6 A Brief History of 30 Years of Model Updating in Structural Dynamics 69 “Pride” Assume that the code is correct. “Sloth” Only do a qualitative comparison ( e.g., the “viewgraph norm”). “Envy” Use problem-specific settings. “Wrath” Use only code-to-code comparisons. “Avarice” Use only a single mesh. “Gluttony” Only show results that make the code look good. “Lust” Don’t differentiate between accuracy and robustness-to-uncertainty. a b Fig. 6.8 A metaphor of commonly encountered flaws in test-analysis correlation. (a) H. Bosch’s “Seven Deadly Sins,” 1485. (b) “Sins” of testanalysis correlation [credit: Prado Museum, Madrid, Spain (a) and [64] (b)] 6.4.7 Calibration of FE Representations for Nonlinear Dynamics Model updating is typically applied to linear representations, using Fourier-based responses (resonant frequencies, mode shapes, etc.). When the response is significantly nonlinear and/or only very short time histories are available, assumptions underpinning the Fourier analysis can be violated. Sources of nonlinearity which can disrupt these assumptions are: nonlinear material response, contact, friction, other energy loss mechanisms and short-duration responses. Nonlinearity, irrespective of its source, offers a foundational challenge to updating because the response can no longer be decoupled via modal analysis. Approaches have been proposed to expand the conventional space-time decoupling of the EOM to nonlinear systems [60, 61]. While these approaches have shown promise, applicability remains limited to “mild” nonlinearities that, for example, are isolated on the structure or do not perturb the (linear) response too severely. A nonexhaustive review of nonlinear model updating is proposed in [12]. Defining a general-purpose FE calibration technique, applicable to arbitrary nonlinear dynamics, seems an unattainable goal due to the vast diversity of sources and types of nonlinearities. One noticeable attempt is a formulation for nonlinear system identification, grounded in concepts of optimal control [62, 63]. These works highlight the significant computational burden of tracking a nonlinear time-domain response at multiple locations. To the best of the author’s knowledge, this approach has not been applied to “real-life” problems. Fundamentally, a nonlinear response is described by three independent kinetic fields (displacement, velocity, acceleration) at every point of the structure. Experimentally, these three fields would have to be measured separately; computationally, they would have to be evolved independently. Neither experimental techniques nor computational methods are currently mature enough to meet these stringent requirements. 6.4.8 Closure In closure, we re-iterate that technology for FE model updating has made great progress and achieved undeniable successes in three decades from the mid-1960s to the mid-1990s. This is especially the case for linear statics or linear dynamics. The technology, originally limited to closed-form corrections of master matrices, has evolved towards general-purpose sensitivity methods able to calibrate individual design parameters using diverse data (resonant frequency, mode shape, frequency response function, etc.). Current advances in modeling and analysis, pre- and post-processing software, and experimental methods for vibration testing, are likely to push forward the FE model updating technology even more. Difficulties, some of which are discussed above, have also seriously hindered the transfer of FE model updating to industry. We prognosticate that some of these challenges will progressively disappear as simulation capabilities and experimental techniques keep improving. It should be the case for the quality of solutions (Sect. 6.4.1) and mismatch between measurement locations and FE discretization nodes (Sect. 6.4.2). Other difficulties, such as lower bounds on the value of information learned during calibration (Sect. 6.4.3) and nonlinear dynamics (Sect. 6.4.7), are foundational challenges to model updating. Another significant challenge is educational: “poor practices” of test-analysis comparison, illustrated in Fig. 6.8, are often encountered [64].
RkJQdWJsaXNoZXIy MTMzNzEzMQ==