Early stage blade casing rub-impact fault feature extraction method based on acceleration signal

Abstract

The invention relates to the technical field of aero-engine rub-impact fault diagnosis, in particular to an early blade casing rub-impact fault feature extraction method based on acceleration signals, and aims to solve the problems that early weak signals are difficult to capture, multiple measuring points exist, and the severity of faults is difficult to quantify in a traditional method. The method comprises the following steps: S1, installing an acceleration sensor at the far end of a potential rub-impact point of a cartridge receiver, and synchronously setting a rub-impact force sensor to mark a data type; s2, building a fitness function based on kurtosis and margin indexes, and selecting an optimal frequency band by using a genetic algorithm; s3, filtering the acceleration time-domain signal acquired in the step S1 by adopting a band-pass filtering algorithm based on the optimal frequency band to obtain an acceleration time-domain signal; s4, judging whether a rub-impact fault occurs or not according to the acceleration signal based on a periodic pulse signal in the time domain signal; and S5, the fault severity is quantified according to comprehensive indexes such as effective values. The method can accurately capture early faults, is adaptive to limited working conditions of measuring points, reduces the cost, and supports accurate maintenance.

Description

Technical Field

[0001] This invention relates to the field of aero-engine collision and rubbing fault diagnosis technology, and more specifically to a method for extracting early blade-casing collision and rubbing fault features based on acceleration signals. Background Technology

[0002] As the core power component of aircraft, the operational reliability of aero engines directly affects flight safety. In actual operation, due to factors such as high-speed rotation of the rotor system (typically reaching tens of thousands of revolutions per minute), thermal deformation, and assembly errors, rubbing failures between the blades and the casing occur frequently. Statistics show that rubbing failures account for over 30% of engine mechanical failures, making it one of the leading causes of unplanned downtime. Traditional vibration monitoring methods are limited by sensor placement and signal-to-noise ratio, limiting their ability to detect early, subtle rubbing characteristics. Alarms are often only triggered when the fault has progressed to a severe stage (such as blade breakage or casing perforation), at which point irreversible damage has already occurred. Therefore, diagnostic methods for early rubbing failures are of great significance.

[0003] Blade-casing rubbing in aero-engines is one of the core faults leading to unplanned shutdowns. Existing rubbing diagnostic technologies have three main shortcomings: One example is the invention with announcement number CN120121301A, which involves a method for identifying engine rotor blade rubbing faults. Although it can identify rubbing between rotor blades and stator / coated casing at multiple locations, it only targets non-early rubbing signals (requires multiple location sensors to collect vibration data of sufficient intensity), and cannot capture early weak signals (original acceleration without obvious impact). Furthermore, the engineering application cost of complex deep neural networks is relatively high.

[0004] Secondly, traditional methods can only qualitatively determine whether there is contact or friction, but cannot quantify the severity, and the sensor layout does not take into account the limited number of actual engine measurement points.

[0005] Third, it requires the collection of data from multiple sensors, without taking into account the actual limited number of measurement points on aero engines. Summary of the Invention

[0006] In view of this, the present invention provides a method for extracting early blade casing rubbing fault features based on acceleration signals. To solve the above problems, this technology proposes a technical solution based on acceleration signals to address the insufficiently covered need for "early blade casing rubbing": early weak signals are collected by remote sensors, the optimal frequency band is optimized using a genetic algorithm to extract pulse features, and multi-dimensional indicators are combined to achieve early diagnosis and severity quantification, filling the gap in early warning and engineering adaptability of existing technologies.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for extracting early blade casing rubbing fault features based on acceleration signals includes the following steps: S1: On the casing of the aero-engine rotor tester, the acceleration sensor is installed at the farthest point from the potential contact point of the blade casing, and the contact force sensor is set at the contact point simultaneously; the sampling parameters of the acceleration sensor are set, the vibration acceleration signal under different working conditions is collected, and the data type is marked as normal working condition data, light contact data or heavy contact data in combination with the contact force sensor signal. S2: A fitness function is established based on kurtosis and margin indices, and the optimal frequency for adapting to early rubbing signals is selected through iterative screening using a genetic algorithm. bring ,in This is the lower limit of the frequency band. This is the upper limit of the frequency band; S3: Based on the optimal frequency band The acceleration time-domain signal acquired in step S1 is filtered using a bandpass filtering algorithm to obtain the filtered acceleration time-domain signal. S4: For acceleration time-domain signals, periodic pulse signals in the time domain are identified through autocorrelation analysis function and cepstral analysis function to determine whether there is an early blade casing rubbing fault; S5: If step S4 determines that a rubbing fault exists, based on the effective value and the cepstral spectrum... The severity of the rubbing fault is determined by a comprehensive index composed of the frequency corresponding to the maximum amplitude and spectrum value, and the average energy of the modulation frequency of the rotational speed frequency. This represents the rotational speed at the current moment.

[0008] Further, in step S1, the sampling frequency of the accelerometer is set to 10KHz, and the rotational speed of the aero-engine rotor tester is set to 600r / min or 1200r / min; the light and heavy impacts are distinguished by the impact force values ​​measured by the impact force sensor, and the collected data are also marked with rotational speed and impact type characteristics.

[0009] Furthermore, in step S2, a fitness function is established based on the kurtosis index and the margin index, and the calculation formula is as follows: Kurtosis index: ; Margin indicators: ; Fitness function: ; In the formula The first time domain signal x Numerical value Let x be the mean of the time-domain signal. Let x be the number of signals. denoted as the maximum value of the time-domain signal x. It represents the standard deviation of the time-domain signal x.

[0010] Further, in step S2, the execution process of the genetic algorithm includes: ① Encoding and Population Initialization: This involves setting the frequency band... Mapped to chromosomes, an initial population of 20-100 individuals is randomly generated; ② Fitness assessment: The fitness value of each individual is calculated based on the fitness function and used as a criterion for judging its quality; ③ Genetic operations: Selection operations use roulette wheel, tournament, or elite retention methods; crossover operations use single-point or multi-point crossover; mutation operations use bit flipping. ④ Terminating the iteration: Repeat steps ②-③ until the preset maximum number of iterations is reached or the fitness value tends to stabilize.

[0011] Furthermore, the criterion for determining whether the fitness value tends to be stable in step ④ is that the difference between the maximum fitness values ​​of three consecutive iterations is less than 0.01.

[0012] Further, in step S3, the execution process of the bandpass filtering algorithm includes: ① Construct the normalized transfer function of the bandpass filter: ; in Let the filter order be . The cutoff frequency (rad / s) For Laplace variables, It is a complex frequency; ② By using bilinear transformation Mapped to , The digital filter coefficients [b, a] are obtained, where This represents the sampling period, which is the reciprocal of the sampling frequency. ③ Based on coefficients [b, a] and optimal frequency band The acceleration time-domain signal is filtered.

[0013] Furthermore, the formula for calculating the autocorrelation analysis function is as follows: ; The formula for calculating the cepstral analysis function is as follows: ; in The two-sided power spectrum or self-power spectrum of the signal. This is the inverse Fourier transform. It is the inverse frequency variable. This is the time offset. This represents the maximum delay.

[0014] Furthermore, in step S5: The formula for calculating the effective value is: ; In the cepstral The amplitude is: ,in The rotational speed at the current moment; The average energy of the frequency corresponding to the maximum spectral value and the modulation frequency of the rotational speed is: ； in For spectral amplitude, For the number of modulations, This is the frequency corresponding to the maximum value of the spectrum.

[0015] Furthermore, in step S1, the criteria for determining mild impact is a force sensor reading of 40-60N, and the criteria for determining severe impact is a force sensor reading of 80-120N.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1. Accurately capturing early-stage impact-related faults to avoid irreversible damage: Background technology indicates that traditional vibration monitoring methods and comparative patents (CN120121301A) can only identify non-early-stage impact-related signals (requiring sufficiently strong vibration data), failing to capture early, weak signals. This often leads to alarms only being triggered when the fault has progressed to a severe stage (such as blade breakage). This method, through a technology chain of "remote accelerometer signal acquisition + genetic algorithm to select the optimal frequency band suitable for early signals + bandpass filtering to extract periodic weak pulses + autocorrelation / cephalospectral analysis to suppress noise," can identify early-stage impact-related characteristics from raw signals without obvious impact, shifting the fault diagnosis point to the nascent stage and effectively avoiding irreversible damage caused by fault deterioration. It can not only qualitatively identify whether an impact-related fault has occurred but also quantitatively determine the severity of the fault.

[0017] 2. Adapting to the limited operating conditions of actual engine measurement points and reducing engineering application costs, this method only requires one acceleration sensor to be placed at the "farthest point from the potential contact point" of the casing, and one contact force sensor to mark the data simultaneously. It does not require multiple measurement points to cover, which not only meets the structural limitations of actual engines, but also reduces the number of sensors deployed and installation costs, significantly improving the engineering feasibility.

[0018] 3. To quantify the severity of rubbing faults and support precise maintenance decisions, this method, after determining the presence of a rubbing fault, uses "Reliable Mean Square (RMS) + cepstrum" to... Amplitude + Spectral Modulation Frequency Average Energy ( The comprehensive index, consisting of "40-60N" and "80-120N", can clearly distinguish between light impact and wear and heavy impact and wear, providing maintenance personnel with a quantitative basis for fault level, avoiding over-maintenance (e.g., light impact and wear does not require shutdown and major repair) or under-maintenance (e.g., heavy impact and wear is not dealt with in time), and improving maintenance efficiency and economy.

[0019] 4. No complex model required, reducing computation and sample dependence, and improving engineering practicality. The core of this method relies on genetic algorithm (convergence after 12-18 iterations) and time-domain / frequency-domain analysis algorithm. There is no complex network model, the sample requirement is low (240s of data collection for a single working condition is sufficient), the computational resource consumption is low, and no professional algorithm personnel are required for model training and optimization, making it easier to quickly deploy and apply in engineering scenarios. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0021] Figure 1 The flowchart shows the early blade casing rubbing fault diagnosis method based on casing acceleration signal; Figure 2 A schematic diagram of the test apparatus for simulating blade casing rubbing failure; Figure 3 The results of the non-collision, mild collision, and severe collision tests of the present invention are shown in (a) and (b) are the collision force signals of the non-collision, mild collision, and severe collision tests, respectively. Figure 4 The results of the non-collision, light collision, and heavy collision tests of the present invention are shown in (c) and (d) are detailed magnified views of the collision force and the casing acceleration signal. Figure 5 The genetic algorithm flow of this invention; Figure 6a The optimal frequency band selection result for the acceleration signal of the non-collision test casing; Figure 6b The optimal frequency band selection result for the acceleration signal of the casing in the light impact test; Figure 6c The optimal frequency band selection result for the acceleration signal of the casing in the severe impact and friction test; Figure 7(a) and (b) are the results of the casing acceleration signal filtering in the present invention; (a) and (b) are the results of the casing acceleration signal filtering in the non-collision test. Figure 8 (c) and (d) are the results of the casing acceleration signal filtering in the present invention; (d) are the results of the casing acceleration signal filtering in the light impact test. Figure 9 (e) and (f) are the results of the casing acceleration signal filtering in this invention; (e) and (f) are the results of the casing acceleration signal filtering in the heavy impact test. Figure 10 The cepstrum and autocorrelation results of the casing acceleration signal of the present invention are shown below; (a) cepstrum of the casing acceleration filter signal in the non-collision test, (b) autocorrelation of the casing acceleration filter signal in the non-collision test. Figure 11 (c) The cepstrum and autocorrelation results of the casing acceleration signal of the present invention; (d) The cepstrum of the casing acceleration filter signal under mild impact test; Figure 12 The cepstral and autocorrelation results of the casing acceleration signal of the present invention; (e) cepstral of the casing acceleration filter signal under severe impact test; (f) autocorrelation of the casing acceleration filter signal under severe impact test. Figure 13 The graph shows the variation of the friction intensity index of the present invention, (a) effective value, and (b) cepstrum. (c) Average energy; Figure labels: 1. Engine rotor tester; 2. Impact generation device; 3. Acceleration sensor. Detailed Implementation

[0022] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] This embodiment is based on a rotor test apparatus for rubbing fault simulation testing of an aero-engine, and describes a method for extracting early blade-casing rubbing fault features based on acceleration signals. Figure 1 It includes the following five steps: Step 1 A collision generating device 2 is installed on the casing of the aero-engine rotor test chamber 1. An acceleration sensor 3 is installed at the farthest point from the potential collision point of the blade casing, and a collision force sensor is simultaneously installed at the collision location. The sampling parameters of the acceleration sensor 3 are set to collect vibration acceleration signals under different operating conditions. The data type is marked as normal operating condition data, mild collision data, or severe collision data based on the collision force sensor signal. The criteria for determining mild collision is a collision force sensor measurement value of 40-60N, and the criteria for determining severe collision is a collision force sensor measurement value of 80-120N.

[0024] like Figure 2 As shown, the accelerometer 3 is installed on the casing at the farthest point from the point of impact between the blade and the casing. Various fault tests are conducted, including normal (no impact), mild impact (impact force approximately 50N), and severe impact (impact force approximately 100N). The degree of impact is determined by the impact force signal measured by the impact force sensor contained in the impact generating device 2. The sampling frequency is set to 10kHz, the tester speed is set to 1200r / min, and the characteristics of the collected data, such as speed and impact type, are marked. Figures 3-4 The results shown are those of no impact, slight impact, and heavy impact tests. Figure 3 (a) shows the impact force signals for no impact, light impact, and heavy impact tests. It is clear from the figure that the impact force in the heavy impact test > the impact force in the light impact test > the impact force in the no impact test. Figure 3 (b) represents the casing acceleration signals under relative no-impact, light-impact, and heavy-impact tests. Figure 4 (c) is a magnified view of the impact force details. The image clearly shows the impact force as an impact signal, and the corresponding... Figure 4 (d) The detailed diagram of the casing acceleration signal does not show any obvious rubbing or impact signal. Therefore, if the analysis is based solely on the original casing acceleration signal, it is impossible to conclude whether a rubbing or impact failure has occurred.

[0025] Step 2 A fitness function was established based on kurtosis and margin indices, and the optimal frequency band for early-stage rubbing signals was selected through iterative screening using a genetic algorithm. ,in This is the lower limit of the frequency band. This is the upper limit of the frequency band.

[0026] A fitness function is established based on the kurtosis and margin indices, and the calculation formula is as follows: Kurtosis index: ; Margin indicators: ; Fitness function: ; In the formula The first time domain signal x Numerical value Let x be the mean of the time-domain signal. Let x be the number of signals. Let x be the maximum value of the time-domain signal. It represents the standard deviation of the time-domain signal x.

[0027] The genetic algorithm process is as follows: ① Encoding and Population Initialization: The problem solution is mapped to chromosomes (e.g., binary / real number encoding), and an initial population of 50 individuals is randomly generated. In this invention, the optimal frequency is selected, i.e., two variables: upper and lower frequency band limits.

[0028] ② Fitness assessment: Calculate the fitness value (e.g., objective function value) for each individual as a criterion for judging its fitness. Higher fitness indicates a greater probability of survival. In this invention, this refers to the fitness function established in step S2.

[0029] ③ Genetic selection: Selecting high-quality individuals based on fitness; in this example, a roulette wheel selection method is used: the higher the fitness, the greater the probability of selection. Crossover: Recombination of parental genes to produce new individuals; in this example, multi-point crossover and multi-position exchange are used to enhance diversity. Mutation: Randomly modifying genes with a small probability to avoid premature convergence.

[0030] ④ Terminate the iteration. Repeat the genetic operation until the termination condition is met, reaching the maximum number of iterations (15) and the fitness tends to stabilize (converge). The genetic algorithm flowchart is as follows: Figure 5 As shown, for the casing acceleration signal collected in step S1, the optimal frequency band is selected based on a genetic algorithm, and the result is as follows. Figures 6a-6c As shown.

[0031] Step 3 Based on the optimal frequency band The acceleration time-domain signal acquired in step S1 is filtered using a bandpass filtering algorithm. The filtering function is butter and the filtering order is selected as 6th order to obtain the filtered acceleration time-domain signal.

[0032] The execution process of the bandpass filtering algorithm includes: ① Construct the normalized transfer function of the bandpass filter: in Let the filter order be . The cutoff frequency (rad / s) For Laplace variables, It represents the imaginary unit and the complex frequency.

[0033] ② By using bilinear transformation Mapped to , The digital filter coefficients [b, a] are obtained, where This represents the sampling period, which is the reciprocal of the sampling frequency.

[0034] ③ Based on coefficients [b, a] and optimal frequency band The acceleration time-domain signal is filtered.

[0035] The filtered results of the casing acceleration signals from no-impact, light-impact, and heavy-impact tests are as follows: Figures 7-9 As shown. Figure 7 (a) and (b) show the filtered results of the acceleration signal from the casing during the non-collision test. The detailed images show no obvious pulse signal. Figure 8 (c) and (d) show the filtered results of the casing acceleration signal during the mild impact test. The detailed images reveal the casing acceleration pulse signal. Figure 9 (e) and (f) show the filtered results of the casing acceleration signal from the heavy impact test. A clear pulse signal can be seen in the detail images. This is significantly different from the casing acceleration signal before filtering.

[0036] Step 4 For acceleration time-domain signals, periodic pulse signals in the time domain are identified by autocorrelation analysis function and cepstral analysis function to determine whether there is an early blade casing rubbing fault.

[0037] The formula for calculating the autocorrelation analysis function is as follows: , The cepstral analysis function: , in The two-sided power spectrum or self-power spectrum of the signal. This is the inverse Fourier transform. It is the inverse frequency variable. This is the time offset. This represents the maximum delay.

[0038] Based on the casing acceleration filter signal obtained in step S3, to determine whether rubbing has occurred, it is necessary not only to check whether a pulse signal exists in the time domain signal, but also to perform further cepstral analysis and autocorrelation analysis on the signal. For example... Figures 10-12 As shown, the cepstral spectrum and normalized autocorrelation plot of the acceleration signal of the casing under no-collision, light-collision, and heavy-collision tests for a certain second are shown. It can be seen that the peak value in the cepstral spectrum and autocorrelation plot of heavy-collision test is greater than that in the cepstral spectrum and autocorrelation plot of light-collision test, which is greater than that in the cepstral spectrum and autocorrelation plot of heavy-collision test. Therefore, this further corroborates the diagnosis result of the collision fault.

[0039] Step 5 If step S4 determines that a rubbing fault exists, based on the effective value and the cepstral spectrum... The severity of the rubbing fault is determined by a comprehensive index consisting of the amplitude, the frequency corresponding to the maximum spectral value, the modulation frequency of the rotational speed, and the average energy. This represents the rotational speed at the current moment.

[0040] The formula for calculating the effective value is: ; In the cepstral The amplitude is: ,in The rotational speed at the current moment; The frequency corresponding to the maximum spectral value and the average energy of the modulation frequency of the rotational speed are: ; in It represents the amplitude of the spectrum, which is the amplitude value of a signal at a specific frequency point in the frequency domain; The modulation order is a positive integer, representing the number of frequency modulation harmonics considered. The frequency corresponding to the maximum value of the spectrum is the frequency point with the largest amplitude in the signal power spectrum.

[0041] Based on the casing acceleration filter signal obtained in step 3, the above indicators are extracted, such as... Figure 13 As shown, the effective value and the cepstrum are clearly visible. The average energy of the frequency corresponding to the maximum value in the spectrum and the modulation frequency of the rotation speed frequency (at the amplitude, frequency of the maximum value in the spectrum ... modulation frequency, frequency of the rotation speed frequency, frequency of the modulation frequency, frequency of the modulation frequency, frequency of the amplitude, frequency of the maximum value in the spectrum, frequency of the modulation frequency, Changes in indicators such as ( ) are strongly correlated with no impact, light impact, and heavy impact, and the severity of impact failure can be judged based on these indicators.

[0042] The various embodiments described in this specification are presented in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for extracting early blade casing rubbing fault features based on acceleration signals, characterized in that, Includes the following steps: S1: On the casing of the aero-engine rotor tester, the acceleration sensor is installed at the farthest point from the potential contact point of the blade casing, and the contact force sensor is simultaneously set at the contact point. Set the sampling parameters of the accelerometer, collect vibration acceleration signals under different working conditions, and combine them with the collision force sensor signal to mark the data type as normal working condition data, light collision data, or heavy collision data; S2: A fitness function is established based on kurtosis and margin indices, and the optimal frequency for adapting to early rubbing signals is selected through iterative screening using a genetic algorithm. bring ,in This is the lower limit of the frequency band. This is the upper limit of the frequency band; S3: Based on the optimal frequency band The acceleration time-domain signal acquired in step S1 is filtered using a bandpass filtering algorithm to obtain the filtered acceleration time-domain signal. S4: For acceleration time-domain signals, periodic pulse signals in the time domain are identified through autocorrelation analysis function and cepstral analysis function to determine whether there is an early blade casing rubbing fault; S5: If step S4 determines that a rubbing fault exists, based on the effective value and the cepstral spectrum... The severity of the rubbing fault is determined by a comprehensive index composed of the frequency corresponding to the maximum amplitude and spectrum value, and the average energy of the modulation frequency of the rotational speed frequency. This represents the rotational speed at the current moment.

2. The method for extracting early blade casing rubbing fault features based on acceleration signals according to claim 1, characterized in that, In step S1, the sampling frequency of the accelerometer is set to 10KHz, and the rotational speed of the aero-engine rotor tester is set to 600r / min or 1200r / min. The light and heavy impacts are distinguished by the impact force values ​​measured by the impact force sensor, and the collected data are also marked with rotational speed and impact type characteristics.

3. The method for extracting early blade casing rubbing fault features based on acceleration signals according to claim 1, characterized in that, In step S2, a fitness function is established based on the kurtosis and margin indices, and the calculation formula is as follows: Kurtosis index: ; Margin indicators: ; Fitness function: ; In the formula The first time domain signal x Numerical value Let x be the mean of the time-domain signal. Let x be the number of signals. denoted as the maximum value of the time-domain signal x. It represents the standard deviation of the time-domain signal x.

4. The method for extracting early blade casing rubbing fault features based on acceleration signals according to claim 3, characterized in that, In step S2, the execution process of the genetic algorithm includes: ① Encoding and Population Initialization: This involves setting the frequency band... Mapped to chromosomes, an initial population of 20-100 individuals is randomly generated; ② Fitness assessment: The fitness value of each individual is calculated based on the fitness function and used as a criterion for judging its quality; ③ Genetic operations: Selection operations use roulette wheel, tournament, or elite retention methods; crossover operations use single-point or multi-point crossover; mutation operations use bit flipping. ④ Terminating the iteration: Repeat steps ②-③ until the preset maximum number of iterations is reached or the fitness value tends to stabilize.

5. The method for extracting early blade casing rubbing fault features based on acceleration signals according to claim 4, characterized in that, The criterion for determining whether the fitness value tends to be stable in step ④ is that the difference between the maximum fitness values ​​of three consecutive iterations is less than 0.

01.

6. The method for extracting early blade casing rubbing fault features based on acceleration signals according to claim 1, characterized in that, In step S3, the execution process of the bandpass filtering algorithm includes: ① Construct the normalized transfer function of the bandpass filter: ； in Let the filter order be . The cutoff frequency (rad / s) For Laplace variables, It is a complex frequency; ② By using bilinear transformation Mapped to , The digital filter coefficients [b, a] are obtained, where This represents the sampling period, which is the reciprocal of the sampling frequency. ③ Based on coefficients [b, a] and optimal frequency band The acceleration time-domain signal is filtered.

7. The method for extracting early blade casing rubbing fault features based on acceleration signals according to claim 1, characterized in that: The formula for calculating the autocorrelation analysis function is as follows: ； The formula for calculating the cepstral analysis function is as follows: ； in The two-sided power spectrum or self-power spectrum of the signal. This is the inverse Fourier transform. It is the inverse frequency variable. This is the time offset. This represents the maximum delay.

8. The method for extracting early blade casing rubbing fault features based on acceleration signals according to claim 1, characterized in that, In step S5: The formula for calculating the effective value is: ； In the cepstral The amplitude is: ,in The rotational speed at the current moment; The average energy of the frequency corresponding to the maximum spectral value and the modulation frequency of the rotational speed is: ； in For spectral amplitude, For the number of modulations, This is the frequency corresponding to the maximum value of the spectrum.

9. The method for extracting early blade casing rubbing fault features based on acceleration signals according to claim 2, characterized in that, In step S1, the criteria for determining mild impact is a force sensor reading of 40-60N, and the criteria for determining severe impact is a force sensor reading of 80-120N.

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