基于微形变分析的电容式MEMS加速度计温漂误差精密估计方法

doi:10.12305/j.issn.1001-506X.2024.07.25

Abstract

Abstract:

Owing that the conventional temperature drift error (TDE) estimation method for capacitive micro-electro-mechanical system (MEMS) accelerometers (CMA) has demerits of inaccurate TDE traceability and tedious model establishing process, low accuracy and high complexity are introduced inevitably. A precise TDE estimation method of CMA based on micro-deformation analysis is proposed. Firstly, TDE is traced accurately with micro-deformation analysis, and a modified TDE estimation model is established with radial basis function neural network (RBFNN). Secondly, an accurate model identification method is proposed under Expert-Fuzzy assisted decision-making based on expert experience and fuzzy theory, which offers effective structural configuration guidance to the modified model. Then, temperature experiment is designed to test CMA, and the conventional and modified models are evaluated in performance by comparing their bias stability. Experimental results show that the establishing process for the modified model is greatly simplified, and its bias stability is improved by 35%. It ensures that TDE of CMA can be estimated much more precisely, which decouples temperature dependency of Si-based material and improves the environmental adaptability of CMA.

Key words: micro-electro-mechanical system (MEMS), temperature drift error (TDE) estimation, micro-deformation analysis, Expert-Fuzzy aided decision-making, radial basis function neural network (RBFNN)

CLC Number:

TH714
TN409

Bing QI, Jianhua CHENG, Yanchi ZHAO, Zili WANG. Precise temperature drift error estimation method for capacitive MEMS accelerometers based on micro-deformation analysis[J]. Systems Engineering and Electronics, 2024, 46(7): 2437-2445.

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References 21

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序号	名称	表达式	神经层
1	径向基函数	$\phi_{j}(x)=\mathrm{e}^{-\left\\|x-c_{j}\right\\|^{2} / 2 \sigma_{j}^{2}}$	隐藏层
2	对称S形函数	$\tan \operatorname{sig}(x)=\frac{2}{1+\mathrm{e}^{-2 x}}-1$	隐藏层
3	对数S形函数	$\log \operatorname{sig}(x)=\frac{1}{1+\mathrm{e}^{-x}}$	隐藏层
4	线性函数	$y=x$	隐藏层输出层
5	对称线性饱和函数	$y=\left\{\begin{array}{l}-1, x <-1 \\x, x \in[-1,1] \\1, x>1\end{array}\right.$	隐藏层输出层

提升倍数 P	输入模糊集合1	计算时间 T_P/s	输入模糊集合2	论域
指标1	PG	指标1	PG	(0, 1)
指标2	PB	指标2	PB	(1, 2)
指标3	PM	指标3	PM	(2, 3)
指标4	PS	指标4	PS	(3, 4)
指标5	PZ	指标5	PZ	(4, 5)
指标6	NZ	指标6	NZ	(5, 6)
指标7	NS	指标7	NS	(6, 7)
指标8	NM	指标8	NM	(7, 8)
指标9	NB	指标9	NB	(8, 9)
指标10	NG	指标10	NG	(9, 10)

输入模糊集合1	输入模糊集合2	输出模糊集合 (隐含层/输出层函数)	论域
元素1	元素1	径向基/线性	(0, 5)
元素2	元素2	对称S形/线性	(5, 15)
元素3	元素3	对数S形/线性	(15, 25)
元素4	元素4	均为线性	(25, 35)
元素5	元素5	对称线性饱和/线性	(35, 45)
元素6	元素6	径向基/对称线性饱和	(45, 55)
元素7	元素7	对称S形/对称线性饱和	(55, 65)
元素8	元素8	对数S形/对称线性饱和	(65, 75)
元素9	元素9	线性/对称线性饱和	(75, 85)
元素10	元素10	均为对称线性饱和	(85, 90)

输出层	隐含层	提升倍数P	计算时间T_P/s
线性函数	径向基函数	5.22×10³	4.22×10^-4
	对称S形函数	4.07×10¹¹	3.82×10^-4
	对数S形函数	5.29×10¹⁰	3.38×10^-4
	线性函数	1.65×10¹⁷	3.13×10^-4
	对称线性饱和函数	4.29×10¹¹	3.07×10^-4
对称线性饱和函数	径向基函数	68.53	3.67×10^-4
	对称S形函数	97.02	3.47×10^-4
	对数S形函数	99.35	3.58×10^-4
	线性函数	100.45	2.96×10^-4
	对称线性饱和函数	96.89	3.08×10^-4

P	模糊集合1	T_P(s)	模糊集合2
1.65×10¹⁷	PB	4.22×10^-4 3.82 ×10^-4 3.67×10^-4 3.58 ×10^-4	PB
5.29×10¹⁰ 4.07×10¹¹ 4.29 ×10¹¹	PM	-	-
5.22×10³	PS	3.38×10^-4 3.47×10^-4	PS
100.45	NS	3.13×10^-4 3.07 ×10^-4 2.96×10^-4 3.08 ×10^-4	NB
97.02 99.35 96.89	NM	-	-
68.53	NB	-	-

Precise temperature drift error estimation method for capacitive MEMS accelerometers based on micro-deformation analysis

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模糊集合1	模糊集合2	输出集合(隐含层/输出层)
PS	PB	径向基/线性函数
PM	PB	对称S形/线性函数
PM	PS	对数S形/线性函数
PB	NB	线性函数
PM	NB	对称线性饱和/线性函数
NB	PB	径向基/对称线性饱和
NM	PS	对称S形/对称线性饱和
NM	PB	对数S形/对称线性饱和
NS	NB	线性函数/对称线性饱和
NM	NB	对称线性饱和函数

类别	组别	原始数据	传统模型	改进模型
MSE/g²	第1组	3.653×10^-2	4.766×10^-5	2.909×10^-5
	第2组	3.641×10^-2	4.510×10^-5	2.819×10^-5
	第3组	3.652×10^-2	4.916×10^-5	3.112×10^-5
计算时间/s	第1组	4.132×10^-4	3.553×10^-4	3.625×10^-4
	第2组	4.129×10^-4	3.504×10^-4	3.576×10^-4
	第3组	4.118×10^-4	3.268×10^-4	3.349×10^-4

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