The paper discusses Structural Health Monitoring (SHM) based on ultrasonic guided waves for damage detectionin structures. Guided waves allow inspection over long distances and inaccessible features, but are also sensitiveto changes in environmental and operating conditions (EOC). The focus of this paper is on temperaturecompensation methods for guided waves. The compensation techniques include Baseline Signal Stretch (BSS),Optimal Baseline Selection (OBS), OBS+BSS, and Dynamic Time-Warping (DTW). In particular, a new, fastapproximation of DTW is evaluated and compared with conventional but computationally expensive DTW. TheFDTW algorithm utilizes a multilevel approach inspired by graph bisection principles to achieve precise warpingpath determination with linear computational complexity.The study evaluates the compensation performance of FDTW using a single baseline at a single temperature, thusaddressing the complexity and inaccessibility issues of obtaining an extensive database of baseline signals inpractical applications. The Open Guided Wave (OGW) dataset is employed for a fair comparison with othercompensation methods.Results indicate that FDTW performs well, demonstrating comparable warping performance to DTW but withsignificantly reduced computational complexity. The analysis also includes comparisons with BSS, OBS+BSS,and DTW across a range of temperatures, highlighting the effectiveness of FDTW in mitigating errors introducedby larger temperature variations.

Introduction: Guided waves being highly sensitive to temperature variations, temperature compensation algorithms, such as Optimal Baseline Selection, Baseline Signal Stretch and Scale Transform demonstrate effective performance under limited conditions. Dynamic Time Warping (DTW) has shown excellent compensation performance, however it comes with a substantial computational burden of O(N*N), where N represents the number of samples in each signal. Methodology: DTW works by construction of cost matrix that maps every point in one time series to all the points in the other time series, that results in complexity O(N*N).This problem can be solved by narrowing the search window using global constraints. The two most common constraints in the literature are the Sakoe-Chiba band and the Itakura Parallelogram. This paper uses Sakoe-Chiba band as a global constraint, the Sakoe-Chiba band is defined through a window size parameter which determines the largest temporal shift allowed from the diagonal. Temperature compensation performance of DTW Sakoe-Chiba is tested using the available OGW dataset #2 provided by Jochen Moll et al. The OGW dataset has been generated using 12 number of piezoelectric transducers bounded to CFRP (Carbon Fiber Reinforced Plastic) plate and varying the temperature from 20-60 degree with an increment of 0.5 degree. The signal is recorded for 1300 microseconds, that results in 13000 samples/time stamps(N). Initial results show that the Sakoe-Chiba constraint based DTW performs well and at a significantly lower cost, as indicated below. Result: The largest temporal shift (r) is estimated using Local Peak Coherence (LPC),for signal at 20 and 60 degree r is 135 samples. This results in complexity O(N*2r) which is very less than conventional DTW compensation technique O(N*N). In the final paper, the analysis will be replicated across a range of temperatures, and the performance of damage detection will be thoroughly discussed.

The paper explores Structural Health Monitoring (SHM) using ultrasonic guided waves, to detect structural damage. Guided waves are highly sensitive to changes in material properties and environmental and operating conditions (EOCs), with temperature being a significant factor. A key challenge in guided waves based SHM is differentiating between damage and temperature-induced changes. This paper focuses on warping-based methods for temperature compensation. Dynamic Time-Warping (DTW) encounters challenges due to its quadratic complexity. However, applying constraints to DTW accelerates the warping process by limiting the scope of the warping path to specified areas. The applied constraint should align with the characteristics of the signal. In this paper, we propose a global constraint for temperature compensation of guided waves, referred to as the Triangular global constraint (Tri-DTW). The performance of the proposed method will be compared with the Sakoe-Chiba global constraint (SC-DTW). Tri-DTW performs well, demonstrating better warping performance with four times reduced computational complexity. The analysis also includes comparisons of warping performance, warping performance with respect to temperature and damage detection performance.