Low-coherence interference demodulation method based on modal decomposition and radial basis function neural network

Abstract

The invention discloses a low-coherence interference demodulation method based on modal decomposition and a radial basis function neural network, and the method comprises the steps: carrying out the empirical mode decomposition of a filtered low-coherence interference signal, extracting the effective time-frequency domain features of each IMF and the mathematical statistics time domain features of the low-coherence interference signal, and forming a low-coherence interference signal feature data set; constructing and training a radial basis neural network, establishing a nonlinear model between low-coherence interference signal features and pressure, setting an input layer to correspond to a fusion feature vector, setting a hidden layer to adopt a radial basis function as an activation function, realizing nonlinear mapping by using a Gaussian kernel function, and outputting a layer to correspond to a pressure value; the network is trained through the feature data set, a mean square error is used as a loss function, a gradient descent method is adopted to optimize the weight and threshold of the network, and iterative training is carried out until the error converges; and inputting a low-coherence interference signal acquired by an optical fiber Fabry-Perot pressure demodulation device, and demodulating the signal through the trained radial basis function neural network model to obtain a corresponding pressure value.

Description

Technical Field

[0001] The present invention relates to the technical fields of fiber optic sensing technology and intelligent signal processing technology, and particularly relates to a low-coherence interference demodulation method based on modal decomposition and radial basis neural network. Background Art

[0002] Due to its advantages such as high sensitivity, small size, and strong anti-interference ability, fiber optic Fabry-Perot sensors have received extensive attention and applications in the fields of industry, medicine, aerospace, etc. Low-coherence interference measurement technology has become a commonly used demodulation technology in fiber optic Fabry-Perot sensors due to its characteristics suitable for measuring any physical quantity that can be converted into absolute displacement. Among them, the demodulation system based on a low-coherence light polarization birefringence interferometer is widely used because of its simple structure, stability, no moving parts, and low cost. In the traditional fiber optic Fabry-Perot low-coherence interference demodulation method, the demodulation method based on the spatial frequency and phase information of the interference pattern has higher demodulation accuracy than the demodulation method based on the position information of the interference pattern. This method converts the low-coherence interference fringes in the spatial domain to the spatial frequency domain by Fourier transform, monotonically expands the phase information in the spatial frequency domain, and performs a phase-frequency linear fit to obtain the microcavity phase of the central wavelength. However, since the low-coherence interference system uses a broadband light source, the dispersion problem of the birefringent crystal in the optical path is inevitable, which leads to the distortion of the interference fringes. The spatial frequency-phase is no longer a linear relationship theoretically. Therefore, the frequency-phase linear fit will generate an analytical error, causing the interference order to jump and affecting the cavity length demodulation accuracy.

[0003] In recent years, with the development of artificial intelligence and signal processing technology, data-driven demodulation methods have gradually received attention. Among them, empirical mode decomposition (EMD), as an adaptive signal decomposition method, can decompose complex signals into several intrinsic mode functions (IMFs) and extract the time-frequency domain characteristics of the signals, which is particularly suitable for the processing of non-linear and non-stationary signals. However, it is difficult to construct a complex mapping relationship between the fiber optic Fabry-Perot interference signal and the pressure only relying on empirical mode decomposition. Radial basis function neural network (RBFNN), as a typical artificial neural network model, has been widely used in the fields of pattern recognition, data fitting, etc. due to its strong non-linear mapping ability and efficient training characteristics. Combining the radial basis neural network with empirical mode decomposition can establish a non-linear mapping relationship between the low-coherence interference signal and the pressure through the synergistic effect of feature extraction and non-linear modeling, so as to achieve high-precision demodulation of fiber optic Fabry-Perot sensing.

[0004] In summary, the traditional low-coherence interference demodulation method for fiber optic Fabry-Perot sensing is affected by the birefringence dispersion effect, resulting in a non-linear distortion of the relationship between the spatial frequency and phase of the interference fringes, thus causing interference order jumps and affecting the demodulation accuracy. In addition, traditional signal processing methods have poor robustness and adaptability to noise in complex situations and cannot fully cope with the non-linear and non-stationary characteristics in low-coherence interference signals. With the rapid development of signal processing technology and deep learning algorithms, especially the breakthroughs in the field of signal feature extraction and non-linear modeling, new technical ideas are provided to solve the non-linear problems caused by birefringence dispersion. Summary of the Invention

[0005] The present invention provides a low-coherence interference demodulation method based on modal decomposition and radial basis neural network. The demodulation system of the present invention uses a low-coherence polarization birefringence interferometer. The fiber optic Fabry-Perot sensor is used as the sensing module, and its cavity length changes with the external pressure. The birefringent crystal optical wedge is used as the demodulation module to generate a continuous spatial optical path difference. When the optical path differences generated by the demodulation module and the sensing module match, low-coherence interference fringes will be generated at the corresponding positions of the linear array CCD. Pressure demodulation is achieved by analyzing the low-coherence interference fringes. Empirical mode decomposition is used to extract the characteristics of the low-coherence interference signal, and then a non-linear mapping model between the characteristics of the low-coherence interference signal and the pressure is established through a radial basis neural network to achieve fiber optic Fabry-Perot sensing demodulation. The details are described below:

[0006] A low-coherence interference demodulation method based on modal decomposition and radial basis neural network, the method comprising:

[0007] Perform empirical mode decomposition on the filtered low-coherence interference signal, extract the effective time-frequency domain characteristics of each IMF and the mathematical statistical time-domain characteristics of the low-coherence interference signal, and constitute a low-coherence interference signal feature dataset;

[0008] Construct and train a radial basis neural network, establish a non-linear model between the characteristics of the low-coherence interference signal and the pressure, set the input layer corresponding to the fused feature vector, use the radial basis function as the activation function in the hidden layer, and use the Gaussian kernel function to achieve non-linear mapping. The output layer corresponds to the pressure value; the network is trained through the feature dataset, the mean square error is used as the loss function, and the gradient descent method is used to optimize the network weights and thresholds, and iterative training is performed until the error converges;

[0009] Input the low-coherence interference signal collected by the fiber optic Fabry-Perot pressure demodulation device, and demodulate the signal through the trained radial basis neural network model to obtain the corresponding pressure value.

[0010] Wherein, the method further comprises: normalizing the input and output of the feature dataset and dividing the dataset, using zscore standardization to convert the feature dataset into a standard normal distribution.

[0011] Among them, the effective time-frequency domain features include: standard deviation, skewness, kurtosis, main frequency, and spectral centroid.

[0012] Among them, the composition of the low-coherence interference signal feature dataset includes:

[0013] Perform mathematical statistical analysis on the low-coherence interference signal, extract effective time-domain features, and the features include the fringe peak position and the variance of the fringe peak position;

[0014] Fuse the time-domain features with the time-frequency domain features extracted by empirical mode decomposition to construct a feature dataset with high expression ability for subsequent neural network training and demodulation model establishment.

[0015] The beneficial effects of the technical solution provided by the present invention are:

[0016] 1. The present invention combines the advantages of fiber optic sensing technology, signal processing technology, and the field of deep learning, combines the signal feature extraction ability of empirical mode decomposition with the non-linear modeling ability of radial basis neural network, provides a new technical path for low-coherence interference signal demodulation, and has significant innovation;

[0017] 2. The present invention uses empirical mode decomposition to extract effective time-frequency domain features from low-coherence interference signals, and at the same time establishes a non-linear mapping model through radial basis neural network, which can efficiently process non-linear and non-stationary signals, making pressure demodulation more stable and reliable;

[0018] 3. The present invention can provide reference for the demodulation of other similar fiber optic Fabry sensors such as acoustic wave sensors and acceleration sensors. Description of the Drawings

[0019] Figure 1 It is a schematic diagram of a low-coherence interference demodulation device based on modal decomposition and radial basis neural network;

[0020] Figure 2 It is an experimental flowchart of a low-coherence interference demodulation method based on modal decomposition and radial basis neural network;

[0021] Figure 3 It is a flowchart of empirical mode decomposition;

[0022] Figure 4 It is the result of empirical mode decomposition of low-coherence interference signal when the pressure is 100 kPa;

[0023] Figure 5 It is a structure diagram of a radial basis neural network;

[0024] Figure 6 It is a schematic diagram of the fiber optic Fabry pressure demodulation error based on empirical mode decomposition and radial basis neural network.

[0025] The list of components represented in the drawings is as follows:

[0026] 1. White light LED light source; 2. Fiber optic coupler;

[0027] 3. Fiber optic Fabry - Perot sensor; 4. Cylindrical lens;

[0028] 5. Polarizer; 6. Birefringent crystal optical wedge;

[0029] 7. Analyzer; 8. Linear array CCD. Specific implementation manners

[0030] To make the objectives, technical solutions and advantages of the present invention clearer, the following further describes the embodiments of the present invention in detail.

[0031] As Figure 1 shown, it is a schematic diagram of a fiber optic Fabry - Perot pressure demodulation device based on empirical mode decomposition and radial basis neural network provided by an embodiment of the present invention. The light emitted by the white light LED light source 1 enters the fiber optic Fabry - Perot sensor 3 through the fiber optic coupler 2. The modulated optical signal of the fiber optic Fabry - Perot sensor 3 is transmitted out through the outlet of the fiber optic coupler 2, and successively passes through the cylindrical lens 4, polarizer 5, birefringent crystal optical wedge 6 and analyzer 7, and finally reaches the linear array CCD 8. When the optical path difference caused by the birefringent crystal optical wedge 6 matches the optical path difference caused by the fiber optic Fabry - Perot sensor 3, obvious low - coherence interference signals will be generated in the corresponding local area of the linear array CCD 8.

[0032] This device also includes: a signal processing software module, which is used to implement signal decomposition, feature extraction, neural network training and demodulation model construction. During the experiment, the atmospheric pressure is controlled to increase from 5 kPa to 250 kPa at intervals of 0.1 kPa. The low - coherence interference fringe signals under different pressure conditions are collected through the linear array CCD 8, and the corresponding real pressure values are recorded to generate an original data set. The effective pixel number of the linear array CCD 8 is 3000, that is, each frame of data collected consists of 3000 off - line points.

[0033] The experimental process of a low - coherence interference demodulation method based on modal decomposition and radial basis neural network provided by an embodiment of the present invention is as Figure 2 shown, and the specific implementation steps are as follows:

[0034] The first step: Pre - process the collected original low - coherence interference signal. Fourier pass - band filtering is used to filter out irrelevant frequency components and background noise, and the pass - band range of the filtering is determined according to the amplitude - frequency characteristic curve obtained by the Fourier transform of the low - coherence interference signal.

[0035] The second step: Perform empirical mode decomposition on the filtered low - coherence interference signal to extract the IMFs of the signal. The empirical mode decomposition process is asFigure 3 As shown below, the specific process includes the following steps:

[0036] 1. Detect local maxima and minima. Through the detection of maxima and minima, all local maximum points p i and local minimum points q j in the signal x(t) to be processed are identified. Generally, algorithms such as analyzing the gradient of the signal are used to find these extreme points.

[0037] 2. Construct the envelope. Use the spline interpolation method to construct the upper and lower envelopes of the signal. For the upper envelope U(t), interpolation is performed based on the local maximum points p i ; for the lower envelope L(t), interpolation is performed based on the local minimum points q j .

[0038] 3. By averaging the upper and lower envelopes, the mean envelope m(t) is obtained:

[0039]

[0040] 4. Subtract the mean envelope m(t) from the original signal to obtain the preliminary mode function h(t):

[0041] h(t) = x(t) - m(t) (2)

[0042] 5. Check whether h(t) meets the conditions of the IMF. If not, repeat steps 1 to 5 until an effective IMF is obtained, which can be expressed by the following formula:

[0043] IMF k (t) = h(t) (3)

[0044] According to the defined conditions of the IMF, the above steps are repeated until the kth IMF is extracted. After decomposition, the signal x(t) can be expressed as the sum of each IMF plus the residual term r(t):

[0045]

[0046] where N is the number of IMFs obtained by decomposition. The final residual term r(t) usually represents the low-frequency component or trend term of the signal.

[0047] In the third step, extract the effective time-frequency domain features of each IMF and the mathematical statistical time-domain features of the low-coherence interference signal to form a low-coherence interference signal feature dataset. The input of this dataset is the fused features, and the output is the pressure value corresponding to each feature.

[0048] Among them, the effective time-frequency domain features of the IMF include: standard deviation σ, skewness x sk , kurtosis xku , the main frequency x df , the spectral centroid x sc . The standard deviation σ is used to measure the dispersion of data, can evaluate the volatility of IMF, and helps to identify periodic and random components; the kurtosis x ku is a statistic describing the peakedness in the data distribution, measures the tail thickness and concentration of the data distribution, and reflects the flatness or sharpness of the distribution; the main frequency x df is used to reveal the main periodic characteristics of IMF and can be obtained by analyzing the spectrum of IMF; the spectral centroid x sc is used to describe the central position of the signal in the frequency domain, reflects the distribution characteristics of the signal's frequency components, and can identify the concentration trend of frequencies in IMF. The standard deviation σ, skewness x sk , kurtosis x ku , spectral centroid x sc The calculation formulas are as follows:

[0049]

[0050] where i represents the sampling point serial number of IMF, is the mean value of the IMF signal, and N represents the number of sampling points of the low-coherence interference signal. S(f i ) represents the spectrum of the Fourier transform of IMF, and f i represents the frequency.

[0051] The mathematical statistical time-domain characteristics of the low-coherence interference signal include: the fringe peak position x p and the variance of the peak position where the fringe peak position x p extracts the peak position through cubic spline interpolation; the variance of the peak position is a statistical feature used to quantify the degree of variation of the peak position in the signal. It can reveal the relative position change of the signal peak in different samples, and its calculation formula is as follows:

[0052]

[0053] where μ p is the mean value of the peak position.

[0054] Step 4: Normalize the input and output of the feature dataset and divide the dataset. Adopt the zscore standardization method to convert the feature dataset into a standard normal distribution with a mean of 0 and a standard deviation of 1. Through this standardization method, the influence of dimensions can be eliminated, making different features comparable, which helps to accelerate the training process of the neural network. Then randomly divide the standardized feature dataset with 75% for training, 10% for validation, and 15% for testing to ensure the generalization ability of the model on unknown data.

[0055] Step 5: Construct and train a radial basis neural network to establish a non - linear model between the features of the low - coherence interference signal and the pressure. Set the input layer corresponding to the fused feature vector, use the radial basis function as the activation function in the hidden layer, and use the Gaussian kernel function to achieve non - linear mapping. The output layer corresponds to the pressure value. Train the network with the feature dataset, use the mean square error as the loss function, and adopt the gradient descent method to optimize the network weights and thresholds, and iterate the training until the error converges.

[0056] Step 6: Input the low - coherence interference signal collected by the fiber optic Fabry - Perot sensing demodulation system, and demodulate the signal through the trained radial basis neural network model to obtain the corresponding pressure value.

[0057] Figure 4 is the empirical mode decomposition result of the low - coherence interference signal when the pressure is 100 kPa. Figure 5 is the structure diagram of the radial basis neural network. Under the same pressure range and experimental conditions as the above - mentioned original dataset, collect a new set of low - coherence interference signals and extract features as the dataset according to the above steps, and then use the trained neural network model for pressure prediction. The linear fitting coefficient R of the predicted pressure value 2 reaches 0.99999. As Figure 6 shown in the predicted pressure error, the prediction error is between - 0.098 kPa and 0.091 kPa within the pressure range of 250 kPa.

[0058] For the models of each device in the embodiments of the present invention, unless otherwise specified, the models of other devices are not limited, as long as the devices can perform the above - mentioned functions.

[0059] Those skilled in the art can understand that the drawings are only schematic diagrams of a preferred embodiment. The serial numbers of the above - mentioned embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0060] The above - mentioned are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A low coherence interference demodulation method based on modal decomposition and radial basis neural network, characterized in that: The method comprises: Perform empirical mode decomposition on the filtered low-coherence interference signal to extract the effective time-frequency domain features of each IMF and the mathematical statistical time-domain features of the low-coherence interference signal to form a low-coherence interference signal feature data set; Construct and train a radial basis neural network, establish a nonlinear model between low-coherence interference signal characteristics and pressure, set the input layer to correspond to the fusion feature vector, use the radial basis function as the activation function of the hidden layer, use the Gaussian kernel function to achieve nonlinear mapping, and the output layer corresponds to the pressure value; train the network through the feature data set, use the mean square error as the loss function, use the gradient descent method to optimize the network weights and thresholds, and iterate the training until the error converges; The low-coherence interference signal collected by the fiber Fabry-Perot pressure demodulation device is input, and the signal is demodulated through the trained radial basis neural network model to obtain the corresponding pressure value.

2. The low coherence interference demodulation method based on modal decomposition and radial basis function neural network according to claim 1, characterized in that: The method further includes: normalizing the input and output of the feature data set and dividing the data set, using zscore standardization to convert the feature data set into a standard normal distribution.

3. The low coherence interference demodulation method based on modal decomposition and radial basis neural network according to claim 1, characterized in that: The effective time-frequency domain features include: standard deviation, skewness, kurtosis, main frequency, and spectrum centroid.

4. The low coherence interference demodulation method based on modal decomposition and radial basis neural network according to claim 1, characterized in that: The low coherence interference signal characteristic data set comprises: Perform mathematical and statistical analysis on low-coherence interference signals to extract effective time-domain features, including fringe peak position and fringe peak position variance; The time domain features are fused with the time-frequency domain features extracted by empirical mode decomposition to construct a highly expressive feature dataset for subsequent neural network training and demodulation model establishment.

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