多功能传感器信号重构方法及实验研究
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摘要
近年来,在科学试验工程应用中越来越多地采用多功能传感技术,这是因为和传统的传感器比较,它有很多优越性,如体积小、能耗低和功能灵活等,这些优点增加了测量系统判决和估计的精确性、稳健性以及在对抗环境下的生存能力。多功能传感器技术的迅猛发展,对信号处理理论和方法提出了新的要求。传统的信号重构技术已经不能满足多功能传感器发展的全部要求,诸如信号非线性、拟合精度和粗差处理等问题用经典的重构算法已经无法解决。为此,本文系统研究了非线性多功能传感器的信号重构问题,并提出了若干种解决上述问题的算法,旨在为多功能传感器的开发应用奠定理论和技术基础。
在非线性多功能传感器的信号重构过程中,训练样本集不可避免地夹杂粗差数据。为了得到既有较强鲁棒性又有较高效率的估值,本文分别从抗差估计和粗差剔除两个层面给出了解决方案。其中抗差估计的研究又分为M估计法和抗差最小二乘法两部分。一方面,M估计法利用极大似然估计原理,对残差取1范数,抑制了离群数据对整体误差的影响,从而弥补了在实验数据存有奇异值情况下,最小二乘法重构误差较大的缺点。另一方面,抗差最小二乘估计通过等价权原理,把抗差估计与加权最小二乘结合在一起,因此在抵御粗差影响的同时保持了最小二乘法的优点。非线性信号重构的粗差抑制结果表明,无论是M估计法,还是抗差最小二乘法,都具有良好的抗差能力和收敛性。
在粗差剔除研究中,分别将交叉验证法和F-S检验法用于粗差数据的定位、剔除和修复。其中,交叉验证法利用交叉验证原理和径向基神经网络对实验训练数据进行多次随机取样和重构检验,通过对重构结果的寻优处理,确定不含粗差数据的最优样本和系统模型。而F-S检验法考虑到传统粗差检验方法容易对高杠杆点和粗差点产生误判,因此在结合学生氏和外学生氏残差检验的基础上有效地区分了两者。定位粗差后,利用径向基神经网络拟合法重建粗差点,从而完成训练样本集的修复。仿真结果证实了交叉验证法和F-S检验法在粗差数据定位和修复中的有效性。
针对传统最小二乘法全局拟合的局限性,本文将一种新型的数值算法,移动最小二乘法应用于非线性多功能传感器的信号重构。通过详细研究插值函数的构造方法及性质,合理地选取基函数和权函数,移动最小二乘法能够得到精确的信号重构值。另外,由于移动最小二乘法在对固定点的重构中将退化为传统最小二乘法,为了避免求解奇异方程,本文给出了改进算法。通过选取等价正交基函数,改进移动最小二乘法在避免奇异情况产生的同时,简化了信号重构的进程。
为了检验非线性信号重构算法在实际应用中的效果,本文进行了盐油水溶液的浓度测量实验。实验选用四电极超声波多功能传感器,对不同含油率、含盐率和温度值的混合溶液进行了测量,并得到了电导率和超声波渡越时间的实测数据。最后,利用改进移动最小二乘法拟合实验数据,构造出了传感器的逆模型,实现了输入信号的重构。实验结果令人满意,证明了非线性传感器的信号重构算法在实际应用中的可行性。
In recent years, multifunctional sensing techniques have become pervasive and essential in particular engineering and science fields, which draw much more attention than traditional sensor. Since multifunctional sensors ensure the merits of small package, low consumption and smart function, they coherently improve the precision and stability of estimation and judgment for measurement system, moreover increase the exist probability in antagonistic environment. Consequently, the rapid development of multifunctional sensing technique brings many new requests to signal processing theories and methods. Since traditional signal reconstruction technologies can not solve the existing problem such as nonlinearity, regressing precision and gross error detection, this thesis systemically studies nonlinear signal reconstruction of multifunctional sensor and presents several practical strategies according to these problems inorder to prompt the further development and application of multifunctional sensors.
In terms of actual situation that the training sample set of multifunctional sensor inevitably comprises gross error, our research presents robust estimation and gross error rejection strategies separately, which aim at achieving better robustness and higher efficiency in signal reconstruction. As one of robust estimation studies, M-estimator bases on maximum likelihood estimation theory. By calculating 1-morm of residual, this method can efficiently restrain the effect to whole errors caused by outliers, furthermore make up for the deficiency of Least Squares in case of experimental data comprising gross error. On the other hand, based on equivalent weight thought, Robust Least Squares algorithm combines Weighted Least Squares method and robust estimation to resist the effect of gross error and maintain the merits of traditional Least Squares. Emulation results show that both M-estimator and Robust Least Squares are provided with excellent robustness and convergency.
In gross error detection and rejection study, Cross Validation and F-S test are brought forward. Therein, Cross Validation algorithm proceeds repeated random sampling and regresses the experimental data with Radial Basis Function neural network. Then optimal training data and systemic model are finally determined through optimizing above calculations. Additionally, for considering that traditional methods of gross error detection are easy to misjudge potential case and gross error, F-S test is founded upon the studentized residual and externally studentized to be capable of distinguishing these two cases efficiently. Thereafter, gross errors will be located and replaced with the estimations. Simulation results verify the wonderful validities of Cross Validation and F-S test algorithm in gross error detection and recovery aspect.
A novel numerical solution method, Moving Least Squares is employed to solve nonlinear reconstruction of multi-functional sensor with a view that Least Squares is restricted in global regression. On the basis of construction method and characters of interpolated function, Moving Least Squares reasonably chooses basis and weight function, and then acquires the reconstructed value of input signals precisely. However, according to each single point, Moving Least Squares will degenerate to Least Squares method. In order to avoid the singular solution, this thesis proposes a modified algorithm, namely Improved Moving Least Squares. In terms of calculating the equivalent orthogonal basis function, this improved method prevents solving the singular functions and simplifies the reconstruction procedure simultaneously.
For the purpose of verifying effectiveness of nonlinear signal reconstruction methods in practical model, the research proceeds a concentration measurement experiment of ternary solution. The multifunctional sensor integrated with four-electrode and ultrasonic sensitive material can obtain the information of mixed solution like oil content, salt content and temperature in different cases, and output corresponding signal as conductivity and transit time. Finally, Improved Moving Least Squares method is applied to regress the obtained data, and accomplishes the input signal reconstruction through establishing the inverse model of sensor. Experimental results are satisfying and definitely prove the feasibility of the proposed signal reconstruction method in practical application.
在非线性多功能传感器的信号重构过程中,训练样本集不可避免地夹杂粗差数据。为了得到既有较强鲁棒性又有较高效率的估值,本文分别从抗差估计和粗差剔除两个层面给出了解决方案。其中抗差估计的研究又分为M估计法和抗差最小二乘法两部分。一方面,M估计法利用极大似然估计原理,对残差取1范数,抑制了离群数据对整体误差的影响,从而弥补了在实验数据存有奇异值情况下,最小二乘法重构误差较大的缺点。另一方面,抗差最小二乘估计通过等价权原理,把抗差估计与加权最小二乘结合在一起,因此在抵御粗差影响的同时保持了最小二乘法的优点。非线性信号重构的粗差抑制结果表明,无论是M估计法,还是抗差最小二乘法,都具有良好的抗差能力和收敛性。
在粗差剔除研究中,分别将交叉验证法和F-S检验法用于粗差数据的定位、剔除和修复。其中,交叉验证法利用交叉验证原理和径向基神经网络对实验训练数据进行多次随机取样和重构检验,通过对重构结果的寻优处理,确定不含粗差数据的最优样本和系统模型。而F-S检验法考虑到传统粗差检验方法容易对高杠杆点和粗差点产生误判,因此在结合学生氏和外学生氏残差检验的基础上有效地区分了两者。定位粗差后,利用径向基神经网络拟合法重建粗差点,从而完成训练样本集的修复。仿真结果证实了交叉验证法和F-S检验法在粗差数据定位和修复中的有效性。
针对传统最小二乘法全局拟合的局限性,本文将一种新型的数值算法,移动最小二乘法应用于非线性多功能传感器的信号重构。通过详细研究插值函数的构造方法及性质,合理地选取基函数和权函数,移动最小二乘法能够得到精确的信号重构值。另外,由于移动最小二乘法在对固定点的重构中将退化为传统最小二乘法,为了避免求解奇异方程,本文给出了改进算法。通过选取等价正交基函数,改进移动最小二乘法在避免奇异情况产生的同时,简化了信号重构的进程。
为了检验非线性信号重构算法在实际应用中的效果,本文进行了盐油水溶液的浓度测量实验。实验选用四电极超声波多功能传感器,对不同含油率、含盐率和温度值的混合溶液进行了测量,并得到了电导率和超声波渡越时间的实测数据。最后,利用改进移动最小二乘法拟合实验数据,构造出了传感器的逆模型,实现了输入信号的重构。实验结果令人满意,证明了非线性传感器的信号重构算法在实际应用中的可行性。
In recent years, multifunctional sensing techniques have become pervasive and essential in particular engineering and science fields, which draw much more attention than traditional sensor. Since multifunctional sensors ensure the merits of small package, low consumption and smart function, they coherently improve the precision and stability of estimation and judgment for measurement system, moreover increase the exist probability in antagonistic environment. Consequently, the rapid development of multifunctional sensing technique brings many new requests to signal processing theories and methods. Since traditional signal reconstruction technologies can not solve the existing problem such as nonlinearity, regressing precision and gross error detection, this thesis systemically studies nonlinear signal reconstruction of multifunctional sensor and presents several practical strategies according to these problems inorder to prompt the further development and application of multifunctional sensors.
In terms of actual situation that the training sample set of multifunctional sensor inevitably comprises gross error, our research presents robust estimation and gross error rejection strategies separately, which aim at achieving better robustness and higher efficiency in signal reconstruction. As one of robust estimation studies, M-estimator bases on maximum likelihood estimation theory. By calculating 1-morm of residual, this method can efficiently restrain the effect to whole errors caused by outliers, furthermore make up for the deficiency of Least Squares in case of experimental data comprising gross error. On the other hand, based on equivalent weight thought, Robust Least Squares algorithm combines Weighted Least Squares method and robust estimation to resist the effect of gross error and maintain the merits of traditional Least Squares. Emulation results show that both M-estimator and Robust Least Squares are provided with excellent robustness and convergency.
In gross error detection and rejection study, Cross Validation and F-S test are brought forward. Therein, Cross Validation algorithm proceeds repeated random sampling and regresses the experimental data with Radial Basis Function neural network. Then optimal training data and systemic model are finally determined through optimizing above calculations. Additionally, for considering that traditional methods of gross error detection are easy to misjudge potential case and gross error, F-S test is founded upon the studentized residual and externally studentized to be capable of distinguishing these two cases efficiently. Thereafter, gross errors will be located and replaced with the estimations. Simulation results verify the wonderful validities of Cross Validation and F-S test algorithm in gross error detection and recovery aspect.
A novel numerical solution method, Moving Least Squares is employed to solve nonlinear reconstruction of multi-functional sensor with a view that Least Squares is restricted in global regression. On the basis of construction method and characters of interpolated function, Moving Least Squares reasonably chooses basis and weight function, and then acquires the reconstructed value of input signals precisely. However, according to each single point, Moving Least Squares will degenerate to Least Squares method. In order to avoid the singular solution, this thesis proposes a modified algorithm, namely Improved Moving Least Squares. In terms of calculating the equivalent orthogonal basis function, this improved method prevents solving the singular functions and simplifies the reconstruction procedure simultaneously.
For the purpose of verifying effectiveness of nonlinear signal reconstruction methods in practical model, the research proceeds a concentration measurement experiment of ternary solution. The multifunctional sensor integrated with four-electrode and ultrasonic sensitive material can obtain the information of mixed solution like oil content, salt content and temperature in different cases, and output corresponding signal as conductivity and transit time. Finally, Improved Moving Least Squares method is applied to regress the obtained data, and accomplishes the input signal reconstruction through establishing the inverse model of sensor. Experimental results are satisfying and definitely prove the feasibility of the proposed signal reconstruction method in practical application.
引文
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