A crown blade root loosening and crown falling off fault online diagnosis method

Abstract

The application provides an online diagnosis method for crown blade root loosening and crown loss, relates to the technical field of aero-engine state monitoring and fault diagnosis, and comprises the following steps: installing a blade tip timing sensor on a casing in a circumferential direction; collecting the arrival time of adjacent crown blades under a target steady state condition; and calculating a first arrival time difference sequence. Autocorrelation functions are calculated for each sequence, and a loosening modulation peak value in a blade rotation period delay range is extracted. Meanwhile, the offset of a current time period mean value relative to a healthy benchmark mean value is calculated. If the loosening modulation peak value of a single pair of blades appears to be locally abnormally high relative to the overall level, and the mean value offset does not exceed an alarm threshold, the blade root loosening fault is determined. If the mean value offset exceeds the threshold, and the loosening modulation peak value does not appear to be locally abnormal, the crown loss fault is determined. The joint decoupling of autocorrelation dynamic modulation characteristics and mean value static bias characteristics realizes the online differentiation of two typical crown blade faults, and improves the diagnosis accuracy and real-time performance.

Description

Technical Field

[0001] This invention belongs to the field of aero-engine condition monitoring and fault diagnosis technology, specifically relating to an online diagnostic method for crowned blade root loosening and crown loss faults. Background Technology

[0002] Crowned blades are a common configuration of turbine rotor blades in aero-engines, with a crown structure at the blade tip. When the engine reaches a certain speed, the crowns of adjacent blades press against each other under the action of centrifugal force, forming a full-ring contact, thereby increasing blade rigidity, suppressing vibration, and improving aerodynamic efficiency.

[0003] During engine service, two typical types of failures commonly occur with crowned blades: one is blade root loosening, where the connection stiffness between the blade and the rotor disk tenon decreases, resulting in abnormal gaps and vibrations; the other is crown detachment, where the blade crown breaks off due to crack propagation or impact damage. The severity and handling methods for these two types of failures are drastically different—in the early stages of blade root loosening, operation can continue to be monitored, while crown detachment is a serious failure; the detached blade crown fragments may damage downstream blades, requiring immediate shutdown and repair. Therefore, online differentiation between these two failures is crucial for ensuring flight safety and rationally planning maintenance schedules.

[0004] Existing blade vibration monitoring methods based on tip timing typically analyze the arrival time or amplitude of a single blade, using features such as frequency and amplitude to determine if an anomaly exists. However, for crowned blades, both root loosening and crown loss can manifest as frequency shifts or amplitude increases in the vibration signal of a single blade, making it difficult to reliably distinguish between the two faults based solely on the vibration characteristics of a single blade. Some methods require comparison with pre-established finite element models of blades or historical fault sample libraries, but model accuracy is affected by manufacturing tolerances and operational wear, and establishing such sample libraries is costly and has limited coverage.

[0005] Therefore, how to distinguish between leaf root loosening and crown loss faults of crowned blades online using leaf tip timing signals without relying on precise mechanical models and large-scale fault sample libraries is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0006] In view of the above-mentioned defects or deficiencies in the prior art, an online diagnostic method for loosening and crowning faults of crowned blades is provided. The crowned blade has a crown at its tip. When the engine is running, at least when the target steady-state condition is reached, the crowns of adjacent crowned blades abut against each other under the action of centrifugal force to form a complete ring contact. The method includes the following steps: Multiple blade tip timing sensors are installed circumferentially on the engine casing. When the engine runs to the target steady-state condition, the arrival times of multiple pairs of adjacent crowned blades in each revolution are collected synchronously. Each pair of adjacent crowned blades consists of two crowned blades with their crowns pressed against each other. The first arrival time difference of each pair of adjacent crowned blades in each revolution is calculated to obtain the first arrival time difference sequence corresponding to each pair of adjacent crowned blades. Calculate the autocorrelation function for each of the first arrival time difference sequences, and extract the loosening modulation peak from the autocorrelation function. The loosening modulation peak is the peak value of the autocorrelation function within a preset time delay range corresponding to the blade rotation period. Calculate the mean offset for each first arrival time difference sequence, where the mean offset is the difference between the mean arrival time difference in the current time period and the mean arrival time difference in the reference time period; the mean arrival time difference in the reference time period is the mean first arrival time difference of the pair of blades measured under the target steady-state operating condition when the engine is in a healthy state. For each pair of adjacent crowned blades, when the loosening modulation peak value meets the first determination condition and the mean offset does not exceed the preset offset alarm threshold, it is determined that there is a leaf root loosening fault in the pair of adjacent crowned blades. The first determination condition requires that the loosening modulation peak value of a single pair of adjacent crowned blades and the overall loosening modulation peak value level of multiple pairs of adjacent crowned blades show a local abnormal increase. When the mean offset exceeds the offset alarm threshold and the loosening modulation peak does not meet the first determination condition, it is determined that there is a crown loss fault in the pair of adjacent crowned blades.

[0007] According to the technical solution provided in this application, the first determination condition is: The peak value of the loosening modulation of the pair of adjacent crowned blades exceeds the preset loosening alarm threshold, and the ratio of the peak value of the loosening modulation of the pair of adjacent crowned blades to the average value of the peak values ​​of the loosening modulation of the other pairs of adjacent crowned blades exceeds the preset relative difference threshold.

[0008] According to the technical solution provided in this application, it also includes a step of diagnosis when the engine undergoes a unidirectional speed change process, wherein the unidirectional speed change process is the process of the engine monotonically changing from a first speed to a second speed, and during the process, the blades of adjacent crowned blades always remain in close contact with each other. During the unidirectional speed change process, the arrival time of each pair of adjacent crowned blades is continuously collected, and the arrival time difference of each pair of adjacent crowned blades in each revolution during the unidirectional speed change process is calculated to obtain the second arrival time difference sequence of the speed change process. The second arrival time difference sequence is detrended to remove the overall trend of arrival time difference caused by the change in rotational speed, resulting in a detrended second arrival time difference sequence that fluctuates around zero. The transient offset pulse is extracted from the detrended second arrival time difference sequence. The transient offset pulse is a signal segment in which the detrended second arrival time difference continuously deviates from zero within multiple consecutive cycles and the deviation exceeds a preset transient offset threshold. When a transient offset pulse occurs in a pair of adjacent crowned blades during the unidirectional speed change, and the transient offset pulse is a single pulse, and the average offset of the pair of adjacent crowned blades after the speed stabilizes does not exceed the offset alarm threshold, it is determined that there is a blade root loosening fault in the pair of adjacent crowned blades.

[0009] According to the technical solution provided in this application, after determining that a pair of adjacent crowned leaves have a loose leaf root fault, the method further includes the following steps: Establish an absolute spatial reference: Observe along the direction from the engine intake end to the exhaust end, take the counterclockwise rotation direction of the rotor as the positive circumferential direction, and designate the blade on the clockwise side of the pair of adjacent crowned blades as the first blade and the blade on the counterclockwise side as the second blade. Extract waveform asymmetry features from the transient offset pulse; Based on the waveform asymmetry characteristics, the asymmetric direction of the transient offset pulse is determined; The asymmetric direction is compared with a pre-defined fault direction mapping rule. The fault direction mapping rule is determined by the geometric locking directionality of the blade crown contact surface, specifying the asymmetric direction corresponding to the loosening of the first blade root and the asymmetric direction corresponding to the loosening of the second blade root. The asymmetric direction corresponding to the loosening of the second blade root is opposite to the asymmetric direction corresponding to the loosening of the first blade root. The geometric locking directionality of the blade crown contact surface refers to the locking structure characteristic that allows only unidirectional sliding of the blade crown contact surface under circumferential aerodynamic load. When the asymmetric direction of the transient offset pulse is consistent with the asymmetric direction corresponding to the loosening of the first blade root, the first blade is determined to be a faulty blade; otherwise, the second blade is determined to be a faulty blade.

[0010] According to the technical solution provided in this application, determining the asymmetric direction of the transient offset pulse based on the waveform asymmetry characteristics specifically involves: The waveform asymmetry feature includes the ratio of the pulse rising edge slope to the falling edge slope; When the ratio is greater than the theoretical symmetry ratio 1, the asymmetric direction is determined to be the first direction; when the ratio is less than the theoretical symmetry ratio 1, the asymmetric direction is determined to be the second direction opposite to the first direction.

[0011] According to the technical solution provided in this application, the waveform asymmetry feature also includes the rate of change of the ratio of the pulse rising edge slope to the falling edge slope as a function of the engine speed. Before determining the asymmetric direction of the transient offset pulse, the following steps are also included: The instantaneous rotational speed change rate corresponding to the moment the transient offset pulse occurs during the unidirectional rotational speed change process is obtained; Based on the correspondence between the offline pre-calibrated speed change rate and the slope ratio correction amount, the ratio of the pulse rising edge slope to the falling edge slope is corrected. The asymmetric direction is determined based on the corrected ratio.

[0012] According to the technical solution provided in this application, the correspondence between the rotational speed change rate and the slope ratio correction amount is obtained through the following calibration steps: On the test bench, at least one pair of standard faulty crowned blades with known loose leaf roots were subjected to multiple unidirectional rotation speed changes at different rates. The arrival times were collected and the second arrival time difference sequence after detrending was calculated. The transient offset pulses in each process were extracted. For each rate of change of rotational speed, calculate the ratio of its rising edge slope to its falling edge slope; obtain the reference ratio of the rising edge slope to the falling edge slope of the standard faulty crowned blade measured under steady-state or no speed change conditions. The difference between the ratio calculated at each speed change rate and the reference ratio is used as the slope ratio correction amount corresponding to that speed change rate.

[0013] According to the technical solution provided in this application, after determining that the first blade or the second blade is a faulty blade, the following confirmation step is also included: Identify the other adjacent blade pair that the faulty blade is involved in besides the current blade pair, and obtain the diagnostic results for that other adjacent blade pair; When another adjacent blade pair is also determined to have a loose blade root fault, and the faulty blade located therein is the same physical blade as the currently determined faulty blade, the location result of the faulty blade is confirmed.

[0014] According to the technical solution provided in this application, the average arrival time difference of the reference period is obtained as follows: when the engine is first run to the target steady-state condition after factory testing or overhaul, the first arrival time difference of multiple revolutions of the pair of blades is continuously collected, the arithmetic mean is calculated and stored as the reference value; or, multiple steady-state condition periods confirmed to be fault-free in the engine's historical operation record are selected, the average arrival time difference of the corresponding period is calculated, and the statistical processing is used as the average arrival time difference of the reference period.

[0015] According to the technical solution provided in this application, the preset time delay range is determined based on the blade rotation period T under the target steady-state condition, specifically [K×T-Δt, K×T+Δt], where K is an integer greater than or equal to 1, representing the number of autocorrelation delay periods, and Δt is a preset time tolerance, which at least covers the autocorrelation peak offset range caused by the vibration phase modulation of adjacent blades due to blade root loosening.

[0016] Compared with existing technologies, the beneficial effects of this application are: it solves the problem that existing leaf tip timing monitoring methods are unable to distinguish between loosening of the leaf root and crown loss of crowned leaves online. Its core principle is: instead of using the arrival time of a single leaf as the analysis object, it uses a pair of adjacent crowned leaves as the basic unit, and extracts the unique physical characteristics of loosening and crown loss from the dynamic changes in the arrival time difference between this pair of leaves.

[0017] The physical basis of this approach lies in the fact that when a crowned blade is operating normally, adjacent blade crowns are pressed together under centrifugal force, forming a complete ring contact, and the blade crown contact surface is in a stable compressed state. At this time, the arrival time difference between a pair of blades is a steady-state signal with a small fluctuation around a fixed mean. When the blade root loosens, the constraint stiffness between the blade and the wheel hub decreases. Under the action of periodic aerodynamic loads, the loosened blade will produce rigid body oscillations or large-amplitude vibrations synchronized with its rotational speed. This abnormal vibration will periodically compress and release the blade crown contact surface, causing the blade crown contact state to be modulated: the degree of compression of the contact surface changes periodically in each revolution. This periodic change in the contact state is directly reflected in the periodic fluctuation of the arrival time difference between the pair of blades. By calculating the autocorrelation function of the arrival time difference sequence, this modulation phenomenon will form a peak value in the autocorrelation function corresponding to the blade rotation period, namely the loosening modulation peak value. The physical significance of this peak value is that it captures the contact anomaly that repeatedly occurs in each revolution of the loosened blade, and is a unique fingerprint left by the loosening of the blade root in the time difference domain.

[0018] When the leaf crown breaks off, the contact surface between the leaf crown and the blade is completely destroyed, irreversibly altering the force balance between the blades. The blade without the crown undergoes permanent deflection under aerodynamic loads, resulting in a static positional shift in the blade's arrival time. This shift is directly manifested as a significant jump in the mean of the arrival time difference sequence, i.e., the mean shift. The essential difference between crown loss and leaf root loosening is that crown loss causes a permanent static geometric shift, while loosening causes a periodic dynamic modulation. Therefore, the mean shift is a unique fingerprint of crown loss in the time difference domain.

[0019] This invention distinguishes between two conditions using a combined judgment logic: when only the loosening modulation peak is abnormal while the mean deviation is within limits, it indicates the presence of periodic contact modulation but no permanent positional shift, and is judged as blade root loosening; when only the mean deviation exceeds limits while the loosening modulation peak is normal, it indicates the presence of permanent positional shift but no periodic modulation, and is judged as crown loss. This judgment logic does not require a pre-established precise dynamic model of the blade, nor does it require accumulating a large number of fault samples for comparison; it can complete the online distinction using only the statistical characteristics of the arrival time difference sequence. The entire scheme has low computational load and strong real-time performance, making it suitable for deployment and operation in airborne monitoring systems or ground-based real-time analysis platforms. Attached Figure Description

[0020] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 The flowchart illustrates the steps of the online diagnostic method for leaf root loosening and crown loss faults of crowned leaves provided in this application. Detailed Implementation

[0021] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0022] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0023] As mentioned in the background section, this application proposes an online diagnostic method for loosening and crowning faults at the blade root of a crowned blade. The crowned blade has a crown at its tip. During engine operation, at least when the target steady-state condition is reached, the crowns of adjacent crowned blades abut against each other under centrifugal force, forming a complete ring contact. Figure 1 As shown, the method includes the following steps: S1. Install multiple blade tip timing sensors along the circumferential direction on the engine casing. When the engine runs to the target steady-state condition, synchronously collect the arrival time of multiple pairs of adjacent crowned blades in each revolution. Each pair of adjacent crowned blades consists of two crowned blades with their crowns pressed against each other. Calculate the first arrival time difference of each pair of adjacent crowned blades in each revolution to obtain the first arrival time difference sequence corresponding to each pair of adjacent crowned blades. S2. Calculate the autocorrelation function of each of the first arrival time difference sequences, and extract the loosening modulation peak from the autocorrelation function. The loosening modulation peak is the peak value of the autocorrelation function within a preset time delay range corresponding to the blade rotation period. S3. Calculate the mean offset of each first arrival time difference sequence, where the mean offset is the difference between the mean arrival time difference of the current time period and the mean arrival time difference of the reference time period; the mean arrival time difference of the reference time period is the mean first arrival time difference of the pair of blades measured under the target steady-state condition when the engine is in a healthy state. S41. For each pair of adjacent crowned blades, when the loosening modulation peak value meets the first determination condition and the mean offset does not exceed the preset offset alarm threshold, it is determined that there is a leaf root loosening fault in the pair of adjacent crowned blades. The first determination condition requires that the loosening modulation peak value of a single pair of adjacent crowned blades and the overall loosening modulation peak value level of multiple pairs of adjacent crowned blades show a local abnormal increase. S42. When the mean offset exceeds the offset alarm threshold and the loosening modulation peak does not meet the first determination condition, it is determined that there is a crown drop fault in the pair of adjacent crowned blades.

[0024] Specifically, a crowned blade refers to a blade with a circumferentially extending crown structure at its tip. During engine operation, as the speed increases, centrifugal force causes the crown contact surfaces of adjacent blades to press against each other. When the engine reaches the target steady-state condition, a complete ring contact is formed between the crowns, meaning that the crowns of all blades in the entire stage abut against each other to form a closed ring structure, significantly improving the bending and torsional stiffness of the entire ring. The blade root loosening fault to be diagnosed by this method refers to a state in which the preload of the connection between the tenon at the blade root and the mortise and tenon of the wheel disc decreases, and microscopic or macroscopic relative motion occurs at the contact surface. The initial stage of loosening may only be fretting wear, while in severe cases, a perceptible gap appears between the tenon and the mortise and tenon. Crown detachment fault refers to the partial breakage of the crown and its detachment from the blade body, resulting in a gap or complete loss of contact between the originally abutting adjacent crowns. These two types of faults often exhibit similar characteristics in whole-machine vibration monitoring and are difficult to distinguish using conventional methods. This method utilizes timing sensor signals from the blade tip to achieve online identification of both.

[0025] In practical implementation, multiple blade tip timing sensors are first installed circumferentially on the engine casing. The sensors should be installed on the inner wall of the casing at the section corresponding to the blade tip in the axial direction. A uniform circumferential distribution is acceptable. The number of sensors is determined based on the number of blades and diagnostic requirements; for example, four to eight sensors can be installed for a stage with dozens of blades. The sensor type can be magnetoelectric, eddy current, or capacitive. When a blade sweeps across the sensor end face, the sensor outputs a pulse signal. The signal conditioning circuit shapes the pulse into a square wave and sends it to the high-speed acquisition unit. The acquisition unit uses a reference pulse provided by the key-phase sensor for each revolution to assign an absolute timestamp and revolution number label to each blade arrival pulse. The target steady-state operating condition refers to the operating state where the engine speed is stable within a preset range and thermodynamic parameters such as exhaust temperature are also relatively stable, such as the engine's maximum continuous speed operating point or the commonly used cruising speed operating point. Under this condition, while keeping the engine state unchanged, the arrival time data of the blades from each sensor for multiple consecutive revolutions are collected synchronously.

[0026] Next, we need to divide adjacent blade pairs and calculate the first arrival time difference sequence. Assume there are M crowned blades in the entire stage, numbered 1 to M in circumferential order. The i-th blade and the (i+1)-th blade are close together at the crown, and the M-th blade and the 1-th blade are also close together, forming M pairs of adjacent crowned blades. For the signal measured by the same sensor, in the j-th cycle, the arrival time of the i-th blade is denoted as t_i(j), and the arrival time of the (i+1)-th blade is denoted as t_{i+1}(j). The first arrival time difference of this pair of adjacent crowned blades in the j-th cycle is defined as Δt_i(j) = t_{i+1}(j) - t_i(j). In actual calculations, the order in which the blades pass the sensor is known, and they need to be correctly paired according to this order to avoid confusion caused by the sensor's installation position. After continuously collecting data for K cycles, the first arrival time difference sequence of this pair of blades is obtained as Δt_i(1), Δt_i(2), ..., Δt_i(K). The value of K should ensure the statistical reliability of subsequent autocorrelation calculations, and is generally taken to be several hundred revolutions or more. For example, collecting 30 seconds of data under the target steady-state condition corresponds to several thousand revolutions.

[0027] After obtaining the first arrival time difference sequences for all M pairs of adjacent blades, the autocorrelation function needs to be calculated for each sequence. The autocorrelation function is calculated as follows: for an arrival time difference sequence x(n) of length K, the unbiased autocorrelation function estimate R(m) is calculated using the following formula: Here, m is the number of delay cycles, ranging from 0 to M_max. M_max is generally taken as an integer not exceeding K / 4 to ensure estimation quality. After calculating R(m), the loosening modulation peak needs to be extracted. The loosening modulation peak is defined as the peak value of the autocorrelation function within a preset time delay range corresponding to the blade rotation cycle. This delay range is transformed from the time domain to the number of delay cycles domain, where the number of delay cycles corresponding to one rotation of the blade is m=1. Considering that the vibration phase modulation caused by blade root loosening may cause the autocorrelation peak to deviate from the precise single-cycle delay position, the preset delay range is taken as m∈[1-Δm,1+Δm], where Δm is the delay cycle tolerance, usually taken as 1 or 2. The specific value is determined by estimating the maximum phase shift caused by loosening through blade modal tests or finite element analysis. The maximum value of R(m) within this range is the loosening modulation peak. To improve the reliability of peak extraction, an effectiveness check can be added: the peak value must be greater than a preset multiple of the average value of the autocorrelation values ​​at m=2 and m=3, for example, 2 times, to avoid misjudging the fluctuations of broadband random noise as characteristic peak values.

[0028] In parallel with the autocorrelation calculation, the mean offset of each first arrival time difference sequence needs to be calculated. The mean offset is defined as the difference between the mean arrival time difference of the current time period and the mean arrival time difference of the reference time period. The mean arrival time difference of the reference time period is obtained as follows: during the first test run after the engine leaves the factory or after a major overhaul, the engine is run to the target steady-state condition, and multiple data segments are continuously collected, each segment lasting for 30 seconds. The arithmetic mean of the arrival time difference of the blade pair is calculated for each data segment, resulting in M_1, M_2, ..., M_L. Then, the overall average of these segmented means, M_base, is calculated as the reference value, and the standard deviation σ_base of the segmented means is calculated and recorded for later use. When obtaining the reference value using the historical record method, multiple historical steady-state condition time periods confirmed to be fault-free by borehole probing and vibration analysis are selected. The mean arrival time difference of each time period is calculated in the same way, and M_base is obtained after statistical processing. During online diagnosis, the arithmetic mean of the arrival time differences of a continuous segment of data under the current target steady-state condition is taken as M_current, and the mean offset is ΔM=M_current-M_base.

[0029] The diagnostic decision-making process employs a logic that combines the loosening modulation peak value and the mean offset. First, the overall level of the loosening modulation peak values ​​for all M pairs of blades within the current acquisition period is assessed. The assessment method involves sorting all M loosening modulation peak values ​​from smallest to largest, removing the largest and smallest values ​​to eliminate interference from potentially faulty blades or outliers on the overall background level, and calculating the arithmetic mean of the remaining values ​​as the overall loosening modulation peak value level for multiple pairs of adjacent crowned blades. For each pair of adjacent crowned blades, the first judgment condition requires that the loosening modulation peak value of that pair of blades meets the characteristic of a local abnormal increase. The determination of a local abnormal increase can combine two levels: absolute threshold and relative threshold. The absolute level requires that the loosening modulation peak value exceeds a preset loosening alarm threshold. This threshold is obtained by calibration on a test bench using faulty blades with known loosening amounts. Specifically, the loosening modulation peak value of blades with different loosening gaps is measured, and the peak value corresponding to the minimum loosening amount required for an alarm in engineering is multiplied by a safety factor to determine the threshold. The relative level requires that the ratio of the loosening modulation peak value to the aforementioned overall loosening modulation peak value level exceeds a preset relative difference threshold, for example, 2.0. When both of the above conditions are met, the first condition is considered to be valid.

[0030] When the loosening modulation peak value of a pair of adjacent crowned blades meets the first judgment condition, and its mean deviation does not exceed the preset deviation alarm threshold, it is determined that there is a blade root loosening fault in the pair of adjacent crowned blades. The deviation alarm threshold is set according to the segmented mean standard deviation σ_base of the reference time period, and can be taken as deviation alarm threshold = k × σ_base, with the coefficient k usually taken as 6, corresponding to an extremely low probability of normal fluctuation exceeding the limit. When the mean deviation of a pair of adjacent crowned blades exceeds the deviation alarm threshold, and its loosening modulation peak value does not meet the first judgment condition, it is determined that there is a crown loss fault in the pair of adjacent crowned blades. If both indicators exceed the limit at the same time, it is preferentially determined to be a crown loss or a more serious combined fault, and a borehole inspection review recommendation is triggered.

[0031] The technical principle of this solution lies in decoupling two types of faults—blade root loosening and crown detachment—in the signal domain. Blade root loosening alters the boundary constraints of the blade, causing a slight change in its natural frequency. Under the coupling effect of centrifugal force and periodic aerodynamic forces, it generates parametric vibrations synchronized with the rotational speed frequency. This vibration modulates the circumferential relative position of adjacent blades, manifesting as a characteristic peak delayed by the rotational period in the autocorrelation function of the arrival time difference sequence. Crown detachment, on the other hand, is an irreversible geometric change caused by the fracture of the blade crown structure. The contact state between adjacent blade crowns is permanently altered, reflected as a mean jump at the static operating point of the arrival time difference. Dynamic modulation features are extracted through autocorrelation analysis, while static bias features are extracted through mean analysis. These two methods are complementary and do not interfere with each other, enabling accurate identification and differentiation of the two types of faults in a single steady-state data acquisition.

[0032] In a preferred embodiment, the first determination condition is: The peak value of the loosening modulation of the pair of adjacent crowned blades exceeds the preset loosening alarm threshold, and the ratio of the peak value of the loosening modulation of the pair of adjacent crowned blades to the average value of the peak values ​​of the loosening modulation of the other pairs of adjacent crowned blades exceeds the preset relative difference threshold.

[0033] Specifically, calibrating the loosening alarm threshold is a crucial step in this implementation. Its purpose is to establish an absolute judgment threshold directly related to the actual physical loosening amount of the blade. The specific calibration process is as follows: On an engine rotor test bench or a real engine, several sets of crowned blades are prepared. A small amount of material is removed from the tenon contact surface using precision machining, or by inserting thin shims of known thickness and then tightening them. Blades with different loosening gaps at the blade root are quantitatively prefabricated. The loosening gap levels can be divided based on engineering experience, for example, four levels: 0.02 mm, 0.05 mm, 0.08 mm, and 0.12 mm, representing different stages from slight loosening to severe loosening. These test blades with known loosening amounts are installed one set at a time onto the test disc. After each blade replacement, the test device is started and run to the target steady-state condition. The first arrival time difference sequence of each pair of adjacent blades and the corresponding loosening modulation peak value are measured and calculated. The test needs to be repeated multiple times under the same operating condition to ensure data stability. After measurement, a calibration curve is plotted with the loose gap amount as the x-axis and the loose modulation peak value as the y-axis. The loose modulation peak value corresponding to the minimum loose gap amount deemed necessary to trigger an alarm in engineering terms is found on the curve and denoted as P_min. To balance sensitivity and false alarm rate, the loose alarm threshold is set to P_thr = α × P_min, where α is a safety factor ranging from 0.7 to 0.9. This ensures early alarm when the loose gap amount has significantly deviated from the normal level but has not yet reached a dangerous level, while also allowing for a margin to avoid missed alarms due to calibration uncertainties.

[0034] The average value of the loosening modulation peak values ​​of the remaining pairs of adjacent crowned blades is used as a relative benchmark for judging local anomalies. When calculating this average value, it is not appropriate to simply sum and average the loosening modulation peak values ​​of all blade pairs except the current pair, as this may include other blade pairs that have already failed or are in a critical state. Including these abnormal values ​​in the average would raise the background level, causing the relative difference threshold criterion to fail. The correct approach is to sort the M loosening modulation peak values ​​calculated from all M pairs of blades in the current monitoring period, and remove the largest and smallest values. If M is large, the largest and smallest values ​​can also be removed. After removal, calculate the arithmetic mean of the remaining values. This average value represents the normal loosening modulation background level of healthy blades under the current operating conditions. Then, divide the loosening modulation peak value of the current blade pair to be judged by this background average value to obtain the relative ratio R_rel.

[0035] A preset relative difference threshold is used to determine whether the relative ratio is significantly greater than 1. When the engine is in good health and there are no loosening faults in all stages of blades, the loosening modulation peaks of each blade pair should be concentrated near the background average, with the ratio of the individual to the background average close to 1. When a pair of blades experiences root loosening, its loosening modulation peak will increase significantly, while the peaks of other healthy blade pairs remain basically unchanged or only change slightly synchronously due to minor adjustments in the overall engine operating conditions. Therefore, the relative ratio of the faulty blade pair will increase significantly. The specific value of the relative difference threshold is determined by statistically analyzing historical health data and known loosening fault data. A large amount of monitoring data under healthy conditions can be collected, and the statistical distribution of the relative ratio of each blade pair in each measurement can be calculated. The 99.9th percentile of this distribution can be taken, or the maximum relative ratio under healthy conditions can be multiplied by a coefficient of 1.2 to 1.5 as the relative difference threshold. Typical threshold values ​​are 2.0 or 2.5.

[0036] In implementing the diagnostic logic, the judgment process is as follows: First, calculate the loosening modulation peak value of the current blade pair and determine whether it is greater than the loosening alarm threshold P_thr. If it is not greater, the first judgment condition is directly determined to be invalid, and the judgment process for the loosening fault of the blade pair ends; if it is greater, proceed to the second step. Second, calculate the average anti-pollution value of the loosening modulation peak value of the other blade pairs besides the current blade pair as the background level, calculate the ratio of the loosening modulation peak value of the current blade pair to the background level, and determine whether the ratio is greater than the relative difference threshold. If it is not greater, the first judgment condition is invalid; if it is greater, the first judgment condition is valid. Third, after confirming that the first judgment condition is valid, read the mean offset of the blade pair in the current time period. If the mean offset does not exceed the offset alarm threshold, it is finally determined to be a blade root loosening fault; if the mean offset exceeds the offset alarm threshold, it is preferentially determined to be a crown drop fault or a combined fault, and a corresponding alarm is issued.

[0037] In a preferred embodiment, the method further includes a step of diagnosis when the engine undergoes a unidirectional speed change process, wherein the unidirectional speed change process is the process of the engine monotonically changing from a first speed to a second speed, and the blades of adjacent crowned blades always remain in contact with each other during the process. During the unidirectional speed change process, the arrival time of each pair of adjacent crowned blades is continuously collected, and the arrival time difference of each pair of adjacent crowned blades in each revolution during the unidirectional speed change process is calculated to obtain the second arrival time difference sequence of the speed change process. The second arrival time difference sequence is detrended to remove the overall trend of arrival time difference caused by the change in rotational speed, resulting in a detrended second arrival time difference sequence that fluctuates around zero. The transient offset pulse is extracted from the detrended second arrival time difference sequence. The transient offset pulse is a signal segment in which the detrended second arrival time difference continuously deviates from zero within multiple consecutive cycles and the deviation exceeds a preset transient offset threshold. When a transient offset pulse occurs in a pair of adjacent crowned blades during the unidirectional speed change, and the transient offset pulse is a single pulse, and the average offset of the pair of adjacent crowned blades after the speed stabilizes does not exceed the offset alarm threshold, it is determined that there is a blade root loosening fault in the pair of adjacent crowned blades.

[0038] Specifically, during the unidirectional speed change, the blade tip timing sensor operates in a continuously triggered manner, recording the arrival time of each blade in real time for each revolution. The sampling method is the same as in the steady-state condition, but during this stage, the speed continuously changes, and the rotation period of each revolution is different. Therefore, the acquisition system needs to have a sufficiently high time resolution, typically using a clock frequency of no less than tens of megahertz to time the arrival time. During the speed change, the arrival time of each blade is recorded on a revolution-by-revolution basis. Then, following the same blade pairing principle as the steady-state method, the arrival time difference of adjacent crowned blades is calculated for each revolution, obtaining the second arrival time difference sequence of that pair of blades as the number of revolutions changes throughout the entire speed change process.

[0039] The fundamental difference between the second arrival time difference sequence and the steady-state sequence lies in the fact that, due to the continuous change in rotational speed, the circumferential relative position of the blades undergoes a continuous overall shift with the change in centrifugal force. Simultaneously, the aerodynamic load on the blades also changes, resulting in an overall trend in the arrival time difference sequence related to rotational speed. To extract the transient features superimposed on this trend, caused by blade root loosening and slippage, the second arrival time difference sequence must be detrended. The specific algorithm for detrending is the locally weighted regression scatter smoothing method, i.e., the LOESS or LOWESS method. This method does not pre-determine the global polynomial order but instead performs low-order polynomial fitting within a local window adjacent to each data point. The implementation steps are as follows: using the loop number as the independent variable and the second arrival time difference as the dependent variable, a smoothing window width is set. This window width is represented by the proportion of the total number of data points, typically between 15% and 25%. For each fitted point, data points within half the window width on both sides are selected. Weights are assigned to the data points within the window using a three-cubic weighting function, with data points closer to the fitted point having a larger weight and those farther away having a smaller weight. Within the weighted window, least squares fitting is performed using a first- or second-order polynomial to obtain the trend value at the fitted point. After performing the above local fitting on all data points, a smooth trend line for the entire acceleration process is obtained. The corresponding trend value is subtracted point by point from the original second arrival time difference sequence to obtain the detrended second arrival time difference sequence, which fluctuates around zero.

[0040] Next, transient offset pulses are extracted from the detrended sequence. A transient offset pulse is defined as a signal segment in which the time difference after detrended continuously deviates from zero over multiple consecutive cycles, and the absolute value of the deviation exceeds a preset transient offset threshold. The transient offset threshold is set as follows: take the stationary segment of the detrended sequence that has been confirmed to contain no transient pulses, calculate the standard deviation σ_det of this segment, and set the transient offset threshold as T_trans = C × σ_det, where the coefficient C ranges from 5 to 8 to ensure that normal random fluctuations do not trigger pulse detection. The starting cycle number of the pulse segment is determined by the cycle in which the absolute value of the detrended value first exceeds T_trans; the ending cycle number of the pulse segment is determined by the hysteresis criterion, requiring that after exceeding the threshold, the absolute value of the detrended value falls back to less than one-third of T_trans and remains below this level for at least 5 consecutive cycles. The hysteresis termination criterion is introduced to prevent the signal from fluctuating around the threshold line, causing a complete physical slip event to be incorrectly divided into multiple independent pulse segments.

[0041] After segmenting the pulse, it is necessary to determine whether the pulse is a single pulse. The criterion for determining a single pulse is: during the entire unidirectional rotational speed change, according to the pulse segmentation method described above, there must be exactly one independent pulse segment that can be identified and meets the condition that the maximum absolute amplitude exceeds T_trans. If two or more independent pulse segments are identified during a single speed change, the condition for a single pulse is not met. In this case, the transient signal may originate from intermittent contact of the leaf crown, interference from fallen leaf crown fragments, or other non-loosening mechanisms.

[0042] The final step in the judgment logic is to jointly analyze the pulse characteristics of the speed change process with the average offset after the speed stabilizes. After the unidirectional speed change process ends, the engine enters a new steady-state condition, and the average offset of the pair of adjacent crowned blades in the new steady state is calculated. If a transient offset pulse conforming to the definition of a single pulse occurs during the unidirectional speed change of the pair of blades, and its average offset does not exceed the offset alarm threshold in the new steady state, it is determined that the pair of adjacent crowned blades has a blade root loosening fault. If multiple pulses occur during the speed change process, or the average offset exceeds the threshold in the new steady state, it is diagnosed as another type of fault or a compound fault.

[0043] In a preferred embodiment, after determining that a pair of adjacent crowned leaves have a loose leaf root fault, the method further includes the following steps: Establish an absolute spatial reference: Observe along the direction from the engine intake end to the exhaust end, take the counterclockwise rotation direction of the rotor as the positive circumferential direction, and designate the blade on the clockwise side of the pair of adjacent crowned blades as the first blade and the blade on the counterclockwise side as the second blade. Extract waveform asymmetry features from the transient offset pulse; Based on the waveform asymmetry characteristics, the asymmetric direction of the transient offset pulse is determined; The asymmetric direction is compared with a pre-defined fault direction mapping rule. The fault direction mapping rule is determined by the geometric locking directionality of the blade crown contact surface, specifying the asymmetric direction corresponding to the loosening of the first blade root and the asymmetric direction corresponding to the loosening of the second blade root. The asymmetric direction corresponding to the loosening of the second blade root is opposite to the asymmetric direction corresponding to the loosening of the first blade root. The geometric locking directionality of the blade crown contact surface refers to the locking structure characteristic that allows only unidirectional sliding of the blade crown contact surface under circumferential aerodynamic load. When the asymmetric direction of the transient offset pulse is consistent with the asymmetric direction corresponding to the loosening of the first blade root, the first blade is determined to be a faulty blade; otherwise, the second blade is determined to be a faulty blade.

[0044] Specifically, step S4-1: Establish an absolute spatial reference.

[0045] An absolute spatial reference is used to convert the temporal sequence of sensor signals into the physical identification of blades. The observation direction is uniformly defined as: looking from the engine intake end to the exhaust end, with the counterclockwise rotation direction of the rotor as the positive circumferential direction. Based on this reference, the two adjacent crowned blades in the pair where blade root loosening has been determined are assigned roles: the one on the clockwise side is designated as the first blade, and the one on the counterclockwise side is designated as the second blade.

[0046] The specific operational procedure for associating sensor signals with spatial orientation is as follows. First, when installing the blade tip timing sensors, record the installation angle position of each sensor in the circumferential direction of the casing. Using a fixed structural feature on the casing (such as a vertical reinforcing rib or a locating pin hole) as the circumferential zero-degree reference, measure the installation angle of each sensor in a counterclockwise direction. Second, determine the relationship between the circumferential sequence of the blades and the triggering sequence of the sensors. During rotor rotation, for the same sensor, each blade sweeps past the sensor in sequence, and the triggering sequence is the circumferential arrangement order of the blades. For two adjacent crowned blades labeled as number i and number i+1, if blade i triggers the sensor first, then blade i is located in front of the rotation direction, i.e., counterclockwise; blade i+1 is located behind, i.e., clockwise. In actual operation, the correspondence between blade number and sensor triggering sequence can be determined by a low-speed rotation: during the rotation, record the order in which each blade passes a certain sensor, and manually confirm the number of each blade to establish a mapping table between blade number and triggering sequence. Therefore, for any pair of adjacent blades, the mapping table can determine which blade triggers the sensor first and which triggers later. The blade that triggers first is the second blade (counterclockwise side), and the blade that triggers later is the first blade (clockwise side). The establishment of the spatial reference is completed in one go, and the calibration results are stored in the diagnostic system for use in all subsequent diagnostics.

[0047] Step S4-2: Obtain the transient offset pulse and extract the waveform asymmetry features.

[0048] From the processing results, the detrended second arrival time difference sequence has been obtained, and a transient offset pulse satisfying the single-pulse condition has been detected in this sequence. The peak circle number of this pulse is denoted as j_peak, and the number of circles covered by the pulse is [j_start, j_end]. This signal data is extracted separately and used as the raw input for waveform analysis.

[0049] The extraction process for waveform asymmetry features is as follows: First, the pulse signal is smoothed using a three-point moving average to suppress high-frequency noise. The processing method is as follows: for the signal value y(n) at circle number n, the smoothed value y_smooth(n) = [y(n-1) + y(n) + y(n+1)] / 3. Endpoint preservation is applied to the pulse start and end points, i.e., no smoothing is performed. Second, the start and end boundaries of the rising and falling edges are located on the smoothed pulse signal. Using the absolute value of the pulse peak, |A_peak|, as the reference amplitude, in the rising segment where the signal transitions from zero to peak, the circle number where the signal value first exceeds 0.1 × |A_peak| is designated as the rising start circle number (n_rise_start), and the circle number where it first exceeds 0.9 × |A_peak| is designated as the rising end circle number (n_rise_end). In the falling segment where the signal falls back from peak to zero, the circle number where the signal value first falls below 0.9 × |A_peak| is designated as the falling start circle number (n_fall_start), and the circle number where it first falls below 0.1 × |A_peak| is designated as the falling end circle number (n_fall_end). If noise causes the signal to repeatedly cross near the threshold, the first crossing is taken as the standard, and a minimum number of consecutive circles is required (e.g., the start is confirmed only after two consecutive circles exceed the threshold) to avoid false detections. The third step involves performing least-squares linear fitting on the data points of the rising edge segment [n_rise_start, n_rise_end] and the falling edge segment [n_fall_start, n_fall_end] respectively, to obtain the rising edge slope S_rise and the falling edge slope S_fall. The slope ratio R = S_rise / |S_fall| is then calculated. This ratio R is the waveform asymmetry characteristic value.

[0050] Step S4-3: Determine the asymmetric direction and compare it with the fault direction mapping rule.

[0051] Compare the magnitudes of R and 1. If R > 1, the asymmetric direction is determined as the first direction; if R < 1, the asymmetric direction is determined as the second direction. If R is exactly equal to 1 or very close to 1 (e.g., between 0.98 and 1.02), the direction cannot be determined, and a "positioning uncertain" message is output. It is recommended to confirm with other information.

[0052] The fault direction mapping rule is obtained through offline calibration, the calibration process of which is as follows: Prepare a standard faulty blade known to have root loosening: On the contact surface of the tenon side of a crowned blade of the same model as the actual machine, remove 0.05 mm of material using precision grinding to simulate the loosening gap. This blade, as a known faulty component, is used during installation, and its role in the adjacent blade pair—whether it is the first or second blade—is clearly recorded; the remaining blades are considered healthy. Install the entire stage of blades onto a rotating test bench with precisely controllable speed change rate. The test bench is equipped with the same blade tip timing sensor as the online system. Perform a uniform acceleration process, ensuring the blade crown remains in contact throughout. Extract transient offset pulses and calculate the R value using the same method as in step S4-2, recording whether R>1 or R<1, i.e., recording the asymmetric direction of the pulse. Then, reverse the role of the standard faulty blade (by replacing the faulty blade with the other blade in the pair, or by changing the tenon machining surface of the faulty blade), repeat the speed change test, and record the asymmetric direction under the opposite role. The calibration results form a definite mapping rule. For example, if the known faulty component is the first blade and the measured R>1 corresponds to the first direction, and the known faulty component is the second blade and the measured R<1 corresponds to the second direction, then the mapping rule is "the first direction corresponds to the first blade being loose, and the second direction corresponds to the second blade being loose." This mapping rule is directly related to the specific geometry of the blade contact surface. Different blade designs may yield opposite specific correspondences, but the method for establishing the rule itself is universal.

[0053] During online diagnosis, the asymmetric direction determined in step three is compared with the mapping rule described above. If it matches the direction of the first blade loosening, the first blade is determined to be a faulty blade; if it matches the direction of the second blade loosening, the second blade is determined to be a faulty blade.

[0054] In a preferred embodiment, determining the asymmetric direction of the transient offset pulse based on the waveform asymmetry characteristics specifically involves: The waveform asymmetry feature includes the ratio of the pulse rising edge slope to the falling edge slope; When the ratio is greater than the theoretical symmetry ratio 1, the asymmetric direction is determined to be the first direction; when the ratio is less than the theoretical symmetry ratio 1, the asymmetric direction is determined to be the second direction opposite to the first direction.

[0055] Specifically, after extracting the transient offset pulse data segment from the detrended second arrival time difference sequence, the polarity of the pulse is first determined. If the pulse is negative, i.e., the peak value is negative, the entire data segment is multiplied by negative one to flip it to positive, unifying subsequent processing. Let the processed pulse data sequence be (1,y1),(2,y2),...,(N_p,y_Np), where the horizontal axis is the relative cycle number and the vertical axis is the detrended time difference value.

[0056] The rising and falling edges are defined using the percentage amplitude method. First, the maximum value in the sequence is searched as the peak value A_max, and the corresponding cycle number n_peak is recorded. The starting and ending cycle numbers n_start_up and n_end_up of the rising edge are determined as follows: starting from n=1, search towards n_peak, finding the first cycle number that satisfies y_n>0.1×A_max as n_start_up; then, search backwards from n_peak towards n_start_up, finding the first cycle number that satisfies y_n>0.9×A_max as n_end_up. The starting and ending cycle numbers n_start_down and n_end_down of the falling edge are determined as follows: starting from n_peak, search towards the end of the sequence, finding the first cycle number that satisfies y_n<0.9×A_max as n_start_down; then, continue searching backwards, finding the first cycle number that satisfies y_n<0.1×A_max as n_end_down.

[0057] To suppress noise interference in the determination of start and end points, a hysteresis confirmation mechanism is introduced during the search process: when a circle number that meets the threshold condition is found, the next two consecutive circles must remain within the same threshold range (above the threshold for the rising segment, and below the threshold for the falling segment) before the circle is finally confirmed as the start and end point. If this condition cannot be met near the pulse start point due to noise, it is appropriately relaxed to confirm for one consecutive circle, and the confidence level of this determination is marked in the diagnostic log.

[0058] Perform a least-squares linear fit on the set of data points (t_i, y_i) within the rising edge interval [n_start_up, n_end_up]. Assume there are M data points in this interval, and calculate the rising edge slope S_rise = [M × Σ(t_i × y_i) - Σt_i × Σy_i] / [M × Σ(t_i...] 2 )-(Σt_i) 2 The summation range is i from 1 to M. Similarly, for N data points within the falling edge interval [n_start_down, n_end_down], the falling edge slope S_fall is calculated using the same formula. The slope ratio R is calculated as R = S_rise / |S_fall|. When the denominator |S_fall| is extremely small (less than a preset value, such as 0.001), it indicates that the falling edge is nearly vertical. In this case, R is directly determined to be much greater than 1, and there is no need to calculate the precise ratio.

[0059] When R > 1, the rising edge slope is greater than the falling edge slope, resulting in a steeper pulse rise, and the asymmetric direction is determined as the first direction. When R < 1, the falling edge slope is greater, resulting in a steeper pulse fall, and the asymmetric direction is determined as the second direction. When R equals 1 or the difference between the two is within a preset tolerance range (e.g., between 0.95 and 1.05), the pulse is determined to be symmetrical, and the direction cannot be determined based on this.

[0060] In a preferred embodiment, the waveform asymmetry feature further includes the rate of change of the ratio of the pulse rising edge slope to the falling edge slope as a function of the engine speed. Before determining the asymmetric direction of the transient offset pulse, the following steps are also included: The instantaneous rotational speed change rate corresponding to the moment the transient offset pulse occurs during the unidirectional rotational speed change process is obtained; Based on the correspondence between the offline pre-calibrated speed change rate and the slope ratio correction amount, the ratio of the pulse rising edge slope to the falling edge slope is corrected. The asymmetric direction is determined based on the corrected ratio.

[0061] First, calculate the instantaneous speed change rate at the moment the transient offset pulse occurs. The specific calculation method is as follows: The key phase sensor outputs one pulse per revolution, and the arrival time of two adjacent key phase pulses is recorded. The time interval Δt_key is the rotation period of that revolution. The instantaneous speed of the kth revolution is n_k = 60 / Δt_key(k), in revolutions per minute (rpm). During the unidirectional speed change process, the sequence of speed change with revolution number is obtained by plotting the revolution number as the x-axis and the instantaneous speed n_k as the y-axis. The peak revolution number of the transient offset pulse is j_peak. The speed values ​​of 11 revolutions (5 revolutions before and after j_peak) are subjected to least-squares linear fitting. The slope of the fitted line is the instantaneous speed change rate a at j_peak, in revolutions per minute (rpm). The specific fitting formula is a = [11 × Σ(k_i × n_i) - Σk_i × Σn_i] / [11 × Σ(k_i × n_i)]. 2 )-(Σk_i) 2 ]×(60 / Δt_bar), where k_i is the revolution number, n_i is the rotational speed of the corresponding revolution, and Δt_bar is the average period of the 11 revolutions, used to convert the change in rotational speed per revolution into the change per second. If the bond phase pulse happens to be within the range of these 11 revolutions, the time interval of the bond phase pulse can be used directly for more accurate differential calculation, and a similar fitting can be performed with the bond phase pulse number as the independent variable.

[0062] Then, based on the offline calibrated correspondence between the speed change rate and the slope ratio correction amount, the correction amount ΔR corresponding to the current speed change rate a is calculated. This correspondence is stored in the diagnostic system in the form of a data table. The table contains the speed change rates a_1, a_2, ..., a_L and their corresponding correction amounts ΔR_1, ΔR_2, ..., ΔR_L, arranged in ascending order of speed change rate. When the online measured a is exactly equal to a_i in the table, the corresponding ΔR_i is directly taken; when a is between a_i and a_{i+1}, linear interpolation is used to calculate ΔR = ΔR_i + (ΔR_{i+1} - ΔR_i) × (a - a_i) / (a_{i+1} - a_i). If a is outside the range of the table, the ΔR value of the nearest endpoint is taken. The original ratio R_raw is subtracted from the correction amount ΔR to obtain the corrected ratio R_corrected = R_raw - ΔR.

[0063] Finally, the asymmetric direction is determined based on the corrected ratio R_corrected: if R_corrected>1, it is determined to be the first direction; if R_corrected<1, it is determined to be the second direction.

[0064] In a preferred embodiment, the correspondence between the rotational speed change rate and the slope ratio correction amount is obtained through the following calibration steps: On the test bench, at least one pair of standard faulty crowned blades with known loose leaf roots were subjected to multiple unidirectional rotation speed changes at different rates. The arrival times were collected and the second arrival time difference sequence after detrending was calculated. The transient offset pulses in each process were extracted. For each rate of change of rotational speed, calculate the ratio of its rising edge slope to its falling edge slope; obtain the reference ratio of the rising edge slope to the falling edge slope of the standard faulty crowned blade measured under steady-state or no speed change conditions. The difference between the ratio calculated at each speed change rate and the reference ratio is used as the slope ratio correction amount corresponding to that speed change rate.

[0065] Specifically, S7-1, prepare a standard faulty blade. Select a crowned blade of the same model as the actual machine, and remove 0.05 mm of material from one side of the tenon contact surface using precision grinding to create a known loose gap. When this blade is installed on the wheel, its role in the adjacent blade pair is clearly recorded. All other blades remain in good condition. Assemble all blades in the stage onto a high-speed rotating test bench with precisely controllable rotational speed change rate. The test bench is equipped with blade tip timing sensors and key phase sensors of the same model as those in the online system.

[0066] S7-2, Design the test matrix for the rate of change of engine speed. Select multiple uniform acceleration levels covering the actual operating range of the engine, such as increases of 300 rpm, 500 rpm, 1000 rpm, 2000 rpm, and 3000 rpm per minute. Uniform deceleration levels can also be added; if the dynamics of deceleration and acceleration are asymmetrical, they need to be calibrated separately. Repeat the test at each rate level at least five times to evaluate repeatability.

[0067] S7-3, Perform the test and collect data. For each test at each speed level, start the test bench and accelerate uniformly from the initial speed to the final speed, maintaining blade contact throughout. Collect tip timing and bond pulse data. Process the data according to the aforementioned method, extract the transient offset pulses of the known faulty blade pair, and calculate the ratio of the rising edge to the falling edge slope. For multiple repeated test results at the same speed level, first perform a discreteness test: calculate the standard deviation σ_R of the ratio R_j obtained from each test at that speed. If the R_j of a certain test deviates from the mean of all tests at that speed by more than three times the standard deviation, it is considered an outlier and is removed. After removing outliers, calculate the arithmetic mean of the remaining valid data to obtain the average ratio R_v corresponding to that speed change rate.

[0068] S7-4, Obtain the baseline ratio R_base. On the same test bench, perform a single unidirectional speed change process at an extremely slow, uniform acceleration rate (no more than 50 revolutions per minute). At this rate, the effect of speed change on sliding kinetics is negligible. Extract the transient offset pulse and calculate the ratio using the same method. Repeat this extremely slow test at least 5 times. After removing outliers through a discreteness check, take the average as the baseline ratio R_base. R_base represents the inherent asymmetric ratio determined solely by the directionality of the blade crown's geometric locking.

[0069] S7-5, calculate the slope ratio correction for each speed level. For the v-th speed level, the correction ΔR_v = R_v - R_base. Record the speed change rate value a_v of speed level v with ΔR_v to form a calibration data table. Linear interpolation of adjacent points in the data table yields the correction for any intermediate speed.

[0070] S7-6, Optional verification step. Use another independent verification blade with known looseness, install it in the same way, select an intermediate speed level different from the calibration, and conduct a variable speed test. Calculate the corrected ratio R_corrected, and verify whether its asymmetric direction judgment result is consistent with the known fault identity of the verification blade. If consistent, the calibration result is valid, and the data table is fixed into the diagnostic system software; if inconsistent, the test process needs to be checked and recalibrated.

[0071] In a preferred embodiment, after determining that the first blade or the second blade is a faulty blade, the following confirmation step is further included: Identify the other adjacent blade pair that the faulty blade is involved in besides the current blade pair, and obtain the diagnostic results for that other adjacent blade pair; When another adjacent blade pair is also determined to have a loose blade root fault, and the faulty blade located therein is the same physical blade as the currently determined faulty blade, the location result of the faulty blade is confirmed.

[0072] Specifically, in S8-1, determine the other adjacent blade pair involved by the faulty blade besides the current blade pair. Given a clear circumferential blade numbering, each blade has two adjacent blades. Assume the currently identified faulty blade pair is composed of blade i and blade i+1, and the located faulty blade is the first blade, i.e., blade i+1 (clockwise side). Then, the other adjacent blade pair involved by blade i+1 is the pair composed of blade i+1 and blade i+2, where the role of blade i+1 in this other pair may change to the second blade (because it is now a counter-clockwise side blade). This physical operation is a simple table lookup, because the circumferential order and numbering of all blades in the stage are determined and entered into the diagnostic system during installation, and the system can automatically find the indices of the two adjacent blade pairs for that physical blade.

[0073] The second step is to obtain the diagnostic results for the other adjacent blade pair. This other blade pair has already undergone all the analysis steps and generated corresponding diagnostic conclusions during the previous diagnostic process. The diagnostic system retrieves the diagnostic markers for this other blade pair from the database, including whether it has been determined to have a loose blade root fault, and if so, which of the two blades is identified as the faulty blade. If this other blade pair is not determined to have a loose blade root fault, or if it is determined to have a loose blade but the identified faulty blade is inconsistent with the currently determined blade, cross-confirmation cannot be completed. In this case, the operator should be informed that the positioning result may be misjudged, and it is recommended to further verify it using methods such as borescope probing.

[0074] The third step involves confirming the location of the faulty blade when another adjacent blade pair is also determined to have a loose blade root fault, and the faulty blade located therein is the same physical blade as the currently determined faulty blade. Upon confirmation, the diagnostic system outputs a report stating "Blade XX Root Looseness Location Confirmed" and escalates the alarm level to one requiring immediate maintenance. If the faulty blades located by the two blade pairs are inconsistent—for example, the current pair is located as blade i+1, while the other pair is located as blade i+2—it indicates a contradiction, which may be due to signal interference or complex multi-point loosening. In this case, a "Location Conflict" warning should be output, and manual intervention should be recommended.

[0075] The effectiveness of this technical solution lies in leveraging the dual constraints of each blade within the crown-ring contact structure. It uses redundant information from adjacent blade pairs to verify the self-consistency of the positioning results. While a single blade pair's diagnostic results may be misjudged due to local signal anomalies or measurement noise, the probability of the same blade being identified as a faulty blade in two independent diagnostic channels is far lower than the misjudgment probability in a single channel, thus significantly improving the reliability of the positioning. This method requires no additional sensors and can be implemented using only existing multi-pair monitoring data, making it a low-cost and effective means to improve diagnostic reliability.

[0076] In a preferred embodiment, the mean arrival time difference of the reference period is obtained as follows: when the engine is first run to the target steady-state condition after factory testing or overhaul, the first arrival time difference of multiple revolutions of the pair of blades is continuously collected, the arithmetic mean is calculated and stored as the reference value; or, multiple steady-state condition periods confirmed to be fault-free in the engine's historical operation record are selected, the mean arrival time difference of the corresponding period is calculated, and the result is statistically processed as the mean arrival time difference of the reference period.

[0077] Specifically, the first method involves acquiring data during the engine's factory test run or first test run after a major overhaul. The specific process is as follows: After the engine is assembled and undergoes low-speed break-in, it is run to the target steady-state condition according to the test run procedure. Parameters such as engine speed, exhaust temperature, and fuel flow rate must be stable within a preset window. After confirming stable operation, data is collected from the blade tip timing sensor. The collection time should be at least three consecutive minutes to ensure a sufficient number of revolutions; for example, for a speed of several thousand revolutions per minute, three minutes can accumulate nearly ten thousand revolutions. The collected data is grouped according to adjacent blade pairs, and the first arrival time difference for each revolution is calculated to obtain the first arrival time difference sequence for that blade pair. Then, the entire collection period is divided into data segments of 30 seconds each. The arithmetic mean of the first arrival time difference for each blade pair is calculated for each data segment, resulting in six segmental means: M1, M2, ..., M6. Finally, the overall arithmetic mean M_base is calculated for these six segmental means, along with the standard deviation σ_base. M_base is used as the average arrival time difference of the blade pair for the reference period, and σ_base is used as the basis for setting the offset alarm threshold. Both are stored in the engine's health record database. This segmented statistical method can effectively examine the stability of the operating conditions and the repeatability of the measurements, avoiding distortion of the reference value due to occasional anomalies in a certain data segment.

[0078] The second method involves selecting multiple confirmed fault-free steady-state operating periods from the engine's historical operating records. When an engine has been in service for a long time, the factory baseline data may no longer be applicable due to normal blade break-in. In this case, the historical data method can be used. The specific process is as follows: Retrieve all operating records of the engine under the target steady-state condition from the engine's historical operating database. Select operating periods that have been confirmed fault-free through various means such as vibration analysis, performance parameter monitoring, and borehole inspection. The criteria for confirming fault-free operation include: the total vibration value of the unit does not exceed the warning value, there are no abnormal frequency components in the spectrum, the exhaust temperature is uniformly distributed, and the most recent borehole inspection did not find blade crown cracks or chipping. Select at least five independent time periods that meet the above conditions, with each time period lasting no less than two minutes. For each time period, calculate the arithmetic mean of the first arrival time difference of the blade pair within that time period using the same method as the first method. After obtaining the five time period means, perform statistical processing: First, calculate the mean and standard deviation of these five means, and then check if any mean deviates from the mean by more than twice the standard deviation. If so, it is removed as an outlier. After removing outliers, the remaining valid means are averaged again to obtain the corrected M_base, which serves as the baseline. When historical data is abundant enough, the median can also be used as the baseline to enhance robustness against outliers.

[0079] Regardless of the method used, once the baseline value is determined, it is locked until recalibration is performed after the next major overhaul or a major fault. During online diagnostics, the difference between the real-time average and M_base is used as the average offset, combined with the offset alarm threshold set by σ_base, to determine crown loss faults. This technical solution ensures the accuracy and traceability of the diagnostic baseline, avoiding false alarms and missed alarms caused by unreliable baseline values.

[0080] For example, during factory testing, a certain type of engine is run to the target steady-state condition (high-pressure rotor speed N2 = 15000 rpm, after stabilization). A pair of adjacent crowned blades (labeled blade A and blade B) are selected, and the baseline value is obtained using the first method. The single data acquisition time is set to 3 minutes, divided into 6 data segments of 30 seconds each. The mean arrival time difference of each segment is calculated, and finally, the overall mean and standard deviation are calculated.

[0081] Table 1: Data Acquisition and Statistics of Factory Test Drive Baseline Data

[0082] As shown in Table 1, the statistical results are as follows: the total mean M_base is 1250.47 microseconds and the standard deviation σ_base is 0.46 microseconds.

[0083] For example: After one service cycle, the baseline values ​​of the same engine need to be updated. Five steady-state operating conditions confirmed to be fault-free by borehole probing are selected from the historical database, their mean arrival time differences are calculated and statistically processed, and outliers are removed.

[0084] Table 2: Example Table of Benchmark Values ​​Obtained Using Historical Data Method

[0085] As shown in Table 2, after statistical processing to remove outliers, the number of valid means is 4, the corrected baseline M_base is 1251.00 microseconds, and the standard deviation σ_base is 0.81 microseconds.

[0086] As can be seen from Tables 1 and 2, the mean arrival time difference of the reference period is not an arbitrarily assigned fixed constant, but a precise statistical quantity that characterizes the steady-state relative position of the blade pair under healthy conditions, obtained through rigorous segmented statistics and outlier removal. The standard deviation σ_base in Table 1 is only 0.46 microseconds, reflecting the consistency of manufacturing and assembly and the stability of measurement. It directly serves as the basis for setting the offset alarm threshold (e.g., threshold = 6 * σ_base ≈ 2.76 microseconds), enabling the diagnostic system to adapt to the individual differences of each engine.

[0087] In a preferred embodiment, the preset time delay range is determined based on the blade rotation period T under the target steady-state condition, specifically [K×T-Δt, K×T+Δt], where K is an integer greater than or equal to 1, representing the number of autocorrelation delay periods, and Δt is a preset time tolerance, which at least covers the autocorrelation peak offset range caused by the vibration phase modulation of adjacent blades due to blade root loosening.

[0088] Specifically, the blade rotation period T under the target steady-state condition is first determined. T is calculated as: T = 60 / (n × N_b), where n is the rotor speed under the target steady-state condition in revolutions per minute (rpm), and N_b is the total number of blades in that stage. Alternatively, the actual rotor rotation period T_rotor can be used more directly, taking the time interval between two adjacent pulses from the key phase sensor as the actual rotor rotation period T_rotor, then the blade rotation period T = T_rotor / N_b. Under the target steady-state condition, the average rotation period over multiple consecutive revolutions is taken as the nominal value of T.

[0089] The parameter K is an integer greater than or equal to 1, representing the number of autocorrelation delay periods. In practical applications, K is set to 1 because the modulation caused by leaf root loosening is mainly reflected at the fundamental frequency, i.e., once per revolution, and the autocorrelation peak is most significant at a delay of one revolution period. If it is necessary to detect higher harmonic modulation, K can be set to 2 or 3, but in general, K=1 is sufficient.

[0090] Determining the time tolerance Δt is crucial for sufficient disclosure. Δt must at least cover the range of autocorrelation peak shifts caused by the phase modulation of vibration between adjacent blades due to blade root loosening. The specific determination method can be implemented using the following steps: First, establish a finite element model of the crowned blade and perform modal analysis on the blade under normal conditions and with different blade root loosening gaps (e.g., 0.02 mm, 0.05 mm, 0.1 mm) to obtain the first few natural frequencies of the blade in the centrifugal force field and their variation with the loosening gap. Second, apply a rotational periodic aerodynamic excitation load to the blade and perform forced vibration response analysis to calculate the changes in vibration amplitude and phase of the blade in the loosened state relative to the healthy state. Third, convert the vibration response into a fluctuating signal of the arrival time difference between adjacent blades, simulate the first arrival time difference sequence under different loosening states, calculate its autocorrelation function, and observe the shift of the peak position of the autocorrelation function near the rotation period relative to the ideal unloosened state. Take the maximum value of the shift in all simulated conditions and denote it as Δτ_max. The fourth step involves considering actual speed fluctuations and measurement noise, and adding a certain engineering margin to Δτ_max, for example, by 20% to 30%, to obtain Δt. For instance, assuming the blade rotation period T under the target operating condition is 0.01 seconds, simulation shows the maximum peak offset caused by loosening is ±0.0004 seconds. After adding a 25% margin, Δt is set to 0.0005 seconds. Therefore, the preset time delay range is set to [1×0.01-0.0005, 1×0.01+0.0005], which is [0.0095, 0.0105] seconds.

[0091] If finite element simulation is not feasible, Δt can be calibrated through bench testing. Using a standard faulty blade with known loosening on a test bench, and operating it under target steady-state conditions, the first arrival time difference sequence is measured, and the autocorrelation function is calculated. The deviation between the time delay of the loosening modulation peak and T is directly measured. The maximum deviation from multiple tests is taken as the benchmark for Δt, plus a margin. The preset time delay range determined by this method ensures that the peak representing loosening in the autocorrelation function can be accurately searched under different degrees of loosening. This avoids missed detections due to an excessively small search range and prevents interference from irrelevant noise peaks introduced by an excessively large search range, thus guaranteeing the reliability of loosening modulation peak extraction.

[0092] For example: In order to determine Δt within the preset time delay range for searching the loosening modulation peak, the finite element simulation method is used to analyze the autocorrelation peak shift caused by different amounts of blade root loosening gaps under the target steady-state condition (rotation period T = 0.008 seconds) for a certain stage of crowned blade.

[0093] Table 3: Autocorrelation Peak Delay Time Offset under Different Loosening Gap Conditions in Finite Element Simulation

[0094] As shown in Table 3, the maximum absolute value of the offset under all loosening conditions is taken from the simulation results: Δτ_max = 0.000720 seconds. Considering the modeling uncertainty and the small fluctuations in actual rotational speed, an engineering margin of 25% is added. The time tolerance Δt = Δτ_max × (1 + 25%) = 0.000720 × 1.25 = 0.0009 seconds. Finally, in this embodiment, the preset time delay range of this type of blade under the target steady-state condition is determined as: [T - Δt, T + Δt] = [0.008 - 0.0009, 0.008 + 0.0009] = [0.0071, 0.0089] seconds.

[0095] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. An online diagnostic method for loosening and crown loss of crowned blades, wherein the crowned blades have a crown at the tip, and during engine operation, at least when the target steady-state condition is reached, the crowns of adjacent crowned blades abut against each other under centrifugal force to form a complete ring contact, characterized in that... The method includes the following steps: Multiple blade tip timing sensors are installed circumferentially on the engine casing. When the engine runs to the target steady-state condition, the arrival times of multiple pairs of adjacent crowned blades in each revolution are collected synchronously. Each pair of adjacent crowned blades consists of two crowned blades with their crowns pressed against each other. The first arrival time difference of each pair of adjacent crowned blades in each revolution is calculated to obtain the first arrival time difference sequence corresponding to each pair of adjacent crowned blades. Calculate the autocorrelation function for each of the first arrival time difference sequences, and extract the loosening modulation peak from the autocorrelation function. The loosening modulation peak is the peak value of the autocorrelation function within a preset time delay range corresponding to the blade rotation period. Calculate the mean offset for each first arrival time difference sequence, where the mean offset is the difference between the mean arrival time difference in the current time period and the mean arrival time difference in the reference time period; the mean arrival time difference in the reference time period is the mean first arrival time difference of the pair of blades measured under the target steady-state operating condition when the engine is in a healthy state. For each pair of adjacent crowned blades, when the loosening modulation peak value meets the first determination condition and the mean offset does not exceed the preset offset alarm threshold, it is determined that there is a leaf root loosening fault in the pair of adjacent crowned blades. The first determination condition requires that the loosening modulation peak value of a single pair of adjacent crowned blades and the overall loosening modulation peak value level of multiple pairs of adjacent crowned blades show a local abnormal increase. When the mean offset exceeds the offset alarm threshold and the loosening modulation peak does not meet the first determination condition, it is determined that there is a crown loss fault in the pair of adjacent crowned blades.

2. The online diagnostic method for leaf root loosening and crown loss faults of crowned leaves according to claim 1, characterized in that, The first determination condition is: The peak value of the loosening modulation of the pair of adjacent crowned blades exceeds the preset loosening alarm threshold, and the ratio of the peak value of the loosening modulation of the pair of adjacent crowned blades to the average value of the peak values ​​of the loosening modulation of the other pairs of adjacent crowned blades exceeds the preset relative difference threshold.

3. The online diagnostic method for leaf root loosening and crown loss faults of crowned leaves according to claim 1, characterized in that, It also includes a diagnostic step when the engine undergoes a unidirectional speed change process, wherein the unidirectional speed change process is the process in which the engine monotonically changes from a first speed to a second speed, and during the process, the blades of adjacent crowned blades always remain in close contact with each other. During the unidirectional speed change process, the arrival time of each pair of adjacent crowned blades is continuously collected, and the arrival time difference of each pair of adjacent crowned blades in each revolution during the unidirectional speed change process is calculated to obtain the second arrival time difference sequence of the speed change process. The second arrival time difference sequence is detrended to remove the overall trend of arrival time difference caused by the change in rotational speed, resulting in a detrended second arrival time difference sequence that fluctuates around zero. The transient offset pulse is extracted from the detrended second arrival time difference sequence. The transient offset pulse is a signal segment in which the detrended second arrival time difference continuously deviates from zero within multiple consecutive cycles and the deviation exceeds a preset transient offset threshold. When a transient offset pulse occurs in a pair of adjacent crowned blades during the unidirectional speed change, and the transient offset pulse is a single pulse, and the average offset of the pair of adjacent crowned blades after the speed stabilizes does not exceed the offset alarm threshold, it is determined that there is a blade root loosening fault in the pair of adjacent crowned blades.

4. The online diagnostic method for leaf root loosening and crown loss faults of crowned leaves according to claim 3, characterized in that, After determining that a pair of adjacent crowned leaves have a loose leaf root fault, the following steps are also included: Establish an absolute spatial reference: Observe along the direction from the engine intake end to the exhaust end, take the counterclockwise rotation direction of the rotor as the positive circumferential direction, and designate the blade on the clockwise side of the pair of adjacent crowned blades as the first blade and the blade on the counterclockwise side as the second blade. Extract waveform asymmetry features from the transient offset pulse; Based on the waveform asymmetry characteristics, the asymmetric direction of the transient offset pulse is determined; The asymmetric direction is compared with a pre-defined fault direction mapping rule. The fault direction mapping rule is determined by the geometric locking directionality of the blade crown contact surface, specifying the asymmetric direction corresponding to the loosening of the first blade root and the asymmetric direction corresponding to the loosening of the second blade root. The asymmetric direction corresponding to the loosening of the second blade root is opposite to the asymmetric direction corresponding to the loosening of the first blade root. The geometric locking directionality of the blade crown contact surface refers to the locking structure characteristic that allows only unidirectional sliding of the blade crown contact surface under circumferential aerodynamic load. When the asymmetric direction of the transient offset pulse is consistent with the asymmetric direction corresponding to the loosening of the first blade root, the first blade is determined to be a faulty blade; otherwise, the second blade is determined to be a faulty blade.

5. The online diagnostic method for leaf root loosening and crown loss faults of crowned leaves according to claim 4, characterized in that, The determination of the asymmetric direction of the transient offset pulse based on the waveform asymmetry characteristics specifically involves: The waveform asymmetry feature includes the ratio of the pulse rising edge slope to the falling edge slope; When the ratio is greater than the theoretical symmetry ratio 1, the asymmetric direction is determined to be the first direction; when the ratio is less than the theoretical symmetry ratio 1, the asymmetric direction is determined to be the second direction opposite to the first direction.

6. The online diagnostic method for leaf root loosening and crown drop faults of crowned leaves according to claim 5, characterized in that, The waveform asymmetry feature also includes the rate of change of the ratio of the pulse rising edge slope to the falling edge slope as a function of the engine speed. Before determining the asymmetric direction of the transient offset pulse, the following steps are also included: The instantaneous rotational speed change rate corresponding to the moment the transient offset pulse occurs during the unidirectional rotational speed change process is obtained; Based on the correspondence between the offline pre-calibrated speed change rate and the slope ratio correction amount, the ratio of the pulse rising edge slope to the falling edge slope is corrected. The asymmetric direction is determined based on the corrected ratio.

7. The online diagnostic method for leaf root loosening and crown loss faults of crowned leaves according to claim 6, characterized in that, The correspondence between the rate of change of rotational speed and the slope ratio correction amount is obtained through the following calibration steps: On the test bench, at least one pair of standard faulty crowned blades with known loose leaf roots were subjected to multiple unidirectional rotation speed changes at different rates. The arrival times were collected and the second arrival time difference sequence after detrending was calculated. The transient offset pulses in each process were extracted. For each rate of change of rotational speed, calculate the ratio of its rising edge slope to its falling edge slope for the transient offset pulse. Obtain the reference ratio of the rising edge to the falling edge slope of the standard faulty crowned blade under steady-state or no speed change influence conditions; The difference between the ratio calculated at each speed change rate and the reference ratio is used as the slope ratio correction amount corresponding to that speed change rate.

8. The online diagnostic method for leaf root loosening and crown loss faults of crowned leaves according to claim 4, characterized in that, After determining that the first or second blade is a faulty blade, the following confirmation steps are also included: Identify the other adjacent blade pair that the faulty blade is involved in besides the current blade pair, and obtain the diagnostic results for that other adjacent blade pair; When another adjacent blade pair is also determined to have a loose blade root fault, and the faulty blade located therein is the same physical blade as the currently determined faulty blade, the location result of the faulty blade is confirmed.

9. The online diagnostic method for leaf root loosening and crown loss faults of crowned leaves according to claim 1, characterized in that, The method for obtaining the mean arrival time difference of the reference period is as follows: when the engine is first run to the target steady-state condition after factory test or overhaul, the first arrival time difference of multiple revolutions of the pair of blades is continuously collected, the arithmetic mean is calculated and stored as the reference value. Alternatively, select multiple steady-state operating periods from the engine's historical operating records that have been confirmed to be fault-free, calculate the average arrival time difference for the corresponding periods, and use the statistically processed average arrival time difference for the reference period.

10. The online diagnostic method for leaf root loosening and crown loss faults of crowned leaves according to claim 1, characterized in that, The preset time delay range is determined based on the blade rotation period T under the target steady-state condition, specifically [K×T-Δt, K×T+Δt], where K is an integer greater than or equal to 1, representing the number of autocorrelation delay periods, and Δt is a preset time tolerance, which at least covers the autocorrelation peak offset range caused by the vibration phase modulation of adjacent blades due to blade root loosening.

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