水下障碍物声波探测与识别的拓扑灵敏度方法研究

The inverse problem of detecting and identifying underwater obstacles e.g. reef, pile and wreck is of great importance in many fields such as ocean exploration and channel regulation. This study is concerned with the development of a non-iterative, topological sensitivity-based obstacle reconstruction method for the acoustic detection and identification of underwater elastic obstacles. First, the concepts of topological sensitivity and higher-order topological sensitivity will be extended to deal with the inverse scattering of an elastic inclusion in a background acoustic medium. The corresponding topological sensitivity formulas will be derived through first- and higher-order asymptotic expansions of the cost functional. Second, a boundary integral numerical analysis approach for the fluid-solid interaction problem will be established and the topological sensitivity-based obstacle reconstruction method will be implemented. Third, the effectiveness of this method will be verified through numerical experiments. Combining the experimental results and further theoretical analysis, the possible limitations of this method as well as its sensitivity to measurement error will be discussed. Finally, based on the above developments, laboratory and field tests will be designed and conducted, and the performance of the reconstruction method will be examined by real experimental data. In summary, the study proposed here is expected to overcome the limitations of existing inverse scattering solutions and be applicable in a wide range of disciplines such as underwater probing, geological exploration and medical imaging.

水下障碍物如礁石、桥桩、沉船等的探测与识别在海洋探测、航道治理等领域应用十分广泛。本课题以水下弹性障碍物的声波探测与识别为目的，拟发展基于扩展拓扑灵敏度概念的非迭代弹性障碍物重建方法。首先针对弹性障碍物的声波反散射问题，扩展一阶和高阶拓扑灵敏度的概念并推导相应的公式；然后发展流-固耦合情况下波传播问题的边界积分数值计算方法，实现基于拓扑灵敏度概念的弹性障碍物重建；采用数值试验验证该方法的有效性，并与理论分析相结合探讨该方法的应用范围和对测量误差的敏感性；最后进行室内和现场试验，验证该方法对真实试验数据的有效性。本项目的研究成果可突破现有声波反散射问题求解方法的局限性，在水下探测、地质勘探和医学成像等领域具有广泛的应用前景。

水下障碍物的探测与识别在海洋探测、航道治理等领域应用十分广泛。本项目以水下弹性障碍物的声波探测与识别为目的，发展了基于扩展拓扑灵敏度概念的弹性障碍物重建方法。（1）将拓扑灵敏度的概念扩展到弹性障碍物的声波反散射问题，基于边界积分方程、极限分析和流体力学附加质量公式，推导了弹性障碍物在无粘性流体中引起的声波散射场的一阶渐近行为，得到了拓扑灵敏度的直接和辅助场计算公式；（2）开发了可考虑流-固耦合声波散射问题的边界积分数值计算方法，验证了散射场一阶渐近行为公式的正确性，实现了基于拓扑灵敏度的水下障碍物初步重建方法，通过数值试验验证了其有效性并分析了入射波频谱、波源和接收器的布置范围和间距、障碍物的大小以及彼此之间的距离等因素对重建效果的影响；（3）推导了当声传播参考体中包含已知障碍物时的拓扑灵敏度公式，建立了基于迭代的水下物体三维重建方法，数值试验结果表明经过有限次（低至几次）迭代该方法就可以显著提高障碍物几何重建的精度；（4）采用大型水箱（2.5m*1.8m）中PVC空心圆筒声波散射试验的数据初步验证了所建立的拓扑灵敏度障碍物重建方法的实用性。综上所述，本项目扩展了拓扑灵敏度的概念，建立了基于拓扑灵敏度和迭代的水下物体三维重建方法，并通过数值试验和大型水箱试验验证了该方法的有效性和实用性，为进一步研发高效、实用的水下物体声波探测与识别设备奠定了理论和试验基础。