Research And Elementary Application On Statistical Validation Of Numerical Computation

As the technology associated is developing rapidly, and become more mature, numerical simulation, which tries to imitate the real nature, is becoming more and more perfect and widely applied, which makes it one of the three main methods to solve physical problems, equivalent to experiment research and theory analysis. Computation models, which are established according to some certain problems, must be checked before applied. Validation is the method evaluating the degree of capability of computation model to simulate the real world, and then judging whether the numerical result is believable. To accomplish all above, we need the aid of experiment data, comparing the simulation result with experiment data, and defining threshold of accepting. Validation of computation model is not merely used after the model is set up, it's also applied when the target of model, the model itself or related uncertainties change. Traditional means of validation of computation model are deficient due to the lack of quantification and objective, and don't consider the uncertainties which is present everywhere, so that the result of assessment is different person to person. However, statistical validation method overcomes such defect. It incorporates the effect of uncertainties attached to input arguments and measurement error, which affects the process and result of validation. Moreover, validation activities would first quantify those uncertainties as set off, and then get the statistical distribution of model response by the mean of propagation of uncertainties. Finally, quantifying the difference between numerical result and experiment data, and judging whether this kind of difference is significant according to the predefined threshold. This article does a thorough and comprehensive research of theory and elementary application of statistical validation, the main research and conclusion obtained are as follows:①We make a comprehensive survey on the development of statistical validation and the current situation domestic and abroad. We conclude that although statistical validation has a period of several decades from budding, until recent ten years, its foundation gradually set up. But some issues still need to be solved to get the validation improved.②Introducing the main process, basic conception and theory of statistical validation. We try to make the difference between some confusing concepts clear, and expound the related theory of probability and mathematics statistics, design of computation and validation metrics in detail.③Make an review on the common statistical validation method, including Monte Carlo, surrogate and first order sensitivity analysis method. And we make a comparative analysis on the application of the above three methods. ④We apply Monte Carlo and surrogate method to the example of damped spring mass system, to conduct propagation of uncertainty. With the help of hypothesis test and area metric, we do a quantification of the difference between computation results and experiments data. Besides, we compare the differences between them. All of these are helpful to understand the elementary concepts and procedure of statistical validation, and it's meaningful to aid solve more complicated problems.⑤We take one dimensional transient heat conduction difference program as an example, apply first order sensitivity analysis to assess the correctness of it. We either evaluate the confidence of the temperature calculated, or assess the validity of the program whose output changes to border heat flux, using the same experiment data and uncertainty model as the one above. This illustrates the realization of hierarchy validation.⑥Finally, we apply the first order sensitivity analysis to the applicability of the concrete RHT constitutive model. To achieve this, we assess the validity of the finite element model of steel projectile penetrating through concrete target board. Of the RHT constitutive model, we only take several important arguments as parameters containing uncertainty. The result shows that, at the level of 5% significance, there is no significant difference between numerical computation and experiment data, thus the RHT constitutive model is applicable.