and loads uncertainty is inherent in most designs of mechanical components and vibration control systems. The random model is used to deal with systems with uncertain parameters. Based on the random model,the methods of the reliability-based design, the reliability-based optimization design and reliability-based sensitivity analysis are established. These methods have extensive application prospects on account of significance in improving product quality, making performance stability and improving engineering design with the consideration of the uncertainties. In this dissertation, on the basis of summarizing the reliability-based design theory, the reliability-based sensitivity design method and the idea of optimal design in the world, the methods of the reliability-based analysis, the reliability-based sensitivity analysis and the reliability-based optimal design are put forward. The methods are suitable for solving the problem about the correlated random variants obeying normal and nonnormal distributions. Using the perturbation theory, the methods of the reliability-based analysis of eigenvalues and responses of closed-loop vibration control systems with uncertain parameters are discussed. The theories of the reliability analysis of mechanical components and vibration control systems are developed.There are some details as follows:1. A most probable point perturbation method (MPPPM) for reliability analysis is presented. The method is suitable for solving the problem about the correlated random variants obeying normal and nonnormal distributions. A practical and effective numerical method of reliability-based optimization design with the correlated random variants obeying normal and nonnormal distributions is proposed. Techniques from the perturbation method, the reliability-based design theory and the constrained complex method are employed to present the approach. The reliability-based optimal design of systems with uncertain parameters are discussed, which is approximated with the corresponding deterministic one. So the problem of the reliability-based optimal design is preferably solved.2. Based on MPPPM a numerical method for the reliability-based sensitivity analysis is presented. The numerical method of reliability-based sensitivity design was studied from the level of the mean, the standard deviation and the correlation coefficients of basic random variants obeying normal and nonnormal distributions. The influences of the mean, the standard deviation and the correlation coefficients of basic random variants are discussed. The reliability-based sensitivity design theory is made much more perfect.3. Based on the analysis of the eigenvalues of closed-loop systems with uncertain parameters and the quasi-failure analysis method for resonant problem the methods of the reliability-based analysis of eigenvalues of closed-loop vibration control systems with uncertain parameters are proposed. Based on the analysis of responses of closed-loop systems with uncertain parameters and the quasi-failure analysis method for the problem of first exceeding tolerances the methods of the reliability-based analysis of responses of closed-loop vibration control systems with uncertain parameters are proposed, too.