Traversing the fuzzy valley: problems caused by reliance on default simulation and parameter identification programs for discontinuous models

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-berg-Marquardt 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.