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1 Journal of Achievements in Materials and Manufacturing Engineering

1 2011

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Demonstration of First-Principle Data-Driven models using numerical case studies

Czop P., Sławik D., Wszołek G.

Journal of Achievements in Materials and Manufacturing Engineering

2011

Vol. 45, nr 2

170--177

Purpose: The paper consists of two parts. The first part presents and discusses a process of formulation and identification of First-Principle Data-Driven (FPDD) models, while the second part demonstrates numerical examples of identification of FPDD models. Design/methodology/approach: First-Principle (FP) model is formulated using a system of continuous ordinary differential equations capturing usually nonlinear relations among variables of the model. The considering model applies three categories of parameters: geometrical, physical and phenomenological. Geometrical and physical parameters are deduced from construction or operational documentation. The phenomenological parameters are the adjustable ones, which are estimated or adjusted based on their roughly known values, e.g. friction/damping coefficients. Findings: A few phenomenological parameters were successfully estimated from numerically generated data. The error between the true and estimated value of the parameter occurred, however its magnitude is low at level below 2%. Research limitations/implications: Adjusting a model to data is, in most cases, a non-convex optimization problem and the criterion function may have several local minima. This is a case when multiple parameters are simultaneously estimated. Practical implications: FPDD models are an excellent tool for understanding, optimizing, designing, and diagnosing technical systems since they are updatable using operational measurements. This opens application area, for example, for model-based design and early warning diagnostics. Originality/value: First-Principle (FP) models are frequently adjusted by trial-and-error, which can lead to non-optimal results. In order to avoid deficiencies of the trial-and-error approach, a formalized mathematical method using optimization techniques to minimize the error criterion, and find optimal values of tunable model parameters, was proposed and demonstrated in this work.