Geometry parameters recognition method for an underwater target model based on Kriging surrogate model
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摘要:
目的 水下目标参数识别可为目标分类识别提供依据，为此，提出一种基于Kriging代理模型的水下目标参数识别方法。 方法 首先，对敷设声学覆盖层的水下目标模型在螺旋桨和主辅机激励情况下的结构表面低频振动声辐射与声辐射灵敏度进行分析；然后，基于分析结果建立低频声辐射功率代理模型，并基于该代理模型构造由低频声辐射响应特征和目标参数组成的样本空间；最后，基于所构建的样本空间，建立目标参数识别代理模型并选取测试点进行模型验证。 结果 结果显示，测试样本的实际目标参数值与所构建代理模型的目标参数预测值吻合良好；利用有限元法和边界元方法，可以实现考虑阻尼材料频变特性的粘弹性阻尼结构的低频声辐射分析，并能解决商业软件无法大批量处理振动结果文件的问题；影响水下目标模型低频振动声辐射的主要目标参数为目标长度、最大半径、基层壳厚度和声学覆盖层厚度。 结论 基于Kriging代理模型的水下目标参数识别方法可以通过声辐射线谱特征准确预测水下目标模型的主要目标参数值。 Abstract:Objectives Underwater target parameters recognition can provide the basis for target classification and recognition, for this reason, a method was proposed for underwater target parameters recognition based on the Kriging surrogate model. Methods First, the low-frequency acoustic radiation of structure surface and its sensitivity of underwater target model covered with acoustic layer were analyzed under the propeller and main and auxiliary engine excitation. Then, a low-frequency acoustic radiation power surrogate model was established based on the above analysis results, and a sample space consisting of acoustic radiation response features and target parameters was constructed based on the surrogate model. Finally, the surrogate model of target parameters recognition was established based on the sample space, and test points were selected for model validation. Results The results show that the actual target parameter values of the test samples match well with the predicted target parameter values of the constructed surrogate model. The finite element method (FEM) and boundary element method (BEM) can realize the low-frequency acoustic radiation analysis of the viscoelastic damping structure considering the frequency-dependence characteristics of the damping material, and are able to solve the problem that the commercial software may not process the vibration result files in large quantities. The main target parameters affecting the low-frequency vibro-acoustic radiation of the underwater target model are the model length, the maximum radius of the target, the model thickness, and the thickness of the acoustic layer. Conclusions The underwater target parameters recognition method based on the surrogate model is able to predict the main target parameter values of underwater targets model by acoustic radiation line spectral features. -
图 4 水下目标模型声功率级对比
Figure 4. Comparison of the acoustic power level of the underwater target model
图 5 水下目标模型关于13个目标参数的声学灵敏度
Figure 5. Acoustic sensitivity regarding 13 target parameters of the underwater target model
图 6 水下目标模型关于各目标参数的声学灵敏度（$T_{\text{s}}^1$和$T_{\text{s}}^2$除外）
Figure 6. Acoustic sensitivity regarding each target parameter of the underwater target model (except $T_{\text{s}}^1$ and $T_{\text{s}}^2$)
图 7 不同目标参数的水下目标模型的低频声辐射功率级
Figure 7. Low-frequency acoustic radiation power level of underwater target model with different target parameters
图 9 测试点代理模型与FEM/BEM方法的声功率级对比
Figure 9. Comparison of sound power level of test points between surrogate model and FEM/BEM
图 10 前4个样本点的功率谱特征
Figure 10. Power spectrum characteristics of the first four sample points
表 1 水下目标模型参数值
Table 1. Parameters of the underwater target model
艇体参数 数值 指挥室参数 数值 艉舵参数 数值 $ L_{\text{s}}^1 $/m 7.0 $L_{\text{r}}^1$/m 3.85 $H_{\text{t}}^1$/m 1.0 $L_{\text{s}}^2$/m 42 $L_{\text{r}}^2$/m 2.31 $L_{\text{t}}^2$/m 1.5 $L_{\text{s}}^3$/m 4.87 $L_{\text{r}}^3$/m 3.32 $L_{\text{t}}^3$/m 10.0 $L_{\text{s}}^4$/m 8.13 $L_{\text{r}}^4$/m 3.32 ${B_{\text{t}}}$/m 0.44 $D_{\text{s}}^1$/m 7.5 $L_{\text{r}}^5$/m 19.0 ${H_{\text{t}}}$/m 7 $ D_{\text{s}}^2 $/m 5.98 $B_{\text{r}}^1$/m 2.2 $D_{\text{s}}^3$/m 0.7 $ B_{\text{r}}^2 $/m 1.9 $T_{\text{s}}^1$/m 0.04 $B_{\text{r}}^3$/m 1.2 $T_{\text{s}}^2$/m 0.05 ${H_{\text{r}}}$/m 3.5 
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表 2 VHB4955 GHM模型拟合参数
Table 2. Fitting parameters of VHB4955 GHM model
参数 i = 1 i = 2 i = 3 ${G^0}$/Pa 7.622 5×105 7.622 5×105 7.622 5×105 ${\alpha _i}$ 8.748 7×107 6.838 9×106 1.227 3×106 ${\beta _i}$ 4.194 7×104 3.814 8×106 1.905 6×108 ${\delta _i}$ 1.999 6×109 3.241 4×109 9.000 0×109
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表 3 主辅机的不平衡力/力矩频率与幅值
Table 3. Frequencies and amplitudes of main and auxiliary machine unbalance force/torque
发动机 不平衡力矩/力 2.25 Hz 4.5 Hz 主机 $M_x^1 = 145\;539.8{\text{N}} \cdot {\text{m}}$
$M_y^1 = 62\;014.4{\text{N}} \cdot {\text{m}}$$M_x^2 = 52\;077.2{\text{N}} \cdot {\text{m}}$
$M_y^2 = 52\;077.2{\text{N}} \cdot {\text{m}}$辅机 $F_{1x}^1 = 2\;187.5{\text{N}}$
$F_{1y}^1 = - 3\;788.86{\text{N}}$$F_{1x}^2 = - 2\;574.5{\text{N}}$
$F_{1y}^2 = - 4\;459.16{\text{N}}$
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表 4 设计变量的取值范围
Table 4. Design variables' value range
设计变量 取值范围 艇长${L_{\text{s}}}/{\text{m}}$ 49.6～74.4 艇体最大半径$ L_{\text{s}}^1/{\text{m}} $ 3～4.5 艇体基层壳厚度$T_{\text{s}}^1/{\text{m}}$ 0.032～0.048 阻尼层厚度$T_{\text{s}}^2/{\text{m}}$ 0.04～0.06
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表 5 代理模型样本点设计变量
Table 5. Sample points' design variables of the surrogate model
样本 ${L_{\text{S}}}/{\text{m}}$ $R_{\text{S}}^1/{\text{m}}$ $T_{\text{S}}^1/{\text{m}}$ $T_{\text{S}}^2/{\text{m}}$ 样本 ${L_{\text{S}}}/{\text{m}}$ $R_{\text{S}}^1/{\text{m}}$ $T_{\text{S}}^1/{\text{m}}$ $T_{\text{S}}^2/{\text{m}}$ 1 70.584 62 4.5 0.046 359 0.057 436 21 62.317 95 4.423 077 0.036 923 0.041 026 2 58.502 56 3.692 308 0.032 410 0.054 872 22 61.682 05 3.076 923 0.043 077 0.058 974 3 57.866 67 4.461 538 0.039 795 0.046 154 23 69.948 72 3.769 231 0.038 564 0.048 718 4 66.133 33 3.038 462 0.040 205 0.053 846 24 50.871 79 3.423 077 0.041 846 0.046 667 5 53.415 38 3 0.033 641 0.042 564 25 73.128 21 4.076 923 0.038 154 0.053 333 6 65.497 44 3.807 692 0.047 590 0.045 128 26 60.410 26 4.230 769 0.044 718 0.044 615 7 72.492 31 4.307 692 0.032 821 0.050 256 27 63.589 74 3.269 231 0.035 282 0.055 385 8 51.507 69 3.192 308 0.047 179 0.049 744 28 54.051 28 3.730 769 0.041 436 0.051 282 9 64.861 54 4.115 385 0.042 667 0.04 29 55.323 08 4.153 846 0.032 0.047 692 10 59.138 46 3.384 615 0.037 333 0.06 30 68.676 92 3.346 154 0.048 0.052 308 11 71.856 41 3.230 769 0.042 256 0.043 077 31 64.225 64 3.653 846 0.045 128 0.059 487 12 52.143 59 4.269 231 0.037 744 0.056 923 32 59.774 36 3.846 154 0.034 872 0.040 513 13 66.769 23 3.538 462 0.036 103 0.050 769 33 69.312 82 4.192 308 0.040 615 0.042 051 14 57.230 77 3.961 538 0.043 897 0.049 231 34 54.687 18 3.307 692 0.039 385 0.057 949 15 73.764 10 3.461 538 0.044 308 0.055 897 35 52.779 49 3.884 615 0.045 538 0.054 359 16 50.235 90 4.038 462 0.035 692 0.044 103 36 71.220 51 3.615 385 0.034 462 0.045 641 17 74.4 3.115 385 0.036 513 0.047 179 37 62.953 85 3.5 0.038 974 0.043 590 18 49.6 4.384 615 0.043 487 0.052 821 38 61.046 15 4 0.041 026 0.056 410 19 68.041 03 3.923 077 0.033 231 0.058 462 39 67.405 13 4.346 154 0.045 949 0.048 205 20 55.958 97 3.576 923 0.046 769 0.041 538 40 56.594 87 3.153 846 0.034 051 0.051 795
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表 6 目标参数识别模型样本点设计变量
Table 6. Design variables of sample points of the target parameter recognition model
样本 线谱数 ${\omega _1}$/Hz ${\omega _2}$/Hz ${\omega _3}$/Hz 样本 线谱数 ${\omega _1}$/Hz ${\omega _2}$/Hz ${\omega _3}$/Hz 样本 线谱数 $ \omega_{1} $/Hz $ \omega_{2} $/Hz $ \omega_{3} $/Hz 1 12 1.2 2.1 35.6 15 10 1.2 19.8 33.4 29 7 1.5 16.4 34.7 2 10 1.5 14.5 30.8 16 8 1.7 18.8 38.6 30 11 1.3 9.7 35.3 3 9 1.4 16.3 33.6 17 10 1.2 1.7 32.6 31 9 11.5 26.5 37.6 4 12 2 11.5 35.8 18 6 0.8 1.7 20.3 32 9 1.4 6.3 30.1 5 9 0.7 1.7 31.2 19 10 1.4 28 38.7 33 9 1.2 11.6 25.8 6 8 1.3 11.8 26.4 20 7 1.5 14.2 31.9 34 8 0.7 13.7 31.4 7 7 1.2 24.7 34.4 21 8 1.3 14.5 30.8 35 8 0.7 1.6 35.6 8 10 14.3 32.2 39.5 22 12 12.2 23.9 38.8 36 9 1.2 3.4 34.5 9 10 1.3 6.3 27.7 23 9 1.2 10.2 35.2 37 7 1.4 11.6 26.8 10 12 12.4 28.6 39.9 24 7 1.7 16 35.6 38 7 1.4 13.7 30.1 11 9 1.2 3.4 33.4 25 9 1.2 1.7 34.3 39 10 0.5 1.2 1.8 12 8 0.7 1.6 37.2 26 9 1.4 14.5 31.1 40 10 1.6 12.5 29.3 13 8 1.3 10.7 35.8 27 12 1.4 10.7 37.5 14 6 1.5 14.9 32.8 28 8 0.7 1.6 34.1
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