Research On State Evaluation Method Of High-dimensional Stochastic System Based On Probability Density Evolution Theory

With the development of society and technology,major engineering infrastructures appeared at an unprecedented speed.Under the background of climate change,frequent disasters,carbon neutrality and resilient cities,the engineering and academic circles put forward higher requirements for the evaluation of major projects.The state evaluation of major projects during service should comprehensively consider the multiple uncertainties caused by multi-dimensional parameters of the structure and load.However,it makes the cost of structural reliability analysis increase geometrically with the dimension,resulting in the so-called "dimension disaster".At present,the existing structural reliability calculation theories such as first-order second moment,response surface method,Monte Carlo simulation,Bayesian method and Probability Density Evolution Theory have their own advantages in solving the above problems,but they also face a common technical bottleneck,that is,the calculation efficiency will be reduced due to the increase of the dimension of system random parameters,especially for small probability events.When there is a lack of parameter statistical information in the system,the analysis error of the system will accumulate with the increase of dimension.Under the background of carbon neutralization,how to reduce the calculation time and the consumption of calculation resources while maintaining the calculation accuracy is a challenge for the random structural response and reliability analysis.Based on the Probability Density Evolution Theory,this paper focuses on the scientific problems of slow order-reduction,low efficiency,difficult decoupling and large error in the state evaluation of high-dimensional stochastic system.Put forward two new deconstruction technologies: probability density evolution-sensitivity analysis /probability density evolution-substructure reconstruction,starting from the two aspects of rapid refining the key parameters affecting the structural state and reverse solving the random response.The fast order-reduction and decoupling of high-dimensional stochastic systems are realized,and the computational efficiency is significantly improved compared with the classical Monte Carlo simulation method.The method provides a new idea to overcome the limitations of probability density evolution method(PDEM)in highdimensional variables(small probability events)or data scarcity.The above technology can effectively solve the problem of probability evaluation of stochastic structures.At present,the engineering application achievements include: the dynamic coupling problem of biped pedestrian-structure interaction system,quantitative evaluation of safety performance of Tibetan ancient wooden structures with Que-Ti inclination effect,and the response and reliability calculation of seven-story benchmark frame,which can provide a reference for high-rise ancient building structures.The main research contents and conclusions of this paper are as follows:(1)Aiming at the problems of slow order reduction and low efficiency of traditional probabilistic sensitivity analysis(PSA)for high-dimensional stochastic systems,a new efficient probabilistic sensitivity analysis method is derived by embedding KullbackLeibler(K-L)relative entropy into the probability density evolution method(PDEM).Combined with the equivalent extreme value method in probability density evolution theory,the sensitivity based on extreme value control and reliability control in KL-PDEM makes use of the advantages of PDEM in short time and small area,respectively.The sensitivity indices are estimated by obtaining the probability distribution characteristics of structural performance,response extreme value or the stable value of dynamic reliability.This method can reduce the number of representative points of each variable suggested by the classical PDEM theory from 70-250 to only 3 representative points,and the accurate sensitivity ranking is obtained through a small number of sample points.Different from the traditional probabilistic sensitivity analysis based on Monte Carlo simulation,it needs a large number of system solutions,and the accuracy is limited by the number of simulated samples.That is,the calculation cost increases exponentially with the accuracy requirements.The proposed method not only ensures the accuracy,but also significantly improves the computational efficiency,and realizes the rapid sensitivity analysis of high-dimensional stochastic systems.(2)Aiming at the problem that the computational cost of dynamic response analysis of high-dimensional stochastic system increases with dimension,and the direct probability density evolution analysis is inefficient or even unsolvable sometimes.The response analysis of high-dimensional stochastic system is decomposed into two lowdimensional calculation processes,namely KL-PDEM probabilistic sensitivity analysis and PDEM based low-dimensional stochastic system.The reduced-dimension point set is used to solve the probability density evolution equation instead of the initial point set,which provides a new idea for the probability response analysis of PDEM in complex high-dimensional stochastic systems.And it reduces the demand for complex point selection technology of uncertain variables in high-dimensional stochastic systems to a certain extent.The method is successfully applied to the dynamic response analysis of biped pedestrian-structure interaction system with random self-driving mechanism.(3)Aiming at the high-dimensional random characteristics of structural system caused by incomplete deterioration information.A probability sensitivity analysis method(HM-PDEM)combining Hellinger measure and PDEM is proposed,which can measure the contribution of random variables to the probability density function(PDF)of structural bearing capacity.The reliability of complex Tibetan frame structure considering deterioration uncertainties under existing load is evaluated efficiently and accurately through low-dimensional random variable group.The method provides an alternative strategy for the protection and safety evaluation of heritage buildings.(4)Aiming at the problems of difficult decoupling and large error in response analysis of high-dimensional stochastic systems when data is scarce,the Stochastic Substructure Response Reconstruction Method(SSRRM)is proposed for inverse analysis of system response.SSRRM overcomes the limitation of the existing forward solution of stochastic dynamic response when data is scarce by combining the frequency-domain response reconstruction method based on the concept of transmissibility with the probability density evolution equation(PDEE).Identify the contact force as the substructural load,and integrate the propagation of the randomness of structural parameters into the substructural response reconstruction.Then,the measured response in the substructure is used to replace the calculated response of the overall finite element model,and the method for dynamic response analysis and reliability evaluation of stochastic system based on partial measured response is proposed.This method is still applicable to the situation that some structural parameters,boundary conditions are unknown or the finite element model is inaccurate.Taking the seven-story plane frame structure as an example,the transcendental probabilities of reconstruction response under different variable distributions and different thresholds are compared.Then the influence of measurement noise on stochastic response reconstruction is studied,and the contribution of finite uncertain factors to reconstructed dynamic response and dynamic reliability is analyzed.It is verified that SSRRM has high computational efficiency and accuracy by comparing with other methods.