Decoupling method of gas turbine vibration signal based on triaxial order-aware multi-objective optimization vmd

Abstract

The application discloses a three-shaft order sensing multi-objective optimization VMD (Vibration Mode Decomposition) gas turbine vibration signal decoupling method and belongs to the technical field of gas turbine state monitoring and signal processing. The application aims at the problem that the traditional VMD method appears serious mode aliasing due to the multi-shaft order deep coupling of three-shaft gas turbine vibration signals and strong wideband combustion noise. First, the order prior information of three-shaft rotors is fused, a three-shaft order decoupling entropy index is proposed, and a four-dimensional multi-objective optimization system containing average envelope entropy, three-shaft order decoupling entropy, combustion noise suppression index and instantaneous frequency stability is constructed. Then, the NSGA-III algorithm is used for multi-objective global optimization, and the objective decision of optimal parameters is completed through the entropy weight TOPSIS method. Finally, the adaptive decomposition and order decoupling of vibration signals are realized based on the optimal parameters. The application can completely solve the problem of mode aliasing caused by multi-shaft order coupling, and greatly improves the decoupling effect and feature extraction accuracy of three-shaft gas turbine vibration signals.

Description

Technical Field

[0001] This invention belongs to the field of gas turbine condition monitoring and signal processing technology, and more specifically, to a gas turbine acoustic and vibration signal decoupling method based on three-axis order-sensing multi-objective optimization (VMD). It is applied to the identification of rotor speed, condition monitoring, and fault diagnosis of three-axis gas turbines in the fields of shipbuilding, power generation, and aerospace. Background Technology

[0002] Three-shaft gas turbines possess advantages such as high power density and strong adaptability to varying operating conditions, making them core power equipment in ship propulsion, aviation auxiliary power systems, and industrial power generation. During operation, the rotational motion of the low-pressure compressor rotor, high-pressure compressor rotor, and power turbine rotor generates corresponding harmonic characteristics in the acoustic and vibration signals, serving as the core information carrier for rotor speed monitoring and fault diagnosis.

[0003] However, the three rotors of a three-shaft gas turbine are arranged coaxially and rotate at independent speeds, resulting in deep coupling of multi-axis order features in the acoustic and vibration signals. At the same time, the strong broadband combustion noise in the combustion chamber will drown out weak order features, making the measured acoustic and vibration signals exhibit strong non-stationarity, multi-component coupling, and low signal-to-noise ratio characteristics. Traditional time-domain and frequency-domain analysis methods are difficult to extract effective shaft-specific features.

[0004] Variational Mode Decomposition (VMD), an adaptive non-recursive signal decomposition method proposed in 2014, has a solid foundation in variational theory. Compared to Empirical Mode Decomposition (EMD) methods, it fundamentally avoids problems such as mode aliasing and endpoint effects, and has been widely applied in the field of rotating machinery signal processing. However, the decomposition effect of VMD is highly dependent on the selection of two core parameters: the number of modes k and the second-order penalty factor α. Too few modes will lead to the aliasing of multi-order features in the same mode, while too many modes will result in spurious modes. Too small a penalty factor will lead to excessive mode bandwidth and severe noise interference, while too large a penalty factor will lead to the loss of effective order information. In current engineering applications, VMD parameters are mostly selected manually based on experience, which cannot adapt to the complex multi-order coupling scenarios of three-axis gas turbines. Improper parameter selection will lead to severe mode aliasing and a significant decrease in feature extraction accuracy.

[0005] Existing research on the adaptive selection of VMD parameters mainly falls into two categories: single-objective optimization and multi-objective optimization. Single-objective optimization methods often aim to minimize indicators such as envelope entropy and kurtosis, using swarm intelligence algorithms to search for optimal parameters. However, single-objective optimization can only improve a single characteristic of the mode and cannot simultaneously address multiple engineering requirements such as decoupling, noise suppression, and feature fidelity, resulting in poor generalization in multi-axis coupled scenarios. Multi-objective optimization methods can simultaneously optimize multiple conflicting objectives, better meeting the practical needs of VMD parameter optimization. Existing research often uses the NSGA-II algorithm for optimization, constructing a multi-objective system including envelope entropy, correlation coefficient, and permutation entropy. However, existing methods have two core drawbacks: first, the objective function does not incorporate prior information about the order of rotating machinery, resulting in insufficient physical meaning and an inability to achieve specific optimization for multi-axis coupled scenarios; second, the convergence and diversity of the NSGA-II algorithm decrease significantly in multi-objective optimization with dimensions of 3D and above, making it prone to getting trapped in local optima. Currently, there is no dedicated VMD multi-objective parameter optimization and signal decoupling method for the multi-rotor order coupling scenario of a three-axis gas turbine. Summary of the Invention

[0006] The purpose of this invention is to address the aforementioned deficiencies in existing technologies by providing a method for decoupling gas turbine acoustic and vibration signals using a three-axis order-sensing multi-objective optimization (VMD) approach. This method solves the problems of deep multi-axis order coupling of three-axis gas turbine acoustic and vibration signals, severe mode aliasing caused by strong broadband combustion noise in traditional VMD methods, reliance on manual experience for parameter selection, lack of integration of order priors in multi-objective optimization, and poor convergence in high-dimensional optimization. It achieves accurate order decoupling and high-fidelity feature extraction of three-axis gas turbine acoustic and vibration signals.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] A method for decoupling acoustic and vibration signals of gas turbines using a three-axis order-sensing multi-objective optimization VMD method, comprising the following steps:

[0009] S1: Collect the acoustic and vibration signals of the three-shaft gas turbine and the synchronous speed data of the three-shaft rotor, preprocess the signals to obtain the acoustic and vibration time sequence signals to be decomposed and the order prior information of the three-shaft rotor;

[0010] S2: Using the number of modes k and the quadratic penalty factor α of VMD as optimization variables, and integrating the order prior information of the triaxial rotor, four mutually orthogonal optimization objective functions are constructed, namely, the average envelope entropy MEE, the triaxial order decoupling entropy TS-ODE, the order-related combustion noise suppression index OC-CNSI, and the instantaneous frequency stability IFS, forming a multi-objective optimization problem.

[0011] S3: Initialize the population parameters of the NSGA-III algorithm, use the multi-objective optimization system constructed in step S2 as the fitness function, perform iterative optimization, and output the Pareto optimal front solution set;

[0012] S4: For the Pareto optimal frontier solution set obtained in step S3, the entropy weight TOPSIS method is used to calculate the comprehensive closeness of each non-dominated solution, and the k and α corresponding to the solution with the highest closeness are selected as the global optimal parameters of VMD.

[0013] S5: Using the globally optimal parameters obtained in step S4, VMD decomposition is performed on the preprocessed acoustic and vibration signals to obtain multiple intrinsic mode function (IMF) components, thus completing the order decoupling and feature extraction of the three-axis gas turbine acoustic and vibration signals.

[0014] Further, in step S1, the three-axis rotor includes a low-pressure compressor shaft, a high-pressure compressor shaft, and a power turbine shaft; the order prior information includes a list of characteristic orders of each shaft system, real-time speed and corresponding fundamental frequency; the preprocessing includes signal detrending, outlier removal, and synchronization alignment processing.

[0015] Further, in step S2, the average envelope entropy (MEE) is minimized, and its calculation steps are as follows:

[0016] S211: Perform Hilbert transform on the i-th IMF component obtained from VMD decomposition to obtain its analytic signal, and calculate the envelope sequence of the analytic signal;

[0017] S212: Normalize the envelope sequence to obtain the probability distribution sequence;

[0018] S213: The envelope entropy of the i-th IMF is calculated based on the probability distribution sequence. The average envelope entropy (MEE) is obtained by averaging the envelope entropies of all effective modes. The expression for MEE is as follows:

[0019]

[0020] In the formula, N is the number of effective modes. denoted as the envelope entropy of the i-th IMF component; the smaller the MEE value, the better the overall energy concentration of the effective modes and the better the narrowband characteristics.

[0021] Furthermore, in step S2, the triaxial order decoupling entropy TS-ODE is maximized, and its calculation steps are as follows:

[0022] S221: Calculate the center frequency of the i-th IMF component using the power spectrum centroid method. ;

[0023] S222: For the j-th shaft system, obtain the fundamental frequency based on its real-time rotational speed. With preset feature order list The Gaussian kernel function is used to calculate the matching degree between the modal center frequency and the axis system order, thus obtaining the maximum order matching degree between the i-th mode and the j-th axis system. ;

[0024] S223: Perform row normalization on the matching degree matrix of all valid modes to obtain the mode-axis membership matrix, where the element in the i-th row and j-th column is... for:

[0025]

[0026] In the formula, To avoid the minimum value of division by zero;

[0027] S224: Calculating Decoupling Entropy Based on Membership Matrix And define the triaxial order decoupling entropy TS-ODE as:

[0028]

[0029] In the formula, The theoretical maximum value of decoupling entropy is TS-ODE. The value range is [0,1]. The closer the value is to 1, the higher the degree of exclusive correlation between the mode and the axis system, and the better the multi-axis decoupling effect.

[0030] Further, in step S2, the order-related combustion noise suppression index OC-CNSI is minimized, defined as the proportion of the energy of the effective mode in the combustion noise frequency band to the total energy of the effective modes, expressed as:

[0031]

[0032] In the formula, N is the number of effective modes. Let i be the energy of the i-th IMF component within the combustion noise frequency band B. The total energy of the i-th IMF component; the combustion noise frequency band B is determined by 1.5-3 times the triaxial average fundamental frequency; the smaller the OC-CNSI value, the lower the content of combustion noise in the effective mode and the better the noise suppression effect.

[0033] Furthermore, in step S2, the instantaneous frequency stability (IFS) is maximized, and its calculation steps are as follows:

[0034] S241: For the i-th IMF component, calculate its instantaneous frequency sequence through Hilbert transform, and suppress noise interference through median filtering;

[0035] S242: Calculate the coefficient of variation of an instantaneous frequency sequence, which is the ratio of the standard deviation to the mean, to measure the degree of frequency fluctuation.

[0036] S243: Calculate the frequency stability of a single mode and average it over all effective modes to obtain the overall instantaneous frequency stability IFS, which ranges from [0,1]. The closer the value is to 1, the more stable the instantaneous frequency of the effective mode is and the better the feature fidelity is.

[0037] Further, in step S3, the specific execution steps of the NSGA-III algorithm are as follows:

[0038] S31: The Das-Dennis method is used to generate reference directions that are uniformly distributed on the normalized target hyperplane. The number of reference directions is determined by the target dimension and the number of segments.

[0039] S32: Population initialization, randomly generate an initial population, the population size is an integer multiple of the number of reference directions, the optimization variables are the number of VMD modes k and the quadratic penalty factor α, set the value range of k to [2,10], and the value range of α to [100,3000];

[0040] S33: Genetic operation, generating offspring population by simulating binary crossover (SBX) and polynomial mutation (PM), and merging parent and offspring populations;

[0041] S34: Perform non-dominated ranking on the merged population to divide individuals into different non-dominated fronts;

[0042] S35: Individuals are selected sequentially starting from the first non-dominated frontier until the preset population size is reached; for individuals in the critical layer, individuals are selected through a niching mechanism with associated reference directions to ensure population diversity;

[0043] S36: If the maximum number of iterations is reached, output the Pareto optimal front solution set of the final population; otherwise, return to step S33 to continue iterating.

[0044] Further, in step S4, the execution steps of the entropy weight TOPSIS method are as follows:

[0045] S41: Suppose that the Pareto optimal front contains m non-dominated solutions, each of which corresponds to 4 objective values. Construct a decision matrix.

[0046] S42: Take the negative value of the minimization objective, unify all objectives into the maximization objective, and then perform 0-1 normalization to obtain the normalized decision matrix;

[0047] S43: Calculate the objective weights of each target using the entropy weight method to avoid subjective bias from manual weighting;

[0048] S44: Construct a weighted decision matrix based on objective weights to determine the ideal optimal solution and the ideal worst solution;

[0049] S45: Calculate the Euclidean distance between each solution and the ideal optimal solution and the ideal worst solution, and then calculate the overall closeness. The closeness range is [0,1]. The closer the value is to 1, the better the overall performance of the solution.

[0050] S46: Select the k and α corresponding to the solution with the highest similarity as the global optimal parameters for VMD.

[0051] Furthermore, in step S5, the VMD decomposition uses the Alternating Direction Multiplier Method (ADMM) to iteratively solve the constrained variational problem, alternately updating the IMF components, center frequency, and Lagrange multipliers until the convergence condition is met, thus completing the adaptive decomposition of the signal.

[0052] Furthermore, the three-shaft gas turbine includes three-shaft gas turbines for shipboard use, power generation, and aviation auxiliary power; the acoustic and vibration signals include sound pressure signals, vibration acceleration signals, and vibration velocity signals.

[0053] The beneficial effects of this invention are as follows:

[0054] For the first time, the Triaxial Order Decoupling Entropy (TS-ODE) index is proposed, which can accurately quantify the specific correlation between the decomposition mode and the order of the triaxial rotor. It provides a core objective that fits the engineering physics meaning for multi-objective optimization, and solves the defects of existing VMD optimization methods that do not integrate prior information of rotating machinery order and lack physical meaning. It can be specifically adapted to the scenario of multi-rotor order coupling of triaxial gas turbine.

[0055] A four-dimensional multi-objective optimization system integrating order priors was constructed. From four orthogonal dimensions—energy concentration, shaft system specificity, noise immunity, and dynamic fidelity—coordinated optimization of modal purity, shaft system decoupling, noise suppression capability, and feature fidelity was achieved. This solved the problem that single-objective optimization can only improve a single performance and has poor generalization. It can fully adapt to the characteristics of strong non-stationarity, multi-component coupling, and low signal-to-noise ratio of acoustic and vibration signals of triaxial gas turbines.

[0056] The NSGA-III algorithm is used for high-dimensional multi-objective global optimization, which solves the problem that the traditional NSGA-II algorithm suffers from a significant decrease in convergence and diversity and is prone to getting trapped in local optima in 3-dimensional and above multi-objective optimization. At the same time, the entropy weight TOPSIS method is used to achieve objective decision-making of the optimal solution, which completely avoids the subjective bias caused by human experience in weighting and realizes the fully adaptive selection of VMD core parameters.

[0057] Verification results based on measured acoustic and vibration signals of a three-axis gas turbine show that the three-axis order decoupling entropy of the method of this invention can reach 0.9688, which is 187% higher than the empirical parameter VMD. The matching degree between the core mode and the corresponding shaft system is as high as 0.999, which can completely solve the mode aliasing problem caused by multi-axis order coupling. It provides highly robust feature support for subsequent gas turbine rotor speed identification, operating condition monitoring and fault diagnosis, and has extremely high engineering application value. Attached Figure Description

[0058] The present invention will now be described in further detail with reference to the accompanying drawings and specific implementation methods.

[0059] Figure 1 This is a flowchart illustrating the overall process of the gas turbine acoustic and vibration signal decoupling method using three-axis order sensing multi-objective optimization VMD as described in this invention.

[0060] Figure 2 This is the Pareto optimal frontier distribution diagram output by the NSGA-III algorithm in this embodiment of the invention;

[0061] Figure 3 This is a time-domain waveform diagram of the intrinsic mode function (IMF) component obtained by VMD decomposition under optimal parameters in an embodiment of the present invention.

[0062] Figure 4 This is a comparison chart of the convergence curves of the four optimization objectives of the present invention and the comparative method;

[0063] Figure 5 A bar chart comparing the results of the present invention and the comparative method for four optimization objectives;

[0064] Figure 6 A comparison of the modal-axis order matching heatmaps of the present invention and the comparative method;

[0065] Figure 7 This is a comparison chart of the entropy weight TOPSIS comprehensive scores of the present invention and the comparative method. Detailed Implementation

[0066] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0067] This embodiment provides a method for decoupling acoustic and vibration signals of a gas turbine using a three-axis order-sensing multi-objective optimization (VMD) approach. The method specifically addresses the decoupling of measured steady-state acoustic and vibration signals from a certain type of three-axis gas turbine used for power generation. The detailed implementation steps are as follows:

[0068] Step 1: Data Preprocessing

[0069] The experimental data used in this embodiment comes from a performance monitoring test bench for a three-shaft gas turbine used for power generation. The gas turbine radiated noise signal is collected by a high-precision sound pressure sensor, and the rotational speed data of the low-pressure compressor shaft (L-axis), high-pressure compressor shaft (H-axis), and power turbine shaft (P-axis) are collected simultaneously by a speed sensor. The signal sampling frequency is set to 51200Hz.

[0070] The rotor order prior information of the three-shaft gas turbine is shown in Table 1:

[0071] Table 1. Rotor Order Configuration of Three-Shaft Gas Turbine

[0072] Shaft system name Feature order list Low-pressure compressor shaft (L) [1,15,17,22,27,36,40,46,51,89] High-pressure compressor shaft (H) [1,65,66,89] Power turbine shaft (P) [1,76]

[0073] The experiment selected measured data under rated load steady-state conditions. Under these conditions, the measured speeds of the three shafts were: 6988 rpm for the low-pressure shaft, 8999 rpm for the high-pressure shaft, and 4489 rpm for the power turbine, corresponding to fundamental frequencies of 116.47 Hz, 149.98 Hz, and 74.82 Hz, respectively. The sound pressure signal from the middle 0.25 seconds of a single file was selected for processing, corresponding to 12800 sampling points.

[0074] The collected sound pressure signal and rotational speed data are preprocessed, including detrending, outlier removal, and time synchronization alignment of the sound vibration signal and rotational speed signal, to obtain the sound vibration time sequence signal to be decomposed and the order prior information of the three-axis rotor.

[0075] Step 2: Construct a multi-objective optimization system with three-axis order sensing

[0076] Using the number of VMD modes k and the quadratic penalty factor α as optimization variables, with k ranging from [2, 10] and α ranging from [100, 3000], and incorporating the prior order information of the triaxial rotor, four mutually orthogonal optimization objective functions are constructed to form a multi-objective optimization problem. The four objective functions are as follows:

[0077] (1) Mean Envelope Entropy (MEE) (Minimization Objective)

[0078] MEE is used to measure the overall energy concentration of effective modes, and its calculation steps are as follows:

[0079] ① The i-th IMF component obtained from VMD decomposition Perform a Hilbert transform to obtain the analytic signal:

[0080]

[0081] In the formula, For Hilbert transform operators;

[0082] ② Calculate the envelope sequence of the analytic signal ;

[0083] ③ Normalize the envelope sequence to obtain the probability distribution sequence:

[0084]

[0085] In the formula, L is the number of signal sampling points, and in this embodiment, L=12800;

[0086] ④ Calculate the envelope entropy of the i-th IMF:

[0087]

[0088] ⑤ Take the average envelope entropy of all effective modes to obtain the average envelope entropy:

[0089]

[0090] In the formula, N represents the number of effective modes.

[0091] (2) Three-axis order decoupling entropy TS-ODE (maximizing objective)

[0092] TS-ODE is used to quantify the specific correlation between decomposition modes and triaxial rotor orders. It is the core innovative indicator of this invention, and its calculation steps are as follows:

[0093] ① The center frequency of the i-th IMF component is calculated using the power spectrum centroid method. :

[0094]

[0095] In the formula, In this embodiment, the signal sampling frequency is... , For Fast Fourier Transform;

[0096] ②For the j-th axis system, its fundamental frequency is The feature order list is as follows The Gaussian kernel function is used to calculate the degree of matching between the modal center frequency and the axis order:

[0097]

[0098] In the formula, The Gaussian kernel bandwidth is set to 5Hz in this embodiment. The value range is [0,1], and the closer it is to 1, the higher the matching degree between the mode and a certain order of the axis system;

[0099] ③ Perform row normalization on the matching degree matrix of all valid modes to obtain the mode-axis membership matrix, where the element in the i-th row and j-th column is:

[0100]

[0101] In the formula, To avoid the minimum value of division by zero;

[0102] ④ Calculate the decoupling entropy based on the membership matrix:

[0103]

[0104] ⑤ Define the three-axis order decoupling entropy:

[0105]

[0106] The value range of TS-ODE is [0,1]. The closer it is to 1, the better the multi-axis order decoupling effect.

[0107] (3) Order-related combustion noise suppression index OC-CNSI (minimization target)

[0108] OC-CNSI is used to measure the energy proportion of combustion noise in the effective modes. In this embodiment, the triaxial average fundamental frequency is (116.47+149.98+74.82) / 3≈113.76Hz. Therefore, the combustion noise frequency band B is set to 170.64Hz-341.28Hz (1.5-3 times the average fundamental frequency). The expression for OC-CNSI is:

[0109]

[0110] The smaller the OC-CNSI value, the better the noise suppression effect.

[0111] (4) Instantaneous Frequency Stability (IFS) (Maximization Target)

[0112] IFS is used to measure the stability of modal instantaneous frequencies and characterize eigenficiency. Its calculation steps are as follows:

[0113] ① For the i-th IMF component The instantaneous phase is calculated using the Hilbert transform. The instantaneous frequency sequence is obtained by differentiating the instantaneous phase. The instantaneous frequency sequence is smoothed by a median filter with a window length of 5 to suppress noise interference;

[0114] ② Calculate the coefficient of variation of the instantaneous frequency sequence. ,in , The mean;

[0115] ③ Calculate the frequency stability of a single mode. The overall instantaneous frequency stability is obtained by averaging the frequency stability of all effective modes:

[0116]

[0117] The value range of IFS is [0,1], and the closer it is to 1, the better the feature fidelity.

[0118] Step 3: Multi-objective global optimization based on NSGA-III algorithm

[0119] Initialize the NSGA-III algorithm parameters as follows: target dimension is 4, number of reference direction splits is 4, number of reference directions is 35, population size is 70 (twice the number of reference directions), maximum number of iterations is 30, crossover probability is 0.9, mutation probability is 0.1, and random seed is set to 42.

[0120] Using the 4-dimensional multi-objective optimization system constructed in step 2 as the fitness function, NSGA-III iterative optimization is performed. The specific process is as follows:

[0121] ① The Das-Dennis method is used to generate 35 reference directions that are uniformly distributed on the 4-dimensional normalized target hyperplane;

[0122] ② The initial population is randomly generated, and each individual contains two optimization variables: the number of modes k (integer, [2,10]) and the quadratic penalty factor α (integer, [100,3000]).

[0123] ③ By simulating binary crossover (SBX) and polynomial mutation (PM), offspring populations are generated, and parent and offspring populations are merged to obtain a merged population of size 140;

[0124] ④ Perform non-dominated sorting on the merged population to divide individuals into different non-dominated fronts;

[0125] ⑤ Individuals are selected sequentially starting from the first non-dominated frontier until the preset population size of 70 is reached; for individuals in the critical layer, individuals are selected through a niching mechanism with associated reference directions to ensure population diversity.

[0126] ⑥ If the maximum number of iterations (30) is reached, output the Pareto optimal front solution set of the final population; otherwise, return to step ③ to continue iterating.

[0127] The Pareto optimal front obtained in this embodiment contains 35 non-dominated solutions, each solution corresponding to a set of (k, α) parameters and 4 objective function values.

[0128] Step 4: Optimal solution decision based on entropy-weighted TOPSIS

[0129] For the Pareto optimal frontier solution set obtained in step 3, the entropy-weighted TOPSIS method is used to make the optimal solution decision. The specific steps are as follows:

[0130] ① Constructing the decision matrix Each row corresponds to a nondominated solution, and each column corresponds to an objective function value;

[0131] ② Take the negative value of the minimization objective (MEE, OC-CNSI), unify all objectives into the maximization objective, and then perform 0-1 normalization to obtain the normalized decision matrix Y;

[0132] ③ The objective weights of the four objectives are calculated using the entropy weight method, specifically as follows:

[0133] Calculate the information entropy of the j-th target:

[0134] Calculate the information utility value:

[0135] Calculate objective weights:

[0136] ④ Construct a weighted decision matrix ;

[0137] ⑤ Determine the ideal optimal solution The worst-case scenario ;

[0138] ⑥ Calculate the Euclidean distance between each solution and the ideal optimal solution. Euclidean distance from the worst-case solution ;

[0139] ⑦ Calculate the overall closeness of each solution: ;

[0140] ⑧ Select the k and α corresponding to the solution with the highest similarity as the global optimal parameters of VMD.

[0141] In this embodiment, the final globally optimal parameters are: number of modes k=7, and quadratic penalty factor α=1071.19.

[0142] Step 5: VMD decomposition and feature extraction under optimal parameters

[0143] Using the globally optimal parameters (k=7, α=1071.19) obtained in step 4, VMD decomposition is performed on the preprocessed acoustic and vibration signals. The constrained variational problem is solved iteratively using the Alternating Direction Multiplier Method (ADMM). The IMF components, center frequency, and Lagrange multipliers are updated alternately until the convergence condition is met. Finally, seven intrinsic mode functions (IMF) components are obtained, completing the order decoupling and feature extraction of the three-axis gas turbine acoustic and vibration signals.

Claims

1. A method for decoupling acoustic and vibration signals of gas turbines using three-axis order-sensing multi-objective optimization VMD, characterized in that, Includes the following steps: S1: Synchronously acquire the acoustic and vibration signals of the three-shaft gas turbine, the rotor speed data of the low-pressure compressor shaft, the high-pressure compressor shaft, and the power turbine shaft. After detrending, outlier removal, and time-series synchronization alignment preprocessing, output the acoustic and vibration time-series signal to be decomposed and the order prior information containing the characteristic order of each shaft, real-time speed, and fundamental frequency of the shaft system. S2: Selecting VMD mode number k and quadratic penalty factor α as optimization variables, and relying on the prior information of the three-axis rotor order, construct four orthogonal optimization objectives in physical dimensions: minimizing the average envelope entropy MEE, maximizing the three-axis order decoupling entropy TS-ODE, minimizing the order-related combustion noise suppression index OC-CNSI, and maximizing the instantaneous frequency stability IFS, and build a four-dimensional multi-objective optimization model. S3: Configure the basic parameters of the NSGA-III algorithm, use the four indicators of S2 as the population fitness function for iterative optimization, and output the Pareto optimal front non-dominated solution set after iterative convergence through reference direction generation, population initialization, genetic crossover and mutation, non-dominated sorting, and reference direction niche screening. S4: The Pareto solution set is processed by the TOPSIS objective weighting method of entropy weight. The polarity of the optimization target is unified and normalized. The weight of each index is determined based on the information entropy. The comprehensive closeness of each candidate solution is solved by the distance of the ideal solution. The k and α corresponding to the maximum closeness are selected as the global optimal parameters of VMD. S5: Based on the optimal k and α parameters, the ADMM alternating direction multiplier method is used to complete the constraint variational solution. The VMD adaptive decomposition is performed on the preprocessed acoustic and vibration signals to obtain multi-order IMF components, thereby realizing the decoupling of multi-axis coupling order and the extraction of fault features of the three-axis gas turbine.

2. The gas turbine acoustic and vibration signal decoupling method for three-axis order-sensing multi-objective optimization VMD according to claim 1, characterized in that, The acoustic and vibration signals mentioned in S1 include sound pressure signals, vibration acceleration signals, and vibration velocity signals; applicable equipment covers ship propulsion type, power generation type, and aviation auxiliary power type three-shaft gas turbines.

3. The gas turbine acoustic and vibration signal decoupling method for three-axis order-sensing multi-objective optimization VMD according to claim 1, characterized in that, The average envelope entropy (MEE) in S2 is used to characterize the energy concentration of the IMF. The steps to minimize the MEE are as follows: S211: Perform Hilbert transform on IMFs of each order to obtain analytical signals and extract envelope sequences; S212: Normalize the envelope sequence to generate a probability distribution sequence; S213: The MEE is obtained by taking the arithmetic mean after solving the single-mode envelope entropy step by step; the smaller the MEE value, the better the modal energy concentration and narrowband characteristics.

4. The gas turbine acoustic and vibration signal decoupling method for three-axis order-sensing multi-objective optimization VMD according to claim 1, characterized in that, The triaxial order decoupling entropy (TS-ODE) in S2 is an original quantitative index of this method, used to characterize the matching specificity between the mode and the triaxial rotor. The steps to maximize TS-ODE are as follows: S221: Power spectrum centroid method for stepwise calculation of IMF center frequency; S222: Based on the fundamental frequency of each axis and the preset order table, the Gaussian kernel function is introduced to calculate the single-mode-single-axis order matching coefficient; S223: Row normalization of the matching coefficient matrix generates the modal-axis membership matrix; S224: Calculate the decoupling entropy based on the membership matrix and normalize it to obtain the TS-ODE with a value of [0,1]. The closer the index is to 1, the better the multi-axis order decoupling effect.

5. The gas turbine acoustic and vibration signal decoupling method for three-axis order-sensing multi-objective optimization VMD according to claim 1, characterized in that, The S2 intermediate order correlation combustion noise suppression index OC-CNSI is a quantification parameter of the proportion of combustion noise energy. The combustion noise frequency band B is limited to 1.5 to 3 times the triaxial average fundamental frequency. The smaller the OC-CNSI, the better the combustion noise filtering effect within the mode.

6. The gas turbine acoustic and vibration signal decoupling method for three-axis order-sensing multi-objective optimization VMD according to claim 1, characterized in that, The instantaneous frequency stability (IFS) in S2 is used to characterize the feature fidelity performance. The steps to maximize the IFS are as follows: S241: Hilbert transform to obtain the instantaneous frequency sequence of the IMF, followed by median filtering for smoothing and noise reduction; S242: The frequency fluctuation is characterized by the instantaneous frequency variation coefficient; S243: The average value of the single-mode stability is obtained as an IFS with a value of [0,1]. The closer the value is to 1, the higher the feature fidelity after decomposition.

7. The gas turbine acoustic and vibration signal decoupling method for three-axis order-sensing multi-objective optimization VMD according to claim 1, characterized in that, The NSGA-III algorithm in S3 includes the following steps: S31: Generate uniformly distributed reference directions on the normalized target hyperplane using the Das-Dennis method. The number of reference directions is determined by the target dimension and the number of segments. S32: Initialize the population. The population size is an integer multiple of the number of reference directions. The optimization variables are the number of VMD modes k and the quadratic penalty factor α. Set the value range of k to [3,15] and the value range of α to [1000,20000]. S33: Use SBX to simulate binary crossover and PM polynomial mutation to obtain the offspring population, and then merge the parent and offspring populations; S34: Perform non-dominated sorting on the merged population and delineate the non-dominated frontier at each level; S35: Individuals are selected sequentially from the leading non-dominant front to the rated population capacity, and individuals in the critical layer are selected based on the reference direction niche rule to maintain population diversity; S36: If the number of iterations reaches the target, output the Pareto optimal solution set; otherwise, return to S33 to continue the calculation.

8. The gas turbine acoustic and vibration signal decoupling method for three-axis order-sensing multi-objective optimization VMD according to claim 1, characterized in that, The entropy weight TOPSIS optimization step in S4: S41: Construct an m×4 dimensional original decision matrix using the Pareto solution set; S42: Minimize the index in reverse to achieve target alignment, and then perform 0-1 standardization; S43: The entropy weight method objectively allocates weights based on the information entropy of the indicators, avoiding the subjectivity of manual assignment. S44: Construct a weighted standard decision matrix to define positive and negative ideal solutions; S45: Calculate the Euclidean distance of each candidate solution from the positive and negative ideal solutions, and solve for the overall closeness. S46: Select the VMD parameter corresponding to the peak of proximity.

9. The gas turbine acoustic and vibration signal decoupling method for three-axis order-sensing multi-objective optimization VMD according to claim 1, characterized in that, In the S5 ADMM algorithm iteration process, the IMF components, mode center frequencies, and Lagrange multipliers are updated alternately. The iteration terminates after the convergence threshold is met, and all decomposed modes are output.

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