Uncertainty estimation for linearised inverse problems comparing Bayesian inference and a pseudoinverse approach for acoustic transmission measurements

Feldmann, Nadine; Bause, Fabian; Henning, Bernd

doi:10.1515/teme-2016-0022

Cited by 3 publications

(1 citation statement)

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“…Similar trends have been observed by Eghtesadi and McAuley who compared LO and PI approaches for parameter estimation. In addition, Feldmann et al showed that the PI approach tends to give unreliable parameter estimates in study comparing PI and Bayesian approaches.…”

Section: Linear Regression Examplementioning

confidence: 99%

Sequential Model-Based A-Optimal Design of Experiments When the Fisher Information Matrix Is Noninvertible

Shahmohammadi

McAuley

2018

Ind. Eng. Chem. Res.

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The sequential model-based optimal design of experiments (e.g., A-, D-, and E-optimal design) is a well-known technique for selecting experimental conditions that lead to informative data for obtaining reliable parameter estimates and model predictions. An important computational step for selecting new model-based experiments is to compute the inverse of the Fisher information matrix (FIM) which may not be invertible. In this study, three different methodologies for selecting new experiments are compared for situations where the FIM is noninvertible. The first approach finds and leaves out problematic parameters that make FIM noninvertible and then designs experiments using a reduced FIM (LO approach). The second approach uses a Moore-Penrose pseudoinverse of the FIM in A-optimal design calculations (PI approach). The third methodology is an ad hoc approach which does not require optimization. In this MS approach, the modeler selects settings at corners of the specified design space. Comparisons are made using two linear regression models and a nonlinear dynamic model for production of a pharmaceutical agent. Monte Carlo simulation results show that experimental settings obtained by LO and PI approaches give better parameter estimates on average than the MS approach, with the LO approach giving the best estimates in 20 of 24 linear situations studied. The LO approach also gives the best parameter estimates on average for the nonlinear pharmaceutical model.

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Section: Linear Regression Examplementioning

confidence: 99%

Sequential Model-Based A-Optimal Design of Experiments When the Fisher Information Matrix Is Noninvertible

Shahmohammadi

McAuley

2018

Ind. Eng. Chem. Res.

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Using prior parameter knowledge in model‐based design of experiments for pharmaceutical production

Shahmohammadi

McAuley

2020

AIChE Journal

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Sequential model-based design of experiments (MBDoE) uses information from previous experiments to select new experimental conditions. Computation of MBDoE objective functions can be impossible due to a noninvertible Fisher information matrix (FIM). Previously, we evaluated a leave-out (LO) approach that designed experiments by removing problematic model parameters from the design process. Unfortunately, the LO approach can be computationally expensive due to its iterative nature. In this study, we propose a simplified Bayesian approach that makes the FIM invertible by accounting for prior parameter information. We compare the proposed simplified Bayesian approach to the LO approach for sequential A-optimal design. Results from a pharmaceutical case study show that the proposed approach is superior, on average, for design of experiments. We suggest that simplified Bayesian MBDoE should be combined with a subset-selection-based approach for parameter estimation. This combined methodology gave the best results on average for the case study.

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Lamb wave based approach to the determination of acoustic material parameters

Johannesmann

Claes

Feldmann

et al. 2022

Tm - Technisches Messen

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In this paper a measurement procedure to identify viscoelastic material parameters of plate-like samples using broadband ultrasonic waves is presented. Ultrasonic Lamb waves are excited via the thermoelastic effect using laser radiation and detected by a piezoelectric transducer. The resulting measurement data is transformed to yield information about multiple propagating Lamb waves as well as their attenuation. These results are compared to simulation results in an inverse procedure to identify the parameters of an elastic and a viscoelastic material model.

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Uncertainty estimation for linearised inverse problems comparing Bayesian inference and a pseudoinverse approach for acoustic transmission measurements

Cited by 3 publications

References 0 publications

Sequential Model-Based A-Optimal Design of Experiments When the Fisher Information Matrix Is Noninvertible

Sequential Model-Based A-Optimal Design of Experiments When the Fisher Information Matrix Is Noninvertible

Using prior parameter knowledge in model‐based design of experiments for pharmaceutical production

Lamb wave based approach to the determination of acoustic material parameters

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