Time Domain Reconstruction Optimization of Pyrotechnic Shock ResponseSpectrum via Adaptive Genetic Algorithm
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摘要: 为解决现有爆炸冲击响应谱(Shock Response Spectrum，SRS)加速度重构方法依赖于大量试验数据的问题，对比了阻尼正弦与小波两种不同加速度重构方法在合成爆炸冲击响应谱时的性能。将对重构SRS质量的评估转化为与目标谱匹配度的最小值优化问题，并首次将自适应遗传算法(Adaptive Genetic Algorithm, AGA)应用于SRS重构的优化问题中。对比了交叉先行、变异先行和不定向3种不同的AGA在爆炸冲击响应谱时域重构优化中的性能，并与基本遗传算法(Genetic Algorithm, GA)进行对比。结果表明，AGA的优化结果比GA有较大幅度的改善，且不定向AGA所得结果是3种AGA方法中最好的，其SRS各频点数值均在(–3/+6)dB容差范围之内，与目标谱的匹配度更好。仿真对比算例验证了该方法在冲击响应谱的时域重构应用中具有较高的准确性和实用性，为进一步提高航天器结构在爆炸冲击载荷下响应的计算精度提供了支撑。Abstract: In order to solve the problem that the existing acceleration reconstruction methods rely on a large number of test data, this paper compares the performances of two different acceleration reconstruction methods, the damped sine and the wavelet. The evaluation of the quality in reconstructing shock response spectrum (SRS) is transformed into the minimum optimization problem of the matching degree of the reconstructed SRS with the target spectrum. The adaptive genetic algorithm (AGA) is applied to the optimization problem of SRS reconstruction for the first time. This paper compares the performances of three different AGAs in time domain reconstruction and optimization of SRS, which are crossover first, mutation first and uncertain-order AGAs, and compares them with the genetic algorithm (GA). Numerical tests show that AGA’s optimization results are much better than GA’s, and the results obtained by uncertain-order AGA are the best among the three AGA methods, through which all frequency points are within the tolerance range of (–3/+6)dB. This research provides support for further improving the response simulation accuracy of spacecraft structure under pyrotechnic shock loads.
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图 4 参数灵敏度分析前后远场SRS结果对比
Figure 4. Comparison results of empirical parameters and optimized parameters for far-field SRS
图 5 参数灵敏度分析前后中场和近场SRS结果对比
Figure 5. Comparison results of empirical parameters and optimized parameters for mid-field and near-field SRS
图 9 不同种群数目下中场目标SRS结果对比
Figure 9. Comparison results of mid-field SRS under different population numbers
表 1 决策变量的取值范围
Table 1. Variation ranges of the decision variables
Optimization variable Variation range Am (1/4 to 1/3)A0 (g) tdm [0.0001, 0.015] (s) ${\xi _{{m} } }$ [0.001, 0.1] Nm [5, 27] (odd number) 
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表 2 典型爆炸冲击响应谱规范
Table 2. Specification of SRS
Far field Medium field Near field Frequency/Hz Amplitude/g Frequency/Hz Amplitude/g Frequency/Hz Amplitude/g 100 80 100 150 200 250 450 600 300 200 1 000 4 000 900 1 000 1 500 3 000 1 200 5 000 10 000 1 000 10 000 3 000 10 000 5 000
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表 3 阻尼正弦与小波合成SRS计算结果对比
Table 3. Comparison results of damped sine and wavelet
Parameter Far field Medium field Near field Damped sine Wavelet Damped sine Wavelet Damped sine Wavelet Objective function value/g 44.2 294.9 103.7 890.1 155.5 1491 Time/s 142.2 142.1 139.7 139.2 81.9 80.2
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表 4 AGA选用参数
Table 4. Parameters of AGA
Parameter Value Parameter Value Parameter Value Population 40 Pm1 0.1 ${{P_{{\rm{c}}0}}}$ 0.75 Maximum evolutionary generation 200 Pm2 0.05 ${P_{\rm{m}}^{{\rm{LB}}}}$ 0.01 Pc1 0.9 Pm3 0.005 ${P_{\rm{m}}^{{\rm{UB}}}}$ 0.1 Pc2 0.5 ${P_{\rm{c}}^{{\rm{LB}}}}$ 0.5 ${{P_{{\rm{m}}0}}}$ 0.05 Pc3 0.1 ${P_{\rm{c}}^{{\rm{UB}}}}$ 0.9
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表 5 GA与AGA优化结果对比
Table 5. Comparison results of GA and AGA (OFV: objective function value)
Algorithm Far field Medium field Near field OFV/g Current generation Total time/s OFV/g Current generation Total time/s OFV/g Current generation Total Time/s GA 44.20 200 142.2 103.7 200 139.7 155.5 200 81.9 Crossover first AGA 44.05 115 147.1 102.9 102 135.1 156.8 127 82.9 Mutation first AGA 44.29 128 139.8 103.9 137 136.1 155.4 158 83.6 Uncertain-order AGA 44.25 89 172.1 103.1 87 143.0 155.3 98 102.2
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表 6 不同种群数目下中场目标SRS优化值与计算时间对比
Table 6. Comparison of optimization values and calculation time for mid-field SRS under different population numbers
Population Final optimization value/g Calculation time of
200 generations/s20 77.94 53.34 40 48.48 139.70 60 44.53 148.80 80 37.93 159.70 100 27.88 221.80
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