| 引用本文: | 赵录峰,吕震宙,王璐.随机-区间混合不确定性多输出模型确认指标[J].哈尔滨工业大学学报,2018,50(4):78.DOI:10.11918/j.issn.0367-6234.201706126 |
| ZHAO Lufeng,LU Zhenzhou,WANG Lu.Validation metric for multi-output model with mixed uncertainty of random and interval variables[J].Journal of Harbin Institute of Technology,2018,50(4):78.DOI:10.11918/j.issn.0367-6234.201706126 |
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| 摘要: |
| 为解决随机和区间变量共存条件下的多输出模型确认问题，提出了一种新的模型确认指标.首先，依据概率方法和区间理论，分析了随机输入变量在实现值条件下随机-区间混合不确定性多输出模型的特点；然后，将基于马氏距离的随机不确定性多输出模型确认方法，推广到随机-区间混合不确定性因素影响下的多输出模型确认之中，定义了一种新的多输出模型确认指标.该指标运用模型输出响应量与试验输出响应量的上、下界马氏距离分布函数曲线之间的面积差异，度量随机-区间混合不确定性条件下多输出模型预测结果与试验结果之间的不一致性.最后，讨论了所提指标的数学性质，给出了指标的计算方法和步骤，通过一个数值算例和一个工程算例验证了指标的正确性与有效性.研究结果表明，当样本数据量充足时，新的模型确认指标能够有效地度量模型输出响应量与试验结果之间差异程度，正确地判断不同多输出模型的优劣，适合于随机-区间混合不确定性因素影响下的多输出模型确认问题.
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| 关键词: 模型确认 指标 随机变量 区间变量 混合不确定性 多输出模型 |
| DOI：10.11918/j.issn.0367-6234.201706126 |
| 分类号:O212.4；TP391.9 |
| 文献标识码:A |
| 基金项目:国家自然科学基金(51475370)；中央高校基本科研业务费专项资金(3102015BJ(II)CG009) |
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| Validation metric for multi-output model with mixed uncertainty of random and interval variables |
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ZHAO Lufeng,LU Zhenzhou,WANG Lu
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(School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China)
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| Abstract: |
| Aiming at dealing with the model validation issue for multi-output model with the mixture of random and interval inputs, a new model validation metric is proposed. Based on the probability method and interval theory, characteristics of multi-output model involving both random and interval inputs under the fixed random variables are analyzed. The new multi-output model validation metric is defined by extending the multi-output model validation method based on Mahalanobis distance (MD) under random inputs to multi-output model with the mixture of random and interval inputs. This metric provides a comparison between the MD cumulative distribution function (CDF) curves of the upper and lower bounds from model responses to which from experimental one, and meanwhile shows disagreement with model predictions and corresponding physical observations. Finally, estimation procedures are presented with a discussion of new metric properties and the correctness and effectiveness of the proposed metric are demonstrated by a numerical and an engineering case, respectively. Results show that: the new metric, on one hand, is able to measure the difference between system responses with experimental results under sufficient physical observations; and, on the other hand, can correctly differentiate models in worse or better accuracy.
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| Key words: model validation metric random variable interval variable mixed uncertainty multi-output model |
