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

2021 ◽  
pp. 1-13
Author(s):  
Johannes Ellinger ◽  
Thomas Semm ◽  
Michael F. Zäh
Keyword(s):  
Sensitivity Analysis ◽  
Machine Tool ◽  
Parameter Identification ◽  
Machine Tools ◽  
Global Sensitivity Analysis ◽  
Reference Model ◽  
Evaluation Criteria ◽  
Unknown Parameters ◽  
Global Sensitivity ◽  
Process Simulations

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.

scholarly journals Deeper understanding of non-linear geodetic data inversion using a quantitative sensitivity analysis

2005 ◽  
Vol 12 (3) ◽  
pp. 373-379 ◽  
Author(s):  
C. Tiede ◽  
K. Tiampo ◽  
J. Fernández ◽  
C. Gerstenecker
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Unknown Input ◽  
Volcanic Area ◽  
Unknown Parameters ◽  
Linear Inversion ◽  
Reliable Determination ◽  
Global Sensitivity ◽  
Non Linear ◽  
Input Parameters

Abstract. A quantitative global sensitivity analysis (SA) is applied to the non-linear inversion of gravity changes and displacement data which measured in an active volcanic area. The common inversion of this data is based on the solution of the generalized Navier equations which couples both types of observation, gravity and displacement, in a homogeneous half space. The sensitivity analysis has been carried out using Sobol's variance-based approach which produces the total sensitivity indices (TSI), so that all interactions between the unknown input parameters are taken into account. Results of the SA show quite different sensitivities for the measured changes as they relate to the unknown parameters for the east, north and height component, as well as the pressure, radial and mass component of an elastic-gravitational source. The TSIs are implemented into the inversion in order to stabilize the computation of the unknown parameters, which showed wide dispersion ranges in earlier optimization approaches. Samples which were computed using a genetic algorithm (GA) optimization are compared to samples in which the results of the global sensitivity analysis are integrated by a reweighting of the cofactor matrix in the objective function. The comparison shows that the implementation of the TSI's can decrease the dispersion rate of unknown input parameters, producing a great improvement the reliable determination of the unknown parameters.

Benefits of Global Sensitivity Analysis and Reduced Order Modeling for Basin-Scale Process Simulations

2021 ◽  
Author(s):  
Denise Degen ◽  
Mauro Cacace ◽  
Cameron Spooner ◽  
Magdalena Scheck-Wenderoth ◽  
Florian Wellmann
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Sensitivity Analyses ◽  
Rock Properties ◽  
Reduced Basis ◽  
Global Sensitivity ◽  
Temporal Domain ◽  
Basin Scale ◽  
Process Simulations ◽  
Basis Method

<p>Geophysical process simulations pose several challenges including the determination of i) the rock properties, ii) the underlying physical process, and iii) the spatial and temporal domain that needs to be considered.</p><p>Often it is not feasible or impossible to include the entire complexity of the given application. Hence, we need to evaluate the consequences of neglecting certain processes, properties, etc. by using, for instance, sensitivity analyses. However, this evaluation is for basin-scale application non-trivial due to the high computational costs associated with them. These high costs arise from the high-dimensional character of basin-scale applications in the parameter, spatial, and temporal domain.</p><p>Therefore, this evaluation is often not performed or via computationally fast algorithms as, for example, the local sensitivity analysis. The problem with local sensitivity analyses is that they cannot account for parameter correlations. Thus, a global sensitivity analysis is preferential. Unfortunately, global sensitivity analyses are computationally demanding.</p><p>To allow the usage of global sensitivity analysis for a better evaluation of the changes in the influencing parameters, we construct in this work a surrogate model via the reduced basis method.</p><p>The reduced basis method is a model order reduction technique that is physics-preserving.  Hence, we are able to retrieve the entire state variable (i.e. temperature) instead of being restricted to the observation space.</p><p>To showcase the benefits of this methodology, we demonstrate with the Central European Basin System how the influences of the thermal rock properties change when moving from a steady-state to a transient system.</p><p>Furthermore, we use the case study of the Alpine Region to highlight the influences of the spatial distribution of measurements on the model response. This latter aspect is especially important since measurements are often used to calibrate and validate a given geological model. Thus, it is crucial to determine which amount of bias is introduced through our commonly unequal data distribution.</p>

A new geometric error budget method of multi-axis machine tool based on improved value analysis

2018 ◽  
Vol 232 (22) ◽  
pp. 4064-4083 ◽  
Author(s):  
Qiang Cheng ◽  
Lifang Dong ◽  
Zhifeng Liu ◽  
Jiaying Li ◽  
Peihua Gu
Keyword(s):  
Sensitivity Analysis ◽  
Correlation Analysis ◽  
Machine Tool ◽  
Global Sensitivity Analysis ◽  
Geometric Error ◽  
Machining Accuracy ◽  
Analysis Method ◽  
Value Analysis ◽  
Error Budget ◽  
Global Sensitivity

The improvement of the accuracy grade of main components in the production process through balancing between function and cost helps to improve the overall accuracy of machine tools. Therefore, this paper presents an improved value analysis method and uses the method of global sensitivity analysis and geometric error correlation analysis to analyze and optimize the error parameters of a 4-axis machining tool based on the proposed method. The geometric error modeling of the 4-axis machine tool was established by using the homogeneous transformation matrices (HTMs). By using global sensitivity analysis, the degree of influence of each error parameter on the accuracy of machine tool was obtained, and functional coefficient and cost coefficient of value analysis were gained by correlation analysis. An optimization model for geometric error budget of machine tool was established according to the improved value analysis theory, and the machining accuracy of machine tool was optimized according to the improved value analysis method.

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