Probabilistic investigation of sensitivities of advanced test-analysis model correlation methods

Abstract

Correlation of test and analysis mode shapes using reduced Test Analysis Models (TAMs) has become an industry standard method used to validate finite element models. Some organizations have even mandated specific metrics regarding the allowable deviations in the orthogonality of mode shapes, using the TAM mass matrix, that a model must meet to be considered valid. As a result, significant effort has been directed towards developing robust TAMs and in comparing the robustness of the various approaches. The static or Guyan reduction method has been touted as the most robust, although the evidence in the literature seems quite inconclusive. This work takes a new view on test analysis orthogonality, utilizing a probabilistic framework to accurately quantify the sensitivity of the Static, Modal and IRS reduction methods to errors in a set of mode shapes for a general satellite FEA model. The results show that the orthogonality calculation is highly sensitive to errors, so that the Static and IRS TAM models have a very small probability of passing the orthogonality criteria, when the true mode shapes are used, contaminated by only a small level of noise. This study also shows that the performance of the Modal TAM depends heavily on the sensor set chosen; the sensitivity of the modal TAM was observed to increase fourfold when a Static TAM sensor set was used rather than one that was optimized specifically for the Modal TAM. The results are also evaluated in light of one theory that relates sensitivity to the natural frequencies of the system constrained at the sensor locations, revealing that the theory fails for the Modal TAM yet may perhaps hold for the IRS TAM. While a conclusive ranking of the TAM methods cannot be achieved using a single model, this work presents the tools, based on a probabilistic framework, that can be used to correctly ascertain the sensitivity of test analysis models and to evaluate to model validation methodology. 1 Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U.S. Department of Energy under Contract DE-AC04-94AL85000. FEM, called a test-analysis model (TAM) must be generated. The orthogonality of the modes can then be computed with respect to the reduced analytical mass matrix, or TAM mass matrix [1]. The use of these metrics, and the required values for test/analysis correlation, are dictated by agencies such as NASA [2] and the United States Air Force [1]. Depending on the agency, the requirements are different. For example, the Air Force requires test/analysis frequency errors less than or equal to 3.0%, cross-generalized mass values greater than 0.95, and coupling terms between modes of less than 0.10 in test-orthogonality and test-FEM cross-orthogonality.

Robustness of System Equivalent Reduction Expansion Process on Spacecraft Structure Model Validation

“…The accuracy of the technique, however, is dependent upon the number of principal directions used in the model reduction. Bergman et al [15] used a probabilistic investigation to quantify the effect of errors in the experimental mode shapes on the test-analysis orthogonality. They analyzed a typical spacecraft structure using static, modal, and IRS reduction methods, and then observed that the test-analysis orthogonality is highly sensitive to the experimental errors.…”

On the use of SEREP for satellite FEM validation

“…In fact it has been demonstrated that certain algorithms can produce reduced models which are so sensitive to noise that even minor differences in the mode shapes EC 29,6 (analysis vs experiment) may prevent the model from meeting the COC specification (Bergman et al, 2010). In this case the following phase of FEM updating becomes a worthless exercise, simply correcting the model to produce mode shapes that match the experimental results distorted by their "noise".…”

Model Reduction and Sensor Placement Methods for Finite Element Model Correlation

“…There have already been several studies [6][7][8][9][10][11][12] comparing the various methods including; Static (or Guyan) reduction [13], Improved Reduction System (IRS) [14], Dynamic reduction [15], Modal reduction [5], System Equivalent Reduction Expansion Process (SEREP) [16], Hybrid [17] and Craig-Bampton [18]. Here the focus is on: the Guyan reduction method, which has some historical basis and availability within FE tools such as MSC-NASTRAN [19]; and SEREP which has been identified as potentially more suitable for generating spacecraft TAMs [20,21].…”

“…Bergman et al [6] also explored different reduction methods, and proposed that many previous studies, such as those by Chung [8], Freed and Flanigan [9], and Avitabile et al [11], had failed to account for the fact that different reduction methods require different sensor placement optimization methods. Most previous work exploring reduction methods had taken a single sensor set, determined from a particular sensor placement optimization method, and had compared the reduction methods for that particular set.…”

“…Most previous work exploring reduction methods had taken a single sensor set, determined from a particular sensor placement optimization method, and had compared the reduction methods for that particular set. As such, Bergman et al [6] attempted to compensate for this by applying different sensor placement methods as appropriate for each reduction method, in order to assess the quality and robustness of the resulting TAMs with respect to the same original full FEM. Of the sensor placement methods considered, SEREP performed best when EfI [27] was applied to ensure optimum linear independence of target modes, whereas for static reductions, a KE based technique was employed.…”