Statistical Energy Analysis by Principal Components for Mid-Frequency Analysis

Hasselman, T. K.; Yap, Keng C.; Yan, Harold; Parrett, Alan

doi:10.2514/6.2002-1395

Cited by 4 publications

(7 citation statements)

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“…In a recent paper, Hasselman et al [9] made this observation on FEA as the frequency reaches the mid-frequency range:…”

Section: Low-frequency Vibration Analysismentioning

confidence: 99%

“…In addition, and partly because of this variability/uncertainty, FEM meshes have not been pushed to the limits of what modern computer software and hardware are capable of. [9] Thus, in the mid-frequency range, a deterministic model may not match the actual structural dynamics due to parameter variations. More precisely, above some frequency the deterministic model represents-at best-one member in a population of structures with the same nominal design.…”

Section: Low-frequency Vibration Analysismentioning

confidence: 99%

“…[9] It is interesting to note that although they adopted an SEA approach, Hasselman et al emphasized the use of FEA as a starting point for an effective mid-frequency power flow analysis.…”

Section: Principal Components Analysismentioning

confidence: 99%

“…Although different from classical SEA, the proposed approach is both statistical and energy-based, and therefore is considered to be a form of statistical energy analysis. [18] More recently, Hasselman and co-workers [9] took the association of principal components analysis with SEA even further, when they introduced an approach called principal components-based statistical energy analysis (PC/SEA). In PC/SEA, the principal components method is used to determine damping and coupling loss factors for SEA.…”

Section: Principal Components Analysismentioning

confidence: 99%

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Mid-Frequency Dynamics of Complex Structural Systems: Assessing the State of the Art and Defining Future Research Directions

Pierre¹,

Castanier²

2002

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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, searchi AUTHOR(S)PROFESSOR CHRISTOPHER PIERRE Approved for public rsleas3 ; distribution unlinätsd, PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)8 ABSTRACT (Maximum 200 words)One of the last frontiers of structural dynamics is mid-frequency vibration analysis of complex structures. In the low-frequency range, finite element analysis (FEA) is well established as the standard method, However, as the frequency of vibration increases, the cost of FEA becomes prohibitive due to the necessary refinement of the finite element mesh to capture the shorter wavelength of vibration. Furthermore, the system response becomes sensitive to small parameter variations at higher frequencies, which means that a statistical analysis should be employed to make confident response predictions. In the high-frequency range, statistical energy analysis (SEA) is popular. However, SEA provides only averaged response predictions and cannot capture the resonant behavior in the response that becomes evident as frequency decreases. ABSTRACTOne of the last frontiers of structural dynamics is mid-frequency vibration analysis of complex structures. In the low-frequency range, finite element analysis (FEA) is well established as the standard method. However, as the frequency of vibration increases, the cost of FEA becomes prohibitive due to the necessary refinement of the finite element mesh to capture the shorter wavelength of vibration. Furthermore, the system response becomes sensitive to small parameter variations at higher frequencies, which means that a statistical analysis should be employed to make confident response predictions. In the high-frequency range, statistical energy analysis (SEA) is popular. However, SEA provides only averaged response predictions and cannot capture the resonant behavior in the response that becomes evident as frequency decreases. Thus, there exists a midfrequency range in which there is no established analysis technique analogous to FEA or SEA. The goal of this research is to produce a review paper on mid-frequency vibration analysis that will provide a survey of the relevant literature, identify the key technical challenges, formulate an assessment of the state of the art, and propose directions for future research. OBJECTIVESThe main objectives of this research are as follows: 1. Perform a comprehensive literature search on mid-frequency vibration analysis and related topics, and collect an extensive set of references 2. Review the relevant literature and summarize the mid-frequency approaches and techniques that have been developed to date 3. Assess the state of the art by determining the major research challenges in the field and drawing conclusions on research progress to date, including applications to realistic complex structures 4. Based on these findings, propose general directions and specific topics for future research 5. Write a review paper that p...

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“…In a recent paper, Hasselman et al [9] made this observation on FEA as the frequency reaches the mid-frequency range:…”

Section: Low-frequency Vibration Analysismentioning

confidence: 99%

Section: Low-frequency Vibration Analysismentioning

confidence: 99%

“…[9] It is interesting to note that although they adopted an SEA approach, Hasselman et al emphasized the use of FEA as a starting point for an effective mid-frequency power flow analysis.…”

Section: Principal Components Analysismentioning

confidence: 99%

Section: Principal Components Analysismentioning

confidence: 99%

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Mid-Frequency Dynamics of Complex Structural Systems: Assessing the State of the Art and Defining Future Research Directions

Pierre¹,

Castanier²

2002

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“…To obtain a parameter set that reconciles the model with test, nonlinear optimization as described by Lewis [16] is used with a quadratic objective function to minimize the error between test and analysis. Hasselman [17] also used PC in a procedure he calls a PC-based statistical energy analysis, for generic uncertainty quantification and comparison of frequency responses. Our approach is very similar with the addition of PV maximum and minimum bounds.…”

mentioning

confidence: 99%

Finite Element Model Calibration Approach for Ares I-X

Horta

Reaves

Buehrle

et al. 2011

Structural Dynamics, Volume 3

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Ares I-X is a pathfinder vehicle concept under development by NASA to demonstrate a new class of launch vehicles. Although this vehicle is essentially a shell of what the Ares I vehicle will be, efforts are underway to model and calibrate the analytical models before its maiden flight. Work reported in this document will summarize the model calibration approach used including uncertainty quantification of vehicle responses and the use of nonconventional boundary conditions during component testing. Since finite element modeling is the primary modeling tool, the calibration process uses these models, often developed by different groups, to assess model deficiencies and to update parameters to reconcile test with predictions. Data for two major component tests and the flight vehicle are presented along with the calibration results. For calibration, sensitivity analysis is conducted using Analysis of Variance (ANOVA). To reduce the computational burden associated with ANOVA calculations, response surface models are used in lieu of computationally intensive finite element solutions. From the sensitivity studies, parameter importance is assessed as a function of frequency. In addition, the work presents an approach to evaluate the probability that a parameter set exists to reconcile test with analysis. Comparisons of pre-test predictions of frequency response uncertainty bounds with measured data, results from the variancebased sensitivity analysis, and results from component test models with calibrated boundary stiffness models are all presented.

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Finite Element Model Calibration for Ares I-X Flight Vehicle

et al. 2011

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Ares I-X is a flight test vehicle developed by NASA to demonstrate a new class of crew launch vehicle. For this first flight test, the first stage was a four segment solid rocket booster with mass simulators used to represent the other sections of the Ares I vehicle. Although this vehicle is significantly simpler than the Ares I, model calibration was required for the finite element model used in loads analysis and flight control evaluations before its maiden flight. The process of calibrating models involves updating parameters and reconciling predictions with test data. This work presents a probabilistic approach to the calibration process. The approach uses Analysis of Variance (ANOVA) for parameter sensitivity, nonlinear optimization to minimize the error between test and analysis, and multiple FEM models to bound the system response and to assess the probability of finding a reconciling solution. To reduce the computational burden associated with ANOVA, response surface models are used in lieu of computationally intensive finite element solutions. Uncertainty in the parameters and their effect on the frequency response function is studied in terms of Principal Values of the frequency response functions. Uncertainty bounds of the principal values are established across multiple models to allow one to determine the probability of finding a solution that reconciles analysis with test results. Results from applying this model calibration process to the Ares I-X project are described. Findings presented in the paper confirmed that the baseline model used for pre-flight assessments was within the acceptable range established for guidance and control.

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Statistical Energy Analysis by Principal Components for Mid-Frequency Analysis

Cited by 4 publications

References 1 publication

Mid-Frequency Dynamics of Complex Structural Systems: Assessing the State of the Art and Defining Future Research Directions

Mid-Frequency Dynamics of Complex Structural Systems: Assessing the State of the Art and Defining Future Research Directions

Finite Element Model Calibration Approach for Ares I-X

Finite Element Model Calibration for Ares I-X Flight Vehicle

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