Modeling of uncertain spectra through stochastic autoregressive systems

Yiwei Wang, X. Q. Wang, Marc Mignolet, Shuchi Yang, P. C. Chen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The focus of this investigation is on the formulation and validation of a modeling strategy of the uncertainty that may exist on the specification of the power spectral density of scalar stationary processes and on the spectral matrices of vector ones. These processes may, for example, be forces on a structure originating from natural phenomena which are coarsely modeled (i.e., with epistemic uncertainty) or are specified by parameters unknown (i.e., with aleatoric uncertainty) in the application considered. The propagation of the uncertainty, e.g., to the response of the structure, may be carried out provided that a stochastic model of the uncertainty in the power spectral density/matrix is available from which admissible samples can be efficiently generated. Such a stochastic model will be developed here through an autoregressive-based parameterization of the specified baseline power spectral density/matrix and of its random samples. Autoregressive (AR) models are particularly well suited for this parametrization since their spectra are known to converge to a broad class of spectra (all nonpathological spectra) as the AR order increases. Note that the characterization of these models is not achieved directly in terms of their coefficients but rather in terms of their reflection coefficients which lie (or their eigenvalues in the vector process case) in the domain [0,1) as a necessary and sufficient condition for stability. Maximum entropy concepts are then employed to formulate the distribution of the reflection coefficients in both scalar and vector process case leading to a small set of hyperparameters of the uncertain model. Depending on the information available, these hyperparameters could either be varied in a parametric study format to assess the effects of uncertainty or could be identified, e.g., in a maximum likelihood format, from observed data. The validation and assessment of these concepts is finally achieved on the response of an uncertain 4-degree of freedom system subjected to white noise and on the response of an F-15 aircraft to random buffeting loads.

Original languageEnglish (US)
Title of host publicationUNCECOMP 2015 - 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering
PublisherNational Technical University of Athens
Pages757-780
Number of pages24
StatePublished - 2015
Event1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2015 - Hersonissos, Crete, United Kingdom
Duration: May 25 2015May 27 2015

Other

Other1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2015
CountryUnited Kingdom
CityHersonissos, Crete
Period5/25/155/27/15

Fingerprint

Power Spectral Density
Uncertainty
Spectral Density Matrix
Power spectral density
Modeling
Hyperparameters
Reflection Coefficient
Stochastic Model
Stochastic models
Scalar
Epistemic Uncertainty
Buffeting
Maximum Entropy
Autoregressive Model
Stationary Process
White noise
Parametrization
Unknown Parameters
Parameterization
Maximum Likelihood

Keywords

  • Maximum Entropy
  • Maximum Likelihood Identification
  • Random Matrices
  • Stochastic Autoregressive Models
  • Uncertain Power Spectral Densities

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Science Applications

Cite this

Wang, Y., Wang, X. Q., Mignolet, M., Yang, S., & Chen, P. C. (2015). Modeling of uncertain spectra through stochastic autoregressive systems. In UNCECOMP 2015 - 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering (pp. 757-780). National Technical University of Athens.

Modeling of uncertain spectra through stochastic autoregressive systems. / Wang, Yiwei; Wang, X. Q.; Mignolet, Marc; Yang, Shuchi; Chen, P. C.

UNCECOMP 2015 - 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering. National Technical University of Athens, 2015. p. 757-780.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Wang, Y, Wang, XQ, Mignolet, M, Yang, S & Chen, PC 2015, Modeling of uncertain spectra through stochastic autoregressive systems. in UNCECOMP 2015 - 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering. National Technical University of Athens, pp. 757-780, 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2015, Hersonissos, Crete, United Kingdom, 5/25/15.
Wang Y, Wang XQ, Mignolet M, Yang S, Chen PC. Modeling of uncertain spectra through stochastic autoregressive systems. In UNCECOMP 2015 - 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering. National Technical University of Athens. 2015. p. 757-780
Wang, Yiwei ; Wang, X. Q. ; Mignolet, Marc ; Yang, Shuchi ; Chen, P. C. / Modeling of uncertain spectra through stochastic autoregressive systems. UNCECOMP 2015 - 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering. National Technical University of Athens, 2015. pp. 757-780
@inproceedings{c1a2886137424a70b5c087e6e7a845f0,
title = "Modeling of uncertain spectra through stochastic autoregressive systems",
abstract = "The focus of this investigation is on the formulation and validation of a modeling strategy of the uncertainty that may exist on the specification of the power spectral density of scalar stationary processes and on the spectral matrices of vector ones. These processes may, for example, be forces on a structure originating from natural phenomena which are coarsely modeled (i.e., with epistemic uncertainty) or are specified by parameters unknown (i.e., with aleatoric uncertainty) in the application considered. The propagation of the uncertainty, e.g., to the response of the structure, may be carried out provided that a stochastic model of the uncertainty in the power spectral density/matrix is available from which admissible samples can be efficiently generated. Such a stochastic model will be developed here through an autoregressive-based parameterization of the specified baseline power spectral density/matrix and of its random samples. Autoregressive (AR) models are particularly well suited for this parametrization since their spectra are known to converge to a broad class of spectra (all nonpathological spectra) as the AR order increases. Note that the characterization of these models is not achieved directly in terms of their coefficients but rather in terms of their reflection coefficients which lie (or their eigenvalues in the vector process case) in the domain [0,1) as a necessary and sufficient condition for stability. Maximum entropy concepts are then employed to formulate the distribution of the reflection coefficients in both scalar and vector process case leading to a small set of hyperparameters of the uncertain model. Depending on the information available, these hyperparameters could either be varied in a parametric study format to assess the effects of uncertainty or could be identified, e.g., in a maximum likelihood format, from observed data. The validation and assessment of these concepts is finally achieved on the response of an uncertain 4-degree of freedom system subjected to white noise and on the response of an F-15 aircraft to random buffeting loads.",
keywords = "Maximum Entropy, Maximum Likelihood Identification, Random Matrices, Stochastic Autoregressive Models, Uncertain Power Spectral Densities",
author = "Yiwei Wang and Wang, {X. Q.} and Marc Mignolet and Shuchi Yang and Chen, {P. C.}",
year = "2015",
language = "English (US)",
pages = "757--780",
booktitle = "UNCECOMP 2015 - 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering",
publisher = "National Technical University of Athens",

}

TY - GEN

T1 - Modeling of uncertain spectra through stochastic autoregressive systems

AU - Wang, Yiwei

AU - Wang, X. Q.

AU - Mignolet, Marc

AU - Yang, Shuchi

AU - Chen, P. C.

PY - 2015

Y1 - 2015

N2 - The focus of this investigation is on the formulation and validation of a modeling strategy of the uncertainty that may exist on the specification of the power spectral density of scalar stationary processes and on the spectral matrices of vector ones. These processes may, for example, be forces on a structure originating from natural phenomena which are coarsely modeled (i.e., with epistemic uncertainty) or are specified by parameters unknown (i.e., with aleatoric uncertainty) in the application considered. The propagation of the uncertainty, e.g., to the response of the structure, may be carried out provided that a stochastic model of the uncertainty in the power spectral density/matrix is available from which admissible samples can be efficiently generated. Such a stochastic model will be developed here through an autoregressive-based parameterization of the specified baseline power spectral density/matrix and of its random samples. Autoregressive (AR) models are particularly well suited for this parametrization since their spectra are known to converge to a broad class of spectra (all nonpathological spectra) as the AR order increases. Note that the characterization of these models is not achieved directly in terms of their coefficients but rather in terms of their reflection coefficients which lie (or their eigenvalues in the vector process case) in the domain [0,1) as a necessary and sufficient condition for stability. Maximum entropy concepts are then employed to formulate the distribution of the reflection coefficients in both scalar and vector process case leading to a small set of hyperparameters of the uncertain model. Depending on the information available, these hyperparameters could either be varied in a parametric study format to assess the effects of uncertainty or could be identified, e.g., in a maximum likelihood format, from observed data. The validation and assessment of these concepts is finally achieved on the response of an uncertain 4-degree of freedom system subjected to white noise and on the response of an F-15 aircraft to random buffeting loads.

AB - The focus of this investigation is on the formulation and validation of a modeling strategy of the uncertainty that may exist on the specification of the power spectral density of scalar stationary processes and on the spectral matrices of vector ones. These processes may, for example, be forces on a structure originating from natural phenomena which are coarsely modeled (i.e., with epistemic uncertainty) or are specified by parameters unknown (i.e., with aleatoric uncertainty) in the application considered. The propagation of the uncertainty, e.g., to the response of the structure, may be carried out provided that a stochastic model of the uncertainty in the power spectral density/matrix is available from which admissible samples can be efficiently generated. Such a stochastic model will be developed here through an autoregressive-based parameterization of the specified baseline power spectral density/matrix and of its random samples. Autoregressive (AR) models are particularly well suited for this parametrization since their spectra are known to converge to a broad class of spectra (all nonpathological spectra) as the AR order increases. Note that the characterization of these models is not achieved directly in terms of their coefficients but rather in terms of their reflection coefficients which lie (or their eigenvalues in the vector process case) in the domain [0,1) as a necessary and sufficient condition for stability. Maximum entropy concepts are then employed to formulate the distribution of the reflection coefficients in both scalar and vector process case leading to a small set of hyperparameters of the uncertain model. Depending on the information available, these hyperparameters could either be varied in a parametric study format to assess the effects of uncertainty or could be identified, e.g., in a maximum likelihood format, from observed data. The validation and assessment of these concepts is finally achieved on the response of an uncertain 4-degree of freedom system subjected to white noise and on the response of an F-15 aircraft to random buffeting loads.

KW - Maximum Entropy

KW - Maximum Likelihood Identification

KW - Random Matrices

KW - Stochastic Autoregressive Models

KW - Uncertain Power Spectral Densities

UR - http://www.scopus.com/inward/record.url?scp=84942895549&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84942895549&partnerID=8YFLogxK

M3 - Conference contribution

SP - 757

EP - 780

BT - UNCECOMP 2015 - 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering

PB - National Technical University of Athens

ER -