Abstract:Variations in ambient temperature can cause significant fluctuations in ultrasonic signals, complicating the distinction of target parameters such as damage and stress. To address this issue, this study investigates the characteristics and mathematical representation of temperature effects on ultrasonic signals. The influence of temperature on ultrasonic signals ultimately manifests as spatial changes in signal vectors. Therefore, we construct characteristic vectors in the time-domain vector space using a specific set of functions, allowing the temperature effect to be directly projected into several acoustic measurement features within the ultrasonic time domain, represented by basis functions. The magnitude of these features is determined by the temperature increment and the choice of basis function, with their signs consistent with the projection direction. Experimental ultrasonic test signals were collected from laboratory concrete beams, while theoretical solutions based on wave equations provided time-domain signals under varying temperatures. We constructed a characteristic vector space using power function bases and employed power-law features to describe the nonlinear effects of temperature. Results show that both experimental and theoretical signals exhibit identical distribution patterns in their temperature-effect power-law features, reflecting the energy magnitude of temperature effects. These features decrease exponentially with increasing order of the basis function. Based on power-law characteristics, distinct characteristic values at the same temperature can be derived, each representing temperature effect information across different dimensions. The relationship between a given characteristic and temperature increments follows a power-law mapping, while different characteristic values at identical temperatures exhibit an exponential relationship with increasing power exponents. This establishes a mathematical description of temperature effects during ultrasonic testing, providing an effective tool for characterizing temperature effects across various scenarios.
