Signal Noise Reduction Method of Ground-Penetrating Radar of Traditional Tibetan Architecture Based on Successive Variational Mode Decomposition
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摘要:
藏式古建筑石砌体墙结构形式的特殊性和材料组成的复杂性，加之环境因素的干扰，使得墙体内隐蔽性损伤的精准检测面临巨大挑战. 针对传统方法在目标信号识别方面存在的局限性，应用逐次变分模态分解(SVMD)方法，实现探地雷达信号的高效分解与有效信号的精确提取. 通过探地雷达检测藏式石砌体墙体的试验数据，验证数值模拟结果的可靠性；随后系统分析有效波的传播特性，重点考察不同GPR天线中心频率、GPR离墙体间距以及裂缝宽度等因素对回波特性的影响规律；运用SVMD方法对信号进行分解及重构，分析此方法在不同噪声水平和裂缝宽度下的稳定性，目标信号识别方面的适用范围及相比于现有技术的优势. 结果表明：SVMD方法首次应用于藏式古建筑石砌体墙的GPR信号降噪处，在特定条件下，相较于EMD和VMD方法，其信噪比可分别提升58.36%和18.67%，并能够有效分离目标信号、背景墙信号和噪声信号，为藏式古建筑墙体损伤特征的准确提取提供了可靠的技术支持.
Abstract:Due to the unique structural form of stone masonry walls in traditional Tibetan architecture, the complexity of the material composition, and the interference of environmental factors, the accurate detection of hidden damage in the wall is extremely challenging. To address the limitations of traditional methods in target signal identification, experimental data obtained from ground-penetrating radar (GPR) testing of Tibetan stone masonry walls were used to verify the reliability of the numerical simulation results. Then, the propagation characteristics of the effective wave were systematically analyzed, with the focus on the effects of different GPR antenna center frequencies, GPR spacing from the wall, and crack width on the echo characteristics. Finally, the successive variational mode decomposition (SVMD) method was applied for signal decomposition and reconstruction. Its stability, applicability in target signal identification, and its advantages over existing techniques were evaluated across varying noise levels and crack widths. The results have shown that when the SVMD method is applied to the noise reduction of GPR signals in masonry walls of traditional Tibetan architecture under specific conditions, it improves the signal-to-noise ratio by 58.36% and 18.67% compared to the empirical mode decomposition (EMD) and variational mode decomposition (VMD) methods, respectively. It can effectively separate the target signals, background wall signals, and noise signals, providing reliable technical support for extracting damage characteristics in masonry walls of traditional Tibetan architecture.
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图 1 藏式三叶墙构造及常见的损伤类型
Figure 1. Tibetan three-leaf wall construction and common types of damage
图 2 墙体内部裂缝埋置图及墙体厚度方向说明
Figure 2. Embedded cracks inside the wall and illustration of wall thickness direction
图 6 不同中心频率反射波波形特性
Figure 6. Characteristics of reflected waves with different center frequencies
图 7 不同检测高度下电磁波特性
Figure 7. Electromagnetic wave characteristics at different detection heights
图 8 不同裂缝宽度的电磁波特征
Figure 8. Electromagnetic wave characteristics of different crack widths
图 9 基于SVMD电磁波的分解结果（高斯白噪声为2 dB）
Figure 9. Decomposition results based on SVMD electromagnetic waves (Gaussian white noise is 2 dB)
图 10 原始信号与重构信号相关性（裂缝宽度为45 mm）
Figure 10. Correlation between original and reconstructed signals (Crack width is 45 mm)
表 1 探地雷达参数表
Table 1. Parameters of GPR
中心频
率/MHz波速/
（m·ns−1）采样时
窗/ns采样点
数/点道间
距/mm介电
常数1700 0.10 10 512 5 4 
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表 2 模型材料参数及厚度参数
Table 2. Material and thickness parameters of model
材料 介电常数 电导率 磁导率 宽度/mm 黄泥 3 0 0.100 50 花岗岩 5 0 0.001 175 空气 1.000 0 1.000 20～45
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相关系数 相关性程度 0.8≤ $ \left| P \right| $<1.0 极度相关 0.6≤ $ \left| P \right| $<0.8 高度相关 0.4≤ $ \left| P \right| $<0.6 中度相关 0.2≤ $ \left| P \right| $<0.4 弱相关 0< $ \left| P \right| $<0.2 几乎无关
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表 4 不同方法降噪效果比较
Table 4. Comparison of noise reduction effects of different methods
高斯白噪声/dB EMD VMD SVMD −10 −9.77 −9.79 3.23 −8 −7.80 −7.78 6.01 −6 −5.85 −5.76 7.27 −4 −3.92 −3.75 7.81 −2 −2.03 −1.74 10.06 2 1.57 2.29 13.53 4 3.22 4.30 15.14 6 4.73 6.31 16.76 8 6.06 8.29 18.36 10 7.18 10.23 18.55
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表 5 不同裂缝宽度的电磁波特征
Table 5. Electromagnetic wave characteristics of different crack widths
dB 高斯白噪声/dB 裂缝宽度/mm 20 22 25 27 30 32 37 40 42 45 −10 4.75 4.15 5.65 4.80 3.30 2.55 1.71 1.95 1.36 1.86 −8 8.15 5.20 5.36 6.65 6.05 5.15 3.66 4.01 3.51 3.80 −6 9.01 8.90 9.01 7.80 7.30 5.65 5.15 4.01 5.55 5.76 −4 10.40 10.36 10.36 10.15 7.85 8.51 7.61 7.75 7.61 7.75 −2 12.85 12.80 11.40 11.71 10.10 10.45 9.46 9.46 9.50 7.26 2 14.25 14.41 13.35 13.85 13.55 14.75 13.01 13.25 12.00 12.85 4 15.45 14.41 16.50 14.20 15.15 15.45 14.50 14.75 14.95 14.45 6 15.70 18.46 17.95 14.70 16.80 16.45 15.85 16.05 16.75 15.65 8 16.40 19.30 16.15 17.75 18.40 17.90 16.95 17.20 18.35 16.55 10 18.55 20.10 20.23 18.50 18.60 18.80 17.85 18.46 19.75 18.60
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