Time-Dependent Reliability Estimation for Dynamic Problems Using a Niching Genetic Algorithm

A time-dependent reliability analysis method is presented for dynamic systems under uncertainty using a niching genetic algorithm (GA). The system response is modeled as a parametric random process. A double-loop optimization algorithm is used. The inner loop calculates the maximum response in time, using a hybrid (global-local) optimization algorithm. A global GA quickly locates the vicinity of the global maximum, and a gradient-based optimizer subsequently refines its location. A time-dependent problem is, therefore, transformed into a time-independent one. The outer loop calculates multiple most probable points (MPPs), which are commonly encountered in vibration problems. The dominant MPPs with the highest contribution to the probability of failure are identified. A niching GA is used because of its ability to simultaneously identify multiple solutions. All potential MPPs are initially identified approximately, and their location is efficiently refined using a gradient-based optimizer with local metamodels. For computational efficiency, the local metamodels are built using mostly available sample points from the niching GA. Among all MPPs, the significant and independent ones are identified using a correlation analysis. Approximate limit states are built at the identified MPPs, and the system failure probability is estimated using bimodal bounds. The vibration response of a cantilever plate under a random oscillating pressure load and a point load is used to illustrate the present method and demonstrate its robustness and efficiency. A finite-element model is used to calculate the plate response.