Isight中关于近似模型误差的计算公式

cellcowboy

两年前用过Isight里面的Approximation Component，然后就当然地涉及到误差分析，因为这关系到你的近似模型的有效性。简单说就是，你的误差分析不达标，你的近似模型就没用。但是Isight用户手册没有直接写误差分析的数学公式（至少就我所知是这样），而是进行了文字描述，还是英文的。这导致了很多同学不能正确写出误差计算公式，或者甚至就不进行误差分析，真是极不正常的一件事情。最近两天有个孩子问到了这个问题，我也给TA做了讲解，也就顺便把公式写下来，供大家参考。
首先我们来上Isight用户手册的原文描述：
Average：
The differences between the actual (simulation process flow execution) and predicted (approximation model execution) values for all error samples are averaged and then normalized by the range of the actual values for each response. Therefore, the value is a fraction of the response data range for the error sample points. Normalizing the error value allows the error level of different responses with different magnitudes to be compared with respect to the quality of predictions in the approximation model.

Maximum：
The maximum difference between the actual (simulation process flow execution) and predicted (approximation model execution) values for all error samples is taken and then normalized by the range of the actual values for each response. Therefore, the value is a fraction of the response data range for the error sample points. Normalizing the error value allows the error level of different responses with different magnitudes to be compared with respect to the quality of predictions in the approximation model.

Root Mean Square：
The squared differences between the actual (simulation process flow execution) and predicted (approximation model execution) values for all error samples are averaged. The square root is taken, and the result is normalized by the range of the actual values for each response. Therefore, the value is a fraction of the response data range for the error sample points. Normalizing the error value allows the error level of different responses with different magnitudes to be compared with respect to the quality of predictions in the approximation model.

R-Squared：
The coefficient of determination is calculated based on the error samples. The coefficient of determination always ranges between 0 and 1, where 1 represents a perfect fit (or no prediction error).

参考文献：
R. JIN, W. CHEN  & SIMPSON, T. W. 2001. Comparative studies of metamodeling techniques under multiple modeling criteria. Structural and Multidisciplinary Optimization.
2015. ISIGHT 5.9 User's Guide. Providence, RI, USA.: Dassault Systèmes.

最后的最后，希望大家能enjoy这个近似模型这个模块啦！

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cellcowboy

zmc1027 发表于 2017-10-29 16:24
楼主有心了

:D:D:D:D

cellcowboy

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zmc1027

楼主有心了

a554178555

谢谢牛顿哥