A liner paper drying temperature abnormal state early warning method

Abstract

The present application belongs to the field of face paper drying, and particularly relates to a face paper drying temperature abnormal state early warning method, which comprises collecting a drying equipment multi-measurement point time series temperature matrix, obtaining a multi-dimensional state trajectory through phase space reconstruction, and extracting a characteristic tensor through fractional wavelet transform; constructing a kernel function space model with the characteristic tensor as input, training an initial model based on normal working condition samples using a target function containing an experience risk term and a weighted Schatten p norm regularization term; converting real-time temperature data into real-time characteristic tensors and inputting the real-time characteristic tensors into the model, calculating a projection residual and a residual dynamics statistical index, constructing a composite risk assessment function, and outputting an early warning when the threshold is exceeded; and updating the order p and the model parameters when the threshold is not exceeded to adjust the state discrimination boundary. The present application improves the accuracy and robustness of abnormal early warning.

Description

Technical Field

[0001] This invention belongs to the field of face paper drying, and particularly relates to a method for early warning of abnormal temperature conditions in face paper drying. Background Technology

[0002] Facing paper is a commonly used industrial substrate in building materials, packaging products, and other fields. Its drying quality directly affects the paper's moisture content uniformity, mechanical strength, flatness, surface properties, and the stability of subsequent lamination processes. In the continuous production of facing paper, drying equipment typically consists of multiple drying cylinders, a hot air circulation unit, and a dehumidification system. The equipment is large in scale, with complex heat transfer paths, and significant temperature coupling relationships exist between different areas. If localized temperature anomalies, uneven heat distribution, or continuous accumulation of temperature fluctuations occur, it can easily lead to paper warping, decreased strength, increased energy consumption, and even equipment operational risks. Therefore, in industrial settings, multiple temperature monitoring points are typically deployed in different areas of the drying equipment to continuously collect multi-dimensional time-series temperature data to reflect changes in the equipment's thermal state and operating conditions.

[0003] Chinese patent application CN104264524A discloses a wireless detection system for the surface temperature of a paper machine drying cylinder. The system includes several wireless temperature sensors embedded in the working wall of the drying cylinder, an RF antenna, a wireless data receiver, and an industrial control computer. Each wireless temperature sensor is connected by an RF signal line, the output of which is connected to the RF antenna. The RF antenna is mounted on the side wall of the drying cylinder and transmits temperature data to the wireless data receiver. The wireless data receiver is connected to the industrial control computer via a communication cable. The temperature data from the drying cylinder surface is transmitted to the wireless receiver via the wireless temperature sensors, and the wireless receiver transmits the received temperature data to the industrial control computer. The industrial control computer then reads the detected data, enabling real-time online measurement of the drying cylinder surface temperature.

[0004] However, the drying process of face paper is affected by factors such as the moisture content of the base paper, operating speed, steam pressure, ambient temperature and humidity, and equipment aging. Temperature data often exhibits nonlinear, time-varying, and strongly correlated characteristics. Traditional alarm methods based on fixed thresholds mainly focus on whether the temperature at a single point exceeds the limit, making it difficult to identify early anomalies in the coupling relationship of multiple measurement points. Although conventional data-driven methods can build monitoring models using historical samples, they are easily affected by noise disturbances, dimensional redundancy, and operating condition drift during the processing of high-dimensional time-series data, resulting in rigid warning boundaries and insufficient generalization ability, leading to false alarms or missed alarms. Especially in long-term continuous operation scenarios, the normal operating conditions of the equipment will change slowly with the production cycle, seasonal environment, and component aging. If the model cannot extract multi-scale time-frequency features, constrain the core state structure, and adaptively adjust the state boundaries, it will be difficult to maintain a stable anomaly identification capability, and it will also be detrimental to the timely intervention of on-site process personnel. Therefore, there is an urgent need for an early warning method for abnormal temperature states in face paper drying that can integrate multi-measurement point time-series evolution features, time-frequency feature analysis, and online boundary update mechanisms. Summary of the Invention

[0005] To address the problems of existing technologies where pre-warning of face paper drying temperature relies on fixed thresholds, struggles to exploit multi-point temporal coupling characteristics, and lacks adaptability to operational condition drift, leading to false alarms or missed alarms, this invention proposes, in a first aspect, a pre-warning method for abnormal state of face paper drying temperature, comprising the following steps: S1. Obtain the time-series temperature matrix of multiple temperature measurement points of the face paper drying equipment; reconstruct the phase space of the time-series temperature matrix to generate a multidimensional state trajectory; decompose the multidimensional state trajectory using fractional wavelet transform to obtain the feature tensor. S2. Construct a kernel function space model with feature tensors as input. The objective function of the kernel function space model includes an empirical risk term and a weighted Schatten p-norm regularization term. The weighted Schatten p-norm regularization term imposes a low-rank constraint penalty on the singular values ​​of the model mapping operator. The weights of the singular values ​​are determined according to the energy concentration of the corresponding spatial pattern, and the order p is a parameter. Optimize the objective function using the feature tensors of historical normal operating conditions to obtain the initial state space model. S3 processes real-time temperature data into real-time feature tensors and projects them onto the current model, calculating the projection residuals. Continuous projection residuals are then used to construct a residual time series, and the dynamic statistical indices of the residual time series are calculated within a sliding time window. A composite risk assessment function is constructed based on the norm of the projection residuals and the dynamic statistical indices. When the value of the composite risk assessment function exceeds a preset warning threshold, a warning signal is output. When the value of the composite risk assessment function does not exceed the warning threshold, the order p is adjusted online according to the dynamic statistical indices, and the current model is iteratively updated to adjust the state space boundary.

[0006] By reconstructing the phase space and performing fractional wavelet transform on the time-series temperature matrix of multiple temperature measurement points, the characteristic information of temperature data in three dimensions—temporal evolution, spatial coupling, and multi-scale time-frequency—can be fully extracted, solving the problem that traditional methods struggle to capture the coupling relationship between multiple measurement points. A kernel function space model with weighted Schatten p-norm regularization is constructed, and singular value weights are assigned based on the energy concentration of the spatial pattern, effectively suppressing noise interference and characterizing the low-rank state structure under normal operating conditions. During the monitoring phase, a composite risk assessment function is constructed by fusing the projection residual norm and kinetic statistical indicators, significantly improving the stability and sensitivity of anomaly identification compared to a single residual evaluation method. Simultaneously, when no warning is triggered, the order p is adjusted online and the model is updated using kinetic statistical indicators, enabling the state space boundary to adaptively track the slow drift of the operating conditions, overcoming the shortcomings of fixed thresholds and static models that are prone to false alarms or missed alarms.

[0007] Preferably, the phase space reconstruction of the time-series temperature matrix to generate a multidimensional state trajectory includes: calculating the discrete autocorrelation sequence of the temperature time series of each temperature measurement point using the autocorrelation function, and determining candidate time delays based on each discrete autocorrelation sequence; calculating the ratio of false nearest neighbors under different embedding dimensions using the false nearest neighbor method, and determining candidate embedding dimensions based on each false nearest neighbor ratio; determining a globally unified time delay based on each candidate time delay, and determining a globally unified embedding dimension based on each candidate embedding dimension; performing phase space reconstruction on the temperature time series of each temperature measurement point according to the globally unified time delay and the globally unified embedding dimension to generate a dimension-aligned high-dimensional state matrix; and concatenating the dimension-aligned high-dimensional state matrices corresponding to each temperature measurement point to generate a multidimensional state trajectory.

[0008] Candidate time delays and candidate embedding dimensions for each temperature measurement point are determined using the autocorrelation function and the spurious nearest neighbor method, respectively. Then, globally unified parameters are determined, ensuring that the dimensions of each measurement point are aligned after reconstruction and can be stitched together into a unified multidimensional state trajectory, providing a data structure foundation for subsequent feature extraction. This method balances the individual dynamic characteristics of each measurement point with global consistency, avoiding state space distortion or information loss caused by improper parameter selection.

[0009] Preferably, the multidimensional state trajectory is decomposed using fractional wavelet transform to obtain a feature tensor, including: setting the rotation angle of the fractional Fourier transform; constructing a fractional wavelet transform network containing low-pass and high-pass branches using a multi-scale filter bank; inputting the multidimensional state trajectory into the fractional wavelet transform network and performing a 5-level decomposition operation; extracting the approximate components and detail components after decomposition level by level, combining them to form a multi-scale frequency coefficient matrix, and using the matrix as a feature tensor representing temperature.

[0010] By setting the rotation angle of the fractional Fourier transform, a multi-scale filter bank network containing low-pass and high-pass branches is constructed. This network performs a five-level decomposition of the multidimensional state trajectory and extracts approximate and detail components at each level, enabling refined analysis of the temperature signal in the time-frequency domain. This allows for the capture of both slow drift trends and sudden fluctuations. The multi-scale frequency coefficient matrix, used as a feature tensor, provides highly discriminative and robust input features for subsequent modeling.

[0011] Preferably, the objective function is optimized using the feature tensors of historical normal operating conditions to obtain the initial state space model. This includes: selecting temperature data with a total duration of 24 hours under historical normal operating conditions and calculating the corresponding normal feature tensor set; inputting the normal feature tensor set into the kernel function space model and optimizing the objective function using the alternating direction multiplier method; setting an upper limit for the number of iterations and an error convergence threshold between two iterations; stopping the iteration operation when the iteration error is less than the convergence threshold or reaches the upper limit for the number of iterations, outputting the current optimal model parameters, and obtaining the initial state space model.

[0012] By constructing a training set using temperature data from historical normal operating conditions with a total duration of 24 hours, the sufficiency and representativeness of the training samples were ensured. The objective function containing the regularization term was optimized using the alternating direction multiplier method, and an iteration upper limit and convergence threshold were set. This ensured the accuracy of the solution while controlling the computational cost, and enabled the stable output of the optimal model parameters, providing a reliable baseline state space for the real-time monitoring stage.

[0013] Preferably, the calculation of dynamic statistical indicators of the residual time series within a sliding time window includes: setting the window length and sliding step size of the sliding time window; truncating the residual time series through the sliding time window to obtain multiple sliding data segments; for each data segment, calculating the mean, variance, and information entropy of the projected residuals of the data segment, and normalizing them respectively; concatenating the normalized mean, variance, and information entropy to construct a feature vector representing the current dynamic characteristics of the system, which serves as the dynamic statistical indicator.

[0014] By extracting residual sequence segments through a sliding time window, the mean, variance, and information entropy are calculated and normalized, then concatenated into a feature vector. This approach characterizes the system's real-time dynamics from three perspectives: central tendency, dispersion, and complexity. Compared to using only residual amplitude, this indicator reflects the microscopic changes in the system's state evolution, providing richer decision-making support for composite risk assessment and model boundary adjustments.

[0015] Preferably, when the value of the composite risk assessment function does not exceed the warning threshold, the order p is adjusted online according to the dynamic statistical index and the current model is iteratively updated to achieve the adjustment of the state space boundary. This includes: calculating the Euclidean distance between the dynamic statistical index corresponding to the current sliding time window and the historical normal statistical index; inputting the Euclidean distance into the negative exponential function and performing a positive nonlinear mapping based on 1 minus the output value of the negative exponential function to obtain a positive mapping value between 0 and 1; multiplying the positive mapping value by a preset amplitude coefficient and adding it to the initial order benchmark value to obtain the latest order p, and restricting the order p to a range greater than 0 and not exceeding 1; substituting the latest order p into the weighted Schatten p-norm regularization term to re-solve and update the current model.

[0016] By calculating the Euclidean distance between the current dynamic statistical indicators and historical normal indicators, and then dynamically adjusting the order p after a negative exponential function positive nonlinear mapping, p adaptively increases as the degree of deviation from the operating condition increases, thereby achieving a balance between the strength of regularization constraints and the flexibility of the model. This mechanism continuously updates the model within the normal drift range that does not trigger an early warning, allowing the state space boundary to evolve slowly with factors such as equipment aging and environmental changes, maintaining the long-term monitoring reliability.

[0017] Preferably, a composite risk assessment function is constructed based on the norm of the projection residual and dynamic statistical indicators. When the value of the composite risk assessment function exceeds a preset warning threshold, a warning signal is output. This includes: calculating the L2 norm of the current real-time projection residual matrix and normalizing the L2 norm by combining it with the extreme values ​​of the L2 norm of historical normal residuals, which serves as the first risk indicator; extracting the information entropy from the dynamic statistical indicators, normalizing the information entropy, and multiplying it by a preset coefficient, which serves as the second risk indicator; adding the first and second risk indicators to obtain the output value of the composite risk assessment function; determining whether the output value is greater than the warning threshold. If it is, the drying temperature of the face paper is determined to be abnormal, triggering the alarm controller and outputting a warning signal.

[0018] The first risk indicator, normalized to the L2 norm of the projected residuals, reflects the overall magnitude of the current residuals; the second risk indicator, normalized to the information entropy, reflects the degree of disorder in the system dynamics; the two are weighted and summed to obtain the comprehensive risk value. This composite assessment mechanism takes into account both residual strength and state complexity. Compared with single-indicator judgment, it can effectively distinguish between normal fluctuations and real anomalies, reduce the false alarm rate, and output early warning signals in a timely manner when real anomalies occur.

[0019] Preferably, before obtaining the time-series temperature matrix of multiple temperature measurement points of the face paper drying equipment, the process includes: collecting temperature signals by means of distributed temperature sensors deployed on the surface of the drying cylinder of the face paper drying equipment; transmitting the temperature signals to the host computer through a programmable logic controller to obtain the original time-series temperature matrix; and performing smoothing filtering and noise reduction on the original time-series temperature matrix.

[0020] Smoothing and filtering of the original time-series temperature matrix eliminates the impact of sensor noise and random interference on subsequent feature extraction, improves data quality, and ensures the accuracy and stability of the early warning method from the source.

[0021] Preferably, the method for calculating information entropy is as follows: dividing the residual interval into a preset number of statistical quantiles; calculating the probability of each statistical quantile; multiplying the probability of each statistical quantile by its corresponding base-2 logarithmic value to obtain the product of each statistical quantile; summing the products of all statistical quantiles and taking the negative value to obtain the information entropy.

[0022] By dividing the residual interval into predetermined statistical quantiles and calculating the probability of each quantile before incorporating it into the entropy formula, the uniformity and uncertainty of the residual sequence distribution can be quantified. When the system tends towards anomalies, the residual distribution often becomes more discrete and random, and the information entropy increases accordingly. This indicator is sensitive to state changes, is easy to calculate, and is suitable for real-time online calculations in industrial settings.

[0023] Preferably, the construction of a kernel function space model with feature tensors as input includes: expanding the feature tensors sequentially according to the time dimension, the temperature measurement point spatial dimension, and the wavelet scale dimension to form a one-dimensional sample feature vector; normalizing each one-dimensional sample feature vector to obtain a standardized sample feature matrix; using the Gaussian radial basis kernel function to calculate the nonlinear similarity between any two sample feature vectors to generate a kernel matrix; and constructing a kernel function space model in the form of kernel principal component analysis based on the kernel matrix.

[0024] The feature tensor is expanded and normalized along the three dimensions of time, space, and scale. A Gaussian radial basis function kernel is used to calculate the nonlinear similarity between samples and generate a kernel matrix, thereby constructing a kernel function space model in the form of kernel principal component analysis. This process effectively maps high-dimensional feature tensors to the kernel space, fully leveraging the nonlinear processing capabilities of kernel methods, enabling the model to characterize the nonlinear and time-varying correlation features in temperature data.

[0025] The present invention has the following technical effects: This invention characterizes the state evolution features of temperature data from multiple measurement points by reconstructing the phase space of the time-series temperature matrix and performing fractional wavelet transform, and extracts feature tensors with high discriminative power. By establishing a kernel function space model and introducing a weighted Schatten p-norm regularization term into the objective function, singular value weights are assigned based on the energy concentration of the spatial pattern to constrain the model mapping operator, thereby suppressing redundant noise and characterizing the low-rank state structure under normal operating conditions. In the real-time monitoring phase, a composite risk assessment function is constructed by combining the projection residual norm with residual dynamic statistical indices, improving the stability and sensitivity of anomaly warnings. When no warning is triggered, the order p is adjusted online and the model is updated based on dynamic statistical indices, enabling the state space boundary to adapt to the slow drift under normal operating conditions. Attached Figure Description

[0026] Figure 1 This is a flowchart of a method for early warning of abnormal drying temperature of face paper according to the present invention.

[0027] Figure 2 This is a bar chart comparing the fault detection performance indicators of the four comparative models of this invention. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] In the first embodiment, the present invention proposes a method for early warning of abnormal drying temperature of face paper, such as... Figure 1 As shown, it includes the following steps: S1, based on phase space reconstruction and fractional wavelet transform, extracts the feature tensor of time-series temperature data.

[0030] Obtain the time-series temperature matrix of multiple temperature measurement points of the face paper drying equipment; reconstruct the phase space of the time-series temperature matrix to generate a multidimensional state trajectory; decompose the multidimensional state trajectory using fractional wavelet transform to obtain the feature tensor.

[0031] Temperature signals are collected by distributed PT100 temperature sensors deployed on the surface of the drying cylinder of the paper drying equipment. These signals are transmitted to a host computer via a programmable logic controller (PLC) to obtain the original time-series temperature matrix. Smoothing and filtering are performed to reduce noise. Based on Takens' delay embedding theorem, the smoothed temperature matrix is ​​reconstructed in phase space. The candidate time delay for each temperature measurement point is calculated using a mutual information algorithm or autocorrelation function. The candidate embedding dimension for each temperature measurement point is calculated using a spurious nearest neighbor algorithm. Based on the candidate results, a globally unified time delay and a globally unified embedding dimension are determined, mapping the time-series signals of each temperature measurement point into a dimension-aligned multidimensional state trajectory. An algorithm combining fractional Fourier transform with wavelet filter banks or continuous wavelet transform is used. A fractional-order transform matrix is ​​introduced into the time-frequency transformation process to perform multi-scale time-frequency decomposition of the multidimensional state trajectory, obtaining the scale feature matrix of the multidimensional state trajectory in the corresponding fractional-order domain and at different wavelet scales. The feature matrices of multiple temperature measurement points at the globally unified embedding dimension and different wavelet scales are tensor-quantized and concatenated to generate a third-order feature tensor.

[0032] In an optional embodiment, phase space reconstruction of the time-series temperature matrix to generate a multidimensional state trajectory includes: calculating the discrete autocorrelation sequence of the temperature time series of each temperature measurement point using an autocorrelation function, and determining candidate time delays based on each discrete autocorrelation sequence; calculating the ratio of false nearest neighbors under different embedding dimensions using the false nearest neighbor method, and determining candidate embedding dimensions based on each false nearest neighbor ratio; determining a globally unified time delay based on each candidate time delay, and determining a globally unified embedding dimension based on each candidate embedding dimension; performing phase space reconstruction on the temperature time series of each temperature measurement point according to the globally unified time delay and the globally unified embedding dimension to generate a dimension-aligned high-dimensional state matrix; and concatenating the dimension-aligned high-dimensional state matrices corresponding to each temperature measurement point to generate a multidimensional state trajectory.

[0033] In practical deployment, temperature time series data are collected from each temperature measurement point. Assuming a data sampling frequency of 1Hz, a single capture window contains N=10000 discrete data points. The autocorrelation sequence for each temperature measurement point is calculated using the discrete autocorrelation function. The lag steps corresponding to the initial decrease of each correlation sequence to a set threshold, such as 0.368 or 0.2 of the maximum value, are used as candidate time delays. Statistical processing is performed on the candidate time delays obtained from multiple temperature measurement points, for example, taking the median to obtain a globally unified time delay τ, for example, τ=5, corresponding to a time of 5 seconds. After determining the time delay, the spurious nearest neighbor method is used. By gradually increasing the test dimension m, for example, starting from m=2 and traversing to the upper limit m=15, the spatial Euclidean distance expansion rate of adjacent points when projected from low dimension to high dimension is calculated. If this expansion rate exceeds a preset judgment threshold, such as 15.0, then this expansion rate is counted as a spurious nearest neighbor. The proportion of false nearest neighbors to the total phase space points in each dimension is statistically recorded. The minimum dimension corresponding to the first time the false nearest neighbor ratio falls below a preset proportion threshold is determined as the candidate embedding dimension of the temperature measurement point. The preset proportion threshold is preferably 1% to 5%, such as 2%. The global unified embedding dimension is determined based on the candidate embedding dimensions of each temperature measurement point. For example, m=6 is obtained by taking the median or mode.

[0034] For a one-dimensional single-point temperature sequence with an original input length of 10000 Using the globally unified parameters τ=5 and m=6 determined above, phase space is reconstructed to generate multidimensional phase point vectors. The vector contains sequential elements. , , , , , A single sequence generates a high-dimensional state matrix with a dimension of 9975×6. If the current paper drying equipment has a total of 20 temperature measuring points, then by horizontally splicing these 20 dimensionally aligned high-dimensional state matrices, a multi-dimensional state trajectory matrix with a dimension of 9975×120 is generated as the multi-dimensional state trajectory.

[0035] In an optional embodiment, the multidimensional state trajectory is decomposed using fractional wavelet transform to obtain a feature tensor, including: setting the rotation angle of the fractional Fourier transform; constructing a fractional wavelet transform network containing low-pass and high-pass branches using a multi-scale filter bank; inputting the multidimensional state trajectory into the fractional wavelet transform network and performing a 5-level decomposition operation; extracting the approximate components and detail components after decomposition level by level, combining them to form a multi-scale frequency coefficient matrix, and using the matrix as a feature tensor representing temperature.

[0036] The rotation angle of the fractional Fourier transform is set to α = 3π / 4, corresponding to a fractional order of a = 1.5. The input to this fractional wavelet transform network is a multidimensional state trajectory, containing 5 levels of decomposition nodes. Each level of decomposition node is configured with a dual-channel multi-scale filter bank consisting of a low-pass filter and a high-pass filter. The decomposition nodes at each level are connected by downsampling. The Daubechies wavelet basis function is selected, and the phase of the wavelet basis function is modulated by the fractional Fourier operator to construct a dual-channel fractional multi-scale filter bank matching the α = 3π / 4 transform domain, including low-pass filter branches and high-pass filter branches. The multidimensional state trajectory matrix with a dimension of 9975 × 120 is input column-wise into the fractional wavelet transform network to perform 5-level decomposition operations. In each level of decomposition, the network performs high-frequency and low-frequency convolution processing and binary downsampling on the signal. After completing the 5-level decomposition, the 5th-level approximate component cA5 and detail components cD1 to cD5 are extracted. To reduce the sequence length difference caused by downsampling, interpolation techniques were used to reconstruct the cA5 and cD1 to cD5 components to the original time length of 9975. The reconstructed six sets of two-dimensional feature matrices were stacked and aligned along the tensor depth direction to form a multi-scale frequency coefficient matrix with dimensions of 9975×120×6, which was used as the feature tensor.

[0037] S2, construct a kernel function space model with weighted Schatten p-norm regularization and perform initialization training.

[0038] A kernel function space model is constructed with feature tensors as input. The objective function of the kernel function space model includes an empirical risk term and a weighted Schatten p-norm regularization term. The weighted Schatten p-norm regularization term imposes a low-rank constraint penalty on the singular values ​​of the model mapping operator. The weights of the singular values ​​are determined according to the energy concentration of the corresponding spatial pattern, and the order p is a parameter. The objective function is optimized using the feature tensors of historical normal operating conditions to obtain the initial state space model.

[0039] The feature tensors obtained under historical normal operating conditions are used as training samples. For each training sample, it is expanded sequentially according to the time dimension, the temperature measurement point spatial dimension, and the wavelet scale dimension to form a one-dimensional sample feature vector. The feature vectors of each sample are then subjected to mean normalization or min-max normalization to obtain a standardized sample feature matrix. The nonlinear similarity between any two sample feature vectors is calculated using the Gaussian radial basis kernel function to generate a kernel matrix. The bandwidth parameter of the kernel function can be determined based on the average Euclidean distance or cross-validation results between the sample feature vectors. Based on the kernel matrix, a kernel function space model in the form of kernel principal component analysis is constructed, and the sample projection reconstruction error is used as an empirical risk term.

[0040] In the regularization constraint process, singular value decomposition is performed on the model mapping operator matrix to obtain a sequence of singular values. The proportion of the square of each singular value to the sum of the squares of all singular values ​​is calculated as the energy concentration of the corresponding spatial mode. The reciprocal of the sum of the energy concentration and the minimum constant is taken to obtain the weight corresponding to that singular value. Thus, the dominant mode with a higher energy concentration corresponds to a smaller weight and is subject to a weaker penalty, while the redundant mode with a lower energy concentration corresponds to a larger weight and is subject to a stronger penalty. The weighted p-th powers of all singular values ​​are summed to form a weighted Schatten p-norm regularization term, which, together with the empirical risk term, constitutes the objective function. The initial order p is 0.5.

[0041] The Alternating Direction Multiplier (ADMM) algorithm is used to optimize the objective function. Within the ADMM framework, the model mapping operator and kernel weight matrix are iteratively updated using a generalized soft thresholding shrinkage operator. The objective function is optimized when the L2 norm of the gradient difference between two adjacent iterations is less than 10. -5 When convergence is determined, iteration stops, and the initial state-space model parameters that minimize the reconstruction error are output.

[0042] In an optional embodiment, the objective function is optimized using the feature tensors of historical normal operating conditions to obtain the initial state space model. This includes: selecting temperature data with a total duration of 24 hours under historical normal operating conditions and calculating the corresponding normal feature tensor set; inputting the normal feature tensor set into the kernel function space model and optimizing the objective function using the alternating direction multiplier method; setting an upper limit for the number of iterations and an error convergence threshold between two iterations; stopping the iteration operation when the iteration error is less than the convergence threshold or reaches the upper limit for the number of iterations, outputting the current optimal model parameters, and obtaining the initial state space model.

[0043] Outlier data was removed, and temperature data under normal operating conditions with a total duration of 24 hours were selected. Based on a sampling frequency of 1Hz, this dataset contains 86,400 sampling points. Following the previous steps, this dataset was converted into a normal feature tensor set with time length alignment. For example, with a globally uniform time delay τ=5, a globally uniform embedding dimension m=6, and 20 temperature measurement points, a normal feature tensor set with a time length of approximately 86,375, a spatial dimension of 120, and a scale dimension of 6 can be formed. Alternatively, the time dimension can be unified through boundary padding or interpolation alignment before being input into the kernel function space model. The kernel function space model was constructed, using a Gaussian radial basis function with its bandwidth control parameter preset to σ=5.0. The objective function was optimized using the alternating direction multiplier method, with the augmented Lagrange penalty parameter initially set to ρ=1.0 and the incremental update rate set to 1.05. In the iterative solution, the upper limit of the number of iterations is set to 100,000, and the relative change ratio of the Frobenius norm of the weight matrix W between adjacent generations is calculated as the iteration error. When the iteration error is less than the convergence threshold of 0.0002, or when the number of iterations reaches 100,000, the iterative operation is stopped, and the currently optimized parameters are output as the optimal model parameters, thus obtaining the initial state-space model.

[0044] S3 integrates projection residuals and dynamic statistical indicators to trigger anomaly warnings and supports dynamic updates of model boundaries under normal operating conditions.

[0045] Real-time temperature data is processed into real-time feature tensors and projected onto the current model to calculate projection residuals. Continuous projection residuals are used to construct a residual time series, and the dynamic statistical index of the residual time series is calculated within a sliding time window. A composite risk assessment function is constructed based on the norm of the projection residuals and the dynamic statistical index. When the value of the composite risk assessment function exceeds a preset warning threshold, a warning signal is output. When the value of the composite risk assessment function does not exceed the warning threshold, the order p is adjusted online according to the dynamic statistical index, and the current model is iteratively updated to adjust the state space boundary.

[0046] Real-time temperature data is read online and processed into real-time feature tensors according to the filtering, phase space reconstruction, and wavelet decomposition steps described above. The real-time feature tensors are then converted into real-time sample feature vectors using the same dimensional expansion method as in the training phase. The kernel function value between the real-time sample feature vectors and the training sample feature vectors is calculated to form real-time kernel vectors. Based on the real-time kernel vectors, the real-time samples are projected onto the principal component subspace of the current kernel function space model. The difference between the real-time sample features and the model reconstruction features is calculated to obtain the projection residuals.

[0047] A first-in, first-out (FIFO) sliding time window with a length of 250 sampling periods is constructed to buffer continuous projected residuals, forming a residual time series. The information entropy and variance of the residual time series are calculated, and both are used as dynamic statistical indicators. A composite risk assessment function is constructed by weighting and summing the Frobenius norm, information entropy, and variance of the projected residuals using a linear weighting algorithm. A kernel density estimation algorithm is used to model the assessment function values ​​of historical normal data to obtain a probability density distribution. The cumulative distribution function corresponding to this probability density distribution is then calculated, and the 99th percentile of this cumulative distribution function is set as the warning threshold. When the value of the composite risk assessment function calculated in real time exceeds the warning threshold, an warning mechanism is triggered, outputting an alarm shutdown signal command to the downstream control node via the Modbus protocol bus of the device's programmable logic controller.

[0048] When the value of the composite risk assessment function is less than or equal to the warning threshold, the Euclidean distance between the current dynamic statistical index and the historical normal statistical index is calculated. The Euclidean distance is input into a negative exponential function to obtain the basic mapping value, and the positive mapping value is obtained by subtracting the basic mapping value from the positive mapping value. The positive mapping value is multiplied by a preset amplitude coefficient and added to the initial order benchmark value to obtain the latest order p. The order p is restricted to a range greater than 0 and not exceeding 1, so that the order p is not lower than the initial order benchmark value and increases with the increase of the Euclidean distance. Subsequently, an incremental online solution strategy is adopted. Combining the current real-time feature tensor and the updated order p, the model mapping operator matrix and the high-dimensional orthogonal basis are updated in small steps to realize the update and adjustment of the spatial boundary of the slow aging state of the face paper drying equipment.

[0049] In an optional embodiment, the dynamic statistical index of the residual time series is calculated within a sliding time window, including: setting the window length and sliding step size of the sliding time window; truncating the residual time series through the sliding time window to obtain multiple sliding data segments; for each data segment, calculating the mean, variance, and information entropy of the projected residuals of the data segment, and normalizing them respectively; concatenating the normalized mean, variance, and information entropy to construct a feature vector representing the current dynamic characteristics of the system, which serves as the dynamic statistical index.

[0050] For the residual time series output by the state-space model, set the window length and sliding step size of the sliding time window. The residual time series is then truncated using the sliding time window to obtain a sliding data segment vector R of length 120, containing sequence elements. to For each data segment R, calculate the arithmetic mean μ and the sample variance of that data segment. The residual interval was divided into 20 statistical quantiles, and the probability of each quantile was calculated. Using the formula Calculate the information entropy H. Use min-max normalization to map the three indicators to the range of 0 to 1, and concatenate these three normalized components to construct the feature vector V, which contains the normalized average value. Sample variance and information entropy This vector is used as a dynamic statistical index.

[0051] In an optional embodiment, when the value of the composite risk assessment function does not exceed the warning threshold, the order p is adjusted online according to the dynamic statistical index and the current model is iteratively updated to achieve the adjustment of the state space boundary. This includes: calculating the Euclidean distance between the dynamic statistical index corresponding to the current sliding time window and the historical normal statistical index; inputting the Euclidean distance into a negative exponential function and performing a positive nonlinear mapping based on 1 minus the output value of the negative exponential function to obtain a positive mapping value between 0 and 1; multiplying the positive mapping value by a preset amplitude coefficient and adding it to the initial order benchmark value to obtain the latest order p, and restricting the order p to a range greater than 0 and not exceeding 1; substituting the latest order p into the weighted Schattenp norm regularization term to re-solve and update the current model.

[0052] When the value of the composite risk assessment function does not exceed the warning threshold, obtain the dynamic statistical indicators of historical normal operating conditions. Calculate the dynamic statistics corresponding to the current sliding time window. and The Euclidean distance d between them, for example, yields an Euclidean distance d = 0.68. Using a negative exponential function, for example... The attenuation factor is set to 1.0 for mapping. Using this function with an input distance of 0.68, the mapped value y = 0.506 is calculated, which is between 0 and 1. Since the base mapped value y decreases as the Euclidean distance d increases, a forward mapped value q = 1 - y is calculated, so that the forward mapped value q increases as the Euclidean distance d increases. The calculation is performed using the formula p = 0.5 + 0.2 × q, where 0.5 is the baseline order used in the initial model training phase, and 0.2 is a preset amplitude coefficient. Since q is limited to the range of 0 to 1, the calculated hyperparameter p is limited to between 0.5 and 0.7. Substituting q = 0.494, the latest order p = 0.5988 is calculated. This latest order p is then substituted into the weighted Schatten p-norm regularization term, and an incremental online solution strategy is used, such as limiting the number of iterations to no more than 30, to re-solve and update the current model.

[0053] In an optional embodiment, a composite risk assessment function is constructed based on the norm of the projection residual and dynamic statistical indicators. When the value of the composite risk assessment function exceeds a preset warning threshold, a warning signal is output. This includes: calculating the L2 norm of the current real-time projection residual matrix and normalizing the L2 norm by combining it with the extreme values ​​of the L2 norm of historical normal residuals, which serves as the first risk indicator; extracting the information entropy from the dynamic statistical indicators, normalizing the information entropy, and multiplying it by a preset coefficient, which serves as the second risk indicator; adding the first risk indicator and the second risk indicator to obtain the output value of the composite risk assessment function; determining whether the output value is greater than the warning threshold. If it is greater, the drying temperature of the face paper is determined to be abnormal, triggering the alarm controller and outputting a warning signal.

[0054] Extract the principal singular values ​​of the current projected residual matrix and calculate its L2 norm. Combine this with the maximum and minimum extreme values ​​of the residual L2 norm measured in historical statistical data (e.g., maximum Max = 65.0 and minimum Min = 8.0). If the currently obtained L2 norm value is 53.6, normalize this value to calculate the first risk indicator. The resulting value is 0.8. Extract the normalized scalar of the information entropy. For example, if the value is 0.9, the normalized scalar of the information entropy is multiplied by a coefficient of 0.1 to calculate the second risk indicator. =0.09. Adding these two indicators, we get the output value S=0.89 of the composite risk assessment function. Compare this output value S with the warning threshold, for example, Th=0.85. When 0.89>0.85, it is determined that the drying temperature of the face paper is in an abnormal state, triggering the alarm controller and outputting a warning signal.

[0055] The experimental conditions were set using a temperature monitoring dataset from 72 consecutive hours of operation of a paper drying equipment, with a sampling frequency of 1 Hz and containing 259,200 discrete time points. The first 24 hours were used for training under normal operating conditions. Four sets of models were compared: a model with the complete technical solution, a model that removed fractional wavelet transform features and input multidimensional state trajectories, a model that removed the online update mechanism and fixed the regularization term order to 0.5, and a model that abandoned the composite evaluation of dynamic statistical indicators and only used the residual L2 norm for early warning. For all models, the iterative convergence threshold for the alternating direction multiplier method was set to 0.0002, and the early warning trigger threshold was set to 0.85.

[0056] The complete solution model achieved a fault detection accuracy of 98.5% on the test set, with a false alarm rate as low as 1.2% and an average anomaly detection time of 12.5 seconds. The model without fractional-order wavelet transform, lacking multi-scale time-frequency feature analysis, saw its accuracy drop to 91.3%, and its false alarm rate rise to 4.5%. The fixed-order model, unable to track the evolution of operating conditions, achieved an accuracy of 93.8%, but its detection time increased to 18.2 seconds. The model omitting composite evaluation showed poor sensitivity to small system drifts, resulting in a detection time lag of 26.5 seconds and a false alarm rate of 5.1%. Figure 2 As shown.

[0057] Introducing fractional wavelet transform to extract multi-scale approximations and detail components improves early warning accuracy by 7.2% on this experimental dataset. An online order update mechanism based on Euclidean distance positive nonlinear mapping enhances the system's operational condition tracking capabilities, reducing the average detection time by 5.7 seconds under these experimental conditions. A composite risk assessment mechanism integrating global residual strength and local dynamic entropy features helps reduce false alarms caused by normal fluctuations, resulting in a 3.9% reduction in the overall false alarm rate on this experimental dataset, thereby improving the sensitivity and reliability of drying temperature monitoring.

[0058] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for early warning of abnormal drying temperature of face paper, characterized in that, include: S1, obtain the time-series temperature matrix of multiple temperature measurement points of the face paper drying equipment; The phase space of the time-series temperature matrix is ​​reconstructed to generate a multidimensional state trajectory. The multidimensional state trajectory is then decomposed using fractional wavelet transform to obtain the feature tensor. S2. Construct a kernel function space model with feature tensors as input. The objective function of the kernel function space model includes an empirical risk term and a weighted Schatten p-norm regularization term. The weighted Schatten p-norm regularization term imposes a low-rank constraint penalty on the singular values ​​of the model mapping operator. The weights of the singular values ​​are determined according to the energy concentration of the corresponding spatial pattern, and the order p is a parameter. Optimize the objective function using the feature tensors of historical normal operating conditions to obtain the initial state space model. S3 processes real-time temperature data into real-time feature tensors and projects them onto the current model to calculate projection residuals; constructs a residual time series from the continuous projection residuals and calculates the dynamic statistical index of the residual time series within a sliding time window; constructs a composite risk assessment function based on the norm of the projection residuals and the dynamic statistical index, and outputs a warning signal when the value of the composite risk assessment function exceeds the preset warning threshold. When the value of the composite risk assessment function does not exceed the warning threshold, the order p is adjusted online according to the dynamic statistical index and the current model is iteratively updated to adjust the state space boundary.

2. The method for early warning of abnormal drying temperature of face paper according to claim 1, characterized in that, A phase space reconstruction of the time-series temperature matrix is ​​performed to generate a multidimensional state trajectory, including: calculating the discrete autocorrelation sequence of the temperature time series at each temperature measurement point using the autocorrelation function, and determining candidate time delays based on each discrete autocorrelation sequence; calculating the ratio of false nearest neighbors under different embedding dimensions using the false nearest neighbor method, and determining candidate embedding dimensions based on each false nearest neighbor ratio; determining a global unified time delay based on each candidate time delay, and determining a global unified embedding dimension based on each candidate embedding dimension; performing phase space reconstruction on the temperature time series at each temperature measurement point based on the global unified time delay and the global unified embedding dimension to generate a dimension-aligned high-dimensional state matrix; and concatenating the dimension-aligned high-dimensional state matrices corresponding to each temperature measurement point to generate a multidimensional state trajectory.

3. The method for early warning of abnormal drying temperature of face paper according to claim 1, characterized in that, The multidimensional state trajectory is decomposed using fractional wavelet transform to obtain a feature tensor. This process includes: setting the rotation angle of the fractional Fourier transform; constructing a fractional wavelet transform network with low-pass and high-pass branches using a multi-scale filter bank; inputting the multidimensional state trajectory into the fractional wavelet transform network and performing a 5-level decomposition operation; extracting the approximate and detail components after decomposition level by level, and combining them to form a multi-scale frequency coefficient matrix, which is then used as a feature tensor representing temperature.

4. The method for early warning of abnormal drying temperature of face paper according to claim 2, characterized in that, The objective function is optimized using the feature tensors of historical normal operating conditions to obtain the initial state space model. This process includes: selecting temperature data with a total duration of 24 hours under normal operating conditions and calculating the corresponding normal feature tensor set; inputting the normal feature tensor set into the kernel function space model and optimizing the objective function using the alternating direction multiplier method; setting an upper limit for the number of iterations and an error convergence threshold between two iterations; stopping the iteration operation when the iteration error is less than the convergence threshold or reaches the upper limit for the number of iterations, outputting the current optimal model parameters, and obtaining the initial state space model.

5. The method for early warning of abnormal drying temperature of face paper according to claim 1, characterized in that, The calculation of dynamic statistical indices for residual time series within a sliding time window includes: setting the window length and sliding step size of the sliding time window; truncating the residual time series through the sliding time window to obtain multiple sliding data segments; for each data segment, calculating the mean, variance, and information entropy of the projected residuals of the data segment, and normalizing them respectively; concatenating the normalized mean, variance, and information entropy to construct a feature vector representing the current dynamic characteristics of the system, which serves as the dynamic statistical indices.

6. The method for early warning of abnormal drying temperature of face paper according to claim 1, characterized in that, When the value of the composite risk assessment function does not exceed the warning threshold, the order p is adjusted online according to the dynamic statistical index, and the current model is iteratively updated to achieve the adjustment of the state space boundary. This includes: calculating the Euclidean distance between the dynamic statistical index corresponding to the current sliding time window and the historical normal statistical index; inputting the Euclidean distance into the negative exponential function and performing a positive nonlinear mapping based on 1 minus the output value of the negative exponential function to obtain a positive mapping value between 0 and 1; multiplying the positive mapping value by a preset amplitude coefficient and adding it to the initial order benchmark value to obtain the latest order p, and restricting the order p to a range greater than 0 and not exceeding 1; substituting the latest order p into the weighted Schatten p-norm regularization term to resolve and update the current model.

7. The method for early warning of abnormal drying temperature of face paper according to claim 1, characterized in that, A composite risk assessment function is constructed based on the norm of the projection residual and dynamic statistical indicators. When the value of the composite risk assessment function exceeds a preset warning threshold, a warning signal is output. The process includes: calculating the L2 norm of the current real-time projection residual matrix and normalizing the L2 norm by combining it with the extreme values ​​of the L2 norm of historical normal residuals, which serves as the first risk indicator; extracting the information entropy from the dynamic statistical indicators, normalizing the information entropy, and multiplying it by a preset coefficient, which serves as the second risk indicator; adding the first and second risk indicators to obtain the output value of the composite risk assessment function; determining whether the output value is greater than the warning threshold. If it is, the drying temperature of the face paper is determined to be abnormal, triggering the alarm controller and outputting a warning signal.

8. The method for early warning of abnormal drying temperature of face paper according to claim 1, characterized in that, Before obtaining the time-series temperature matrix of multiple temperature measurement points in the paper drying equipment, the process includes: collecting temperature signals through distributed temperature sensors deployed on the surface of the drying cylinder of the paper drying equipment; transmitting the temperature signals to the host computer through a programmable logic controller to obtain the original time-series temperature matrix; and performing smoothing filtering and noise reduction on the original time-series temperature matrix.

9. The method for early warning of abnormal drying temperature of face paper according to claim 5, characterized in that, The method for calculating information entropy is as follows: divide the residual interval into a preset number of statistical quantiles; calculate the probability of each statistical quantile; multiply the probability of each statistical quantile by its corresponding base-2 logarithmic value to obtain the product of each statistical quantile; sum the products of all statistical quantiles and take the negative value to obtain the information entropy.

10. The method for early warning of abnormal drying temperature of face paper according to claim 1, characterized in that, The kernel function space model with feature tensors as input is constructed as follows: the feature tensors are expanded sequentially according to the time dimension, the temperature measurement point spatial dimension, and the wavelet scale dimension to form one-dimensional sample feature vectors; the one-dimensional sample feature vectors are normalized to obtain a standardized sample feature matrix; the Gaussian radial basis kernel function is used to calculate the nonlinear similarity between any two sample feature vectors to generate a kernel matrix; and a kernel function space model in the form of kernel principal component analysis is constructed based on the kernel matrix.

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