Conference Agenda

Piezoelectric shunts can be employed as passive dampers to mitigate vibrations of mechanical structures. Connecting an inductance to a piezoelectric capacitance generates an electrical resonance which, when tuned to a mechanical resonance, enhances energy transfers between the two domains. Adding adequate resistance to the circuit ensures optimal energy dissipation, leading to significant vibration reduction. This technique, known as resonant shunt damping, is however quite sensitive to the tuning of the circuit parameters, particularly the inductance which directly governs the resonance frequency of the piezoelectric shunt.

In operational environments where excitation is unknown, traditional modal analysis techniques may not be applicable to detect and eventually correct inaccurate shunt parameters, i.e. inductance and resistance values. In this context, Operational Modal Analysis offers a powerful alternative, enabling the identification of modal parameters of the shunted structure from output-only time data. More specifically, this study shows that the parameters of a resonant piezoelectric shunt can be obtained from Stochastic Subspace Identification (SSI) applied to a single time voltage signal across the shunt terminals. The proposed approach involves extracting the modal frequencies and damping ratios of the coupled electromechanical system directly from the voltage measurement, followed by an identification of the shunt parameters from classical analytical equations ruling resonant piezoelectric damping.

The effectiveness of the method is first demonstrated numerically on a test case involving a single degree-of-freedom piezoelectric structure connected to a deliberately detuned resonant shunt. The covariance-driven SSI algorithm successfully identifies modal parameters from operational data, which then leads to the actual shunt parameters as well as a proposed correction with respect to the optimal circuit. Moreover, a Monte Carlo–based uncertainty analysis is implemented to provide uncertainty bounds on the extracted electrical parameters, representing crucial information when evaluating the robustness of the proposed identification. Once numerically validated, the method is tested on experimental time signals measured on a blade equipped with a resonant piezoelectric shunt. It is shown that modal and electrical parameters can be retrieved from operational modal analysis. Additionally, the evaluation of standard deviations for the electrical parameters shows that the estimated values offer a sufficient tolerance when considering shunt tuning in realistic applications. This uncertainty analysis also helps determine an adequate acquisition duration compatible with future real-time implementation in embedded sensor platforms, which can be critical in case of limited computational capabilities.

In the end, this work contributes to the advancement of piezoelectric vibration mitigation techniques by integrating a robust identification method based on a single voltage measurement. No additional sensor is required, contrary to more classical retuning techniques based on a phase condition between both electrical and mechanical signals. This paves the way for adaptive control systems, satisfying real-world constraints such as temperature variations or modifications of structural properties over time.

In the context of assessing the structural condition of critical points along a portion of an urban highway in Italy, accelerometric recordings from two spans of nearby viaducts are currently being used for continuous, long-term structural health monitoring (SHM). The accelerometer layout enables vibration-based monitoring through output-only modal identification of the decks of the prestressed reinforced concrete viaducts under study, which are representative of a common short-to-medium span bridge typology in the national highway network. Dynamic identification was performed using a custom-made, recently introduced Automated Operational Modal Analysis (AOMA) algorithm. The procedure was performed using SSI-DATA algorithm integrated with DBSCAN clustering analysis to automate the extraction of modal parameters (i.e., natural frequencies, damping ratios, and mode shapes). These results will serve as a reference for the ongoing continuous monitoring of this strategic infrastructure within a highly trafficked road network.

This contribution presents, verifies and illustrates a method for time-domain constrained mode decomposition via autoregressive modeling (TCMD-AR). TCMD-AR is a recently proposed data-driven signal decomposition method aimed at reliable (1) identification of complex eigenvalues (modal frequencies and damping ratios) and (2) extraction of pure single-mode free decay signals from recorded structural free responses.

The core idea of the TCMD-AR method is to form single-mode signals as linear combinations of the measured structural free responses. The combination coefficients are determined by enforcing a time-domain characteristic constraint equation. This equation is derived based on specific characteristics of the autoregressive (AR) model of a single-mode signal, and it yields a constraint matrix whose null space encodes the free decay signal of the targeted mode. In contrast to many existing data-driven decomposition methods, which often suffer from modal aliasing and limited physical interpretability, the approach of TCMD-AR ensures that the resulting decomposed single-mode signals show negligible modal aliasing (see an example in the attached figure) and have a transparent physical interpretation. In fact, as linear combinations of structural responses, they are guaranteed to satisfy the structural equation of motion.

In TCMD-AR, the process of modal identification and signal decomposition proceeds iteratively by (1) estimating candidate complex eigenvalues using the Yule--Walker equations, (2) eliminating spurious eigenvalues, and (3) decomposing the signal based on the determined true eigenvalues. The basic decomposition tool is a single- or multi-eigenvalue constraint FIR filter, based on the autoregressive model and Prony polynomial, which is designed to target and/or suppress specific eigenvalues in the input response.

The effectiveness of TCMD-AR is confirmed in numerical and experimental tests. Numerical experiments on simulated structures are used to quantify robustness to noise and stability of the results, and for comparison with typical approaches such as VMD and CEEMDAN. Experimental tests, conducted in laboratory conditions using a shear frame structure, confirm the accuracy of identification results (modal frequencies and damping rations) by comparing them with the results obtained from the eigensystem realization algorithm (ERA) and signal processing through power-exponential window techniques.

The choice of misfit metric in frequency domain formulations strongly affects the performance of inverse identification methods in structural dynamics. This study investigates the influence of two commonly used metrics, the L₂ norm and the Wasserstein distance, within a multi level adjoint based optimization framework for identifying spatially distributed structural parameters. The forward simulations are performed in the time domain using transient structural dynamic analyses, while the misfit is evaluated in the frequency domain through discrete Fourier transforms of the measured and simulated responses. A hierarchical optimization strategy is applied to improve robustness and computational efficiency, starting from low frequency content and progressively including higher frequencies. Synthetic measurement data from a beam structure with spatially varying Young’s modulus are used to compare the two metrics with respect to convergence behavior, robustness to measurement noise, and reconstruction accuracy. The results show that the Wasserstein distance provides enhanced stability and resilience to modal mismatches, while the L₂ norm remains computationally advantageous when the experimental and simulated spectra are well aligned. The findings offer practical guidance for selecting suitable discrepancy measures in frequency domain inverse problems.