Non-probabilistic Reliability Analysis And Optimization Based On The Imperialist Competitive Algorithm

As the increasingly deepening study of the structural reliability, the recognization of theuncertainty has been developed. From the beginning of the twentieth century, whenpeople regarded the uncertainties as stochastic events, to the end of ten years of thetwentieth century, when the convex set model appeared, lots of endeavors had beendone for the sake of the structural safty. Knowing the probability density function of theuncertain parameters, the failure probability and the reliability index were resolved,using the complicated probability theory and mathematical statistics. However, besidesthe difficulties of solving the joint probability density functions, it was also difficult toattain the probability density function of only one random variable, which usuallyneeded lots of experimental datum, restricting the probabilistic reliability method onsome special industries.The convex set based non-probabilistic reliability method can be a supplement tothe one above. Only through knowing the roughly changing ranges, the degree of theuncertainty could be calculated. Based on this kind of structural non-probabilisticreliability theory, and combining the imperialist competitive algorithm, thenon-probabilistic reliability model based on the imperialist competitive algorithm, thenon-probabilistic reliability model based on the imperialist competitive algorithm andresponse surface method, the stochastic and non-probabilistic system reliability modelbased on the imperialist competitive algorithm and the non-probabilistic reliabilitybased optimization model based on the imperialist competitive algorithm wereproposed.The main contents and some conclusions are briefed as below:(1) The comparison study of the artificial intelligent algorithm.The specific steps and application conditions of the traditional optimizationalgorithms and general artificial intelligence algorithms were studied, showing someadvantages of the imperialist competitive algorithm, through comparisons with some of those algorithms. The global convergent ability of the imperialist competitive algorithmis good and the multiple global optimal solutions can be attained simultaneously by thealgorithm, without the need for repeated starts. The requirements of the objectivefunction are very low, just by solving the optimization objective functions, the operationcan be carried out without the need for further analysis of the gradient function. Bytransforming the equality constrained optimization problem into the inequalityconstrained optimization, the penalty function method could be applied convenientlyand the feasible solution could be found quickly. This algorithm is suitable for a widerange of engineering applications. The imperialist competitive algorithm was used inthis dissertation to optimize the six peak hump function and the truss structure,obtaining some ideal optimal results.(2) Study of the structural non-probabilistic reliability analysis.A non-probabilistic reliability model based on the imperialist competitivealgorithm was proposed. By studying the solving strategy of elliptical model basednon-probabilistic reliability index, combining the research in artificial intelligencealgorithms, the proposed model was attained. This model does not need any sensitivityanalysis of the complex performance functions, being suitable for both the explicit andimplicit performance functions. This model was applied to the mechanical drive shaft,truss structure and the leg of an engineering machinery vehicle, getting accurate resultsand having a good effect of the convergence.(3) Study of the ICA-RSM hybrid algorithm.On the basis of the non-probabilistic reliability model based on the imperialcompetition algorithm, the non-probabilistic reliability model based on ICA-RSMhybrid algorithm was proposed. Response surface method was used to simulate the trueresponses of the actual performance function, and therefore, can substitute the trueperformance function. This can reduce the cost of estimating the performance functionvalue, and can improve the computational efficiency of the imperialist competitivealgorithm, which requires a lot of calculations of the performance function. Theorthogonal combination design and the uniform design method were used to choose thesample points, generating the ideal response surfaces The hybrid model was applied to the fracture analysis of the uniaxial tensile oblique crack plate and the truss structure,and the results showed that the proposed hybrid model is feasible.(4) Study of the structural stochastic and non-probabilistic system reliabilityOn the basis of the study of the structural stochastic system reliability and thenon-probabilistic system reliability, a structural stochastic and non-probabilistic systemreliability based on the imperialist competitive algorithm was proposed. Whenanalyzing the system reliability, the probability distribution functions of some uncertainparameters can be attained, while other uncertain parameters cannot get theirs, with onlythe boundary being known. The imperialist competitive algorithm was applied toestimate the range of the hybrid reliability index. Then, the range of the system hybridreliability index was achieved by using the Monte Carlo Importance Sampling method.The double-loop optimization problem of solving the maximum value of the hybridreliability index was solved by the imperialist competitive algorithm. Through the studyof the lathe spindle and the vehicle side impact worthiness, the results showed that theproposed model was correct and feasible.(5) Study of the structural non-probabilistic reliability based optimizationA non-probabilistic reliability based optimization model based on the imperialistcompetitive algorithm was proposed. Added by the constrains of reliability, thecomputing cost of the structural optimization design was increased fiercely. To balancethe precision and the computing cost, two strategy were applied, both applying theimperialist competitive algorithm to optimize the outer loop. When structure was simple,such as the truss structures, the amended iteration method was applied to optimize theinner loop. When complicated structures and the gradient information were hard to get,the response surface method was used to replace the true performance function, with thethe target performance method judging the reliability constraint. Through optimizing thetruss structure and the vehicle frame, the proposed model was proved to be feasible andcorrect.