Non-probabilistic Reliability Analysis And Optimization Design Of The Structure Based On The Interval Model

The theoretical analysis and algorithm research of the uncertainty problems has been a hot point in the structural engineering.Reliability analysis is one of the effective approaches to deal with uncertainties.The interval model is described by the upper and lower bounds of the uncertain parameters.Based on the interval model,the non-probabilistic reliability and the non-probabilistic reliability optimization design are studied with the throretical analysis and algorithm research separately.Then,the non-probabilistic reliability analysis and the reinforcement optimization design are applied in the RC bridge.The main works are as follows:(1)The theory and algorithm of the non-probabilistic reliability of the structure based on the interval model are proposed.According to the geometric meaning of non-probabilistic reliability index,the design point of the linear function is located at the corner point of the hypercube box and the design points of nonlinear function is located at tangent point of the hypercube box and the failure surface.The design point of the hypercube box is decided by the positive and negative gradient vector of interval variables.Then,the enchanced one-dimensional optimization algorithm is put forward for the linear function.And the subinterval optimization method and the subinterval target performance method are put forward for the nonlinear functions.A comparision between with the relationship between the non-probabilistic reliability index and the probabilistic reliability index based on the non-probabilistic reliability model and probabilistic reliability model is presented,and their interrelation and difference are illustrated.The non-probabilistic safety factor and non-probabilistic reliability method is compared.The consistency of the non-probabilistic safety factor and non-probabilistic reliability index is discussed.(2)The theory and algorithm of the non-probabilistic reliability based on the stress-strength interference model are presented.According to the geometric representation of the interval possibility degree,the non-probabilistic set-based reliability is expressed as the volume of structural safe region to the total volume of the interval variables.Therefore,the expression of the non-probabilistic set-based reliability of the linear function is established.When the nonlinear degree of performance function is low,the calculation expression of non-probabilistic set-based reliability is established by the linear approximate programming of failure surface.As for the complex nonlinear function,the subinterval method is put forward,in which more sample points sampling within the sub-domain fall into the failure domain and the sampling points distribute uniformly.The probabilistic metric of the non-probabilistic set-based reliability is discussed.It is proved that the non-probabilistic reliability is essentiality the probabilistic reliability when stress and strength is distributed uniformly in the interval.The reliabilities of the non-probabilistic set-based reliability model,interval numbers of normal distribution model and truncated interval distribution model are compared.The researches show that non-probabilistic set-based reliability is more conservative.(3)The non-probabilistic reliability and the non-probabilistic probability reliability optimization design are studied.According to the geometric meaning of the non-probabilistic reliability index,the target performance method based on the subinterval is presented,in which the constraint of non-probabilistic reliability index is converted to minimizing the performance function.In the inner optimization,solving non-probabilistic reliability index is converted to finding the minimum of all performance function.This method avoids the double-layer optimization that the non-probabilistic reliability index is sloved in the inner optimization.Then,the iteration numbes is decreased and the computation cost is reduced.Based on the subinterval optimization method which is used to solve the non-probabilistic reliability index,a double-layer optimization design is presented,in which the non-probabilistic reliability index can be slove directly in the inner-layer.The active constraint is firstly judged and the active constraint of the non-probabilistic reliability index is only considered.The non-probabilistic reliability optimization of the linear function is a single-loop optimization problem.The design points of the uncertain parameters that satisfy the constraints of non-probabilistic reliability index are located at the corner of the hypercube box.The expression between the single-layer non-probabilistic reliability optimization model with the uncertain parameters is clear and the calculation cost is reduced.The non-probability set-based reliability of the linear functional functions is the dominant function of uncertain parameters.Penalty function is introduced to transform the constrained optimization into the unconstrained optimization.The improved PSO algorithm is used to obtain the global optimal solution for the outer-layer optimization design with fast convergence speed.Based on the interval probability,a double-layer optimization design is proposed for the non-probabilistic set-based reliability of the nonlinear functional functions,which uses the sub-interval analysis method in the inner layer and the improved PSO method in the outer layer.(4)The application of the non-probabilistic reliability analysis and the optimization design in reliability evaluation and reinforcement of RC bridges are studied.The probability reliability and non-probability reliability of the reinforced concrete column strengthened by enlarging section method under the axial compression are compared.The research shows that whatever the dead loads,the live loads and the resistance are different distribution types,the non-probabilistic reliability is more conservative than the probabilistic reliability with uncertain parameter in the interval of [?-3?,?+3?] in the case of the same?and?.That is,the assessment of the non-probabilistic reliability is safe for bridge components,and the assessment of the probabilistic reliability is also safe.Based on the relationship of probability reliability and the non-probability reliability,the non-probabilistic target reliability index and the non-probabilistic target probability reliability of the bridge bearing capacity evaluation are proposed.The probabilistic reliability of the reinforced concrete axial column under the non-probabilistic target reliability index and the non-probabilistic target probability reliability optimization results meet the requirements.In other words,the non-probabilistic reliability of the axial compression column meets the requirements,and the probabilistic reliability also meet the requirements.