A method for inverting the charge of abnormal charged particles in the gas path of a gas turbine

Abstract

This invention provides a method for inverting the charge quantity of abnormal charged particles in the gas path of a gas turbine, applicable to the field of early fault diagnosis in gas turbines. The method includes: determining a parameter set; constructing a forward model function based on the parameter set to map the mapping relationship between point charges within a closed conductive cavity and the potential at any point on the inner wall; constructing an objective function based on the potential measurement vector output by an electrostatic sensor and the forward model function; iteratively solving the objective function using a nonlinear optimization algorithm, and finding the optimal parameter vector that best matches the measured value with the theoretical value by minimizing the objective function; and substituting the optimal parameter vector into the forward model function to obtain the charge quantity. This invention achieves quantitative monitoring and location of charged particles in the gas path of a gas turbine, and has advantages such as high inversion accuracy, strong anti-interference ability, and suitability for online real-time fault early warning.

Description

Technical Field

[0001] This invention relates to the field of early fault diagnosis of gas turbines, and more particularly to a method for inverting the charge of abnormal charged particles in the gas path of a gas turbine. Background Technology

[0002] Gas turbines, as core power equipment with high technological integration, are widely used in electric power generation, ship propulsion, aviation power, and industrial drives. Gas turbines typically operate under complex conditions of high temperature, high pressure, and high speed, making their internal components prone to wear, particulate matter accumulation, and other malfunctions. As operating time accumulates, the risk of malfunctions gradually increases. If not detected and addressed in a timely manner, this can lead to decreased gas turbine efficiency, unplanned shutdowns, or even equipment damage, resulting in significant economic losses and safety risks. Therefore, achieving early warning and fault diagnosis for heavy-duty gas turbines is of great significance for ensuring their long-term stable operation.

[0003] Currently, fault monitoring of gas turbines mainly relies on conventional sensor signals such as vibration, temperature, and pressure. In the early stages of faults, such as abnormal gas path and generation of tiny charged particles, the signal changes of conventional sensors are weak, feature values ​​are difficult to extract, and they are easily affected by noise and fluctuations in operating conditions, resulting in insufficient diagnostic accuracy. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a method for inverting the charge quantity of abnormally charged particles in the gas turbine's gas path. Without significantly affecting the integrity and safety of the main equipment structure, it calculates the internal charge quantity and radial position information based on the potential measurement of electrodes on the inner wall of the conductor cavity, ultimately achieving online early warning of abnormally charged particles. Specifically, it includes: A method for inverting the charge of abnormally charged particles in the gas turbine's gas path, comprising deploying M electrostatic sensors inside the gas path piping of the gas turbine, the method including: S1. Determine the parameter set: The parameter set includes the geometric parameters (G) of the closed conductor cavity, the spatial coordinates (P) of each electrostatic sensor, the potential measurement vector (V) output by the electrostatic sensor, and the initial guess value (X0) of the parameter to be inverted. S2. Construct a positive model function F(X) based on the parameter set to establish the mapping relationship between point charges inside a closed conductor cavity and the potential at any point on the inner wall; S3. Construct the objective function G(X) based on the potential measurement vector (V) output by the electrostatic sensor and the positive model function F(X); S4. Iteratively solve the objective function G(X) using a nonlinear optimization algorithm. By minimizing the objective function G(X), find the optimal parameter vector X that best matches the measured value with the theoretical value. ; S5. Transfer the optimal parameter vector X The charge is obtained by substituting it into the positive model function F(X).

[0005] Optionally, the initial guess value (X0) of the parameter to be inverted includes: The initially guessed charge (q) of the charged particle and the initially guessed two-dimensional position coordinates of the charged particle. .

[0006] Optionally, the forward model function F(X) of S2, which constructs the mapping relationship between point charges within a closed conductive cavity and the potential at any point on the inner wall based on the parameter set, is as follows: Based on electromagnetic field theory, and combined with the geometric parameters (G) of the closed conductor cavity, a positive model function F(X) is constructed to represent the mapping relationship between point charges inside the closed conductor cavity and the potential at any point on the inner wall.

[0007] Optionally, the forward model function F(X) is an analytical solution obtained by solving the Poisson equation using the method of separation of variables and satisfying the Dirichlet boundary conditions, and its expression is formula (1): (1) in, The polar coordinates of the projection of the perpendicular distance between a point in space and the z-axis onto the xy-plane; Let θ be the angle between the projection onto the xy-plane and the positive x-axis, z be the displacement along the z-axis, and q be the initially guessed charge of the charged particle, set near the center of the cavity. The vacuum permittivity, For the first kind of m-order modified Bessel function, For the second kind of m-order modified Bessel function, , Let n be the coordinates of a point charge in cylindrical coordinates; n is an integer. Where is the axial wave number and L is the pipe length. express The smaller one, express The larger one.

[0008] Optionally, the initial guess value X0 of the parameter to be inverted is set to The guessed value can be set directly to this.

[0009] Optionally, the construction of the objective function G(X) based on the potential measurement vector (V) output by the electrostatic sensor and the positive model function F(X) in step S3 includes: The ratio of M potential measurements is obtained based on the potential measurement vector V output by the electrostatic sensor. ), The ratio of M theoretical potential values ​​is obtained based on the positive model function F(X); Based on the ratio of M potential measurements ( The objective function G(X) is constructed by summing the squares of the differences between the ratios of X to M theoretical potential values.

[0010] Optionally, in step S4, the objective function G(X) is iteratively solved using a nonlinear optimization algorithm. By minimizing the objective function G(X), the optimal parameter vector X that best matches the measured value with the theoretical value is found. include: The nonlinear optimization algorithm is the Levenberg-Marquardt algorithm. S401. Calculate the theoretical potential value, residual vector r, and Jacobian matrix J under the current parameters; S402, Constructing a system of linear equations Solve for parameter update step size ; in, It is the damping factor; S403. Calculate the objective function value based on the updated parameters, and determine whether to accept the update and adjust the damping factor based on whether the objective function value decreases. S404. Determine whether the convergence condition of the Levenberg-Marquardt algorithm is met. If it is met, stop the iteration and output the result; otherwise, return to step S401 to continue the iteration.

[0011] Optionally, the expression for the objective function G(X) is formula (2); (2) It is the first The measured voltage of each sensor, For the first The conversion coefficient of each sensor, It is the first The theoretical potential at each sensor.

[0012] Optionally, the installation of M electrostatic sensors within the gas turbine's gas path piping includes: M=4; Four electrostatic sensors are evenly distributed on the same axial section of the inner wall of the gas pipeline, and the azimuth angles of the four electrostatic sensors on the section are 0°, 90°, 180° and 270° respectively.

[0013] Optionally, measure the peak voltage. With theoretical potential The conversion relationship is given by formula (3): ;(3)

[0014] The above technical solution has at least the following advantages compared with the existing technology: This invention achieves accurate quantitative inversion of charge: it can accurately calculate the specific charge of abnormally charged particles inside, providing a reliable quantitative indicator for fault assessment; This invention has the ability to spatially locate fault sources: through the inversion algorithm, not only is the amount of charge obtained, but the two-dimensional spatial position of charged particles in the cavity can also be determined simultaneously.

[0015] This invention significantly improves the adaptability and reliability of the system: by constructing an objective function of "ratio of measured value to theoretical value" and introducing individual sensor calibration coefficient S, the common influence of signal baseline drift caused by changes in operating conditions can be eliminated. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart illustrating a technical implementation of this invention; Figure 2 This is a schematic diagram of sensor installation provided in an embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0019] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms “first,” “second,” and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms “an,” “a,” or “the,” and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms “comprising,” “including,” or “including,” and similar terms mean that the element or object preceding the word encompasses the element or object listed following the word and its equivalents, without excluding other elements or objects. The terms “connected,” “linked,” or “connected,” and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect.

[0020] like Figures 1 to 2 As shown, a method for inverting the charge of abnormally charged particles in the gas turbine's gas path involves installing M electrostatic sensors inside the gas turbine's gas path piping. M=4; Four electrostatic sensors are evenly distributed on the same axial section of the inner wall of the gas pipeline, and the azimuth angles of the four electrostatic sensors on the section are 0°, 90°, 180° and 270° respectively.

[0021] The method includes: S1. Determine the parameter set: The parameter set includes the geometric parameters (G) of the closed conductive cavity, the spatial coordinates (P) of each electrostatic sensor, the potential measurement vector (V) output by the electrostatic sensor, and the initial guessed values ​​(X0) of the parameters to be inverted; the initial guessed values ​​(X0) of the parameters to be inverted include: the initially guessed charge (q) of the charged particle and the initially guessed two-dimensional position coordinates of the charged particle. .

[0022] S2. Construct a positive model function F(X) based on the parameter set to establish the mapping relationship between point charges inside a closed conductor cavity and the potential at any point on the inner wall; Based on electromagnetic field theory, and combined with the geometric parameters (G) of the closed conductor cavity, a positive model function F(X) is constructed to represent the mapping relationship between point charges inside the closed conductor cavity and the potential at any point on the inner wall.

[0023] The positive model function F(X) is the analytical solution obtained by solving the Poisson equation based on the method of separation of variables and satisfying the Dirichlet boundary conditions, and its expression is formula (1): (1) in, The polar coordinates of the projection of the perpendicular distance between a point in space and the z-axis onto the xy-plane; is the angle between the projection on the xy plane and the positive x-axis direction, z is the displacement along the z-axis direction; q is the initial guessed charge of the charged particle, set near the center of the cavity is the vacuum permittivity, is the modified Bessel function of the first kind of order m, is the modified Bessel function of the second kind of order m, 、 are the coordinates of the point charge in the cylindrical coordinate system; n is an integer; is the axial wave number, L is the length of the pipeline, denotes the smaller one in denotes the larger one in

[0024] The specific principle of this step is as follows: The present invention solves the inverse problem by establishing a strict physical and mathematical model and using a non-linear optimization algorithm. The principle of the inversion method is based on the strict electromagnetic field theory of the potential distribution of a point charge in a closed conductor cavity. For a grounded conductor cylindrical pipeline with a length of L and a radius of R (i.e., inside the gas pipeline), a point charge q located at the point inside it generates an electric potential at any in the pipeline, and its strict analytical solution can be obtained by solving the Poisson equation and satisfying the Dirichlet boundary condition, and the expression is formula (1).

[0025] In actual calculations, the infinite series needs to be truncated, and taking 100, 200 can achieve sufficient engineering accuracy. This formula establishes an accurate and quantitative mapping relationship between the internal charge parameter and the electric potential at any point inside the pipeline, that is, the forward model.

[0026] In this forward model, combined with the actual situation and simulation of the gas turbine, it can be considered that the particles move uniformly along the axis , the sensor is arranged at the axial midpoint z = . In a certain period of time, when a charged abnormal particle passes through the midpoint plane, it will generate the maximum electric potential value at the sensor. The theoretical value of the electric potential is in the plane , the measured value V = , is a constant related to the system. For the sensor measuring the electric potential, due to factors such as different working temperatures and positions close to the air flow, the conversion coefficient of each sensor arranged is different, that is, the conversion coefficient is a fixed value for each sensor, but there are differences among the sensors. Each sensor can be calibrated through experiments to obtain the conversion coefficient , .

[0027] S3. Construct the objective function G(X) based on the potential measurement vector (V) output by the electrostatic sensor and the positive model function F(X); The ratio of M potential measurements is obtained based on the potential measurement vector V output by the electrostatic sensor. ), The ratio of M theoretical potential values ​​is obtained based on the positive model function F(X); Based on the ratio of M potential measurements ( The objective function G(X) is constructed by summing the squares of the differences between the ratios of X to M theoretical potential values.

[0028] The expression for the objective function G(X) is formula (2); (2) It is the first The measured voltage of each sensor, For the first The conversion coefficient of each sensor, It is the first The theoretical potential at each sensor.

[0029] Measure peak voltage With theoretical potential The conversion relationship is given by formula (3): ;(3)

[0030] S4. Iteratively solve the objective function G(X) using a nonlinear optimization algorithm. By minimizing the objective function G(X), find the optimal parameter vector X that best matches the measured value with the theoretical value. ; The nonlinear optimization algorithm is the Levenberg-Marquardt algorithm. S401. Calculate the theoretical potential value, residual vector r, and Jacobian matrix J under the current parameters; S402, Constructing a system of linear equations Solve for parameter update step size ; in, It is the damping factor; S403. Calculate the objective function value based on the updated parameters, and determine whether to accept the update and adjust the damping factor based on whether the objective function value decreases. S404. Determine whether the convergence condition of the Levenberg-Marquardt algorithm is met. If it is met, stop the iteration and output the result; otherwise, return to step S401 to continue the iteration.

[0031] S5. Transfer the optimal parameter vector X The charge is obtained by substituting it into the positive model function F(X).

[0032] Wherein, the initial guess value X0 of the parameter to be inverted is set to .

[0033] Based on this forward model, this invention uses inversion calculations to achieve the reverse process of solving for internal charge parameters from the potential value of the measured point. A detailed flowchart is shown below. Figure 1 As shown, the specific technical solution is as follows: The processor receives and stores the following input parameters: Geometric parameters of a closed conductor cavity : Input the radius of the cylindrical cavity and length The cylindrical cavity is theoretically considered an ideal conductor and grounded.

[0034] Coordinates of measurement point To accurately input the specific spatial coordinates of the four electrostatic sensors on the inner wall, this invention mounts the sensor electrodes at the axial midpoint. To obtain raw potential measurement data with a higher signal-to-noise ratio, the sensitive elements of the four electrostatic sensors are arranged at a certain radial offset distance from the inner wall of the grounded conductor cavity. Simulation calculations show that an electrode length of 0.1R yields the best results. Therefore, the coordinates of the four sensors are... , .

[0035] Potential measurement vector ( Input: The actual measurement obtained by the sensor over a period of time. A vector composed of potential peaks And find their ratio. .

[0036] Initial guess value : Set the initial value vector of the parameters to be inverted for the iterative optimization algorithm .in: This is an initial guess of the charge quantity. The initial guessed coordinates of the point charge location are set to be near the center of the cavity. .

[0037] Pre-program a positive model function This function takes a parameter vector. Calculate and return the result under the given parameter settings. The theoretical potential at each measurement point For the specific geometry of an infinitely long conducting cylindrical cavity, the point charge inside... exist The electric potential generated at the point has a rigorous analytical solution obtained based on the method of separation of variables. This solution is in the form of an infinite series. The Each component The calculation formula is:

[0038] and They represent and The smaller and the larger Obtain the theoretical value vector And find their ratio. .

[0039] The inversion problem is a nonlinear least squares optimization problem, and the objective function is defined as follows: It is the sum of squares of the differences between the measured values ​​and the theoretical values ​​at all measurement points.

[0040] in Is the forward model function at the th The output values ​​at each measurement point. The goal of this method is to find an optimal parameter vector. , so that the objective function Obtain the global minimum value.

[0041] The Levenberg-Marquard algorithm (hereinafter referred to as the LM algorithm) is used to iteratively optimize and solve the objective function GX. This algorithm is an iterative algorithm specifically designed for solving nonlinear least squares problems. By adaptively adjusting the damping factor, it combines the global convergence of the steepest descent method with the local fast convergence of the Gauss-Newton method. It can effectively handle this nonlinear inversion problem and suppress the influence of measurement noise through its inherent damping mechanism, thereby stably obtaining the optimal solution.

[0042] During optimization, the parameters are configured as follows: Maximum number of iterations The value is set to a sufficiently large value based on the measurement results to prevent the algorithm from terminating prematurely if it fails to converge. This invention sets the number of iterations to 200.

[0043] Function tolerance The tolerance value is set to a small positive value based on the required measurement accuracy. When the change in the objective function value between two consecutive iterations is less than this value, convergence is considered achieved, and iteration stops. The tolerance value set in this invention is 1. .

[0044] Parameter tolerance ( The parameter tolerance is set to a small positive value based on the required measurement accuracy. When the change in the parameter vector between two consecutive iterations is less than this value, convergence is considered achieved, and iteration stops. This invention sets the parameter tolerance to 1. .

[0045] Damping factor The initial value can be set to a small positive value, and the L-M algorithm can adaptively adjust it. When the value of increases, it tends towards the steepest descent method, which is stable; when it decreases, it tends towards the Gauss-Newton method, which is rapid.

[0046] Iterative process: The algorithm starts from the initial guess Initially, the Levenberg-Marquardt (LM) algorithm is used to evaluate the objective function in each iteration. The algorithm performs iterative optimization to find the solution. It starts from the initial guess... Begin by repeating the following steps: 401. Calculate the residuals and Jacobian matrix: Call the forward model function. Calculate the theoretical potential ratio and residual vector under the current parameters. and Jacobi matrix ,in Forward model function The first-order partial derivative matrix with respect to each parameter.

[0047] in

[0048] S402. Constructing and solving a linear system: Constructing a system of linear equations:

[0049] in And it is a positive definite matrix. Given the identity matrix, solving this system of equations yields the parameter update step size. .

[0050] S403, Trial Update and Evaluation: Calculate Trial Parameters And calculate the objective function value under the new parameters. .

[0051] Determine whether to accept the update: like If so, then accept the update: Let and reduce the damping factor .

[0052] like If so, reject the update: increase the damping factor. and return to step Recalculate step size .

[0053] S404. Check convergence: Determine if the stopping condition is met. If ( Then stop and output the current optimal solution. ; Otherwise, if Stop and output the current optimal solution. ; Otherwise, if Then stop and output the current optimal solution. ; otherwise, Return to step S401 to continue the next iteration.

[0054] The optimal solution vector obtained from the optimization algorithm In the process, the inverted charge is obtained in Substitute the radial position and polar angle at that location into... The theoretical values ​​of the potential at each sensor position are obtained, and then substituted into the forward model to solve for the... Furthermore, the average of the four values ​​can be calculated to reduce calculation errors.

[0055] In one specific implementation, this embodiment simulates the operating condition of a certain type of heavy-duty gas turbine where abnormal charged particles are generated in the compressor section due to blade wear. The required system parameters are as follows: geometric parameters of the closed cylindrical conductor cavity. Cavity radius Axial length of cavity The cavity is theoretically an ideal conductor that is grounded.

[0056] Electrostatic sensor arrangement As per the instruction manual Figure 1 As shown, the cross-section of the four electrostatic sensor electrodes at the midpoint of the axial direction. The electrodes are circumferentially distributed, with a certain radial offset between them and the inner wall to optimize the signal-to-noise ratio. Specifically, the radial coordinates are... Coordinates of each sensor position , .

[0057] Sensor calibration coefficient Due to individual differences and variations in the installation microenvironment, the sensitivity coefficients of each sensor have been calibrated through preliminary experiments, and it is assumed that: , , This coefficient is used to establish the measured voltage peak value. With theoretical potential Conversion relationship .

[0058] Generation of simulated charge measurement data: To verify the inversion accuracy of the method of the present invention, a simulated charged particle is preset as the inversion target: Simulated charge ; Simulated spatial location ; Substituting the above parameters into the forward analytical model established in this invention, the theoretical potential values ​​at the four sensor locations are calculated. According to the formula Generate a simulated vector of measured voltage peaks: ; 3. Inversion Calculation Process The inversion process of the method of this invention is as shown in the appendix to the specification. Figure 1 As shown, the specific steps are as follows: Upper computer data input: a. Input geometric parameters Sensor coordinates Calibration coefficient ; b. Input the measured peak potential vector ; c. Set the initial guess values ​​for the parameters to be inverted. ; Construct the objective function: The objective function is defined as the sum of squares of the differences between the relative ratios of measured values ​​and theoretical values:

[0059] Optimization solution: The Levenberg-Marquardt algorithm is used to iteratively optimize and solve the objective function G(X). The iterative process, as described in the patent text, includes calculating the residuals and Jacobian matrix, constructing and solving the linear system equations, tentative updates and evaluations, adaptive adjustment of the damping factor, and convergence determination.

[0060] 4. Inversion Results and Accuracy Analysis

[0061] The optimization algorithm converged after 21 iterations, and the convergence process was stable. The optimal parameter vector obtained through inversion is as follows: Inversion position (0.19m, ) The inverted location information and Substituting the forward model of the first sensor into the inverted charge yields the inverted charge. The relative error between the actual value and the true value is 1.3%.

[0062] The method described in this invention demonstrates effectiveness and accuracy, achieving quantitative inversion of the charge quantity of charged particles within a closed conductive cavity, with a relative error of only 1.3%. The method exhibits good robustness and convergence under simulated noise conditions, and possesses potential for online real-time monitoring applications.

[0063] This invention achieves accurate quantitative inversion of charge: it can accurately calculate the specific charge of abnormally charged particles inside, providing a reliable quantitative indicator for fault assessment; This invention has the ability to spatially locate fault sources: through the inversion algorithm, not only is the amount of charge obtained, but the two-dimensional spatial position of charged particles in the cavity can also be determined simultaneously.

[0064] This invention significantly improves the adaptability and reliability of the system: by constructing an objective function of "ratio of measured value to theoretical value" and introducing individual sensor calibration coefficient S, the common influence of signal baseline drift caused by changes in operating conditions can be eliminated.

[0065] The following points need to be explained: (1) The accompanying drawings of the embodiments of the present invention only involve the structures involved in the embodiments of the present invention. Other structures can refer to the general design.

[0066] (2) For clarity, the thickness of layers or regions is enlarged or reduced in the drawings used to describe embodiments of the invention, i.e., these drawings are not drawn to scale. It is understood that when an element such as a layer, film, region or substrate is referred to as being “above” or “below” another element, the element may be “directly” located “above” or “below” the other element or there may be intermediate elements.

[0067] (3) Where there is no conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other to obtain new embodiments.

[0068] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for inverting the charge quantity of abnormally charged particles in the gas path of a gas turbine, characterized in that, The method involves installing M electrostatic sensors within the gas pipeline of a gas turbine, comprising: S1. Determine the parameter set: The parameter set includes the geometric parameters (G) of the closed conductor cavity, the spatial coordinates (P) of each electrostatic sensor, the potential measurement vector (V) output by the electrostatic sensor, and the initial guess value (X0) of the parameter to be inverted. S2. Construct a positive model function F(X) based on the parameter set to establish the mapping relationship between point charges inside a closed conductor cavity and the potential at any point on the inner wall; S3. Construct the objective function G(X) based on the potential measurement vector (V) output by the electrostatic sensor and the positive model function F(X); S4. Iteratively solve the objective function G(X) using a nonlinear optimization algorithm. By minimizing the objective function G(X), find the optimal parameter vector X that best matches the measured value with the theoretical value. ; S5. Transfer the optimal parameter vector X The charge is obtained by substituting it into the positive model function F(X).

2. The method for inverting the charge quantity of abnormal charged particles in the gas turbine gas path according to claim 1, characterized in that, The initial guessed values ​​(X0) of the parameters to be inverted include: The initially guessed charge (q) of the charged particle and the initially guessed two-dimensional position coordinates of the charged particle. .

3. The method for inverting the charge of abnormal charged particles in the gas turbine gas path according to claim 2, characterized in that, The positive model function F(X) of S2, which constructs the mapping relationship between point charges inside a closed conductive cavity and the potential at any point on the inner wall, based on the parameter set, is as follows: Based on electromagnetic field theory, and combined with the geometric parameters (G) of a closed conductor cavity, a positive model function F(X) is constructed to represent the mapping relationship between point charges inside the closed conductor cavity and the potential at any point on the inner wall.

4. The method for inverting the charge quantity of abnormal charged particles in the gas turbine gas path according to claim 3, characterized in that, The positive model function F(X) is the analytical solution obtained by solving the Poisson equation based on the method of separation of variables and satisfying the Dirichlet boundary conditions, and its expression is formula (1): ； （1） in, The polar coordinates of the projection of the perpendicular distance between a point in space and the z-axis onto the xy-plane; Let θ be the angle between the projection onto the xy-plane and the positive x-axis, z be the displacement along the z-axis, and q be the initially guessed charge of the charged particle, set near the center of the cavity. The vacuum permittivity, For the first kind of m-order modified Bessel function, For the second kind of m-order modified Bessel function, Let n be the coordinates of a point charge in cylindrical coordinates; n is an integer. Where is the axial wave number and L is the pipe length. express The smaller one, express The larger one.

5. The method for inverting the charge quantity of abnormal charged particles in the gas turbine gas path according to claim 4, characterized in that, The initial guess value X0 of the parameter to be inverted is set to .

6. The method for inverting the charge quantity of abnormal charged particles in the gas turbine gas path according to claim 5, characterized in that, The objective function G(X) constructed in S3 based on the potential measurement vector (V) output by the electrostatic sensor and the positive model function F(X) includes: The ratio of M potential measurements is obtained based on the potential measurement vector V output by the electrostatic sensor. ), The ratio of M theoretical potential values ​​is obtained based on the positive model function F(X); Based on the ratio of M potential measurements ( The objective function G(X) is constructed by summing the squares of the differences between the ratios of X to M theoretical potential values.

7. The method for inverting the charge quantity of abnormal charged particles in the gas turbine gas path according to claim 6, characterized in that, In step S4, a nonlinear optimization algorithm is used to iteratively solve the objective function G(X). By minimizing the objective function G(X), the optimal parameter vector X that best matches the measured value with the theoretical value is found. include: The nonlinear optimization algorithm is the Levenberg-Marquardt algorithm; S401. Calculate the theoretical potential value, residual vector r, and Jacobian matrix J under the current parameters; S402, Constructing a system of linear equations Solve for parameter update step size ; in, It is the damping factor; S403. Calculate the objective function value based on the updated parameters, and determine whether to accept the update and adjust the damping factor based on whether the objective function value decreases. S404. Determine whether the convergence condition of the Levenberg-Marquardt algorithm is met. If it is met, stop the iteration and output the result; otherwise, return to step S401 to continue the iteration.

8. The method for inverting the charge quantity of abnormal charged particles in the gas turbine gas path according to claim 7, characterized in that, The expression for the objective function G(X) is formula (2); ；（2） It is the first The measured voltage of each sensor, For the first The conversion coefficient of each sensor, It is the first The theoretical potential at each sensor.

9. The method for inverting the charge quantity of abnormal charged particles in the gas turbine gas path according to claim 8, characterized in that, The installation of M electrostatic sensors within the gas turbine's gas pipeline includes: M=4； Four electrostatic sensors are evenly distributed on the same axial section of the inner wall of the gas pipeline, and the azimuth angles of the four electrostatic sensors on the section are 0°, 90°, 180° and 270° respectively.

10. The method for inverting the charge quantity of abnormal charged particles in the gas turbine gas path according to claim 8, characterized in that, Measure peak voltage With theoretical potential The conversion relationship is given by formula (3): ；（3）。

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