Structural Reliability Analysis Based On Orthogonal Neural Network

Title:Structural reliability analysis based on orthogonal neural networkSafety and reliablity are two main aims of structural design. Various of uncertainties exist in engineering structures, including randomness and fuzziness which are two main kinds of uncertainties and belong to different types, whereas reliability theory is an effective tool to deal with the uncertainties. The study on the structural reliability is of great importance to help designers to determine the safety limit of a structure and control influence of the uncertainties on structural safety, thus make the designed performance have better coincidence with the actual performance, and ensure the structure has a sufficient safety and reliability.The reliability-based optimization design of the structure is a combination of the structural reliability theory and mathematical optimization methods. As the structural reliability theory is introduced into structural optimization, the uncertainties in practical projects can be more reasonable considered, and the structural reliability in optimization design can quantitatively described, hence it will reach a whole best balance of the safety, the performace and the cost, the obvious technical and economic benefits will be reached besides the structural reliability.Artificial neural network is a complex network system which consists of a large number of simple interconnected neurons. Although a single neuron has very simple structure and basic function, but a large number of neurons in a network interconnection system is able to achieve various of complex functions. Artificial neural network system is a complex nonlinear dynamic system, which has the characteristics of self-organizing, adaptive and self-learning, thus it has been successfully applied in various of research fields and has achieved a great deal of research results.In this paper, the developments and current situations of structural reliability theory and reliability-based optimization design is reviewed both domestic and international. Whereafter, the artificial neural network technique is applied to reliability analysis and reliability-based optimization design. The proposed method provides an effective tool and method in the study on reliability analysis and reliability-based optimization design.The main achievements of this dissertation are:1. An orthogonal neural network model was established with a set of Fourier orthogonal basis functions. Based on the numerical approximation theory, an orthogonal neural network model was established, with a set of Fourier orthogonal basis functions acting as the activation functions of the hidden layer neurons. Since all the hidden layer neuron activation function is a different orthogonal basis functions, this make the artificial neurons are much closer to biological neurons, thus convergence performance of the network can be effectively improved. Meanwhile, since the best square approximation polynomial is unique, the orthogonal neural network can avoid the local minimum problem, which the BP neural network often encountours, and the orthogonal neural network has fast convergence speed and short training time, and high approximation precision, as well. The orthogonal neural network can be applied to all kinds of function approximations. When the number of hidden layer neurons increases, which means that the number of orthogonal basis functions increases, the orthogonal neural network will be trained with a much faster convergence speed, moreover, the convergence error decreases, therefore, the number of hidden layer neurons can be determined according to the demanded approximation error accuracy.2. A reliability analysis method was proposed based on orthogonal neural network response surface method. Since the orthogonal neural network has a strong approximation ability and nonlinear mapping capacity, it was used to replace the traditional response surface. Compared with the traditional response surface, the orthogonal neural network response surface has the advantages of high accuracy and better flexibility. The relationship between structure response and random variables was established through an orthogonal neural network, so as to simulate the relationship between the performance function and the random variables, hence an explicit performance function can be obtained. Then with the explicit expression, the partial derivatives with respect to the basic random variables can be calculated, and the reliability of the performace function can be calculated with the first-order reliability(FORM).3. Based on the structural reliability analysis with orthogonal neural network response surface method, a reliability-based optimization method was put forwards, a reliability-based optimization model was established. The orthogonal neural network response surface method can be used for structural reliability analysis, when the design variables in the design space take different values, the corresponding reliability can be obtained. Then an orthogonal neural network was adopted to simulate the ralationship between the design variables and reliability. Thus an explicit expression of the reliability and the design variables can be obtained. The obtained expression acted as an optimization objective function, or as a constraint function, then with the optimize method to solving the problem to get a best design, this can ensure the economic in the design process and the security operation.4. An orthogonal neural network based fuzzy reliability analysis method was proposed based on the orthogonal neural network response surface method. The orthogonal neural network response surface method was used to solve the structural reliability problem with both random variables and fuzzy variables. With the entropy equivalent method, an arbitrary fuzzy variable can be transformed into a normally distributed random variable, hence the fuzzy reliability can be changed into reliability problem with only random variables. Entropy is the commoness of the fuzzy factor and random factors, the fuzzy variable and random variable can be interactive transformed with the entropy equivalent method. Since the normal distribution is the most commonly used in reliabilty analysis, the fuzzy membership function always be transformed into into an equivalent normal random variable. Then the fuzzy reliability analysis of structure can be performed using the orthogonal neural network based response surface method. With the fuzzy uncertainties and random uncertainties being considered, the reliability analysis of the structure will be much reliable, and the analysis result will meet the needs of the security of the structure.