...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Calculation of Hessian under constraints with applications to Bayesian system identification
【24h】

Calculation of Hessian under constraints with applications to Bayesian system identification

机译：约束条件下的Hessian计算及其在贝叶斯系统辨识中的应用

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

In Bayesian system identification with globally identifiable models, the posterior (i.e., given data) probability density function (PDF) of model parameters can be approximated by a Gaussian PDF. The most probable value (MPV) of the parameters is equal to the mean of the Gaussian PDF. It maximises the posterior PDF, or equivalently, minimises the negative of logarithm (NL) of the posterior PDF. The covariance matrix of the Gaussian PDF is equal to the Hessian of the NL at the MPV. Model parameters can be subjected to constraints, which must be accounted for in the calculation of the posterior covariance matrix. In applications such as modal identification, existing strategies define a set of free parameters and map them to the model parameters so that the constraints are always satisfied. The Hessian of the NL with respect to the free parameters is obtained and then transformed to give the posterior covariance matrix of the model parameters where constraints are accounted for. Analytical expressions for this Hessian are complicated because of the composite actions of the NL and the mapping; and this creates significant burden in computer coding. In this work, a theoretical framework is developed for evaluating the Hessian of a function under constraints in a systematic manner. It is applied to obtain new analytical expressions for evaluating the posterior covariance matrix in Bayesian operational modal analysis. The resulting expressions are simpler than existing ones based on direct differentiation. They allow problems with similar mathematical structures to be computer-coded in a coherent manner. Numerical examples are presented to illustrate consistency and computational aspects. (C) 2017 Elsevier B.V. All rights reserved.
机译：在具有全局可识别模型的贝叶斯系统识别中，模型参数的后验（即给定数据）概率密度函数（PDF）可以由高斯PDF近似。参数的最可能值（MPV）等于高斯PDF的平均值。它使后PDF最大化，或者等效地，使后PDF的对数（NL）的负数最小。高斯PDF的协方差矩阵等于MPV上NL的Hessian。模型参数可能会受到约束，这必须在后协方差矩阵的计算中加以考虑。在模态识别等应用中，现有策略定义了一组自由参数并将其映射到模型参数，以便始终满足约束条件。获得关于自由参数的NL的Hessian，然后将其转换为考虑约束的模型参数的后协方差矩阵。由于NL和映射的复合作用，该Hessian的解析表达式很复杂。这给计算机编码带来了沉重的负担。在这项工作中，建立了一个理论框架来系统地评估约束条件下的函数的黑森州。它被用于获得新的分析表达式，以评估贝叶斯操作模态分析中的后协方差矩阵。结果表达式比基于直接区分的现有表达式更简单。它们允许将具有相似数学结构的问题以连贯的方式进行计算机编码。给出了数值示例以说明一致性和计算方面。 （C）2017 Elsevier B.V.保留所有权利。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号