Parametric Model Order Reduction of Guided Ultrasonic Wave Propagation in Fiber Metal Laminates with Damage

Abstract

This paper focuses on parametric model order reduction (PMOR) of guided ultrasonic wave propagation and its interaction with damage in a fiber metal laminate (FML). Structural health monitoring in FML seeks to detect, localize and characterize the damage with high accuracy and minimal use of sensors. This can be achieved by the inverse problem analysis approach, which employs the signal measurement data recorded by the embedded sensors in the structure. The inverse analysis requires us to solve the forward simulation of the underlying system several thousand times. These simulations are often exorbitantly expensive and trigger the need for improving their computational efficiency. A PMOR approach hinged on the proper orthogonal decomposition method is presented in this paper. An adaptive parameter sampling technique is established with the aid of a surrogate model to efficiently update the reduced-order basis in a greedy fashion. A numerical experiment is conducted to illustrate the parametric training of the reduced-order model. The results show that the reduced-order solution based on the PMOR approach is accurately complying with that of the high fidelity solution.

Numerical Analysis of the Main Wave Propagation Characteristics in a Steel-CFRP Laminate Including Model Order Reduction

“…The total number of degrees of freedom in the system is given by N and the number of discretized time steps is indicated by m. The adapted model order reduction method is as described in Ref. [44] and summarized below.…”

“…A detailed description of the procedure along with its algorithms can be found in Ref. [44], wherein the authors have applied the proposed PMOR method to approximate the GUW propagation in FML containing a damage. In this paper, the analysis is restricted to the GUW propagation in an intact plate.…”

A numerical study on planar gradient acoustic impedance matching for guided ultrasonic wave detection

“…Similar to other authors who have investigated comparable wave propagation phenomena (Bellam Muralidhar et al, 2021), an excitation force of F^=1 N is used here in the simulation. The model shown in Figure 2 was calculated in ABAQUS ® using an explicit scheme.…”

Numerical Analysis of the Main Wave Propagation Characteristics in a Steel-CFRP Laminate Including Model Order Reduction

“…The vector θ ∈ D ⊂ R N p contains N p parameters that define the system from parametric domain D and t ∈ [0, t max ] is the time variable. The total number of degrees of freedom in the system is given by N and the number of discretized time steps is indicated by m. The adapted model order reduction method is as described in [44] and summarized below. The projection of basis functions, using a projection matrix Φ(θ) ∈ R N×n with n << N, from high-dimensional space R N allows the order reduction of the high-fidelity model to its lower dimensional space R n u ≈ Φu r , ü ≈ Φ ür .…”

“…The training phase resulted in global reduced-order basis which could approximate the HiFi solution with a very high accuracy. A detailed description of the procedure along with its algorithms can be found in [44], wherein the authors have applied the proposed PMOR method to approximate the GUW propagation in FML containing a damage. In this paper, the analysis is restricted to the GUW propagation in an intact plate.…”