Structural Reliability Analysis And Hybrid Harmony Search Optimization Algorithm Based On Subset Simulation

Structural reliability analysis and design optimization design are two important research topics of domestic and foreign scholars in the field of engineering mechanics. Reliability analysis is crucial to the safety assessment and prediction of the service life of structures as well as their normal operation. Structural optimization design can make the performance of the structure to achieve the best, and make the resources have a more reasonable use to reduce the engineering cost. As an efficient method to estimate small failure probabilities in reliability analysis of engineering systems, Subset simulation has been applied to the field of structural optimization. This thesis modifies the basic harmony search algorithm by utilizing the concept of the Markov Chain in subset simulation, and establishes the hybrid harmony search algorithm. Moreover, the application of subset simulation to stochastic reliability analysis and dynamic optimization design of structures are investigated. Specific works are listed as follows:In engineering practice, the external load and the structural parameters are usually stochastic. Seismic action is a typical stochastic load, and the efficiency analysis of structural dynamic reliability under the time-varying random earthquake action is a challenging problem. The subset simulation as a kind of efficient numerical simulation method provides an effective tool to solve such a type of problem of reliability evaluation of random structure. Through introducing the intermediate failure events with greater failure probability, the subset simulation transforms the small failure probability to the product of a sequence of greater failure probability. Meanwhile, these greater failure probabilities can be acquired by estimating the conditional sampling point with the Markov chain simulation in order to significantly improve the computational efficiency. The analysis of random structural dynamic reliability indicates that subset simulation greatly reduces the numbers of structural analysis and improves the computational efficiency.Moreover, engineering structures are inevitably affected by the external impact or vibration. The structural dynamic optimization design is particularly important in order to ensure the safe and reliable operation under dynamic load action. On the other hand, the subset method of optimization design transforms the extremum problem of optimization into the one of small failure probability. By using the subset simulation optimization algorithm, this thesis effectively solves the optimal design of the sizing and shapes of the trusses with the frequency constraints, and the sizing of frames subjected to dynamic loads.Finally, according to the limitations of basic harmony search algorithm such as difficulty to achieve the high precision solutions, easy to fall into local optimum and the low efficiency, the hybrid harmony search algorithm based on subset simulation (SSHS) is proposed. In SSHS, the existing dynamic harmony memory considering rate, pitch adjusting rate and bandwidth of harmony search is combined with the subset simulation algorithm. Benchmark mathematical examples and truss optimization design show that, the SSHS presents the better capabilities of searching for the optima accurately and robustness, as well as the property of fast convergence to the optimal solution. For multidimensional optimization problem, the SSHS presents the good computational performance.