非线性温度效应的超声投影幂律特征

Ultrasonic projection power law features of nonlinear temperature effects

摘要:

环境温度变化会导致超声信号的显著波动,使得区分损伤、应力等目标参数变得复杂,为此,有必要研究超声信号的温度效应特征及其表达形式。温度对超声信号的影响最终体现为信号向量的空间变化,故使用特定函数系在时域向量空间构造特性向量,使得温度效应可以在超声时域直接投影为若干声测特征,并由基函数表示。这些特征的大小由温度增量和基函数决定,符号与投影方向一致。采集实验室混凝土梁超声测试信号,同时基于波动方程的理论解得到温度变化下的时域信号。构造幂函数基的特性向量空间,利用幂律特征描述温度的非线性效应。结果表明,实验和理论两种信号的温度效应幂律特征具有相同的分布规律,其反应了温度效应的能量大小,并随基函数阶次升高服从指数递减规律。上述幂律特征可以得到同一温度下的不同特征值,分别表征了不同维度的温度效应信息,同一特征与温度增量之间遵循幂函数映射,同一温度的不同特征值随幂次的增加呈指数映射。实现了超声测试过程中温度效应的数学描述,为不同场景下的温度效应表征提供了有效工具。

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.