The Application of HHT in Mechanical Nanoscale Displacement Sensor of PZT Actuator*

HU Huan，YU Yong，WANG Hui，WU Qian，GE Yunjian

(1.Department of Automation，University of Science and Technology of China，Hefei 230027，China; 2.Graduate School of Science and Engineering，Kagoshima University，Kagoshima 890－0065，Japan; 3.Institute of Intelligent Machines，Chinese Academy of Sciences，Hefei 230031，China)

The Application of HHT in Mechanical Nanoscale Displacement Sensor of PZT Actuator*

HU Huan1，3，YU Yong2，WANG Hui3*，WU Qian1，3，GE Yunjian3

(1.Department of Automation，University of Science and Technology of China，Hefei 230027，China; 2.Graduate School of Science and Engineering，Kagoshima University，Kagoshima 890－0065，Japan; 3.Institute of Intelligent Machines，Chinese Academy of Sciences，Hefei 230031，China)

A relatively new algorithm called Hilbert-Huang transform(HHT)is proposed.It utilizes empirical mode decomposition(EMD)to filter noise in a nanoscale displacement sensor，which is actuated by PZT.However，even after the pre-filtering，the random noise still cannot be fully eliminated.The noise limits the resolution of the sensor and affects the dynamic range of the whole system.So the signal need to be further processed to increase the Signal to Noise Ratio(SNR)and then improve the performance of the sensor.Two kinds of methods are attempted.One is filtering the highest frequency noise of intrinsic mode functions(IMFs)after EMD.And the other one is to just filter the first and second IMFs.Finally，experiments are conducted to verify the effectiveness of the HHT algorithm and the improvement of sensor’s linearity.

nanoscale displacement sensor;piezoelectric ceramic actuator;HHT;EMD;signal processing

Nanoscale technology is one of the most important sciences in 21 century;which will bring a new industrial revolution［1］.Micro-displacement actuators can provide output of displacement in nanoscale.It has wide range of application in many areas，such as optical engineering，microelectronic engineering，aeronautics and astronautics and mechanical manufacture，etc.［2］.PZT actuator has drawn broad attention with its advantages of small volume，fast response，high stiffness，high accuracy，low heat generation and frictionless actuation［2－3］.

Hence，it is usually preferred as the actuating component for Micro-displacement actuators.The shape of sensor is cylindrical and the resolution is 3 nm with the measurement range of 1 micrometer.Also，PZT plays a vital role in the area of precision measurement and manufacturing.However，its hysteresis and nonlinear charac-teristic decrease the accuracy of measurement and slower the speed of the transient response［4］.Thus，the improvement of the micro-displacement stage’s position accuracy is greatly influenced.In order to solve these problems，we designed a Mechanical Nanoscale Displacement Sensor，which includes two parts.The first part is the mechanical structure of the sensor，which works as a mechanical displacement.The structure，mainly constructed by several levers and flexure hinges，enlarges the nanoscale displacement and finally transforms it into the stain of the strain gauge.The mechanical configuration of the fourth generation sensor is shown in Fig.1.

Fig.1The mechanical configuration of the fourth generation sensor

The second part refers to the real-time data acquisition and processing module，which mainly includes an instrumentation amplifier，an analog Low pass Filter，a zeroing module and a microcontroller module.This part detects the stain of the gauge and then converts it into voltage signal.After the process of hardware，the linearity of the digital signal has already been greatly improved.Generally speaking，in a data acquisition system，the noise problems can be divided into four subcategories:device’s noise，conducted noise，radiated noise，and external signal sources noise［5］.So，the nonlinear error of sensor can’t be avoided.This paper use software-related methods to increase linearity［6］.Software-related methods can be adopted to further increase the signal to noise ratio and then the performance of the sensor could be improved.The part of data acquisition and processing is shown in Fig.2.

Fig.2Data acquisition and processing module of the fourth generation sensor

At present，there is no special algorithm and system for processing micro-signal of PZT actuators in the world.The traditional time-frequency analysis methods，such as wavelet transformation and short-time Fourier transformation，are widely used in engineering application.However，most of these methods are based on the theory of Fourier transformation.In addition，these concepts are global.It is very easy to get spurious signal and aliasing.At the same time，Genetic Algorithms (Hou，Yang et al.2008)and micro-signal detection in Markov pattern recognition noises(Lee，Kang，et al.2006)are all have to be built model of the signal，which limits the real-time detection requirement.Therefore，this paper adopts the HHT to further process the signal collected and then digitally filters it.In this way，the performance of the sensor can be improved to a great extent.In 1998，HHT was proposed by Professor E Huang，member of National Academy of Engineering in America［7］.It is a kind of adaptive filtering method，which is effective in analysis of non-stable signal and nonlinear signal［8－9］.Our signal collected in the experiments happens to have those features.The HHT consists of two components:the EMD technique and the Hilbert transform.

1 The Hilbert-Huang Transform

The HHT is an empirically based on time-frequency analysis method.It takes advantage of the EMD to decompose original signal into a series of(IMFs)［8－10］.Each individual IMF is an oscillating component through a sifting process.Then，each IMF is processed by Hilbert transform.

1.1 Introduction of EMD

EMD is realized in MATLAB software by compiling M files.Given an arbitrary signal x(t)，following the EMD method，a decomposition of the signal into orders of IMFs and a residual rn(t)can be achieved and shown as:

The IMFs，C1(t)，C2(t)，…，Cn(t)are nearlymonocomponent signals and include different frequency bands ranging from high to low.The frequency components contained in each frequency band are different and they change with the variation of original signal x (t)，while rn(t)represents the central tendency of original signal x(t).

1.2 The Hilbert Transform

After obtaining the IMFs，we apply to the HT on each IMF.

Where P denotes the principal Cauchy value.

By definition，the analytic signal corresponding to each IMF is

Where aj(t)and θj(t)are the instantaneous amplitude and the instantaneous phase，respectively，of the signal at time t.

According to the analytic signal，Cj(t)can be represented as:

The instantaneous amplitude and instantaneous phase of the analytic signal are defined in the usual manner which can respectively be represented as:

The analytic signal represents the time-series as lowly varying amplitude envelope modulating a faster varying phase function［12］.The IF is then given by

2 Set of Experiment Platform and Acquisition of Data

The experiments have been done in a platform called the 6-axis scanning and nano positioning system manufactured by PI Company in Germany.It provides a linear travel range of 800 μm×800 μm×200 μm with the positioning resolution well under 1 nm and rotation range up to 1 mrad［11］，which outclasses those of our nanoscale displacement sensor.Thus，it can meet the sensor calibration and test requirements.And the environment of the experiments is something like vibration isolation，electromagnetic isolation，non-dust and constant temperature［12－13］.The experiment platform is shown in Fig.3.

Fig.3The experiment platform

After going through mechanical amplification and data processing hardware circuit，the digital voltage signal is got.Then we record the final output data of the nanometer displacement sensor.When the sampling frequency is 400 Hz，a group of stable output data of the nanometer scale displacement is shown in Fig.4.

Fig.4Stable output data of the nanometer scale displacement

3 Dataprocessing with HHT

3.1Frequency Spectrum Analysis of Data

Before digital filtering，frequency-domain characteristics analysis is essential to get frequency distribution condition of signal and noise.We use Fast Fourier transform tool in MATLAB in this condition to get amplitude curve and phase curve.The curves are shown in the Fig.5.From the curve，we can see most components of signal are distributed in the low frequency domain.So it can prove that the high frequency noise has been restrained through hardware circuit of data acquisition.3.2The Empirical Mode Decomposition for Signal

EMD method is developed from the simple assumption that any signal consists of different simple intrinsic modes of oscillations.In this way，each signal could be decomposed into a number of IMFs，each of which must satisfy the following two conditions:(a)Inthe whole data set，the number of extreme and the number of zero-crossings must either equal or differ at most by one;(b)At any point，the mean value of the envelope defined by local maxima and the envelope defined by the local minima is zero.

Fig.5The amplitude curve and phase curve

And so，the primary output data of the nanometer scale displacement signal can be discomposed to be five IMFs and the last remaining component.Seen from Fig.6，every IMF stands for primary signal component with different frequency from highest frequency to lowest frequency.HHT can exactly depict the feature of signal.Each IMF component and the last remaining component of two systems are shown in Fig.6.

3.3 Analysis for Results

The first solution:As you know，most of noise is concentrate on the high frequency.So we use the first IMF as the noise to be filtered and get curve after being filtered.The new signal is shown in Fig.7.From Fig.7，we can know that signal has become more smoothly.

The second solution:So we use the first and second IMF as the high noise to be filtered and get curve after being filtered.The comparison between two kinds of method and original data in one group of data is shown in Table 1.

Fig.6Waveform of EMD of the process system output signal

Fig.7Stable output data after being filtered

The calibration experiment is on the basis of displacement input and the voltage output，and from which we could see that the nonlinearity usually happens in the initial steps of the measurement scale.As a consequence，we use the original data and two filter solutions to do the experiments.We do the experiments 200 nm distance of travel with every 10 nm step and 100 nm distance of travel with every 5 nm step，and 60 nm distance of travel with every 3 nm step in the three groups.In order to make the comparison among thethree groups more objective，we transfer the output voltage of the sensor into the value of displacement proportionally.So we can compare the three groups in a same criterion.In addition，the error curves are given.The input/output curves and the error curves are shown in Fig.8～Fig.13.

By comparing the experimental data of the three groups，we can see that both filter solution can improve accuracy and linearity when adopted in the nanometer displacement sensor.Moreover，we calculate the value of the Pearson product-moment correlation coefficient R2and the nonlinear error δ of these input/output curves，and the results are shown in Table 2.

Table 1The comparasion of one group of data

Fig.8Input/output curves of 10 nm interval

Fig.9Error curves of 10 nm interval

Fig.10Input/output curves of 5 nm interval Table 2The value of R2and nonlinear error

Fig.11Error curves of 5 nm interval

Fig.12Input/output curves of 3 nm interval

Fig.13Error curves of 3 nm interval

4 Conclusion

In this paper，a calibration method for mechanical nanometer displacement sensor of PZT was presented based on a newly developed signal processing technique named as Hilbert-Huang transform.And we use HHT to filter noise signal.After going through the EMD，the original signals can be decomposed into intrinsic modes.We adopt two methods to filter and construct new signal.The experimental results validate that both methods namely filtering high frequency noise has better noise control capability than the original data.At the same time，comparing with two filter method，we can get the conclusion that the noise is focused on the highest frequency.Thus，we can safely say the first filter solution is an effective way in filtering the nanoscale signal and improving performance of sensor.

Acknowledgements

The authors gratefully acknowledge Renbing Chen and Zhengwei Li for providing great technological instructions.The authors would like to thank the financialsupports of the National Science Foundation of China (Grant#60635040)，the natural science foundation of Anhui Province(grant#1208085QF121)and the postdoctoral scientific research plan of Jiangsu Province(grant# 1102038C).We are very grateful to unknown referees for valuable remarks.

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Hu Huan(1989－)，female，Tujia nationality，Hunan，master student，the main research field is detection and control of sensors，hhd626@mail.ustc.edu.cn;

Yu Yong(1957－)，male，Han nationality，doctoral supervisor，associate prof of Kagoshima University，editor of"Interna-tional Journal of Information Acqui-sition(IJIA).The main research field is the principle of the new robot sensor techno-logy and initiative assessment of intelligent robot to working environment etc.，yu@mech.kagoshima－u.ac.jp;

Wang Hui(1980－)，female，Han nationality，associate researcher of graduate supervisor.The main research field contains the characteristics and applications of Hilbert-Huang Transform(HHT)algorithm，asynchronous Brain-Computer Interface(BCI) based on multi-motor imaginary EEG，biomimetic sensing and the advanced technology of robot，etc.，wanghui@iim.ac.cn.

胡欢1，3，余永2，王慧3*，吴倩1，3，葛运建3
(1.中国科学技术大学自动化系，合肥230027;2.鹿儿岛大学科学与工程学院，日本890－0065; 3.中科院合肥智能机械研究所，合肥230031)

从传感器中采集到的信号即使经过了模拟滤波，但是其通过数据采集系统后仍然会含有随机噪声。然而，这些随机噪声会限制传感器的分辨率和影响系统的动态范围。针对这一问题，利用HHT算法的经验模态分解对从基于压电陶瓷驱动的微纳米传感器中采集到的数字信号进行数字滤波，进而对采集到的微弱信号进行进一步处理，以提高微纳米传感器在稳态输出时信号的信噪比从而提高传感器的性能。主要采用两种方法:一种方法是滤掉经过模态分解后信号中的最高频噪声，另一种方法是滤掉经过模态分解后信号中的前两阶噪声。最后对比实验结果证实了此算法的有效性，其能够有效的改善传感器的线性度。

纳米位移传感器;压电陶瓷驱动器;希尔伯特－黄变换算法;经验模态分解;信号处理

274

A

1004－1699(2014)04－0456－07

2013－12－31修改日期:2014－04－16

C:7220;7230M

10.3969/j.issn.1004－1699.2014.04.007

项目来源:CNSF(60635040);National“863”((2007AA04Z20)

HHT算法在压电陶瓷驱动器的微纳米位移传感器中的应用*