Optical fiber EFPI-FBG composite sensing spectrum demodulation method

Abstract

This invention provides a fiber optic EFPI-FBG composite sensing spectral demodulation method, belonging to the field of fiber optic sensing technology. The method includes: separating the FBG reflection peak and the initially extracted EFPI interference fringes from the composite spectrum; determining a coarse estimate of the cavity length after normalizing the amplitude of the EFPI interference fringes; constructing a Pearson correlation coefficient objective function based on this coarse estimate; obtaining the optimal cavity length and complete interference spectrum of EFPI through an artificial bee colony-particle swarm optimization algorithm; inverting and compensating for the FBG reflection peak and obtaining the center wavelength through Gaussian fitting; and calculating the absolute physical parameter values ​​by combining the calibrated sensitivity coefficient. This invention effectively solves the demodulation problem caused by strong multiplicative coupling of composite signals, balancing demodulation accuracy and real-time performance, and achieving synchronous high-precision demodulation of two physical parameters.

Description

Technical Field

[0001] This invention relates to the field of fiber optic sensing technology, and specifically to a fiber optic EFPI-FBG composite sensing spectral demodulation method. Background Technology

[0002] In fiber optic sensing technology, the eigenvalue Fabry-Perot Interferometer (EFPI)-Fiber Bragg Grating (FBG) composite sensor has the advantages of compact structure, strong anti-electromagnetic interference capability, easy integration, and the ability to achieve simultaneous measurement of dual parameters such as temperature and pressure / strain / displacement / vibration. It has good application prospects in monitoring parameters in complex environments.

[0003] However, in the spectrum of the EFPI-FBG composite sensor, there is a strong multiplicative coupling between the narrow band reflection peak of FBG and the broadband interference fringes of EFPI. The EFPI fringes will cause FBG peak shape distortion and peak position shift. The traditional direct fitting method has low accuracy and poor stability. At the same time, the traditional EFPI cavity length demodulation algorithm is easily affected by the amplitude and has mode jumps, making it difficult to balance accuracy and real-time performance.

[0004] Therefore, the existing core technical problem is that the composite signal of the EFPI-FBG composite sensor cannot be effectively demodulated due to the strong multiplicative coupling between the narrow-band reflection peak of FBG and the broadband interference fringes of EFPI. Furthermore, traditional methods cannot balance accuracy and real-time performance, and cannot meet the requirements for synchronous demodulation of two parameters. Summary of the Invention

[0005] In view of this, it is necessary to provide a fiber optic EFPI-FBG composite sensing spectral demodulation method to solve the problems in the existing technology where strong multiplicative coupling leads to the inability to effectively demodulate composite signals and the difficulty in balancing accuracy and real-time performance.

[0006] To address the aforementioned technical problems, this invention provides a fiber optic EFPI-FBG composite sensor spectral demodulation method, comprising: The FBG reflection peak and the initially extracted EFPI interference fringes were separated from the composite spectrum of the fiber EFPI-FBG composite sensor. After normalizing the amplitude of the initially extracted EFPI interference fringes, a coarse estimate of the EFPI cavity length is determined. Based on the coarse estimate of the cavity length, a target function is constructed using the Pearson correlation coefficient. The artificial bee colony algorithm is used to search for the cavity length optimal region corresponding to the minimum value of the target function. Then, the particle swarm optimization algorithm is used to quickly converge the cavity length optimal region to obtain the optimal EFPI cavity length and the complete EFPI interference spectrum. Based on the complete EFPI interferometric spectrum, the reflection peak of the FBG is inverted, compensated, and fitted with Gaussian to obtain the center wavelength of the FBG. The absolute physical parameter values ​​are calculated based on the physical parameter sensitivity coefficient calibrated by the fiber optic EFPI-FBG composite sensor, combined with the center wavelength of the FBG and the optimal cavity length of the EFPI.

[0007] In one possible implementation, before separating the FBG reflection peak and the initially extracted EFPI interference fringes from the composite spectrum of the fiber EFPI-FBG composite sensor, the composite spectrum is preprocessed; the preprocessing includes: Adaptive SG filtering is applied to the composite spectrum of the fiber optic EFPI-FBG composite sensor to obtain a noise-reduced composite spectrum. The denoised composite spectrum is truncated into several segments of appropriate length in an overlapping manner, and after applying a window function to the segments, the spectra are fused to obtain a clean composite spectrum.

[0008] In one possible implementation, before the amplitude normalization of the initially extracted EFPI interference fringes is performed, local cubic spline interpolation is performed on the initially extracted EFPI interference fringes to obtain continuous EFPI interference fringes.

[0009] In one possible implementation, determining the coarse estimate of the cavity length of the EFPI after amplitude normalization of the initially extracted EFPI interference fringes includes: The amplitude of the initially extracted EFPI interference fringes was normalized using upper and lower envelope correction. The amplitude-normalized EFPI interference fringes are zero-padded in their wavelength domain, and the zero-padded EFPI interference fringes are subjected to a fast Fourier transform to obtain the frequency domain amplitude spectrum corresponding to the EFPI interference fringes. Three-point Gaussian interpolation is performed in the neighborhood of the main peak of the frequency domain amplitude spectrum to obtain the sub-grid peak position shift corresponding to the main peak; The main frequency of the EFPI interference fringes is obtained by summing the subgrid peak position shift and the peak main frequency of the frequency domain amplitude spectrum. Based on the linear relationship between the main frequency after EFPI interference fringe correction and the EFPI cavity length, a rough estimate of the EFPI cavity length is obtained.

[0010] In one possible implementation, the step of constructing an objective function based on the coarse estimate of the cavity length using the Pearson correlation coefficient includes: Using the coarse estimate of the cavity length as the center, the cavity length search interval for the simulated interference fringes is determined with a preset error range; For each candidate cavity length within the cavity length search interval, simulated interference fringes are generated based on the EFPI reflection spectral model; Based on the normalized Pearson correlation coefficient between the simulated interference fringes and the measured interference fringes, an objective function is constructed to measure the degree of matching between the simulated interference fringes and the measured interference fringes corresponding to the candidate cavity length; the measured interference fringes are the EFPI interference fringes initially extracted after preprocessing.

[0011] In one possible implementation, the step of using the artificial bee colony algorithm to search for the cavity length-optimal region corresponding to the minimum value of the objective function includes: The candidate cavity lengths within the cavity length search interval are mapped to the positions of individual bees in the artificial bee colony algorithm, and the objective function value corresponding to each individual value is calculated. The positions of individual bee colonies are updated by neighborhood search. The iteration stops when the preset maximum number of iterations is reached or the objective function value converges, thus obtaining the cavity length optimal region corresponding to the minimum value of the objective function.

[0012] In one possible implementation, the step of rapidly converging the cavity length-optimal region using a particle swarm optimization algorithm to obtain the optimal EFPI cavity length and the complete EFPI interferogram includes: Using the region with excellent cavity length as the search range of the particle swarm optimization algorithm, the candidate cavity lengths within the region with excellent cavity length are mapped to particle positions; Using the objective function value as the fitness, the position and velocity of each particle are iteratively updated based on the velocity-position update formula of the particle swarm optimization algorithm, and the individual optimal position of each particle and the global optimal position of the entire particle swarm are recorded simultaneously. Convergence is determined when the preset maximum number of iterations is reached or the global optimal fitness value remains unchanged after continuous iterations, and the optimal cavity length and the corresponding complete EFPI interferometric spectrum are output.

[0013] In one possible implementation, the step of performing inversion compensation and Gaussian fitting on the FBG reflection peak based on the complete EFPI interferometric spectrum to obtain the FBG center wavelength includes: The EFPI-FBG composite spectral coupling model is transformed into a univariate quadratic equation concerning the FBG reflection spectrum. The quadratic equation concerning the FBG reflection spectrum is solved by using the quadratic formula, and the pure FBG reflection spectrum with EFPI multiplicative distortion eliminated is obtained by inversion. Gaussian fitting was performed on the reflection spectrum of the pure FBG to obtain the center wavelength of the FBG.

[0014] In one possible implementation, the step of calculating the absolute physical parameter value based on the physical parameter sensitivity coefficient calibrated by the fiber EFPI-FBG composite sensor, combined with the center wavelength of the FBG and the optimal cavity length of the EFPI, includes: Calculate the wavelength change of the FBG center wavelength relative to the pre-calibrated initial wavelength and the cavity length change of the EFPI optimal cavity length relative to the pre-calibrated initial cavity length. Based on the wavelength change, the cavity length change, and the sensitivity coefficients of the physical parameters of FBG and EFPI calibrated by the fiber optic EFPI-FBG composite sensor, a set of sensor response equations is established. Solve the sensor response equations to obtain the changes in physical parameters, and combine them with the initial physical parameter values ​​to obtain the absolute physical parameter values.

[0015] In one possible implementation, the fiber optic EFPI-FBG composite sensor consists of an EFPI sensor and an FBG sensor. The physical parameters detected by the EFPI sensor include pressure, strain, displacement, and vibration. The physical parameters detected by the FBG sensor include temperature.

[0016] The beneficial effects of this invention are as follows: The fiber optic EFPI-FBG composite sensor spectral demodulation method provided by this invention first separates the FBG reflection peak and the initially extracted EFPI interference fringes from the composite spectrum of the composite sensor, laying the foundation for breaking the strong multiplicative coupling between the two signals; secondly, it normalizes the amplitude of the initially extracted EFPI interference fringes and determines a coarse estimate of the cavity length, which can effectively weaken amplitude interference and suppress mode jumps; then, it constructs an objective function using the Pearson correlation coefficient and adopts a hybrid optimization method of artificial bee colony optimization and particle swarm optimization, which improves the convergence speed while ensuring global search capability, and balances demodulation accuracy and real-time performance. This process yields a high-precision EFPI optimal cavity length and a complete EFPI interference spectrum. Then, based on the complete EFPI interference spectrum, inversion compensation and Gaussian fitting are performed on the FBG reflection peak. This eliminates the FBG peak shape distortion and peak position shift caused by EFPI fringes, overcoming the shortcomings of low accuracy and poor stability in traditional direct fitting methods, and accurately obtaining the FBG center wavelength. Finally, combined with the calibrated physical parameter sensitivity coefficient, the absolute physical parameter values ​​are calculated using the FBG center wavelength and the EFPI optimal cavity length, achieving dual-parameter synchronous high-precision demodulation. This effectively solves the problems of difficult demodulation of composite signals due to strong multiplicative coupling and the inability of traditional methods to balance accuracy and real-time performance. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic flowchart of an embodiment of the fiber optic EFPI-FBG composite sensing spectral demodulation method provided by the present invention; Figure 2 A schematic flowchart of an embodiment for preprocessing composite spectra provided by the present invention; Figure 3 A schematic diagram of an embodiment of the theoretical spectrum of the fiber optic EFPI-FBG composite sensor provided by the present invention; Figure 4 This is a schematic diagram of an embodiment of adaptive SG filtering of composite spectra provided by the present invention; Figure 5 A schematic diagram of an embodiment of the separation effect between the FBG peak region and the EFPI interference fringes in the spectrum of the composite sensor provided by the present invention; Figure 6 This is a schematic diagram of an embodiment of the present invention for local cubic spline interpolation to complete the initially extracted EFPI interference fringes; Figure 7 This is an example of the flowchart illustrating the process of determining the coarse estimate of the cavity length of the EFPI after amplitude normalization of the initially extracted EFPI interference fringes following local cubic spline interpolation and completion, as provided by the present invention. Figure 8 A schematic diagram illustrating an embodiment of the amplitude normalization effect of the initially extracted EFPI interference fringes provided by the present invention; Figure 9 This is a schematic flowchart of an embodiment of the present invention that uses the Pearson correlation coefficient to construct an objective function; Figure 10 This is a schematic flowchart of an embodiment of the present invention that uses the artificial bee colony algorithm to search for the optimal cavity length region corresponding to the minimum value of the objective function; Figure 11 A schematic diagram of an embodiment of the global exploration distribution evolution of the artificial bee colony algorithm provided by the present invention; Figure 12 This is a schematic diagram illustrating an embodiment of the present invention that uses a particle swarm optimization algorithm to rapidly converge in a cavity length-optimal region to obtain the optimal cavity length of EFPI and the complete EFPI interferogram. Figure 13 This is a schematic diagram of an embodiment of the particle position convergence trajectory and the evolution of the optimal point in the human particle swarm optimization algorithm provided by the present invention. Figure 14 This is a schematic flowchart of an embodiment of EFPI signal splitting and demodulation provided by the present invention; Figure 15 This is a schematic diagram of an embodiment of the present invention, which involves inverting and compensating the reflection peak of the FBG based on the complete EFPI interferometer spectrum and performing Gaussian fitting to obtain the center wavelength of the FBG. Figure 16 Provided by the present invention Figure 1 A flowchart of one embodiment of S104; Figure 17 This is a schematic diagram illustrating an embodiment of the FBG peak signal inversion compensation effect provided by the present invention; Figure 18 This is a schematic flowchart of another embodiment of the fiber optic EFPI-FBG composite sensing spectral demodulation method provided by the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0020] In the description of the embodiments of the present invention, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.

[0021] The terms "first," "second," etc., used in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a technical feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.

[0022] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0023] Before demonstrating the embodiments, the following terms will be explained.

[0024] EFPI (Extrinsic Fabry-Perot Interferometer): Also known as an external cavity fiber optic FP interferometer, it consists of an interference cavity formed by an air gap or other medium gap between the end faces of two optical fibers, belonging to the external cavity interference structure. When incident light is reflected at both end faces, interference occurs, and the interference spectrum changes with the cavity length, which responds to external physical quantities such as strain, pressure, displacement, or vibration. EFPI has advantages such as high sensitivity, small probe size, and resistance to electromagnetic interference, making it particularly suitable for dynamic micro-displacement measurement and sensing applications in harsh environments such as high temperature and strong interference.

[0025] FBG (Fiber Bragg Grating): It is a narrowband reflection filter formed by periodically modulating the refractive index within the fiber core through methods such as ultraviolet exposure. Specific wavelengths satisfying the Bragg condition are reflected, while other wavelengths are transmitted. The center wavelength of this Bragg grating is related to the grating period and the effective refractive index of the fiber core. When the external temperature or strain changes, the grating period and refractive index change accordingly, causing a linear shift in the center wavelength. Absolute measurement of temperature and strain can be achieved through high-precision wavelength demodulation, and multiple FBGs of different wavelengths can be connected in series on a single fiber to form a quasi-distributed sensing network.

[0026] This invention provides a fiber optic EFPI-FBG composite sensor spectral demodulation method, which is described in detail below.

[0027] Figure 1 This is a schematic flowchart of an embodiment of the fiber optic EFPI-FBG composite sensing spectral demodulation method provided by the present invention, as shown below. Figure 1 As shown, the fiber optic EFPI-FBG composite sensor spectral demodulation method includes: S101. Separate the FBG reflection peak and the initially extracted EFPI interference fringes from the composite spectrum of the fiber EFPI-FBG composite sensor. S102. After normalizing the amplitude of the initially extracted EFPI interference fringes, determine the coarse estimate of the EFPI cavity length; based on the coarse estimate of the cavity length, construct the objective function using the Pearson correlation coefficient; use the artificial bee colony algorithm to search for the cavity length region corresponding to the minimum value of the objective function, and then use the particle swarm optimization algorithm to quickly converge the cavity length region to obtain the optimal EFPI cavity length and the complete EFPI interference spectrum. S103. Based on the complete EFPI interferometric spectrum, the FBG reflection peak is inverted, compensated, and fitted with Gaussian to obtain the FBG center wavelength. S104. Based on the sensitivity coefficient of the physical parameters calibrated by the fiber optic EFPI-FBG composite sensor, the absolute physical parameter values ​​are calculated by combining the center wavelength of the FBG and the optimal cavity length of the EFPI.

[0028] In summary, the fiber EFPI-FBG composite sensor spectral demodulation method provided in this embodiment of the invention first separates the FBG reflection peak and the initially extracted EFPI interference fringes from the composite spectrum of the composite sensor, laying the foundation for breaking the strong multiplicative coupling between the two signals. Secondly, it normalizes the amplitude of the initially extracted EFPI interference fringes and determines a coarse estimate of the cavity length, effectively reducing amplitude interference and suppressing mode jumps. Then, it constructs an objective function using the Pearson correlation coefficient and employs a hybrid optimization method combining artificial bee colony optimization and particle swarm optimization, improving convergence speed while ensuring global search capability, thus balancing demodulation accuracy and real-time performance. The optimal cavity length of EFPI and the complete EFPI interference spectrum are obtained with high precision. Then, based on the complete EFPI interference spectrum, the reflection peak of FBG is inverted and compensated and Gaussian fitted, which can eliminate the peak shape distortion and peak position shift of FBG caused by EFPI fringes, overcome the defects of low accuracy and poor stability of traditional direct fitting methods, and accurately obtain the center wavelength of FBG. Finally, combined with the calibrated physical parameter sensitivity coefficient, the absolute physical parameter values ​​are calculated using the center wavelength of FBG and the optimal cavity length of EFPI, realizing dual-parameter synchronous high-precision demodulation. This effectively solves the problems that composite signals are difficult to demodulate effectively due to strong multiplicative coupling and that traditional methods cannot balance accuracy and real-time performance.

[0029] In some embodiments of the present invention, the composite spectrum is preprocessed before separating the FBG reflection peak and the initially extracted EFPI interference fringes from the composite spectrum of the fiber optic EFPI-FBG composite sensor; such as... Figure 2 As shown, the preprocessing includes: S201. Adaptive SG filtering is applied to the composite spectrum of the fiber optic EFPI-FBG composite sensor to obtain a noise-reduced composite spectrum. S202. The noise-reduced composite spectrum is truncated into several segments of appropriate length in an overlapping manner, and after applying a window function to the segments, the spectra are fused to obtain a clean composite spectrum.

[0030] It should be noted that the core idea of ​​adaptive SG filtering is to dynamically adjust the filter window width or polynomial order based on the local characteristics of the signal, rather than using fixed parameters throughout.

[0031] In some embodiments of the present invention, the adaptive SG filter first calculates the local rate of change point by point in the spectrum, and obtains the normalized adaptive factor by comparing it with the maximum rate of change of the whole spectrum; then, the filter window length is dynamically adjusted according to the factor, a smaller window is used in the signal detail region (such as FBG peak) with high factor value to preserve features, and a larger window is used in the baseline flat region with low factor value to enhance the denoising effect. At the same time, a fixed-order polynomial is used to fit the data of each window, and finally a denoised spectrum that takes into account both noise suppression and detail preservation is obtained. The window length of the adaptive SG filter is adaptively determined by the local rate of change of the signal: for data points within the spectrum Local rate of change As shown in Equation 1: (1) in, and These are the spectral intensity values ​​at the wavelength preceding the current data point and the spectral intensity values ​​at the wavelength following the current data point, respectively. Normalized adaptive factor As shown in Equation 2: (2) in, This represents the maximum local rate of change at all points in the entire spectrum; Window length of SG filter Follow The sampling points are dynamically adjusted within the range of 5 to 35, and the polynomial order is set to 4.

[0032] In some embodiments of the present invention, the window function applied to the spectral segments can be a smooth weighted window, including but not limited to the Hanning window, Hamming window, Blackman window, or rectangular window. By weighting the signals of each segment, the spectral leakage caused by truncation can be effectively reduced, and the accuracy of subsequent spectral fusion and signal analysis can be improved.

[0033] This embodiment effectively filters out spectral noise and reduces spectral leakage by sequentially performing adaptive SG filtering and segmented windowing fusion preprocessing on the composite spectrum, resulting in a cleaner and more stable composite spectrum. This provides a high-quality signal foundation for the subsequent separation of FBG reflection peaks and EFPI interference fringes. The adaptive SG filtering adjusts the filter window length according to the local spectral change rate, using a smaller window in signal detail regions such as FBG peaks to preserve signal characteristics, and a larger window in flat baseline regions to enhance denoising. This achieves a balance between noise suppression and signal detail preservation, avoiding peak distortion or insufficient denoising problems caused by traditional fixed-parameter filtering. This, in turn, improves the accuracy and stability of subsequent FBG center wavelength and EFPI cavity length demodulation.

[0034] In some embodiments of the present invention Figure 3This is a schematic diagram of an embodiment of the theoretical spectrum of the fiber optic EFPI-FBG composite sensor provided by the present invention; the horizontal axis represents wavelength (unit: nm), and the vertical axis represents normalized light intensity (unit: au). The figure shows the typical characteristics of the composite spectrum: it contains an FBG reflection peak region, which appears as a sharp, narrow-band reflection peak; at the same time, it is superimposed with an effective EFPI interference fringe region that spans the entire wavelength range, which appears as a periodic, broadband fluctuating signal. Together, these two constitute the typical morphology of the composite sensing spectrum.

[0035] In some embodiments of the present invention Figure 4 This is a schematic diagram of an embodiment of adaptive SG filtering of composite spectra provided by the present invention; the diagram shows, from top to bottom: the original noise-free spectrum (green), the spectrum after adding noise (blue), the spectrum after ordinary SG filtering (red), and the spectrum after adaptive parameter filtering (black).

[0036] It should be noted that: Noise is artificially added to the theoretical composite spectrum, followed by noise reduction using an adaptive SG filter. The use of the theoretical composite spectrum and artificial noise addition is to construct a controllable, noisy spectral testing environment highly consistent with the actual acquisition scenario, used to verify the denoising performance of the adaptive SG filtering algorithm in this invention, and to compare the processing effect with that of ordinary SG filtering. Here, MSE represents the mean square error between the processed composite spectrum and the "noise-free original spectrum"; a larger value indicates a larger deviation and more severe noise residue or signal distortion. Figure 4 As shown, after denoising the composite spectrum (MSE=0.010722) using ordinary SG filtering and adaptive SG filtering respectively, the MSE values ​​are 0.005064 and 0.00049, respectively, which indicates that the denoising effect of adaptive SG filtering is better than that of ordinary SG filtering.

[0037] In some embodiments of the present invention Figure 5 This is a schematic diagram of an embodiment of the separation effect between the FBG peak region and the EFPI interference fringes in the spectrum of the composite sensor provided by the present invention, consisting of two sub-images on the left and right.

[0038] The left subplot shows the separated FBG spectrum, with the horizontal axis representing wavelength (nm) and the vertical axis representing normalized light intensity (au). It exhibits a narrow-band reflection peak with a complete shape and prominent peak. The right subplot shows the separated EFPI spectrum, with the horizontal axis representing wavelength (nm) and the vertical axis representing normalized light intensity (au). It exhibits regular periodic interference fringes without interference from the FBG reflection peak. This figure visually verifies that the present invention can effectively separate the FBG reflection peak from the EFPI interference fringes, laying the foundation for subsequent FBG center wavelength demodulation and EFPI cavity length determination.

[0039] In some embodiments of the present invention, before normalizing the amplitude of the initially extracted EFPI interference fringes, local cubic spline interpolation is performed on the initially extracted EFPI interference fringes to obtain continuous EFPI interference fringes.

[0040] It should be noted that cubic spline interpolation, or spline interpolation for short, is a process of obtaining a set of curve functions by solving a set of three moment equations through a smooth curve obtained from a series of shape points.

[0041] This embodiment uses local cubic spline interpolation to complete the initially extracted EFPI interference fringes, which can restore discrete EFPI interference fringes with missing data to a continuous signal. This eliminates the adverse effects of signal breakpoints on subsequent amplitude normalization, frequency domain transformation, and cavity length calculation, providing a complete and continuous interference fringe data foundation for subsequent processing and ensuring the accuracy and stability of subsequent demodulation steps.

[0042] In some embodiments of the present invention Figure 6 This diagram illustrates an embodiment of the present invention that uses local cubic spline interpolation to complete initially extracted EFPI interference fringes. The blue curve represents EFPI interference fringes with missing data, the green curve represents the area where local cubic spline interpolation is performed, and the two red vertical lines indicate the range of the interpolation process. Through interpolation, the originally discontinuous interference fringes are smoothly completed, forming a complete and continuous signal pattern. This visually demonstrates that the method can eliminate signal breakpoints and provide a continuous EFPI interference fringe data foundation for subsequent amplitude normalization, frequency domain transformation, and other processing.

[0043] In some embodiments of the present invention, the cavity length of the initially extracted EFPI interference fringes is coarsely estimated after amplitude normalization, such as... Figure 7 As shown, it includes: S701. The amplitude of the initially extracted EFPI interference fringes is normalized by using upper and lower envelope correction. S702. The amplitude-normalized EFPI interference fringes are zero-padded in their wavelength domain. The zero-padded EFPI interference fringes are then subjected to a fast Fourier transform to obtain the frequency domain amplitude spectrum corresponding to the EFPI interference fringes. S703. Perform three-point Gaussian interpolation in the neighborhood of the main peak of the frequency domain amplitude spectrum to obtain the sub-grid peak position shift corresponding to the main peak. S704. Sum the subgrid peak position shift and the peak dominant frequency of the frequency domain amplitude spectrum to obtain the dominant frequency after EFPI interference fringe correction. S705. Based on the linear relationship between the main frequency after EFPI interference fringe correction and the EFPI cavity length, a rough estimate of the EFPI cavity length is obtained.

[0044] It should be noted that upper and lower envelope correction is an amplitude normalization method based on the upper and lower envelopes of a signal. It is used to standardize the amplitude range of the original signal to the 0-1 interval, while eliminating the effects of baseline drift and overall amplitude shift. By calculating the upper and lower envelopes of the signal, a point-by-point linear transformation is performed on the signal, changing only the overall amplitude and baseline position, without altering the relative fluctuation pattern of the signal itself (such as the periodicity of interference fringes). This eliminates the impact of signal amplitude non-uniformity and baseline shift on subsequent processing (such as frequency domain analysis and correlation matching), allowing signals of different amplitudes to be compared and calculated on the same scale.

[0045] In some embodiments of the present invention, upper and lower envelope correction is used to normalize the amplitude of the initially extracted EFPI interference fringes; wherein, upper and lower envelope correction, The original EFPI signal, The normalized EFPI signal. For the lower envelope, The upper envelope is shown in Equation 3: (3) First use the original signal Subtract the lower envelope This process eliminates the overall baseline offset of the signal, making the lower limit of the signal zero; then, the baseline-removed signal is divided by the above envelope. The upper limit of the signal is stretched to 1, resulting in a normalized signal in the range of 0 to 1.

[0046] Figure 8 This is a schematic diagram illustrating an embodiment of the amplitude normalization effect of the initially extracted EFPI interference fringes provided by the present invention. The solid black lines in the diagram represent the original EFPI interference fringes before amplitude normalization (the initially extracted EFPI interference fringes), while the dashed red lines represent the interference fringes after amplitude normalization following upper and lower envelope correction. It can be seen that after normalization, the overall amplitude of the interference fringes is standardized, while retaining the periodic fluctuation characteristics of the original fringes. This intuitively verifies that the method can eliminate the influence of amplitude unevenness while preserving effective signal information, providing a standardized signal basis for subsequent frequency domain analysis and cavity length determination.

[0047] In some embodiments of the present invention, three-point Gaussian interpolation is performed in the neighborhood of the main peak of the frequency domain amplitude spectrum to obtain the sub-grid peak position shift corresponding to the main peak. As shown in Equation 4: (4) in, , , The peak dominant frequency in the amplitude spectrum after zero-padding The amplitude of the two points before and after it; The sub-grid peak position shift and the peak dominant frequency of the frequency domain amplitude spectrum are summed to obtain the dominant frequency after EFPI interference fringe correction. Based on the linear relationship between the dominant frequency after EFPI interference fringe correction and the EFPI cavity length, a rough estimate of the EFPI cavity length is obtained, as shown in Equation 5. (5) in, At the speed of light, The refractive index within the cavity, The length after padding with zeros, The wavenumber interval.

[0048] This embodiment achieves a high-precision solution for the coarse estimate of the cavity length by performing amplitude normalization, frequency domain transformation, and sub-grid correction on the initially extracted EFPI interference fringes. Amplitude normalization in the upper and lower envelope corrections eliminates the influence of fringe amplitude fluctuations, ensuring the accuracy of subsequent frequency domain analysis. Zero-padding, fast Fourier transform, and three-point Gaussian interpolation of the frequency domain main peak neighborhood yield the corrected main frequency. Combining this with the linear relationship between the main frequency and the cavity length, a more accurate coarse estimate of the EFPI cavity length is obtained, effectively narrowing the subsequent cavity length search interval, reducing the computational load of the hybrid optimization algorithm, and improving the initial accuracy of the cavity length solution. This provides a reliable initial boundary for subsequent artificial bee swarm-particle swarm hybrid optimization, avoiding the problems of low optimization efficiency or getting trapped in local optima due to an excessively large initial interval.

[0049] In some embodiments of the present invention, based on a coarse estimate of the cavity length, a target function is constructed using the Pearson correlation coefficient, such as... Figure 9 As shown, it includes: S901. Using the coarse estimate of the cavity length as the center, determine the cavity length search interval for the simulated interference fringes based on the preset error range; S902. For each candidate cavity length within the cavity length search interval, generate its simulated interference fringes based on the EFPI reflection spectrum model. S903. Based on the normalized Pearson correlation coefficient between simulated and measured interference fringes, an objective function is constructed to measure the degree of matching between simulated and measured interference fringes corresponding to candidate cavity lengths; the measured interference fringes are the EFPI interference fringes initially extracted after preprocessing.

[0050] In some embodiments of the present invention, the cavity length search interval for simulated interference fringes is determined based on a coarse estimate of the cavity length and a preset error range, wherein the allowable error range is set to ±4μm.

[0051] In some embodiments of the present invention, the objective function is constructed using the normalized Pearson correlation coefficient (NPCC), as shown in Equation 6: (6) in, For actual stripe measurements, To simulate stripes, The first EFPI interference fringe measured The light intensity value at each sampling point To measure the average light intensity of the interference fringes, The length of the cavity is Simulated EFPI interference fringes The light intensity value at each sampling point The length of the cavity is The average light intensity of the simulated interference fringes, The length of the cavity is Normalized Pearson correlation coefficient between measured and simulated interference fringes; The measured interference fringes were quantified by normalizing the Pearson correlation coefficient. With cavity length Simulated interference fringes The degree of linear correlation between the two stripes. This coefficient eliminates the influence of signal amplitude and baseline offset, and only reflects the similarity between the two stripe waveforms. The value range is [-1, 1]. The closer it is to 1, the higher the matching degree between the two stripes.

[0052] The objective function is shown in Equation 7: (7) in, For the length of the cavity The objective function is the independent variable, with To minimize the optimization objective.

[0053] correlation coefficient Convert to objective function This makes the objective function value smaller when the matching degree is higher, thus transforming the cavity length problem into an optimization problem of minimizing the objective function, providing a clear optimization direction for subsequent artificial bee colony-particle swarm optimization algorithms.

[0054] This embodiment uses a coarse estimate of the cavity length as a basis to construct an objective function based on the normalized Pearson correlation coefficient, providing a reliable evaluation basis for subsequent cavity length optimization. First, by centering on the coarse estimate of the cavity length and determining the cavity length search interval according to a preset error range, the optimization range can be effectively narrowed, reducing the computational load of subsequent algorithms. Second, by generating simulated interference fringes corresponding to each candidate cavity length based on the EFPI reflectance spectral model, the consistency between the simulated signal and the measured signal in the physical model can be ensured. Finally, by constructing an objective function based on the normalized Pearson correlation coefficient of the simulated and measured interference fringes, the matching degree of the two waveforms can be accurately measured, providing a clear optimization objective for the artificial bee swarm-particle swarm optimization algorithm. This ensures that the algorithm can quickly and accurately converge to the cavity length value that best matches the measured fringes, improving the accuracy and efficiency of EFPI cavity length demodulation.

[0055] In some embodiments of the present invention, an artificial bee colony algorithm is used to search for the optimal cavity length region corresponding to the minimum value of the objective function, such as... Figure 10 As shown, it includes: S1001. Map the candidate cavity lengths within the cavity length search interval to the positions of individual bees in the artificial bee colony algorithm, and calculate the objective function value corresponding to each individual value. S1002. Update the position of individual bee colonies through neighborhood search. Stop iterating when the preset maximum number of iterations is reached or the objective function value converges, and obtain the cavity length good region corresponding to the minimum value of the objective function.

[0056] Figure 11 This diagram illustrates an embodiment of the global exploration distribution evolution of the artificial bee colony algorithm provided by this invention. The gray dots represent the distribution of nectar sources among candidate cavity length solutions, and the red curve represents the evolution trajectory of the global optimal solution (gbest). The entire process is divided into three stages: Stage I is the initial global exploration stage, where nectar sources are widely distributed within the cavity length search interval; Stage II is the clustering stage towards the dominant region, where nectar sources gradually concentrate in the cavity length region with a better objective function; Stage III is the optimal neighborhood convergence stage, where nectar sources stably cluster near the optimal cavity length, and the trajectory tends to stabilize. This diagram intuitively demonstrates the process of the artificial bee colony algorithm from global exploration to locking onto the optimal cavity length region, verifying its ability to effectively complete the global search and define a reliable range for subsequent fine optimization.

[0057] It should be noted that: convergence of the objective function value means that, during the iterative optimization process, the objective function value no longer decreases significantly after multiple iterations and the value tends to stabilize, indicating that the algorithm has approached the optimal solution and further iterations cannot significantly improve the optimization effect.

[0058] This embodiment employs the artificial bee colony algorithm for searching optimal cavity length regions. By mapping candidate cavity lengths to individual bee colony positions and calculating corresponding objective function values, it can quickly traverse the cavity length search interval through a global search. It updates individual positions using neighborhood search and terminates iteration when an iteration threshold is reached or the objective function value converges. This efficiently locks down the optimal cavity length regions corresponding to the minimum objective function value, ensuring comprehensiveness of the search while avoiding invalid iterations. It also precisely defines the range for subsequent fine-grained local optimization in particle swarm optimization, significantly improving the efficiency and accuracy of cavity length demodulation and effectively avoiding the pitfalls of single algorithms easily getting trapped in local optima.

[0059] In some embodiments of the present invention, a particle swarm optimization algorithm is used to rapidly converge the cavity length in the optimal region, thereby obtaining the optimal cavity length for EFPI and the complete EFPI interferogram, such as... Figure 12 As shown, it includes: S1201. Using the region with excellent cavity length as the search range of the particle swarm optimization algorithm, the candidate cavity lengths within the region with excellent cavity length are mapped to particle positions. S1202. Using the objective function value as the fitness, iteratively update the position and velocity of each particle based on the velocity-position update formula of the particle swarm optimization algorithm, and simultaneously record the individual optimal position of each particle and the global optimal position of the entire particle swarm. S1203. When the preset maximum number of iterations is reached or the global optimal fitness value remains unchanged after continuous iterations, convergence is determined, and the optimal cavity length and the corresponding complete EFPI interference spectrum are output.

[0060] Figure 13 This is a schematic diagram illustrating an embodiment of the particle position convergence trajectory and optimal point evolution of the human particle swarm optimization algorithm provided by the present invention; the yellow dots in the diagram represent the distribution of the particle swarm, and the red trajectory represents the global optimal solution (gbest). t The evolution path of the particle swarm optimization algorithm is illustrated in the figure, with the dashed line marking the center of the optimal cavity length region output by the artificial bee colony algorithm (ABC). As the iteration progresses, particles rapidly converge from their initial distribution state to the optimal cavity length region defined by the ABC algorithm, eventually converging stably to the optimal point with a stable trajectory. This figure visually demonstrates the rapid convergence process of the particle swarm optimization algorithm within the optimal cavity length region, verifying its ability to efficiently approximate the optimal cavity length and improve demodulation accuracy and stability.

[0061] This embodiment utilizes the particle swarm optimization algorithm for fine-grained convergence within a region with optimal cavity length. By limiting the search range to a pre-determined optimal interval, it can quickly and accurately locate the optimal cavity length for EFPI and reconstruct the complete EFPI interferometric spectrum. Using the region with optimal cavity length as the search range effectively narrows the optimization dimensionality and significantly reduces computational complexity. Iterative optimization through the velocity-position update formula, while simultaneously recording individual and global optimal positions, enables efficient exploration within a local range. Outputting results when the iterative convergence condition is met ensures both convergence speed and solution accuracy, ultimately achieving stable and high-precision demodulation of the EFPI cavity length, providing reliable data support for subsequent accurate compensation of the FBG peak.

[0062] It should be noted that this invention employs a hybrid algorithm combining Artificial Bee Colony (ABC) and Particle Swarm Optimization (PSO)—the ABC-PSO hybrid optimization algorithm. This combines the advantages of ABC's strong global search capability and resistance to local optima with PSO's fast convergence speed and high accuracy in finding local optima. First, ABC quickly locates the optimal region of the objective function within the cavity length search interval. Then, PSO iterates precisely within this region, significantly improving the efficiency and accuracy of finding the optimal cavity length. Simultaneously, it effectively avoids the premature convergence or local optima problems that can easily occur with a single algorithm in complex spectral matching scenarios.

[0063] In some embodiments of the present invention, the ABC-PSO hybrid optimization algorithm satisfies: The neighborhood search of the Artificial Bee Colony Algorithm ABC is shown in Equation 8: (8) in For the first Generation, First The newly generated neighborhood positions (new nectar source positions) corresponding to each candidate cavity length. For the first Candidate cavity length, ∈[-1,1] represents random coefficients. For the first Another nectar source location randomly selected from the candidate cavity length set ( (used for neighborhood disturbances). The speed update of the Particle Swarm Optimization (PSO) algorithm is shown in Equation 9: (9) in, For the first The generation The updated velocity of each particle; For the first The generation The current velocity of each particle; For the first The two random numbers are both within the range of 1. Random perturbations are introduced for both individual learning terms and social learning terms to avoid getting trapped in local optima. For the first A linearly decreasing inertial weight is used to control the degree to which particles inherit historical velocities; This is the individual learning factor, which controls the weights by which a particle learns to its own historical best position. This is a social learning factor, controlling the weights by which particles learn to align with the global optimal position; For the first The middle generation The individual best position in the history of each particle. For the first The global optimal position of the entire particle swarm; Among them, the Linearly decreasing inertia weights Satisfying Equation 10: (10) in, , These are the preset maximum inertia weight (used in the early stages of the algorithm, focusing on global exploration) and the preset minimum inertia weight (used in the later stages of the algorithm, focusing on fine-grained local search). This represents the current iteration number. This is the preset maximum number of iterations.

[0064] Figure 14 This is a schematic flowchart of an embodiment of EFPI signal splitting and demodulation provided by the present invention. First, the spectrum is preprocessed, and the cavity length is roughly estimated using a Fast Fourier Transform. Based on this rough estimate, possible cavity length values ​​are determined within a preset error range, constructing a candidate cavity length set. Then, an artificial bee colony-particle swarm optimization algorithm is used to search this set, generating simulated spectra corresponding to different cavity lengths. Next, the matching degree between the measured spectrum and the simulated spectrum is calculated, and an objective function is constructed. Minimizing the objective function value is the goal, ultimately determining the optimal cavity length and completing demodulation. This EFPI signal splitting and demodulation process achieves efficient and high-precision demodulation of the EFPI cavity length through a method of rough estimation to narrow the range and then fine optimization.

[0065] In this invention, the ABC-PSO hybrid optimization algorithm combines the global exploration capability of the Artificial Bee Colony (ABC) algorithm with the local convergence advantage of the Particle Swarm Optimization (PSO) algorithm, achieving efficient and high-precision demodulation of the EFPI cavity length. ABC first identifies the optimal cavity length region through neighborhood search, and then PSO quickly converges to the optimal solution within this region. This avoids the shortcomings of traditional algorithms that are prone to getting trapped in local optima, and significantly improves demodulation efficiency and stability, providing reliable cavity length data support for the subsequent accurate compensation of the FBG spectrum.

[0066] In some embodiments of the present invention, based on the complete EFPI interferometric spectrum, inversion compensation and Gaussian fitting are performed on the FBG reflection peak to obtain the FBG center wavelength, such as... Figure 15 As shown, it includes: S1501. Transform the EFPI-FBG composite spectral coupling model into a univariate quadratic equation concerning the FBG reflection spectrum. S1502. Solve the quadratic equation in one variable concerning the FBG reflection spectrum using the quadratic formula, and invert the pure FBG reflection spectrum to eliminate the multiplicative distortion of EFPI. S1503. Perform Gaussian fitting on the pure FBG reflection spectrum to obtain the center wavelength of the FBG.

[0067] In some embodiments of the present invention, the FBG reflection peak and the initially extracted EFPI interference fringes are separated from the composite spectrum of the fiber EFPI-FBG composite sensor, based on a coupling model of the composite spectrum: In the composite spectrum of the EFPI-FBG sensor, the measured composite spectrum is as follows: The true FBG reflectance spectrum is EFPI interferometry spectrum is The coupling model of the composite spectrum is shown in Equation 11: (11) Rearranging it into a quadratic equation and solving it yields the pure FBG spectrum, as shown in Equation 12: (12) In the formula After demodulating the initially extracted EFPI interference fringes to obtain the complete EFPI interference spectrum, the complete EFPI interference spectrum can be substituted into Equation 12 to obtain the pure FBG reflection spectrum. In some embodiments of the present invention, the model for Gaussian fitting of the pure FBG reflection spectrum is shown in Equation 13: (13) in, For the first The wavelength value corresponding to each sampling point; Indicates wavelength as The reflected light intensity value of the FBG at that location; This represents the peak amplitude of the FBG reflection peak (the maximum value of the fitted curve). The center wavelength of the FBG to be solved (the peak position of the fitted curve) is denoted as λ. This parameter represents the width of the FBG reflection peak, reflecting the peak width. Taking the logarithm of both sides of the above equation and transforming it into a quadratic polynomial form, as shown in Equation 14: (14) in, To The value after taking the natural logarithm, i.e. ; , , The least squares criterion is used to estimate. , , The objective function is constructed as shown in Equation 15: (15) in, This represents the total number of sampling points involved in the fitting process. The sum of squared residuals measures the deviation between the fitted curve and the actual data, with the goal of minimizing it; , , Taking the partial derivatives and setting them to zero yields the normal equation system, which can be solved as shown in Equation 16: (16) in, To obtain the final center wavelength of the FBG, when When < 0, the conic section opens downwards and has a unique maximum, the wavelength of which is the center wavelength. .

[0068] This embodiment achieves high-precision demodulation of the FBG center wavelength by performing inversion compensation and Gaussian fitting on the FBG reflection peak. First, the EFPI-FBG composite spectral coupling model is transformed into a quadratic equation in the FBG reflection spectrum. Then, by solving the quadratic formula, the pure FBG reflection spectrum, free from EFPI multiplicative distortion, is obtained through inversion. Finally, Gaussian fitting is performed on the pure FBG reflection spectrum to obtain the FBG center wavelength. This method effectively eliminates the modulation interference of the EFPI signal on the FBG reflection peak, restoring the distortion-free FBG spectrum, providing a reliable foundation for accurate identification of the FBG center wavelength, and significantly improving the accuracy and stability of wavelength demodulation.

[0069] In some embodiments of the present invention, the absolute physical parameter values ​​are calculated based on the physical parameter sensitivity coefficient calibrated by the fiber optic EFPI-FBG composite sensor, combined with the FBG center wavelength and the optimal cavity length of the EFPI. Figure 16 As shown, it includes: S1601. Calculate the wavelength change of the FBG center wavelength relative to the pre-calibrated initial wavelength and the cavity length change of the EFPI optimal cavity length relative to the pre-calibrated initial cavity length, respectively. S1602. Based on the wavelength change, cavity length change, and the sensitivity coefficients of the physical parameters of FBG and EFPI calibrated by the fiber optic EFPI-FBG composite sensor, establish a set of sensor response equations. S1603. Solve the sensor response equations to obtain the changes in physical parameters, and combine them with the initial physical parameter values ​​to obtain the absolute physical parameter values.

[0070] In some embodiments of the present invention, taking temperature-pressure composite measurement as an example, the absolute physical parameter values ​​of temperature and pressure are calculated based on the physical parameter sensitivity coefficient calibrated by the fiber optic EFPI-FBG composite sensor, combined with the center wavelength of the FBG and the optimal cavity length of the EFPI. The specific process is as follows: (1) Read the demodulation results of the FBG center wavelength and the EFPI optimal cavity length, and calculate the changes in the initial wavelength and initial cavity length relative to the pre-calibrated initial state; (2) Based on the FBG temperature sensitivity coefficient, FBG pressure sensitivity coefficient, EFPI temperature sensitivity coefficient, and EFPI pressure sensitivity coefficient pre-calibrated by the sensor, and combined with the above wavelength change and cavity length change, establish a set of binary linear response equations that include temperature change and pressure change. (3) Solve the system of response equations to obtain the temperature change and pressure change, respectively; (4) Add the temperature change and pressure change to the initial temperature and initial pressure pre-calibrated by the sensor to obtain the absolute temperature and absolute pressure values ​​under the current environment, and complete the synchronous calculation of temperature and pressure.

[0071] This embodiment combines the calibration of the sensitivity coefficient of the fiber optic EFPI-FBG composite sensor. By analyzing the change in the FBG center wavelength and the optimal cavity length of the EFPI, a set of sensor response equations is established and solved to obtain the absolute physical parameter values. This method relies on two-parameter decoupling to achieve high-precision, absolute demodulation of physical quantities, effectively improving the measurement accuracy and practicality of the composite sensing system.

[0072] In some embodiments of the present invention Figure 17This diagram illustrates an embodiment of the FBG peak signal inversion compensation effect provided by the present invention. The left and right figures show the FBG reflection spectra and Gaussian fitting results before and after compensation, respectively. The left figure shows the FBG reflection peak before compensation; due to the multiplicative distortion of the EFPI signal, the FBG reflection peak exhibits an asymmetrical shape, and the deviation of the fitted curve from the original peak position is 0.0189 nm. The right figure shows the FBG reflection peak after compensation; after inversion to eliminate EFPI interference, the FBG reflection peak restores its symmetrical shape, and the deviation of the fitted curve from the peak position is reduced to 0.0023 nm. The comparison shows that this method significantly eliminates EFPI modulation distortion and greatly improves the demodulation accuracy of the FBG center wavelength.

[0073] In some embodiments of the present invention, the fiber optic EFPI-FBG composite sensor is composed of an EFPI sensor and an FBG sensor. EFPI sensors are used to detect physical parameters including pressure, strain, displacement, and vibration. The physical parameters that FBG sensors are used to detect include temperature.

[0074] It should be noted that the EFPI sensor has a high sensitivity response to physical parameters such as pressure, strain, displacement, and vibration, and the parameters it detects are not limited to the above types. It is mainly used to detect dynamic physical quantities. The FBG sensor has stable wavelength response characteristics to temperature changes and is mainly used to detect temperature parameters. Through the integration of the two, it is possible to simultaneously measure temperature and multiple dynamic physical quantities (e.g., temperature-strain, temperature-vibration), providing a foundation for multi-parameter collaborative monitoring.

[0075] In some embodiments of the present invention Figure 18 A schematic flowchart of another embodiment of the fiber optic EFPI-FBG composite sensing spectral demodulation method provided by the present invention is shown below: Step 1: Perform adaptive SG filtering and segmented windowing preprocessing on the spectrum of the EFPI-FBG composite fiber optic sensor to suppress high-frequency noise and reduce spectral leakage; Step 2: After separating the FBG reflection peaks by FBG peak region location and peak region removal, inversion compensation is performed to eliminate the peak position shift caused by EFPI interference fringes, and Gaussian fitting is used to demodulate the center wavelength. Step 3: The EFPI interference fringe signal after removing the FBG reflection peak is completed by local cubic spline interpolation and then normalized and standardized in amplitude. Step 4: After the amplitude is normalized and standardized, zero-padding is performed on the wavelength domain of the EFPI signal to increase the bandwidth. Then, FFT is performed and Gaussian interpolation is used to fit the signal in the main peak area of ​​the frequency domain to obtain the main frequency and calculate a rough estimate of the EFPI cavity length. Step 5: Introduce the Pearson correlation coefficient as a matching criterion to construct the objective function of the subsequent search algorithm; Step 6: After the artificial bee colony algorithm completes the global exploration and screening of the superior regions, the particle swarm optimization algorithm is used to quickly converge the superior regions to approximate the optimal solution EFPI cavity length. Step 7: Output the demodulated FBG center wavelength and EFPI cavity length to complete the inversion of physical parameters such as temperature and pressure.

[0076] This invention uses adaptive spectral preprocessing, decoupling of strongly coupled signals, ABC-PSO hybrid optimization, and FBG peak inversion compensation as its core technologies. It specifically addresses the problems of peak distortion, peak position shift, and easy abrupt changes in cavity length demodulation caused by strong multiplicative coupling between FBG and EFPI in EFPI-FBG composite sensing. It overcomes the shortcomings of traditional methods, such as low demodulation accuracy, poor stability, and inability to balance accuracy and real-time performance, and achieves synchronous, efficient, and high-precision demodulation of dual physical parameters.

[0077] The fiber optic EFPI-FBG composite sensing spectral demodulation method provided by this invention has been described in detail above. Specific examples have been used to illustrate the principle and implementation of this invention. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A fiber optic EFPI-FBG composite sensor spectral demodulation method, characterized in that, include: The FBG reflection peak and the initially extracted EFPI interference fringes were separated from the composite spectrum of the fiber EFPI-FBG composite sensor. After normalizing the amplitude of the initially extracted EFPI interference fringes, a coarse estimate of the EFPI cavity length is determined. Based on the coarse estimate of the cavity length, a target function is constructed using the Pearson correlation coefficient. The artificial bee colony algorithm is used to search for the cavity length optimal region corresponding to the minimum value of the target function. Then, the particle swarm optimization algorithm is used to quickly converge the cavity length optimal region to obtain the optimal EFPI cavity length and the complete EFPI interference spectrum. Based on the complete EFPI interferometric spectrum, the reflection peak of the FBG is inverted, compensated, and fitted with Gaussian to obtain the center wavelength of the FBG. The absolute physical parameter values ​​are calculated based on the physical parameter sensitivity coefficient calibrated by the fiber optic EFPI-FBG composite sensor, combined with the center wavelength of the FBG and the optimal cavity length of the EFPI.

2. The fiber optic EFPI-FBG composite sensing spectral demodulation method according to claim 1, characterized in that, Before separating the FBG reflection peak and the initially extracted EFPI interference fringes from the composite spectrum of the fiber optic EFPI-FBG composite sensor, the composite spectrum is preprocessed; the preprocessing includes: Adaptive SG filtering is applied to the composite spectrum of the fiber optic EFPI-FBG composite sensor to obtain a noise-reduced composite spectrum. The denoised composite spectrum is truncated into several segments of appropriate length in an overlapping manner, and after applying a window function to the segments, the spectra are fused to obtain a clean composite spectrum.

3. The fiber optic EFPI-FBG composite sensing spectral demodulation method according to claim 2, characterized in that, Before normalizing the amplitude of the initially extracted EFPI interference fringes, local cubic spline interpolation is performed on the initially extracted EFPI interference fringes to obtain continuous EFPI interference fringes.

4. The fiber optic EFPI-FBG composite sensing spectral demodulation method according to claim 1, characterized in that, The step of determining a coarse estimate of the cavity length of the EFPI after normalizing the amplitude of the initially extracted EFPI interference fringes includes: The amplitude of the initially extracted EFPI interference fringes was normalized using upper and lower envelope correction. The amplitude-normalized EFPI interference fringes are zero-padded in their wavelength domain, and the zero-padded EFPI interference fringes are subjected to a fast Fourier transform to obtain the frequency domain amplitude spectrum corresponding to the EFPI interference fringes. Three-point Gaussian interpolation is performed in the neighborhood of the main peak of the frequency domain amplitude spectrum to obtain the sub-grid peak position shift corresponding to the main peak; The main frequency of the EFPI interference fringes is obtained by summing the subgrid peak position shift and the peak main frequency of the frequency domain amplitude spectrum. Based on the linear relationship between the main frequency after EFPI interference fringe correction and the EFPI cavity length, a rough estimate of the EFPI cavity length is obtained.

5. The fiber optic EFPI-FBG composite sensing spectral demodulation method according to claim 1, characterized in that, Based on the coarse estimate of the cavity length, the objective function is constructed using the Pearson correlation coefficient, including: Using the coarse estimate of the cavity length as the center, the cavity length search interval for the simulated interference fringes is determined with a preset error range; For each candidate cavity length within the cavity length search interval, simulated interference fringes are generated based on the EFPI reflection spectral model; Based on the normalized Pearson correlation coefficient between the simulated interference fringes and the measured interference fringes, an objective function is constructed to measure the degree of matching between the simulated interference fringes and the measured interference fringes corresponding to the candidate cavity length; the measured interference fringes are the EFPI interference fringes initially extracted after preprocessing.

6. The fiber optic EFPI-FBG composite sensing spectral demodulation method according to claim 5, characterized in that, The step of using the artificial bee colony algorithm to search for the optimal cavity length region corresponding to the minimum value of the objective function includes: The candidate cavity lengths within the cavity length search interval are mapped to the positions of individual bees in the artificial bee colony algorithm, and the objective function value corresponding to each individual value is calculated. The positions of individual bee colonies are updated by neighborhood search. The iteration stops when the preset maximum number of iterations is reached or the objective function value converges, thus obtaining the cavity length optimal region corresponding to the minimum value of the objective function.

7. The fiber optic EFPI-FBG composite sensing spectral demodulation method according to claim 6, characterized in that, The process of rapidly converging the cavity length-optimal region using a particle swarm optimization algorithm to obtain the optimal cavity length for EFPI and the complete EFPI interferogram includes: Using the region with excellent cavity length as the search range of the particle swarm optimization algorithm, the candidate cavity lengths within the region with excellent cavity length are mapped to particle positions; Using the objective function value as the fitness, the position and velocity of each particle are iteratively updated based on the velocity-position update formula of the particle swarm optimization algorithm, and the individual optimal position of each particle and the global optimal position of the entire particle swarm are recorded simultaneously. Convergence is determined when the preset maximum number of iterations is reached or the global optimal fitness value remains unchanged after continuous iterations, and the optimal cavity length and the corresponding complete EFPI interferometric spectrum are output.

8. The fiber optic EFPI-FBG composite sensing spectral demodulation method according to claim 1, characterized in that, The process of inverting and compensating for the FBG reflection peak based on the complete EFPI interferometric spectrum to obtain the FBG center wavelength includes: The EFPI-FBG composite spectral coupling model is transformed into a univariate quadratic equation concerning the FBG reflection spectrum. The quadratic equation concerning the FBG reflection spectrum is solved by using the quadratic formula, and the pure FBG reflection spectrum with EFPI multiplicative distortion eliminated is obtained by inversion. Gaussian fitting was performed on the reflection spectrum of the pure FBG to obtain the center wavelength of the FBG.

9. The fiber optic EFPI-FBG composite sensing spectral demodulation method according to claim 1, characterized in that, The absolute physical parameter values ​​are calculated based on the physical parameter sensitivity coefficient calibrated by the fiber optic EFPI-FBG composite sensor, combined with the center wavelength of the FBG and the optimal cavity length of the EFPI, including: Calculate the wavelength change of the FBG center wavelength relative to the pre-calibrated initial wavelength and the cavity length change of the EFPI optimal cavity length relative to the pre-calibrated initial cavity length. Based on the wavelength change, the cavity length change, and the sensitivity coefficients of the physical parameters of FBG and EFPI calibrated by the fiber optic EFPI-FBG composite sensor, a set of sensor response equations is established. Solve the sensor response equations to obtain the changes in physical parameters, and combine them with the initial physical parameter values ​​to obtain the absolute physical parameter values.

10. The fiber optic EFPI-FBG composite sensing spectral demodulation method according to claim 1, characterized in that, The fiber optic EFPI-FBG composite sensor consists of an EFPI sensor and an FBG sensor. The physical parameters detected by the EFPI sensor include pressure, strain, displacement, and vibration. The physical parameters detected by the FBG sensor include temperature.

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