Application of a joint algorithm based on L-T to pulse pressure detection signal of fiber Fabry-Perot nano pressure sensor

FENG Fei，QIN Li

(1. Key Laboratory of Instrumentation Science and Dynamic Measurement(North University of China)，Ministry of Education,Taiyuan 030051,China；2. Science and Technology on Electronic Test &Measurement Laboratory，North University of China，Taiyuan 030051,China)

Abstract：An improved denoising method and its application in pulse beat signal denoising are studied.The proposed denoising algorithm takes the advantages of local mean decomposition (LMD)and time-frequency peak filtering (TFPF),called L-T algorithm.As a classical time-frequency filtering method,TFPF can effectively suppress random noise with signal amplitude retained when selecting a longer window length,while the signal amplitude will be seriously attenuated when selecting a shorter window length.In order to maintain effective signal amplitude and suppress random noise,LMD and TFPF are improved.Firstly,the original signal is decomposed into progression-free survival (PFS)by LMD,and then the standard error of mean (SEM) of each product function is calculated to classify many PFSs into useful component,mixed component and noise component.Secondly,by using the shorter window TFPF for useful component and the longer window TFPF for mixed component,noise component is removed and the final signal is obtained after reconstruction.Finally,the proposed algorithm is used for noise reduction of an Fabry-Perot (F-P) pressure sensor.Experimental results show that compared with traditional wavelet,L-T algorithm has better denoising effect on sampled data.

Key words：local mean decomposition (LMD)；time-frequency peak filtering (TFPT)；noise reduction;Fabry-Perot (F-P) sensor

0 Introduction

Optical fiber Fabry-Perot (F-P) sensor has been widely concerned due to its small size,simple structure,high sensitivity,chemical passivation,and strong anti-electromagnetic interference ability[1-3].It is usually used to detect various physical parameters such as pressure,temperature,strain,displacement,etc.[4-9],but it is easily affected by extreme environment.

The periodic contraction and relaxation of the ventricles in human body lead to the corresponding contraction and relaxation of the aorta in human body,which makes the pressure of blood flow spread from the root of the aorta along the whole arterial system in the form of wave,which is called pulse wave.The intensity,shape,speed and rhythm of the pulse wave can reflect the blood flow characteristics of a person’s cardiovascular system to a large extent.The traditional pulse measurement usually adopts pulse diagnosis method,which is easily influenced by human and environment,and the measurement accuracy is not high.The acquisition quality of pulse signal also directly affects the effect of data processing,therefore the selection of pulse sensor is very important.The basic function of pulse sensor is to convert some physical quantities such as pulse pressure and artery beating pressure into electric quantities that can be measured.The pulse signal contains rich physiological and pathological characteristics of human body,and it is a window to transmit and peep the changes of body functions.By means of pulse detectors,the pressure fluctuations of pulse signal,electrocardiogram (ECG) signal,vibration signal and other physical information can be accurately analyzed,which opens a new way for the diagnosis of human pulse[10-11].However,due to the particularity of pulse signal,as a weak low-frequency signal,it is easily affected by pulse detectors,human body and other factors.The collected information contains a variety of noises,which is unfavourable for the subsequent processing of pulse signal.Therefore,it is necessary to reduce the noise of pulse signal.Compared with finite impulse response (FIR) digital filter,infinite impulse response (IIR) digital filter has the advantages of less coefficients,higher operation efficiency,and some good characteristics of analog filter.In this study,we propose an algorithm that combines the advantages of local mean decomposition (LMD) and time-frequency peak filtering (TFPF),called L-T algorithm.The L-T algorithm is used to reduce the noise of pulse signal collected by pulse detector,which has achieved the function of filtering out the noise and is conducive to the post-processing of pulse signal[11-13].

For the collected pulse signal,the waveform denoising method performs smoothing denoising,that is,taking several points before and after each smoothing point for fitting to make the best estimation of the smoothing point.Although smoothing denoising can smooth the signal,it has the disadvantages of signal distortion and low spectral resolution[14].The Fourier transform is to map the pulse wave signal from time domain to frequency domain and to analyze the distribution of signal energy in frequency domain.However,Fourier transform can only get the whole spectrum of the pulse wave signal,and it is difficult to get the local characteristics of the pulse wave signal.For the nonlinear non-stationary signal such as pulse wave signal,Fourier transform cannot save the corresponding information in frequency domain and time domain,thus it is not satisfactory in filtering and denoising.

In 1960,Kalman filter made the best estimation of the system state through the input and output data of the observation system[15].It uses statistical estimation theory and time-domain method by taking the state equation as the mathematical tool and recursive algorithm.Because the interference and other forms of noise in the system have a certain impact on the observed data,the mathematical theory of Kalman filter is relatively complex and the filtering parameters are time-varying.In addition,Kalman filter is not suitable for the denoising of real pulse wave signal because it can obtain the optimal filter only when the statistical characteristics of signal and noise are known[16-18].Empirical mode decomposition (EMD) is an effective method for the denoising of nonlinear and non-stationary complex signals composed of multiple time-scale oscillation waves.It can select different basis functions according to the different characteristics of signals to separate the intrinsic mode function (IMF) step by step,but there is no screening standard for the noise and pseudo components in the decomposed mode function,therefore high-frequency noise and pseudo components cannot be avoided.In this study,the EMD combined with correlation coefficient method and Hilbert transform is used to establish a more suitable natural mode function screening standard for pulse wave denoising,and a large number of simulated data are used to demonstrate the denoising effect.Then the improved EMD method is used for denoising of the real pulse wave data collected by the oxygen indicator handle[19].

1 Materials and methods

1.1 LMD based on sample entropy

Local mean decomposition (LMD) technology has two key parts:IMF and screening process.IMF is a function satisfying two conditions as follows:

1) The extreme times and zero transit times should be equal or the difference should not exceed one;

2) The local mean defined by the mean of the maximum and minimum envelopes is zero,and both envelopes are locally symmetric around the envelope mean.

In short,LMD method can determine the instantaneous equilibrium position according to time series,that is,the average value of the upper and lower envelopes.Thus the non-stationary signal is decomposed into a set of linear and smooth IMFs.For a given signalx(t),the first step of LMD is to identify all local maxima and minima[20].All local maxima are connected,and the upper envelope is a cubic splineeu(t);Similarly,all local minima are connected and the lower envelope is a splineel(t).The average of the two envelopes is expressed asm1(t)=[eu(t)+el(t)]/2,subtracting it from the original signal,and the we can get the first originalh1(t) as

h1(t)=x(t)-m1(t).

(1)

1.2 TFPF

The collected signal includes real signal and noise,and it can be expressed as

y(n)=x(n)+r(n),

(2)

wherex(n) is the pure gear signal components,r(n) is the additive random noise,andnis the sampling point.The noisy signaly(n) is encoded by frequency modulation as the instantaneous frequency of a unit amplitude analytic signal,so as to actualize TFPF.

1.3 L-T denoising algorithm

In order to combine the advantages of LMD and TFPF,a hybrid noise reduction algorithm,L-T algorithm,is proposed,in which signalx(t) is expressed as

x(t)=cos(2πt/2 400)+cos(2πt/60).

(3)

In this algorithm,we expect to get three components:useful component,mixed component and noise component.The useful component refers to the pure noiseless signal,the mixed component refers to the mixed signal of pure signal and pure noise,and the noise component refers to the pure noise.Effective denoising results can be obtained by retaining the useful component,denoising the mixed component,and removing the noise component[21].In order to divide progression-free survivals (PFS) decomposed by LMD into thethree components,the standard error of mean(SEM) of each peak frequency is calculated,and then it is classified according to the similarity of its SEM.Each of the three areas is selected by means of observation.

Although traditional electrical sensors have many advantages in terms of measurement accuracy and sensor miniaturization,the sensors based on electrical components are subject to electromagnetic and high-temperature interference,resulting in a decrease in measurement accuracy[22-25].However,reasonable high temperature design can overcome these shortcomings,and appropriate temperature compensation can reduce the temperature drift caused by the huge temperature difference in a working environment.

Fig.1 is a schematic diagram of a typical high-temperature pressure sensor with temperature compensation structure.It can be seen that if the incident beam is assumed to be monochromatic,the incident beam and the two reflecting surfaces forming the enamel cavity are perpendicular to each other,and the two reflecting surfaces are parallel to each other,thus the incident beam will be reflected time after time by the left and right reflecting surfaces,and coherent superposition of multiple beams will be formed in the fibre.According to the theory of multi-beam interference,if the spectral distribution (spectral density) of the light source isI0(k),the reflectivity of the two reflection planes isR,the interval between the reflection surfaces isd,the refractive index of the medium in the middle is 3n,and the medium is generally air,regarded as equal to 1,the spectral density functionIFP-R(k,d) of the light reflected by the fibre optic opaque sensor can be expressed as

Fig.1 Structure of fiber Fabry-Perot sensor

(4)

Also it can be approximately expressed as

IFP-R(k,d)=2RI0(k)[1-cos(2kd)].

(5)

Changes in the measurement environment of the sensor lead to changes in the cavity length of the sensor.The spectrum modulated by the cavity length conforms to the relationship of Eq.(5).Long information demodulation has the advantages of high accuracy and high stability,and there are many types of measurement interferometers that conform to this demodutation.Considering the complexity of demodulation system debugging and woking environment,it is suitable choice to use Fizeau interferometer as the measurement interferometer of the demodulation system[26-29].When the length of the cavity to be demodulated is small,the thickness of the designed Fizeau interferometer is usually small.Therefore,so the Fizeau interferometer is usually constructed using a wedge-shaped air house constructed by two splitting plates,and its structure is shown in Fig.2.

Fig.2 Schematic diagram of Fizeau interferometer

In the demodulation optical path,the light exit port of the coupler is placed at the focal point of the collimator lens,and the light emitted by the coupler is collimated into parallel light,which is perpendicularly incident into the Fizeau interferometer.Among them,the beam based on output feed back (OFB) passes through the beam collimators 1 and 2 and directly enters pointDon the imaging surface of the camera.The beam based on optogalvanic effect (OGE),passes through the beam collimator 1 and then it is reflected at the beam collimator 2.The reflected beam is reflected by the beam collimator 1 again and then passes through the beam collimator 2.When it is incident at pointD,the two beams will interfere.Assuming that the spectral density of the light exit port of the coupler isIsou,when the reflectivity of both beam collimator isr,the spectral densityIoutreceived by the camera imaging surface satisfyHT9.

Iout=Isou(1-r)2+Isou(1-r)2r2+

(6)

The above formula can be simplified to

Iout=Isouη[1+Kcos(kd)],

(7)

whereηrepresents the light intensity attenuation coefficient,andKrepresents the fringe contrast.According to Fermat’s principle,if the lens has an equal optical path,the optical paths of all beams that reach the plane through the lens are equal,that is,the optical paths of the beams based on OGE and OFB are equal.In addition,when the angle of the Fizeau interferometer is very small,the thickness distance can be ignored.Therefore,the length of the difference between the geometric paths of the two beams causing interference is determined,which is twice the thickness of the Fizeau interferometer.When the thickness ishand the refractive index of Fizeau interferometer is 1,the optical path differenceMof the two beams forming interference meets

M-2nh=2h.

(8)

In Eq.(4),the spectrumIsouof the light exiting from the coupler port is the spectrumIFP-R(k,d) modulated by the fibre optic sensor.Therefore,when the cavity length of the sensor isd,the obtained spectral densityIoutof satisfies

Iout(d,h)=2RηI0(k)[1-cos(2kd)][1+Kcos(2kd)].

(9)

The total light intensity received by this pixel (different pixels corresponding to different thicknesses of the wedge-shaped air house) is the superposition of the intensities of different spectral components.Therefore,the total light intensityIof the corresponding pixel received by the camera pixel at the thicknesshof the Fizeau interferometer is expressed as

(10)

2 Experimental result and analysis

In order to verify the theoretical analysis in the previous sections,the proposed adaptive demodulation method is used for pulse pressure measurement,and segmentation,calibration and experiment of F-P sensor are carried out.The silicon chip of the sensor is sensitive to pressure,and its bending will cause the change of the length of the F-P cavity.The F-P sensor used in this study is a diaphragm sensor.

The schematic diagram of low-cost demodulation part of experimental system based on supercontinuum spectrum light source is shown in Fig.3.The light from the light source propagates in the multimode fiber (MMF) and enters the F-P sensor through the 3 dB coupler,with the wavelength range of the light source from 1 510 nm to 1 590 nm.The light reflected by the sensor is successively introduced into the interference fringes composed of a focusing lens,a polarizer,a birefringent wedge,an analyzer and a linear CCD.Due to the difference of refractive index between the ordinary light and the extraordinary light,the wedge can produce continuous optical path difference.When the pulse width of the wedge is equal to twice the cavity length of F-P sensor,the interference fringes appear in the corresponding position of CCD.The position of the fringes varies with the length of the F-P cavity as well as the pressure and temperature.

Fig.3 Schematic diagram of experimental system

Fig.4 is the orignal signal that is a segment of pulse signal sampling data provided by volunteers.

Fig.4 Original signal

It can be seen from the curve that the pulse signal is noisy in taking.The frequency and power of the original spectrum are filtered and recombined by L-T algorithm,and the results are shown in Fig.5.

(a) Spectrum curve

By comparing the denoised pulse wave patterns,it can be seen that the high-frequency noise and drift in the original signal have been removed.Then L-T algorithm is used to determine the delay time and the embedded dimension value in the phase space so as to expand the dimension pulse wave into the multi-dimensional pulse wave time series.In order to further understand the trend of human pulse wave data,support vector machine is used to predict the reconstructed multi-dimensional pulse wave time series.

Fig.6 is the signal diagram of the sampled data after wavelet filtering analysis.The sampled data are not suitable for wavelet algorithm.

Fig.6 Wavelet algorithm of sampled data signal

Although wavelet algorithm is not widely used.It is very effective when the frequency range of noise is known and the frequency bands of signal and noise are separated.For the white noise widely existing in practical application,its denoising effect is poor.In our work,wavelet algorithm is not applicable for sampling data.

3 Conclusions

This paper presents an L-T denoising algorithm,which takes the advatanges of LMD and TFPF.The correlation coefficient method is used to filter the decomposed components.However,there is no uniform standard for this method due to human error.Therefore,the proposed algorithm is used to avoid human error and to find the component combination that can minimize the noise after denoising.Using the proposed algorithm,different length simulation pulse wave data have been improved and the high frequency noise and drift of the original signal have been removed to a large extent.The improved denoising method is also used for noise reduction of actual collected pulse waves.It not only filters out the trend items in the original noisy signal,but also retains the waveform components of the pulse wave signal,which shows the practicability of this algorithm.