# Wavelet-Based Estimation of Damping from Multi-Sensor, Multi-Impact Data
###### Abstract  
Accurate damping estimation is crucial for structural health monitoring and machinery diagnostics. This article introduces a novel wavelet-based framework for extracting the damping ratio from multiple impulse responses of vibrating systems. Extracting damping ratios is a numerically sensitive task, further complicated by the common assumption in the literature that impacts are perfectly aligned--a condition rarely met in practice. To address the challenge of non-synchronized recordings, we propose two wavelet-based algorithms that leverage wavelet energy for improved alignment and averaging in the wavelet domain to reduce noise, enhancing the robustness of damping estimation. Our approach provides a fresh perspective on the application of wavelets in damping estimation. We conduct a comprehensive evaluation, comparing the proposed methods with four traditional algorithms. The assessment is strengthened by incorporating both numerical simulations and experimental analysis. Additionally, we apply the analysis of variance (ANOVA) test to assess the significance of algorithm performance across varying numbers of recordings. The results highlight the sensitivity of damping estimation to time shifts, noise levels, and the number of recordings. The proposed wavelet-based approaches demonstrate outstanding adaptability and reliability, offering a promising solution for real-world applications. d 2025 6 13 2  
There are several methodologies for conducting modal analysis, including Experimental Modal Analysis (EMA) and Operational Modal Analysis (OMA). EMA involves physically exciting a structure and measuring its response to identify its modal parameters [1]. In contrast, OMA analyzes a structure's response to ambient or operational loads [15]. Both methods have unique advantages and limitations, making them essential tools for ensuring the safety, durability, and performance of structures. OMA provides a more realistic assessment of a structure's behavior under actual operating conditions, while EMA offers greater accuracy in determining precise modal parameters [16]. One of the fundamental tasks in EMA is identifying the damping from the observed impulse response of a machine or mechanical structure. The process of extracting damping properties typically requires the measurement and interpretation of the system's impact response. However, this extraction is significantly more sensitive to noise compared to the determination of stiffness and mass properties, particularly in multi-degree-of-freedom (MDOF) systems [14; 17]. This sensitivity arises mainly from the use of noisy sensors, such as inertia measurement units (IMUs), which can result in inaccurate conclusions about the system's behavior. To address this challenge, various methodologies for damping extraction have been proposed, including time-domain methods, fast Fourier transform (FFT)-based approaches, and wavelet-based techniques. Wavelets have been widely utilized for denoising, compression, and feature extraction in various signal processing applications [18; 19; 20]. Among these modal analysis methods, the continuous time wavelet transform (CTWT) has shown good resistance to noise [21; 22; 23]. However, it is also numerically less demanding [24; 25]. The current literature, including comparative studies such as [23; 26], often assumes perfect alignment of impulse responses, meaning that the impact occurs at a known and synchronized time. However, in practical applications, this assumption rarely holds due to variations in impact timing and signal acquisition, leading to estimation inaccuracies. Most existing methods do not account for misaligned signals, which are common in real-world applications. Without proper synchronization, damping extraction can become highly unreliable, as phase variations and time shifts distort the estimated parameters.