Incremental Parameter Estimation under Rank-Deficient Measurement Conditions

Kris Villez,Julien Billeter,Dominique Bonvin

doi:10.3390/pr7020075

Abstract

The computation and modeling of extents has been proposed to handle the complexity of large-scale model identification tasks. Unfortunately, the existing extent-based framework only applies when certain conditions apply. Most typically, it is required that a unique value for each extent can be computed. This severely limits the applicability of this approach. In this work, we propose a novel procedure for parameter estimation inspired by the existing extent-based framework. A key difference with prior work is that the proposed procedure combines structural observability labeling, matrix factorization, and graph-based system partitioning to split the original model parameter estimation problem into parameter estimation problems with the least number of parameters. The value of the proposed method is demonstrated with an extensive simulation study and a study based on a historical data set collected to characterize the isomerization of α -pinene. Most importantly, the obtained results indicate that an important barrier to the application of extent-based frameworks for process modeling and monitoring tasks has been lifted.

Highlights

Despite advances in model identification theory, parameter estimation can still be very challenging in practice
We focus on a novel method to tackle the computational challenge associated with the identification of kinetic parameters in large dynamic models
We present the method and demonstrate its applicability to cases that could not be handled in an extent-based incremental model identification framework before

Summary

Introduction

Despite advances in model identification theory, parameter estimation can still be very challenging in practice. Such challenges include the lack of identifiability, large computational cost, the need to formulate appropriate experimental designs, and the fact that many methods, such as those for uncertainty analysis, are still being investigated and not standardized. To handle the computational challenge, it is typical to devise a protocol for model fitting and model validation. A protocol for environmental system models is proposed in [2] These protocols incorporate significant expertise specific to the particular application domain, thereby leading to protocols that are fine-tuned for that domain. While they tend to be similar on a conceptual level, it is rather difficult to apply these protocols universally

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Discussion

Conclusion