Complex aerospace structures typically include unknown states, parameters, or inputs. The unknown parameters may be due to changes in the structure that are not captured by the mathematical model assumed. These models are often reduced order models (ROM) that have simplified physics or have been obtained through data-driven techniques, such as trained neural networks. In this paper, we evaluate two data assimilation techniques to perform parameter estimation of dynamical systems by leveraging measured responses to correct process model predictions. We study two different noise models: discontinuous and continuous Gaussian noises. We use ensemble Kalman filter and Kalman-Bucy filter techniques on representative structures, such as the slender flat beam with nonlinear features to illustrate how this approach could be applied to more complex structures.
The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system ‘as-is’. In enabling this task, this paper implements a parametric Model Order Reduction (pMOR) scheme for nonlinear structural dynamics, and the particular case of material nonlinearity. A physics-based parametric representation is developed, incorporating dependencies on system properties and/or excitation characteristics. The pMOR formulation relies on use of a Proper Orthogonal Decomposition applied to a series of snapshots of the nonlinear dynamic response. A new approach to manifold interpolation is proposed, with interpolation taking place on the reduced coefficient matrix mapping local bases to a global one. We demonstrate the performance of this approach firstly on the simple example of a shear-frame structure, and secondly on the more complex 3D numerical case study of an wind turbine tower under a ground motion excitation. Parametric dependence pertains to structural properties, as well as the temporal and spectral characteristics of the applied excitation. The developed parametric Reduced Order Model (pROM) can be exploited for a number of tasks including monitoring and diagnostics, control of vibrating structures, and residual life estimation of critical components.
Neural networks (NNs) are known as universal function approximators and can interpolate nonlinear functions between observed data points. However, when the target domain for deployment shifts from the training domain and NNs must extrapolate, the results are notoriously poor. Prior work Martinez et al. (2019) has shown that NN uncertainty estimates can be used to correct binary predictions in shifted domains without retraining the model. We hypothesize that this approach can be extended to correct real-valued time series predictions. As an exemplar, we consider two mechanical systems with nonlinear dynamics. The first system consists of a spring-mass system where the stiffness changes abruptly, and the second is a real experimental system with a frictional joint that is an open challenge for structural dynamicists to model efficiently. Our experiments will test whether 1) NN uncertainty estimates can identify when the input domain has shifted from the training domain and 2) whether the information used to calculate uncertainty estimates can be used to correct the NN’s time series predictions. While the method as proposed did not significantly improve predictions, our results did show potential for modifications that could improve models’ predictions and play a role in structural health monitoring systems that directly impact public safety.
Soft ferromagnetic alloys are often utilized in electromagnetic applications due to their desirable magnetic properties. In support of these applications, the ferromagnetic alloys are also required to bear mechanical load under various loading and environmental conditions. In this study, a Fe–49Co–2V alloy was dynamically characterized in tension with a Kolsky tension bar and a Drop–Hopkinson bar at various strain rates and temperatures. Dynamic tensile stress–strain curves of the Fe–49Co–2V alloy were obtained at strain rates ranging from 40 to 230 s−1 and temperatures from − 100 to 100 °C. All dynamic tensile stress–strain curves exhibited an initial linear elastic response to an upper yield followed by Lüders band response and then a nearly linear work-hardening behavior. The yield strength of this material was found to be sensitive to both strain rate and temperature, whereas the hardening rate was independent of strain rate or temperature. The Fe–49Co–2V alloy exhibited a feature of brittle fracture in tension under dynamic loading with no necking being observed.
Fe-Co-2V is a soft ferromagnetic alloy used in electromagnetic applications due to excellent magnetic properties. However, the discontinuous yielding (Luders bands), grain-size-dependent properties (Hall-Petch behavior), and the degree of order/disorder in the Fe-Co-2V alloy makes it difficult to predict the mechanical performance, particularly in abnormal environments such as elevated strain rates and high/low temperatures. Thus, experimental characterization of the high strain rate properties of the Fe-Co-2V alloy is desired, which are used for material model development in numerical simulations. In this study, the high rate tensile response of Fe-Co-2V is investigated with a pulse-shaped Kolsky tension bar over a wide range of strain rates and temperatures. Effects of temperature and strain rate on yield stress, ultimate stress, and ductility are discussed.
Cylindrical dog-bone (or dumbbell) shaped samples have become a common design for dynamic tensile tests of ductile materials with a Kolsky tension bar. When a direct measurement of displacement between the bar ends is used to calculate the specimen strain, the actual strain in the specimen gage section is overestimated due to strain in the specimen shoulder and needs to be corrected. The currently available correction method works well for elastic-perfectly plastic materials but may not be applicable to materials that exhibit significant work-hardening behavior. In this study, we developed a new specimen strain correction method for materials possessing an elastic-plastic with linear work-hardening stress–strain response. A Kolsky tension bar test of a Fe-49Co-2V alloy (known by trade names Hiperco and Permendur) was used to demonstrate the new specimen strain correction method. This new correction method was also used to correct specimen strains in Kolsky tension bar experiments on two other materials: 4140 alloy, and 304L-VAR stainless steel, which had different work-hardening behavior.
In computational structural dynamics problems, the ability to calibrate numerical models to physical test data often depends on determining the correct constraints within a structure with mechanical interfaces. These interfaces are defined as the locations within a built-up assembly where two or more disjointed structures are connected. In reality, the normal and tangential forces arising from friction and contact, respectively, are the only means of transferring loads between structures. In linear structural dynamics, a typical modeling approach is to linearize the interface using springs and dampers to connect the disjoint structures, then tune the coefficients to obtain sufficient accuracy between numerically predicted and experimentally measured results. This work explores the use of a numerical inverse method to predict the area of the contact patch located within a bolted interface by defining multi-point constraints. The presented model updating procedure assigns contact definitions (fully stuck, slipping, or no contact) in a finite element model of a jointed structure as a function of contact pressure computed from a nonlinear static analysis. The contact definitions are adjusted until the computed modes agree with experimental test data. The methodology is demonstrated on a C-shape beam system with two bolted interfaces, and the calibrated model predicts modal frequencies with <3% total error summed across the first six elastic modes.