Diagnostic and positioning method of high-frequency interference resistance for weak DC bias trend signal

Abstract

The present application relates to the technical field of system operation state monitoring and fault diagnosis, and provides a weak DC bias trend signal anti-high-frequency interference diagnosis and positioning method.The method comprises the following steps: establishing an original diagnosis signal model; obtaining a low-frequency bias trend characteristic component and a high-frequency disturbance component; calculating a low-frequency abnormality intensity index, a high-frequency interference intensity index and a direction stability index; setting a low-frequency abnormality intensity index threshold and a direction stability index threshold; outputting a state branch; establishing a single abnormality source fingerprint library; calculating the signed similarity between a current low-frequency trend direction vector and each single abnormality source fingerprint, and repositioning the abnormality source; defining a fingerprint matching confidence, and then judging the bias direction and estimating the abnormality intensity; establishing an extended fingerprint library; calibrating the amplitude proportion coefficient under a single calibration sample; self-learning to construct the fingerprint library; and outputting the diagnosis and positioning result.The present application can improve the detection sensitivity of weak early abnormalities.

Description

Technical Field

[0001] This invention relates to the technical field of system operation status monitoring and fault diagnosis, and more specifically, to a method for diagnosing and locating weak DC bias trend signals against high-frequency interference. Background Technology

[0002] In fields such as industrial control, energy equipment, transportation systems, aerospace, robotics, motor drives, power electronics, process industries, energy storage systems, medical testing, and structural health monitoring, system operating status is typically characterized through various sensors, estimators, or residual generation modules. Early anomalies in real-world systems often do not immediately manifest as large abrupt changes, but rather as weak DC bias, low-frequency drift, slow trends, or continuously accumulating offsets. For example, sensor zero-point drift may create a small DC bias in the measurement signal; early faults in current sensors may manifest as low-amplitude biases; aging of pressure, temperature, flow, or voltage measurement channels may manifest as slow drifts; consistency degradation in battery systems may manifest as low-frequency trend differences; and early damage in mechanical systems may also create stable offsets in certain residual characteristics. These anomalies initially have low amplitudes and often do not trigger traditional protection thresholds, but if not identified in time, they may further develop into serious faults.

[0003] However, actual acquired signals typically contain high-frequency noise, periodic ripple, switching harmonics, impulse disturbances, load fluctuations, environmental noise, and measurement random errors. The instantaneous amplitudes of these high-frequency or pulsating components may be significantly larger than the target's weak DC bias signal, thus masking target anomalies. Traditional methods based on instantaneous amplitude, root mean square value, peak value, spectral energy, or fixed thresholds are prone to two types of problems in this scenario: first, false alarms when high-frequency interference is strong; and second, missed diagnoses when the target bias signal is weak.

[0004] To address the two types of problems mentioned above, existing methods typically establish specific criteria for a particular type of equipment or fault, lacking versatility. When the target signal shares common characteristics such as "low amplitude, slow change, stable direction, and long-term existence," while the interference signal shares common characteristics such as "high frequency, rapid change, unstable direction, and large instantaneous energy," it is necessary to propose a more universal method for detecting and locating weak DC bias trend signals. Summary of the Invention

[0005] The present invention aims to solve at least one of the technical problems existing in the prior art or related art.

[0006] Therefore, the purpose of this invention is to propose a method for diagnosing and locating weak DC bias trend signals against high-frequency interference.

[0007] To achieve the above objectives, the present invention provides a method for diagnosing and locating weak DC bias trend signals against high-frequency interference. This method includes: Step 1: establishing an original diagnostic signal model based on the acquired original diagnostic signal; Step 2: obtaining low-frequency bias trend characteristic components and high-frequency disturbance components based on the original diagnostic signal model; Step 3: calculating a low-frequency abnormality intensity index based on the calculated healthy baseline mean, the constructed weighting matrix, and the low-frequency bias trend characteristic components. Step 4: Calculate the high-frequency interference intensity index based on the high-frequency disturbance components; Step 5: Calculate the directional stability index based on the calculated current low-frequency trend direction vector, and then set the low-frequency anomaly intensity index threshold and the directional stability index threshold to form a weak DC bias trend candidate criterion; Step 6: Output the state branch according to the constructed anti-high-frequency interference state decision logic; Step 7: Establish a single anomaly source fingerprint database; wherein, the single anomaly source fingerprint database consists of all single anomaly source fingerprints; Step 8: Calculate the signed similarity between the current low-frequency trend direction vector and each single anomaly source fingerprint, and then locate the anomaly source based on the similarity; Step 9: Define the fingerprint matching confidence, then determine the bias direction, and then estimate the anomaly intensity; Step 10: Establish an extended fingerprint database to handle the situation of multiple sources simultaneously causing anomalies; Step 11: Calibrate the amplitude ratio coefficient under a single calibration sample; Step 12: When there is no explicit model, construct the fingerprint database through self-learning; Step 13: Output the diagnosis and location results of the weak DC bias trend signal.

[0008] Preferably, step 1 specifically includes: Step 1.1: Obtain the original diagnostic signal and establish the original diagnostic signal model; wherein, the expression of the original diagnostic signal model is: (1) In equation (1), This is the original diagnostic signal; The weak DC bias trend signal to be detected; This includes high-frequency disturbances, periodic ripples, impulse noise, or other non-target interference. For random measurement noise; This is the mapping matrix from the weak bias signal to the diagnostic signal space; This is the mapping matrix from high-frequency disturbances to the diagnostic signal space; For continuous time; Step 1.2: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] Modeled as a slowly varying signal, the corresponding expression is: (2) In equation (2), for The time derivative; For low-frequency trend dynamic parameters, ; For slowly changing trend drivers; Step 2 specifically includes: Step 2.1: Perform low-pass dynamic processing on the original diagnostic signal to obtain the low-frequency or DC trend component of the original diagnostic signal. ;in, The expression for the time derivative is: (3) In equation (3), This refers to the low-frequency or DC trend component of the original diagnostic signal; for The time derivative; This is the low-pass cutoff angular frequency; Step 2.2: Use discrete form to... Low-pass processing is performed to obtain the low-frequency trend component; the expression for the low-frequency trend component is: (4) In equation (4), For discrete sampling sequence numbers; For the first Low-frequency trend components at each sampling time; For the first The original diagnostic signal at each sampling time; For discrete low-pass coefficients, ; In equation (4), The expression is: (5) In equation (5), The sampling period; It is the low-pass time constant, and ; It is a natural exponential function; Step 2.3: Based on the original diagnostic signals and low-frequency trend components The high-frequency disturbance component is obtained; the expression for the high-frequency disturbance component is: (6) In equation (6), For the first High-frequency disturbance components at each sampling time; Step 2.4: In a length of Within a sliding window, the low-frequency bias trend characteristic component is calculated; whereby the expression for the low-frequency bias trend characteristic component is: (7) In equation (7), These are low-frequency bias trend feature components used for anomaly diagnosis and localization; The length of the sliding window; Use the index for summation within the window.

[0009] Preferably, step 3 specifically includes: Step 3.1: Calculate the healthy baseline mean; where the expression for the healthy baseline mean is: (8) In equation (8), This represents the mean of low-frequency characteristics under normal conditions. The first under normal conditions Low-frequency characteristics of a sliding window; This represents the normal sample size. This is a normal sample index; Step 3.2: Calculate the healthy baseline covariance matrix; whereby the expression for the healthy baseline covariance matrix is: (9) In equation (9), This is the covariance matrix of low-frequency features under normal conditions; superscript Indicates transpose; Step 3.3: Perform baseline correction on the current low-frequency bias trend characteristic components. The corresponding expression is: (10) In equation (10), The low-frequency bias trend characteristic component after baseline correction; Step 3.4: Construct the weighting matrix as follows: (11) In equation (11), It is a weighted matrix; This is a small amount of regularization used to avoid matrix singularities; It is the identity matrix; superscript This represents finding the inverse of a matrix. Step 3.5: Calculate the low-frequency anomaly intensity index as follows: (12) In equation (12), For the first The abnormal intensity of low-frequency bias trend in each diagnostic window; For square root operations; Step 4, specifically: Within the same sliding window, calculate the high-frequency interference intensity index based on the high-frequency disturbance components; wherein, the expression for the high-frequency interference intensity index is: (13) In equation (13), For the first High-frequency interference intensity index for each diagnostic window; It is the vector norm; Step 5 specifically includes: Step 5.1: Based on the low-frequency bias trend feature components after baseline correction, calculate the current low-frequency trend direction vector; where the expression for the current low-frequency trend direction vector is: (14) In equation (14), For the first Low-frequency trend direction vector of each diagnostic window; To prevent positive numbers from being divided by zero; Step 5.2: In a length of Within the directional stability evaluation window, the directional stability index is calculated; the expression for the directional stability index is: (15) In equation (15), This is a directional stability index; The length of the directional stability evaluation window; Step 5.3: Set thresholds for low-frequency anomaly intensity and directional stability to form candidate criteria for weak DC bias trends, and require that the low-frequency anomaly intensity index continuously... Within a diagnostic window, the intensity of the low-frequency abnormality index exceeds the threshold, and the directional stability index remains within a continuous range. Within each diagnostic window, the value is greater than the directional stability index threshold; among them, the expression for the candidate criterion for weak DC bias trend is: (16) (17) Low-frequency anomaly intensity index in continuous Within a diagnostic window, the intensity of the low-frequency abnormality index exceeds the threshold, and the directional stability index is within a continuous range. The expression for a value greater than the directional stability index threshold within a diagnostic window is: (18) In equations (16), (17), and (18), The threshold for low-frequency anomaly intensity index; The threshold for directional stability index; To continuously confirm the number of windows; Step 6 specifically includes: Step 6.1: Based on S[k], C[k], and H[k], construct the state decision logic for resisting high-frequency interference as follows: (19) (20) (twenty one) In equations (19), (20), and (21), This indicates whether the strength of the low-frequency bias trend exceeds a threshold; Indicates whether the low-frequency direction is stable; Indicate whether the high-frequency interference is significant; This is the threshold for high-frequency interference intensity. Step 6.2: Based on the above three logical quantities, the output state branches are shown in the table below: Table 1 Output State Branches .

[0010] Preferably, step 7 specifically includes: Step 7.1: Let the set of candidate anomaly sources be: (twenty two) In equation (22), For the set of candidate anomaly sources; Indicates the first Sources of anomalies similar to weak bias trends; The total number of candidate sources; For source index; Step 7.2: Mapping matrix from weak bias signal to diagnostic signal space When known, construct the first The unit fingerprint direction from which the weak bias trend anomaly originates is: (twenty three) In equation (23), For the first The unit fingerprint direction corresponding to the source of the weak bias trend anomaly; Step 7.3: The single anomaly source fingerprint database is composed of all fingerprints from a single source of anomaly. (twenty four) In equation (24), A fingerprint database for single anomaly sources.

[0011] Preferably, step 8 specifically includes: Step 8.1: Calculate the signed similarity between the current low-frequency trend direction vector and the fingerprint of each single anomaly source; wherein the expression for the similarity is: (25) In equation (25), For the first The current low-frequency trend direction in the diagnostic window is related to the first... Signed similarity between fingerprints representing anomalies; Step 8.2: Use absolute similarity to determine the anomaly source number: (26) In equation (26), The number of the source of the maximum matching anomaly; This represents the index at which the objective function is maximized; Step 8.3: Introduce a fingerprint matching threshold and a fingerprint similarity margin threshold, and set the following conditions: (27) (28) In equations (27) and (28), The signified similarity is the result of the match with the largest absolute value. The signed similarity corresponds to the second largest absolute similarity. This is the fingerprint matching threshold; This is the fingerprint similarity margin threshold; Step 8.4: When equations (16), (17), (18), (27), and (28) are all true, output the weak DC bias trend anomaly and the fault source location result; if equation (16) is true, but If equation (17) is not satisfied, or equation (28) is not valid, the output will show a state of uncertain diagnosis or multi-source competition.

[0012] Preferably, step 9 specifically includes: Step 9.1: Define the fingerprint matching confidence level as: (29) In equation (29), For the first Fingerprint matching confidence level for each diagnostic window; A saturation function, used to restrict its own input to a certain range. Within the range; Step 9.2: Match the source with the largest absolute value using the signed similarity. Determine the bias direction: (30) In equation (30), The bias direction; For sign functions; when When, it indicates a positive bias trend; when When, it indicates a negative bias trend; Step 9.3: Estimate the anomaly intensity based on the calibration scaling factor: (31) In equation (31), For the first Anomaly intensity estimates for each diagnostic window; For the first The proportionality coefficient between the actual bias amplitude and the diagnostic signal amplitude for anomalies.

[0013] Preferably, step 10 specifically includes: Step 10.1: When multiple sources may simultaneously produce a weak bias trend, define a combined source set. One of the combined sources Represented as: (32) In equation (32), For the combined source set; Sourced from a certain combination; A single-source number for the portfolio; The number of sources in the combination; Step 10.2: Construct the combined source basis vectors: (33) In equation (33), To combine the source basis vectors; For the first in the combination The relative amplitude or sign of each source; Step 10.3: Mapping matrix from weak bias signal to diagnostic signal space When known, the source of the combination The unit fingerprint is: (34); Step 10.4: When using data calibration, the combined source is obtained by normalizing the mean of the combined outlier samples. The unit fingerprint is: (35) In equation (35), The average low-frequency features of the combined abnormal samples; Step 10.5: Based on the single anomaly source fingerprint database and the combined source fingerprint database, construct the extended fingerprint database as follows: (36) In equation (36), To expand the fingerprint database; For combined source fingerprint databases; Represents the union of sets; Step 10.6: Transfer the current low-frequency trend direction vector and The system performs maximum similarity matching on all fingerprints and outputs anomaly diagnosis results.

[0014] Preferably, step 11 specifically includes: Step 11.1: In a healthy state, obtain the results according to steps 3.1 and 3.2 respectively. and ; Step 11.2: For the first A known amplitude is applied to an anomaly source. The bias, or the application of historical samples with known amplitude; Step 11.3: Following step 2.4, calculate the low-frequency bias trend characteristic component, and perform baseline correction on this low-frequency bias trend characteristic component to obtain the... The low-frequency characteristics of baseline correction for anomaly sources under calibration conditions are as follows: (37); Step 11.4: Calculation The source fingerprint is: (38) Step 11.5: Calculate the amplitude scaling factor for a single calibration sample: (39) In equation (39), For the first Amplitude scaling factor for anomaly sources; The abnormal bias amplitude applied or known during calibration; Step 11.6: If multiple calibration amplitudes or multiple calibration samples are used, then take: (40) In equation (40), For the first Number of calibrated samples from each source; For the first Baseline-corrected low-frequency characteristics of each calibration sample; For the first The known bias amplitude corresponding to each calibration sample.

[0015] Preferably, step 12 specifically includes: Step 12.1: Mapping matrix from weak bias signal to diagnostic signal space When accurate fingerprints cannot be obtained, a fingerprint database is constructed through self-learning using calibrated data or historical data. Step 12.2: Let the first... The mean baseline-corrected low-frequency features of this type of anomaly generated in calibration experiments or historical samples are: (41) In equation (41), For the first Average low-frequency characteristics of anomalies; For the first The first class of exceptions One baseline-corrected low-frequency feature sample; Step 12.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] The self-learning fingerprint is defined as: (42).

[0016] Preferably, in step 13, the output diagnosis and localization results are as follows: Table 2 Diagnostic and Localization Results

[0017] In Table 2, BiasFlag, SourceIndex, BiasPolarity, BiasAmplitude, Confidence, MultiSourceFlag, HFIndex, TrendFeature, and DecisionState are all output variable names of the anti-high frequency interference diagnosis and localization method for this weak DC bias trend signal.

[0018] The method for diagnosing and locating weak DC bias trend signals against high-frequency interference provided by this invention has the following beneficial effects: (1) This invention is aimed at a general type of signal characteristics, namely, weak abnormal signals with low amplitude, slow change, and DC bias or low frequency trend, and is not limited to a certain type of equipment or a certain type of fault. This invention separates the low frequency bias trend component from the high frequency disturbance component, which can reduce the probability of false alarm when high frequency noise, periodic ripple, impact disturbance, switching harmonics or broadband interference are present. (2) This invention does not rely on the instantaneous amplitude of the original signal, but uses low-frequency intensity, directional stability and persistence to make a joint judgment, thus improving the detection sensitivity of weak early anomalies; (3) The present invention achieves anomaly source location by fingerprint database matching, which can not only determine whether there is a weak bias trend anomaly, but also identify the anomaly source channel, bias direction and trend strength; (4) The present invention can establish a fingerprint database based on the system model or a self-learning fingerprint database based on historical data or calibration experiments, and is applicable to different scenarios where the model is known and the model is difficult to establish accurately; (5) This invention can distinguish between high-frequency interference enhancement and low-frequency bias trend abnormality. When the high-frequency interference is strong but the low-frequency bias trend is not obvious, no bias abnormality alarm is output; when the low-frequency trend is stable, continuous detection can be performed even if its amplitude is low. (6) This invention can be applied to early current sensor failure, sensor zero drift, measurement channel bias, slow health degradation, low frequency leakage characteristics, system bias drift and other weak trend anomalies, and has strong versatility and engineering promotion value.

[0019] Additional aspects and advantages of the invention will become apparent from the description which follows, or may be learned by practice of the invention. Attached Figure Description

[0020] Figure 1 A flowchart illustrating a method for diagnosing and locating weak DC bias trend signals against high-frequency interference, according to an embodiment of the present invention, is shown. Detailed Implementation

[0021] To better understand the above-mentioned objects, features, and advantages of the present invention, such as Figure 1 As shown in the accompanying drawings and specific embodiments, the present invention will be further described in detail below. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0022] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0023] Figure 1 A flowchart illustrating a method for diagnosing and locating weak DC bias trend signals against high-frequency interference, according to an embodiment of the present invention, is shown. Figure 1 As shown, the method for diagnosing and locating the weak DC bias trend signal against high-frequency interference includes: Step 1: Based on the acquired original diagnostic signals, establish an original diagnostic signal model; Step 2: Based on the original diagnostic signal model, obtain the low-frequency bias trend characteristic component and the high-frequency disturbance component; Step 3: Calculate the low-frequency anomaly intensity index based on the calculated health baseline mean, the constructed weighted matrix, and the low-frequency bias trend feature components; Step 4: Calculate the high-frequency interference intensity index based on the high-frequency disturbance components; Step 5: Based on the calculated current low-frequency trend direction vector, calculate the directional stability index, and then set the threshold for the low-frequency anomaly intensity index and the threshold for the directional stability index to form a candidate criterion for weak DC bias trend; Step 6: Output the state branch based on the constructed anti-high frequency interference state decision logic; Step 7: Establish a single anomaly source fingerprint database; wherein, the single anomaly source fingerprint database consists of all fingerprints from single anomaly sources; Step 8: Calculate the signed similarity between the current low-frequency trend direction vector and the fingerprint of each single anomaly source, and then locate the anomaly source based on the similarity; Step 9: Define the fingerprint matching confidence level, then determine the bias direction, and then estimate the anomaly strength; Step 10: Establish an extended fingerprint database to handle simultaneous anomalies from multiple sources; Step 11: Calibrate the amplitude scaling factor for a single calibration sample; Step 12: When there is no explicit model, construct a fingerprint database through self-learning; Step 13: Diagnostic and location results of outputting weak DC bias trend signals.

[0024] In this embodiment, the method targets weak anomalous signals with low amplitude, slow change, and primarily exhibiting DC bias, low-frequency drift, or a slow trend. These signals can originate from sensors, observers, estimators, residual generators, state monitoring modules, or data acquisition systems. The core of this method is not to directly compare the instantaneous amplitude of the original signal, but rather to first extract the low-frequency bias trend component, and then combine it with high-frequency interference intensity, directional stability, and fingerprint database matching to achieve anomaly detection, source location, bias direction determination, and trend intensity estimation.

[0025] The technical solution of the present invention will be demonstrated below with reference to specific embodiments 1 and 2.

[0026] Specific Implementation Example 1: A method for diagnosing and locating weak DC bias trend signals against high-frequency interference; The method for diagnosing and locating weak DC bias trend signals against high-frequency interference in this specific embodiment 1 is implemented through the following steps: 1) Step 1: Establish the original diagnostic signal model; Step 1.1: Obtain the raw or residual signal for diagnosis and represent it as a multidimensional vector: ; in, The original diagnostic signal can be a measurement signal, an estimation error signal, a residual signal, or a feature vector. The weak DC bias trend signal to be detected; This includes high-frequency disturbances, periodic ripples, impulse noise, or other non-target interference. For random measurement noise; This is the mapping matrix from the weak bias signal to the diagnostic signal space; This is the mapping matrix from high-frequency disturbances to the diagnostic signal space; For continuous time; Step 1.2: Model the weak DC bias trend signal as a slowly varying signal: ; in, for The time derivative; For low-frequency trend dynamic parameters, satisfy ; This is a slowly changing trend-driven term. Within a finite diagnostic window, It can be approximated as a constant DC bias or a slowly changing low-frequency trend.

[0027] 2) Step 2: Extract the low-frequency bias trend component and separate the high-frequency interference component; Step 2.1: Perform low-pass dynamic processing on the original diagnostic signal to obtain the low-frequency or DC trend component: ; in, This refers to the low-frequency or DC trend component of the original signal. Its time derivative, This is the low-pass cutoff angular frequency; Step 2.2: Implement low-pass processing in a discrete manner in a digital controller or embedded processor: ; ; in, For discrete sampling sequence numbers; For the first Low-frequency trend components at each sampling time; For the first The original diagnostic signal at each sampling time; For discrete low-pass coefficients, satisfying ; The sampling period; It is the low-pass time constant, and ; It is a natural exponential function; Step 2.3: Obtain the high-frequency disturbance component based on the original signal and the low-frequency trend component: ; in, For the first High-frequency disturbance components at each sampling time; Step 2.4, in a length of Calculate the low-frequency bias trend characteristics within the sliding window: ; in, This is a low-frequency bias trend feature vector used for diagnosis and localization; The length of the sliding window; Use the index for summation within the window.

[0028] 3) Step 3: Establish a healthy baseline and calculate the intensity index of low-frequency anomalies; Step 3.1: Collect data under normal conditions Calculate the mean of the healthy baseline from a window of samples without abnormalities: ; in, This represents the mean of low-frequency characteristics under normal conditions. The first under normal conditions Low-frequency characteristics of a sliding window This is the normal sample size. This is a normal sample index; Step 3.2: Calculate the healthy baseline covariance matrix: ; in, This is the covariance matrix of low-frequency features under normal conditions, with superscript... Indicates transpose; Step 3.3: Perform baseline correction on the current low-frequency bias trend characteristics: ; in, The low-frequency bias trend characteristics after baseline correction; Step 3.4: Construct the weighting matrix: ; in, It is a weighted matrix; This is a small amount of regularization used to avoid matrix singularities; It is the identity matrix; superscript This represents finding the inverse of a matrix. Step 3.5: Calculate the low-frequency anomaly intensity index: ; in, For the first The intensity of the low-frequency bias trend anomaly in each diagnostic window This is for square root operations.

[0029] 4) Step 4: Calculate the high-frequency interference intensity index; Step 4.1: Within the same sliding window, calculate the high-frequency interference intensity based on the high-frequency disturbance components: ; in, For the first High-frequency interference intensity index for each diagnostic window; This is the vector norm. This indicator is used to determine whether the current signal is mainly affected by high-frequency noise, switching harmonics, periodic ripple, or impulse disturbances.

[0030] 5) Step 5: Calculate the low-frequency trend direction and directional stability index; Step 5.1: Calculate the current low-frequency trend direction based on the baseline-corrected low-frequency characteristics: ; in, For the first Low-frequency trend direction vector of each diagnostic window; To prevent small positive numbers from being divided by zero.

[0031] Step 5.2: In a length of Within the directional stability evaluation window, calculate the directional stability index: ; in, As a directional stability index, The length of the directional stability evaluation window; when the low-frequency bias trend direction is stable. Approaching 1; when the signal is mainly dominated by high-frequency disturbances or random noise, Smaller; Step 5.3: Set the low-frequency anomaly intensity threshold and directional stability threshold to form a candidate criterion for weak DC bias trend: ; ; And require it to be continuous Established within a single diagnostic window: ; in, The threshold for low-frequency anomaly intensity. The directional stability threshold, To continuously confirm the number of windows.

[0032] 6) Step 6: Construct state decision logic resistant to high-frequency interference; Step 6.1: According to , and Define three logical quantities: ; ; ; in, This indicates whether the strength of the low-frequency bias trend exceeds a threshold. This indicates whether the low-frequency direction is stable. Indicates whether high-frequency interference is significant. This is the threshold for high-frequency interference intensity. Step 6.2: Output the state branch based on the above logic values: Table 1 Output State Branches ; Step 6.3: For low-frequency bias candidate states and low-frequency bias and high-frequency interference coexistence states, during online operation, continue to perform fingerprint matching, source localization, bias direction judgment and intensity estimation in steps 8 to 10 based on the established fingerprint database.

[0033] 7) Step 7: Establish a single anomaly source fingerprint database; Note: Steps 7, 11, and 12 represent three alternative methods for constructing the fingerprint database, corresponding to model-driven, calibration-driven, and data-driven approaches, respectively. In practical applications, one method should be selected based on the availability of system information. Steps 7, 10.1 to 10.5, 11, and 12, including fingerprint database establishment, combined fingerprint expansion, and proportional coefficient calibration, are typically completed offline before system deployment. During online operation, the established fingerprint database is primarily used to perform matching and localization calculations in steps 8, 9, and 10.6. Step 7.1: Let the set of candidate anomaly sources be: ; in, For the set of candidate anomaly sources, Indicates the first Sources of anomalies similar to weak bias trends The total number of candidate sources. For source index; Step 7.2: Mapping matrix from the source of the anomaly to the diagnostic signal space When known, construct the first Unit fingerprint of the source of the anomaly: ; in, For the first The direction of the unit fingerprint corresponding to the source of the class exception. For the first The basis vector or calibration vector from which the anomaly originates; Step 7.3: Compile a single-source fingerprint database from all single-source fingerprints: ; in, It is a single-source fingerprint database.

[0034] 8) Step 8: Locate the source of the anomaly based on fingerprint similarity; Step 8.1: Calculate the signed similarity between the current low-frequency trend direction and each single-source fingerprint: ; in, For the first The current low-frequency trend direction in the diagnostic window is related to the first... Signed similarity between fingerprints representing anomalies; Step 8.2: Determine the anomaly source number using absolute similarity: ; in, This represents the source number of the largest matching anomaly. This represents the index at which the objective function is maximized. Step 8.3: To avoid mislocalization caused by similar fingerprints, a maximum matching threshold and a similarity margin threshold are introduced: ; ; in, The signified similarity is the result of the matching source with the largest absolute value. The signed similarity corresponds to the second highest absolute similarity. The fingerprint matching threshold, This is the fingerprint similarity margin threshold; Step 8.4: When the persistence condition of Step 5.3, the matching threshold condition of Step 8.3, and the matching margin condition are all met simultaneously, output the weak DC bias trend anomaly and source location result. If Exceeding the threshold but If the conditions are not met, or the fingerprint matching margin is insufficient, the output will be "Diagnosis uncertain" or "Multi-source competition".

[0035] 9) Step 9: Determine the bias direction, confidence level, and anomaly strength; Step 9.1: Define fingerprint matching confidence: ; in, For the first Fingerprint matching confidence level for each diagnostic window; A saturation function, used to restrict the input to a certain range. Within the range; Step 9.2: Determine the bias direction based on the signed similarity: ; in, For the bias direction, For sign functions; when When indicates a positive bias trend, Time indicates a negative bias trend; Step 9.3: Estimate the anomaly intensity based on the calibration scaling factor: ; in, For the first Anomaly intensity estimates for each diagnostic window. For the first The proportionality coefficient between the actual bias amplitude and the diagnostic signal amplitude for anomalies.

[0036] 10) Step 10: Establish a combined source fingerprint database to handle simultaneous anomalies from multiple sources; Step 10.1: When multiple sources may simultaneously produce a weak bias trend, define a combined source set. One of the combined sources Represented as:

[0037] in, For the combined source set, For a certain combination of sources, The single-source code for participating in the combination. The number of sources in the combination; Step 10.2: Construct combined basis vectors: ; in, To combine the source basis vectors, For the first in the combination The relative amplitude or sign of each source; when the bias magnitudes of each source are approximately the same and only in-direction combinations are considered, we can take... When it is necessary to consider the combination of positive and negative directions, one can take... When the magnitudes of the biases from each source have a priori proportions or can be obtained through calibration, It can be set according to the prior ratio or the calibration ratio; Step 10.3: When the mapping matrix is ​​known, the combined fingerprint is: ; in, For the source of the combination unit fingerprint; Step 10.4: When using data calibration, the combined fingerprint is obtained by normalizing the mean of the combined outlier samples: ; in, The average low-frequency features of the combined abnormal samples; Step 10.5: Combine single-source fingerprints and combined-source fingerprints to form an extended fingerprint database: ; in, To expand the fingerprint database, To combine the source fingerprint database, Represents the union of sets; Step 10.6: Direct the current low-frequency trend. and Perform maximum similarity matching on all fingerprints in the database; If the combined fingerprint similarity is higher than that of any single-source fingerprint and meets the matching threshold and margin conditions, then the output is "multi-source simultaneous anomaly"; if the similarity of multiple single-source fingerprints is close but no combined fingerprint meets the conditions, then the output is "multi-source competition" or "diagnostic uncertainty".

[0038] 11) Step 11: Calibrate the amplitude scaling factor; Step 11.1: Obtain the desired result while in a healthy state, as per Step 3. and ; Step 11.2: For the first A known amplitude is applied to an anomaly source. A small bias, or select historical samples with known amplitudes; Step 11.3: Calculate the low-frequency characteristics and perform baseline correction according to steps 2 and 3, to obtain: ; in, For the first Low-frequency characteristics of the anomaly source under calibration conditions after baseline correction; Step 11.4: Calculate the source fingerprint: ; Step 11.5: Calculate the amplitude scaling factor for a single calibration sample: ; in, For the first The amplitude proportionality coefficient of the anomaly source, The abnormal bias amplitude applied or known during calibration; Step 11.6: If multiple calibration amplitudes or multiple calibration samples are used, then take: ; in, For the first Number of calibrated samples from each source For the first Baseline-corrected low-frequency characteristics of each calibration sample For the first The known bias amplitude corresponding to each calibration sample.

[0039] 12) Step 12: Construct a fingerprint database through self-learning when there is no explicit model; Step 12.1: When the mapping matrix When accurate fingerprint data is not readily available, a fingerprint database can be constructed using calibration data or historical data. Step 12.2: Let the first... The mean baseline-corrected low-frequency features of this type of anomaly generated in calibration experiments or historical samples are: ; in, For the first The average low-frequency characteristics of this type of anomaly For the first The first class of exceptions One baseline-corrected low-frequency feature sample; Step 12.3: Define the self-learning fingerprint of this type of anomaly as: ; This approach makes the method applicable not only to systems with known models, but also to complex systems where fingerprint databases are established through data calibration.

[0040] 13) Step 13: Output the diagnostic and localization results; Step 13.1: After executing steps 1 to 12, the following results will be output: Table 2 Diagnostic and Localization Results ; In Table 2, BiasFlag, SourceIndex, BiasPolarity, BiasAmplitude, Confidence, MultiSourceFlag, HFIndex, TrendFeature, and DecisionState are all names of algorithm output variables, which can be adjusted according to the naming rules of specific controllers or diagnostic systems.

[0041] The above-described specific embodiment 1 belongs to the field of signal processing, condition monitoring, and fault diagnosis technology, specifically relating to a method for high-frequency interference-resistant diagnosis and localization of weak DC bias trend signals. Specific embodiment 1 is applicable to various signals output by sensors, observers, estimators, residual generators, condition monitoring modules, or data acquisition systems. When the target abnormal signal has a low amplitude, changes slowly, and mainly manifests as DC bias, low-frequency drift, slow trend, or weak cumulative offset, specific embodiment 1 can extract the target low-frequency bias signal and achieve anomaly detection, source localization, and trend strength estimation even in the presence of high-frequency noise, impulse disturbances, periodic ripple, switching harmonics, or broadband interference.

[0042] The core idea of ​​the above specific embodiment 1 is: instead of directly diagnosing based on the instantaneous amplitude of the original signal, the original signal is decomposed into low-frequency bias trend components and high-frequency disturbance components, and low-frequency abnormal intensity indicators, high-frequency interference intensity indicators and directional stability indicators are constructed respectively. Then, the abnormal source is located by combining the preset fingerprint database or channel mapping relationship.

[0043] The above specific embodiment 1 is applicable to signals of the following forms: 1. The target anomaly amplitude is low, making it difficult to identify directly using instantaneous thresholds; 2. The target anomaly exhibits characteristics such as DC bias, low-frequency drift, slow trend, or cumulative offset; 3. The original signal contains high-frequency noise, periodic ripple, switching harmonics, impulse disturbances, or broadband interference; 4. Different sources of anomalies have different directional characteristics or different channel fingerprints in the multidimensional signal space.

[0044] Compared to simple low-pass filtering methods, the above-described specific embodiment 1 not only outputs the filtered low-frequency signal, but also further constructs a joint criterion for low-frequency anomaly intensity, high-frequency interference intensity, directional stability, and fingerprint similarity. Compared to conventional residual direction analysis, the above-described specific embodiment 1 restricts direction matching to low-frequency / DC trend characteristics and eliminates transient high-frequency misjudgments through high-frequency interference indicators. Compared to conventional PCA or statistical monitoring methods, the above-described specific embodiment 1 not only determines whether an anomaly has occurred, but also uses directional fingerprints to locate the source of the anomaly and determine the bias direction. Therefore, the focus of the above-described specific embodiment 1 is on the combined diagnostic mechanism of "low-frequency trend extraction, directional stability verification, high-frequency interference elimination, and source fingerprint localization".

[0045] Early current sensor failures, zero-point drift, sensor bias, slow gain error, weak leakage signals, system bias drift, low-frequency health degradation characteristics, etc., can all be used as specific application objects of the above-mentioned specific embodiment 1 of the present invention.

[0046] Specific Implementation Example 2: Method for Diagnosis and Localization of Multi-channel Weak Bias Trend Signals; The multi-channel weak bias trend signal diagnosis and localization method of this specific embodiment 2 is implemented through the following process: In a One possible source of abnormality, and the dimension of the diagnostic signal is: In a multi-channel system, the following data was collected: ; in, To diagnose the signal dimension, The number of possible sources of anomalies. For the first Diagnostic signals for each channel at each sampling time.

[0047] For the There are 1 possible sources of anomalies, and their basis vectors are defined as follows: ; in, The One element is 1, and the rest are 0.

[0048] If the system mapping relationship is known, then the first... The directional fingerprints of each anomaly source in the diagnostic signal space are: ; If the system mapping relationship is unknown, it can be calculated using historical data or calibration experiments: ; ; This establishes a fingerprint database: ; in, This is a fingerprint database for anomaly sources in multi-channel systems.

[0049] When running online, the following calculations are performed sequentially: ; ; ; ; ; ; ; ; When the following conditions are met: ; And continuous When a window is established, a candidate for a weak DC bias trend anomaly is determined; if the following conditions are met simultaneously: ; If the current signal is determined to be mainly characterized by enhanced high-frequency interference, no weak bias trend abnormal alarm will be output.

[0050] Upon detecting a slight anomaly in the bias trend, the following calculations are performed: ; And it was determined that: ; If the following conditions are met: ; as well as: ; The source of the anomaly is determined to be the first... Each channel, component, measurement loop, or feature source. The bias direction and anomaly intensity are determined by the following formulas: ; ; The above-described specific embodiment 2 can be used for scenarios such as zero drift in multiple sensor channels, low-frequency bias in multiple measurement loops, continuous offset in multiple estimation residuals, early degradation trend in multiple health features, and early current sensor failure in motor drive systems.

[0051] The above-described specific embodiment 2 can be directly applied to the following scenarios: 1. Zero drift or slight bias occurs in one of the multiple sensor channels; 2. A slow trend of shift occurs in one of the multiple measurement loops; 3. A persistent low-frequency bias occurs in the direction of one of the multiple estimated residuals; 4. One of the multiple health characteristics shows an early deterioration trend; 5. Among the monitoring data of multiple subsystems, one subsystem shows an abnormal low-frequency trend.

[0052] For example, in a motor drive system, an early current sensor failure can be considered a special case of the aforementioned multi-channel weak bias trend anomaly. In this case, it is not necessary to limit the above-described specific embodiment 2 to a certain motor model or a certain coordinate transformation. It is only necessary to use the bias direction of different current measurement channels as candidate sources in the fingerprint database, and the detection, location, and direction determination of low-amplitude bias faults can be completed using the above-described specific embodiment 2.

[0053] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for diagnosing and locating weak DC bias trend signals against high-frequency interference, characterized in that, include: Step 1: Based on the acquired original diagnostic signals, establish an original diagnostic signal model; Step 2: Based on the original diagnostic signal model, obtain the low-frequency bias trend characteristic component and the high-frequency disturbance component; Step 3: Calculate the low-frequency anomaly intensity index based on the calculated health baseline mean, the constructed weighted matrix, and the low-frequency bias trend feature components; Step 4: Calculate the high-frequency interference intensity index based on the high-frequency disturbance components; Step 5: Based on the calculated current low-frequency trend direction vector, calculate the directional stability index, and then set the threshold for the low-frequency anomaly intensity index and the threshold for the directional stability index to form a candidate criterion for weak DC bias trend; Step 6: Output the state branch based on the constructed anti-high frequency interference state decision logic; Step 7: Establish a single anomaly source fingerprint database; wherein, the single anomaly source fingerprint database consists of all fingerprints from single anomaly sources; Step 8: Calculate the signed similarity between the current low-frequency trend direction vector and the fingerprint of each single anomaly source, and then locate the anomaly source based on the similarity; Step 9: Define the fingerprint matching confidence level, then determine the bias direction, and then estimate the anomaly strength; Step 10: Establish an extended fingerprint database to handle simultaneous anomalies from multiple sources; Step 11: Calibrate the amplitude scaling factor for a single calibration sample; Step 12: When there is no explicit model, construct a fingerprint database through self-learning; Step 13: Output the diagnostic and location results of the weak DC bias trend signal; Step 3 specifically includes: Step 3.1: Calculate the healthy baseline mean; where the expression for the healthy baseline mean is: （8） In equation (8), This represents the mean of low-frequency characteristics under normal conditions. The first under normal conditions Low-frequency characteristics of a sliding window; This represents the normal sample size. This is a normal sample index; Step 3.2: Calculate the healthy baseline covariance matrix; whereby the expression for the healthy baseline covariance matrix is: （9） In equation (9), This is the covariance matrix of low-frequency features under normal conditions; superscript Indicates transpose; Step 3.3: Perform baseline correction on the current low-frequency bias trend characteristic components. The corresponding expression is: （10） In equation (10), The low-frequency bias trend characteristic component after baseline correction; Step 3.4: Construct the weighting matrix as follows: （11） In equation (11), It is a weighted matrix; This is a small amount of regularization used to avoid matrix singularities; It is the identity matrix; superscript This represents finding the inverse of a matrix. Step 3.5: Calculate the low-frequency anomaly intensity index as follows: （12） In equation (12), For the first The abnormal intensity of low-frequency bias trend in each diagnostic window; For square root operations; Step 4, specifically: Within the same sliding window, calculate the high-frequency interference intensity index based on the high-frequency disturbance components; wherein, the expression for the high-frequency interference intensity index is: （13） In equation (13), For the first High-frequency interference intensity index for each diagnostic window; It is the vector norm; Step 5 specifically includes: Step 5.1: Based on the low-frequency bias trend feature components after baseline correction, calculate the current low-frequency trend direction vector; where the expression for the current low-frequency trend direction vector is: （14） In equation (14), For the first Low-frequency trend direction vector of each diagnostic window; To prevent positive numbers from being divided by zero; Step 5.2: In a length of Within the directional stability evaluation window, the directional stability index is calculated; the expression for the directional stability index is: （15） In equation (15), This is a directional stability index; The length of the directional stability evaluation window; Step 5.3: Set thresholds for low-frequency anomaly intensity and directional stability to form candidate criteria for weak DC bias trends, and require that the low-frequency anomaly intensity index continuously... Within a diagnostic window, the intensity of the low-frequency abnormality index exceeds the threshold, and the directional stability index is within a continuous range. Within each diagnostic window, the value is greater than the directional stability index threshold; among them, the expression for the candidate criterion for weak DC bias trend is: （16） （17） Low-frequency anomaly intensity index in continuous Within a diagnostic window, the intensity of the low-frequency abnormality index exceeds the threshold, and the directional stability index is within a continuous range. The expression for a value greater than the directional stability index threshold within a diagnostic window is: （18） In equations (16), (17), and (18), The threshold for low-frequency anomaly intensity index; The threshold for directional stability index; To continuously confirm the number of windows; Step 6 specifically includes: Step 6.1: Based on S[k], C[k], and H[k], construct the state decision logic for resisting high-frequency interference as follows: （19） （20） （21） In equations (19), (20), and (21), This indicates whether the strength of the low-frequency bias trend exceeds a threshold; Indicates whether the low-frequency direction is stable; Indicate whether the high-frequency interference is significant; This is the threshold for high-frequency interference intensity. Step 6.2: Based on the above three logical quantities, the output state branches are shown in the table below: Table 1 Output State Branches 。 2. The method for diagnosing and locating weak DC bias trend signals against high-frequency interference according to claim 1, characterized in that, Step 1 specifically includes: Step 1.1: Obtain the original diagnostic signal and establish the original diagnostic signal model; wherein, the expression of the original diagnostic signal model is: （1） In equation (1), This is the original diagnostic signal; The weak DC bias trend signal to be detected; This includes high-frequency disturbances, periodic ripples, impulse noise, or other non-target interference. For random measurement noise; This is the mapping matrix from the weak bias signal to the diagnostic signal space; This is the mapping matrix from high-frequency disturbances to the diagnostic signal space; For continuous time; Step 1.2: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] Modeled as a slowly varying signal, the corresponding expression is: （2） In equation (2), for The time derivative; For low-frequency trend dynamic parameters, ; For slowly changing trend drivers; Step 2 specifically includes: Step 2.1: Perform low-pass dynamic processing on the original diagnostic signal to obtain the low-frequency or DC trend component of the original diagnostic signal. ;in, The expression for the time derivative is: （3） In equation (3), This refers to the low-frequency or DC trend component of the original diagnostic signal; for The time derivative; This is the low-pass cutoff angular frequency; Step 2.2: Use discrete form to... Low-pass processing is performed to obtain the low-frequency trend component; the expression for the low-frequency trend component is: （4） In equation (4), For discrete sampling sequence numbers; For the first Low-frequency trend components at each sampling time; For the first The original diagnostic signal at each sampling time; For discrete low-pass coefficients, ; In equation (4), The expression is: （5） In equation (5), The sampling period; It is the low-pass time constant, and ; It is a natural exponential function; Step 2.3: Based on the original diagnostic signals and low-frequency trend components The high-frequency disturbance component is obtained; the expression for the high-frequency disturbance component is: （6） In equation (6), For the first High-frequency disturbance components at each sampling time; Step 2.4: In a length of Within a sliding window, the low-frequency bias trend characteristic component is calculated; whereby the expression for the low-frequency bias trend characteristic component is: （7） In equation (7), These are low-frequency bias trend feature components used for anomaly diagnosis and localization; The length of the sliding window; Use the index for summation within the window.

3. The method for diagnosing and locating weak DC bias trend signals against high-frequency interference according to claim 2, characterized in that, Step 7 specifically includes: Step 7.1: Let the set of candidate anomaly sources be: （22） In equation (22), For the set of candidate anomaly sources; Indicates the first Sources of anomalies similar to weak bias trends; The total number of candidate sources; For source index; Step 7.2: Mapping matrix from weak bias signal to diagnostic signal space When known, construct the first The unit fingerprint direction from which the weak bias trend anomaly originates is: （23） In equation (23), For the first The unit fingerprint direction corresponding to the source of the weak bias trend anomaly; Step 7.3: The single anomaly source fingerprint database is composed of all fingerprints from a single source of anomaly. （24） In equation (24), A fingerprint database for single anomaly sources.

4. The method for diagnosing and locating weak DC bias trend signals against high-frequency interference according to claim 3, characterized in that, Step 8 specifically includes: Step 8.1: Calculate the signed similarity between the current low-frequency trend direction vector and the fingerprint of each single anomaly source; wherein the expression for the similarity is: （25） In equation (25), For the first The current low-frequency trend direction in the diagnostic window is related to the first... Signed similarity between fingerprints representing anomalies; Step 8.2: Use absolute similarity to determine the anomaly source number: （26） In equation (26), The maximum matching anomaly source number; This represents the index at which the objective function is maximized; Step 8.3: Introduce a fingerprint matching threshold and a fingerprint similarity margin threshold, and set the following conditions: （27） （28） In equations (27) and (28), The signified similarity is the result of the match with the largest absolute value. The signed similarity corresponds to the second largest absolute similarity. This is the fingerprint matching threshold; This is the fingerprint similarity margin threshold; Step 8.4: When equations (16), (17), (18), (27), and (28) are all true, output the weak DC bias trend anomaly and the fault source location result; if equation (16) is true, but If equation (17) is not satisfied, or equation (28) is not valid, the output will show a state of uncertain diagnosis or multi-source competition.

5. The method for diagnosing and locating weak DC bias trend signals against high-frequency interference according to claim 4, characterized in that, Step 9 specifically includes: Step 9.1: Define the fingerprint matching confidence level as: （29） In equation (29), For the first Fingerprint matching confidence level for each diagnostic window; A saturation function, used to restrict its own input to a certain range. Within the range; Step 9.2: Match the source with the largest absolute value using the signed similarity. Determine the bias direction: （30） In equation (30), The bias direction; For sign functions; when When, it indicates a positive bias trend; when When, it indicates a negative bias trend; Step 9.3: Estimate the anomaly intensity based on the calibration scaling factor: （31） In equation (31), For the first Anomaly intensity estimates for each diagnostic window; For the first The proportionality coefficient between the actual bias amplitude and the diagnostic signal amplitude for anomalies.

6. The method for diagnosing and locating weak DC bias trend signals against high-frequency interference according to claim 5, characterized in that, Step 10 specifically includes: Step 10.1: When multiple sources may simultaneously produce a weak bias trend, define a combined source set. One of the combined sources Represented as: （32） In equation (32), For the combined source set; Sourced from a certain combination; A single-source number for the portfolio; The number of sources in the combination; Step 10.2: Construct the combined source basis vectors: （33） In equation (33), To combine the source basis vectors; For the first in the combination The relative amplitude or sign of each source; Step 10.3: Mapping matrix from weak bias signal to diagnostic signal space When known, the source of the combination The unit fingerprint is: （34）； Step 10.4: When using data calibration, the combined source is obtained by normalizing the mean of the combined outlier samples. The unit fingerprint is: （35） In equation (35), The average low-frequency features of the combined abnormal samples; Step 10.5: Based on the single anomaly source fingerprint database and the combined source fingerprint database, construct the extended fingerprint database as follows: （36） In equation (36), To expand the fingerprint database; For combined source fingerprint databases; Represents the union of sets; Step 10.6: Transfer the current low-frequency trend direction vector and The system performs maximum similarity matching on all fingerprints and outputs anomaly diagnosis results.

7. The method for diagnosing and locating weak DC bias trend signals against high-frequency interference according to claim 6, characterized in that, Step 11 specifically includes: Step 11.1: In a healthy state, obtain the results according to steps 3.1 and 3.2 respectively. and ; Step 11.2: For the first A known amplitude is applied to an anomaly source. The bias, or the application of historical samples with known amplitude; Step 11.3: Following step 2.4, calculate the low-frequency bias trend characteristic component, and perform baseline correction on this low-frequency bias trend characteristic component to obtain the... The low-frequency characteristics of baseline correction for anomaly sources under calibration conditions are as follows: （37）； Step 11.4: Calculation The source fingerprint is: （38） Step 11.5: Calculate the amplitude scaling factor for a single calibration sample: （39） In equation (39), For the first Amplitude scaling factor for anomaly sources; The abnormal bias amplitude applied or known during calibration; Step 11.6: If multiple calibration amplitudes or multiple calibration samples are used, then take: （40） In equation (40), For the first Number of calibrated samples from each source; For the first Baseline-corrected low-frequency characteristics of each calibration sample; For the first The known bias amplitude corresponding to each calibration sample.

8. The method for diagnosing and locating weak DC bias trend signals against high-frequency interference according to claim 7, characterized in that, Step 12 specifically includes: Step 12.1: Mapping matrix from weak bias signal to diagnostic signal space When accurate fingerprints cannot be obtained, a fingerprint database is constructed through self-learning using calibrated data or historical data. Step 12.2: Let the first... The mean baseline-corrected low-frequency features of this type of anomaly generated in calibration experiments or historical samples are: （41） In equation (41), For the first Average low-frequency characteristics of anomalies; For the first The first class of exceptions One baseline-corrected low-frequency feature sample; Step 12.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would The self-learning fingerprint is defined as: （42）。 9. The method for diagnosing and locating weak DC bias trend signals against high-frequency interference according to claim 8, characterized in that, In step 13, the output diagnosis and localization results are as follows: Table 2 Diagnostic and Localization Results In Table 2, BiasFlag, SourceIndex, BiasPolarity, BiasAmplitude, Confidence, MultiSourceFlag, HFIndex, TrendFeature, and DecisionState are all output variable names of the anti-high frequency interference diagnosis and localization method for this weak DC bias trend signal.

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