An industrial production line health state analysis method and system

Abstract

This invention discloses a method and system for analyzing the health status of industrial production lines, relating to the field of state analysis technology. It constructs a basic health status vector by extracting equipment vibration and displacement characteristics from physical acquisition signals. Process control parameters and production result metrics are converted into process input vectors and system observation vectors. An augmented health representation state vector is generated based on the basic health status vector and the process input vector. An augmented state evolution equation and an observation output equation are constructed from the system augmented state transition matrix and the control input coupling matrix, generating a first discrete state space equation set. An adaptive forgetting factor is established based on the prediction error gradient of the system observation vector and incorporated into a recursive least squares algorithm to update the system augmented state transition matrix and the control input coupling matrix, generating a second discrete state space equation set. When the degradation rate representation value is greater than the dynamic steady-state physical boundary, a quadratic programming function is solved, and the optimal process control compensation component is superimposed onto the process input vector.

Description

Technical Field

[0001] This invention relates to the field of condition analysis technology, and in particular to a method and system for analyzing the health status of industrial production lines. Background Technology

[0002] With the continuous evolution of industrial automation technology, the operational complexity and process precision requirements of industrial production lines have increased significantly. During continuous operation, industrial production lines not only need to ensure that the production output metrics meet stringent quality standards, but also need to maintain the underlying core mechanical components in good health.

[0003] However, existing technologies for analyzing and controlling the health status of industrial production lines still suffer from the following critical shortcomings. First, at the state modeling level, current technologies treat natural degradation and process intervention as independent linear superpositions, neglecting the nonlinear and vulnerable response of sub-healthy equipment to high-load processes. Commonly used black-box neural networks lack the matrix analysis capability for the evolution of underlying physical states, while univariate time-series prediction models ignore the multi-order cross-coupling interference between equipment vibration displacement, process parameters, and production metrics, making it impossible for the model to accurately represent the health evolution trajectory under complex operating conditions. Second, at the parameter identification level, existing technologies mostly employ offline identification or recursive least squares algorithms with fixed forgetting factors. When faced with sudden changes in operating conditions such as a sharp increase in cutting load, existing algorithms cannot dynamically adjust the convergence speed based on prediction error fluctuations, easily leading to divergence in the identification of the state transition matrix and control input matrix, completely losing the ability to quickly track and resist disturbances in the dynamic degradation trajectory. Finally, at the control and compensation level, existing closed-loop compensation strategies typically use the original displacement signal containing high-frequency noise for simple threshold judgment, failing to accurately extract the dynamic health degradation rate that reveals the physical essence of degradation. Existing strategies severely neglect the physical limits and hard constraints of the underlying actuators when calculating process adjustment instructions. Compensation instructions generated by unconstrained optimization are prone to exceeding physical boundaries, triggering overshoot alarms or secondary mechanical damage. They cannot achieve closed-loop adaptive linkage to mitigate degradation rates within a safe physical limit. Summary of the Invention

[0004] The technical problem solved by this invention is that existing technologies are difficult to accurately establish a dynamic physical coupling model between the nonlinear degradation law of industrial equipment and multivariable process parameters. Furthermore, the parameter identification mechanism based on fixed parameters is prone to failure under abrupt operating conditions. Traditional black-box methods are constrained by high-frequency physical signal noise interference and cannot accurately extract vibration velocity features that characterize the true health degradation rate. Consequently, under strict objective physical constraints, it is impossible to output a closed-loop process compensation component with physical interpretability.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for analyzing the health status of an industrial production line, comprising the following steps: Step S1: Extract the equipment vibration displacement characteristics from the physical acquisition signals of the equipment, construct the basic health state vector, construct the process control parameters and production result measurement values ​​as the process input vector and the system observation vector respectively, and generate the augmented health characterization state vector based on the basic health state vector and the process input vector. Step S2: Define the system augmented state transition matrix and control input coupling matrix, and construct the augmented state evolution equation and observation output equation by combining the augmented health characterization state vector, process input vector and system observation vector, and jointly generate the first discrete state space equation set. Step S3: Calculate the prediction error gradient of the system observation vector, construct an adaptive forgetting factor that is negatively correlated with the magnitude of the prediction error gradient, embed the adaptive forgetting factor into the recursive least squares algorithm, update the system augmented state transition matrix and control input coupling matrix, and generate the identified updated second discrete state space equation set. Step S4: Extract the actual vibration velocity features as the degradation rate characterization value. When the degradation rate characterization value is greater than the dynamic steady-state physical boundary, construct a quadratic programming function, solve the quadratic programming function to find the optimal process control compensation component, and superimpose it into the process input vector.

[0006] Preferably, step S1 includes the following sub-steps: Step S101: Obtain the discrete time series index of the industrial production line. The equipment's physical acquisition signals, process control parameters, and production result metrics at any given moment; Step S102: Extract the equipment vibration displacement features from the physical acquisition signals of the equipment, arrange the equipment vibration displacement features into a first column vector according to a preset first dimension, and construct the first column vector into a basic health state vector; Step S103: After numerical processing of the process control parameters, arrange them into a second column vector according to the preset second dimension, and construct the second column vector into a process input vector; The production result metrics are arranged into a third column vector according to a preset third dimension, and the third column vector is used to construct the system observation vector.

[0007] Preferably, step S1 further includes the following sub-steps: Step S104: Calculate the Kronecker product of the basic health state vector and the process input vector to obtain the cross-mapping tensor. Perform matrix concatenation operation on the basic health state vector and the cross-mapping tensor to calculate the augmented health representation state vector.

[0008] Preferably, step S2 includes the following sub-steps: Step S201: Define the parameter matrix for constructing the multivariable discrete state-space equation system. The parameter matrix includes the system augmented state transition matrix, the control input coupling matrix, the system observation mapping matrix, and the feedforward correlation matrix. Step S202: Based on the augmented health characterization state vector, process input vector, system augmented state transition matrix, and control input coupling matrix, an augmented state evolution equation is constructed, and the predicted augmented health characterization state vector is calculated through the augmented state evolution equation.

[0009] Preferably, step S2 further includes the following sub-steps: Step S203: Based on the system observation vector, augmented health characterization state vector, process input vector, system observation mapping matrix, and feedforward correlation matrix, construct the observation output equation; By combining the augmented state evolution equation and the observation output equation, the first discrete state space equation set is generated.

[0010] Preferably, step S3 includes the following sub-steps: Step S301: Establish an online parameter identification mechanism for the first discrete state-space equation set. The specific logic is as follows: Obtain the index of the system observation vector in the discrete time series. The actual detected value at time t is used as the predicted output value of the system observation vector, and the value calculated by the observation output equation in the first discrete state space equation set is used as the predicted output value. The difference between the predicted output value and the actual detected value is calculated to obtain the prediction error. The partial derivative of the prediction error is calculated to obtain the prediction error gradient. Step S302: Calculate the magnitude of the prediction error gradient, construct the adaptive forgetting factor, and establish a negative correlation mapping relationship between the adaptive forgetting factor and the magnitude of the prediction error gradient.

[0011] Preferably, step S3 further includes the following sub-steps: Step S303: Embed the adaptive forgetting factor into the recursive least squares algorithm. Using the recursive least squares algorithm with the adaptive forgetting factor, receive the real-time data stream of the augmented health representation state vector, process input vector, and system observation vector under the continuous time sampling sequence. Solve online and dynamically update the matrix element values ​​in the system augmented state transition matrix and control input coupling matrix. Substitute the system augmented state transition matrix and control input coupling matrix with the updated matrix element values ​​into the first discrete state space equation set to generate the identified and updated second discrete state space equation set.

[0012] Preferably, step S4 includes the following sub-steps: Step S401: Based on the second discrete state-space equation set, deduce the health evolution trajectory of the industrial production line. The specific logic is as follows: The Savitzky-Golay filter is used to perform polynomial smoothing fitting on the equipment vibration displacement characteristics in the augmented health characterization state vector. The first-order time partial derivative of the fitted polynomial at the center point of the sliding window is calculated to obtain the true vibration velocity characteristics after filtering out high-frequency noise components. The true vibration velocity characteristics are defined as the degradation rate characterization value.

[0013] Preferably, step S4 further includes the following sub-steps: Step S402: Set a dynamic steady-state physical boundary associated with the current operating condition. When the degradation rate characterization value is detected to be greater than the dynamic steady-state physical boundary, trigger the process compensation optimization mechanism, specifically: Construct a quadratic programming function, taking minimizing the expected degradation rate deviation and minimizing the process adjustment range as the joint objective of the quadratic programming function, and inject the physical limit hard constraint inequality of the process control parameters into the quadratic programming function; Step S403: Solve the quadratic programming function using the interior point method. Within the feasible region limited by the physical limit hard constraint inequality, use the updated matrix element values ​​of the control input coupling matrix to iteratively find the optimal process control compensation component in the current state. Then, superimpose the optimal process control compensation component into the process input vector of the next control cycle.

[0014] An industrial production line health status analysis system includes a characterization module, a modeling module, an identification module, and an optimization module; The characterization module is used to extract the vibration displacement characteristics of the equipment from the physical acquisition signals of the equipment, construct a basic health state vector, construct process control parameters and production result metrics as process input vector and system observation vector respectively, and generate an augmented health characterization state vector based on the basic health state vector and process input vector. The modeling module is used to define the system augmented state transition matrix and control input coupling matrix, and to construct the augmented state evolution equation and observation output equation by combining the augmented health characterization state vector, process input vector and system observation vector, and jointly generate the first discrete state space equation set. The identification module is used to calculate the prediction error gradient of the system observation vector, construct an adaptive forgetting factor that is negatively correlated with the magnitude of the prediction error gradient, embed the adaptive forgetting factor into the recursive least squares algorithm, update the system augmented state transition matrix and control input coupling matrix, and generate the second discrete state space equation set after identification and update. The optimization module is used to extract the actual vibration velocity characteristics as the degradation rate characterization value. When the degradation rate characterization value crosses the dynamic steady-state physical boundary, a quadratic programming function is constructed, the quadratic programming function is solved to find the optimal process control compensation component, and it is superimposed on the process input vector.

[0015] The beneficial effects of this invention are as follows: By calculating the Kronecker product of the basic health state vector and the process input vector, an augmented health representation state vector containing multi-order coupling cross terms is generated. The augmented state transition matrix of the system and the control input coupling matrix are combined to construct a first discrete state space equation set, accurately quantifying the nonlinear evolution of equipment health state and the coupling mechanism of process parameters. An adaptive forgetting factor that is negatively correlated with the magnitude of the predicted error gradient is constructed. The adaptive forgetting factor is embedded in a recursive least squares algorithm to update the augmented state transition matrix and the control input coupling matrix of the system online, generating a second discrete state space equation set. The process group solves the problem of easy failure of fixed parameter identification under sudden operating conditions, endows the online parameter identification mechanism with anti-disturbance and fast tracking capabilities, extracts the real vibration velocity characteristics as the degradation rate characterization value, and solves the quadratic programming function with injected physical limit hard constraint inequality when the degradation rate characterization value crosses the dynamic steady-state physical boundary. Iteratively optimizes the optimal process control compensation component in the current state and superimposes it into the process input vector. Under the dual guarantee of mathematical matrix analysis and boundary constraints, it outputs execution instructions with physical executability, realizing closed-loop process adaptive linkage to smooth the healthy degradation rate. Attached Figure Description

[0016] Figure 1 A flowchart illustrating the steps of an industrial production line health status analysis method according to an embodiment of the present invention; Figure 2 This is a basic flowchart of an industrial production line health status analysis system provided in one embodiment of the present invention. Detailed Implementation

[0017] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0018] Example 1, referring to Figure 1 This paper provides a method for analyzing the health status of an industrial production line, which includes the following steps: Step S1, obtain The equipment's physical acquisition signals, process control parameters, and production result metrics are collected at any given time. The equipment vibration and displacement characteristics of the physical acquisition signals are extracted to construct a basic health state vector. The process control parameters and production result metrics are respectively constructed as process input vector and system observation vector. The Kronecker product of the basic health state vector and the process input vector is calculated and concatenated to generate an augmented health characterization state vector.

[0019] Step S2: Define the system augmented state transition matrix and control input coupling matrix, and construct the augmented state evolution equation and observation output equation by combining the augmented health characterization state vector, process input vector and system observation vector, and jointly generate the first discrete state space equation set.

[0020] Step S3: Calculate the prediction error gradient of the system observation vector, construct an adaptive forgetting factor that is negatively correlated with the prediction error gradient, embed the adaptive forgetting factor into the recursive least squares algorithm, update the system augmented state transition matrix and control input coupling matrix, and generate the identified updated second discrete state space equation set.

[0021] Step S4: Extract the actual vibration velocity features as the degradation rate characterization value. When the degradation rate characterization value is greater than the dynamic steady-state physical boundary, construct a quadratic programming function, solve the quadratic programming function to find the optimal process control compensation component, and superimpose it into the process input vector.

[0022] This invention generates an augmented health representation state vector containing multi-order coupling cross terms by calculating the Kronecker product of the basic health state vector and the process input vector. It then constructs a first discrete state space equation set by combining the system's augmented state transition matrix and the control input coupling matrix, accurately quantifying the nonlinear evolution of equipment health state and the coupling mechanism of process parameters. An adaptive forgetting factor, negatively correlated with the magnitude of the predicted error gradient, is constructed and embedded into a recursive least squares algorithm to update the system's augmented state transition matrix and the control input coupling matrix online, generating a second discrete state space equation set. This solves the problem of easy failure of fixed parameter identification under abrupt operating conditions, endowing the online parameter identification mechanism with disturbance resistance and rapid tracking capabilities. It extracts real vibration velocity features as degradation rate representation values. When the degradation rate representation value crosses the dynamic steady-state physical boundary, it solves a quadratic programming function with injected physical limit hard constraint inequalities, iteratively optimizing the optimal process control compensation component in the current state and superimposing it onto the process input vector. Under the dual guarantee of mathematical matrix analysis and boundary constraints, it outputs physically executable execution instructions, realizing closed-loop adaptive process linkage to mitigate health degradation rates.

[0023] Step S1 includes the following sub-steps: Step S101: Obtain the discrete time series index of the industrial production line. The equipment's physical acquisition signals, process control parameters, and production result metrics at any given time.

[0024] In a specific embodiment, discrete time series indexing The continuous time axis passes through a fixed sampling period. Discretized time step number.

[0025] Step S102: Extract the equipment vibration displacement characteristics from the physical acquisition signals of the equipment. The specific logic is as follows: The physical acquisition signals of the equipment are obtained in real time by high-frequency sensors deployed on key mechanical nodes of the industrial production line, such as the high-frequency vibration signal of the spindle bearing acquired by a piezoelectric accelerometer. A low-pass filter is performed on the vibration acceleration sequence in the physical acquisition signal to remove high-frequency environmental electrical noise. Two discrete numerical integration operations are then performed on the filtered vibration acceleration sequence in the time domain to calculate the equipment vibration displacement characteristics reflecting the deformation of the gap between the spindle and the bearing.

[0026] The equipment vibration displacement characteristics are determined according to a preset first dimension. Arrange them into the first column vector, and construct the basic health state vector from the first column vector. Preset first dimension The value is uniquely determined by the actual number of vibration monitoring points deployed on the industrial production line. If there are... If there are 10 measurement points, then at 10 ... Time-parallel extraction The equipment vibration displacement characteristics at each measuring point, and The vibration displacement characteristics of each device are arranged from top to bottom in order of measurement point number, and the generation dimension is... The first column vector. Define the first column vector as the basic health state vector. .

[0027] Step S103: After numerical processing of the process control parameters, arrange them into a second column vector according to the preset second dimension, and construct the second column vector into a process input vector; the process control parameters are the equipment operating condition input instructions set by the programmable logic controller, such as cutting feed speed, spindle set speed and coolant pump pressure.

[0028] Define the unprocessed initial process control parameter vector as follows: For the initial process control parameter vector The first in Each element is processed using the following numerical formula: ; in, The first element, after numerical processing, is arranged into the second column vector. A standard process input element, Initial process control parameter vector The first in One original collected element, For the first The threshold value of the statistical average value of a certain process control parameter under normal historical operating conditions. For the first The statistical standard deviation threshold of a process control parameter under normal historical operating conditions. All standard process input elements, after being processed by the standard deviation standardization algorithm, are then analyzed according to a preset second dimension. (i.e., the number of controlled process variables) arranged from top to bottom with dimension [dimension number missing]. The second column vector is used to construct the process input vector. .

[0029] The production result measurement value is determined according to a preset third dimension. Arrange them into the third column vector, and construct the system observation vector from the third column vector. Production outcome metrics are objective statistical data reflecting the output quality and energy consumption of the current industrial production line, such as the absolute value of product dimensional deviation and the energy consumption per unit processing cycle. A third dimension is pre-defined based on the quantity of production outcome indicators. Arrange the production result metrics into dimensions. The third column vector is used to construct the system observation vector. .

[0030] Step S104: Calculate the basic health state vector With process input vector The Kronecker product yields a cross-mapping tensor characterizing the nonlinear mapping extension, which represents the underlying health state vector. Perform a matrix concatenation operation with the cross-mapping tensor to construct an augmented health representation state vector in the form of a free state vector. Augmented health representation state vector The mathematical structure expression under the initial mapping reference is: ; in, This is the Kronecker product operator. This is the matrix transpose operator. Based on the basic health state vector, For process input vector, To augment the health representation state vector.

[0031] Existing technologies typically assume that equipment degradation patterns and process operating environments are independent linear superpositions, failing to capture the nonlinear, vulnerable responses of equipment to specific high-load process parameters in a sub-optimal state. This embodiment introduces the Kronecker product operator. , with dimensions as Basic health state vector With dimension process input vector Tensor multiplication was performed, generating a vector with dimension . Cross-mapping tensor Each element in the cross-mapping tensor represents the physical product of a device vibration displacement characteristic at a specific location and a specific process control parameter. This purely analytical mathematical mapping forces the nonlinear coupling interference in the original low-dimensional space to be flattened into linear cross terms in a high-dimensional space. Subsequently, the matrix transpose operator is used... Transpose the first column vector and the cross-mapping tensor into row vectors respectively, perform matrix concatenation in the horizontal direction, and finally apply the matrix transpose operator to the outer curly braces. Thus, without violating the rules of matrix operations, a matrix with dimension is constructed. augmented health representation state vector Augmented health representation state vector This approach retains the linear terms describing the basic evolution trajectory of the equipment while objectively introducing multi-order coupled cross-terms characterizing the collaborative decline of process health. This provides a solid matrix numerical foundation for subsequent online solutions to state-space equations with multivariate physical constraints. Under the initial mapping datum, the augmented health characterization state vector retains the linear terms describing the basic evolution trajectory of the equipment while introducing multi-order coupled cross-terms characterizing the collaborative decline of process health. Through the construction of the initial mapping datum, the augmented health characterization state vector is transformed into a free state vector form in subsequent evolutions. This effectively removes the hard algebraic constraint that each recursive step must satisfy the Kronecker product polynomial expansion, providing a solid and mathematically consistent matrix numerical foundation for subsequent online solutions to state-space equations with multivariate physical constraints.

[0032] In a specific embodiment, it is important to note that due to the high complexity of equipment degradation in actual industrial settings, requiring the augmented health representation state vector to satisfy the polynomial expansion hard algebraic constraint structure in every time step of the multivariate discrete state-space equation system's recursion would lead to an unsolvable mathematical contradiction in matrix evolution, thereby causing the parameter identification algorithm to diverge. Therefore, this invention configures the augmented health representation state vector as a free state vector when establishing the state space. Specifically, the mathematical structure expression in step S104 is only used to complete the nonlinear mapping initialization from the low-dimensional physical measurement space to the high-dimensional state feature space during system cold start or at a specific reference time. The forced algebraic reconstruction at each step in the recursive process of the discrete state-space equation system is eliminated. After entering the recursive evolution in step S2, the augmented health representation state vector, as an implicit free state variable, undergoes continuous dynamic evolution under the physical constraints of the system's augmented state transition matrix and control input coupling matrix. This mechanism, while preserving the nonlinear coupling characteristics, ensures the mathematical convergence and stability of the subsequent linear least squares identification.

[0033] Step S2 includes the following sub-steps: Step S201: Define the parameter matrix used to construct the multivariable discrete state-space equation system. The parameter matrix includes the system augmented state transition matrix. Control input coupling matrix System observation mapping matrix and feedforward correlation matrix .

[0034] To ensure the absolute validity of subsequent matrix operations in the mathematical space and to eliminate the cold-start divergence problem in the initial construction of multivariable discrete state-space equations, it is essential to strictly define the physical dimensions of the parameter matrices and the initial assignment mechanism. Assume that the dimensions of the basic health state vectors arranged according to preset dimensions are defined as follows: The dimension of the process input vector is defined as The system observation vector dimension is defined as According to the Kronecker product expansion rule, the dimension of the augmented health representation state vector is defined as follows: , where the dimension value Based on the above dimensional definitions, the system augmented state transition matrix... The physical dimension of the matrix is ​​defined as , control input coupling matrix The physical dimension of the matrix is ​​defined as System observation mapping matrix The physical dimension of the matrix is ​​defined as Feedforward correlation matrix The physical dimension of the matrix is ​​defined as .

[0035] The initial assignment mechanism for the parameter matrix is ​​configured as follows: Extract the first historical running data segment of the industrial production line after it has been newly commissioned and is in an absolutely healthy state, with a continuous running time meeting a preset time window. Use a subspace identification algorithm to extract the feature values ​​of the first historical running data segment, calculate a set of constant reference constant matrices, and directly assign these reference constant matrices to the parameter matrix as the index time of the discrete time series. The initial matrix values ​​at time t.

[0036] Step S202, based on the augmented health representation state vector Process input vector System augmented state transition matrix and control input coupling matrix An augmented state evolution equation is constructed, and the predicted augmented health representation state vector is calculated using this equation. The mathematical structure expression for the predicted augmented health representation state vector is as follows: ; in, To predict the augmented health representation state vector, For the augmented state transition matrix of the system, To control the input coupling matrix, To augment the health representation state vector, This is the process input vector.

[0037] At the level of objective physics, the augmented state evolution equations characterize the trans-temporal evolution of the degradation of the underlying mechanical structure of an industrial production line. (System augmented state transition matrix) The self-evolutionary inertia of inherent physical degradation characteristics, such as bearing wear in equipment, is quantified. Control input coupling matrix. The externally injected process input vector was quantized. (e.g., different cutting loads) apply acceleration or deceleration physical intervention weights to the degradation evolution trajectory.

[0038] Step S203, based on system observation vector Augmented health representation state vector Process input vector System observation mapping matrix and feedforward correlation matrix Construct the observation-output equation, and the mathematical structure expression of the observation-output equation is as follows: ; in, For the system observation vector, For the system observation mapping matrix, This is the feedforward correlation matrix.

[0039] By combining the augmented state evolution equation and the observation output equation, a first discrete state-space equation set is generated to quantitatively describe the coupling mechanism between the nonlinear evolution of equipment health status and process parameters.

[0040] At the level of objective physics, the observation output equation establishes a deterministic spatial mapping bridge between underlying physical degradation parameters and upper-level process production indicators. (System observation mapping matrix) Responsible for transforming the augmented health representation state vector existing in a high-dimensional invisible space Dimensionality reduction projection to externally observable production outcome dimensions (such as product surface roughness or overall energy consumption deviation). Feedforward correlation matrix This is used to compensate for the direct, time-delay-free physical impact of real-time switching of process parameters during high-frequency fluctuations on the system's observation vector. Finally, by combining the augmented state evolution equation and the observation output equation, a first discrete state-space equation set is generated to quantify the coupling mechanism between the nonlinear evolution of equipment health and process parameters. The observation output equation is used to express the state vector of the augmented health, which cannot be directly observed. Mapping to the dimension of observable production results provides a mathematical foundation for observability verification and subspace identification of the initial parameter matrix. During the online operation phase, the state prediction residual... It is obtained directly from the deviation between the measured vector of the augmented state and the predicted value of the state equation, without relying on the indirect calculation of the observed output equation.

[0041] By constructing the first discrete state-space equation set, this invention abandons the traditional black-box neural network inference mode and provides a rigorous matrix analysis benchmark for subsequent mathematical derivation and reverse analysis of the real physical degradation rate.

[0042] Step S3 includes the following sub-steps: Step S301: Establish an online parameter identification mechanism for the first discrete state-space equation set. The specific logic is as follows: Obtain system observation vectors In discrete time series index Actual detection value at time The numerical values ​​of the output calculated from the observation-output equation in the first discrete state-space equation set are used as the system observation vector. The predicted output value is obtained, the difference between the predicted output value and the actual detected value is calculated, the prediction error is obtained, the partial derivative of the prediction error is calculated, and the prediction error gradient is obtained. Define the augmented state transition matrix of the system Coupling matrix with control input The matrix formed by splicing together the components is the system parameter matrix. For prediction error Regarding the system parameter matrix By performing partial derivative operations, the prediction error gradient is calculated. Prediction error gradient The mathematical expression is: ; in, The gradient matrix of the prediction error. For the prediction error vector, This is the system parameter matrix from the previous time step.

[0043] Step S302, calculate the prediction error gradient The matrix norm is used as the modulus of the prediction error gradient. Construct an adaptive forgetting factor Establish an adaptive forgetting factor With the magnitude of the prediction error gradient The negative correlation between them means that as the magnitude of the prediction error gradient increases, the adaptive forgetting factor... The corresponding value decreases.

[0044] To ensure an adaptive forgetting factor It can achieve rapid tracking under abrupt changes and maintain parameter smoothness under steady-state conditions. The negative correlation mapping relationship is specifically configured using a negative exponential decay function, and the mathematical structure expression of the negative correlation mapping relationship is as follows: ; in, An adaptive forgetting factor. For the natural constant The symbol for the exponential function with base 0. The magnitude of the prediction error gradient, This is a preset lower limit constant threshold for the forgetting factor, used to ensure that the matrix identification algorithm does not diverge and collapse during drastic changes. It is usually set to a value between 0.90 and 0.95. The preset dynamic adjustment margin constant for the forgetting factor limits the maximum fluctuation range of the forgetting factor. This is a preset gradient sensitivity coefficient constant used to control the decay rate of the exponential function. When As the exponent increases, the negative exponent term rapidly approaches zero, making The corresponding value is reduced to This allows the model to quickly forget old historical data, thus accelerating its process of learning from nearby sources.

[0045] Step S303, adjust the adaptive forgetting factor Embedded recursive least squares algorithm, utilizing an adaptive forgetting factor The recursive least squares algorithm receives the augmented health representation state vector under a continuous-time sampling sequence. Process input vector and system observation vector Real-time data stream, online solution and dynamic update of the system augmented state transition matrix. Coupling matrix with control input The values ​​of the matrix elements in the matrix will be used to update the augmented state transition matrix of the system. Coupling matrix with control input Substitute the first discrete state space equations into the second discrete state space equations to generate the identified and updated second discrete state space equations.

[0046] In a specific embodiment, an adaptive forgetting factor is included. The matrix iteration logic of the recursive least squares algorithm is as follows: Constructing the system regression input vector System regression input vector The mathematical expression is: ; in, For the system regression input vector, and These are the transposes of the augmented health characterization state vector and the process input vector, respectively.

[0047] Calculate matrix gain Matrix gain The mathematical expression is: ; in, For matrix gain, It is a column vector of (n1+m1)×1. Let be the covariance matrix of the previous time step. An adaptive forgetting factor. It is a unit constant matrix.

[0048] Update covariance matrix , The mathematical expression is: ; in, This is the updated covariance matrix at the current time.

[0049] Perform system parameter matrix Update The mathematical expression is: ; in, This is the updated system parameter matrix at the current moment. This is the state prediction residual vector generated from the internal calculations of the augmented state evolution equation. Specifically, The dimension generated by the internal calculation of the augmented state evolution equation is State prediction residual vector For dimension The row vector, The dimension is , and the system parameter matrix The dimensions are consistent.

[0050] By performing the matrix operation sequence described above, the system parameter matrix is ​​extracted. The first half of the internal part serves as the updated system augmented state transition matrix. The latter half serves as the updated control input coupling matrix. The augmented state transition matrix of the system after updating the matrix elements. Coupling matrix with control input Substituting the first discrete state space equations into the second discrete state space equations with dynamic disturbance rejection capability, we finally generate the second discrete state space equations after identification and updating.

[0051] Step S4 includes the following sub-steps: Step S401: Based on the second discrete state-space equation set, deduce the health evolution trajectory of the industrial production line. The specific logic is as follows: The Savitzky-Golay filter is used to augment the health representation state vector. The vibration displacement characteristics of the equipment are subjected to polynomial smoothing fitting, and the first-order time partial derivative of the fitted polynomial at the center point of the sliding window is calculated to obtain the true vibration velocity characteristics after filtering out high-frequency noise components. The true vibration velocity characteristics are defined as the degradation rate characterization value. .

[0052] In a specific embodiment, the health evolution trajectory of the industrial production line is deduced based on the second discrete state space equation set. The specific logic is as follows: Define the state mapping matrix Using the state mapping matrix From the augmented health representation state vector The vibration displacement feature elements of the equipment are extracted to form a displacement sequence within a continuous time window.

[0053] A Savitzky-Golay filter was used to perform polynomial smoothing fitting on the displacement sequence, and the first-order time partial derivative of the fitted polynomial at the center point of the sliding window was calculated to obtain the true vibration velocity characteristics after filtering out high-frequency noise components. Since the sliding window requires both front and back... Data from each sampling point, degradation rate characterization value The actual available time is Time, that is, the system with inherent delay · This is done in exchange for improved noise suppression accuracy. In the real-time judgment of step S402, [the following is considered]: Alternative This serves as a criterion for triggering the process compensation optimization mechanism.

[0054] The time derivative of displacement is represented as velocity, and the true vibration velocity characteristic is defined as the degradation rate characterization value. Degradation rate characterization value The mathematical expression for the difference calculation is: ; in, This is a value characterizing the degradation rate. Let be the system discrete sampling time period constant. For the integer value of the half-width of the sliding window of the Savitzky-Golay filter, The difference weighting coefficients are the polynomial fitting coefficients corresponding to the first derivative solution. The state mapping matrix, To extract the augmented health representation state vectors corresponding to each time step of the displacement sequence.

[0055] By executing the differential calculation formula, discrete displacement characteristics are transformed into transient degradation velocities in the continuous physical world.

[0056] Step S402: Set a dynamic steady-state physical boundary associated with the current operating condition and detect the degradation rate characterization value. When the degradation rate characterization value is detected When the value exceeds the dynamic steady-state physical boundary, a process compensation optimization mechanism is triggered, specifically as follows: Define the dynamic steady-state physical boundary as a threshold. threshold The mathematical expression is: ; in, For dynamic steady-state physical boundary threshold, This refers to the pre-calibrated foundation vibration velocity tolerance constant for industrial equipment under no-load conditions. The pre-calibrated load stiffness penalty coefficient constant, It is the mathematical norm of the process input vector at the current moment.

[0057] When the degradation rate characterization value Greater than the dynamic steady-state physical boundary threshold When constructing a quadratic programming function Minimizing the expected degradation rate deviation and minimizing the process adjustment range are used as quadratic programming functions. The joint objective is to inject the physical limit hard constraint inequality of process control parameters into the quadratic programming function.

[0058] Quadratic programming function The mathematical structure expression is: ; in, To find the scalar for the objective optimization, To track the penalty weight coefficient for the preset degradation rate, To predict the degradation rate at the next time step using the second discrete state-space equations. This is a preset benchmark constant for the desired safe degradation rate, typically set to a minimum value close to zero, representing the complete cessation of degradation in the device. The preset process adjustment range suppresses the weighting coefficient. The component representing the process control compensation to be solved is called the component representing the process control compensation.

[0059] The physical limit hard constraint inequality for injecting process control parameters into the quadratic programming function is expressed mathematically as follows: ； ; in, This is the actuator mechanical lower limit vector for process control parameters. The actuator mechanical upper limit vector for process control parameters. This is the process input vector at the current moment. The component to be solved is the process control compensation component. This is the vector representing the maximum allowable step adjustment amplitude within a single control cycle.

[0060] Step S403: Solve the quadratic programming function using the interior-point method. Within the feasible region limited by the physical limit hard constraint inequality, use the control input coupling matrix after updating the matrix element values. Iteratively optimize the optimal process control compensation component under the current state. .

[0061] Compensation component for optimal process control The process input vector is superimposed on the process input vector of the next control cycle to achieve adaptive linkage of the process to mitigate the rate of health degradation.

[0062] To establish the coupling matrix between the quadratic programming function and the control input The closed-loop coupling employs a first-order forward difference to linearly approximate the degradation rate, ensuring the convexity and solvability of the quadratic programming function, and predicts the degradation rate at the next time step. The analytical recursive formula is: ; in, To predict the degradation rate in the next moment, The state mapping matrix, This is the augmented state transition matrix of the system after updating the values ​​of the matrix elements. Let be the augmented health representation state vector at the current moment. The control input coupling matrix after updating the matrix element values. This is the process input vector at the current moment. The component to be solved is the process control compensation component. is the system discrete sampling time period constant.

[0063] Substituting the analytical recurrence formula into the quadratic programming function In this study, the interior-point method is used to calculate the optimal process control compensation component that minimizes the scalar value of the objective optimization solution, while satisfying the physical limit hard constraint inequality. .

[0064] Compensation component for optimal process control The output execution command is superimposed on the process input vector of the next control cycle. Under matrix evolution constraints, the process adaptive linkage is completed to smooth out the rate of health degradation.

[0065] Example 2, refer to Figure 2 This paper presents an industrial production line health status analysis system, which includes a characterization module, a modeling module, an identification module, and an optimization module.

[0066] The characterization module is used to extract the vibration and displacement characteristics of the equipment from the physical acquisition signals of the equipment, construct the basic health state vector, construct the process control parameters and production result metrics as the process input vector and the system observation vector, respectively, and generate the augmented health characterization state vector based on the basic health state vector and the process input vector.

[0067] The modeling module is used to define the augmented state transition matrix and control input coupling matrix of the system. It combines the augmented health representation state vector, process input vector and system observation vector to construct the augmented state evolution equation and observation output equation, and jointly generate the first discrete state space equation set.

[0068] The identification module is used to calculate the prediction error gradient of the system observation vector, construct an adaptive forgetting factor that is negatively correlated with the magnitude of the prediction error gradient, embed the adaptive forgetting factor into the recursive least squares algorithm, update the system augmented state transition matrix and control input coupling matrix, and generate the second discrete state space equation set after identification and update.

[0069] The optimization module is used to extract the actual vibration velocity characteristics as the degradation rate characterization value. When the degradation rate characterization value crosses the dynamic steady-state physical boundary, a quadratic programming function is constructed, the quadratic programming function is solved to find the optimal process control compensation component, and it is superimposed on the process input vector.

[0070] This invention generates an augmented health representation state vector containing multi-order coupling cross terms by calculating the Kronecker product of the basic health state vector and the process input vector. It then constructs a first discrete state space equation set by combining the system's augmented state transition matrix and the control input coupling matrix, accurately quantifying the nonlinear evolution of equipment health state and the coupling mechanism of process parameters. An adaptive forgetting factor, negatively correlated with the magnitude of the predicted error gradient, is constructed and embedded into a recursive least squares algorithm to update the system's augmented state transition matrix and the control input coupling matrix online, generating a second discrete state space equation set. This solves the problem of easy failure of fixed parameter identification under abrupt operating conditions, endowing the online parameter identification mechanism with disturbance resistance and rapid tracking capabilities. It extracts real vibration velocity features as degradation rate representation values. When the degradation rate representation value crosses the dynamic steady-state physical boundary, it solves a quadratic programming function with injected physical limit hard constraint inequalities, iteratively optimizing the optimal process control compensation component in the current state and superimposing it onto the process input vector. Under the dual guarantee of mathematical matrix analysis and boundary constraints, it outputs physically executable execution instructions, realizing closed-loop adaptive process linkage to mitigate health degradation rates.

[0071] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media containing computer-usable program code. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The function specified in one or more boxes.

[0072] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the protection scope of the present invention. All data acquisition actions in this application are carried out in compliance with the relevant data protection laws and policies of the country where the application is located and with the authorization granted by the owner of the corresponding device.

Claims

1. A method for analyzing the health status of an industrial production line, characterized in that, The steps include the following: Step S1: Extract the equipment vibration displacement characteristics from the physical acquisition signals of the equipment, construct the basic health state vector, construct the process control parameters and production result measurement values ​​as the process input vector and the system observation vector respectively, and generate the augmented health characterization state vector based on the basic health state vector and the process input vector. Step S2: Define the system augmented state transition matrix and control input coupling matrix, and construct the augmented state evolution equation and observation output equation by combining the augmented health characterization state vector, process input vector and system observation vector, and jointly generate the first discrete state space equation set. Step S3: Calculate the prediction error gradient of the system observation vector, construct an adaptive forgetting factor that is negatively correlated with the magnitude of the prediction error gradient, embed the adaptive forgetting factor into the recursive least squares algorithm, update the system augmented state transition matrix and control input coupling matrix, and generate the identified updated second discrete state space equation set. Step S4: Extract the actual vibration velocity features as the degradation rate characterization value. When the degradation rate characterization value is greater than the dynamic steady-state physical boundary, construct a quadratic programming function, solve the quadratic programming function to find the optimal process control compensation component, and superimpose it into the process input vector.

2. The industrial production line health status analysis method as described in claim 1, characterized in that, Step S1 includes the following sub-steps: Step S101: Obtain the discrete time series index of the industrial production line. The equipment's physical acquisition signals, process control parameters, and production result metrics at any given time; Step S102: Extract the equipment vibration displacement features from the physical acquisition signals of the equipment, arrange the equipment vibration displacement features into a first column vector according to a preset first dimension, and construct the first column vector into a basic health state vector; Step S103: After numerical processing of the process control parameters, arrange them into a second column vector according to the preset second dimension, and construct the second column vector into a process input vector; The production result metrics are arranged into a third column vector according to a preset third dimension, and the third column vector is used to construct the system observation vector.

3. The method for analyzing the health status of an industrial production line as described in claim 2, characterized in that, Step S1 further includes the following sub-steps: Step S104: Calculate the Kronecker product of the basic health state vector and the process input vector to obtain the cross-mapping tensor. Perform matrix concatenation operation on the basic health state vector and the cross-mapping tensor to calculate the augmented health representation state vector.

4. The industrial production line health status analysis method as described in claim 3, characterized in that, Step S2 includes the following sub-steps: Step S201: Define the parameter matrix for constructing the multivariable discrete state-space equation system. The parameter matrix includes the system augmented state transition matrix, the control input coupling matrix, the system observation mapping matrix, and the feedforward correlation matrix. Step S202: Based on the augmented health characterization state vector, process input vector, system augmented state transition matrix, and control input coupling matrix, an augmented state evolution equation is constructed, and the predicted augmented health characterization state vector is calculated through the augmented state evolution equation.

5. The industrial production line health status analysis method as described in claim 4, characterized in that, Step S2 further includes the following sub-steps: Step S203: Based on the system observation vector, augmented health characterization state vector, process input vector, system observation mapping matrix, and feedforward correlation matrix, construct the observation output equation; By combining the augmented state evolution equation and the observation output equation, the first discrete state space equation set is generated.

6. The industrial production line health status analysis method as described in claim 5, characterized in that, Step S3 includes the following sub-steps: Step S301: Establish an online parameter identification mechanism for the first discrete state-space equation system. The specific logic is as follows: Obtain the index of the system observation vector in the discrete time series. The actual detected value at time t is used as the predicted output value of the system observation vector, and the value calculated by the observation output equation in the first discrete state space equation set is used as the predicted output value. The difference between the predicted output value and the actual detected value is calculated to obtain the prediction error. The partial derivative of the prediction error is calculated to obtain the prediction error gradient. Step S302: Calculate the magnitude of the prediction error gradient, construct the adaptive forgetting factor, and establish a negative correlation mapping relationship between the adaptive forgetting factor and the magnitude of the prediction error gradient.

7. The industrial production line health status analysis method as described in claim 6, characterized in that, Step S3 further includes the following sub-steps: Step S303: Embed the adaptive forgetting factor into the recursive least squares algorithm. Using the recursive least squares algorithm with the adaptive forgetting factor, receive the real-time data stream of the augmented health representation state vector, process input vector, and system observation vector under the continuous time sampling sequence. Solve online and dynamically update the matrix element values ​​in the system augmented state transition matrix and control input coupling matrix. Substitute the system augmented state transition matrix and control input coupling matrix with the updated matrix element values ​​into the first discrete state space equation set to generate the identified and updated second discrete state space equation set.

8. The industrial production line health status analysis method as described in claim 7, characterized in that, Step S4 includes the following sub-steps: Step S401: Based on the second discrete state-space equation set, deduce the health evolution trajectory of the industrial production line. The specific logic is as follows: The Savitzky-Golay filter is used to perform polynomial smoothing fitting on the equipment vibration displacement characteristics in the augmented health characterization state vector. The first-order time partial derivative of the fitted polynomial at the center point of the sliding window is calculated to obtain the true vibration velocity characteristics after filtering out high-frequency noise components. The true vibration velocity characteristics are defined as the degradation rate characterization value.

9. The method for analyzing the health status of an industrial production line as described in claim 8, characterized in that, Step S4 further includes the following sub-steps: Step S402: Set a dynamic steady-state physical boundary associated with the current operating condition. When the degradation rate characterization value is detected to be greater than the dynamic steady-state physical boundary, trigger the process compensation optimization mechanism, specifically: Construct a quadratic programming function, taking minimizing the expected degradation rate deviation and minimizing the process adjustment range as the joint objective of the quadratic programming function, and inject the physical limit hard constraint inequality of the process control parameters into the quadratic programming function; Step S403: Solve the quadratic programming function using the interior point method. Within the feasible region limited by the physical limit hard constraint inequality, use the updated matrix element values ​​of the control input coupling matrix to iteratively find the optimal process control compensation component in the current state. Then, superimpose the optimal process control compensation component into the process input vector of the next control cycle.

10. An industrial production line health status analysis system, applied in an industrial production line health status analysis method as described in any one of claims 1-9, characterized in that, It includes a representation module, a modeling module, an identification module, and an optimization module; The characterization module is used to extract the vibration displacement characteristics of the equipment from the physical acquisition signals of the equipment, construct a basic health state vector, construct process control parameters and production result metrics as process input vector and system observation vector respectively, and generate an augmented health characterization state vector based on the basic health state vector and process input vector. The modeling module is used to define the system augmented state transition matrix and control input coupling matrix, and to construct the augmented state evolution equation and observation output equation by combining the augmented health characterization state vector, process input vector and system observation vector, and jointly generate the first discrete state space equation set. The identification module is used to calculate the prediction error gradient of the system observation vector, construct an adaptive forgetting factor that is negatively correlated with the magnitude of the prediction error gradient, embed the adaptive forgetting factor into the recursive least squares algorithm, update the system augmented state transition matrix and control input coupling matrix, and generate the second discrete state space equation set after identification and update. The optimization module is used to extract the actual vibration velocity characteristics as the degradation rate characterization value. When the degradation rate characterization value crosses the dynamic steady-state physical boundary, a quadratic programming function is constructed, the quadratic programming function is solved to find the optimal process control compensation component, and it is superimposed on the process input vector.

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