Optimal experimental design for linear time invariant state-space models

Belmiro P. M. Duarte; Anthony C. Atkinson; Nuno M. C. Oliveira

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Optimal experimental design for linear time invariant state-space models

机译：线性时间不变状态空间模型的最佳实验设计

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摘要

The linear time invariant state–space model representation is common to systems from several areas ranging from engineering to biochemistry. We address the problem of systematic optimal experimental design for this class of model. We consider two distinct scenarios: (i) steady-state model representations and (ii) dynamic models described by discrete-time representations. We use our approach to construct locally D-optimal designs by incorporating the calculation of the determinant of the Fisher Information Matrix and the parametric sensitivity computation in a Nonlinear Programming formulation. A global optimization solver handles the resulting numerical problem. The Fisher Information Matrix at convergence is used to determine model identifiability. We apply the methodology proposed to find approximate and exact optimal experimental designs for static and dynamic experiments for models representing a biochemical reaction network where the experimental purpose is to estimate kinetic constants.

机译：线性时间不变状态空间模型表示对于来自工程到生物化学的几个区域的系统是共同的。我们解决了这类模型系统最优实验设计问题。我们考虑了两个不同的情景：（i）通过离散时间表示描述的稳态模型表示和（ii）动态模型。我们利用我们在非线性编程配方中结合了FISHER信息矩阵的确定性和参数敏感性计算来构造本地D-OPTEMAL设计的方法。全局优化求解器处理产生的数值问题。收敛处的Fisher信息矩阵用于确定模型可识别性。我们应用提出的方法，以查找近似和精确的最佳实验设计，用于代表实验目的是估计动力学常数的生物化学反应网络的模型的静态和动态实验。

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来源
《Statistics and computing》 |2021年第4期|45.1-45.20|共20页
作者
Belmiro P. M. Duarte; Anthony C. Atkinson; Nuno M. C. Oliveira;
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作者单位

Instituto Superior de Engenharia de Coimbra Department of Chemical and Biological Engineering Instituto Politécnico de Coimbra Rua Pedro Nunes Quinta da Nora 3030–199 Coimbra Portugal|CIEPQPF Department of Chemical Engineering University of Coimbra Rua Sílvio Lima – Pólo II 3030-790 Coimbra Portugal;

Department of Statistics London School of Economics London WC2A 2AE UK;

CIEPQPF Department of Chemical Engineering University of Coimbra Rua Sílvio Lima – Pólo II 3030-790 Coimbra Portugal;

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正文语种 eng
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关键词
Optimal design of experiments; Linear time invariant systems; State-space models; Model identifiability; Biochemical reaction networks; 62K05; 90C47;

机译：实验最优设计;线性时间不变系统;状态空间模型;模型可识别性;生物化学反应网络;62k05;90c47;

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1. Linear Optimal FIR Estimation of Discrete Time-Invariant State-Space Models [J] . Shmaliy Y. S. Signal Processing, IEEE Transactions on . 2010,第6期

机译：离散时不变状态空间模型的线性最优FIR估计
2. Explaining savings for visuomotor adaptation: linear time-invariant state-space models are not sufficient. [J] . Zarahn E, Weston GD, Liang J, Journal of Neurophysiology . 2008,第5期

机译：解释视觉运动适应的节省：线性时不变状态空间模型是不够的。
3. A numerical identifiability test for state-space models application to optimal experimental design [J] . Hidalgo ME., Ayesa E. Water Science and Technology . 2001,第7期

机译：用于状态空间模型的数值可识别性测试在最佳实验设计中的应用
4. Optimal input design for parameter estimation in nonlinear state-space models using Pontryagin's minimum principle [C] . Karel J. Keesman IFAC Symposium on System Identification . 2016

机译：使用Pontryagin最低原理的非线性状态空间模型参数估计的最佳输入设计
5. Estimation methods for linear, nonlinear, and multivariate time series: Applications of state-space modeling. [D] . Metoyer, Candace Noelle. 2007

机译：线性，非线性和多元时间序列的估计方法：状态空间建模的应用。
6. Investigation into the optimal linear time-invariant lag correction for radar artifact removal [O] . Jared Starman, Josh Star-Lack, Gary Virshup, -1

机译：去除雷达伪像的最佳线性时不变滞后校正研究
7. Explaining Savings for Visuomotor Adaptation: Linear Time-Invariant State-Space Models Are Not Sufficient [O] . Zarahn, Eric, Weston, Gregory D., Liang, Johnny, 2008

机译：解释节省动力运动的适应性：线性时不变状态空间模型不充分

Optimal experimental design for linear time invariant state-space models

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