Confidence Interval Prediction Method Of Ensemble-of-Surrogates And Its Engineering Application

Surrogate models have been widely used to replace the numerical simulation models in the process of engineering product design to reduce the expensive cost of simulation analysis and improve the design efficiency.Among them,the ensemble-of-surrogates modeling technique,which can make full use of the advantages of different individual surrogates,can avoid choosing inappropriate surrogate models and improve the global prediction accuracy of the surrogate models without increasing the calculation cost.However,the ensemble-of-surrogates based on limited sample points has the uncertainty of prediction,which may lead to the failure of the designed product performance to meet the design requirements.Therefore,how to accurately quantify the predicted uncertainty of the ensemble-of-surrogates model and construct the confidence interval of the predicted response is the key to the successful application of the ensemble-of-surrogates model in engineering product design.Therefore,this paper focuses on the uncertainty quantification method of ensemble-of-surrogates model and its application in engineering product design.The specific research work is as follows:（1）This paper compares the commonly used methods for quantifying the uncertainty of the surrogate model,and analyzes the degree of similarity between the quantization results of different methods and the true error of the ensemble-of-surrogates model under the influence of different problem dimensions,number of sample points,sampling method and noise level through numerical examples.The results show that when the design space is one-dimensional or two-dimensional,the weighted standard deviation index can well evaluate the prediction error of the surrogate model,and when the design space is larger than two-dimensional,leave-one-out error index performs best.（2）This paper proposes a confidence interval prediction method of ensemble-of-surrogates model based on prediction uncertainty,which is used to estimate the confidence intervals of the predicted values and provide necessary reference information for design decisions.In this method,the performance characteristics of weighted standard deviation and leave-one-out error are fully considered and the confidence intervals of the prediction responses of the ensemble-of-surrogates model are calculated according to the dimensions of the problem.Then,different numerical examples are used to test the performance of the proposed method,and the results show that the proposed method can accurately estimate the confidence interval of the ensemble-of-surrogates model.（3）The proposed ensemble-of-surrogates model confidence interval prediction method based on estimated uncertainty is applied to the rapid prediction of the performance of bionic net.In this paper,a finite element model of the bionic net was built,and a simulated water tank test platform was built to test the small-scale bionic net model to verify the accuracy of the simulation model.Then,the proposed confidence interval prediction method of the ensemble-of-surrogates was used to predict the performance responses of the bionic net under different floating-ball sizes,robot masses and underwater flow velocities.The results show that the relative error of the prediction response of the ensemble-of-surrogates is less than 5%,and the confidence interval can well envelop the variation range of the real value,which verifies the engineering applicability of the proposed method.