Research On Sparse Regression Uncertainty Interval Algorithm For Typical Dynamics Problems

The analysis of engineering problems can be affected by many uncertainties,and even small uncertainty can lead to large error or accident.Thus,the quantification of uncertainties is an active field in academic research and engineering.Many methods have been developed for the uncertainty estimation,and those methods can be described by two classes:probabilistic methods and non-probabilistic methods.The probabilistic methods are suitable for the quantification of the uncertainties whose statistical information is available.The non-probabilistic methods can be used when probabilistic methods are unavailable or have deviations in description for uncertain problems.Especially,the non-probabilistic methods can give a better description and quantification for some specific epistemic uncertainty.These epistemic uncertainties may be introduced by incomplete statistical information,idealized mathematical modeling,simplified modeling,etc.Among the non-probabilistic methods,interval method is widely used for the quantification of the uncertainties because the uncertain boundaries are easy to determine and the interval analysis are easy to implement.However,the existing approximate interval algorithms are inefficient and have more overestimation when the uncertain parameters are increased.Therefore,the research on high-efficiency and widely applicable interval algorithm is of great significance.Based on the characteristics of interval algorithm constructed on surrogate model,this thesis presents the general features and universal design pattern.The general features of this type of algorithm require that the surrogate model is composed of basis functions and coefficients,and the interval analysis can be applied to the basis functions.The universal design pattern divides the algorithm into four independent parts:sampling,selection of basis function,calculation of coefficients and interval analysis.This pattern can largely facilitate the development of relevant algorithm and improve the ability to deal with uncertain problems.After the employment of sparse regression in the calculation of coefficients,a new interval algorithm can be established by high-dimension basis functions with lower sample size.For typical dynamics problems,this thesis studies the construction of interval algorithms based on polynomial surrogate model and their efficiency.The proposed algorithms are applied to estimate the interval of the dynamics responses under the effect of uncertainties.The primary work is summarized as followings.Firstly,an uncertain estimation interval algorithm based on sparse regression and orthogonal polynomial surrogate model is presented.The sparse regression Chebyshev interval method is proposed on the background of the dynamic problem which can be modeled by ODEs.In this method,the low degree basis functions constructed by the tensor product of Chebyshev polynomials are selected to reduce the items in regression analysis without loss of precision.The sparse regression named as "Elastic net" is adopted to further decrease the sample size.The Chebyshev interval method improves the efficiency in the construction of polynomial surrogate model.Moreover,this method reduces the overestimation of Chebyshev interval methods by using the functionalities of shrinkage and selection in sparse regression.The parallel sparse regression Legendre interval method is proposed on the background of DAEs formulized multi-body dynamics systems.The Legendre polynomials are used to guarantee the efficiency and accuracy,and a certain type of trigonometric Legendre polynomials are adopted to reduce the overestimation effect in interval analysis.Furthermore,a parallel strategy is proposed to improve the efficiency of implementation for interval algorithm on dynamics problem,which computes the samples and interval estimation in each discrete time simultaneously.Secondly,an uncertain boundary estimation algorithm for control and state variables in the optimal control system with non-probability uncertain parameters is proposed.The interval model is used in the description of the optimal control problem with uncertain parameters,which only needs the uncertain interval bounds of the input uncertain parameters.The non-intrusive polynomial surrogate model based interval algorithm is adopted,which transforms the uncertain optimal control problem into a set of optimal control problems with deterministic variables.The proposed algorithm can perform the uncertain estimation of an optimal control system by using the existing algorithms of solving the optimal control problem.The presented strategy is applied to the collision estimation for spacecraft swarm reconfiguration with uncertain boundary,and effectively predict the possible collision cases and their collision position and time.Finally,a new architecture for surrogate model based interval algorithm is designed based on the service-oriented programming technique in SiPESC.In this architecture,the concept of service-oriented is introduced into the software development for interval algorithm,surrogate model and experiment design.This architecture has a highly flexible developing pattern which contains model,algorithm,parameter and manager,and meets the requirements from both engineering practice and algorithm benchmark.Based on the designed architecture,a series of surrogate model interval algorithms and its relevant surrogate model and experiment design are implemented.In the end,scripting programming languages are utilized to exhibit the function of the developed software in a convenient and flexible manner.