CWT-PSDT-based method and system for monitoring working frequency of hydro-generator

Abstract

The present application belongs to the technical field of hydropower equipment monitoring and diagnosis, and specifically provides a CWT-PSDT-based working frequency monitoring method and system for a hydro-generator, comprising: arranging vibration acceleration sensors at key positions of a stator of the hydro-generator set; collecting vibration acceleration time-history signals of the set under different operating conditions; performing CWT analysis on the vibration acceleration time-history signals to obtain a time-frequency distribution diagram of the signals and identify an energy-concentrated dominant frequency interval as a target frequency band; calculating PSDT functions between different measuring points for the target frequency band to obtain two groups of PSDT function curves and identifying characteristic frequencies under operating conditions of the set through the PSDT function curves; and combining and analyzing CWT energy characteristics and PSDT characteristics to execute hierarchical monitoring logic. The present application can effectively distinguish normal forced responses from abnormal structural resonances under strong background noise and complex excitation environments, and realize precise quantitative evaluation of operating conditions of the set.

Description

Technical Field

[0001] This invention belongs to the field of monitoring and diagnostic technology for hydropower equipment, specifically, it relates to a method and system for monitoring the operating frequency of a hydro-generator based on CWT-PSDT. Background Technology

[0002] Hydropower is a power generation technology that aligns with my country's current situation and meets the needs of environmental protection and energy conservation in its social development. It boasts significant advantages in both economic and social benefits. The safe, stable, and efficient operation of hydropower stations is directly related to people's livelihoods and economic issues. Vibration monitoring of hydro-turbine generator units is one of the key technologies to ensure the safe and stable operation of hydropower stations. Specifically, it involves real-time monitoring and analysis of the frequency of the hydro-turbine generator units to promptly detect potential faults or anomalies, thereby enabling effective preventative measures to reduce unplanned downtime, extend equipment lifespan, and ensure the continuity and reliability of power production.

[0003] Continuous Wavelet Transform (CWT): CWT is a time-frequency analysis tool that transforms signals from the time domain to the time-frequency domain, providing local information about the signal in both time and frequency. Compared to Fourier Transform, CWT is particularly suitable for processing non-stationary signals (such as vibration responses, impact signals, etc.).

[0004] Power spectral density transfer ratio (PSDT): System parameters are identified using only the transfer ratio function of different reference outputs under the same operating conditions. This eliminates the need for multiple tests on the actual engineering structure, making it easier to operate in practical applications.

[0005] Continuous wavelet transform (CWT) analysis alone primarily focuses on characterizing the time-frequency features of the signal itself, lacking the ability to separate the excitation from the inherent structural characteristics from a system dynamics perspective. In generator vibration signals, strong power grid frequency excitation (e.g., 50Hz) may continuously exhibit high energy in the time spectrum, which can easily mask or interfere with the identification of the true structural modes, making it very difficult to directly and accurately identify system poles from complex time-spectrum diagrams. Furthermore, using CWT alone to process vibration acceleration signals is affected by the location of the measurement points, leading to discrepancies in the analysis results. In contrast, near the system poles, the PSDT method's function value tends to be the ratio of the mode shapes between the two measurement points, independent of the reference output and the location of the excitation. This unique property can be used to identify modal parameters. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method and system for monitoring the operating frequency of a hydro-generator based on CWT-PSDT, which can effectively distinguish between normal forced response and abnormal structural resonance under strong background noise and complex excitation environment, and realize accurate quantitative assessment of the unit's operating status.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for monitoring the operating frequency of a hydro-generator based on CWT-PSDT, comprising the following steps: Step 1: Install vibration acceleration sensors at key locations on the stator of the hydro-generator unit; Step 2: Collect vibration acceleration time history signals of the unit under different operating conditions; Step 3.1: Perform CWT analysis on the vibration acceleration time history signal to obtain the time-frequency distribution map of the signal and identify the dominant frequency range of energy concentration as the target frequency band; Step 3.2: For the target frequency band, calculate the PSDT function between different measurement points to obtain two sets of PSDT function curves. By identifying the PSDT function curves, the characteristic frequency of the unit under operating conditions can be obtained. Step 4: Combine the CWT energy characteristics obtained in Step 3.1 with the PSDT characteristics identified in Step 3.2 for analysis, and execute the hierarchical monitoring logic.

[0008] In the preferred embodiment, step 4 includes establishing a dominant operating benchmark, identifying potential structural hazards, and eliminating forced interference.

[0009] In a preferred embodiment, the establishment of the dominant operating benchmark is as follows: the frequency point with an amplitude greater than a first preset threshold in the CWT time-frequency graph and a significant stable peak value in the PSDT function curve is defined as the dominant operating characteristic frequency. The current PSDT amplitude and shape of the dominant operating characteristic frequency point are locked as the healthy operating benchmark of the unit. In subsequent monitoring, if the dominant operating characteristic frequency drifts or the PSDT characteristic changes abruptly or drifts, it is determined that the structure of the hydro-generator unit is abnormal, and a benchmark deviation warning is output.

[0010] In a preferred embodiment, the identification of potential structural hazards is as follows: Frequency points whose amplitudes in the CWT time-frequency graph are between a second preset threshold and a first preset threshold, but which exhibit independent peaks in the PSDT function curve, are defined as potential structural modal frequencies. If the second preset threshold is less than the first preset threshold, the potential structural modal frequencies are included in secondary monitoring. In subsequent operation, if the amplitude of the potential structural modal frequency in the CWT shows a continuous increasing trend, it is determined that the external excitation source drift has caused potential resonance to be activated, and a resonance trend warning is output.

[0011] In a preferred embodiment, the elimination of forced interference is defined as follows: frequencies whose amplitudes in the CWT time-frequency graph are between a second preset threshold and a first preset threshold but whose PSDT function curves show no characteristics are identified as forced interference, wherein the second preset threshold is less than the first preset threshold.

[0012] In a preferred embodiment, the first preset threshold is 90% of the maximum frequency value in the CWT time-frequency graph, and the second preset threshold is 30% of the maximum frequency value in the CWT time-frequency graph.

[0013] In a preferred embodiment, in step 3.1, the CWT uses the complex-valued Morlet wavelet basis function.

[0014] In a preferred embodiment, step 3.2, the method for obtaining the characteristic frequency of the unit under operating conditions by identifying the PSDT function curve is as follows: using two sets of PSDT function curves, construct the reciprocal of the PSDT difference function, and the peak value of the reciprocal function is the characteristic frequency of the unit under operating conditions.

[0015] This invention also provides a CWT-PSDT-based hydro-generator operating frequency monitoring system for performing the monitoring method described above, comprising: The sensor module is used to place vibration acceleration sensors at key locations on the stator of the hydro-generator unit to collect vibration acceleration time history signals of the unit under different operating conditions. The data acquisition module, connected to the sensor module, is used to receive and store the vibration acceleration time history signal in real time. The signal processing module includes a CWT analysis unit, which performs continuous wavelet transform analysis on the vibration acceleration time history signal, generates a time-frequency distribution map of the signal, and identifies the dominant frequency range with concentrated energy as the target frequency band; and a PSDT calculation unit, which calculates the power spectral density transfer ratio function between different measurement points for the target frequency band, and obtains at least two sets of PSDT function curves. The characteristic frequency identification module is used to construct a PSDT difference function through two sets of PSDT function curves, perform a reciprocal transformation on the difference function, and determine the characteristic frequency of the unit under operating conditions based on the peak position of the reciprocal function. The graded monitoring module is used to combine the energy characteristics obtained from CWT analysis with the characteristic frequencies identified by PSDT and execute graded monitoring logic. The early warning module is used to generate and output corresponding early warning signals based on the results of hierarchical monitoring.

[0016] The present invention also provides an electronic device, comprising: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the monitoring method described above by executing the computer instructions.

[0017] The present invention provides a method and system for monitoring the operating frequency of a hydro-generator based on CWT-PSDT, which has the following beneficial effects: 1. This invention breaks through the limitation of traditional vibration monitoring that only focuses on amplitude exceeding the standard. It utilizes CWT to lock the dominant characteristic frequency under different operating conditions and combines it with PSDT to extract the system transmission characteristics at that frequency as a healthy operating benchmark. This method ingeniously transforms the long-standing background forced vibration into a stable probe for detecting changes in structural stiffness, realizing a quantitative assessment of the support status of hydro-generator units in a high-noise environment.

[0018] 2. Through CWT-PSDT analysis, this invention can effectively classify frequencies as dominant characteristic frequencies, potential hazard frequencies, and external harmonic interference. This classification strategy not only avoids misjudging normal responses as resonance faults, but also identifies weak potential resonance hazards from background noise without changing operating conditions, significantly improving the accuracy and foresight of fault warnings.

[0019] 3. This invention does not rely on external excitation equipment or shutdown testing; it can complete the analysis solely using the output response signals during unit operation. Its adaptive dominant frequency locking logic makes it applicable to monitoring rotating machinery of different speeds and types, providing accurate decision-making basis for condition-based maintenance of hydropower station equipment. Attached Figure Description

[0020] The accompanying drawings, which are provided to further illustrate the invention and constitute a part of this invention, do not constitute an undue limitation thereof. In the drawings: Figure 1 This is a flowchart of the algorithm of the present invention; Figure 2 The results of CWT-PSDT recognition under no-load conditions; Figure 3 The results of CWT-PSDT identification under 14kW operating conditions; Figure 4 The results of CWT-PSDT identification under 20kW operating conditions; Figure 5 The results of CWT-PSDT identification under 40kW operating conditions; Figure 6 The results of CWT-PSDT identification under 55kW operating conditions; Figure 7 This serves as a test platform for a mixed-flow turbine model. Figure 8 A schematic diagram showing the sensor placement. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0022] Example 1: This invention provides a method for monitoring the operating frequency of a hydro-generator based on CWT-PSDT. By establishing a healthy operating benchmark and identifying potential modal hazards, it achieves a precise quantitative assessment of the unit's operating status, providing a reference for optimizing and adjusting the hydro-generator unit. Figure 1 As shown, it includes the following steps: Step 1: Install vibration acceleration sensors at key locations on the stator of the hydro-generator unit.

[0023] like Figure 7 This is a test platform for a mixed-flow turbine model. Figure 8 Position the sensors.

[0024] Step 2: Collect vibration acceleration time history signals of the unit under different operating conditions.

[0025] Vibration data of the generator section of a mixed-flow turbine model experimental platform were extracted from sensors at different measuring points under different operating conditions. The sensor sampling frequency was 1000Hz, and the acquisition time was 1 minute. However, due to the large amount of data, only 2000 sampling points were selected for processing. The extracted operating conditions were no-load, and the generator power was 14kW, 20kW, 40kW, and 55kW. Step 3.1: Perform CWT analysis on the vibration acceleration time history signal to obtain the time-frequency distribution map of the signal and identify the dominant frequency range of energy concentration as the target frequency band.

[0026] The definition of continuous wavelet transform is as follows: (1); in: x ( t ) represents the original time-domain signal; ψ(t) represents the mother wavelet function; a This indicates the scale parameter (which controls frequency resolution). a >0); τ Indicates translation parameters (controls time and position); This indicates complex conjugate (which can be ignored for real wavelets); This represents the energy normalization factor.

[0027] In this embodiment, the Morlet wavelet basis function amor is expressed as follows: (2); in: f c Indicates the center frequency (range: 0.5–1.5 Hz); f b This represents the bandwidth parameter (which controls the balance of time and frequency resolution, and its value ranges from 1.0 to 5.0).i The imaginary unit (Morlet wavelet is a complex-valued wavelet).

[0028] Step 3.2: For the target frequency band, calculate the PSDT function between different measurement points to obtain two sets of PSDT function curves. By identifying the PSDT function curves, the characteristic frequency of the unit under operating conditions can be obtained.

[0029] Specifically, the reciprocal of the PSDT difference function is constructed using two sets of PSDT function curves, and the peak value of the reciprocal function is the characteristic frequency of the unit under operating conditions.

[0030] The PSDT method is as follows: For any two output points 、 The response at that point, regarding the reference point The power spectral density transfer ratio is defined as the power spectral density transfer ratio. With power spectrum The ratio: (3); If the reference point is changed Reference point The power spectral density transfer ratio is: (4); It can also be expressed as: (5); when Approaching the system First pole When, its limit satisfies: (6); In the formula: and Degrees of freedom , corresponding Mode shape.

[0031] According to the limit theorem of proportional functions, it can be proved that for functions with the same subscripts in the numerator and denominator... and item Since the limiting ratios are equal, we can conclude that: (7); Similarly, corresponding reference points PSDT function satisfy: (8); Under the same loading condition, subtracting the transfer ratio functions of the response power spectral density at two different reference output measurement points yields: (9); In other words, the extreme points of the system are The zero point. Therefore, according to The reciprocal of the amplitude can determine the poles of the function, which are also the peak values ​​of the function, i.e.: (10).

[0032] The above process can be summarized as follows: Select two different output measurement points and a reference point, and calculate the power spectral density transfer ratio of the two measurement points relative to the reference point, which represents the ratio relationship of vibration response at different locations.

[0033] According to the principles of system dynamics, when the frequency approaches a certain pole of the system (i.e., the characteristic frequency that needs to be determined), the PSDT function exhibits a special limiting property: at the pole, the value of the PSDT function is no longer affected by the excitation location, but tends towards a stability constant determined by the system mode shape. At this point, regardless of which reference point is chosen, the calculated PSDT should converge to the same value at the pole. Subtracting two PSDT functions calculated based on different reference points, at non-pole frequencies, the two function values ​​are different, and the difference is not zero; at pole frequencies, both function values ​​tend towards the same stability constant, and the difference approaches 0. Taking the reciprocal of the difference function, at ordinary frequencies, the difference function has a value, and its reciprocal is also an ordinary value. However, at pole frequencies, the difference function approaches 0, and its reciprocal instantly becomes an extremely large value, approaching infinity (∞). At this point, very obvious sharp peaks appear on the curve of the reciprocal function. The positions corresponding to these peaks are the characteristic frequencies of the system under operating conditions.

[0034] Using the above method, Welch response spectrum estimation was performed on the acceleration time history data at any measurement point on the generator. The window function was a Kaiser window, the signal point length was 2048, the window length was 1024, and the overlap rate was 50%. PSDT function curves under different reference outputs were obtained. Figures 2-6 As shown, it can be seen that under no-load conditions and when the power of the hydro turbine generator is 14kW, 20kW, 40kW and 55kW, the frequency with the greatest impact is around 50Hz.

[0035] Step 4: Combine the CWT energy characteristics obtained in Step 3.1 with the PSDT characteristics identified in Step 3.2 for analysis, and execute the hierarchical monitoring logic.

[0036] The hierarchical monitoring logic includes establishing the dominant operating benchmark, identifying potential structural hazards, and eliminating forced interference, which are specifically divided as follows: 1) Establish the dominant operating benchmark: The frequency point with an amplitude greater than the first preset threshold in the CWT time-frequency graph and a significant stable peak value in the PSDT function curve is defined as the dominant operating characteristic frequency. In this embodiment, the first preset threshold is 90% of the maximum frequency value in the CWT time-frequency graph. The current PSDT amplitude and shape of the dominant operating characteristic frequency point are locked as the healthy operating benchmark of the unit. In subsequent monitoring, if the dominant operating characteristic frequency drifts or the PSDT characteristic changes abruptly or drifts, it is determined that the structure of the hydro-generator unit is abnormal and a benchmark deviation warning is output.

[0037] 2) Identifying potential structural hazards involves searching for frequency points in the CWT time-frequency graph whose amplitude is between the second and first preset thresholds, but which have independent peaks in the PSDT function curve. These are defined as potential structural modal frequencies. The second preset threshold is less than the first preset threshold. In this embodiment, the second preset threshold is 30% of the maximum frequency value in the CWT time-frequency graph. Potential structural modal frequencies are included in secondary monitoring. In subsequent operation, if the amplitude of the potential structural modal frequency in the CWT shows a continuous increasing trend, it is determined that the external excitation source drift has caused the potential resonance to be activated, and a resonance trend warning is output.

[0038] 3) Forced interference removal: Frequency frequencies with amplitudes between the second and first preset thresholds in the CWT time-frequency graph but without characteristics in the PSDT function curve are identified as forced interference, with the second preset threshold being less than the first preset threshold.

[0039] This step classified and determined the different frequency components identified and established a hierarchical monitoring system. The following section provides an explanation based on the specific data. Figures 2-6 : 1. Establishment of global operating benchmark (taking 50Hz as an example) Experimental data shows that, regardless of whether under no-load or grid-connected load conditions, the 50Hz frequency band consistently represents the most significant and stable component in the monitoring signal. During the no-load phase, the signal near 50Hz primarily originates from the mechanical background vibration transmitted to the stator via the auxiliary circulation system of the test bench (such as a power frequency driven water pump) through the base and pipes, as well as the inherent power frequency reference of the test environment. During grid-connected operation, this signal is further superimposed with the electromagnetic excitation force from grid coupling. Although this frequency represents forced vibration rather than structural resonance, its long-term, amplitude-stable background excitation makes it highly suitable as a reference probe for condition monitoring. This method establishes the 50Hz frequency band as the healthy operation reference. As long as the peak shape at this frequency remains stable within the CWT-PSDT method, it demonstrates that there are no structural problems or stiffness degradation in the unit.

[0040] 2. Investigation of potential structural hazards (taking the 150Hz frequency band as an example): Within the 150Hz frequency band, a clear peak was identified in the PSDT spectrum under most operating conditions, but the amplitude at this location was lower in the CWT time-frequency plot. This frequency avoids the power frequency and its harmonics and has clear pole characteristics, indicating it is the unit's true structural inherent mode. The system has marked it as a potential hazard point. Under current operating conditions, this mode is not excited and is in a safe state. However, if the excitation frequency (such as hydraulic pulsation) drifts and covers this area in the future, it may trigger resonance. Therefore, it is also necessary to focus on monitoring the CWT amplitude changes in this frequency band.

[0041] 3. Harmonic interference elimination (taking the 10Hz band as an example): Under all operating conditions, energy is shown in the CWT spectrum, but the PSDT spectrum curve is flat and without peaks. This is determined to be pure harmonic interference, which has no structural characteristic value and is only for reference. If the amplitude changes drastically afterward, components involving the relevant frequencies should be checked.

[0042] In summary, this invention diagnoses hydro-generators using the CWT-PSDT method, not only identifying the dominant vibration frequency but also achieving qualitative classification of the vibration characteristics. This hierarchical early warning mechanism assists maintenance personnel in quickly distinguishing spectral components, greatly improving the intelligence level of hydro-generator health monitoring.

[0043] Example 2: This embodiment provides a CWT-PSDT-based hydro-generator operating frequency monitoring system for executing the monitoring method described in Embodiment 1, including: The sensor module is used to place vibration acceleration sensors at key locations on the stator of the hydro-generator unit to collect vibration acceleration time history signals of the unit under different operating conditions. The data acquisition module, connected to the sensor module, is used to receive and store the vibration acceleration time history signal in real time. The signal processing module includes a CWT analysis unit, which performs continuous wavelet transform analysis on the vibration acceleration time history signal, generates a time-frequency distribution map of the signal, and identifies the dominant frequency range with concentrated energy as the target frequency band; and a PSDT calculation unit, which calculates the power spectral density transfer ratio function between different measurement points for the target frequency band, and obtains at least two sets of PSDT function curves. The characteristic frequency identification module is used to construct a PSDT difference function through two sets of PSDT function curves, perform a reciprocal transformation on the difference function, and determine the characteristic frequency of the unit under operating conditions based on the peak position of the reciprocal function. The graded monitoring module is used to combine the energy characteristics obtained from CWT analysis with the characteristic frequencies identified by PSDT and execute graded monitoring logic. The early warning module is used to generate and output corresponding early warning signals based on the results of hierarchical monitoring.

[0044] Example 3: This embodiment provides an electronic device, including: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the computer instructions to perform the monitoring method as described in Embodiment 1.

[0045] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for monitoring the operating frequency of a hydro-generator based on CWT-PSDT, characterized in that, Includes the following steps: Step 1: Install vibration acceleration sensors at key locations on the stator of the hydro-generator unit; Step 2: Collect vibration acceleration time history signals of the unit under different operating conditions; Step 3.1: Perform CWT analysis on the vibration acceleration time history signal to obtain the time-frequency distribution map of the signal and identify the dominant frequency range of energy concentration as the target frequency band; Step 3.2: For the target frequency band, calculate the PSDT function between different measurement points to obtain two sets of PSDT function curves. By identifying the PSDT function curves, the characteristic frequency of the unit under operating conditions can be obtained. Step 4: Combine the CWT energy characteristics obtained in Step 3.1 with the PSDT characteristics identified in Step 3.2 for analysis, and execute the hierarchical monitoring logic.

2. The method for monitoring the operating frequency of a hydro-generator based on CWT-PSDT according to claim 1, characterized in that, In step 4, the hierarchical monitoring logic includes establishing the dominant operating benchmark, identifying potential structural hazards, and eliminating forced interference.

3. The method for monitoring the operating frequency of a hydro-generator based on CWT-PSDT according to claim 2, characterized in that, The establishment of the dominant operating benchmark is as follows: the frequency point with an amplitude greater than the first preset threshold in the CWT time-frequency graph and a significant stable peak value in the PSDT function curve is defined as the dominant operating characteristic frequency. The current PSDT amplitude and shape of the dominant operating characteristic frequency point are locked as the healthy operating benchmark of the unit. In subsequent monitoring, if the dominant operating characteristic frequency drifts or the PSDT characteristic changes abruptly or drifts, it is determined that the structure of the hydro-generator unit is abnormal and a benchmark deviation warning is output.

4. The method for monitoring the operating frequency of a hydro-generator based on CWT-PSDT according to claim 3, characterized in that, The identification of potential structural hazards is as follows: frequency points with amplitudes between the second and first preset thresholds in the CWT time-frequency graph, but with independent peaks in the PSDT function curve, are defined as potential structural modal frequencies. If the second preset threshold is less than the first preset threshold, the potential structural modal frequencies are included in the secondary monitoring. In subsequent operation, if the amplitude of the potential structural modal frequency in the CWT shows a continuous increasing trend, it is determined that the external excitation source drift has caused the potential resonance to be activated, and a resonance trend warning is output.

5. The method for monitoring the operating frequency of a hydro-generator based on CWT-PSDT according to claim 4, characterized in that, The elimination of forced interference is defined as follows: frequencies whose amplitude in the CWT time-frequency graph is between the second preset threshold and the first preset threshold but whose PSDT function curve has no characteristics are determined as forced interference, where the second preset threshold is less than the first preset threshold.

6. The method for monitoring the operating frequency of a hydro-generator based on CWT-PSDT according to claim 5, characterized in that, The first preset threshold is 90% of the maximum frequency value in the CWT time-frequency graph, and the second preset threshold is 30% of the maximum frequency value in the CWT time-frequency graph.

7. The method for monitoring the operating frequency of a hydro-generator based on CWT-PSDT according to claim 1, characterized in that, In step 3.1, CWT uses the complex-valued Morlet wavelet basis function.

8. The method for monitoring the operating frequency of a hydro-generator based on CWT-PSDT according to claim 1, characterized in that, In step 3.2, the method for obtaining the characteristic frequency of the unit under operating conditions by identifying the PSDT function curve is as follows: construct the reciprocal of the PSDT difference function through two sets of PSDT function curves, and the peak value of the reciprocal function is the characteristic frequency of the unit under operating conditions.

9. A hydro-generator operating frequency monitoring system based on CWT-PSDT, characterized in that, For performing the monitoring method according to any one of claims 1 to 8, comprising: The sensor module is used to place vibration acceleration sensors at key locations on the stator of the hydro-generator unit to collect vibration acceleration time history signals of the unit under different operating conditions. The data acquisition module, connected to the sensor module, is used to receive and store the vibration acceleration time history signal in real time. The signal processing module includes a CWT analysis unit, which performs continuous wavelet transform analysis on the vibration acceleration time history signal, generates a time-frequency distribution map of the signal, and identifies the dominant frequency range with concentrated energy as the target frequency band; and a PSDT calculation unit, which calculates the power spectral density transfer ratio function between different measurement points for the target frequency band, and obtains at least two sets of PSDT function curves. The characteristic frequency identification module is used to construct a PSDT difference function through two sets of PSDT function curves, perform a reciprocal transformation on the difference function, and determine the characteristic frequency of the unit under operating conditions based on the peak position of the reciprocal function. The graded monitoring module is used to combine the energy characteristics obtained from CWT analysis with the characteristic frequencies identified by PSDT and execute graded monitoring logic. The early warning module is used to generate and output corresponding early warning signals based on the results of hierarchical monitoring.

10. An electronic device, characterized in that, include: A memory and a processor are communicatively connected, the memory stores computer instructions, and the processor executes the monitoring method as described in any one of claims 1 to 8 by executing the computer instructions.

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