Structural Reliability Analysis Based On Fourier Orthogonal Neural Network Weighted Response Surface Method

Entering the new century, our country’s economy is developing steadily andrapidly. Engineering construction is in a booming period. Ensuring the safety of theengineering construction is very important and meaningful in engineering design.Structural reliability theory is developed to solve the engineering structural design.The study on the structural reliability theory can help designers to determine thesafety limit of a structure reasonably. The study on the structural reliability is ofgreat importance to help designers to ensure the security and economy ofengineering structures, and the theory has more and more important status inengineering structural design.Among the traditional structural reliability analysis, the limit state function isoften non-linear, involving a large number of uncertain factors. Analysis of thiskind of problem is a complicated and time-consuming process. Besides, in someactual projects with reliability analysis, the limit state function sometimes can’t beset up completely, and the necessary data can only be obtained through theexperimental method. This process brings troubles for calculations and analyses.Plenty of uncertainties widely exist in practical engineering structures, includingrandomness and fuzziness. It is difficult to use common reliability model tocalculate the reliability of the structure when randomness and fuzziness existsimultaneously. And in some cases, the results obtained from inappropriatetraditional reliability model may not be desired or correct.According to this situation, Fourier orthogonal basis neural network wasproposed. And the random reliability model, the fuzzy reliability model and systemreliability model of the structure were established, based on the weighted reponsesurface polynomial based on the Fourier orthogonal basis.The main achievements of this dissertation are:1. Based on the numerical approximation principle, a special three layerfeed-forward weighted neural network model, using Fourier orthogonal polynomial as the activation function in the hidden layer, was proposed. The connectingcoefficients between the hidden layer and the output layer of the network weresolved by using the weighted least square method, with an enough utilization of theconvergent ability of the sample point avoiding the local minimum problem of thegradient descent method in the BP neural network. The proposed orthogonal neuralnetwork could shorten the training time and improve the converging ability of thenetwork training. Through the numerical analyses of different kinds of functions,the results show that the Fourier orthogonal neural network is appropriate to allkinds of function approximations, with advantages of easy programming and highefficiency.2. A reliability analysis model based on Fourier orthogonal neural networkweighted response surface method was proposed. The Fourier orthogonal basisneural network has a strong approximation ability and nonlinear mapping capacity.Therefore, the response surface with Fourier orthogonal basis functions ispresented to substitute the traditional polynomial response surface. The Fourierorthogonal neural network weighted response surface has the advantages of highaccuracy and better flexibility and is easy to program. The unknown connectingcoefficients of the network were calculated by weighted least square method, witha better utilization of the fitting effect of the selected sample points. Aftersimulating the mapping relation between the structural response and the randomvariables, the reliability was analyzed combined with the first order secondmoment method. The numerical examples of the structural performance functionswith high order and multi-dimensional random variables showed that Fourierorthogonal neural network weighted response surface method is correct and hashigh precision, with wider applicability.3. A fuzzy reliability model based on Fourier orthogonal basis neural networkweighted response surface method was proposed, after studying the randomreliability model based on the Fourier orthogonal neural network weightedresponse surface method. According to the structural fuzzy failure criteria, andregarding the structural failure as a fuzzy event, the equivalent performancefunction between the random variables and the fuzzy failure was set up,transforming the structural fuzzy reliability problem to a traditional random reliability model. Meanwhile, the reliability model with hybrid uncertainties offuzzy variables and random ones was analyzed. Through the equivalenttransformation method of the information entropy, the fuzzy variables in structuralreliability analysis were transformed into the equivalent normal random variables.Therefore, the structural random reliability could be analyzed by using the Fourierorthogonal basis neural network weighted response method.4. Structural system reliability model based on Fourier orthogonal basis neuralnetwork weighted response surface was proposed. The mapping relation betweenthe variables and the response was built based on Fourier orthogonal weightedresponse surface. With the help of the built performance function, the sensitivityvector at the checking point, where the single failure mode converged, wascalculated, and the correlation coefficient matrix of the multiple failure modes wasbuilt. According to the different failure state of the structural system, theprobability of failure was computed by using Fourier orthogonal basis neuralnetwork weighted response method. The proposed modal gives a new way toanalyze the structural system reliability.