A Frequency Domain Method for the Generation of Partially Coherent Normal Stationary Time Domain Signals

Smallwood, David O.; Paez, Thomas L.

doi:10.1155/1993/537658

Cited by 49 publications

(36 citation statements)

References 5 publications

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“…Usually this is an eigenvalue, or equivalently a singular value, decomposition but other decompositions are admissible if specific shape function properties are desired [17].…”

Section: Parameter Estimationmentioning

confidence: 99%

Stochastic process models for linear structure behavior

Paez

Lacy

Babuška

2010

Proceedings of the 2010 American Control Conference

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Linear systems are good approximations of the input-output relationship for many real systems. In practice, ensembles of nominally identical systems can seldom be adequately represented by a single linear system. Some accommodation needs to be made for representing inherent ensemble randomness. One approach would be to use a parameterized model of the system, with the random nature captured in discrete parameters of the parameterized model. Another approach is to use data measured from each system in the ensemble to represent the random nature of the ensemble in a non-parametric form. This is the approach described in this paper. There are several different types of data that could be collected from each system in the ensemble, each type capable of capturing the input-output behavior of the linear system: input-output time domain data, perhaps with specific excitation sequences [1,2]; Markov parameters [2,3]; and Frequency Response Functions (FRFs) [2] to name a few. We choose to work with FRF data because many system attributes can be easily interpreted by inspection of the FRF [4]. FRF data can also be used directly for control design [5,6,7]. This paper develops a Karhunen-Loeve expansion [8] representation for linear system behavior based on FRF data to develop a compact representation of the uncertainty inherent in anensemble of systems. This non-parametric, compact, representation of the distribution of linear systems can then be used to characterize the performance and stability of a given feedback control law, as well as for control law design [5,6,7].

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“…Usually this is an eigenvalue, or equivalently a singular value, decomposition but other decompositions are admissible if specific shape function properties are desired [17].…”

Section: Parameter Estimationmentioning

confidence: 99%

Stochastic process models for linear structure behavior

Paez

Lacy

Babuška

2010

Proceedings of the 2010 American Control Conference

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“…Samples of X (n) (t) for times longer than 2π/ω 1 therefore provide the same information as samples of length 2π/ω 1 . A procedure to generate samples of arbitrary length by applying smoothing windows to a collection of overlapped samples of X (n) has been developed [37]. …”

Section: Example 422mentioning

confidence: 99%

Stochastic models: theory and simulation.

Field¹

2008

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Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.3

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“…The former capability is achieved via Cholesky or eigenvalue decomposition of the cross-spectral density matrix of the multiple drives. See Smallwood and Paez (1993) for details on the signal generation algorithm.…”

Section: Control Computermentioning

confidence: 99%

Analysis and Report on SD2000: A Workshop to Determine Structural Dynamics Research for the Millenium

Inman¹

2000

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Public Reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comment regarding this burden estimates or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and The views, opinions and/or findings contained in this report are those of the author(s) and should not be construed as an official Office of Naval Research position, policy or decision, unless so designated by other documentation. This ONR grant was to facilitate the meeting of an international group of researchers to examine the future of structural dynamics. A group of about 40 researchers (see Appendix 1) was brought together from industry, universities and government labs, incorporating several age perspectives. The hope of the group was to help point the way forward for structural dynamicists. Perhaps the greatest wisdom in this regard came from our most experienced member, Dr. Stephen Crandall. He pointed out that during World War II, he came in contact with the newly-formed discipline of automatic control and promptly dismissed it as an intellectual pursuit not useful in structural dynamics. In reflecting back over his career, he now views this as a mistake. We find ourselves exactly in this same situation. New technologies are emerging at a rapid pace (computing, communications, micro-mechanical devices, smart materials, mechatronics, etc.) and determining the appropriate interaction between these new advances and structural dynamics was one of the major concerns addressed by the forum. In addition, significant effort was spent assessing the current state of the art, examining developing technologies, deciding ways to improve the image of structural dynamics and formulating "grand challenge" problems for structural dynamics. FINAL REPORT ON SD2000 MEETINGThis ONR grant was to facilitate the meeting of an international group of researchers toexamine the future of structural dynamics. A group of about 40 researchers (see Appendix 1) was brought together from industry, universities and government labs, incorporating several age perspectives. The hope of the group was to help point the way forward for structural dynamicists. Perhaps the greatest wisdom in this regard came from our most experienced member, Dr. Stephen Crandall. He pointed out that during WorldWar II, he came in contact with the newly-formed discipline of automatic control and promptly dismissed it as an intellectual pursuit not useful in structural dynamics. In reflecting back over his career, he now views this as a mistake. We find ourselves exactly in this same situation. New technologies are emerging at a rapid pace (computing, communications, micro...

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A Frequency Domain Method for the Generation of Partially Coherent Normal Stationary Time Domain Signals

Cited by 49 publications

References 5 publications

Stochastic process models for linear structure behavior

Stochastic process models for linear structure behavior

Stochastic models: theory and simulation.

Analysis and Report on SD2000: A Workshop to Determine Structural Dynamics Research for the Millenium

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