Biological Cell Models and Atomic Force Microscopy - Parameter Estimation with Parallel Computing
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Through several decades, mathematical models have been used to describe real systems. Studying these mathematical models can give us important information about the system and its behavior. The Atomic Force Microscopy (AFM) has been described with a mathematical model and the hope is to identify and estimate unknown parameters. This thesis presents a parameter estimation method for identifying unknown parameters in the system using parallel computing. Introducing a variety of mathematical expression that give base to a set of analyzing tools. These were used to evaluate how the estimated parameter converged to the real values. These simulations were split into experiments, that changed one or multiple parameters that affected the properties of the system. Our experiments illustrated how we can improve the convergence of estimated parameters by tuning parameters that effect the properties of the system with basic analyzing tools (bias, relative tolerance and rate of convergence). The simulations performed, based on previous work, found a gain matrix were the estimated parameters converged exponentially fast to the real values. The results shows that our system contains two local minimizers when optimizing the gain matrix. The cantilever dynamics were described in a linear-in-parameter form, and both the known and unknown parameters were defined along with a filter. This means that the cantilever dynamic can be simulated when finding a input signal that is PE.