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

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.

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Using a variance-based sensitivity analysis for analyzing the relation between measurements and unknown parameters of a physical model

Nonlinear Processes in Geophysics ◽

10.5194/npg-18-269-2011 ◽

2011 ◽

Vol 18 (3) ◽

pp. 269-276 ◽

Cited By ~ 10

Author(s):

J. Zhao ◽

C. Tiede

Keyword(s):

Sensitivity Analysis ◽

Uncertainty Analysis ◽

Physical Model ◽

Three Dimensional ◽

Computational Procedure ◽

Fixed Number ◽

Volcanic Area ◽

Unknown Parameters ◽

Linear Inversion ◽

Input Parameters

Abstract. An implementation of uncertainty analysis (UA) and quantitative global sensitivity analysis (SA) is applied to the non-linear inversion of gravity changes and three-dimensional displacement data which were measured in and active volcanic area. A didactic example is included to illustrate the computational procedure. The main emphasis is placed on the problem of extended Fourier amplitude sensitivity test (E-FAST). This method produces the total sensitivity indices (TSIs), so that all interactions between the unknown input parameters are taken into account. The possible correlations between the output an the input parameters can be evaluated by uncertainty analysis. Uncertainty analysis results indicate the general fit between the physical model and the measurements. Results of the sensitivity analysis show quite different sensitivities for the measured changes as they relate to the unknown parameters of a physical model for an elastic-gravitational source. Assuming a fixed number of executions, thirty different seeds are observed to determine the stability of this method.

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

Journal of Manufacturing Science and Engineering ◽

10.1115/1.4052710 ◽

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.

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Global sensitivity analysis of the climate–vegetation system to astronomical forcing: an emulator-based approach

Earth System Dynamics Discussions ◽

10.5194/esdd-5-901-2014 ◽

2014 ◽

Vol 5 (2) ◽

pp. 901-943 ◽

Cited By ~ 5

Author(s):

N. Bounceur ◽

M. Crucifix ◽

R. D. Wilkinson

Keyword(s):

Sensitivity Analysis ◽

Land Surface ◽

Global Sensitivity Analysis ◽

Climate Model ◽

Arctic Sea Ice ◽

Growing Degree Days ◽

Degree Days ◽

Global Sensitivity ◽

Non Linear ◽

Astronomical Forcing

Abstract. A global sensitivity analysis is used to describe the response of the Earth Climate Model of Intermediate Complexity LOVECLIM to components of the astronomical forcing (longitude of perihelion, obliquity, and eccentricity) assuming interglacial boundary conditions. Compared to previous studies, the sensitivity is global in the sense that it considers the full range of astronomical forcing that occurred during the Quaternary. We provide a geographical description of the variance due to the different components and their combinations and identify non-linear responses. The methodology relies on the estimation of sensitivity measures, which due to the computational cost of LOVECLIM cannot be obtained directly. Instead, we use a fast surrogate of the climate model, called an emulator, in place of the simulator. A space filling design (a maximin Latin hypercube constrained to span the range of astronomical forcings characterising the Pleistocene) is used to determine a set of experiments to run, which are then used to train a reduced-rank Gaussian process emulator. The simulator outputs considered are the principal modes of the annual mean temperature, precipitation, and the growing degree days, extracted using a principal component analysis. The experiments are run on two distinct land surface schemes to address the effect of vegetation response on climate. Sensitivity to initial conditions is also explicitly assessed. Precession and obliquity are found to contribute equally to growing degree days (GDD) in the Northern Hemisphere, and the effects of obliquity on the response of Southern Hemisphere temperature dominate precession effects. Further, compared to the original land-surface scheme with fixed vegetation, the LOVECLIM interactive vegetation induces non-linear responses in the Sahel-Sahara and Arctic sea-ice area. Finally, we find that there is no synergy between obliquity and precession.

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