TDLAS signal denoising method based on piecewise polynomial fitting based on noise intensity constraint

Abstract

The invention discloses a piecewise polynomial fitting TDLAS signal denoising method based on noise intensity constraint, which relates to the field of TDLAS signal denoising, comprising: receiving and obtaining a TDLAS measurement signal; analyzing the TDLAS measurement signal based on a transmission signal corresponding to the TDLAS measurement signal to obtain a linear region of the TDLAS measurement signal; calculating and obtaining the variance of data in the linear region; obtaining a plurality of groups of data by sliding a window in sequence in the linear region; constructing a polynomial fitting function containing unknown coefficients, and solving the plurality of groups of data to obtain a fitting error of the polynomial fitting function and an unknown coefficient value in the polynomial fitting function; establishing an inequality constraint equation group based on the variance, the fitting error and the polynomial fitting function; denoising the TDLAS measurement signal based on the inequality constraint equation group to obtain a denoised signal; the method can suppress the noise of the measured TDLAS signal and improve the measurement accuracy.

Description

Technical Field

[0001] The invention relates to the field of TDLAS signal denoising, and in particular to a TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraints. Background Art

[0002] Laser absorption spectroscopy (TDLAS) has the characteristics of high sensitivity, continuous online, fast response, and strong environmental adaptability. It is currently internationally recognized as the most promising technical means to meet the ultra-low dew point detection requirements of ultra-low temperature wind tunnels. TDLAS technology uses a narrow linewidth semiconductor laser with continuously tunable wavelength as a light source to obtain a high-resolution absorption spectrum of the target gas to invert the state parameters of the gas. The laser wavelength can be tuned by its active region operating temperature and driving current. The temperature tuning response rate is relatively slow (Hz to sub-Hz level), and current tuning is usually used (the maximum response rate is above 100 kHz to MHz). The laser temperature is fixed, and the current tuning mode is used. The wavelength tuning waveform uses a sawtooth wave. Typical measurement optical paths are as follows: Figure 1 As shown, Figure 1 The component on the left is a semiconductor laser. Figure 1 The middle part "gas" is the air mass to be measured. Figure 1 The devices on the right side are photodetectors. Figure 1 Where L is the optical path of the laser through the area to be measured, I0(ν) is the incident laser intensity, and I(ν) is the output light intensity. After the laser emitted by the semiconductor laser is collimated, it passes through the air mass to be measured and is finally received by the photodetector (PD). The absorption of the target gas causes the laser light intensity to attenuate, and the attenuation obeys the Lambert-Beer law, as shown in the following formula:

[0003] I t (ν)=I0(ν)exp[-P·x·L·S(T)·φ(ν-ν0)]=I0(ν)exp[-α]

[0004] Among them, I t (ν) is the transmitted light intensity, S(T) is the absorption line intensity of the target gas, which is only a function of temperature for the selected absorption line; φ(ν-ν0) is the area normalized linear function; P and x are the ambient static pressure and the volume ratio concentration of water vapor, respectively, and P·x is the absolute partial pressure; α is the absorbance, which describes the overall absorption size of the target gas on the path. The typical absorption signal of wavelength tuning using sawtooth wave tuning laser current is shown in the figure. Figure 2 shown.

[0005] In the test optical path, when there is optical interference, there will be mixing noise in the measured TDLAS signal, affecting the measurement accuracy. In addition, as the concentration of the test object approaches the limit, Figure 2There is a lot of noise in the observed signal. How to suppress this noise is an effective way to improve measurement accuracy.

[0006] To address the problem of TDLAS measurement signal enhancement, scholars have proposed a series of methods:

[0007] The first method is: singular value decomposition is used to remove system noise in tunable diode laser absorption spectroscopy;

[0008] The second method is: Suppression of interference fringes in tunable semiconductor laser absorption spectroscopy based on empirical mode decomposition_Guo Xinqian;

[0009] The third method is: Research on noise reduction of TDLAS detection signal based on Gabor transform_Cui Haibin;

[0010] Among the above methods, Gabor transform is an artificially set identification basis method, which needs to rely on artificial experience and has low accuracy; empirical mode decomposition and singular value decomposition are data-driven methods. Among them, empirical mode decomposition decomposes the current signal into a fusion of several signals, and then denoises it through linear combination reconstruction. The level and number of decomposition are uncontrollable, and there is also a problem of low accuracy; singular value decomposition, namely SVD decomposition, is an orthogonal basis method with low reconstruction quality and also has the problem of low accuracy. Summary of the invention

[0011] In order to solve the above-mentioned shortcomings, the present invention provides a TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraints to suppress the measured TDLAS signal noise and improve the measurement accuracy.

[0012] To achieve the above object, the present invention provides a TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraints, the method comprising:

[0013] Step 1: Receive and obtain TDLAS measurement signal;

[0014] Step 2: Analyze the TDLAS measurement signal based on the emission signal corresponding to the TDLAS measurement signal to obtain the linear region of the TDLAS measurement signal;

[0015] Step 3: Calculate the variance of the data in the linear region;

[0016] Step 4: Obtain several sets of data by sliding the window in sequence in the linear region;

[0017] Step 5: construct a polynomial fitting function containing unknown coefficients, and obtain the fitting error of the polynomial fitting function and the unknown coefficient values ​​in the polynomial fitting function based on the plurality of sets of data;

[0018] Step 6: establishing an inequality constraint equation group based on the variance, the fitting error and the polynomial fitting function;

[0019] Step 7: De-noise the TDLAS measurement signal based on the inequality constraint equation group to obtain the denoised signal.

[0020] Among them, this method first obtains the variance of noise through linear data, then fits the data through least squares, and then considers the residual between the actual value and the straight line fitting value to establish an inequality constraint optimization model, and finally obtains the filtered result through intelligent optimization algorithms such as particle swarm to reduce the impact of noise; the present invention can suppress the noise of TDLAS signal measurement and improve the measurement accuracy.

[0021] In some embodiments, step 2 specifically includes:

[0022] Compare the numerical values ​​of the TDLAS measurement signal and the signal points corresponding to the transmission signal;

[0023] Obtain a set of signal points whose value differences are within a preset range;

[0024] The continuous signal points whose number is greater than a threshold value are taken out from the signal point set to obtain a corresponding continuous signal point set;

[0025] Based on the signal regions corresponding to the signal points in the continuous signal point set, the linear region of the TDLAS measurement signal is obtained.

[0026] Among them, although the received signal has certain fluctuations due to the influence of noise, the received signal and the transmitted signal change linearly in some areas. These areas can be used to obtain the linear area of ​​the TDLAS measurement signal, and the linear area measurement signal is used to determine the noise level.

[0027] In some embodiments, step 3 specifically includes:

[0028] Select M data from the linear region, which are: (x1, y1), (x2, y2), ..., (x M ,y M ).

[0029] Let f(x i )=ax i +b, a and b are constants, x i is the horizontal coordinate of the i-th (1≤i≤M) data, f(x i ) is the linear fitting function, whose value is the horizontal coordinate x i The corresponding vertical coordinate;

[0030] Obtain the minimum value θ of the error Φ(a,b) between the measured data and the fitted data;

[0031] The variance of the data in the linear region is obtained by calculating the minimum value θ of the error Φ(a, b) between the measured data and the fitted data.

[0032] The measured data refers to selecting M data from the linear region, and the fitted data refers to i ) data obtained.

[0033] In some embodiments, the minimum value θ of the error Φ(a, b) between the measured data and the fitted data is calculated as:

[0034]

[0035] Where i is the serial number of the data point in the selected segment, and N is the total number of data points in the selected segment;

[0036] The variance σ of the data in the linear region is calculated as:

[0037]

[0038] In some embodiments, step 4 is specifically:

[0039] In the linear region, a window of length N is used to slide once to obtain several sets of data, each set of data includes: (x1, y1), (x2, y2), ..., (x N ,y N );

[0040] The polynomial fitting function in step 5 is Among them, g(x i ) is a third-order polynomial fitting function, which is used to obtain the horizontal coordinate x in the linear region. i The corresponding ordinate, η j , j , α j and β j is the constant parameter corresponding to the j-th sliding of the window;

[0041] The fitting error of the polynomial fitting function is G(η j ,ξ j ,α j ,β j ), the minimum value of the fitting error minG(η j ,ξ j ,α j ,β j )for:

[0042]

[0043] In some embodiments, the inequality constraint equation set is:

[0044]

[0045] Among them, ν and ω are parameters related to the confidence interval, e is the mean square error between the true data and the fitted data, min() is the function for finding the minimum value, mine is the minimum value of the mean square error between the true data and the fitted data, ε i is the acceptable standard deviation.

[0046] In some embodiments, e needs to satisfy the following constraints:

[0047]

[0048] Here, λ is a constant greater than 0.

[0049] In some embodiments, ε i The way to obtain is:

[0050] by is i The value range of As the objective function, and is a constraint obtained by particle swarm algorithm.

[0051] In some embodiments, the method obtains the minimum value θ of the error Φ(a, b) between the measured data and the fitted data by the least square method.

[0052] In some embodiments, the method obtains the minimum value minG(η) of the fitting error by the least square method. j ,ξ j ,α j ,β j ).

[0053] Among them, the least square method can be used to easily obtain data and minimize the sum of squares of errors between the obtained data and the actual data.

[0054] One or more technical solutions provided by the present invention have at least the following technical effects or advantages:

[0055] This method first obtains the variance of noise through linear data, then fits the data through least squares, and then considers the residual between the actual value and the straight line fitting value to establish an inequality constraint optimization model. Finally, the filtered result is obtained through intelligent optimization algorithms such as particle swarm to reduce the impact of noise, which can suppress the noise of TDLAS signal measurement and improve the measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of the present invention, and do not constitute a limitation on the embodiments of the present invention;

[0057] Figure 1 This is a schematic diagram of the TDLAS through-beam measurement principle;

[0058] Figure 2 is a typical absorption signal curve. Figure 2 The abscissa is the sampling point, and the ordinate is the transmitted light intensity;

[0059] Figure 3 The figure is a flowchart of the TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraints.

[0060] Figure 4 is a typical absorption signal curve after labeling. Figure 4 The horizontal axis is the sampling point and the vertical axis is the transmitted light intensity. DETAILED DESCRIPTION

[0061] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0062] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those within the scope of this description. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0063] Embodiment 1

[0064] Please refer to Figure 3 , Figure 3 The figure is a flow chart of a TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraints. Embodiment 1 of the present invention provides a TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraints, the method comprising:

[0065] Step 1: Receive and obtain TDLAS measurement signal;

[0066] Step 2: Analyze the TDLAS measurement signal based on the emission signal corresponding to the TDLAS measurement signal to obtain the linear region of the TDLAS measurement signal;

[0067] Step 3: Calculate the variance of the data in the linear region;

[0068] Step 4: Obtain several sets of data by sliding the window in sequence in the linear region;

[0069] Step 5: construct a polynomial fitting function containing unknown coefficients, and obtain the fitting error of the polynomial fitting function and the unknown coefficient values ​​in the polynomial fitting function based on the plurality of sets of data;

[0070] Step 6: establishing an inequality constraint equation group based on the variance, the fitting error and the polynomial fitting function;

[0071] Step 7: De-noise the TDLAS measurement signal based on the inequality constraint equation group to obtain the denoised signal.

[0072] Among them, this method first takes the linear region data and the overall data of the TDLAS measurement signal to estimate the noise intensity level; specifically, the variance of the noise is obtained through the linear data, and then the data is fitted by least squares; then according to the noise intensity level, an inequality constraint optimization model is established; specifically, considering the residual between the actual value and the straight line fitting value, an inequality constraint optimization model is established; then the absorption spectrum region is piecewise polynomial fitting to estimate the real measurement signal, and specifically, finally the filtered result is obtained through intelligent optimization algorithms such as particle swarm to reduce the impact of noise.

[0073] The purpose of the present invention to perform piecewise polynomial is: Figure 2 As far as I know, Figure 2 The solid line in the middle is the received signal, and the dotted line is the transmitted signal. The overall data is nonlinear. If it is directly fitted, it is very difficult and the error is relatively large. Although the overall data is nonlinear, the data can be understood as linear in a small interval. Therefore, the data is divided into multiple segments with the peak as the boundary, and then the window is used to slide on each segment of the data in turn. Each time it slides, the linear data is fitted with a polynomial.

[0074] The present invention is introduced below in conjunction with specific examples:

[0075] like Figure 4 As shown, Figure 4 It is a typical absorption signal curve after marking, the solid line is the received signal, and the dotted line is the transmitted signal. Although the solid line has certain fluctuations due to the influence of noise, the solid and dotted lines in the elliptical area are linearly changing. The linear area is obtained by comparing the numerical values ​​of the signal points corresponding to the TDLAS measurement signal and the transmitted signal; obtaining a set of signal points whose numerical differences are within a preset range; taking out the continuous signal points in the signal point set whose continuous number is greater than the threshold to obtain the corresponding continuous signal point set; based on the signal area corresponding to the signal points in the continuous signal point set, obtaining the linear area of ​​the TDLAS measurement signal; wherein, in practical applications, the threshold value can be adjusted according to actual needs.

[0076] For this purpose, M data are selected from the elliptical region in the received signal: (x1, y1), (x2, y2), …, (x M ,y M ). Let f(x i )=ax i +b, a and b are constants, then the definition is as follows:

[0077]

[0078] The minimum value of the error Φ(a,b) between the measured data and the fitted data can be obtained by the least squares method, which is recorded as θ. At this time, the variance of the noise in the data is:

[0079]

[0080] Although the overall data is nonlinear, such as Figure 4 As shown, there is a large linear region in the left area of ​​the absorption spectrum. To this end, a single sliding data set (x1, y1), (x2, y2), …, (x N ,y N ).

[0081] Define a polynomial fitting function, let η j , j , α j and β j is the constant parameter corresponding to the j-th sliding of the window; it is defined as follows:

[0082]

[0083] Similarly, the fitting error G(η j ,ξ j ,α j ,β j ), and η j , j , α j and β j .

[0084] Then, considering the residual between the actual value and the straight line fitting value, the following inequality constraint equations are established:

[0085]

[0086] Among them, ν and ω are parameters related to the confidence interval, ε i is the acceptable standard deviation.

[0087] In addition, e needs to satisfy the following formula:

[0088]

[0089] Here, λ is a constant greater than 0.

[0090] For ε i The solution can be obtained by is i The value range of is the objective function, and and As a constraint, it is obtained through intelligent optimization algorithms such as particle swarm. i After that, calculate And as the filtered y i ', based on the filtered y i 'Get the denoised signal.

[0091] Among them, the particle swarm algorithm can refer to a hybrid particle swarm algorithm for solving constrained optimization problems-Liu Yanmin, which will not be described in detail in the present invention.

[0092] Among them, compared with denoising methods such as local weighted regression algorithm and median filtering, the data in this method is strongly nonlinear. This method converts the nonlinear problem into a linear problem, and the effect is better than the local weighted regression algorithm. This method dynamically obtains noise, while the median filter filters according to a finite number. Its filtering effect depends on the length of the data. If the length is not appropriate, the effect is poor.

[0093] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0094] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraints, characterized in that: The method comprises: Step 1: Receive and obtain TDLAS measurement signal; Step 2: Analyze the TDLAS measurement signal based on the emission signal corresponding to the TDLAS measurement signal to obtain the linear region of the TDLAS measurement signal; Step 3: Calculate the variance of the data in the linear region; Step 3 specifically includes: Select M data from the linear region, which are: (x1, y1), (x2, y2), ..., (x M ,y M ); Let f(x i )=ax i +b, a and b are constants, f(x i ) is a linear fitting function, whose value is x i The corresponding ordinate, x i is the horizontal coordinate of the i-th data in the TDLAS measurement signal, 1≤i≤M; Obtain the minimum value θ of the error Φ(a,b) between the measured data and the fitted data; The variance of the data in the linear region for representing the noise is obtained by calculating the minimum value θ of the error Φ(a, b) between the measured data and the fitted data; Step 4: Obtain several sets of data by sliding the window in sequence in the linear region; Step 5: construct a polynomial fitting function containing unknown coefficients, and obtain the fitting error of the polynomial fitting function and the unknown coefficient values ​​in the polynomial fitting function based on the plurality of sets of data; Step 6: establishing an inequality constraint equation group based on the variance, the fitting error and the polynomial fitting function; Step 7: De-noise the TDLAS measurement signal based on the inequality constraint equation group to obtain the denoised signal; specifically, it includes: performing piecewise polynomial fitting on the absorption spectrum region, estimating the true measurement signal, obtaining the filtered result through the particle swarm intelligent optimization algorithm to reduce the influence of noise, and obtaining the denoised signal.

2. The TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraint according to claim 1, characterized in that: The step 2 specifically includes: Compare the numerical values ​​of the TDLAS measurement signal and the signal points corresponding to the transmission signal; Obtain a set of signal points whose value differences are within a preset range; The continuous signal points whose number is greater than a threshold value are taken out from the signal point set to obtain a corresponding continuous signal point set; Based on the signal regions corresponding to the signal points in the continuous signal point set, the linear region of the TDLAS measurement signal is obtained.

3. The TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraint according to claim 1, characterized in that: The minimum value θ of the error Φ(a,b) between the measured data and the fitted data is calculated as: Where i is the serial number of the data point in the selected segment, and N is the total number of data points in the selected segment; The variance σ of the data in the linear region is calculated as follows:

4. The TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraint according to claim 3, characterized in that: The step 4 is specifically as follows: In the linear region, a window of length N is used to slide in sequence to obtain several sets of data, each set of data includes: (x1, y1), (x2, y2), ..., (x N ,y N ); The polynomial fitting function in step 5 is Among them, g(x i ) is a third-order polynomial fitting function, η j , j , α j and β j is the constant parameter corresponding to the j-th sliding of the window; The fitting error of the polynomial fitting function is G(η j ,ξ j ,α j ,β j ), the minimum value of the fitting error minG(η j ,ξ j ,α j ,β j )for:

5. The TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraint according to claim 4, characterized in that: The inequality constraint equations are: Among them, ν and ω are parameters related to the confidence interval, mine is the minimum value of the mean square error between the measured data and the fitted data, and ε i is the acceptable standard deviation.

6. The TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraint according to claim 5, characterized in that: e must satisfy the following constraints: Here, λ is a constant greater than 0.

7. The TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraint according to claim 6, characterized in that: ε i The way to obtain is: by is i The value range of As the objective function, and is a constraint obtained by particle swarm algorithm.

8. The TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraint according to claim 1, characterized in that: The minimum value θ of the error Φ(a, b) between the measured data and the fitted data is obtained by the least squares method.

9. The TDLAS signal denoising method based on piecewise polynomial fitting of noise intensity constraint according to claim 4, characterized in that: The minimum value of the fitting error minG(η) is obtained by the least squares method. j ,ξ j ,α j ,β j ).

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