Inversion of thermal parameters of aircraft fuel tank based on particle swarm optimization
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摘要:
为获取用于定量评估可燃性的飞机燃油箱热参数,从集中参数法建立燃油箱热模型的假设出发,基于粒子群算法和飞行试验数据,对某型飞机中央油箱热参数的反演进行了探索。选取了4种不同的参数作为目标函数,对比研究了目标函数的选取对热参数反演结果的影响。研究结果显示:反演得出的燃油箱热参数模型,其输出值与试验值变化规律一致,证明了该方法的有效性;其次以整体均方差为目标函数的反演结果与试验值最为吻合,模型输出值与试验值最大偏差为2.62 K;最后对整体均方差增加惩罚项的措施能够使反演后热参数模型满足适航规章的要求。
Abstract:In order to obtain the thermal parameters of aircraft fuel tank for quantitative evaluation of flammability, relying on the assumption of establishing fuel tank thermal model with lumped parameter method, the inversion of thermal parameters of a certain aircraft central fuel tank was explored based on particle swarm optimization algorithm and flight test data. Four different parameters were selected as the objective functions to study the influences of the selection of the objective function on the inversion results of thermal parameters. Results showed that the output value of the fuel tank thermal parameter model was consistent with the experimental value, which proved the effectiveness of the method; the maximum deviation between the model output and the experimental value was 2.62 K; finally, adding a penalty term to the overall mean square error could make the inversion thermal parameter model meet the requirements of airworthiness regulations.
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表 1 飞行试验基本信息
Table 1. Essential information of flight tests
序号 地面气温/K 巡航时间/min 备注 Flt-1 306.9 28.5 Flt-2 299.9 1 Flt-3 305.5 27 短航程 Flt-4 307.2 180 长航程 Flt-5 310.1 28 Flt-6 294.5 180 长航程 Flt-7 305.1 30 Flt-8 290.2 28 短航程 Flt-9 287.4 1 表 2 平衡温差变量定义
Table 2. Definition of equilibrium temperature difference
Hp/m ΔT/K 场高 X(1) 609.6 X(2) 3048 X(3) 7620 X(4) 9144 X(5) Hcr X(6) 表 3 热时间常数τ变量定义
Table 3. Definition of thermal time constant τ
s Hp/m Qfr/kg 0 500 1000 2500 满油 场高 X(7) X(8) X(9) X(10) X(11) 3048 X(12) X(13) X(14) X(15) X(16) Hcr X(17) X(18) X(19) X(20) X(21) 表 4 目标函数定义
Table 4. Definition of objective function
序号 参数名 计算公式 备注 条件1 最大偏差 $J(\mathrm{\Delta }T,\tau )=\mathrm{m}\mathrm{a}\mathrm{x}\left(\left|{T}_{pq}-{T}_{ \mathrm{m}, pq}\right|\right)$ 条件2 均方误差 $J(\mathrm{\Delta }T,\tau )=\dfrac{1}{nN}\displaystyle\sum _{p=1}^{N}{\displaystyle\sum _{q=1}^{n}({T}_{pq}-{T}_\mathrm{m},{qp}) ^{2} }$ 条件3 架次最大均方误差 $J(\mathrm{\Delta }T,\tau )=\mathrm{m}\mathrm{a}\mathrm{x}\left[\dfrac{1}{n}{\displaystyle\sum _{p=1}^{n}({T}_{pq}-{T}_\mathrm{m},{pq}) ^{2} }\right]$ 条件4 带惩罚项的
均方误差$J(\mathrm{\Delta }T,\tau )=\dfrac{1}{nN}\displaystyle\sum _{p=1}^{N}{\displaystyle\sum _{q=1}^{n}\left[a\left({T}_{pq}-{T}_\mathrm{m},{pq}\right)\right]^{2} }$ 当Tm, pq−Tpq <−1.1 K时,a取3;其余情况a取1。 表 5 平衡温差ΔT反演结果
Table 5. Inversion results of equilibrium temperature difference ΔT
K 序号 Hp /m 场高 609.6 3048 7620 9144 Hcr 条件1 9.67 2.27 6.97 22.91 22.13 7.95 条件2 0 7.02 10.98 17.60 21.14 10.58 条件3 5.30 2.44 25.06 20.66 15.62 15.29 条件4 9.67 2.27 6.97 22.91 22.13 7.95 表 6 热时间常数τ反演结果
Table 6. Inversion results of thermal time constant τ
s 序号 Hp/m Qfr/kg 0 500 1000 2500 满油 条件1 场高 1442 1 20000 18600 8510 3048 12990 5310 18950 17790 13000 Hcr 14810 8600 20000 10560 2590 条件2 场高 13553 18905 20000 5565 20000 3048 116701 17811 20000 14438 5891 Hcr 17819 13024 20000 2713 15178 条件3 场高 16678 14329 13519 7499 12388 3048 7765 14989 17212 14432 4058 Hcr 4773 1653 20000 695.6 15225 条件4 场高 2413 13398 20000 3851 12687 3048 14124 14580 20000 3281 19373 Hcr 6676 9643 20000 4350 12419 表 7 模型输出值与试验结果对比分析
Table 7. Comparative analysis of model output values and test results
序号 统计参数 Flt-1 Flt-2 Flt-3 Flt-4 Flt-5 Flt-6 Flt-7 Flt-8 Flt-9 条件1 最大偏差/K 2.68 2.81 2.81 2.81 2.66 2.28 1.17 0.61 0.68 架次最大均方差/K2 1.93 1.78 2.14 3.27 2.53 1.72 0.40 0.09 0.09 均方差/K2 1.82 tns/min 32 0 39 62 38 40 0 0 0 条件2 最大偏差/K 2.32 2.62 2.62 1.72 2.37 1.53 2.03 0.88 0.83 架次最大均方差/K2 1.28 1.40 1.63 0.50 1.74 0.33 0.94 0.11 0.14 均方差/K2 0.77 tns/min 17 0 31 0 26 0 0 0 0 条件3 最大偏差/K 2.21 2.90 2.52 3.11 2.22 2.21 2.07 0.97 0.72 架次最大均方差/K2 1.16 1.44 1.44 1.44 1.39 1.10 1.44 0.33 0.17 均方差/K2 1.17 tns/min 17 0 28 0 23 0 0 0 0 条件4 最大偏差/K 0.88 1.87 0.92 0.61 0.83 0.47 1.74 0.49 0.29 架次最大均方差/K2 1.02 5.22 1.06 0.83 0.96 0.33 3.65 0.31 0.18 均方差/K2 1.30 tns/min 0 0 5 0 0 0 0 0 0 -
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