Inertia mass of force transducers based on a modified Monte Carlo calibration method
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摘要:
惯性质量是力传感器模型的重要校准参数，也是影响动态力测量精度的关键因素之一。为了消除参数误差对惯性质量校准模型引起的病态，提出一种改进Monte Carlo校准（MMCC）方法。首先，建立力传感器惯性质量、配重质量与测量响应之间的模型；其次，利用伪随机数生成技术，分别对该模型中的配重质量、加速度和电压进行样本空间的全域模拟；然后，根据区间判断准则筛选出满足预设精度的有效样本；最后，结合有效样本的概率，估计出力传感器的惯性质量，并实现动态校准。为了验证本文方法的准确性，利用正弦激振台对Kistler 9331B型力传感器进行动态校准。实验结果表明，惯性质量的估计值为83.91 g，估计误差为0.67%，标准差为0.74 g；动态力的校准误差范围为[-7.88%，11.46%]。校准误差明显低于传统的二次及多次配重法。
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关键词:
- 力传感器 /
- 估计 /
- 模型病态 /
- Monte Carlo模拟 /
- 动态校准
Abstract:As an important parameter of a force transducer, the inertia mass can reduce the measurement accuracy of a dynamic force unless it has been accurately estimated. To eliminate the ill-posedness of an calibration model of the inertia mass caused by parameter errors, a modified Monte Carlo calibration (MMCC) method is proposed. Firstly, the mathematical model among the inertia mass, the additional mass, and the measurement response of the force transducer is built. Secondly, the parameter samples of this model including additional mass, acceleration, and voltage are simulated by pseudo-random number generation globally. Thirdly, the valid samples of these parameters are selected by interval screening technique. Finally, the inertia mass of the force transducer is estimated by solving the probability of these valid samples as well as the calibration of the force transducer. The accuracy of the MMCC method is verified by dynamic calibrating a Kistler 9331B force transducer with a sinusoidal vibration exciter. The experimental results show that the estimate of the inertia mass is 83.91g, the estimation error is 0.67%, the standard deviation is 0.74 g, and the calibration error range of the dynamic force is[-7.88%, 11.46%]. It indicates that the calibration error of MMCC method is less than the traditional secondary additional mass method and the multi-additional mass method.
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Key words:
- force transducers /
- estimation /
- ill-posedness of model /
- Monte Carlo simulation /
- dynamic calibration
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图 3 惯性质量的伪随机数模拟分布
Figure 3. Simulated distribution of pseudo-random numbers for inertia mass
图 5 力传感器动态校准装置
1—隔振基座；2—正弦激振台；3—被校准力传感器；4—配重；5—双频激光干涉仪；6—二维精密微动平台；7—测量支架；8—信号传输线；9—传感器基座。
Figure 5. Dynamic calibration device of a force transducer
图 6 不同配重质量的有效样本概率
Figure 6. Probability of valid samples for different additional mass
表 1 力传感器的激励与响应
Table 1. Excitations and responses of force transducer
No. 117.931 g配重 229.562 g配重 4 476.340 g配重 7 621.833 g配重 ai(t)/(m·s-2) Ui(t)/mV ai(t)/(m·s-2) Ui(t)/mV ai(t)/(m·s-2) Ui(t)/mV ai(t)/(m·s-2) Ui(t)/mV 1 151.92 623.69 158.78 650.83 165.65 679.46 178.68 732.70 2 152.61 623.46 159.47 654.34 166.33 682.31 179.37 736.02 3 153.29 629.81 160.16 656.49 167.02 685.99 180.05 739.03 4 153.98 633.01 160.84 659.73 167.70 688.37 180.74 739.89 5 154.67 634.48 161.53 662.12 168.39 691.56 181.43 745.46 6 155.35 636.03 162.21 665.26 169.08 694.24 182.11 747.95 7 156.04 636.83 162.90 668.72 169.76 696.18 182.79 750.59 8 156.73 642.98 163.59 669.61 170.45 699.95 183.48 753.29 9 157.41 645.64 164.27 670.38 171.13 702.01 184.17 755.78 10 158.09 648.50 164.96 673.33 165.65 679.46 184.86 758.45 
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表 2 传统配重法的估计误差
Table 2. Estimation error of traditional additional mass method
方法 估计值/g 标准差/g 估计误差/% 二次配重法 85.70 2.24 2.13 多次配重法 84.98 1.34 1.28
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