The Fisher Information Matrix as a Relevant Tool for  Sensor Selection in Engine Health Monitoring

Borguet, Sébastien; Léonard, Olivier

doi:10.1155/2008/784749

Cited by 20 publications

(14 citation statements)

References 14 publications

(14 reference statements)

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“…That literature sometimes uses Fisher information as the optimality criterion with respect to design (Borguet & Lé onard, 2008). Application of that design perspective with regard to information may provide insight into biological problems.…”

Section: Evolution Of the Coordinate Systemmentioning

confidence: 99%

Natural selection. V. How to read the fundamental equations of evolutionary change in terms of information theory

Frank

2012

J of Evolutionary Biology

120

155

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The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and regressions. Population genetic equations depend on genetic variances. How can we read those statistical expressions with respect to the meaning of natural selection? One possibility is to relate the statistical expressions to the amount of information that populations accumulate by selection. However, the connection between selection and information theory has never been compelling. Here, I show the correct relations between statistical expressions for selection and information theory expressions for selection. Those relations link selection to the fundamental concepts of entropy and information in the theories of physics, statistics and communication. We can now read the equations of selection in terms of their natural meaning. Selection causes populations to accumulate information about the environment.There are difficulties in applying information theory in genetics. They arise principally, not in the transmission of information, but in its meaning (Maynard Smith, 2000, p. 181).

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Section: Evolution Of the Coordinate Systemmentioning

confidence: 99%

Natural selection. V. How to read the fundamental equations of evolutionary change in terms of information theory

Frank

2012

J of Evolutionary Biology

120

155

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“…We have: (13) Assuming that the system is completely observable, that is r = n, applying SVD to the observability matrix Qk and substituting the result into Eq. (13) yields [18] (14) Let US defitne Ví:2í (15) From Eqs.…”

Section: Observability Matrixmentioning

confidence: 99%

“…Finally, the degree of observability of the linear model is analyzed. Provost [12] and Borguet et al [13] introduced the degree of observability analysis methods based on the influence coefficient matrix, respectively. They used the proposed method to optimize the measurement selections in gas path diagnostics.…”

Section: Introductionmentioning

confidence: 99%

A Novel Degree of Observability Used for Measurement Selections in Gas Path Diagnostics

Pu¹,

Liu²,

Jiang

et al. 2012

Journal of Engineering for Gas Turbines and Power

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A novel method for measurement selections of gas path diagnostics has been developed. This method is based on the singular value decomposition of the observability matrix of linear systems, which are a good approximation of the nonlinear ones for small deviations. It also employs the concept of'the degree of observability to formulate the criteria. The states with high degree of observability and the measurement sets with high overall degree of observability result in high estimation accuracy in gas path diagnostics. A heavy-duty gas turbine model is used to validate this method. The influence of the gas turbine nonlinearity, the measurement noise, and the overdetermined measurement on degree of observability is analyzed. The overall degree of observability is calculated for different measurement sets of heavy-duty gas turbine. The gas path diagnostics simulations with different measurement sets using the weighted least-squares estimation method and the extended Kaiman filter are conducted. The quality of gas path diagnostics simulation with different measurement sets is assessed and the results demonstrate the capability of the developed method for measurement selections in gas path diagnostics.

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“…Udwadia [3] proposed the Fisher information criterion for OSP in parameter identification, in which the optimal configuration corresponds to that maximizing the trace of the FIM. Fisher information was also introduced by Borguet & Léonard [4] in the field of engine health monitoring, where the weighted sum of the condition number, trace and determinant of the FIM was selected as the performance criterion. Papadimitriou [5] introduced the concept of information entropy for the purpose of minimizing the uncertainty in the model parameter estimation; the effect of prediction error correlation was further examined recently by Papadimitriou & Lombaert [6].…”

Section: Introductionmentioning

confidence: 99%

Robust optimal sensor placement for operational modal analysis based on maximum expected utility

Kiureghian

2016

Mechanical Systems and Signal Processing

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Optimal sensor placement is essentially a decision problem under uncertainty. The maximum expected utility theory and a Bayesian linear model are used in this paper for robust sensor placement aimedat operational modal identification.To avoid nonlinear relations between modal parameters and measured responses, we choose to optimize the sensor locations relative to identifying modal responses.Since the modal responses contain all the information necessary to identify the modal parameters, the optimal sensor locations for modal response estimation provide at least asuboptimalsolution for identification of modal parameters. First, aprobabilistic model for sensor placement considering model uncertainty, load uncertainty and measurement error is proposed.The maximum expected utility theory is then applied with this model by considering utility functions based on three principles: Shannon information, quadratic loss, and K-L divergence.In addition, the prior covariance of modal responses under band-limited white-noise excitation is derived and the nearest Kronecker product approximation is employed to accelerate evaluation of the utility function. As demonstration and validation examples, sensor placements in a 16-degrees-of-freedom sheartype building and in Guangzhou TV Towerunder ground motion and wind load areconsidered. Placements of individual displacement meter, velocimeter, accelerometer and placement of mixed sensors are illustrated.

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The Fisher Information Matrix as a Relevant Tool for Sensor Selection in Engine Health Monitoring

Cited by 20 publications

References 14 publications

Natural selection. V. How to read the fundamental equations of evolutionary change in terms of information theory

Natural selection. V. How to read the fundamental equations of evolutionary change in terms of information theory

A Novel Degree of Observability Used for Measurement Selections in Gas Path Diagnostics

Robust optimal sensor placement for operational modal analysis based on maximum expected utility

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