Cross-check based framework for fault-tolerant system of vibration measurement channels of frame gauge

Abstract

This invention relates to the field of fault handling technology and discloses a fault-tolerant system for vibration measurement channels of frame instruments based on cross-validation. The system includes: first, extracting the attitude observation vectors of each channel and stripping the rigid body motion-induced components to obtain the channel quantities to be validated; then, constructing an angular cyclic imprinting basis matrix and separating the validated channel quantities and parasitic imprinting components from the attitude observation vectors; subsequently, performing leave-one-out cross-validation on the validated quantities to generate residual energy, and inverting the parasitic components to the corresponding components according to the channel routing to obtain the risk intensity; finally, fusing the residual energy and risk intensity to generate continuous health weights, weighting them to obtain the common frame vibration state and fault-tolerant output quantity, while simultaneously accumulating the risk output degradation index according to angular travel. This invention effectively eliminates common-mode coherent interference and improves the system's dynamic fault tolerance capability.

Description

Technical Field

[0001] This invention relates to the field of fault handling technology, and more specifically, to a fault-tolerant system for vibration measurement channels of frame instruments based on cross-validation. Background Technology

[0002] Frame-based instruments typically integrate components such as inner and outer frames, orthogonal shafts, motors, and vibration acquisition front-ends. The signal and power supply links for their measurement channels need to cross moving parts via slip rings or flexible cables. During actual operation, objective factors such as slip ring brush contact, repeated cable bending, bearing rolling, and permanent magnet motor disturbances modulate real mechanical vibrations, contact resistance fluctuations, and micro-short breaks into parasitic interference components that cyclically repeat with the frame's angular position. When multiple vibration measurement channels share the same transmission path, this cyclic parasitic interference appears synchronously in multiple channels, exhibiting significant coherence and therefore cannot be considered as independent random sensor noise. Existing conventional cross-calibration schemes face significant challenges in processing such composite multi-channel data: on the one hand, conventional calibration methods easily mistake synchronous pseudo-vibrations caused by shared contamination for genuine frame vibrations; on the other hand, the readings of the measuring sensors naturally project and change with the angles inside and outside the frame, and fixed diagnostic mechanisms are prone to misinterpreting these normal posture-induced reading fluctuations as channel anomalies. In addition, traditional diagnostic methods often rely on pre-set fixed thresholds for hard switching judgments, which are difficult to adapt to the dynamic degradation phenomena exposed by rotary joints at different operating angles. Summary of the Invention

[0003] This invention provides a fault-tolerant system for vibration measurement channels of frame instruments based on cross-validation, which solves the technical problems mentioned in the background art.

[0004] This invention provides a fault-tolerant system for vibration measurement channels of frame instruments based on cross-validation. It is applied to homogeneous measurement equipment comprising a frame, shaft, rotating transmission components, and vibration measurement channels. The system sets continuous sampling timing and initializes the structural coupling modulation coefficients and local noise variance, and is configured to execute: The attitude observation vectors of each channel are extracted based on the frame reference benchmark, and relative kinematics calculations are performed to remove rigid body motion-induced components, thereby obtaining the channel quantities that reflect pure structural deformation. Based on the spatial periodic characteristics of the rotating transmission part, an angular domain periodic disturbance basis matrix is ​​constructed to characterize contact degradation and rotor disturbance. Robust state estimation is performed by combining the attitude observation vector with the angular domain periodic interference basis matrix to separate the verifiable channel quantity and structurally coupled modulation component that filter out coherent interference. After removing the channels to be predicted, leave-one-out cross-prediction operation is performed on the verifiable channel quantities to generate a physical residual energy index characterizing the degree of independent anomaly of a single channel. Based on the channel routing correlation matrix, the structural coupling modulation components are spatially and physically mapped, and the path degradation intensity is obtained by tracing back to the rotating transmission part. Then, the channel risk assessment quantity is obtained by fusion. By combining the physical residual energy index with the channel risk assessment quantity, an adaptive continuous health weight is generated for dynamically adjusting the channel trust level, and the common frame vibration state and fault-tolerant fusion measurement output are estimated accordingly. The structural coupling modulation coefficient and the local noise variance are updated online by using the fault-tolerant fusion deviation along the continuous sampling time sequence, and the path degradation intensity is accumulated by combining the real angular travel sequence to generate an angular travel cumulative degradation message.

[0005] The beneficial effects of this invention are as follows: by jointly separating the real mechanical vibration and parasitic imprint components, it avoids the defects of conventional judgment methods that mistake common contamination for real vibration or normal changes caused by the projection of operating posture for abnormality; this invention abandons fixed hard criterion thresholds and adopts data adaptive scale and continuous health weight for online smooth adjustment, which can not only suppress sudden anomalies, but also trace parasitic interference to specific rotating transmission components, significantly improving the data reliability and online monitoring level of the same source measurement equipment under complex operating conditions. Attached Figure Description

[0006] Figure 1 This is a flowchart of the fault-tolerant system for the vibration measurement channel of a frame instrument based on cross-validation according to the present invention. Detailed Implementation

[0007] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0008] like Figure 1 As shown, a fault-tolerant system for the vibration measurement channel of a frame instrument based on cross-validation is applied to a homogeneous measurement equipment that includes a frame, shaft, rotating transmission parts, and vibration measurement channel. Continuous sampling timing is set, and the structural coupling modulation coefficients and local noise variance are initialized. The system is configured to execute: The attitude observation vectors of each channel are extracted based on the frame reference benchmark, and relative kinematics calculations are performed to remove rigid body motion-induced components, thereby obtaining the channel quantities that reflect pure structural deformation. Based on the spatial periodic characteristics of the rotating transmission part, an angular domain periodic disturbance basis matrix is ​​constructed to characterize contact degradation and rotor disturbance. Robust state estimation is performed by combining the attitude observation vector with the angular domain periodic interference basis matrix to separate the verifiable channel quantity and structurally coupled modulation component that filter out coherent interference. After removing the channels to be predicted, leave-one-out cross-prediction operation is performed on the verifiable channel quantities to generate a physical residual energy index characterizing the degree of independent anomaly of a single channel. Based on the channel routing correlation matrix, the structural coupling modulation components are spatially and physically mapped, and the path degradation intensity is obtained by tracing back to the rotating transmission part. Then, the channel risk assessment quantity is obtained by fusion. By combining the physical residual energy index with the channel risk assessment quantity, an adaptive continuous health weight is generated for dynamically adjusting the channel trust level, and the common frame vibration state and fault-tolerant fusion measurement output are estimated accordingly. The structural coupling modulation coefficient and the local noise variance are updated online by using the fault-tolerant fusion deviation along the continuous sampling time sequence, and the path degradation intensity is accumulated by combining the real angular travel sequence to generate an angular travel cumulative degradation message.

[0009] This embodiment operates on industrial measurement equipment with a multi-axis frame structure, rotating transmission components, and multiple vibration measurement channels originating from the same source. The operating platform includes, but is not limited to, industrial control computers, embedded real-time controllers, and field-programmable gate arrays. Before system operation, hardware deployment and parameter initialization are completed. In the hardware deployment phase, the vibration measurement channels use piezoelectric or capacitive accelerometers. The sensors are installed at preset measurement points on the frame structure, with each measurement point corresponding to a unique channel identifier. The sensitive axis direction and installation posture of the sensors are calibrated using a three-dimensional coordinate measuring machine. The rotating transmission components include slip rings, rolling bearings, and permanent magnet motor rotors. Each rotating transmission component corresponds to a unique component identifier, and each component is equipped with a photoelectric encoder to collect real-time angular position and angular velocity signals of the rotating shaft. Surface-mount temperature sensors are installed near the rotating transmission components to collect local temperature signals.

[0010] Before system operation, the continuous sampling timing is set, and the sampling timing is set according to the following rules: the sampling frequency of the vibration measurement channel is set to 50 to 200 times the highest rotation frequency of the frame, and the lower limit of the sampling frequency is not less than 1kHz; the sampling frequency of the encoder angular position and angular velocity signals is consistent with the sampling frequency of the vibration measurement channel, and all acquisition devices are synchronized by hardware triggering to achieve clock alignment, with the synchronization error not exceeding 5% of the sampling period; the sampling frequency of the temperature signal can be set to 1 / 10 to 1 / 50 of the vibration sampling frequency, and clock alignment with the vibration sampling timing is achieved by linear interpolation.

[0011] Before the system runs, the core parameters are initialized. The initialization rules for all parameters are as follows: The structural coupling modulation coefficients are initialized as all-zero column vectors that match the number of columns in the angular domain periodic interference basis matrix, and the vector dimension is exactly the same as the number of columns in the single-channel interference basis matrix. The local noise variance is initialized to the square of the factory equivalent noise mean square value of the corresponding vibration sensor. The equivalent noise mean square value is obtained from the sensor calibration report and is expressed in meters per second squared. The recursive information matrix is ​​initialized as a diagonal matrix, with the diagonal elements taking values ​​of 10 ... to The matrix dimension is exactly the same as the column number of the single-channel angular domain periodic interference basis matrix; Positive bias constants to prevent singular denominators are divided into two categories. The first category is used to accelerate operations involving units of measurement, and its value is... Meters per second squared, the second type is used in dimensionless calculation scenarios, and takes the value of These two types of constants are used in their respective scenarios and cannot be mixed across scenarios; The maximum number of iterations for iterative optimization is set to 50 to 200, and the iterative convergence threshold is set to... to ; The sliding window length is set to 100 to 1000 sampling points for statistical calculations and moving average processing of historical data.

[0012] Before system operation, the preprocessing flow configuration of the raw sampled data is completed. The preprocessing flow is executed in the following order: First, DC removal processing is performed on the raw sampled data of the vibration channel, and the DC component is filtered out by mean subtraction within a sliding window; Second, power frequency notch filtering is performed on the DC removed data, using a second-order infinite-length unit impulse response notch filter to filter out power frequency interference of 50Hz and its integer multiples; Finally, detrending processing is performed on the filtered data, and low-frequency trend terms are eliminated by polynomial fitting, with the order of the fitting polynomial set to 1 to 3.

[0013] By performing coordinate transformation multiplication operations based on the actual angle sequences of each frame level, the attitude chain transfer matrix is ​​obtained using a unified spatial reference. The corresponding calculation formula is:

[0014] in For the sampling time variable, For channel identifier variables; For channel The sequence of rotating structural edges that are crossed, where each element is a channel. Install the node identifiers corresponding to all rotation axes between the measuring points and the frame reference coordinate system; Path node The actual angle at that point is determined by the photoelectric encoder of the corresponding rotating shaft at the sampling time. Data was collected synchronously, and the unit is radians. Let be the rotation matrix corresponding to this angle. The orthogonal matrix of the dimensions is constructed according to the right-hand rule and the orthogonal installation orientation of the rotation axis. The rotation sequence of the multi-axis frame adopts the ZYX Euler angle sequence, corresponding to the three rotational degrees of freedom of yaw, pitch and roll. Each degree of freedom corresponds to a unique rotation matrix. From the frame reference coordinate system to the channel The initial rotation matrix of the sensitive coordinate system is obtained by calibration using a three-dimensional coordinate measuring device. During the calibration process, a frame reference coordinate system is established with the geometric center when the frame is stationary as the origin and the axial direction of the frame's orthogonal rotation axis as the coordinate axis. A channel sensitive coordinate system is established with the direction of the sensor's sensitive axis as the coordinate axis. The pose transformation relationship between the two coordinate systems is obtained through the three-dimensional coordinate measuring device, and the initial rotation matrix is ​​calculated. For the attitude chain transfer matrix, An orthogonal matrix of dimension is used to convert physical quantities in the frame's reference coordinate system into channels. The corresponding physical quantity in the sensitive coordinate system.

[0015] Spatial projection calculations are performed on the attitude chain transfer matrix using the channel sensitive axis, calibration parameters, and mounting point position vectors to eliminate multi-axis installation coupling deviations and extract the attitude observation vector characterizing unidirectional spatial sensitivity. The corresponding calculation formula is:

[0016] in For channel The sensitive axis unit vector is A column vector of dimension, with elements ranging from -1 to 1, and a vector magnitude of 1, determined by the sensor's sensing direction. A single-axis accelerometer corresponds to a unique sensing axis unit vector. For channel The calibration matrix, composed of calibration parameters, is A diagonal matrix of dimensions, where the diagonal elements are the sensor's sensitivity calibration coefficients, obtained from the sensor's factory calibration report, used to eliminate sensor gain bias; Let be the transpose of the attitude chain transfer matrix. Since the attitude chain transfer matrix is ​​an orthogonal matrix, the transpose is equal to its inverse. It is a third-order unit matrix; For channel The position vector of the mounting point in the frame's reference coordinate system is: The column vectors of dimension, in meters, are obtained through calibration using a three-dimensional coordinate measuring device; Let be the cross product operator matrix of vectors, for a three-dimensional vector Its cross product operator matrix is ; Let be the attitude observation vector, and be The row vector of dimension, with the first 3 elements corresponding to the linear acceleration sensitivity in the frame's reference coordinate system and the last 3 elements corresponding to the angular acceleration sensitivity in the frame's reference coordinate system, is used to characterize the channel. At sampling time The spatially sensitive mapping relationship eliminates the cross-coupling deviation caused by multi-axis installation through spatial projection calculation, and realizes the decoupling of the linear acceleration and angular acceleration sensitivity characteristics.

[0017] Based on the frame angular velocity and the attitude chain transfer matrix, centripetal acceleration and Coriolis acceleration projection calculations are performed to quantify the geometric rotational inertia effect and obtain the rigid body motion induced components. The corresponding calculation formula is:

[0018]

[0019]

[0020] in Let be the three-axis angular velocity vector in the frame's reference coordinate system. A column vector of dimensions, in radians per second, is obtained by combining the angular velocity signals of each encoder shaft through coordinate transformation; Let be the frame angular acceleration vector, and be The column vector of dimension, in radians per second squared, is obtained from the angular velocity vector through central difference operation, with the difference window length set to 3 to 5 sampling points; For channel The linear velocity vector of the mounting point in the frame's reference coordinate system is: A column vector of dimension, in meters per second, is obtained by the cross product of the angular velocity vector and the installation point position vector, satisfying the following condition: ; The centripetal acceleration vector at the mounting point is expressed in meters per second squared, caused by the centrifugal effect generated by the frame rotation. The Coriolis acceleration vector at the installation point is expressed in meters per second squared, and is caused by the coupling effect of frame angular acceleration and rotation. The component induced by rigid body motion is expressed in meters per second squared. It is the projection of the inertial acceleration generated during the rigid body rotation of the frame onto the sensor's sensitive axis. It is independent of the vibration signal generated by the elastic deformation of the frame and is caused solely by the rigid body kinematic effects.

[0021] The rigid body motion-induced component is subtracted from the original channel sampling data, and a benchmark correction operation is performed to filter out macroscopic kinematic projection interference, resulting in the channel quantity to be verified that characterizes the deformation features of the elastic body. The corresponding calculation formula is:

[0022] in For channel At sampling time The preprocessed vibration sampling data is in meters per second squared. The quantity to be verified is measured in meters per second squared. It is the vibration signal after removing the inertial interference of rigid body motion, and contains only the real vibration component generated by the elastic deformation of the frame and the parasitic interference component introduced by the transmission link.

[0023] The DC static reference, sliding friction order, bearing rolling contact order, and motor slot pole harmonic common multiple of the rotating transmission part are extracted to generate a spatial order set to cover the physical periodic laws. The DC static reference of the rotating transmission part corresponds to order 0, the sliding friction order corresponds to the first harmonic of the frame rotation frequency, and the order value is 1; the bearing rolling contact order includes the inner ring raceway contact order, the outer ring raceway contact order, and the rolling element rotation order, wherein the formula for calculating the inner ring raceway contact order is:

[0024] The formula for calculating the contact order of the outer raceway is:

[0025] in This refers to the number of rolling elements in the bearing. The diameter of the rolling element, The bearing pitch circle diameter, The bearing contact angle is specified; all parameters are obtained from the bearing manufacturer's parameter manual. The least common multiple of motor slot-pole harmonics is the least common multiple of the number of stator slots and rotor pole pairs, plus integer multiples of 2 and 3 of this least common multiple; the highest harmonic order does not exceed 20. Spatial order set. This is a set of positive integers representing all the orders mentioned above, with elements arranged in ascending order. It is used to cover all physical orders that might cause periodic interference in the rotating transmission mechanism. Identify variables for the rotating transmission parts. This represents the total number of rotating transmission parts in the system.

[0026] By combining the frame rotational speed amplitude, the square of the rotor imbalance rotational speed, and the zero-mean AC fluctuation of the local temperature, state parameters are spliced ​​to quantify the multi-source physical excitation and construct a dynamic excitation modulation vector. First, all physical excitation parameters are dimensionless; the corresponding dimensionless formula is:

[0027]

[0028]

[0029]

[0030] in Rotary transmission part The local frame angular velocity, in radians per second, is calculated from the encoder differential signal of the corresponding rotating shaft; For part The rated maximum angular velocity, in radians per second, is determined by the equipment design parameters. The motor rotor speed, in radians per second, is obtained from the speed feedback signal of the motor drive system. This is the motor's rated maximum speed, expressed in radians per second. For part The local temperature, in degrees Celsius, is collected by a temperature sensor. This is the average value of the temperature signal within a preset sliding window; and Parts The upper and lower limits of the operating temperature are determined by the equipment design parameters; , , , All of these are dimensionless parameters, with values ​​ranging from 0 to 1.

[0031] The formula for constructing the dynamic excitation modulation vector is:

[0032] in For the dynamic excitation modulation vector, A column vector of dimensions, with all elements being dimensionless, used to characterize the modulation effect of different physical excitations on periodic disturbances.

[0033] Based on the connection indication of the channel routing correlation matrix, the dynamic excitation modulation vector is mapped using trigonometric functions of the spatial order set and the frame angular position to introduce spatial azimuth modulation characteristics and generate a single-order interferometric basis. Channel routing correlation matrix for A Boolean matrix of dimension 1 This represents the total number of vibration measurement channels. The total number of rotational transmission parts, matrix elements It is a Boolean value, when the channel The signal transmission link passes through the rotating transmission part hour, ,otherwise The formula for constructing a single-order interference substrate is:

[0034] in Rotary transmission part Spatial order set, For the corresponding order in this set; For part The real-time angular position of the corresponding frame, in radians, is determined by the encoder at the sampling time. Collected; and The functions are cosine and sine trigonometric functions, with dimensionless radian values ​​as independent variables and dimensionless outputs. For a single-order interference basis, A row vector of dimensionless dimensions, where all elements are dimensionless, used to characterize the rotational transmission part at a single order. For the channel The basic characteristics of the generated periodic interference and the spatial orientation modulation characteristics are realized by the trigonometric function mapping of the angular position, which can accurately characterize the variation law of the interference amplitude with the orientation of the frame rotation.

[0035] An augmented stitching operation is performed along the associated path on all crossed locations and the single-order interference basis at the corresponding order, to construct the angular domain periodic interference basis matrix by polymerizing the physical transmission interference features. The corresponding calculation formula is:

[0036] in The matrix horizontal splicing operator splices all single-order interference bases into a row matrix along the column direction. During the splicing process, the rotation transmission part identifier and the order are strictly executed in ascending order. Let be the periodic disturbance basis matrix of the angular domain, and be... Row vectors of dimension It is the sum of the column numbers of all single-order interference bases. All elements are dimensionless quantities, used to fully characterize the channel. The spatial characteristics of all periodic parasitic interferences it is subjected to have fixed matrix column dimensions, and the number of columns of the interference basis matrix of all channels is completely consistent, ensuring dimension matching for subsequent matrix operations.

[0037] The absolute deviation of the residuals from the median in each channel is calculated, and an unbiased statistical factor is introduced to perform scaling to suppress extreme value fluctuations and obtain a robust noise adaptive scale. The corresponding calculation formula is:

[0038] in For robust noise adaptive scaling, the unit is meters per second squared. To follow the preset sliding window Median operator for the sampled sequence within the window The length is set to 100 to 1000 sampling points; The residual is estimated for a single channel. It is determined by the zero-mean result of the channel quantity to be verified during the initial iteration and is updated in real time by the observation constraint equation during the iteration process. The unit is meters per second squared. 1.4826 is the unbiased statistical factor for converting the absolute median deviation to the standard deviation under a normal distribution. It is used to convert the absolute median deviation into a scaling parameter with the same dimension as the standard deviation. For non-Gaussian distributed spike signals, this scaling parameter can effectively suppress the influence of extreme value abnormal fluctuations.

[0039] Construct the overall attitude matrix and the overall interference basis matrix by augmenting and stitching together the attitude observation vectors from all channels and the angular domain periodic interference basis matrix, respectively. Overall Attitude Matrix for A matrix of dimension, consisting of pose observation vectors from all channels. The matrix is ​​constructed by piecing together elements along the row direction. Corresponding channel attitude observation vector Overall interference basis matrix for A matrix of dimension, consisting of the angular domain periodic interference basis matrix of all channels. The matrix is ​​constructed by piecing together elements along the row direction. Corresponding channel Angular domain periodic disturbance basis matrix , The column number of the single-channel interference basis matrix, and the column number of all channels. The values ​​are completely identical, ensuring matrix dimension matching.

[0040] Under the observation constraint that the number of channels to be verified equals the sum of the overall attitude matrix and the common state, the overall interference basis matrix and the structural coupling modulation coefficients, a joint iterative optimization is performed with the objective of minimizing the logarithmic heavy-tailed loss and the generalized cross-validation smoothing regularization term to overcome the influence of micro-short-term spikes, and the optimal structural coupling modulation coefficients are obtained. The observation constraint equation is:

[0041] in for The overall estimated residual vector of the dimension, in meters per second squared; for A column vector of all channels to be verified in dimension , in meters per second squared; for The common state vector of the dimension has the first 3 elements as linear acceleration in the frame reference coordinate system, in meters per second squared, and the last 3 elements as angular acceleration in the frame reference coordinate system, in radians per second squared, representing the common vibration state of the frame. for The vector of all structurally coupled modulation coefficients of dimension , with all elements in meters per second squared, is used to characterize the interference amplitude corresponding to each order of interference basis.

[0042] Generalized cross-validation is used to determine the optimal regularization matrix, and the corresponding formula is:

[0043] in for A unit matrix of dimensions; The projection smoothing matrix is ​​constructed using the following formula: , for A diagonal regularization matrix of dimension 1, where the diagonal elements are regularization coefficients; It is the square operator for the second norm; The trace operator for a matrix; Let be the optimal regularized smoothing matrix output by generalized cross-validation. A diagonal matrix of dimensionless quantities, where all elements are dimensionless.

[0044] The objective function for joint iterative optimization is:

[0045] in The total length of the sampling sequence within the sliding window; This is the optimal estimated residual vector; This represents the optimal common state vector. The first term of the objective function is the log-tailed loss function, which is used to suppress the influence of short-peak signals. For peak residuals with large amplitudes, the logarithmic function can reduce their weight in the loss function and avoid the iteration results being dominated by extreme signals. The second term is the generalized cross-validation smoothing regularization term, which is used to prevent the model from overfitting.

[0046] The joint iterative optimization is implemented using an iterative reweighted least squares algorithm, and the iterative execution steps are as follows: Step 1, Initialize the structural coupling modulation coefficients Initialize the common state as an all-zero vector. The result is obtained from the least squares solution; Step 2, based on the current and Calculate the estimated residual Calculate the weight corresponding to each residual. ; Step 3: Construct a weighted least squares equation based on the weight matrix and solve for the updated equation. and ; Step 4: Calculate the change in the objective function value between two consecutive iterations. If the change is less than a preset convergence threshold, or if the number of iterations reaches a preset maximum number of iterations, terminate the iteration and output the optimal value. and Otherwise, return to step 2 and continue iterating.

[0047] If a matrix becomes rank deficient during the iteration process, then... A diagonal regularization term is added to the matrix, with the regularization coefficient being the minimum singular value of the matrix. This doubles the matrix to ensure its invertibility and improve numerical stability.

[0048] Common-mode component filtering is performed by subtracting the product of the overall interference basis matrix and the optimal coefficients from the channel quantities to be verified, in order to eliminate spurious vibration coherent contamination. The verifiable channel quantities and the structurally coupled modulation components are then output separately for each channel. The corresponding calculation formula is:

[0049]

[0050] in To decompose into a single channel The optimal coefficient vector is derived from the optimal structure coupling modulation coefficient vector. Corresponding channel The elements were extracted, and the unit is meters per second squared. The verifiable channel quantity is measured in meters per second squared. It is a vibration signal after removing periodic coherent interference, containing only the actual vibration component of the frame and the random noise and fault abnormality components of the channel itself. The structure-coupled modulation component is represented by meters per second squared (m²), and the channel is [channel number missing]. The estimated value of the periodic parasitic interference it suffers can be effectively eliminated by filtering out the common-mode component, thus eliminating the synchronous pseudo-vibration coherent pollution caused by the shared transmission path of multiple channels and distinguishing between real frame vibration and parasitic interference.

[0051] After removing the channels to be predicted, the inverse operation is performed using the current local noise variance of the remaining channels and a positive bias constant to prevent singularity in the denominator, to construct a diagonal inverse variance weight matrix reflecting the dynamic changes in the local signal-to-noise ratio. Leave-one cross-prediction is performed channel-by-channel traversal, and at each sampling time, all... Each channel undergoes a leave-one-out process in turn, removing one channel to be predicted at a time. Keep the remaining Data from each channel; the formula for constructing the diagonal inverse variance weight matrix is:

[0052] in For channel At sampling time The local noise variance is expressed in meters per second squared. This is a type I positive bias constant, with a value of [value missing]. Meters per second squared is used to prevent the denominator from being singular; For traversal Index identifiers for the remaining channels; for The diagonal inverse variance weight matrix of the dimension has diagonal elements representing the inverse variance of the remaining channels and off-diagonal elements representing 0. Lower noise channels have higher weights, which can improve the accuracy of state estimation.

[0053] A weighted generalized inverse mapping operation is performed on the dimensionality-reduced observation matrix formed by the remaining channels and the diagonal inverse variance weight matrix to reduce the interference of ill-conditioned pose on local estimation, generating a prediction uncertainty basis matrix and a leave-one-out state eigenvector. The corresponding calculation formula is:

[0054]

[0055]

[0056]

[0057] in To remove channels The resulting dimensionality-reduced observation matrix is A matrix of dimension, derived from the overall pose matrix. Remove the first After the action, it was obtained; The set of verifiable vectors consisting of the remaining channels is... A column vector of dimension, with units of meters per second squared, consisting of a vector composed of verifiable channels from all channels, excluding the first-order vector. After obtaining the elements; For the Moore-Penrose generalized inverse operator of a matrix; It is a 6th-order identity matrix; for The prediction uncertainty matrix of dimension is used to characterize the uncertainty of leave-one-out state estimation. By adding a diagonal regularization term, the matrix rank deficiency is avoided, and the interference of ill-conditioned pose on local estimation is reduced. for Leave-one-out state feature vectors of dimension , which do not use the channels to be predicted. When using the data, the estimated common vibration state of the frame is obtained. The first three elements are in meters per second squared, and the last three elements are in radians per second squared.

[0058] The attitude observation vector of the channel to be predicted is used to perform a forward spatial projection on the leave-one-out state feature vector to establish a virtual measurement reference without self-verifying cycles, generating a leave-one-out physical prediction. The corresponding calculation formula is:

[0059] in To leave a physical prediction quantity, the unit is meters per second squared, which is the predicted channel based on data from all other normal channels. The ideal output value under fault-free conditions; this prediction process does not use channels. Its own data avoids the failure detection caused by self-verification loops and can be used as a channel. Virtual measurement reference under normal conditions.

[0060] Subtracting the leave-one physical prediction from the verifiable channel quantity, and then performing variance normalization operation using the prediction uncertainty matrix and the positive bias constant, eliminates false alarms caused by local observation blind spots, resulting in the physical residual energy index that measures the intensity of intrinsic faults in a single channel. The corresponding residual calculation formula is:

[0061] The corresponding normalization formula is:

[0062] in To leave a cross-prediction residual, the unit is meters per second squared, representing the channel. The deviation between the actual output and the ideal predicted value; This is the physical residual energy index, a dimensionless parameter. A larger value indicates a higher energy density in the channel. The higher the probability of a fault occurring within itself, the more severe the fault; in the denominator term The variance of the predicted values, expressed in meters per second squared, is used to normalize the residuals, eliminating the impact of changes in observation accuracy caused by frame pose variations on fault detection. When the frame is in a local observation blind zone, the prediction variance increases, and the residual energy index is automatically suppressed, effectively eliminating false alarms. A local observation blind zone refers to the reduced-dimensionality observation matrix caused by frame pose variations. In pose intervals where linear correlation occurs and observation accuracy decreases, normalization of the prediction variance can automatically adapt to changes in observation accuracy, thereby improving the accuracy of fault detection.

[0063] By using the local noise variance, the median of self-interference, and a positive bias constant to prevent denominator singularity, a dimensional unification operation is performed on the square of the structurally coupled modulation component to eliminate absolute amplitude differences and obtain normalized interference energy. The corresponding calculation formula is:

[0064] in For sliding windows Variables at historical sampling times within the data; For channel The square of the structurally coupled modulation component in the sliding window The median, measured in meters per second squared, is used to characterize the channel. Normal interference level; is the normalized interference energy for a single channel, and is a dimensionless parameter used to eliminate the influence of signal amplitude differences between different channels on subsequent inversion calculations.

[0065] A diagonal discrete weight matrix is ​​constructed based on the discrete statistics of the normalized interference energy of each channel to weaken the dominance of high-frequency jump data on physical inversion. The corresponding calculation formula is:

[0066] in for A diagonal discrete weight matrix of dimension, where the diagonal elements are the absolute median difference of the normalized interference energy of the corresponding channel, and the off-diagonal elements are 0; This is a type II positive bias constant, with a value of [value missing]. , is a dimensionless quantity used to prevent singularity in the denominator; the larger the absolute median difference, the greater the fluctuation of the interference energy in the channel, and the lower the weight it is assigned in subsequent inversion, thereby reducing the impact of abnormal jump data on the inversion results and improving the robustness of degradation source tracing.

[0067] Under non-negative physical boundary constraints, with the reconstruction error of the normalized interference energy, the channel routing correlation matrix, and the unknown degradation variables as the objective, least squares solution is performed under the inverse weighting of the diagonal discrete weight matrix to achieve the localization of coherent contamination to the mechanical entity and obtain the path degradation intensity of each of the rotating transmission parts. The corresponding calculation formula is:

[0068] in for The universal normalized disturbance energy splicing vector of dimension, where all elements are dimensionless; for A dimensionless channel routing association matrix, where all elements are dimensionless Boolean values; for The vector of independent variables representing the degradation intensity of a dimension, where all elements are dimensionless. For matrix The weighted square norm operator for inverse weighted factors satisfies ; As a non-negative physical boundary constraint, it means that the degradation intensity of the rotating transmission part cannot be negative; for The path degradation intensity vector is a dimensionless quantity. Each element corresponds to the degree of degradation of a rotational transmission part. The larger the value, the more severe the contact degradation or disturbance of that part.

[0069] The solution process uses the Lawson-Hanson nonnegative least squares algorithm, and the algorithm execution steps are as follows: Step 1: Initialize the active set to an empty set and initialize the solution vector. It is a vector of all zeros; Step 2, calculate the gradient vector The index with the smallest gradient and the corresponding solution element is 0 is selected and added to the active set; Step 3: Solve the unconstrained least squares problem based on the activity set to obtain a temporary solution vector; Step 4: If all elements in the active set of the temporary solution vector are non-negative, update the solution vector to the temporary solution vector and return to step 2; otherwise, adjust the step size, remove the element in the solution vector that first appears with a negative value from the active set, and solve the problem again. Step 5: When the gradients corresponding to all inactive sets are greater than or equal to 0, or the number of iterations reaches the preset maximum number of iterations, terminate the iteration and output the optimal solution. .

[0070] During the solution process, if the channel routing correlation matrix If a rank deficiency occurs, then... A diagonal regularization term is added to the matrix, with the regularization coefficient being the minimum singular value of the matrix. This ensures the uniqueness of the solution and enables precise positioning of coherent contamination to specific rotating mechanical entities.

[0071] The path degradation intensity is aggregated using the channel routing association matrix to quantify the global external transmission physical risk borne by a single channel, generating the channel risk assessment quantity. The corresponding calculation formula is:

[0072] in For the channel routing association matrix The Row vector, is Row vectors of dimension; This is a single-channel risk assessment metric, a dimensionless parameter; the larger the value, the stronger the channel risk. The higher the degree of degradation of the rotating transmission parts it passes through, the greater the risk of the channel being affected by external transmission interference.

[0073] The physical residual energy index and the overpass risk assessment quantity are linearly summed to comprehensively consider internal sensor failures and external transmission risks, generating a comprehensive risk assessment quantity. The corresponding calculation formula is:

[0074] in This is a comprehensive risk assessment metric, a dimensionless parameter that includes both the risk of sensor failure within the channel itself and the interference risk caused by transmission link degradation. A higher value indicates a stronger risk for the channel. The worse one's overall health status, the better.

[0075] A negative exponential smoothing mapping is applied to the comprehensive risk assessment quantity to avoid output step oscillations caused by hard handover fault diagnosis, generating the adaptive continuous health weight that fluctuates continuously in the zero-to-one range. The corresponding calculation formula is:

[0076] in It is a smoothing coefficient with a value of 0.5, which can be adjusted within the range of 0.1 to 1.0 according to the actual working conditions. It is a dimensionless quantity. The adaptive continuous health weights are dimensionless parameters with a value range of [value range missing]. When there is no channel fault or interference risk, the comprehensive risk assessment value is 0 and the health weight is 1. When the channel fault or interference risk increases, the health weight decreases exponentially with the increase of the comprehensive risk assessment value, realizing continuous and smooth adjustment of channel trust, and avoiding the step change of output signal caused by traditional hard threshold switching.

[0077] The adaptive continuous health weights and the local noise variance are used to perform a fusion proportional allocation to dynamically suppress the parameter estimation contribution of failed channels, thus constructing a fault-tolerant fusion weight matrix. The corresponding calculation formula is:

[0078] in for The fault-tolerant fusion weight matrix of the dimension takes into account both the health status and noise level of the channel in its diagonal elements. The better the health status and the lower the noise, the higher the weight is assigned and the greater the contribution to the fusion calculation. The worse the health status of the channel, the lower the weight is assigned, and the impact on the fusion result is dynamically suppressed, realizing the automatic reduction of weight for failed channels.

[0079] By combining the overall attitude matrix and the fault-tolerant fusion weight matrix, a weighted least squares solution is performed on the verifiable channel quantities of all channels to achieve global multidimensional redundancy fault-tolerant calculation and extract the vibration state of the common frame. The corresponding calculation formula is:

[0080] in for The entire verifiable channel quantity observation column vector of dimension, in meters per second squared; for The optimal estimation of the common frame vibration state is achieved by using the first three elements as linear accelerations in the frame's reference coordinate system (m / s²) and the last three elements as angular accelerations in the frame's reference coordinate system (radians / s²). This is the true vibration state of the frame obtained by weighted fusion of the health status of all channels, effectively suppressing the influence of faulty and interference channels on the vibration state estimation. By adding a diagonal regularization term, the solution anomalies caused by matrix rank deficiency are avoided, thus improving numerical stability.

[0081] Physical state reconstruction is performed using the attitude observation vector and the vibration state of the common frame. The reconstruction error is compensated according to the adaptive continuous health weight ratio and added back to the rigid body motion-induced component to retain true high-frequency dynamic characteristics while suppressing spurious vibrations, generating the fault-tolerant fusion measurement output. The corresponding formula for calculating the fault-tolerant verifiable separation quantity is:

[0082] The corresponding final output calculation formula is:

[0083] in This is the fault-tolerant verifiable separation quantity, measured in meters per second squared. This is the final fault-tolerant fusion measurement output for a single channel, expressed in meters per second squared; for channels in good health... Approaching 1, the reconstruction error is fully preserved, and the true high-frequency vibration characteristics of the channel are not lost; for faulty or interfered channels, Approaching 0, the reconstruction error is significantly suppressed, and the faults and interference components of the channel are effectively filtered out. The final output is the vibration measurement value after fault tolerance correction, which achieves the effect of suppressing false vibration while retaining the true high-frequency dynamic characteristics. The frequency boundary of the reconstruction error is determined by the sampling frequency and filter parameters. High-frequency components that are 10 times higher than the frame rotation frequency are identified as true dynamic characteristics and are fully preserved through proportional compensation of health weights.

[0084] The feedback extraction operation is performed by subtracting the sum of the current state reconstruction amount and the prior interference model amount from the current sampling time from the current channel quantity to be verified, in order to obtain the fault-tolerant fusion bias that characterizes the unmodeled dynamic residual. The corresponding calculation formula is:

[0085] in This is the fault-tolerant fusion deviation, expressed in meters per second squared. The vector of structural coupling modulation coefficients delayed from the previous time step is expressed in meters per second squared. This deviation represents the residual portion of the channel signal at the current time step that has not been fitted by the state model and the interference model, and is used for subsequent online updates of model parameters.

[0086] The adaptive continuous health weights are introduced to perform a forgetting decay update operation on the information matrix of the previous sampling time, so as to naturally shield the inverse deterioration of the normal baseline model by fault mutation data, and recursively obtain the information matrix at the current time. The corresponding calculation formula is:

[0087]

[0088] in The information array updated at the current moment, for A matrix of dimension The column number of the single-channel angular domain periodic interference basis matrix; This is the information matrix from the previous time step, with initial values ​​being the diagonal elements. to a diagonal matrix; The Kalman gain vector is used to adjust the step size of parameter updates; the formula adopts a recursive least squares information matrix update form, through adaptive continuous health weights. Adjust the update step size when a channel failure occurs. Approaching zero, the update step size is significantly reduced, preventing fault data from negatively contaminating the interference model and ensuring the stability of the baseline model. During the recursive process, a symmetry correction is performed on the information matrix every 1000 sampling points, using the following correction formula: This avoids matrix asymmetry caused by the accumulation of numerical errors and improves the numerical stability of the recursive process.

[0089] Gain correction is performed using the current information matrix and the fault-tolerant fusion deviation to achieve online adaptive feature fitting and obtain the updated structural coupling modulation coefficients. The corresponding calculation formula is:

[0090] in The current updated structural coupling modulation coefficient vector is expressed in meters per second squared. This formula uses the Kalman gain combined with the deviation weighted by the health weight to perform online correction of the structural coupling modulation coefficient, realizing adaptive tracking and fitting of periodic interference characteristics, and can adapt to the changes in interference characteristics caused by the degradation of rotating transmission parts.

[0091] The adaptive continuous health weights of the historical sampling sequence are used to perform a weighted moving average operation on the squared leave-one-out prediction residuals to filter out occasional random fluctuations, thus updating the local noise variance at the current time. The corresponding calculation formula is:

[0092] in For the index of historical sampling steps within the sliding window, The sliding window length is set to 100 to 1000 sampling points; The current updated local noise variance is expressed in meters per second squared. The historical residual squares are weighted by health weights. The residual data at the time of failure has a very low health weight, so its contribution to the noise variance update is greatly weakened. This avoids the problem of overestimating the noise variance due to failure data and ensures the accuracy of the noise variance estimation.

[0093] The path degradation intensity is subjected to displacement-domain weighted integration with the absolute value of the actual angular travel increment measured by the encoder, replacing pure time integration to preserve the physical memory of spatial wear. This summation yields the cumulative angular travel degradation message. The corresponding cumulative degradation index calculation formula is:

[0094] The corresponding message aggregation formula is:

[0095] in For rotating transmission parts The cumulative degradation index of angular travel is a dimensionless parameter; This represents the local path degradation intensity corresponding to the sampling step; For the corresponding part at time The actual angle is expressed in radians. This cumulative calculation uses the angular travel increment as a weighting coefficient, rather than pure time integration, which can accurately reflect the wear accumulation effect of the rotating transmission part under different rotation angles. It retains the physical memory of wear related to the spatial position of mechanical motion. Under the forward and reverse rotation conditions of the frame, the absolute value of the angular travel increment is included in the accumulation, avoiding the loss of wear memory caused by reverse rotation. For the angular travel cumulative degradation message composed of the global set, { } is a set of operators that aggregate all corresponding channels or rotating transmission parts. The message content includes the fault-tolerant output of all channels, the vibration status of the common frame, the health weight of the channel, the degradation intensity of the rotating part, the cumulative degradation index, the model coefficients and the noise variance. The message output timing is consistent with the sampling timing, and it can be used for online monitoring, fault early warning and health management of the system.

[0096] During system operation, the following adaptation processes are performed for various boundary conditions: For the static frame condition, the frame angular velocity is 0, and the rigid body motion induced component is 0. The angular domain periodic disturbance basis matrix retains only the order corresponding to the DC static reference, and sets the basis corresponding to the other orders to zero to avoid invalid calculations. In the leave-one cross prediction process, an additional regularization term is added to the dimension-reduced observation matrix to improve the stability of state estimation under static conditions.

[0097] For frame variable speed operation, the frequency corresponding to the spatial order is updated in real time, and the encoder angular position signal is interpolated and resampled to ensure the accuracy of the angular domain order; the sliding window length is dynamically adjusted, and the window length is shorter as the speed is faster, which improves the real-time performance of interference feature tracking.

[0098] In response to the packet loss scenario, when the sampled data of a single channel is lost, the health weight of that channel is automatically set to 0 and it will not participate in the fusion calculation and leave-one-out cross-prediction at this sampling time. When the number of consecutive packet losses exceeds 5, the local noise variance of that channel is automatically updated to the preset maximum value until the data is restored to normal.

[0099] For simultaneous failures of multiple channels, when more than 50% of the channel health weights are below 0.1, the system automatically switches to the minimum variance fusion mode, fixing the health weights of all channels to 1 and performing weighted fusion based solely on noise variance. This avoids solution anomalies caused by singularity in the fusion matrix and ensures the continuity of the system output.

[0100] For the rank-deficient matrix operation, a minimum singular value truncation is added to all matrix inversion and generalized inversion operations, with the truncation threshold set to the maximum singular value. This process eliminates singular values ​​close to zero, preventing numerical computation from diverging and ensuring the numerical stability of the algorithm.

[0101] Single-axis rotation matrix To represent the coordinate transformation relationship between two orthogonal coordinate systems after rotation around a specified axis by a corresponding angle, each column of the matrix corresponds to the unit vector of the coordinate axis of the rotated coordinate system in the original coordinate system. The matrix is ​​an orthogonal matrix that satisfies... The determinant value is 1, and there is no mirror transformation.

[0102] Antisymmetric cross product matrix of position vectors To convert the vector cross product operation into an equivalent matrix multiplication operation, the matrix is: An antisymmetric matrix, with all elements on its main diagonal being 0, satisfies ,in Let be any three-dimensional vector.

[0103] Attitude observation vector To map the common vibration state in the frame reference coordinate system to the channel The linear transformation coefficients output by the sensitive axis, the first 3 elements correspond to the sensitivity coefficients of linear acceleration, and the last 3 elements correspond to the sensitivity coefficients of angular acceleration. The magnitude of the coefficients is determined by the sensor mounting pose and the real-time angle of the frame.

[0104] Centripetal acceleration vector This is the normal acceleration generated by the mounting point as the frame rotates, moving outward along the circumference. Its magnitude is proportional to the square of the rotational angular velocity and the perpendicular distance from the mounting point to the axis of rotation.

[0105] Coriolis acceleration vector The acceleration is caused by the change in the angular velocity of the frame rotation and the additional acceleration generated when the mounting point has relative motion in the rotating coordinate system. It consists of two parts: the tangential acceleration caused by the angular acceleration and the Coriolis effect caused by rotational coupling. It only has a non-zero value when the frame rotates at variable speed.

[0106] Rigid body motion induced components This is the projection of the inertial acceleration generated by the rigid rotation of the frame onto the sensor's sensitive axis. This component is caused by the overall rigid motion of the frame and is unrelated to the elastic deformation of the frame structure. It does not belong to the actual structural vibration signal and needs to be separated from the original sampling data.

[0107] Spatial order set The set represents all rotational harmonic orders that may cause periodic interference in the rotating transmission part. Each element in the set corresponds to an interference frequency that repeats cyclically with the frame angular position. The order value is the ratio of the interference frequency to the frame rotation frequency.

[0108] Dynamic excitation modulation vector To quantify the modulation effect of different physical factors on the amplitude of periodic disturbances, each element in the vector corresponds to a physical excitation that affects the amplitude of the disturbance, including rotational speed, rotor imbalance, temperature fluctuation, etc. All elements have been dimensionless and have a uniform value range.

[0109] Angular domain periodic disturbance basis matrix For channel The feature basis set of all periodic parasitic interferences it is subjected to, with each column of the matrix corresponding to an independent interference feature component, is used to fit the parasitic interference signal that changes cyclically with the frame angular position.

[0110] Structural coupling modulation coefficient vector For each interference feature, the amplitude of the interference is represented by the coefficient, which corresponds to the strength of the interference of the corresponding order. The change in the coefficient corresponds to the change in the degree of contact degradation of the rotating transmission part.

[0111] Structure-coupled modulation components For channel The fitted estimate of the periodic parasitic interference is obtained by multiplying the interference basis matrix by the modulation coefficient. This component is the common-mode coherent interference generated by the multi-channel shared transmission path and does not belong to the actual structural vibration.

[0112] Diagonal inverse variance weight matrix In the leave-one cross-prediction process, the trust weight matrix of the remaining channels has weights that are inversely proportional to the noise variance of the channels. Channels with lower noise have higher weights in state estimation.

[0113] Prediction uncertainty matrix The covariance matrix is ​​the leave-one-out state estimation result. The diagonal elements of the matrix correspond to the variance of each component of the state estimation. The larger the variance, the higher the estimation uncertainty of that component and the lower the observation accuracy.

[0114] Leave-one state feature vector To estimate the common vibration state of the frame based on the data of all remaining channels after removing the channels to be predicted, this estimation process does not use any data from the channels to be predicted, thus avoiding fault detection failure caused by self-verification loops.

[0115] Leave-one cross-prediction residuals For channel The deviation between the actual measured value and the predicted value under fault-free conditions directly reflects the degree of abnormality of the channel itself. The residual of a fault-free channel should contain only random noise.

[0116] Physical residual energy index The normalized channel fault intensity is a dimensionless parameter. The larger the value, the higher the probability of sensor failure in the channel and the more severe the fault. The influence of the observation blind zone is eliminated by normalizing the prediction variance.

[0117] Normalized interference energy For channel The relative intensity of the parasitic interference it is subjected to is a dimensionless parameter, which eliminates the influence of signal amplitude differences between different channels and is used for subsequent degradation source tracing and inversion calculations.

[0118] Diagonal Discrete Weight Matrix This is the weight matrix for each channel during the degradation inversion process. The weight is inversely proportional to the fluctuation of the channel's interference energy. The channel with greater fluctuation has a lower weight in the inversion, thus avoiding abnormal jump data from dominating the inversion results.

[0119] Channel routing association matrix This represents the signal transmission path correlation between the vibration measurement channel and the rotating transmission part. The matrix elements are Boolean values, indicating whether the signal link of the channel passes through the corresponding rotating transmission part.

[0120] Path degradation intensity vector The degree of contact degradation and disturbance for each rotating transmission part is a dimensionless parameter. The larger the value, the more severe the degradation phenomena such as wear and poor contact in that part.

[0121] Risk assessment of passageway For channel The sum of the degradation levels of all rotating transmission points along the path is a dimensionless parameter. The larger the value, the higher the risk of interference from external transmission link degradation.

[0122] Comprehensive risk assessment For channel The comprehensive health risk includes both the internal risk of sensor failure within the channel itself and the external interference risk caused by transmission link degradation. It is a dimensionless parameter; the larger the value, the worse the health status of the channel.

[0123] Adaptive Continuous Health Weights For channel The dynamic trust level, with a value range of [value missing]. The healthier the channel, the closer its weight is to 1, and the greater its contribution to the fusion calculation; the weight of a faulty or disturbed channel decreases exponentially with increasing risk, automatically reducing its contribution.

[0124] Fault-tolerant fusion weight matrix This is the final weight matrix for each channel during multi-channel data fusion. It takes into account both the health status and noise level of the channels, and realizes automatic weight reduction for faulty channels and weighted optimization for normal channels.

[0125] Vibration state of common frame The vibration state of the frame structure is obtained by weighted fusion of data from all channels, eliminating common-mode parasitic interference and abnormal data from fault channels. This is the optimal estimation result for the vibration of the frame structure.

[0126] Fault-tolerant fusion measurement output The final vibration measurement value of the channel after fault tolerance correction has been obtained, which has suppressed parasitic interference and fault anomalies, while preserving the true high-frequency vibration characteristics of the channel.

[0127] Fault-tolerant fusion deviation This represents the residual portion of the channel measurements that is not fitted by the state model and the interference model. It reflects the unmodeled dynamic changes and is used to update the coefficients of the interference model online.

[0128] Recursive Information Matrix The covariance matrix is ​​used to characterize the uncertainty of the coefficient estimation for structural coupling modulation coefficients. The inverse of the matrix is ​​the information matrix. The smaller the value, the higher the accuracy of the corresponding coefficient estimation.

[0129] Kalman gain vector The gain is the step size for correcting the coefficients by the residual during the recursive update process. The gain is determined by the channel health weight and the estimation uncertainty. The gain of faulty channels is automatically reduced to avoid faulty data from polluting the model.

[0130] Local noise variance For channel The variance estimate of the measurement noise is used to characterize the measurement accuracy of the channel. The larger the variance, the higher the measurement noise of the channel, and the lower its weight in fusion and estimation.

[0131] Cumulative degradation index of angular travel The cumulative wear and degradation degree of the rotating transmission part throughout its entire life cycle is a dimensionless parameter. The angular stroke weighted integral is used instead of the time integral, which retains the physical memory of wear related to the rotational spatial position and can be used to assess the remaining life of the component.

[0132] Angular travel cumulative degradation message It is a collection of all system state information at each sampling moment, including fault-tolerant output, vibration status, channel health weight, component degradation intensity, cumulative degradation index, model coefficients, noise variance, and other full information, which is used for online monitoring, fault early warning and health management.

[0133] The system power-on initialization process is as follows: After the system is powered on, it first performs a hardware self-test, sequentially checking the communication status of the vibration measurement channel, encoder, and temperature sensor. After confirming that all sensors are online normally, it performs a clock synchronization operation, aligning the sampling clocks of all acquisition devices through a hardware trigger signal. After the synchronization error verification is passed, it begins pre-acquisition of data, with the pre-acquisition frame length set to 1000 sampling points. Based on the pre-acquisition data, it completes the initial parameter calculation, including the initial value of the local noise variance, the initial value of the robust noise adaptive scale, and the initial iterative value of the structural coupling modulation coefficient. After the pre-acquisition is completed and the parameters are successfully initialized, the system enters normal operation.

[0134] The process of multi-source data synchronous acquisition is as follows: Within each sampling period, a hardware synchronous trigger signal is first used to simultaneously start vibration channel AD sampling, encoder angular position sampling, and temperature sensor sampling. After sampling is completed, all collected data are stamped with the same timestamp. For temperature signals with lower sampling frequencies, linear interpolation is used to interpolate the temperature data to the same timestamp as the vibration sampling, thus achieving clock alignment of all data. After alignment, preprocessing is performed on the vibration data, and the preprocessed data enters the subsequent calculation process.

[0135] The leave-one cross-validation process for full-channel traversal is as follows: At each sampling time, all channels are sampled in ascending order of channel identifier. Each vibration channel undergoes a leave-one-out process sequentially. During each process, all data from the current channel to be predicted are discarded, and the remaining data is used as the basis for prediction. The data from each channel is processed using weighted least squares state estimation to obtain a leave-one state feature vector. The leave-one physical prediction and residual energy index of the channel to be predicted are then calculated. After processing the current channel, the process is switched to the next channel until all channels have been traversed, and the physical residual energy index of all channels is obtained.

[0136] The iterative reweighted least squares optimization process is as follows: The iterative optimization process is executed within a sliding window, with each sliding window updating once. First, the iteration count is initialized to 0, the structural coupling modulation coefficients are all-zero vectors, and the common state is the result of the least squares solution. The initial residuals and the corresponding weight matrix are calculated, a weighted least squares equation is constructed, the updated coefficients and state are solved, the objective function value is calculated, and the change in the objective function value between two adjacent iterations is compared. If the change is less than the convergence threshold, or the number of iterations reaches the maximum number of iterations, the iteration is terminated, and the optimal coefficients and state are output. Otherwise, the weight matrix is ​​updated, and the next iteration begins.

[0137] The nonnegative least squares degenerate inversion operation process is as follows: At each sampling time, based on the normalized interference energy vector, the channel routing correlation matrix, and the diagonal discrete weight matrix, a non-negative least squares solution is performed. First, the active set and solution vector are initialized, the gradient vector is calculated, and the inactive index with the smallest gradient is added to the active set. The unconstrained least squares problem is solved based on the active set. If all elements in the solution vector corresponding to the active set are non-negative, the solution vector is updated; otherwise, the step size is adjusted, and elements with negative values ​​are removed from the active set. The solution is then solved again until the convergence condition is met, and the path degradation intensity vector is output.

[0138] The online update process for recursive least squares parameters is as follows: At each sampling time, the fault-tolerant fusion bias is first calculated. Based on the information matrix of the previous time, the Kalman gain vector is calculated. The structural coupling modulation coefficients are updated using the gain vector and the bias. The information matrix of the current time is then updated. Every 1000 sampling points, the information matrix is ​​symmetrically corrected to avoid the accumulation of numerical errors. At the same time, the amplitude of the structural coupling modulation coefficients is limited to prevent coefficient divergence and ensure the stability of the model.

[0139] The boundary condition adaptation process is as follows: For the static frame operation, when the frame angular velocity is detected to be less than 1% of the rated angular velocity for 100 consecutive sampling points, the system automatically switches to the static operation adaptation mode, disables high-order fitting for periodic interference, retains only the DC component, and increases the regularization coefficient of the state estimation to improve estimation stability. For the variable frame operation, the system monitors the rate of change of the frame angular velocity in real time. When the rate of change exceeds 10% per second of the rated value, the sliding window length is automatically shortened to improve the real-time performance of interference feature tracking. For the packet loss operation, when the channel sampling data is detected to have not been updated for more than 3 sampling periods, the health weight of the channel is automatically reset to 0 and it is not included in the current fusion calculation. When the continuous packet loss exceeds 5 sampling periods, the noise variance of the channel is updated to the preset maximum value until the data returns to normal.

[0140] The embodiments of this example have been described above. However, this example is not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of this example, and all of them are within the protection scope of this example.

Claims

1. A fault-tolerant system for vibration measurement channels of a frame instrument based on cross-validation, applied to a homogeneous measurement equipment including a frame, shaft, rotating transmission parts, and vibration measurement channels, characterized by setting continuous sampling timing and initializing structural coupling modulation coefficients and local noise variance, wherein... Configured for execution: The attitude observation vectors of each channel are extracted based on the frame reference benchmark, and relative kinematics calculations are performed to remove rigid body motion-induced components, thereby obtaining the channel quantities that reflect pure structural deformation. Based on the spatial periodic characteristics of the rotating transmission part, an angular domain periodic disturbance basis matrix is ​​constructed to characterize contact degradation and rotor disturbance. Robust state estimation is performed by combining the attitude observation vector with the angular domain periodic interference basis matrix to separate the verifiable channel quantity and structurally coupled modulation component that filter out coherent interference. After removing the channels to be predicted, leave-one-out cross-prediction operation is performed on the verifiable channel quantities to generate a physical residual energy index characterizing the degree of independent anomaly of a single channel. Based on the channel routing correlation matrix, the structural coupling modulation components are spatially and physically mapped, and the path degradation intensity is obtained by tracing back to the rotating transmission part. Then, the channel risk assessment quantity is obtained by fusion. By combining the physical residual energy index with the channel risk assessment quantity, an adaptive continuous health weight is generated for dynamically adjusting the channel trust level, and the common frame vibration state and fault-tolerant fusion measurement output are estimated accordingly. The structural coupling modulation coefficient and the local noise variance are updated online by using the fault-tolerant fusion deviation along the continuous sampling time sequence, and the path degradation intensity is accumulated by combining the real angular travel sequence to generate an angular travel cumulative degradation message.

2. The fault-tolerant system for frame instrument vibration measurement channels based on cross-validation according to claim 1, characterized in that, Extract the attitude observation vector and obtain the channels to be verified, including: Combine the actual angle sequences of each frame level to perform coordinate transformation multiplication operations, and obtain the attitude chain transfer matrix with a unified spatial reference; Spatial projection operation is performed on the attitude chain transfer matrix using the channel sensitive axis, calibration parameters, and installation point position vector to eliminate multi-axis installation coupling deviation and extract the attitude observation vector characterizing the unidirectional spatial sensitivity. Based on the frame angular velocity and the attitude chain transfer matrix, centripetal acceleration and Coriolis mechanical projection calculations are performed to quantify the geometric rotational inertia effect and obtain the rigid body motion induced components. The rigid body motion-induced component is subtracted from the original channel sampling data, and a benchmark correction operation is performed to filter out macroscopic kinematic projection interference, thereby obtaining the channel quantity to be verified that characterizes the deformation features of the elastic body.

3. The fault-tolerant system for frame instrument vibration measurement channels based on cross-validation according to claim 1, characterized in that, Constructing the periodic disturbance basis matrix in the angular domain includes: Extract the DC static reference, sliding friction order, bearing rolling contact order, and motor slot pole harmonic common multiple of the rotating transmission part to generate a spatial order set to cover the physical periodic law; By combining the frame speed amplitude, the square of the rotor unbalance speed, and the zero-mean AC fluctuation of the local temperature, the execution state parameters are spliced ​​to quantify the multi-source physical excitation and form a dynamic excitation modulation vector. According to the connection indication of the channel routing association matrix, the dynamic excitation modulation vector is mapped by the trigonometric function of the spatial order set and the frame angular position to introduce spatial orientation modulation characteristics and generate a single-order interference basis. An augmented splicing operation is performed along the associated path on all crossing locations and the single-order interference basis at the corresponding order to construct the angular domain periodic interference basis matrix by polymerizing the transmission interference features.

4. The fault-tolerant system for frame instrument vibration measurement channels based on cross-validation according to claim 1, characterized in that, Joint estimation yields verifiable channel quantity and structurally coupled modulation components, including: The absolute deviation of the residuals of each channel from the median is calculated and an unbiased statistical factor is introduced to perform scaling to suppress extreme value fluctuations and obtain a robust noise adaptive scale. Construct the overall attitude matrix and the overall interference basis matrix by augmenting and splicing the attitude observation vectors of all channels and the periodic interference basis matrix of the angular domain respectively; Under the observation constraint that the number of channels to be verified is equal to the sum of the overall attitude matrix and the common state, the overall interference basis matrix and the structural coupling modulation coefficient, a joint iterative optimization is performed with the goal of minimizing the log heavy-tailed loss and the generalized cross-validation smoothing regularization term to overcome the influence of micro-short-term spikes and solve for the optimal structural coupling modulation coefficient. The common-mode component is filtered out by subtracting the product of the overall interference basis matrix and the optimal coefficient from the channel quantity to be verified in order to eliminate pseudo-vibration coherent contamination, and the verifiable channel quantity and the structural coupling modulation component of each channel are output accordingly.

5. The fault-tolerant system for frame instrument vibration measurement channels based on cross-validation according to claim 1, characterized in that, Perform leave-one-out cross-prediction to generate physical residual energy indices, including: After removing the channels to be predicted, the inverse operation is performed using the current local noise variance of the remaining channels and the positive bias constant to prevent the denominator from being singular, so as to construct a diagonal inverse variance weight matrix that reflects the dynamic change of the local signal-to-noise ratio. A weighted generalized inverse mapping operation is performed on the dimensionality-reduced observation matrix formed by the remaining channels and the diagonal inverse variance weight matrix to reduce the interference of ill-conditioned pose on local estimation, and to generate a prediction uncertainty matrix and a leave-one state feature vector. The attitude observation vector of the channel to be predicted is used to perform forward spatial projection on the leave-one state feature vector to establish a virtual measurement reference without self-verifying loops and generate leave-one physical prediction quantity. Subtracting the left-one physical prediction from the verifiable channel quantity and then performing variance normalization operation via the prediction uncertainty matrix and the positive bias constant to eliminate false alarms caused by local observation blind spots, the physical residual energy index that measures the intensity of intrinsic faults in a single channel is obtained.

6. The fault-tolerant system for frame instrument vibration measurement channels based on cross-validation according to claim 1, characterized in that, The inversion and tracing of the source path obtains the degradation intensity and the risk assessment of the transit path, including: The square of the structure-coupled modulation component is subjected to dimensionless operation using the local noise variance, the median of its own interference, and the positive bias constant to prevent denominator singularity, so as to eliminate the absolute amplitude difference and obtain the normalized interference energy. A diagonal discrete weight matrix is ​​constructed based on the discrete statistics of the normalized interference energy of each channel to weaken the dominance of high-frequency jump data on physical inversion. Under non-negative physical boundary constraints, with the reconstruction error of the normalized interference energy, the channel routing correlation matrix, and the unknown degradation variables as the objective, least squares solution is performed under the inverse weighting of the diagonal discrete weight matrix to realize the localization of coherent contamination to the mechanical entity and obtain the path degradation intensity of each of the rotating transmission parts. The path degradation intensity is aggregated by performing a forward route aggregation operation on the channel routing association matrix to quantify the global external transmission physical risk borne by a single channel and generate the channel risk assessment quantity.

7. The fault-tolerant system for frame instrument vibration measurement channels based on cross-validation according to claim 1, characterized in that, Generate adaptive continuous health weights and weight them to obtain fault-tolerant fusion measurement outputs, including: The physical residual energy index and the overpass risk assessment quantity are linearly summed to comprehensively consider internal sensor failures and external transmission risks, and a comprehensive risk assessment quantity is generated. The comprehensive risk assessment quantity is subjected to negative exponential smoothing mapping to avoid output step oscillation caused by hard switching fault diagnosis, and the adaptive continuous health weight is generated to continuously fluctuate in the range of zero to one. The adaptive continuous health weights and the local noise variance are used to perform a fusion ratio allocation to dynamically suppress the parameter estimation contribution of the failed channels and construct a fault-tolerant fusion weight matrix. By combining the overall attitude matrix and the fault-tolerant fusion weight matrix, weighted least squares solution is performed on the verifiable channel quantities of all channels to achieve global multidimensional redundancy fault-tolerant calculation and extract the vibration state of the common frame. The physical state is reconstructed using the attitude observation vector and the vibration state of the common frame. The reconstruction error is compensated according to the adaptive continuous health weight ratio and added back to the rigid body motion induced component, so as to retain the real high-frequency dynamic characteristics while suppressing pseudo vibration, and generate the fault-tolerant fusion measurement output.

8. The fault-tolerant system for frame instrument vibration measurement channels based on cross-validation according to claim 1, characterized in that, Update parameters online and generate angular travel cumulative degradation messages, including: Subtract the sum of the current state reconstruction amount and the prior interference model amount at the previous sampling time from the current amount of the channel to be verified, and perform a feedback extraction operation to obtain the fault-tolerant fusion deviation amount that characterizes the unmodeled dynamic residual. The adaptive continuous health weight is introduced to perform a forgetting decay update operation on the information matrix of the previous sampling time, so as to naturally shield the reverse deterioration of the normal baseline model by fault mutation data, and recursively obtain the information matrix at the current time. Gain correction calculation is performed using the information matrix at the current moment and the fault-tolerant fusion deviation to achieve online adaptive feature fitting and obtain the updated structural coupling modulation coefficients; The adaptive continuous health weights of the historical sampling sequence are used to perform a weighted moving average operation on the squared leave-one prediction residuals to filter out occasional random fluctuations and update the local noise variance at the current time. The path degradation intensity is subjected to displacement domain weighted integration with the absolute value of the actual angular travel increment measured by the encoder, in order to replace pure time integration and thus retain the physical memory of spatial wear. The cumulative angular travel degradation message is obtained by summing the results.

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