Research On Inverse Problem Of Seepage Field Based On Differential Evolution Algorithm And Reduced-Order Model

The development of China's hydropower resources has gradually progressed to remote areas in the west.The dam sites of large-scale water conservancy and hydropower projects under construction and planned are mostly located in the western region with deep river valleys and complex geological conditions.Finding out the seepage problem in the reservoir area is very important for the construction and safety management of water conservancy and hydropower projects.The hydraulic conductivity of rock and soil is one of the key parameters to control the groundwater seepage characteristics.The unknown hydraulic conductivity will have a serious impact on the reliability of groundwater simulation.Because the permeability of engineering rock mass often has spatial variability,the traditional field test method alone cannot meet the engineering requirements.Parameter estimation using inverse model is an important part of groundwater simulation.As a typical inversion method,a simulation-optimization method that combines a numerical model and an optimization algorithm requires multiple calls to the numerical model to evaluate a large number of randomly generated candidate solutions.Even with high-speed processors,parameter inversion is a very time-consuming and computationally intensive task.In this paper,the time-consuming problem of simulation-optimization method is studied.On the premise of minimizing the error,the method of reducing the time cost of simulation-optimization method is studied from the three aspects of optimization algorithm,inversion parameters and numerical model.Since the hydraulic head is a nonlinear function of hydraulic conduction coefficient,this paper uses differential evolution algorithm as an optimization algorithm for parameter inversion.The main research contents and results are as follows:(1)The relationship between model calibration and parameter inversion is described,the method of combining the finite element software ADINA and the optimization algorithm is given,and the simulation-optimization model(ADINA-MMRDE)for estimating hydraulic conductivity is established.An example is used to illustrate the importance of parameter sensitivity analysis in parameter inversion.The effects of different objective functions,measurement errors and population size on the performance of the ADINA-MMRDE model are studied.The results show that the objective function has little effect on ADINA-MMRDE,and ADINA-MMRDE is very sensitive to measurement errors.Compared with the ADINA-DE and ADINA-PSO models combined with other optimization algorithms,the ADINA-MMRDE model has higher inversion accuracy and can search for the global optimal solution faster and more stably.(2)Aiming at the problems of slow convergence rate,poor global convergence,and algorithm stagnation of the classic differential evolution algorithm,a new mutation strategy with both local and global convergence performance is proposed.Based on this mutation strategy,a differential evolution algorithm(MMRDE)based on multiple mutation strategies for roulette selection is further proposed.After 49 test function tests,the results show that,compared with some improved differential evolution algorithms,MMRDE can achieve a better balance between exploration and exploitation.(3)In order to reduce the calculation time of the model under the premise of ensuring the simulation accuracy,the order reduction mechanism,construction steps and error estimation method of the order reduction model technology based on the projection method(the proper orthogonal decomposition method and the greedy sample method)are described.The iteration termination conditions of the greedy sample method are improved,the computational cost of the proper orthogonal decomposition method and the greedy sample method are compared,and the performance of the two in the parameter set,grid density and number of parameters are also compared.The results show that when the sample size is small,different sample set generation methods have a greater impact on the reduced-order accuracy;the element size affects the construction time of the reduced-order model,but has little effect on the accuracy of the reduced-order model;The time-saving advantage of the reduced-order model is more obvious.(4)Aiming at some key programming difficulties in applying model reduction technique to parameter inversion,a permeation matrix processing program is designed that integrates identification inversion parameters,matrix blocking technology and boundary processing.A set of efficient memory storage solutions is designed to solve the problem of insufficient memory caused by using the traditional finite element Skyline sparse storage format.Aiming at the problem of hydraulic head calculation when the borehole position is not on the grid node,a finite element interpolation program based on the MMRDE algorithm proposed in this paper is proposed to interpolate the hydraulic head at the borehole.A parameter inversion program(ROM-MMRDE)based on a reduced-order model was designed,and an example was used to test its inversion accuracy,sensitivity to observation errors and time cost.The results show that the greedy sample method with a training parameter scale of 500 is recommended for parameter inversion;The parameter inversion procedure based on the reduced-order model and the original model are very similar to the error sensitivity and inversion accuracy,but the time-consuming difference is large;When the 3D model in the example is used under the same computing power,the inversion time of the parameter inversion program using the reduced-order model is about 16.67%of the full-order model,so it can significantly save time and cost.(5)The inversion procedures based on the ADINA model and the reduced-order model are used together to estimate the permeability coefficient of the dam foundation rock mass of a hydropower station.Both inversion procedures integrate the MMRDE algorithm proposed in this paper.An initial seepage field analysis model(inversion model)was established to estimate the permeability coefficient,and a project operation period model was established on the basis of the inversion model to verify the inversion effect.There are 20 borehole water levels in the exploration period and 13 dam monitoring hole water level data.The former is used as the observation data of parameter inversion,and the latter is used to verify the inversion results.The results show that the difference between the inversion results of the two inversion models is small,but the time cost of the inversion procedure based on the reduced order model is much smaller than that based on the ADINA model(when the dimensions are 6 and 13,the inversion time can be saved by about 19.1 and 21.4 times respectively).Therefore,when using the MMRDE algorithm proposed in this paper as an optimization algorithm,the reduced-order model can replace the original model for the inversion task of the initial seepage field of large projects.