Methods for Parameter Ranking in Nonlinear, Mechanistic Models

Abstract

The paper addresses e¢ cient methods for parameter sensitivity analysis and ranking in large, nonlinear, mechanistic models requiring examination of many points in the parameter space. The paper shows how orthogonal decomposition and permutation of the sensitivity derivative is an intuitive and structured method for automatic ranking of the parameters within a candidate set. Provided the model error is Gaussian, and with the problem on a triangularized form, the additional variance associated with each parameter can easily be found. Ranking according to additional variance is therefore another option. The methods are tested on an industrially used simulator model.

Parameter Estimation for Multistage Processes: A Multiple Shooting Approach Integrated with Sensitivity Analysis

“…Using the efficient implementation developed by Lund et al 15 and Lund and Foss, 16 the SOM exploits the fact that the QR factorization of the sensitivity matrix can be written as…”

“…The lower limit establishes a bound on how “close” the estimate is to the “true” parameter present in the output data. Despite the existence of several methods to extract and analyze the information contained in the sensitivity matrix S and the Hessian matrix H , we shall focus on the SOM proposed by Yao et al using the efficient implementation developed by Lund et al and Lund and Foss . The method of SOM makes it possible to retrieve the parameters that generate specific sensitivity directions.…”

“…Using the efficient implementation developed by Lund et al and Lund and Foss, the SOM exploits the fact that the QR factorization of the sensitivity matrix can be written as where Π is a permutation matrix, Q is an orthogonal matrix, Σ is a diagonal matrix whose nonzero elements are the magnitudes of the orthogonal fractions of the original sensitivity vectors, and R ̃ is an upper triangular matrix whose nonzero elements are the ratio between each vector and their projections onto the other normalized vectors.…”

“…The sensitivity matrix is the main object of analysis in gradientbased operational identifiability, as relevant information can be extracted from it, e.g., the magnitudes of the sensitivity vector, the collinearity indexes, etc. The information can be extracted making use of various matrix decomposition methods such as singular value decomposition (Van den Hof et al 5 ), tuning importance (Seigneur et al, 6 Turańyi, 7 and Degenring et al 8 ), principal component analysis (Jolliffe, 9 Li et al 10 and Degenring et al 8 ), eigenvalue decomposition (Vajda et al, 11 Quaiser et al, 12 and Quaiser and Monnigmann 13 ), and successive orthogonalization method (SOM) (Yao et al, 14 Lund et al, 15 and Lund and Foss 16 ). These methods allow the recognition of the subset of parameters that are identifiable based on a specific metric and cutoff value.…”

Analysis of a Quasi-Chemical Model for Bacterial Growth

“…This is implemented by using an "economy size" QR decomposition of the matrix F , so that F P = QR, where P is a permutation matrix. The order of the permutations give the ranking of the parameters where the rankings are chosen according the 2-norm of the sensitivity with respect to the parameter (see [10] for a detailed description). In [1,5] global techniques similar to those presented here were considered.…”