Aiming to determine the geometric and acoustic parameters of inhomogeneous multi-layer coatings, an ultrasonic pressure reflection coefficient amplitude spectrum (URCAS) is derived using a material-oriented regularization scheme, when wave propagates perpendicularly to the coating surface. Based on the derived theoretical URCAS, a new objective function combining least-squares and cross-correlation algorithm is developed to simultaneously identify the thickness, sound velocity, density, attenuation coefficient amplitude, and attenuation coefficient power-law of the multi-layer coating. Genetic algorithm with the constraint of total multi-layer coating thickness being known is presented to optimize the nonlinear objective function for obtaining global optimal solution. Ultrasonic experiments were implemented on a dual-layer coating specimen with coating1/coating2/substrate structure using a flat immersion transducer with a central frequency of 15 MHz. The inversed thicknesses, sound velocities, and densities of the dual-layer coating were in good agreement with those measured through other methods, with less than 8.1% errors. The inversed attenuation coefficients of the coating 1 and coating 2 were α(f) = 1.02e^-2 × f^1.93 and α(f) = 4.62e^-3 × f^1.97, respectively. The upper bounds of the relative errors ⁺r of inverted parameters were all less than 0.061. The proposed ultrasonic inversion method could be used to quantitatively characterize the surface integrity of inhomogeneous multi-layer coatings.

为了确定非均匀多层涂层的几何和声学参数，当波垂直于涂层表面传播时，使用面向材料的正则化方案推导出超声波压力反射系数振幅谱 (URCAS)。在导出的URCAS理论基础上，开发了一种结合最小二乘法和互相关算法的新目标函数，可以同时识别多层涂层的厚度、声速、密度、衰减系数幅度和衰减系数幂律。提出了已知多层涂层总厚度约束的遗传算法来优化非线性目标函数以获得全局最优解。使用中心频率为 15 MHz 的平面浸入式换能器在具有涂层 1/涂层 2/基材结构的双层涂层试样上进行超声实验。双层涂层的反向厚度、声速和密度与通过其他方法测量的结果非常吻合，误差小于8.1%。涂层 1 和涂层 2 的反衰减系数分别为α ( f ) = 1.02e ^-2  ×  f ^1.93和α ( f ) = 4.62e ^-3  ×  f ^1.97。反演参数的相对误差上限⁺ r均小于0.061。所提出的超声波反演方法可用于定量表征非均匀多层涂层的表面完整性。