The novel method for parameter estimation for large bio-systems

Abstract

In this thesis we propose a new method for the parameter identification of large-scale models. The proposed state substitution method can be applied to parametric, non parametric or hybrid models, but in this work, we will focus on the parametric models, to show methods capabilities of identifying all parameter values. The method aims to decouple the whole system into separate sub-systems, whose parameters can be identified separately, therefore decomposing the solution space. By decreasing the solution space in this manner, traditional parameter identification techniques can be used to identify the parameters of each sub-model. The solved sub-systems are subsequently combined for re-optimisation using a global solver (in this work global search), which ensures statistical optimality of the parameter values. The proposed decoupling method uses state substitution approach, i.e.: measured values (which contain process noise) are used to create a spline, which replaces coupled components in each ODE sub-system. This makes it possible to integrate each of the sub-systems separately, because the sub-systems are only dependant on the unknown model parameters. In addition, dividing the problem into smaller sections, reduces computational time significantly compared to current simultaneous solution methods. The proposed state substitution method is compared with two state-of-art approaches. The derivative method and the integral method. Both state-of-art methods and the proposed state substitution method are used to identify parameters for four different cases studies, where they performance is compared. Cases studies increase in complexity allowing comparison of how each method handles different levels of complexity. First three cases studies use simulated data sets, and fourth one uses real measured data. First case study is an artificial benchmark problem, whereas case studies two, three and four are bio-system models, with increasing complexity. This thesis also proposes ways of evaluating complexity of the system, so systems complexity can be relatively compared to other systems. This allows to assess each systems’ relative complexity, an ensure that correct parameter identification method is chosen for the parameter identification. Complexity evaluation is quantified with three different methods, Principal component analysis visualization, self-organizing map analysis and sorted minimization.