Dimensionality Reduction of High-Fidelity Machine Tool Models by Using Global Sensitivity Analysis

Abstract

Models that are able to accurately predict the dynamic behavior of machine tools are crucial for a variety of applications ranging from machine tool design to process simulations. However, with increasing accuracy, the models tend to become increasingly complex, which can cause problems identifying the unknown parameters which the models are based on. In this paper, a method is presented that shows how parameter identification can be eased by systematically reducing the dimensionality of a given dynamic machine tool model. The approach presented is based on ranking the model's input parameters by means of a global sensitivity analysis. It is shown that the number of parameters, which need to be identified, can be drastically reduced with only limited impact on the model's fidelity. This is validated by means of model evaluation criteria and frequency response functions which show a mean conformity of 98.9 % with the full-scale reference model. The paper is concluded by a short demonstration on how to use the results from the global sensitivity analysis for parameter identification.

Automated Identification of Linear Machine Tool Model Parameters Using Global Sensitivity Analysis

“…In other words, modes can be found that are only affected by a handful of model parameters, leading to the desired partitioning of the overall identification problem. More information can be found in [20], where this was already shown exemplarily.…”

“…As the model's damping parameters do not influence the simulated mode shapes and eigenfrequencies (see Assumption A1 in Section 2.1), the overall identification problem can be further simplified by determining the stiffness parameters first. The partitioning via GSAs leads to N modes N pos (see Equation ( 10)) identification problems with only a handful of search parameters each [20]. Even though the partitioning eliminates most of the local minima of the overall optimization problem, which would lead to only locally valid and non-physical machine tool model parameters, some are still present [20].…”

“…The partitioning via GSAs leads to N modes N pos (see Equation ( 10)) identification problems with only a handful of search parameters each [20]. Even though the partitioning eliminates most of the local minima of the overall optimization problem, which would lead to only locally valid and non-physical machine tool model parameters, some are still present [20]. To overcome this problem, a brute-force approach, which is illustrated by Figure 2, is deployed here: Each of the N modes N pos smaller identification problems is repeated N opt times.…”

“…However, this is not a drawback of the presented approach, but the examined model and could be overcome with more advanced MOR approaches. The model has already been subjected to a dimensionality reduction step [20], resulting in the following 27 unknown machine tool parameters representing the lumped stiffness and damping properties of: Note that the considered machine tool system fulfills all assumptions stated in Section 2.1: Modal parameters can be simulated with high accordance [6], and the machine tool is lightly damped [11,21] (A1 and A2). Suitable bounds can, in this case, be easily chosen since the true model parameters are already known (A3).…”

“…For this, global sensitivity analysis (GSA) is used to partition the overall identification problem into smaller, solvable subproblems, in a way similar to the involvement of expert knowledge in [12,16,17]. Since this has only been demonstrated exemplarily and only with limited success [20], this is the first such implementation in the field of structural dynamic machine tool models.…”