Signal denoising method and device based on MEEMD and northern eagle optimization

Abstract

The invention discloses a signal denoising method and device based on MEEMD and northern eagle optimization, and belongs to the technical field of signal processing and gas detection. The method comprises the following steps: acquiring a second harmonic signal in photoacoustic spectrometry gas detection; performing MEEMD decomposition on the signal to obtain a plurality of intrinsic mode function IMF components and residual errors; calculating the energy ratio of each IMF component and screening effective IMF components; reconstructing the effective IMF component and the residual error to obtain a preliminary de-noised signal; carrying out self-adaptive smoothing processing on the preliminarily denoised signal; gaussian filtering is carried out on the smoothed signal; and optimizing an energy threshold value, a self-adaptive smooth window parameter and a Gaussian filtering parameter by using a northern eagle optimization algorithm to obtain an optimal parameter combination. According to the method, MEEMD modal decomposition, Gaussian filtering and NGO parameter optimization are fused, accurate denoising and feature retention of gas concentration signals are achieved, and the precision and reliability of photoacoustic spectrum gas detection are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of signal processing and gas detection technology, specifically to a signal denoising method and apparatus based on MEEMD (Multivariate Empirical Mode Decomposition) and Northern Goshawk Optimization (NGO) algorithm, which is particularly suitable for second harmonic signal denoising in photoacoustic spectroscopy (PAS) gas detection systems. Background Technology

[0002] In the process of realizing this invention, the inventors discovered at least the following problems in the prior art: Photoacoustic spectroscopy, a highly sensitive gas detection technology, is widely used in industrial safety monitoring, environmental monitoring, and power equipment fault diagnosis. Acetylene, as an important industrial gas and a marker gas for power transformer faults, is crucial for ensuring industrial safety and stable equipment operation.

[0003] Traditional gas detection methods, such as gas chromatography, require offline sampling and have long detection cycles, making it difficult to meet real-time early warning requirements. Electrochemical sensors are susceptible to cross-interference and require frequent replacement of consumables. Photoacoustic spectroscopy, based on the principle of "light absorption-acoustic signal conversion," can achieve online real-time detection with a detection limit down to the ppb level. It requires no consumables, has strong anti-interference capabilities, and is suitable for continuous monitoring in chemical workshops as well as meeting the need for precise detection of trace acetylene in power transformer oil.

[0004] However, photoacoustic spectroscopy gas detection signals in industrial settings are often affected by pump vibrations and ambient temperature fluctuations, leading to a decrease in signal-to-noise ratio. This can range from masking trace gas signals to causing false alarms or missed detections. Applying digital filtering techniques to improve signal-to-noise ratio is an important research direction, but traditional digital filtering, such as low-pass filtering, is only suitable for stationary signals and struggles to handle the non-stationary interferences commonly found in gas detection. Kalman filtering dynamically optimizes the filtering results through "state estimation-error feedback," but it has poor adaptability to nonlinear signals, resulting in a significant decrease in filtering accuracy.

[0005] In recent years, various improved methods have been proposed in the field of signal processing. Shi et al. used SG filtering to improve signal purity for gas detection, achieving an optimal detection limit of 12 ppb for CH4 with a linear fit R² = 0.998. Ji et al. used wavelet denoising combined with SG filtering for methane detection, increasing the SNR from 11.85 to 58.68 with a linear fit R² = 0.9995. Qin et al. applied an improved singular value decomposition algorithm to denoise the ultraviolet spectrum of SO2, achieving an SNR improvement of 18.02% compared to SVDS and 16.86% compared to wavelet transform at low SNR (5 dB). However, these methods still have limitations when processing complex non-stationary signals.

[0006] Empirical Mode Decomposition (EMD) and its improved algorithms have been applied to signal denoising. Xie et al. used an improved EMD to extract signals of interest, but this method relies on prior knowledge, may lose key information, and is prone to mode aliasing. Ning, Cao et al. used Ensemble Empirical Mode Decomposition (EEMD) to add Gaussian white noise to the signal and then perform multiple EMD decompositions to suppress mode aliasing, but it suffers from the drawbacks of high residual noise and large signal reconstruction errors. Qiu et al. used the CEEMDAN algorithm, which balances accuracy and efficiency, but it relies on parameter tuning and needs to be repeatedly optimized for the signal characteristics of specific gases, and residual aliasing still exists under strong interference.

[0007] MEEMD (Multivariate Ensemble Empirical Mode Decomposition) further enhances EEMD by introducing a multivariate signal set. Addressing the issues of mode aliasing, computational efficiency, and residual noise in traditional EMD algorithms, it combines a complementary noise addition strategy with a random detection mechanism for decomposition index thresholds, improving decomposition accuracy while reducing computational load. MEEMD adapts to non-stationary / nonlinear signals, adaptively decomposing noisy signals, separating interference and effective signals into different modal components, accurately filtering out complex interference, significantly suppressing mode aliasing, reducing residual noise and reconstruction errors, and improving the detection signal-to-noise ratio. Yao et al. have applied this method to image thermal imaging diagnosis, and Yang et al. have applied it to motor fault diagnosis, both achieving good results.

[0008] However, the MEEMD method still faces challenges in practical applications, such as difficulty in parameter selection and unstable denoising effects. In particular, for photoacoustic spectral signals with different gas concentrations and environmental conditions, it is necessary to adaptively adjust the decomposition and filtering parameters.

[0009] In summary, a denoising method is needed that can effectively handle non-stationary noise in photoacoustic spectral signals and adaptively select optimal parameters to improve the accuracy and reliability of gas detection. Summary of the Invention

[0010] To address the aforementioned issues, this invention proposes a signal denoising method and apparatus based on MEEMD and Northern Eagle optimization, which can improve the accuracy and reliability of photoacoustic spectroscopy gas detection.

[0011] The technical solution adopted by this invention to solve its technical problem is as follows: On the one hand, a signal denoising method based on MEEMD and Northern Eagle optimization is provided, including the following steps: S1: Acquire the signal to be processed, which is the second harmonic signal in photoacoustic spectroscopy gas detection; S2: Perform MEEMD decomposition on the signal to be processed to obtain multiple intrinsic mode function (IMF) components and residuals; S3: Calculate the energy percentage of each IMF component and filter effective IMF components based on the energy threshold; S4: Reconstruct the selected effective IMF components with the residual to obtain the preliminary denoised signal; S5: Perform adaptive smoothing processing on the preliminary denoised signal; S6: Perform Gaussian filtering on the adaptively smoothed signal; S7: Optimize the energy threshold in step S3, the adaptive smoothing window parameters in step S5, and the Gaussian filter parameters in step S6 using the Northern Eagle optimization algorithm.

[0012] On the other hand, a signal denoising device based on MEEMD and Northern Eagle optimization is provided, including: a signal acquisition module, a MEEMD decomposition module, an energy screening module, a signal reconstruction module, an adaptive smoothing module, a Gaussian filtering module, and a parameter optimization module.

[0013] One of the above technical solutions has the following advantages or beneficial effects: 1. Because it adopts MEEMD decomposition technology, it can effectively process non-stationary and nonlinear signals, overcoming the limitations of traditional filtering methods; at the same time, it adopts a complementary noise addition strategy, which significantly suppresses the mode mixing problem; and combined with Gaussian filtering to further suppress residual noise, it achieves multi-level and multi-scale denoising effect.

[0014] 2. Because the Northern Eagle optimization algorithm is used to automatically optimize key parameters, it can adaptively find the optimal combination of MEEMD energy threshold, adaptive smoothing window and Gaussian filter parameters, overcoming the shortcomings of traditional methods that rely on empirical selection of parameters and are difficult to debug, and improving the stability and reliability of the denoising effect.

[0015] 3. Because a dynamic window adjustment strategy based on local variance is adopted, small window weak smoothing is used in the signal stable region to preserve detailed features, and large window strong smoothing is used in the noisy region to effectively suppress noise, which improves the targeting of denoising and achieves a balance between noise suppression and signal feature preservation.

[0016] 4. Because the MEEMD decomposition and filtering parameters have been optimized to address the characteristics of the second harmonic signal in photoacoustic spectroscopy, the accuracy of gas detection has been significantly improved. It is particularly suitable for industrial safety fields such as chemical acetylene leak monitoring and power transformer fault diagnosis.

[0017] 5. Because the above method constructs the corresponding device, including a signal acquisition module, a MEEMD decomposition module, an energy screening module, a signal reconstruction module, an adaptive smoothing module, a Gaussian filtering module, and a parameter optimization module, it forms a complete hardware implementation scheme, which is conducive to the practical application and industrialization of the technology. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating a signal denoising method based on MEEMD and Northern Eagle optimization according to an exemplary embodiment; Figure 2 This is a schematic diagram of a signal denoising device structure based on MEEMD and Northern Eagle Optimization, according to an exemplary embodiment. Figure 3 This is a flowchart illustrating the specific implementation process of signal denoising based on the MEEMD-Gauss-NGO algorithm in this invention. Figure 4 This is a schematic diagram of a photoacoustic spectroscopy experimental device according to an embodiment of the present invention; Figure 5 This is a comparison diagram of the noise reduction effect of an embodiment of the present invention; Figure 6 This is a spectrum analysis comparison chart according to an embodiment of the present invention; Figure 7 This is a schematic diagram of experimental data of C2H2 spectral signal according to an embodiment of the present invention; Figure 8 This is an experimental data spectrum denoised by the MEEMD-Gauss-NGO algorithm according to an embodiment of the present invention; Figure 9 This is a schematic diagram of the fitting results between the measured peak value and concentration of acetylene photoacoustic spectrum before noise reduction according to an embodiment of the present invention; Figure 10 This is a schematic diagram of the fitting results between the measured peak value and concentration of acetylene photoacoustic spectrum after noise reduction processing using the MEEMD-Gauss-NGO algorithm, according to an embodiment of the present invention. Detailed Implementation

[0019] To more clearly illustrate the technical features of the present invention, the invention will be described in detail below through specific embodiments and in conjunction with the accompanying drawings. The following disclosure provides many different embodiments or examples for implementing different structures of the present invention. To simplify the disclosure of the present invention, the components and arrangements of specific examples are described below. Of course, these are merely examples and are not intended to limit the invention.

[0020] like Figure 1 As shown in the figure, an embodiment of the present invention provides a signal denoising method based on MEEMD and Northern Eagle optimization, which includes the following steps: Step S1: Obtain the signal to be processed.

[0021] In this embodiment, the signal to be processed is the second harmonic signal acquired by the photoacoustic spectroscopy gas detection system. The process of acquiring the signal to be processed is as follows: acquiring the second harmonic signal from the photoacoustic spectroscopy detection system, which includes a laser source, a photoacoustic cell, a microphone, a lock-in amplifier, and a data acquisition unit; the laser source is a distributed feedback laser diode with a center wavelength of 1531.12 nm and a maximum peak output power of 8.3 mW.

[0022] The modulation signal of the laser source is provided by a function generator, including a 0.2Hz sawtooth wave scanning signal and a 2.49kHz high-frequency sine wave modulation signal; the sawtooth wave scanning signal and the sine wave modulation signal are combined in an adder circuit and used to modulate the laser controller so that the laser diode scans within the gas absorption wavelength range.

[0023] The second harmonic signal is generated through the following process: a laser beam passes through a gas sample in a photoacoustic cell, and the gas molecules absorb the light energy and generate heat, which causes a pressure change and generates sound waves; the sound waves are detected by a high-sensitivity microphone and converted into an electrical signal; a lock-in amplifier demodulates the electrical signal to obtain the second harmonic signal.

[0024] The signal to be processed is the second harmonic signal of acetylene gas, with a detection wavenumber of 6529.1719 cm⁻¹. - ¹, corresponding to a wavelength of 1531.58nm, belongs to the near-infrared band.

[0025] The gas concentration range corresponding to the signal to be processed is 200ppm-1100ppm, increasing in increments of 100ppm.

[0026] Step S1 also includes preprocessing the acquired signal: removing the DC offset component; normalizing the signal amplitude to make it within a preset range; and marking the signal with a timestamp and concentration label.

[0027] Step S2 involves performing MEEMD decomposition on the signal to be processed to obtain multiple intrinsic mode functions (IMF) components and residuals. Specifically, the MEEMD decomposition process includes the following steps: Step S21, add complementary white Gaussian noise pairs to the original signal x(t). and This generates two noisy signals: , , in, and Given a pair of complementary Gaussian white noise sequences, satisfying = Both have the same standard deviation ε; the parameters added to the complementary Gaussian white noise pair are: noise logarithm trials = 300; noise standard deviation epsilon = 0.05; maximum number of IMF components is 8; Step S22: Perform empirical mode decomposition on each noisy signal to obtain multiple sets of IMF components and residuals; the obtained IMF components are arranged from high to low frequency, with IMF1 having the highest frequency and IMF8 having the lowest frequency, and the residuals are the trend terms of the signal. Step S23: Perform a ensemble average on the multiple IMF components to obtain the final IMF components and residuals. The mathematical expression for the ensemble average is: k = 1, 2, ..., K; where N is the noise logarithm and K is the total number of IMF components. Let be the k-th IMF component obtained from the i-th decomposition.

[0028] In step S22, the empirical mode decomposition includes the following process: identifying all local maxima and local minima of the signal; connecting all local maxima through cubic spline interpolation to form an upper envelope; connecting all local minima through cubic spline interpolation to form a lower envelope; calculating the average of the upper and lower envelopes to obtain the mean envelope; subtracting the mean envelope from the original signal to obtain candidate IMF components; repeating the above process until the candidate IMF components satisfy the IMF condition; The IMF conditions include: the number of extreme points is equal to or differs by at most one from the number of zero crossings throughout the entire data segment; and at any point, the average of the upper envelope defined by the local maxima and the lower envelope defined by the local minima is zero.

[0029] Step S3: Calculate the energy percentage of each IMF component and filter valid IMF components based on energy thresholds. Specifically, step S3 includes the following steps: Step S31, calculate the energy value of each IMF component: , k=1,2,...,K; where, This represents the value of the k-th IMF component at time t. Step S32, calculate the energy percentage of each IMF component: ; Step S33: Compare the energy percentage with the energy threshold θ, and select IMF components with an energy percentage greater than θ as valid components. The energy threshold θ ranges from 0.5% to 5%, with a default value of 0.5%.

[0030] Step S3 further includes the following step: calculating the total energy of all IMF components. : The energy percentage .

[0031] The process of selecting IMF components with an energy percentage greater than θ as effective components includes: establishing an index set of effective components. Establish a noise component index set The IMF components in the noise component index set N are filtered out as noise components.

[0032] Step S3 further includes a step of sorting the energy percentages: sorting the IMF components from largest to smallest according to their energy percentages; selecting the top M IMF components with the largest energy percentages as valid components, where M is the number determined by the energy threshold θ.

[0033] The principle of filtering effective IMF components based on energy threshold is as follows: the main components of a signal usually have high energy, while noise is mostly low energy; by setting an energy threshold, high-energy IMF components are retained and low-energy noise IMF components are filtered out.

[0034] Step S4: Reconstruct the selected effective IMF components with the residual to obtain the preliminary denoised signal. , in, (t) represents the initial denoised signal, and S is the index set of the effective IMF components. k r(t) is the kth effective IMF component, and r(t) is the residual term.

[0035] The index set S of the effective IMF components is obtained by filtering through the energy threshold in step S3: Among them, P k Let θ be the energy percentage of the k-th IMF component, and θ be the energy threshold. The residual term r(t) is the last component obtained from MEEMD decomposition, representing the trend term or DC component of the signal.

[0036] The signal reconstruction is a linear superposition process, in which the selected effective IMF components are added to the residual terms at corresponding time points. The preliminary denoised signal retains the main frequency components and amplitude characteristics of the original signal while filtering out most of the high-frequency noise components.

[0037] Step S4 also includes quality assessment of the reconstructed signal: calculating the correlation coefficient between the reconstructed signal and the original signal; calculating the signal-to-noise ratio of the reconstructed signal; when the correlation coefficient is lower than a preset threshold or the signal-to-noise ratio is lower than a preset threshold, returning to step S3 to adjust the energy threshold.

[0038] Step S5: Perform adaptive smoothing processing on the preliminary denoised signal.

[0039] Specifically, step S5 includes the following steps: Step S51, calculate the local variance of the signal at each point: , in, The value of the initially denoised signal at point j. This is the initial window size. The initial window size is the local mean. The value range is 3 to 10, with 3 being the preferred value; Step S52: Dynamically adjust the smoothing window size based on local variance. , in, and These are the minimum and maximum window sizes. Let be the local variance at point i, and α be the adjustment parameter; the range of values ​​for the window size is: , The adjustment parameter α can be set to a value between 0.1 and 1.0. Step S53, use the adjusted window to perform moving average smoothing on the signal: , in, This represents the value of the smoothed signal at point i. Let i be the size of the dynamic window at point i.

[0040] The principle of the adaptive smoothing process is as follows: regions with large variance indicate that there are more noise components, so a large window is used for strong smoothing; regions with small variance indicate that the signal is stable, so a small window is used for weak smoothing to preserve detailed features.

[0041] Step S6: Perform Gaussian filtering on the adaptively smoothed signal. , in, Let i be the value of the filtered signal at point i. For the adaptively smoothed signal, is the Gaussian kernel function, and L is the half-width of the filter window.

[0042] Wherein, the Gaussian kernel function The calculation formula is: , Where σ is the standard deviation parameter of the Gaussian filter, which controls the smoothness of the filter. The value of the standard deviation parameter σ ranges from 0.1 to 2.0, and the half-width L of the filter window is usually L=3σ.

[0043] The Gaussian filter is a linear low-pass filter that uses a Gaussian kernel function to perform a weighted average of the signal, thereby suppressing high-frequency noise.

[0044] Furthermore, step S6 also includes peak protection of the Gaussian-filtered signal: identifying the peak region of the signal; applying Gaussian filtering to the non-peak region while keeping the original signal in the peak region; and splicing the processed non-peak region with the original peak region to obtain the final filtered signal.

[0045] The method for identifying the peak region is as follows: calculate the first derivative of the signal, and the point where the derivative is zero is the extreme point; calculate the second derivative of the signal, and the point where the second derivative is less than zero is the peak point; expand the peak region to both sides with the peak point as the center.

[0046] In step S6, Gaussian filtering complements adaptive smoothing in step S5: adaptive smoothing mainly processes the local features of the signal; Gaussian filtering mainly suppresses the high-frequency noise components of the signal; the combination of the two achieves a balance between "noise suppression" and "signal feature preservation".

[0047] Step S7: Use the Northern Eagle optimization algorithm to optimize the energy threshold, adaptive smoothing window parameters, and Gaussian filter parameters to obtain the optimal parameter combination.

[0048] Specifically, the Northern Eagle optimization algorithm includes the following steps: Step S71, initialize algorithm parameters, including population size, maximum number of iterations, and search space boundary; algorithm parameters are set as follows: population size Maximum number of iterations Search space boundaries: , , , ; Step S72, randomly generate an initial population, with each individual representing a set of parameter combinations. , , , ], The MEEMD energy threshold, For adaptive smoothing minimum window; Adaptive smoothing maximum window; The sigma value is the Gaussian filter value. Step S73: The fitness value of each individual is evaluated using a fitness function; the fitness function is constructed based on the denoising effect evaluation index. Where SNR is the signal-to-noise ratio and RMSE is the root mean square error. The correlation coefficient is given by α, β, and γ, which are weighting coefficients: α = 0.5, β = 0.3, and γ = 0.2. Step S74, execute the exploration phase and update the individual's position; the position update rule for the exploration phase is: if : ;otherwise: ;in, P represents the current individual's location, and P represents the randomly selected reference individual's location. For randomly selected individual locations, and A random number in the range [0,1]. The fitness function; Step S75: Execute the development phase and update the individual location; the location update rule for the development phase is as follows: ;in, Let R be the current optimal individual position, and R be the adaptive step size factor; the formula for calculating the adaptive step size factor R is: Where t is the current iteration number, This represents the maximum number of iterations. Step S76, repeat steps S73-S75 until the maximum number of iterations is reached; Step S77: Output the individual with the highest fitness as the optimal parameter combination.

[0049] Furthermore, step S7 also includes verifying the parameter optimization results: using the optimized parameters to denoise the validation set signal; calculating the signal-to-noise ratio, root mean square error, and correlation coefficient of the denoised signal; confirming that the parameter optimization is complete when the performance indicators meet the preset requirements; otherwise, adjusting the optimization algorithm parameters and re-optimizing.

[0050] The advantages of the Northern Eagle optimization algorithm are: strong global optimization capability, which can avoid getting trapped in local optima; adaptive parameter adjustment, which significantly reduces the cost of manual parameter tuning; and efficient parameter search through the balance between the exploration and development phases.

[0051] like Figure 2As shown, an embodiment of the present invention provides a signal denoising device based on MEEMD and Northern Eagle optimization, comprising: The signal acquisition module is used to acquire the signal to be processed, which is the second harmonic signal in photoacoustic spectroscopy gas detection; The MEEMD decomposition module is used to perform MEEMD decomposition on the signal to be processed to obtain multiple intrinsic mode function (IMF) components and residuals. The energy screening module is used to calculate the energy proportion of each IMF component and screen valid IMF components based on energy thresholds. The signal reconstruction module is used to reconstruct the selected effective IMF components with the residual to obtain a preliminary denoised signal; An adaptive smoothing module is used to perform adaptive smoothing processing on the initial denoised signal; The Gaussian filter module is used to perform Gaussian filtering on signals that have undergone adaptive smoothing. The parameter optimization module is used to optimize the energy threshold, adaptive smoothing window parameters, and Gaussian filter parameters using the Northern Eagle optimization algorithm.

[0052] Furthermore, the MEEMD decomposition module includes: a noise addition unit for adding complementary white Gaussian noise pairs to the original signal; an EMD decomposition unit for performing empirical mode decomposition on each noisy signal; and a ensemble averaging unit for performing ensemble averaging on multiple sets of IMF components.

[0053] Furthermore, the adaptive smoothing module includes: a variance calculation unit for calculating the local variance of each point in the signal; and a window adjustment unit for dynamically adjusting the size of the smoothing window based on the local variance.

[0054] Furthermore, the parameter optimization module includes: an exploration unit for executing the exploration phase of the Northern Eagle optimization algorithm; and a development unit for executing the development phase of the Northern Eagle optimization algorithm.

[0055] Furthermore, the signal denoising device also includes a concentration inversion module, which is used to perform concentration inversion on the denoised signal to obtain the gas concentration value.

[0056] The core idea of ​​this invention is to address the problem of non-stationary noise interference in second harmonic signals during photoacoustic spectroscopy gas detection. A collaborative denoising method (i.e., the MEEMD-Gauss-NGO algorithm) integrating MEEMD mode decomposition, Gaussian filtering, and NGO parameter optimization is proposed. This method first uses MEEMD to decompose the complex signal into multiple IMF components. Then, it filters and reconstructs the effective components based on energy thresholds. Next, it further suppresses noise through adaptive smoothing and Gaussian filtering. Finally, it uses the NGO algorithm to optimize key parameters, achieving adaptive and high-precision signal denoising.

[0057] like Figure 3 As shown, this embodiment of the invention provides a specific implementation process for signal denoising based on the MEEMD-Gauss-NGO algorithm, including the following steps: Step S101: Acquire the signal to be processed. In this embodiment, the signal to be processed is the second harmonic signal collected by the photoacoustic spectroscopy gas detection system. Specifically, for acetylene gas detection, the detection wavelength is 1531.58 nm (corresponding to a wavenumber of 6529.1719 cm⁻¹). - ¹). For example Figure 4 As shown, the experimental setup includes a function generator, a laser controller, a distributed feedback laser diode (DFB-LD), a photoacoustic cell, a high-sensitivity microphone, a lock-in amplifier, a computer, and a gas distribution system. The laser source has a center wavelength of 1531.12 nm and a maximum peak output power of 8.3 mW. The function generator provides a 0.2 Hz sawtooth wave scanning signal and a 2.49 kHz high-frequency sine wave modulation signal. These two signals are combined to modulate the laser controller, ensuring that the DFB-LD scans within the gas absorption wavelength range. The photoacoustic signal is generated through a resonant photoacoustic cell with a resonant frequency of 4.98 kHz. The signal is detected by the high-sensitivity microphone and converted into an electrical signal. After second harmonic demodulation by the lock-in amplifier, the signal is transmitted to the computer for acquisition.

[0058] Using a computer-automated gas mixing system manufactured by Beijing Jinxun Electronics Co., Ltd., 4998 ppm standard C2H2 gas was mixed with pure nitrogen to prepare C2H2 gas samples of different concentrations. In this experiment, the gas concentration ranged from 200 ppm to 1100 ppm, increasing in 100 ppm increments, for a total of 10 concentration groups.

[0059] Step S102: Perform MEEMD decomposition on the signal. The MEEMD decomposition process specifically includes: (1) Add complementary Gaussian white noise pairs to the original signal x(t): , , in, and Given a pair of complementary Gaussian white noise sequences, satisfying = Both have the same standard deviation ε; in this embodiment, ε = 0.05 is used. The number of noise pairs is set to 300. By adding complementary noise multiple times, the mean of the decomposed noise approaches zero, reducing reconstruction error.

[0060] (2) Perform EMD decomposition on each noisy signal to obtain multiple IMF components and residuals. EMD decomposition decomposes the signal into multiple IMF components from high frequency to low frequency and a residual term. Each IMF component must meet two conditions: ① The number of extreme points in the entire data segment is equal to or differs from the number of zero crossings by at most one; ② At any point, the average value of the upper envelope defined by the local maximum point and the lower envelope defined by the local minimum point is zero.

[0061] (3) Perform ensemble averaging on multiple IMF components to obtain the final IMF components and residuals: , Where k = 1, 2, ..., K; N is the noise logarithm (N = 300 in this embodiment), and K is the total number of IMF components (K = 8 in this embodiment). Let k be the IMF component obtained from the i-th decomposition. The specific parameter settings for MEEMD decomposition are shown in Table 1.

[0062] Table 1. Parameter settings for MEEMD decomposition:

[0063] Step S103: Filter valid IMF components based on energy thresholds. Calculate the energy percentage of each IMF component: Taking a 500ppm acetylene signal as an example, the energy proportions of each IMF component are shown in Table 2.

[0064] Table 2. Examples of energy percentage for each IMF component (taking a 500ppm acetylene signal as an example):

[0065] An energy threshold θ is set, and IMF components with an energy percentage greater than θ are retained as valid components. The energy threshold θ is optimized using the Northern Eagle optimization algorithm, with an initial value range of 0.5% to 5%. In a specific implementation of this example, the optimized energy threshold is 3.55%, therefore IMF4-IMF7 are retained as valid components (with energy percentages of 42.256%, 4.740%, 4.159%, and 0.937%, respectively).

[0066] Step S104: Signal Reconstruction. The selected effective IMF components are superimposed with the residual to obtain the preliminary denoised signal. , Where S is the set of indices of the effective IMF components, and r(t) is the residual term.

[0067] Step S105: Adaptive smoothing processing. The adaptive smoothing process specifically includes: (1) Calculate the local variance of each point in the signal. : , in, The value of the initially denoised signal at point j. The initial window size (in this embodiment) The value is 3). It is a local mean.

[0068] (2) Dynamically adjust the size of the smoothing window based on local variance: , in, and In this embodiment, the minimum and maximum window sizes are... , ; Let be the local variance at point i, and α be an adjustment parameter with a value of 0.5. When the local variance is large, it indicates that there is a lot of noise in the region, and a larger window is used for strong smoothing; when the local variance is small, it indicates that the signal is stable, and a smaller window is used for weak smoothing to preserve detailed features.

[0069] (3) Use the adjusted window for moving average smoothing: , in, This represents the value of the smoothed signal at point i. Let i be the size of the dynamic window at point i.

[0070] Step S106: Gaussian Filtering. Gaussian filtering is applied to the adaptively smoothed signal to further suppress high-frequency noise. Gaussian filtering is a linear low-pass filter that uses a Gaussian kernel function to perform a weighted average of the signal. , in, Let i be the value of the filtered signal at point i. For the adaptively smoothed signal, is the Gaussian kernel function, and L is the half-width of the filter window.

[0071] in, For Gaussian kernel function:

[0072] Where σ is the standard deviation parameter of the Gaussian filter, controlling the smoothness of the filter. The value of σ is optimized using the Northern Eagle optimization algorithm, and its range is 0.1 to 2.0. In a specific implementation of this example, the optimized σ value is 0.3861. The half-width L of the filter window is usually set to L = 3σ.

[0073] Step S107: Parameter Optimization. The energy threshold θ and adaptive smoothing window parameters are optimized using the Northern Eagle optimization algorithm. and And the Gaussian filter parameter σ. The specific implementation process of the Northern Eagle optimization algorithm includes: (1) Initialization: Randomly generate N individuals (eagle positions), each individual corresponding to a set of parameter combinations. , , , Set the maximum number of iterations. The current iteration number t=0.

[0074] (2) Exploration Phase: The eagle randomly searches for prey in a vast area. For the i-th individual, its position update rule is: if : ; otherwise: ; in, Let P be the current individual position, and let P be the randomly selected reference individual position (the individual position is randomly selected uniformly from the current population, allowing selection of itself, and each individual selects independently once in each iteration). The position of an individual is randomly selected (k≠i) (the position of other individuals except the i-th individual, which are randomly selected uniformly from the current population). and A random number in the range [0,1] (a random number generated independently for each individual in the exploration phase of each iteration, uniformly distributed between [0,1]). This is the fitness function.

[0075] (3) Development Phase: After spotting prey, the eagle launches a high-speed, precise attack. The location update rule is: , in, R represents the current optimal individual position, and R is the adaptive step size factor. R decreases as the number of iterations increases, thus transitioning from global search to local fine-grained search.

[0076] (4) Fitness Assessment: Calculate the fitness value for each individual. The fitness function is constructed based on the evaluation index of denoising effectiveness. , Where SNR is the signal-to-noise ratio and RMSE is the root mean square error. The correlation coefficient is α, β, and γ, which are weighting coefficients. In this embodiment, α = 0.5, β = 0.3, and γ = 0.2.

[0077] (5) Iterative update: Repeat steps (2)-(4) until the maximum number of iterations is reached. (30) Output the optimal parameter combination, as shown in Table 3.

[0078] Table 3: Parameters after NGO optimization:

[0079] Step S108: Concentration Inversion (Optional). Perform concentration inversion on the denoised signal to obtain the gas concentration value. For the second harmonic signal, the peak amplitude has a linear relationship with the gas concentration: , Where C is the gas concentration, A is the signal peak amplitude, and k and b are calibration coefficients. The values ​​of k and b are obtained through linear fitting, and the gas concentration can then be calculated based on the signal amplitude.

[0080] To verify the effectiveness of this invention, simulation and experimental analysis were conducted. In the simulation analysis, second harmonic analog signals with acetylene concentrations ranging from 200ppm to 1100ppm were generated. After adding Gaussian white noise, denoising was performed using EMD-Gauss, MEEMD-WTD, and the MEEMD-Gauss-NGO algorithm proposed in this invention, respectively.

[0081] Figure 5 The comparison chart of denoising effects is shown. The signal denoised by the MEEMD-Gauss-NGO algorithm of this application is closest to the original noiseless signal, with a signal-to-noise ratio of 33.206dB, which is better than the EMD-Gauss algorithm (30.12dB) and the MEEMD-WTD algorithm (31.45dB).

[0082] Figure 6 The spectrum analysis comparison chart shows that after denoising using the MEEMD-Gauss-NGO algorithm, the noise amplitude in the high-frequency region of the signal is significantly reduced, and the effective signal components are well preserved.

[0083] In the experimental data analysis, the second harmonic signal of acetylene gas ranging from 200 ppm to 1100 ppm was acquired using an actual photoacoustic spectroscopy system. The linear fitting results of the peak value and concentration before and after denoising showed that the correlation coefficient R² increased from 0.992 to 0.9998 after denoising, indicating a significant improvement in linearity.

[0084] To better verify the effectiveness of the MEEMD-Gauss-NGO algorithm in processing spectral signals, experimental conditions of 296 K and 1 atm were used. Figure 4The experimental setup shown collected C2H2 spectral signals corresponding to 200ppm-1100ppm, such as... Figure 7 As shown.

[0085] Depend on Figure 7 Analysis reveals significant noise interference in the collected experimental data. The data points fluctuate wildly and are chaotic, especially in the peak and trough regions of amplitude, where noise causes strong spikes in the curves. The curve characteristics corresponding to different concentrations are masked by noise, making it difficult to intuitively distinguish the inherent trends of each concentration's data, resulting in poor data readability.

[0086] Taking a 500ppm signal as an example, after denoising using the MEEMD-Gauss-NGO algorithm, as shown below... Figure 8 As shown, the curve is significantly smoother, the noise spikes are almost completely suppressed, the position and amplitude characteristics of the peaks and valleys are effectively preserved, and the amplitude fluctuations are more in line with the natural pattern of the experimental signal itself.

[0087] After 50 iterations of the NGO optimization algorithm, the final parameters involved in the experiment are shown in Table 3.

[0088] The MEEMD energy threshold is set to 3.55, indicating that IMFs with an energy percentage ≥3.55% are retained, reducing the loss of useful signals. Adaptive smoothing uses a window size of 3-7, a relatively small overall window range, meaning weaker smoothing intensity and maximizing the preservation of local signal details. A small sigma value is chosen, indicating a relatively "mild" denoising process, suppressing only high-frequency noise and having almost no impact on low-frequency background signals. In summary, this denoising process effectively removes most noise while maximizing the preservation of characteristic peak details (such as peak position and intensity) in the gas spectrum. It is suitable for detecting weak signals such as low-concentration gases; the more complete the characteristic peak preservation, the easier it is to identify low-concentration signals.

[0089] Linearity is an important metric for evaluating system performance. For example... Figure 9 and Figure 10 The figure shows the linear relationship between acetylene concentration and corresponding peak value before and after noise reduction. Figure 9 The scatter plot visually presents the fitting results between the measured peak value and concentration of acetylene photoacoustic spectrum, and the corresponding linear equation is as follows: , Figure 10 The fitting result after denoising using the MEEMD-Gauss-NGO algorithm corresponds to the following linear equation: , The correlation coefficient R² of the denoised peak data is 0.9998, which is a significant improvement compared to the measured data. This indicates a very high degree of fit between the model prediction and the standard concentration. The denoised absorption spectrum matches the theoretical shape, highlighting the effectiveness of the algorithm in gas concentration detection.

[0090] This invention improves the signal-to-noise ratio of acetylene detection to 33.206 dB and achieves a correlation coefficient R² of 0.9998 through MEEMD-Gauss-NGO collaborative denoising, which is significantly better than traditional methods.

[0091] This invention introduces the Northern Eagle optimization algorithm to automatically find the optimal combination of MEEMD energy threshold, adaptive smoothing window and Gaussian filter parameters, avoiding the difficulty and subjectivity of manual parameter tuning.

[0092] The MEEMD decomposition of this invention can effectively handle non-stationary and nonlinear signals, and the adaptive smoothing can dynamically adjust the filtering intensity according to the local characteristics of the signal, making it suitable for complex interference environments in industrial settings.

[0093] This invention is not only applicable to acetylene gas detection, but can also be extended to photoacoustic spectral detection of other gases (such as methane, carbon dioxide, etc.), as well as other similar signal processing fields.

[0094] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A signal denoising method based on MEEMD and Northern Eagle optimization, characterized in that, Includes the following steps: Step S1: Obtain the signal to be processed, wherein the signal to be processed is the second harmonic signal in photoacoustic spectroscopy gas detection; Step S2: Perform MEEMD decomposition on the signal to be processed to obtain multiple intrinsic mode function (IMF) components and residuals; Step S3: Calculate the energy percentage of each IMF component and filter out valid IMF components based on the energy threshold; Step S4: Reconstruct the selected effective IMF components with the residual to obtain the preliminary denoised signal; Step S5: Perform adaptive smoothing processing on the preliminary denoised signal; Step S6: Perform Gaussian filtering on the signal that has undergone adaptive smoothing. Step S7: Use the Northern Eagle optimization algorithm to optimize the energy threshold in step S3, the adaptive smoothing window parameters in step S5, and the Gaussian filter parameters in step S6 to obtain the optimal parameter combination.

2. The signal denoising method based on MEEMD and Northern Eagle optimization according to claim 1, characterized in that, The acquisition of the signal to be processed includes: acquiring the second harmonic signal in the photoacoustic spectroscopy detection system, which includes a laser source, a photoacoustic cell, a microphone, a lock-in amplifier, and a data acquisition unit; the laser source is a distributed feedback laser diode with a center wavelength of 1531.12nm and a maximum peak output power of 8.3mW.

3. The signal denoising method based on MEEMD and Northern Eagle optimization according to claim 1, characterized in that, Step S2 includes the following steps: Step S21, add complementary white Gaussian noise pairs to the original signal x(t). and This generates two noisy signals: ， ， in, and Given a pair of complementary Gaussian white noise sequences, satisfying = Both have the same standard deviation ε; Step S22: Perform empirical mode decomposition on each noisy signal to obtain multiple sets of IMF components and residuals; Step S23: Perform ensemble averaging on multiple IMF components to obtain the final IMF components and residuals.

4. The signal denoising method based on MEEMD and Northern Eagle optimization according to claim 3, characterized in that, The empirical mode decomposition includes the following process: identifying all local maxima and local minima of the signal; connecting all local maxima through cubic spline interpolation to form an upper envelope; connecting all local minima through cubic spline interpolation to form a lower envelope; calculating the average of the upper and lower envelopes to obtain the mean envelope; and subtracting the mean envelope from the original signal to obtain candidate IMF components. Repeat the above process until the candidate IMF component meets the IMF condition; The IMF conditions include: the number of extreme points is equal to or differs by at most one from the number of zero crossings throughout the entire data segment; and at any point, the average of the upper envelope defined by the local maxima and the lower envelope defined by the local minima is zero.

5. The signal denoising method based on MEEMD and Northern Eagle optimization according to claim 1, characterized in that, Step S3 includes the following steps: Step S31: Calculate the energy value of each IMF component; Step S32: Calculate the energy percentage of each IMF component; Step S33: Compare the energy percentage with the energy threshold θ, and select the IMF components with an energy percentage greater than θ as valid components.

6. The signal denoising method based on MEEMD and Northern Eagle optimization according to claim 1, characterized in that, The mathematical expression for reconstructing the selected effective IMF components with the residuals is as follows: ， in, (t) represents the initial denoised signal, and S is the index set of the effective IMF components. k r(t) is the kth effective IMF component, and r(t) is the residual term.

7. The signal denoising method based on MEEMD and Northern Eagle optimization according to claim 1, characterized in that, Step S5 includes the following steps: Step S51: Calculate the local variance of the signal at each point; Step S52: Dynamically adjust the size of the smoothing window based on the local variance; Step S53: Use the adjusted window to perform a moving average smoothing on the signal.

8. The signal denoising method based on MEEMD and Northern Eagle optimization according to claim 1, characterized in that, The Gaussian filter is a linear low-pass filter that uses a Gaussian kernel function to perform a weighted average of the signal, thereby suppressing high-frequency noise.

9. The signal denoising method based on MEEMD and Northern Eagle optimization according to any one of claims 1-8, characterized in that, The Northern Eagle optimization algorithm in step S7 includes the following steps: Step S71: Initialize algorithm parameters, including population size, maximum number of iterations, and search space boundary; Step S72, randomly generate an initial population, with each individual representing a set of parameter combinations. , , , ], The MEEMD energy threshold, For adaptive smoothing minimum window; Adaptive smoothing maximum window; The sigma value is the Gaussian filter value. Step S73: Evaluate the fitness value of each individual; Step S74: Perform the exploration phase and update the individual's location; Step S75: Perform the development phase and update the individual location; Step S76, repeat steps S73-S75 until the maximum number of iterations is reached; Step S77: Output the individual with the highest fitness as the optimal parameter combination.

10. A signal denoising device based on MEEMD and Northern Eagle optimization, characterized in that, include: The signal acquisition module is used to acquire the signal to be processed, which is the second harmonic signal in photoacoustic spectroscopy gas detection; The MEEMD decomposition module is used to perform MEEMD decomposition on the signal to be processed to obtain multiple intrinsic mode function (IMF) components and residuals. The energy screening module is used to calculate the energy proportion of each IMF component and screen valid IMF components based on energy thresholds. The signal reconstruction module is used to reconstruct the selected effective IMF components with the residual to obtain a preliminary denoised signal; An adaptive smoothing module is used to perform adaptive smoothing processing on the initial denoised signal; The Gaussian filter module is used to perform Gaussian filtering on signals that have undergone adaptive smoothing. The parameter optimization module is used to optimize the energy threshold, adaptive smoothing window parameters, and Gaussian filter parameters using the Northern Eagle optimization algorithm.

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