Traversing the Fuzzy Valley: Problems Caused by Reliance on Default Simulation and Parameter Identification Programs for Discontinuous Models

Abstract

The Levenberg-Marquardt parameter identification method is often used in tandem with numerical Runge-Kutta model simulation to find optimal model parameter values to match measured data. However, these methods can potentially find erroneous parameter values. The problem is exacerbated when discontinuous models are analyzed.A highly parameterized respiratory mechanics model defines a pressure-volume response to a low flow experiment in an acute respiratory distress syndrome patient. Levenberg-Marquardt parameter identification is used with various starting values and either a typical numerical integration model simulation or a novel error-stepping method.Model parameter values from the error-stepping method were consistently located close to the error minima (median deviation: 0.4%). In contrast, model values from numerical integration were erratic and distinct from the error minima (median deviation: 1.4%).The comparative failure of Runge-Kutta model simulation was due to the method's poor handling of model discontinuities and the resultant lack of smoothness in the error surface. As the Leven-bergMarquardt identification system is an error gradient decent method, it depends on accurate measurement of the model-to-measured data error surface. Hence, the method failed to converge accurately due to poorly defined error surfaces.When the error surface is imprecisely identified, the parameter identification process can produce suboptimal results. Particular care must be used when gradient decent methods are used in conjunction with numerical integration model simulation methods and discontinuous models.

The Regional Conjugate Optimisation Approach: A Novel Method for Three Parameter Identification of Physiological Models

“…Such methods are typically effective for objective surfaces that are well conditioned, but can result in excessive computational cost or failed convergence when this is not the case. In particular, use of gradient descent methods for models with significant parameter tradeoff effects can lead to premature termination (Docherty et al, 2013, Docherty et al, 2012c, Docherty et al, 2012a. It has been shown that in such models, the premature termination most often occurs on the major axes of the objective surface contours (that are often elliptical).…”