| 韩旭,刘杰,陈金龙.结构多源不确定性反问题的流形学习求解方法[J].计算力学学报,2021,38(4):523~530 |
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码上扫一扫！ |
| 结构多源不确定性反问题的流形学习求解方法 |
| A combined active learning Kriging model and sequential importance sampling for hybrid reliability analysis with random and interval variables |
| 投稿时间：2021-06-01 修订日期：2021-06-15 |
| DOI：10.7511/jslx20210601414 |
| 中文关键词: 反问题 多源不确定性 流形学习 多边凸集 λ-PDF |
| 英文关键词:inverse problem multi-source uncertainties manifold learning polygonal convex set λ-PDF |
| 基金项目:国家自然科学基金（51621004；51975199）资助项目. |
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| 摘要点击次数: 670 |
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| 中文摘要: |
| 针对同时考虑测量不确定性和模型不确定性的工程反问题，提出了基于混合度量和流形学习的多源不确定性计算反求方法，高效地实现了未知结构参量的不确定性度量与识别。测量响应中的不确定性采用概率模型进行度量，建模参量的不确定性采用非概率多边凸集模型进行度量。通过建立模型参量与待反求参量累积分布函数之间的流形学习映射模型，实现了测量不确定性反问题与模型不确定性反问题的解耦，将复杂的多源不确定性反问题转化为少数测量不确定性反问题。在此转化过程中，流形学习方法将高维的累积分布函数曲线转化为低维流形空间中特征参数，通过模型参量与特征参数之间的映射模型，实现给定模型参量下相应的反求参量概率分布函数的快速预测。进一步利用衍生λ-PDF和降维积分方法，将测量不确定性反问题转化为少数确定性反问题进行求解，并利用P-box模型对反求参量的不确定性进行度量。本文提出的方法不仅能实现反求参量的高效识别，而且能准确地量化测量不确定性和模型不确定性对反求参量的综合影响。 |
| 英文摘要: |
| In order to effectively solve the multi-source uncertain inverse problem coupling response uncertainties and model uncertainties, the manifold learning method with mixed uncertainty quantification is proposed to realize the identification of uncertainties of the unknown structural parameters. The uncertainties from the measured responses are quantified by using the probability model, and the uncertainties from the modeling parameters are quantified by using the polygon convex set model. By establishing a manifold mapping model between model parameters and the cumulative distribution function (CDF) of unknown parameters, the proposed method realizes the decoupling of the uncertainties from responses and model, and transforms the multi-source uncertain inverse problem into the inverse problem with uncertainty from the measured responses. The manifold learning method can transform the high-dimensional CDF into the characteristic parameters in the low dimensional manifold space. Through establishing the mapping relationship between model parameters and characteristic parameters, the CDF of the inversed parameters under the specific model parameters can be rapidly predicted. Further more, the derivative λ-PDF and dimension reduction integral method is proposed to realize the transformation from the inverse problem considering uncertain measured responses into a deterministic inverse problem. The P-box model is adopted to quantify the uncertainty of the inverse parameters. The proposed method can not only realize the effective identification of the unknown parameters, but also accurately quantify the comprehensive impact of the response uncertainties and model uncertainties on the inverse results. |
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