A method, system, device, and medium for monitoring a last stage blade of a low pressure cylinder

Abstract

The application relates to a low-pressure cylinder last-stage blade monitoring method, system, device and medium, wherein the method comprises the following steps: acquiring a blade vibration amplitude sequence based on an eddy current signal; determining a blade vibration mode based on a root mean square correlation coefficient; determining a blade vibration frequency spectrum through a sparse reconstruction method according to a pre-acquired real blade vibration amplitude sequence and an ideal blade high-frequency vibration amplitude sequence; establishing a relationship function according to last-stage blade inlet and outlet temperature, flow boundary conditions and maximum equivalent thermal stress characteristics; determining the current last-stage moving blade thermal stress based on the relationship function according to actual boundary conditions; and determining a low-pressure cylinder last-stage blade monitoring result based on the blade vibration amplitude sequence, the blade vibration mode, the blade vibration frequency spectrum and the last-stage moving blade thermal stress. The low-pressure cylinder last-stage blade high-precision monitoring is realized, and the safe operation of the low-pressure cylinder last-stage blade is guaranteed. The problem of low precision in the low-pressure cylinder last-stage blade monitoring in the related art is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of low-pressure cylinder last-stage blade monitoring, and in particular to a low-pressure cylinder last-stage blade monitoring method, system, device and medium. BACKGROUND

[0002] At present, in order to cope with the increasing demand for deep peak regulation of combined heat and power units, a large number of combined heat and power units have been reformed to have near-zero output of low-pressure cylinders, but long-term operation deviating from the initial design condition has brought challenges to the operation safety of the low-pressure cylinders.

[0003] When the low-pressure cylinder has zero output, the flow field of the last-stage blade is extremely complex, and the steam cannot fill the flow passage to form complex vortex, which is easy to cause outflow, backflow, back-suction and other phenomena, so that the stress of the blade increases sharply. Under the interaction of bending stress, centrifugal force, thermal stress and the like, the blade is deformed and twisted. When the excitation force frequency and the natural frequency coincide or are close to each other, the blade resonates, causing the blade to break. At present, when the low-pressure cylinder is reformed to have zero output, the operation safety of the unit is only judged by monitoring the inlet and outlet steam temperatures of the last-stage blade, the monitoring precision is low, and problems are often found when the blade breaks down and stops running in actual operation.

[0004] Based on the above reasons, the low-pressure cylinder last-stage blade monitoring in the prior art has the problem of low precision. SUMMARY

[0005] Embodiments of the present application provide a low-pressure cylinder last-stage blade monitoring method, system, device and medium to at least solve the problem of low precision in low-pressure cylinder last-stage blade monitoring in related technologies.

[0006] In a first aspect, the embodiments of the present application provide a low-pressure cylinder last-stage blade monitoring method, which comprises:

[0007] The high-frequency acquisition board card samples the eddy current signal of the low-pressure cylinder last-stage moving blade diaphragm, and the blade vibration amplitude sequence is obtained based on the eddy current signal;

[0008] The root mean square correlation coefficient of the adjacent circle interblade angle is measured by the plurality of sensors, and the blade vibration mode is determined based on the root mean square correlation coefficient;

[0009] The blade vibration frequency spectrum is determined by a sparse reconstruction method according to a pre-acquired real blade vibration amplitude sequence and an ideal blade high-frequency vibration amplitude sequence;

[0010] The relationship function is established according to the inlet and outlet temperature, flow boundary conditions and maximum equivalent thermal stress characteristics of the last-stage blade, and the current last-stage moving blade thermal stress is determined based on the relationship function according to the actual boundary conditions;

[0011] Determine a low-pressure cylinder last-stage blade monitoring result based on the blade vibration amplitude sequence, the blade vibration mode, the blade vibration frequency spectrum, and the last-stage blade thermal stress.

[0012] In an embodiment, the electric eddy current signal sampling on the low-pressure cylinder last-stage blade diaphragm by the high-frequency acquisition board card, based on the electric eddy current signal, obtains a blade vibration amplitude sequence, including:

[0013] The electric eddy current signal arranged on the last-stage blade diaphragm is sampled by the high-frequency acquisition board card, and the continuous electric voltage signal of the electric eddy current is converted into a discrete digital signal;

[0014] The discrete digital signal is compared with a blade reference threshold to obtain a blade arrival sequence of the electric eddy current;

[0015] According to the blade arrival sequence and a reference keying signal of the turbine main shaft, a blade vibration time difference sequence is obtained;

[0016] According to the blade vibration time difference sequence and a reference angular velocity, a blade vibration amplitude sequence is obtained.

[0017] In an embodiment, the root mean square correlation coefficient of the adjacent circle inter-blade angle is measured by the plurality of sensors, and the blade vibration mode is determined based on the root mean square correlation coefficient, including:

[0018] According to the blade tip timing principle, a first circle vibration sequence and a second circle vibration sequence measured by the plurality of sensors of the adjacent circle are obtained;

[0019] According to the reference keying signal sequence, the first circle vibration sequence is converted into a first circle blade included angle sequence, and the second circle vibration sequence is converted into a second circle blade included angle sequence;

[0020] The first circle blade included angle sequence and the second circle blade included angle sequence are subjected to Pearson correlation coefficient calculation to obtain a correlation coefficient of the adjacent circle blade included angle sequence;

[0021] The correlation coefficient of the adjacent circle blade included angle sequence is subjected to root mean square calculation to determine the blade vibration mode.

[0022] In an embodiment, the correlation coefficient of the adjacent circle blade included angle sequence is subjected to root mean square calculation to determine the blade vibration mode, including:

[0023] The correlation coefficient of the adjacent circle blade included angle sequence is subjected to root mean square calculation to obtain a root mean square coefficient;

[0024] When the root mean square coefficient is greater than or equal to a preset coefficient, the blade vibration mode is determined as a synchronous vibration mode;

[0025] When the root mean square coefficient is less than the preset coefficient, it is determined that the blade vibration mode is an asynchronous vibration mode.

[0026] In an embodiment, the blade vibration frequency spectrum is determined according to a pre-acquired real blade vibration amplitude sequence and an ideal blade high-frequency vibration amplitude sequence by a sparse reconstruction method, comprising:

[0027] According to the blade tip timing principle, a real vibration amplitude sequence actually monitored by a plurality of sensors in a preset rotation period and an ideal vibration amplitude sequence in an ideal case are acquired;

[0028] A perception matrix is calculated according to the actual installation position of the sensors to acquire the relationship between the real vibration amplitude sequence and the ideal vibration amplitude sequence;

[0029] According to an inverse Fourier transform matrix, the relationship between the real vibration amplitude sequence and an ideal vibration frequency spectrum is acquired;

[0030] According to a sparse reconstruction method, a characteristic frequency spectrum is calculated with a 1-norm minimum of the ideal vibration frequency spectrum to determine the blade vibration frequency spectrum.

[0031] In an embodiment, the relationship between the real vibration amplitude sequence and the ideal vibration amplitude sequence is acquired according to the actual installation position of the sensors to calculate a perception matrix, comprising:

[0032] According to the installation angle of the eddy current sensor on the blade diaphragm, a perception matrix is constructed;

[0033] According to the perception matrix, a transfer matrix of the real vibration amplitude sequence and the ideal vibration amplitude sequence is established to acquire the relationship between the real vibration amplitude sequence and the ideal vibration amplitude sequence.

[0034] In an embodiment, the relationship function is established according to the last-stage blade inlet and outlet temperature, flow boundary conditions and maximum equivalent thermal stress characteristics, and the current last-stage blade thermal stress is determined according to the actual boundary conditions based on the relationship function, comprising:

[0035] According to the profile lines of the last-stage stationary blade and the moving blade, a three-dimensional model of the stationary blade and the moving blade is established;

[0036] The three-dimensional model is meshed, and the number of meshes at key parts of the blade through-flow is encrypted, and the irrelevance of the meshes is verified, wherein the key parts are parts that generate a larger flow effect;

[0037] Fluid-solid coupling analysis is performed to determine the maximum equivalent thermal stress characteristics of the last-stage moving blade under variable working conditions;

[0038] According to the maximum equivalent thermal stress characteristic and actual measured inlet and outlet temperature and flow boundary conditions of the last stage blade, a relationship function is established;

[0039] According to the current actual boundary conditions, the current last stage blade thermal stress is determined based on the relationship function.

[0040] In a second aspect, the embodiments of the present application provide a low-pressure cylinder last stage blade monitoring system, the system comprising a blade vibration amplitude sequence module, a blade vibration mode module, a blade vibration spectrum module, a last stage blade thermal stress module and a monitoring result module, wherein:

[0041] The blade vibration amplitude sequence module is configured to sample an eddy current signal of a low-pressure cylinder last stage blade diaphragm through a high-frequency acquisition board card, and obtain a blade vibration amplitude sequence based on the eddy current signal.

[0042] The blade vibration mode module is configured to measure a root mean square correlation coefficient of an adjacent circle interblade angle through a plurality of sensors, and determine a blade vibration mode based on the root mean square correlation coefficient.

[0043] The blade vibration spectrum module is configured to determine a blade vibration spectrum through a sparse reconstruction method according to a real blade vibration amplitude sequence and an ideal blade high-frequency vibration amplitude sequence obtained in advance.

[0044] The last stage blade thermal stress module is configured to establish a relationship function according to a last stage blade inlet and outlet temperature and flow boundary condition and a maximum equivalent thermal stress characteristic, and determine a current last stage blade thermal stress based on the relationship function according to actual boundary conditions.

[0045] The monitoring result module is configured to determine a low-pressure cylinder last stage blade monitoring result based on the blade vibration amplitude sequence, the blade vibration mode, the blade vibration spectrum and the last stage blade thermal stress.

[0046] In a third aspect, the embodiments of the present application provide a computer device, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor implements a low-pressure cylinder last stage blade monitoring method according to the first aspect.

[0047] In a fourth aspect, the embodiments of the present application provide a computer readable storage medium, which stores a computer program executable by a processor to implement a low-pressure cylinder last stage blade monitoring method according to the first aspect.

[0048] The low-pressure cylinder last stage blade monitoring method, system, device and medium provided by the embodiments of the present application at least have the following technical effects.

[0049] The low-pressure cylinder last-stage blade monitoring method comprises the following steps: collecting an eddy current signal of a last-stage blade diaphragm of a low-pressure cylinder by a high-frequency acquisition board, obtaining a blade vibration amplitude sequence based on the eddy current signal, measuring a root mean square correlation coefficient of an inter-blade angle of adjacent rings by a plurality of sensors, determining a blade vibration mode based on the root mean square correlation coefficient, determining a blade vibration frequency spectrum by a sparse reconstruction method according to a real blade vibration amplitude sequence and an ideal blade high-frequency vibration amplitude sequence obtained in advance, establishing a relationship function according to a last-stage blade inlet and outlet temperature, a flow boundary condition and a maximum equivalent thermal stress characteristic, determining a current last-stage blade thermal stress based on the relationship function according to an actual boundary condition, and determining a low-pressure cylinder last-stage blade monitoring result based on the blade vibration amplitude sequence, the blade vibration mode, the blade vibration frequency spectrum and the last-stage blade thermal stress. The low-pressure cylinder last-stage blade high-precision monitoring is realized, and the safe operation of the low-pressure cylinder last-stage blade is ensured. The problem of low accuracy in the low-pressure cylinder last-stage blade monitoring in the related art is solved.

[0050] The details of one or more embodiments of the application are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the application will be apparent from the description of the application and from the drawings, and from the claims. BRIEF DESCRIPTION OF DRAWINGS

[0051] The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings:

[0052] Figure 1 is a flow chart of a low-pressure cylinder last-stage blade monitoring method according to an embodiment of the application;

[0053] Figure 2 is a flow chart of step S101 according to an exemplary embodiment;

[0054] Figure 3 is a flow chart of step S102 according to an exemplary embodiment;

[0055] Figure 4 is a flow chart of step S103 according to an exemplary embodiment;

[0056] Figure 5 is a flow chart of step S104 according to an exemplary embodiment;

[0057] Figure 6 is a block diagram of a low-pressure cylinder last-stage blade monitoring system according to an exemplary embodiment;

[0058] Figure 7 is a block diagram of an electronic device according to an exemplary embodiment. DETAILED DESCRIPTION

[0059] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be described and illustrated below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application. Based on the embodiments provided by the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort belong to the scope of the present application.

[0060] Obviously, the accompanying drawings in the following description are only some examples or embodiments of the present application, and for those of ordinary skill in the art, the present application can also be applied to other similar scenarios without creative effort based on the accompanying drawings. In addition, it can be understood that although the efforts made in the development process can be complex and lengthy, for those of ordinary skill in the art related to the content disclosed in the present application, some design, manufacture or production changes based on the technical content disclosed in the present application are only routine technical means, and should not be understood as insufficient disclosure of the content disclosed in the present application.

[0061] In the present application, "embodiment" means that the specific features, structures or characteristics described in conjunction with the embodiment can be included in at least one embodiment of the present application. The phrase appears at various places in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment to other embodiments. It is explicitly and implicitly understood by those of ordinary skill in the art that the embodiments described in the present application can be combined with other embodiments without conflict.

[0062] Unless otherwise defined, technical terms and scientific terms used in the present application shall have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. The terms "a", "an", "one", "this", and similar referents in the context of describing the application are to be construed to be open-ended, referring to one or more than one, unless otherwise noted. The terms "including", "comprising", "having" and variations thereof in this application are meant to encompass the possibility of non-exclusive inclusion, such that processes, methods, systems, products, or apparatuses that comprise a series of steps or modules (units) are not limited to only those steps or units that are listed, but can also include additional steps or units not listed, or can also include other steps or units inherent to the processes, methods, products, or apparatuses. The terms "connected", "coupled", and similar terms in this application are not limited to direct or physical connections, but can include electrical connections, whether direct or indirect. The term "multiple" in this application refers to two or more. The term "and / or" describes the association relationship of the associated objects, which means that there can be three relationships, for example, "A and / or B" can mean that A exists alone, A and B exist together, and B exists alone. The character " / " generally represents an "or" relationship between the associated objects. The terms "first", "second", "third", and the like in this application are only to distinguish similar objects, and do not represent a specific order of the objects.

[0063] In a first aspect, the embodiments of the present application provide a low-pressure cylinder last-stage blade monitoring method, Figure 1 is a flow chart of low-pressure cylinder last-stage blade monitoring, as Figure 1 shown, a low-pressure cylinder last-stage blade monitoring method comprises:

[0064] Step S101, the high-frequency acquisition board card is used to sample the eddy current signal of the low-pressure cylinder last-stage moving blade diaphragm, and the blade vibration amplitude sequence is obtained based on the eddy current signal.

[0065] Step S102, the root mean square correlation coefficient of the adjacent circle inter-blade angle is measured by the plurality of sensors, and the blade vibration mode is determined based on the root mean square correlation coefficient.

[0066] Step S103, according to the real blade vibration amplitude sequence and the ideal blade high-frequency vibration amplitude sequence obtained in advance, the blade vibration frequency spectrum is determined by the sparse reconstruction method.

[0067] Step S104, the relationship function is established according to the last-stage blade inlet and outlet temperature, flow boundary condition and maximum equivalent thermal stress characteristic, and the current last-stage moving blade thermal stress is determined based on the relationship function according to the actual boundary condition.

[0068] Step S105, determining the low-pressure cylinder last-stage blade monitoring result based on the blade vibration amplitude sequence, the blade vibration mode, the blade vibration spectrum and the last-stage blade thermal stress.

[0069] In summary, the application embodiment provides a low-pressure cylinder last-stage blade monitoring method. The high-frequency acquisition board card samples the eddy current signals of the low-pressure cylinder last-stage moving blade diaphragm, obtains the blade vibration amplitude sequence based on the eddy current signals, measures the root mean square correlation coefficients of the adjacent circle blade inter-angle through multiple sensors, determines the blade vibration mode based on the root mean square correlation coefficients, determines the blade vibration spectrum through the sparse reconstruction method according to the pre-obtained real blade vibration amplitude sequence and ideal blade high-frequency vibration amplitude sequence, establishes a relationship function according to the last-stage blade inlet and outlet temperature, flow boundary conditions and maximum equivalent thermal stress characteristics, determines the current last-stage moving blade thermal stress based on the relationship function according to the actual boundary conditions, and determines the low-pressure cylinder last-stage blade monitoring result based on the blade vibration amplitude sequence, the blade vibration mode, the blade vibration spectrum and the last-stage moving blade thermal stress. The low-pressure cylinder last-stage blade high-precision monitoring is realized, and the safe operation of the low-pressure cylinder last-stage blade is ensured. The problem of low accuracy in the related art low-pressure cylinder last-stage blade monitoring is solved.

[0070] Figure 2 is a flow chart of step S101 according to an exemplary embodiment, as shown in Figure 2 Step S101, sampling the eddy current signals of the low-pressure cylinder last-stage moving blade diaphragm through the high-frequency acquisition board card, and obtaining the blade vibration amplitude sequence based on the eddy current signals. Specifically, the following steps are included:

[0071] Step S1011, sampling the eddy current signals arranged on the last-stage moving blade diaphragm through the high-frequency acquisition board card, and converting the continuous voltage signals of the eddy current into discrete digital signals.

[0072] Optionally, a plurality of eddy current probes are installed on the low-pressure cylinder last-stage moving blade diaphragm at intervals, and three eddy current probes are installed in the application embodiment. The high-frequency acquisition board card samples the eddy current signals arranged on the last-stage moving blade diaphragm, and converts the continuous voltage signals of the eddy current into discrete digital signals. Sampling the eddy current signals through the high-frequency acquisition board card can ensure that the details of the slight vibration of the blade during high-speed rotation are captured. By comparing the discrete digital signals with the reference threshold value reached by the blade, it can be accurately judged when each blade passes the position of the eddy current probe.

[0073] Step S1012, comparing the discrete digital signals with the reference threshold value reached by the blade to obtain the blade arrival sequence of the eddy current.

[0074] Optionally, the acquired discrete digital quantity signal is compared with the blade reaching reference threshold value, and the blade reaching sequence t1, t2, t3 measured by the three eddy current sensors is obtained. Specifically, the discrete digital quantity signal is compared with the reference threshold value, and the digital quantity point greater than or equal to the reference threshold value is obtained as the blade reaching sequence point. By creating a time mark for each blade, the time point at which the blade passes through the probe is recorded, thereby providing basic data for subsequent vibration analysis.

[0075] Step S1013: According to the blade reaching sequence and the reference keying signal of the turbine main shaft, a blade vibration time difference sequence is obtained.

[0076] Optionally, the blade reaching sequence t1, t2, t3 monitored by the eddy current sensor is subtracted from the reference keying signal t0 on the shaft, and a blade vibration time difference sequence Δt1, Δt2, Δt3 is obtained. By comparing the blade reaching time measured by the eddy current sensor with the reference keying signal (a fixed reference point) on the shaft, the deviation of each blade relative to the ideal position, i.e., the vibration time difference, can be calculated.

[0077] Step S1014: According to the blade vibration time difference sequence and the reference angular velocity, a blade vibration amplitude sequence is obtained.

[0078] Optionally, the blade vibration time difference sequence is multiplied by the reference angular velocity, and a blade vibration amplitude sequence x1, x2, x3 is obtained. By multiplying the blade vibration time difference sequence by the reference angular velocity, the time difference can be converted into the actual vibration displacement, i.e., the vibration amplitude. According to the vibration amplitude, it is helpful to diagnose whether the blade has imbalance, wear or other faults.

[0079] Step S101 realizes real-time monitoring of the blade vibration condition, which helps to discover potential problems in time and prevent blade damage caused by excessive vibration. In addition, through the multi-point vibration data, the problem occurrence position can be more accurately located, thereby assisting fault diagnosis.

[0080] Figure 3 is a flow chart of step S102 according to an exemplary embodiment, as shown in Figure 3 Step S102: The root mean square correlation coefficient of the inter-blade angle of adjacent rings is measured by a plurality of sensors, and the blade vibration mode is determined based on the root mean square correlation coefficient. Specifically, the following steps are included:

[0081] Step S1021: According to the blade tip timing principle, a first ring vibration sequence and a second ring vibration sequence measured by a plurality of sensors of adjacent rings are obtained.

[0082] Optionally, the first ring vibration sequence x 11 , x 21 , x31 and the second circle vibration sequence x 12 , x 22 , x 32 The principle of blade tip timing is to measure the time when the blade tip passes through the sensor, and then calculate the vibration of the blade. The measurement of adjacent circles can help analyze the vibration characteristics of the blade in different rotation periods. Using multiple eddy current sensors (for example, 3) can obtain vibration data at multiple positions, improving the reliability and accuracy of the measurement. By obtaining the first circle and second circle vibration sequences, the vibration in different rotation periods can be compared, which helps to identify the changes in vibration mode.

[0083] Step S1022, according to the reference keying signal sequence, the first circle vibration sequence is converted into the first circle blade angle sequence, and the second circle vibration sequence is converted into the second circle blade angle sequence.

[0084] Optionally, according to the reference keying signal sequence, the first circle vibration sequence x 11 , x 21 , x 31 and the second circle vibration sequence x 12 , x 22 , x 32 are converted into blade angle sequences, the first circle angle sequence θ 11 , θ 21 , θ 31 and the second circle angle sequence θ 12 , θ 22 , θ 32 The reference keying signal is a fixed reference point for determining the initial position of the blade. By comparing the vibration sequence with the reference keying signal, the angle of each blade relative to the reference position can be calculated. The angle sequence of multiple sensors can provide more comprehensive vibration information, which helps to identify the vibration mode of the blade.

[0085] Step S1023, the first circle blade angle sequence and the second circle blade angle sequence are calculated by Pearson correlation coefficient, and the correlation coefficient of the adjacent circle blade angle sequence is obtained.

[0086] Optionally, the Pearson correlation coefficient of the adjacent circle angle sequence is calculated, and the correlation coefficients ρ1, ρ2, ρ3 of the adjacent circle blade angle sequence monitored by the three eddy current sensors are obtained. The Pearson correlation coefficient is a statistical index used to measure the degree of linear correlation between two variables. By calculating the correlation coefficient of the adjacent circle angle sequence, the similarity of the vibration mode between the two circles can be evaluated. By calculating the correlation coefficients ρ1, ρ2, ρ3 of the adjacent circle blade angle sequence, the similarity of the vibration mode between the two circles can be quantified. The correlation coefficient of the angle sequence of multiple sensors can provide a more comprehensive comparison of the vibration mode, which helps to identify the vibration characteristics of the blade.

[0087] In step S1024, the correlation coefficients of the adjacent blade angle sequences are subjected to root mean square calculation to determine the blade vibration mode. In an embodiment, in step S1024, the root mean square of the correlation coefficients of the adjacent blade angle sequences is calculated to obtain the root mean square coefficient. Specifically, when the root mean square coefficient is greater than or equal to a preset coefficient, it is determined that the blade vibration mode is a synchronous vibration mode; when the root mean square coefficient is less than the preset coefficient, it is determined that the blade vibration mode is an asynchronous vibration mode.

[0088] Optionally, the blade vibration mode is determined according to the root mean square coefficient. When the root mean square coefficient is greater than or equal to a preset coefficient, it is synchronous vibration; and when the root mean square coefficient is less than the preset coefficient, it is asynchronous vibration. The root mean square is a statistical method for calculating the average square root of a group of data. By calculating the root mean square of the correlation coefficient, the similarity of the vibration modes of multiple sensors can be comprehensively evaluated. A preset coefficient (for example, 0.5-0.9, which can be 0.9 in the embodiment of the present application) is set to distinguish between synchronous and asynchronous vibration modes. When the root mean square coefficient is greater than or equal to 0.9, it indicates that the vibration modes of adjacent rings are highly similar, i.e., the blades are in a synchronous vibration mode. Asynchronous vibration: when the root mean square coefficient is less than 0.9, it indicates that the vibration modes of adjacent rings are quite different, i.e., the blades are in an asynchronous vibration mode.

[0089] In step S102, through multi-sensor and multi-ring measurement, the vibration of the blades can be accurately monitored, and the reliability and accuracy of the data can be improved. Through statistical analysis methods (such as Pearson correlation coefficient and root mean square calculation), the vibration mode of the blades can be effectively identified, and synchronous and asynchronous vibrations can be distinguished. The identification of the vibration mode helps to discover abnormal vibration of the blades in time, prevents potential failures, and improves the operation safety and reliability of the turbine.

[0090] Figure 4 is a flow chart of step S103 according to an exemplary embodiment, as shown in Figure 4 Step S103, according to the pre-acquired real blade vibration amplitude sequence and ideal blade high-frequency vibration amplitude sequence, determines the blade vibration spectrum through sparse reconstruction. Specifically, the following steps are included:

[0091] In step S1031, according to the blade tip timing principle, a real vibration amplitude sequence actually monitored by a plurality of sensors in a preset rotation period and an ideal vibration amplitude sequence under ideal conditions are obtained.

[0092] Optionally, based on the blade tip timing principle, a plurality of sensor real-time monitored blade vibration amplitude sequence x[300, 1] in a preset rotation period and ideal blade high-frequency vibration amplitude sequence y[2000, 1] are obtained. In the embodiment of the application, the plurality of sensors can be 3, and the preset rotation period can be 100 preset rotation periods. The blade tip timing principle refers to that the vibration amplitude of the blade can be calculated by measuring the time when the blade tip passes through the sensor. A preset rotation period range (for example, 100 rotation periods) is selected, and real vibration data is collected in the range. Assuming the ideal vibration condition of the blade, an ideal vibration amplitude sequence is generated. The blade vibration amplitude sequence x[300, 1] monitored by the plurality of sensors (for example, 3) in 100 rotation periods can reflect the actual vibration condition of the blade. The high-frequency vibration amplitude sequence y[2000, 1] of the blade in the ideal condition is generated for comparison and calibration of the actual data.

[0093] In step S1032, a perception matrix is calculated according to the actual installation position of the sensor to obtain the relationship between the real vibration amplitude sequence and the ideal vibration amplitude sequence. Specifically, the perception matrix is constructed according to the installation angle of the eddy current sensor on the blade diaphragm; and the transfer matrix of the real vibration amplitude sequence and the ideal vibration amplitude sequence is established according to the perception matrix to obtain the relationship between the real vibration amplitude sequence and the ideal vibration amplitude sequence.

[0094] Optionally, the perception matrix Φ is constructed according to the installation angle of the three eddy current sensors on the blade diaphragm; and the transfer matrix of the real-time monitored blade vibration amplitude sequence and the ideal blade high-frequency vibration amplitude sequence x[300, 1] = Φ*y[2000, 1] is established according to the perception matrix Φ. The perception matrix Φ reflects the influence of the sensor position on the vibration signal, and can convert the ideal vibration amplitude sequence y into the real-time monitored vibration amplitude sequence x. Through the transfer matrix x[300, 1] = Φ*y[2000, 1], the mathematical relationship between the real vibration amplitude sequence and the ideal vibration amplitude sequence can be established, which provides a basis for subsequent analysis.

[0095] In step S1033, the relationship between the real vibration amplitude sequence and the ideal vibration spectrum is obtained according to the inverse Fourier transform matrix.

[0096] Optionally, according to the inverse Fourier transform matrix ψ, the relationship between the ideal blade high-frequency vibration amplitude and the frequency spectrum sequence f under ideal conditions is established: y[2000, 1] = ψ * f[2000, 1]. The relationship between the real monitored blade vibration amplitude sequence x and the frequency spectrum sequence f is established: x[300, 1] = Φ * ψ * f[2000, 1]. The ideal vibration amplitude sequence y is converted into the frequency spectrum sequence f by Fourier transform. The relationship between the ideal vibration amplitude sequence y and the frequency spectrum sequence f is established by the inverse Fourier transform matrix ψ. The relationship between the real vibration amplitude sequence x and the frequency spectrum sequence f is established by combining the perception matrix Φ and the inverse Fourier transform matrix ψ: x[300, 1] = Φ * ψ * f[2000, 1]. The vibration amplitude sequence in the time domain is converted into the frequency spectrum sequence in the frequency domain by Fourier transform, which facilitates the analysis of the frequency components of the vibration. The mathematical relationship between the real vibration amplitude sequence and the frequency spectrum sequence is established, which provides a basis for subsequent sparse reconstruction.

[0097] Step S1034, according to the sparse reconstruction method, the characteristic frequency spectrum is determined by calculating the 1-norm minimum of the ideal vibration frequency spectrum.

[0098] Optionally, based on the sparse reconstruction method, the characteristic frequency spectrum f is calculated by minimizing the 1-norm of the ideal vibration frequency spectrum f0. The main characteristic frequency spectrum f1 is extracted from the frequency spectrum sequence f by using the sparse reconstruction method (such as L1-norm minimization). By minimizing the 1-norm of the frequency spectrum sequence f, the sparsest solution is found, i.e. the main vibration frequency components. Through the sparse reconstruction method, the main characteristic frequency spectrum can be extracted from the complex frequency spectrum, which reflects the main vibration parameters of the blade. It is helpful to diagnose the health status and potential problems of the blade.

[0099] Step S103, by multi-sensor and multi-cycle measurement, the vibration of the blade can be accurately monitored, and the reliability and accuracy of the data can be improved. By Fourier transform and sparse reconstruction, the main vibration frequency spectrum can be effectively extracted from complex vibration data, which is helpful to timely discover abnormal vibration of the blade, prevent potential failure, and improve the safety and reliability of the blade operation.

[0100] Figure 5 is a flow chart of step S104 shown according to an exemplary embodiment, as Figure 5 shown, step S104, according to the last-stage blade inlet and outlet temperature, flow boundary condition and maximum equivalent thermal stress characteristic, a relationship function is established, according to the actual boundary condition, the current last-stage blade thermal stress is determined based on the relationship function. Specifically, the following steps are included:

[0101] Step S1041, according to the profile of the last-stage static blade and the moving blade, a three-dimensional model of the static blade and the moving blade is established.

[0102] Optionally, the Blade Gen module of ANSYS software can be used to create an accurate three-dimensional geometric model based on the profile data of the static and moving blades. ANSYS software is a large general-purpose finite element analysis (FEA) software developed by ANSYS Inc. in the United States. Blade Gen is a module in ANSYS software specifically for blade design. Step S1041 ensures that the geometric parameters of the model are consistent with the actual blades, providing an accurate basis for subsequent simulation analysis. It can include all geometric details of the blades, such as shape, size, angle, etc., to ensure the authenticity and reliability of the model.

[0103] Step S1042, meshing the three-dimensional model, and encrypting the number of grids at key parts of the blade passage, and verifying the irrelevance of the grids, wherein the key parts are parts that produce larger flow effects.

[0104] Optionally, meshing is performed in the TurboGrid module, and the number of grids at key parts of the blade passage is encrypted, and the irrelevance of the grids is verified. Meshing can be performed using the TurboGrid module, especially at key parts of the blade passage (such as blade tips, roots, etc.), to increase the calculation accuracy. By adjusting the grid density, it is ensured that the calculation results do not change significantly due to changes in the grid. By grid encryption, it is ensured that the flow effects and stress distribution of the key parts are accurately captured.

[0105] Step S1043, fluid-structure interaction analysis is performed to determine the maximum equivalent thermal stress characteristics of the last stage moving blade under variable operating conditions.

[0106] Optionally, fluid-structure interaction (FSI, Fluid-Structure Interaction) analysis can be performed in ANSYS software to simulate the influence of fluid on the blade and the structural response of the blade under different operating conditions. The maximum equivalent thermal stress characteristics of the last stage moving blade under variable operating conditions are calculated, considering the influence of thermal stress and mechanical stress. Considering the interaction of fluid flow and structural deformation, a more realistic stress distribution is provided.

[0107] Step S1044, a relationship function is established based on the maximum equivalent thermal stress characteristics and the actual measured inlet and outlet temperature and flow boundary conditions of the last stage blade.

[0108] Optionally, a mathematical relationship model is established between the actual measured inlet and outlet temperature and flow boundary conditions of the last stage blade and the maximum equivalent thermal stress characteristics. Through the relationship function, the maximum equivalent thermal stress of the blade can be quickly estimated under given actual operating conditions without repeating complex CFD simulation. The relationship function can be directly applied to engineering practice to improve the efficiency of monitoring and diagnosis.

[0109] Step S1045, according to the current actual boundary condition, the current last-stage moving blade thermal stress is determined based on the relationship function.

[0110] Optionally, according to the current actual boundary condition (such as inlet and outlet temperature, flow, etc.), the relationship function established in step S1044 is used to calculate and monitor the thermal stress of the last-stage moving blade in real time. The thermal stress state of the blade can be monitored in real time, and potential problems can be found in time. Through real-time monitoring, measures can be taken in advance to prevent blade damage caused by excessive thermal stress and ensure the safe and stable operation of the equipment.

[0111] Step S104 ensures the accuracy of simulation analysis through precise three-dimensional modeling and high-precision meshing. Through fluid-structure interaction analysis, the interaction between fluid and structure is fully considered, and more realistic stress distribution is provided. Through the establishment of the relationship function, the thermal stress of the blade can be quickly evaluated under actual operating conditions, improving the efficiency of monitoring and diagnosis. Real-time monitoring of blade thermal stress is realized, potential problems are found in time, and the safe and stable operation of the equipment is ensured.

[0112] In summary, the application embodiment provides a low-pressure cylinder last-stage blade monitoring method. The low-pressure cylinder last-stage moving blade diaphragm is sampled by a high-frequency acquisition board card, and the blade vibration amplitude sequence is obtained based on the eddy current signal. The root mean square correlation coefficient of the inter-blade angle of adjacent rings is measured by multiple sensors, and the blade vibration mode is determined based on the root mean square correlation coefficient. According to the pre-acquired real blade vibration amplitude sequence and ideal blade high-frequency vibration amplitude sequence, the blade vibration frequency spectrum is determined by the sparse reconstruction method. According to the relationship function established between the last-stage blade inlet and outlet temperature, flow boundary condition and maximum equivalent thermal stress characteristics, the current last-stage moving blade thermal stress is determined based on the relationship function according to the actual boundary condition. Based on the blade vibration amplitude sequence, the blade vibration mode, the blade vibration frequency spectrum and the last-stage moving blade thermal stress, the low-pressure cylinder last-stage blade monitoring result is determined. The low-pressure cylinder last-stage blade high-precision monitoring is realized, and the safe operation of the low-pressure cylinder last-stage blade is ensured. The problem of low accuracy in low-pressure cylinder last-stage blade monitoring in related technologies is solved.

[0113] The beneficial effects of the present application also include: monitoring the vibration and thermal stress of the last stage blade by installing an eddy current sensor on the last stage blade baffle for high-frequency sampling; monitoring the vibration amplitude of the blade in real time based on the blade tip timing principle, and reducing the measurement error through the circumferential arrangement of multiple eddy current sensors; constructing the adjacent circle inter-blade angle sequence, judging the blade vibration mode through the root mean square correlation coefficient measured by multiple sensors, which not only has good anti-interference ability, but also has high resolution of vibration mode recognition; identifying the parameters of the under-sampled blade vibration signal based on the sparse reconstruction method, which has good frequency interval identification and amplitude calculation. The thermal stress characteristics of the unit under variable conditions are analyzed by using computational fluid dynamics software, a relationship function model between the maximum equivalent thermal stress and the key measurement parameters is established, and the thermal stress of the blade is monitored in real time.

[0114] In a second aspect, the embodiments of the present application provide a system for monitoring the last stage blade of the low-pressure cylinder. Figure 6 is a block diagram of a system for monitoring the last stage blade of the low-pressure cylinder according to an exemplary embodiment. As shown in Figure 6 The system includes a blade vibration amplitude sequence module 610, a blade vibration mode module 620, a blade vibration spectrum module 630, a last stage blade thermal stress module 640, and a monitoring result module 650.

[0115] The blade vibration amplitude sequence module 610 is configured to sample the eddy current signal of the last stage blade baffle of the low-pressure cylinder through a high-frequency acquisition board card, and obtain a blade vibration amplitude sequence based on the eddy current signal.

[0116] The blade vibration mode module 620 is configured to measure the root mean square correlation coefficient of the inter-blade angle of the adjacent circle through multiple sensors, and determine the blade vibration mode based on the root mean square correlation coefficient.

[0117] The blade vibration spectrum module 630 is configured to determine the blade vibration spectrum by the sparse reconstruction method according to the real blade vibration amplitude sequence and the ideal blade high-frequency vibration amplitude sequence obtained in advance.

[0118] The last stage blade thermal stress module 640 is configured to establish a relationship function according to the last stage blade inlet and outlet temperature, the flow boundary condition, and the maximum equivalent thermal stress characteristics, determine the current last stage blade thermal stress based on the relationship function according to the actual boundary condition.

[0119] The monitoring result module 650 is configured to determine the monitoring result of the last stage blade of the low-pressure cylinder based on the blade vibration amplitude sequence, the blade vibration mode, the blade vibration spectrum, and the last stage blade thermal stress.

[0120] In conclusion, the low-pressure cylinder last-stage blade monitoring system provided by the embodiments of the present application solves the problem of low accuracy in low-pressure cylinder last-stage blade monitoring in the related art through the blade vibration amplitude sequence module 610, the blade vibration mode module 620, the blade vibration spectrum module 630, the last-stage moving blade thermal stress module 640, and the monitoring result module 650. Specifically, the power prediction file is obtained based on a power prediction model according to historical operation data, and a power prediction file uploading request is triggered; during the power prediction file uploading process, the network connection state and the device state are monitored in real time to obtain real-time monitoring results, and the power prediction file is uploaded according to the target transmission strategy in the transmission strategy library based on the real-time monitoring results; in response to receiving the power uploading file, it is determined whether the power prediction file uploading is successful according to the confirmation signal of the scheduling department; if not, the parameters of the target transmission strategy in the transmission strategy library are adjusted until the power prediction file uploading is successful. Efficient, accurate, and stable uploading of the power prediction file is achieved. The problem of how to dynamically adjust the transmission strategy according to real-time data to improve the data transmission efficiency and stability in the related art is solved.

[0121] It should be noted that the system for monitoring the low-pressure cylinder last-stage blade provided by the embodiments of the present application is used to implement the above-mentioned embodiments, and will not be described again. As used above, the terms "module", "unit", "sub-unit", and the like can be a combination of software and / or hardware that implements a predetermined function. Although the devices described in the above embodiments are preferably implemented in software, hardware, or a combination of software and hardware can also be implemented and conceived.

[0122] In a third aspect, the embodiments of the present application provide an electronic device, Figure 7 is a block diagram of an electronic device according to an exemplary embodiment. As Figure 7 indicated, the electronic device can include a processor 71 and a memory 72 storing computer program instructions.

[0123] Specifically, the above-mentioned processor 71 can include a central processing unit (CPU), or an application specific integrated circuit (ASIC), or can be configured as one or more integrated circuits that implement the embodiments of the present application.

[0124] The memory 72 can include a mass storage for data or instructions. By way of example, and without limitation, the memory 72 can include a hard disk drive (HDD), a floppy disk drive, a solid-state drive (SSD), a flash drive, a compact disc (CD) or DVD, a tape, a magnetic or optical or magneto-optical storage or a combination of two or more of these. The memory 72 can be removable and / or built-in (or fixed) where appropriate. The memory 72 can be internal or external at appropriate. In particular embodiments, the memory 72 is a nonvolatile memory. In particular embodiments, the memory 72 includes a Read-Only Memory (ROM) and a Random-Access Memory (RAM). Where appropriate, this ROM can be mask programmed ROM, Programmable ROM (PROM), Erasable Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), Electrically Alterable ROM (EAROM), or FLASH memory or a combination of two or more of these. Where appropriate, this RAM can be Static Random-Access Memory (SRAM) or Dynamic Random-Access Memory (DRAM), which can be Fast Page Mode Dynamic Random-Access Memory (FPMDRAM), Extended Data Output Dynamic Random-Access Memory (EDODRAM), Synchronous Dynamic Random-Access Memory (SDRAM), or the like.

[0125] The memory 72 can be used to store or buffer various data files required for processing and / or communication, and possible computer program instructions executed by the processor 71.

[0126] The processor 71 realizes the low-pressure cylinder last-stage blade monitoring method in any of the above embodiments by reading and executing the computer program instructions stored in the memory 72.

[0127] In an embodiment, the low-pressure cylinder last-stage blade monitoring device can further include a communication interface 73 and a bus 70. As shown in the figure, the processor 71, the memory 72, and the communication interface 73 are connected through the bus 70 and complete communication with each other. Figure 7

[0128] The communication interface 73 is used to realize communication between various modules, devices, units, and / or equipment in the embodiments of the present application. The communication interface 73 can also realize data communication with other components, such as external devices, image / data acquisition devices, databases, external storage, and image / data processing workstations, etc.

[0129] ​Bus 70 includes hardware, software, or both, to couple various components of a low-pressure cylinder last-stage blade monitoring apparatus to one another and / or to one or more other computer systems or networks. While bus 70 is shown for the sake of clarity as a single bus, bus 70 can include a combination of buses, including, for example, an Accelerated Graphics Port (AGP) or other graphics bus, an Extended Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), a Hyper Transport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an InfiniBand (IB) interconnect, a Low Pin Count (LPC) bus, a memory bus, a Micro Channel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association local (VLB) bus, or another suitable bus or interconnect, or a combination of buses or interconnects. Bus 70 can include one or more buses, where appropriate. Although this application describes and shows a particular bus, this application contemplates any suitable bus or interconnect.

[0130] In a fourth aspect, an embodiment of the present application provides a computer readable storage medium, having stored thereon a program, wherein the program is executed by a processor to implement the low-pressure cylinder last-stage blade monitoring method according to the first aspect.

[0131] More particular, the computer readable storage medium can include, but is not limited to, a portable disc, a hard disk, a random access memory, a read-only memory, an erasable programmable read-only memory, an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0132] In possible implementation manners, the application can also be implemented in the form of a program product, which includes program codes for causing a terminal device to perform steps of a low-pressure cylinder last-stage blade monitoring method provided by the first aspect when the program product is run on the terminal device.

[0133] The program codes for executing the application can be written in any combination of one or more programming languages, and can be executed completely on a user device, partially on a user device, as a stand-alone software package, partially on a user device and partially on a remote device, or completely on a remote device.

[0134] The technical features of the above embodiments can be combined in any manner. To make the description concise, all possible combinations of the technical features in the above embodiments are not described, however, as long as the combinations of the technical features do not exist in contradiction, they shall be considered as falling within the scope of the present application.

[0135] The above embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it shall not be understood as a limitation on the patent scope of the present application. It should be noted that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present application, and these shall fall within the protection scope of the present application. Therefore, the patent protection scope of the present application shall be subject to the appended claims.

Claims

1. A method of monitoring a last stage blade of a low pressure cylinder, characterized by, The method comprises: sampling the eddy current signal of the last stage blade diaphragm of the low-pressure cylinder through a high-frequency acquisition board, and acquiring a blade vibration amplitude sequence based on the eddy current signal; measuring the root-mean-square correlation coefficient of the inter-blade angle of adjacent rings through multiple sensors, and determining a blade vibration mode based on the root-mean-square correlation coefficient; determining a blade vibration spectrum through a sparse reconstruction method according to a pre-acquired real blade vibration amplitude sequence and an ideal blade high-frequency vibration amplitude sequence; establishing a relationship function according to the temperature and flow boundary conditions of the last stage blade and the maximum equivalent thermal stress characteristics, and determining the current thermal stress of the last stage blade based on the relationship function according to the actual boundary conditions; determining a low-pressure cylinder last stage blade monitoring result based on the blade vibration amplitude sequence, the blade vibration mode, the blade vibration spectrum and the thermal stress of the last stage blade.

2. The method of claim 1, wherein, The method of sampling the eddy current signal of the last stage blade diaphragm of the low-pressure cylinder through a high-frequency acquisition board, and acquiring a blade vibration amplitude sequence based on the eddy current signal comprises: sampling the eddy current signal arranged on the last stage blade diaphragm through a high-frequency acquisition board, and converting the continuous voltage signal of the eddy current into a discrete digital signal; comparing the discrete digital signal with a blade reference threshold to acquire a blade arrival sequence of the eddy current; acquiring a blade vibration time difference sequence according to the blade arrival sequence and a reference keying signal of the turbine main shaft; acquiring a blade vibration amplitude sequence according to the blade vibration time difference sequence and a reference angular velocity.

3. The method of claim 1, wherein, The method of measuring the root-mean-square correlation coefficient of the inter-blade angle of adjacent rings through multiple sensors, and determining a blade vibration mode based on the root-mean-square correlation coefficient comprises: acquiring a first ring vibration sequence and a second ring vibration sequence measured by multiple sensors of adjacent rings according to the blade tip timing principle; converting the first ring vibration sequence into a first ring blade included angle sequence and converting the second ring vibration sequence into a second ring blade included angle sequence according to a reference keying signal sequence; performing Pearson correlation coefficient calculation on the first ring blade included angle sequence and the second ring blade included angle sequence to acquire a correlation coefficient of the adjacent ring blade included angle sequence; performing root-mean-square calculation on the correlation coefficient of the adjacent ring blade included angle sequence to determine a blade vibration mode.

4. The method of claim 3, wherein, The method of performing root-mean-square calculation on the correlation coefficient of the adjacent ring blade included angle sequence to determine a blade vibration mode comprises: performing root-mean-square calculation on the correlation coefficient of the adjacent ring blade included angle sequence to acquire a root-mean-square coefficient; when the root-mean-square coefficient is greater than or equal to a preset coefficient, determining that the blade vibration mode is a synchronous vibration mode; when the root-mean-square coefficient is less than the preset coefficient, determining that the blade vibration mode is an asynchronous vibration mode.

5. The method of claim 1, wherein, The method of determining a blade vibration spectrum through a sparse reconstruction method according to a pre-acquired real blade vibration amplitude sequence and an ideal blade high-frequency vibration amplitude sequence comprises: acquiring a real vibration amplitude sequence actually monitored by a plurality of sensors within a preset rotation period and an ideal vibration amplitude sequence under ideal conditions according to the blade tip timing principle; According to the actual installation position of the sensor, a perception matrix is calculated to obtain a relationship between the real vibration amplitude sequence and the ideal vibration amplitude sequence; According to the inverse matrix of Fourier transform, a relationship between the real vibration amplitude sequence and the ideal vibration frequency spectrum is obtained; According to a sparse reconstruction method, a characteristic frequency spectrum is calculated with a 1-norm minimum of the ideal vibration frequency spectrum to determine the blade vibration frequency spectrum.

6. The method of claim 5, wherein, The method further includes the following steps: According to the installation angle of the eddy current sensor on the blade diaphragm, a perception matrix is constructed; According to the perception matrix, a transfer matrix of the real vibration amplitude sequence and the ideal vibration amplitude sequence is established to obtain the relationship between the real vibration amplitude sequence and the ideal vibration amplitude sequence.

7. The method of claim 1, wherein, The method further includes the following steps: According to the profile lines of the last-stage stationary blade and the last-stage moving blade, a three-dimensional model of the stationary blade and the moving blade is established; The three-dimensional model is meshed, and the number of meshes at key flow-through positions of the blade is encrypted, and the irrelevance of the meshes is verified, wherein the key positions are positions that generate a larger flow effect; Fluid-solid coupling analysis is performed to determine the maximum equivalent thermal stress characteristics of the last-stage moving blade under variable working conditions; A relationship function is established according to the maximum equivalent thermal stress characteristics and the actual measured last-stage blade inlet and outlet temperature and flow boundary conditions; The current last-stage moving blade thermal stress is determined according to the current actual boundary conditions and the relationship function.

8. A low pressure turbine last stage blade monitoring system, characterized by, The system includes a blade vibration amplitude sequence module, a blade vibration mode module, a blade vibration frequency spectrum module, a last-stage moving blade thermal stress module, and a monitoring result module. The blade vibration amplitude sequence module is configured to sample an eddy current signal of the last-stage moving blade diaphragm of the low-pressure cylinder through a high-frequency acquisition board card, and obtain a blade vibration amplitude sequence based on the eddy current signal. The blade vibration mode module is configured to measure a root-mean-square correlation coefficient of adjacent inter-blade angles through a plurality of sensors, and determine a blade vibration mode based on the root-mean-square correlation coefficient. The blade vibration frequency spectrum module is configured to determine a blade vibration frequency spectrum through a sparse reconstruction method based on a pre-obtained real blade vibration amplitude sequence and an ideal blade high-frequency vibration amplitude sequence. The last-stage moving blade thermal stress module is configured to establish a relationship function according to the maximum equivalent thermal stress characteristics and the last-stage blade inlet and outlet temperature and flow boundary conditions, and determine a current last-stage moving blade thermal stress based on the relationship function and actual boundary conditions. The monitoring result module is configured to determine a low-pressure cylinder last-stage blade monitoring result based on the blade vibration amplitude sequence, the blade vibration mode, the blade vibration frequency spectrum, and the last-stage moving blade thermal stress.

9. An electronic device, comprising: The system includes a memory and a processor, a computer program stored on the memory and executable on the processor, and the processor executes the computer program to implement the low-pressure cylinder last-stage blade monitoring method according to any one of claims 1 to 7.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program, when executed by the processor, implements a low-pressure cylinder last-stage blade monitoring method according to any one of claims 1 to 7.

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