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

Abstract

Test-analysis models are used in the validation of the finite element models of spacecraft structures. Here, a probabilistic approach is used to assess the robustness of a system equivalent reduction expansion process based testanalysis model when experimental and analytical modes contain different levels of inaccuracy. The approach is applied to three spacecraft models, and Monte Carlo simulations were used to determine the sensitivity of the normalized cross-orthogonality check to the system equivalent reduction expansion process reduced matrix. The effect of parameters used in this reduction and the amount of inaccuracies that can be tolerated in the modes before failing the normalized cross-orthogonality check were also determined. The results show that the probability to pass the normalized cross-orthogonality check is highly determined by the number of modes used in the reduction. The relation between capability of the finite element models to predict the frequency-response function and the quality of the model validation determined using normalized cross-orthogonality check is also investigated, and it is observed that the quantities are not always correlated. This study also shows that the sensor locations can be optimally chosen using the system equivalent reduction expansion process reduced mass matrix, and this can increase the probability to pass the normalized cross-orthogonality check.

Correlation of finite element models of multi-physics systems

“…In this study, only the target modes were used in the SEREP reduction [35]. The viscoelastic system considered in this study has more damping than conventional structures such as spacecraft.…”

Use of Base Force Assurance Criterion for Spacecraft Structure Model Correlation

“…It is considered that, if the mathematical model meets the threshold values specified by the different agencies for these correlation checks, the model is fit for the purpose [8,9]; otherwise, the model needs to be updated. However, it is demonstrated using synthetic experimental results that the MAC and NCO check are not adequate for ensuring the quality of the FEMs to predict the forced response characteristics [10,11]. The frequency response correlation methods, such as the frequency response assurance criterion (FRAC) [12] and the frequency domain assurance criterion (FDAC) [13], have limited application in complex structures where hundreds of frequency responses need to be monitored; hence, their correlation will be a tedious task.…”

Model Reduction and Sensor Placement Methods for Finite Element Model Correlation

“…It is, however, important to also consider that these benefits may be lessened if the TAM is not robust for dealing with noise and errors in the test and/or FEM results, which can make it more difficult to achieve the required levels of correlation as defined by the COC checks [9]. Further investigations into the use of SEREP for spacecraft FEM reduction, such as those of Aglietti et al [20,21], have found that the robustness of the TAM to errors is dependent on the number of modes included in the reduction. It is proposed that the robustness may be improved by inclusion of only the target modes in the reduction.…”

“…The use of real spacecraft in this study has enabled final comparisons to be made between the FEM and the test mode shapes. While previous work has investigated the robustness of reduction methods in theory using analytical models [21], the differences between test and FEM mode shapes can be caused by a wide variety of factors and as such can be difficult to replicate using purely mathematical analyses. In real testing it is possible that: not all vibration modes will be properly excited; the dynamic influence of coupling with the shaker structure can influence the responses; there can be additional uncertainty in the test mode shapes introduced through curve-fitting estimations.…”

“…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]. Where most previous work has focused on small, generic example cases, the main contribution of this work is to show and identify how these methodologies perform with real spacecraft and typical FEMs generated in industry.…”