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摘要:
裂纹矩张量反演方法利用声发射信号求解裂纹信息，是一种有效的裂纹扩展实时监测方法。在工程应用中，传感器接收到的声发射信号总包含一定比例的噪声。噪声信号会影响矩张量反演精度，甚至导致错误结果。研究通过优化传感器排布形式来降低噪声对矩张量反演精度的影响。基于矩张量初至波反演方法，分析了传感器位置选择的理论基础。进而利用人工合成声发射信号，定量研究了在不同传感器排布形式下，矩张量反演精度对噪声的敏感度。结果表明：正五边形传感器排布形式具有较好的精度表现，这种排布形式将5个传感器布置在一个圆环上，相邻传感器的传感器-圆心连线的夹角为72°，第6个传感器布置在圆心。此时矩张量求解方程的条件数较小，当声发射信号幅值因为噪声发生变化时，求解结果具有较高的精度和稳定性。研究针对矩张量反演中的传感器位置选择问题，为相关工程实践提供了建议和理论依据。
Abstract:The moment-tensor inversion method utilizes acoustic-emission signal to obtain cracking information and is regarded as an effective tool to monitor the dynamic growth of cracks. However, in engineering practices, the signal, got by sensors, is always contaminated by noise. The noise will reduce moment-tensor accuracy, and even cause completely wrong results. Sensor arrangements are studied to suppress the effect of noise on moment-tensor accuracy. Based on the first-arrival polarity method, the theory of choosing sensor locations is analyzed. The sensitivity of moment-tensor inversion accuracy to noise is investigated with different sensor arrangements by the use of synthetical acoustic-emission signal. The results show that the pentagonal arrangement of sensors is a superior form, where five sensors locate on a circle, the azimuthal angle between adjacent sensors is 72°, and the sixth sensor locates at the center of the circle. Then the condition number of the equation set achieves a relative small value. When the wave amplitude is changed by noise, the moment-tensor result is quite stable and achieves high accuracy. For the determination of sensor arrangement in moment-tensor inversion, the guidelines and theoretical basis of engineering practices are provided in the study.
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Key words:
- moment tensor /
- sensor arrangement /
- noise /
- stability of solution /
- condition number
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图 1 100种传感器随机排布形式反演得到的矩张量反演误差对比
Figure 1. Comparison of moment-tensor inversion errors calculated with 100 sensor stochastic arrangements
图 3 传感器正五边形排布形式示意图
Figure 3. Schematic of sensors with an arrangement of regular pentagon
图 4 不同噪声水平下多种传感器排布形式反演得到的矩张量反演误差对比
Figure 4. Comparison of moment-tensor inversion errors inverted with different sensor arrangements under different noise levels
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