Method for detecting loosening of ceramic dewatering elements for papermaking based on vibration spectrum analysis

Abstract

The present application relates to a method for detecting loosening of ceramic dewatering elements for papermaking based on vibration spectrum analysis, aiming to solve the problems of difficult early identification of loosening and weak anti-working condition interference ability of ceramic dewatering elements in the running of the paper machine wire section. The scheme synchronously collects vibration signals and multi-dimensional working condition parameters, generates a structured frequency spectrum through time-frequency analysis and power spectrum density processing, and then fuses the knowledge base to match the reference structure template, realizing the topological edit distance quantization of the measured and reference frequency spectrum. Combined with the fuzzy rule engine, the different loosening degrees are dynamically weighted and inferred, and the positioning accuracy is improved through graph structure evolution trajectory analysis and high-resolution order tracking. The technology has high robustness and early loosening identification ability, which is beneficial to improve the intelligentization and intelligent decision level of the health monitoring of the clean production line ceramic elements.

Description

Technical Field

[0001] This invention relates to the field of papermaking equipment fault detection and vibration signal analysis technology, and in particular to a method for detecting looseness of ceramic dewatering elements used in papermaking based on vibration spectrum analysis. Background Technology

[0002] Currently, in the field of fault detection and vibration signal analysis technology for papermaking equipment, especially for monitoring the loosening state of ceramic dewatering components, the industry generally adopts a feature extraction and threshold judgment model based on vibration signals. The mainstream approach typically includes the following technical process: after the vibration sensor acquires data, typical spectral indicators are extracted using methods such as short-time Fourier transform, and then combined with empirical thresholds or traditional machine learning models (such as support vector machines and decision trees) to determine the loosening state. These approaches largely rely on manually set feature sets and a large number of offline labeled samples, completing equipment health status identification through a one-way "feature extraction—model training—threshold judgment" process.

[0003] In actual engineering deployment and long-term operation and maintenance, existing technologies urgently need to overcome several core bottlenecks: First, there is a need for a loosening detection method that can dynamically adapt to changes in spectral structure under multiple operating conditions and avoid cumbersome annotation and frequent retraining. Second, there is a need to improve the robustness of the model to spectral topology drift caused by changes in the operating environment, and to achieve a solution with low false positive rate, interpretability, rapid deployment and deep collaboration with engineers for on-site diagnosis. Summary of the Invention

[0004] This application provides a method for detecting looseness of ceramic dewatering elements for papermaking based on vibration spectrum analysis, aiming to solve one of the problems or issues of the prior art mentioned in the background.

[0005] The method for detecting loosening of ceramic dewatering elements for papermaking based on vibration spectrum analysis provided in this application specifically includes: S1: Simultaneously acquire the original vibration signal of the ceramic dehydration element and three types of key operating parameters, including paper type code, instantaneous value of the mesh running speed and pressure gradient sequence of the vacuum dehydration zone, to generate a composite monitoring dataset containing time-domain waveforms and operating condition labels.

[0006] S2: Perform short-time Fourier transform processing on the time-domain waveforms in the composite monitoring dataset to convert the time-domain vibration signal into an initial spectrum characterizing the frequency energy distribution.

[0007] S3: Based on the paper type code, the instantaneous value of the wire mesh running speed and the pressure gradient sequence of the vacuum dehydration zone, the corresponding reference spectrum template is matched from the preset working condition spectrum structure knowledge base. The reference spectrum template is a graph structure data in which nodes represent the center frequency of harmonic clusters and edges represent the amplitude ratio and phase difference stability.

[0008] S4: The energy density distribution of the initial spectrum is clustered to generate measured nodes, and the dynamic coupling strength between clusters is calculated by sliding window cross-correlation analysis to generate weighted edges, thereby constructing a measured spectrum structure isomorphic to the reference spectrum template.

[0009] S5: Perform a topological comparison calculation between the measured spectrogram structure and the reference spectrogram template to quantify the degree of structural difference between the two and output a graph editing distance value that reflects the relative topological mismatch.

[0010] S6: Based on the graph editing distance value and combined with the topological anomaly pattern set defined for slightly loose, moderately loose and severely loose, the state inference logic is executed through the fuzzy rule engine. At the same time, the rule confidence is dynamically weighted using the working condition parameters to generate a loosening state discrimination result with confidence weight.

[0011] S7: Continuously record the graph structure evolution trajectory corresponding to the loosening state discrimination result, and if three or more sets of spectrum graphs with similar mismatch patterns appear consecutively at the same position, trigger the local spectrum resampling command and start the high-resolution order tracking analysis process.

[0012] S8: Update the current loosening status judgment result according to the enhanced positioning information output by the high-resolution order tracking analysis process, and store the final loosening level identifier and working condition association log into the historical database to complete the detection closed loop.

[0013] The method for detecting loosening of ceramic dewatering elements for papermaking based on vibration spectrum analysis provided in this application has the following advantages: (1) By constructing a closed-loop reasoning mechanism of "operating condition driving - spectrum reconstruction - topology comparison - state deduction", the technical bottleneck of poor adaptability and high false alarm rate of traditional loosening detection methods under dynamic and variable operating conditions is effectively overcome. Existing technologies generally rely on static feature extraction and fixed threshold judgment, which makes it difficult to distinguish between spectral morphological disturbances caused by paper type switching, speed fluctuations or vacuum pressure changes and structural anomalies caused by actual mechanical loosening, and is prone to misjudgment and missed judgment. This scheme innovatively introduces an operating condition parameter coupling mechanism, taking paper type encoding, mesh running speed and dehydration zone pressure gradient as context input, dynamically matching a physically interpretable reference spectrum template from a pre-set knowledge base, and realizing accurate modeling of expected vibration behavior under normal conditions; on this basis, the measured signal is transformed into an isomorphic graph structure, and a lightweight graph editing distance is used for topology mismatch measurement, so that the identification process focuses on the changes in essential correlations such as amplitude ratio between frequency clusters, phase stability and modulation consistency, rather than single frequency point energy fluctuations, which significantly improves the robustness and anti-interference ability of the detection results in complex industrial environments.

[0014] (2) A state deduction framework based on graph structure evolution analysis and fuzzy rule engine collaboration is proposed, which realizes refined identification and enhanced localization of loosening fault levels, and solves the shortcomings of traditional methods in terms of fault degree quantification and interpretability. Unlike the problem that black box deep learning models are difficult for field engineers to understand and trust, this scheme explicitly expresses key harmonic components and their dynamic coupling relationships as graph nodes and weighted edges, giving the spectral features a clear mechanical and physical meaning; by defining a set of topological anomaly patterns for different loosening levels (such as node isolation, edge breakage, weight decay, etc.), and combining the working condition adaptive adjustment of rule confidence, the diagnostic conclusions not only have logical transparency, but also support human experience intervention and rule iterative optimization; furthermore, the system continuously tracks the time series evolution trajectory of the graph structure, and automatically triggers high-resolution order tracking and local resampling mechanism when similar mismatch patterns are continuously detected, thereby realizing a closed-loop upgrade from preliminary warning to precise localization, which greatly improves the ability to detect early weak loosening and the accuracy of fault tracing.

[0015] (3) The entire method abandons the dependence on large-scale offline training data and high-performance computing platforms. All modules are designed for edge deployment, meeting the stringent requirements of paper production lines for real-time performance and reliability. Compared with data-driven models that require repeated collection of labeled samples and time-consuming parameter tuning, this solution is based on mechanistic modeling, integrating expert knowledge and adaptive graph analysis technology. It can adapt to multi-variety, fast-paced production scenarios without frequent model updates. The core algorithm response latency is controlled within 50ms, which can be seamlessly integrated into existing PLCs or edge controllers to achieve online continuous monitoring. At the same time, its modular architecture supports the progressive expansion of graph template library and rule set, and has good scalability and engineering compatibility. In summary, this method not only significantly improves the accuracy and sensitivity of ceramic dewatering element loosening detection, but also builds an intelligent diagnostic system with human-machine collaboration, closed-loop feedback, and both physical interpretability and engineering practicality, providing efficient and reliable technical support for the state perception and predictive maintenance of high-speed papermaking equipment. Attached Figure Description

[0016] Figure 1 This is the main flowchart of a method for detecting loosening of ceramic dewatering elements used in papermaking based on vibration spectrum analysis.

[0017] Figure 2 This is a sub-flowchart of a method for detecting looseness of ceramic dewatering elements used in papermaking based on vibration spectrum analysis.

[0018] Figure 3 This is another sub-flowchart of the method for detecting looseness of ceramic dewatering elements for papermaking based on vibration spectrum analysis. Detailed Implementation

[0019] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0020] The following disclosure provides many different embodiments or examples for implementing different structures of the invention. To simplify the disclosure, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the invention. Furthermore, reference numerals and / or letters may be repeated in different examples; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed.

[0021] like Figure 1 As shown, this application provides a method for detecting loosening of ceramic dewatering elements used in papermaking based on vibration spectrum analysis, specifically including: S1: Simultaneously acquire the original vibration signal of the ceramic dehydration element and three types of key operating parameters, including paper type code, instantaneous value of the mesh running speed and pressure gradient sequence of the vacuum dehydration zone, to generate a composite monitoring dataset containing time-domain waveforms and operating condition labels.

[0022] S2: Perform short-time Fourier transform processing on the time-domain waveforms in the composite monitoring dataset to convert the time-domain vibration signal into an initial spectrum characterizing the frequency energy distribution.

[0023] S3: Based on the paper type code, the instantaneous value of the wire mesh running speed and the pressure gradient sequence of the vacuum dehydration zone, the corresponding reference spectrum template is matched from the preset working condition spectrum structure knowledge base. The reference spectrum template is a graph structure data in which nodes represent the center frequency of harmonic clusters and edges represent the amplitude ratio and phase difference stability.

[0024] S4: The energy density distribution of the initial spectrum is clustered to generate measured nodes, and the dynamic coupling strength between clusters is calculated by sliding window cross-correlation analysis to generate weighted edges, thereby constructing a measured spectrum structure isomorphic to the reference spectrum template.

[0025] S5: Perform a topological comparison calculation between the measured spectrogram structure and the reference spectrogram template to quantify the degree of structural difference between the two and output a graph editing distance value that reflects the relative topological mismatch.

[0026] S6: Based on the graph editing distance value and combined with the topological anomaly pattern set defined for slightly loose, moderately loose and severely loose, the state inference logic is executed through the fuzzy rule engine. At the same time, the rule confidence is dynamically weighted using the working condition parameters to generate a loosening state discrimination result with confidence weight.

[0027] S7: Continuously record the graph structure evolution trajectory corresponding to the loosening state discrimination result, and if three or more sets of spectrum graphs with similar mismatch patterns appear consecutively at the same position, trigger the local spectrum resampling command and start the high-resolution order tracking analysis process.

[0028] S8: Update the current loosening status judgment result according to the enhanced positioning information output by the high-resolution order tracking analysis process, and store the final loosening level identifier and working condition association log into the historical database to complete the detection closed loop.

[0029] Step S1: Simultaneously acquire the original vibration signal of the ceramic dehydration element and three types of key operating condition parameters. These three types of key operating condition parameters include paper type encoding, instantaneous value of the mesh section running speed, and pressure gradient sequence in the vacuum dehydration zone, to generate a composite monitoring dataset containing time-domain waveforms and operating condition labels. Specifically, this includes: S1.1: Perform high-frequency synchronous sampling processing on the analog voltage signal output by the piezoelectric accelerometer mounted on the ceramic dehydration element support to obtain the original vibration signal sequence containing transient impact components and time-domain waveform characteristics.

[0030] The analog voltage signal output from the piezoelectric accelerometer mounted on the ceramic dewatering element support is acquired. This signal carries information about transient impacts and periodic vibrations caused by mechanical loosening. Anti-aliasing filtering is performed on the analog voltage signal. A low-pass filter with a cutoff frequency set at half the sampling frequency is used to filter out high-frequency noise components above the Nyquist frequency, preventing spectral aliasing from contaminating the characteristic information within the effective frequency band. The filtered analog signal is input to a high-precision analog-to-digital converter (ADC). Based on Shannon's sampling theorem and the upper limit of vibration frequency under high-speed paper machine operation, the sampling frequency is determined to be at least 2.56 times the highest frequency of interest to ensure the resolution and dynamic range of the spectral analysis. During the analog-to-digital conversion process, a synchronous triggering mechanism is introduced, using a global clock pulse as the sampling reference to ensure that the time interval between each sampling point is strictly constant, eliminating phase errors caused by clock jitter. DC bias removal processing is performed on the quantized digital signal sequence. The signal mean within the sliding window is calculated and subtracted from the original sequence to eliminate the interference of sensor zero-point drift on subsequent time-domain waveform analysis. Through the above-mentioned high-frequency synchronous sampling and preprocessing process, the continuous analog voltage signal is transformed into a discretized, denoised, and time-base unified vibration original signal sequence, which fully preserves the transient impact components and time-domain waveform characteristics that reflect the loosening state of the ceramic dehydration element, providing a high-fidelity data foundation for subsequent spectral topology mapping.

[0031] For example, in a papermaking production line with a speed of 1200 m / min, an ICP-type piezoelectric accelerometer installed at the support of the ceramic dewatering element outputs a 0-5V analog voltage signal. The highest fault characteristic frequency of interest to the system is set to 5 kHz. Based on the sampling theorem, the sampling frequency of the analog-to-digital converter is set to 12.8 kHz (2.56 times 5 kHz), and the sampling bit depth is set to 16 bits to ensure dynamic range. First, the signal passes through an eighth-order Butterworth low-pass filter with a cutoff frequency of 6 kHz, resulting in attenuation greater than 40 dB / decade, effectively filtering out high-frequency electromagnetic interference and mechanical resonance noise. Subsequently, the ADC module samples the filtered signal at equal intervals at a frequency of 12.8 kHz, generating 12,800 discrete data points per second. The mean value is calculated for the 1-second data block (12,800 points in total). Assuming the mean value is 0.02V, 0.02V is subtracted from each sampling point to complete DC debiasing. The final output vibration signal sequence is a one-dimensional floating-point array of length 12800. The data range is normalized to the acceleration range of -1g to +1g, and the signal-to-noise ratio is improved to over 45dB. It clearly preserves the periodic impact pulse waveform caused by micro-loosening, ensuring the purity and accuracy of the subsequent short-time Fourier transform input.

[0032] S1.2: Based on the paper machine distributed control system bus, the paper type code identifier, the instantaneous value of the wire section running speed and the pressure gradient sequence of the vacuum dewatering zone are read in real time to generate a multi-dimensional working condition parameter vector reflecting the current production environment status.

[0033] Establish a communication connection with the paper machine's distributed control system bus, configure the OPC UA or Modbus TCP / IP protocol stack, and set the acquisition period to match the vibration signal sampling window, typically 100ms to 500ms. Send a read request to the DCS system to obtain the paper type code identifier, the instantaneous value of the wire section's running speed, and the pressure register addresses of each suction box in the vacuum dewatering zone, and initiate periodic polling. Receive the raw operating condition data packets, parse the paper type code into a standardized identifier, forming a discrete operating condition dimension. Convert the instantaneous speed value to meters per minute, remove outliers, and form a continuous speed dimension. Extract pressure data from multiple suction boxes, construct a pressure gradient sequence in the order of arrangement, and calculate the pressure difference between adjacent suction boxes to form a continuous pressure dimension. Perform data cleaning and missing value imputation on the paper type code, speed, and pressure gradients, and use linear interpolation to repair short-term communication interruptions. Structure and splice the cleaned paper type code, speed, and pressure gradients to construct a multi-dimensional operating condition parameter vector, fully characterizing the operating environment of the ceramic dewatering element. Through the above processing, the heterogeneous operating condition data scattered in the DCS is transformed into structured multidimensional vectors, providing an accurate environmental context for spectrum topology mapping and effectively solving the problem of spectrum feature drift caused by operating condition fluctuations.

[0034] S1.3: Use a high-precision global clock source to perform microsecond-level timestamp alignment processing on the original vibration signal sequence and the multi-dimensional operating condition parameter vector to eliminate the transmission delay differences between multi-source heterogeneous data and generate time-synchronized data pairs.

[0035] S1.4: Perform a working condition semantic mapping operation based on the paper type code identifier and the instantaneous value of the network operating speed in the time synchronization data pair to generate a working condition scene label string for identifying a specific operating scenario.

[0036] The system receives synchronized data pairs and extracts the paper type code identifier and the instantaneous speed of the wire mesh unit. It analyzes the binary structure of the paper type code, separating the fiber ratio index, filler content grade, and paper basis weight range identifier to construct a discrete operating condition attribute vector. It reads the floating-point speed value and linearly normalizes it to the 0-1 interval based on the maximum and minimum speeds, generating a continuous speed factor. It establishes a Cartesian product operating condition scenario space model, orthogonally combining discrete attributes and speed factors to define multidimensional hypercube vertices. It introduces an operating condition sensitivity weight matrix to assign contribution coefficients to each attribute. It uses weighted Euclidean distance to calculate the semantic deviation between the current operating condition point and the baseline operating condition. It queries a preset operating condition scenario classification threshold table to determine the operating condition cluster category. Based on the pressure gradient change trend in the vacuum dehydration zone, if the pressure gradient change rate exceeds the jitter threshold, it is marked as a transient transition scenario. It concatenates the operating condition cluster category identifier and the transient transition marker to generate a unique machine-readable operating condition scenario label string. Through the above-mentioned semantic mapping of working conditions, heterogeneous data is transformed into unified-dimensional scene labels, providing clear contextual constraints for subsequent spectrogram template matching.

[0037] S1.5: The original vibration signal sequence, the multidimensional working condition parameter vector, and the working condition scene label string are structurally encapsulated to generate a composite monitoring dataset containing time-domain waveforms and working condition labels.

[0038] Step S2: Perform short-time Fourier transform processing on the time-domain waveforms in the composite monitoring dataset to convert the time-domain vibration signal into an initial spectral map characterizing the frequency energy distribution. Specifically, this includes: S2.1: Perform Hanning window function weighted truncation processing on the time-domain waveforms in the composite monitoring dataset to generate segmented time-domain signal segments with smooth edge characteristics, thereby eliminating the spectral leakage effect caused by signal truncation.

[0039] The original vibration signal sequence, aligned with timestamps, was extracted from the composite monitoring dataset and used as the input for weighted truncation processing using the Hanning window function. This signal sequence contains transient impact components caused by the loosening of ceramic dehydration elements and background noise, requiring segmented processing to adapt to the stationarity assumption of the short-time Fourier transform.

[0040] The window length and overlap rate parameters for segmented processing are determined. The window length is dynamically set based on the instantaneous value of the paper machine wire section running speed and the characteristic fault frequency range of the ceramic dewatering element to ensure that each data segment contains at least 3 complete fundamental frequency cycles. The overlap rate is set to 50% to ensure the continuity of time-frequency analysis and reduce boundary effects.

[0041] A sequence of Hanning window function coefficients matching the window length is constructed. The Hanning window function exhibits a bell-shaped distribution characteristic in the time domain, smoothly decaying to zero at both ends and bulging in the middle. Its mathematical expression is defined as: Where n is the sampling point index, and its value ranges from 0 to N. 1, N is the window length, i.e., the number of sampling points for each signal segment, and π is the constant pi.

[0042] The original vibration signal sequence is truncated by sliding according to a set step size to generate several sub-signal segments. For the k-th sub-signal segment, its time-domain amplitude value is multiplied point by point with the Hanning window function coefficient sequence to achieve weighted truncation processing.

[0043] Through the above weighting operation, the amplitudes at both ends of the sub-signal segment are smoothly suppressed to near zero, effectively eliminating the Gibbs phenomenon caused by directly truncating non-integer period signals, thereby significantly reducing the spectral leakage effect in subsequent spectral analysis.

[0044] The weighted sub-signal segments are subjected to energy normalization verification. The ratio of signal energy before and after weighting is calculated. If the energy loss exceeds the preset threshold, the window position or length is adjusted to ensure that effective vibration characteristic information is preserved.

[0045] The output is a set of segmented time-domain signal segments after weighted truncation using the Hanning window function. Each segment has smooth edge characteristics, providing high-quality input data that meets the stationarity requirements of spectral analysis for performing Fast Fourier Transform.

[0046] By using the Hanning window function weighted truncation method, the continuous time-domain waveform obtained in the previous step is transformed into segmented time-domain signal segments with smooth edge characteristics, eliminating the spectral leakage effect caused by signal truncation, and achieving the expected technical effect of true restoration of spectral energy distribution and high-precision mapping.

[0047] S2.2: Perform a fast Fourier transform operation based on the segmented time-domain signal fragment to convert the time-domain amplitude sequence into a set of discrete frequency-domain coefficients in complex form, thereby realizing the initial mapping of the signal from the time dimension to the frequency dimension.

[0048] A radix-2 FFT is performed on the weighted, truncated segmented time-domain signal to map the time-domain amplitude sequence to complex frequency-domain coefficients. A complex twitch factor matrix is ​​constructed, and the frequency resolution is determined based on the number of sampling points N. Bit reversal sorting is performed to rearrange the time-domain sequence in binary reverse order to meet the FFT data order requirements. A butterfly operation is performed level by level to decompose the data into even and odd subsequences. The phase of the odd subsequences is corrected using the twitch factor and superimposed on the even subsequences. After traversing all levels, a set of complex frequency-domain coefficients containing both real and imaginary parts is output, preserving the amplitude and phase information of the signal, thus achieving an accurate mapping from the time domain to the frequency domain.

[0049] S2.3: Perform modulus square calculation on the discrete frequency domain coefficient set to generate a power spectral density sequence characterizing the energy intensity at each frequency point, thereby quantifying the energy distribution characteristics of the vibration signal at different frequencies.

[0050] The system receives a set of complex frequency domain coefficients and extracts complex values ​​at each frequency point. By squaring the modulus, it calculates the sum of squares of the real and imaginary parts to obtain an estimated power spectral density, adhering to the principle of energy conservation. Dimensional normalization is performed on the power spectral density value sequence, converting the frequency indices into actual frequency values, forming frequency-energy two-dimensional data. Arranged in ascending order of frequency, a complete power spectral density sequence is constructed to quantify the energy distribution characteristics of the vibration signal, providing a standardized data foundation for subsequent smoothing filtering.

[0051] S2.4: Perform moving average filtering smoothing based on the power spectral density sequence to generate a smooth power spectral curve that suppresses random noise interference, thereby improving the signal-to-noise ratio and stability of the spectral features.

[0052] S2.5: Perform two-dimensional matrix reconstruction and operating condition label association encapsulation on the smoothed power spectrum curve to generate an initial spectrum containing frequency axis, energy axis and operating condition metadata, thus completing the final conversion of the time domain signal into frequency domain structured data.

[0053] like Figure 2 As shown, step S3 involves matching a corresponding reference spectrum template from a pre-set operating condition spectrum structure knowledge base based on the paper type code, the instantaneous value of the wire mesh operating speed, and the pressure gradient sequence of the vacuum dehydration zone. The reference spectrum template is a graph structure data where nodes represent the center frequencies of harmonic clusters and edges represent the amplitude ratio and phase difference stability. Specifically, this includes: S3.1: Perform multi-dimensional vector splicing processing on the paper type code, the instantaneous value of the wire section running speed and the pressure gradient sequence of the vacuum dewatering zone to generate a composite working condition feature vector containing information on the current operating status of the paper machine.

[0054] The system receives a composite monitoring dataset containing time-domain waveforms and operating condition labels generated in step S1.5. From this dataset, it extracts the paper type code identifier, the instantaneous value of the wire section running speed, and the pressure gradient sequence in the vacuum dehydration zone as the raw input data for this step. The paper type code identifier undergoes discretization numerical mapping processing. Based on a pre-set papermaking process knowledge base, the paper type codes with different fiber ratios and filler contents are converted into corresponding physical property weight coefficients, forming a static operating condition component characterizing material properties. The instantaneous value of the wire section running speed is obtained, normalized to eliminate dimensional differences, and mapped to a standard interval of 0 to 1, forming a dynamic velocity component characterizing the mechanical motion state. The pressure gradient sequence in the vacuum dehydration zone is extracted, and the mean and variance of this sequence within a preset time window are calculated. A pressure feature vector reflecting the intensity of dehydration load fluctuations is constructed, forming a dynamic pressure component characterizing the fluid dynamics environment. The static operating condition component, dynamic velocity component, and dynamic pressure component are sequentially concatenated according to a predefined dimensional order to construct a high-dimensional composite operating condition feature vector. A weighted Euclidean distance metric is employed to perform structural verification on the spliced ​​vectors, ensuring that the relative weights of each component in the feature space conform to physical constraints and preventing a single, drastically fluctuating parameter from dominating the overall feature representation. Through multi-dimensional vector splicing, heterogeneous discrete codes and continuous physical quantities are transformed into composite operating condition feature vectors of a unified dimension. This achieves a digital panoramic description of the current complex operating state of the paper machine, providing a standardized query index for subsequent accurate retrieval and matching of reference spectrogram templates in high-dimensional space.

[0055] For example, for a large-scale paper production line, the paper type code is identified as "P-250", corresponding to high basis weight coated paper. Looking up the table, its physical property weight coefficient is 0.85. The instantaneous speed of the wire section is 1200 m / min, and after normalization, the dynamic speed component is 0.75 (assuming the maximum design speed is 1600 m / min). The mean value of the pressure gradient sequence in the vacuum dehydration zone within the most recent second is -45 kPa, and the standard deviation is 2.1 kPa. After standardization, the pressure feature vector is [-0.6, 0.3]. These components are concatenated in the order of [static weight, dynamic speed, mean pressure, variance pressure] to generate a four-dimensional composite operating condition feature vector V = [0.85, 0.75, -0.6, 0.3]. This vector fully preserves the key semantic information of the current working condition. The static weights reflect the influence of paper stiffness on vibration transmission, the dynamic velocity determines the position of the fundamental frequency and harmonics, and the pressure features are related to the intensity of the excitation force of the gas-liquid two-phase flow. This composite working condition feature vector is directly used as the input query key for high-dimensional space similarity retrieval in step S3.2, ensuring the working condition specificity of the reference template matching.

[0056] S3.2: Based on the composite operating condition feature vector, locate and extract the candidate reference spectrum template index that best matches the current operating state from the preset operating condition spectrum structure knowledge base.

[0057] The operating condition spectrum structure knowledge base is a structured knowledge set used in this invention to store the mapping relationship between different papermaking production operating conditions (paper type, wire running speed, pressure gradient in the vacuum dewatering zone) and the vibration spectrum topology under the corresponding healthy state. This knowledge base internally maintains a hash mapping table, using operating condition feature vectors (fixed-length binary strings after discretization or hash encoding) as keys and unique identifiers of reference spectrum templates as values ​​to achieve millisecond-level template retrieval. It also stores historically stored sets of reference operating condition feature vectors, used for degraded nearest neighbor search based on weighted Euclidean distance in case of hash collisions or misses. Through this knowledge base, the system can quickly locate the spectrum benchmark template that best matches the current operating state, providing a standard reference for subsequent spectrum topology comparisons.

[0058] The operating condition spectrum structure knowledge base adopts a hybrid storage architecture and includes the following core components: Hash Map: The main index structure, where the key is the operating condition feature vector (a fixed-length binary string generated by a deterministic hash function such as MD5 truncation or CityHash), and the value is the unique ID of the corresponding reference spectrum template. The hash table uses chaining to resolve collisions and maintains an LRU cache to accelerate the retrieval of high-frequency operating conditions.

[0059] Reference working condition feature vector set: Stores all original working condition feature vectors that have been entered into the knowledge base (including paper type encoding, normalized value of network section operating speed, and pressure gradient statistics of vacuum dehydration zone), used to support similarity calculation and neighbor retrieval during incremental updates.

[0060] Reference spectrum template table: Using template ID as the primary key, it stores the graph structure data of each template (node ​​set: harmonic cluster center frequency, type, reference amplitude; edge set: directed connection, nominal amplitude ratio, phase difference stability threshold, etc.).

[0061] Version and Verification Table: Records the version number, update time, data source, and integrity verification hash value of the knowledge base.

[0062] Construction method: Offline calibration: Under healthy conditions of the ceramic dehydration element, vibration signals under various typical operating conditions (different paper types, speed ranges, and pressure gradients) are collected. Reference spectrum templates are generated through steps S2 and S4, and the corresponding operating condition feature vectors are extracted and stored in the historical reference operating condition feature vector set. A unique ID is assigned to each template, and a mapping of "operating condition feature hash code → template ID" is established in the hash mapping table.

[0063] Hash table construction: For each working condition feature vector, a deterministic hash algorithm is used to generate a fixed-length hash key, which is then stored in a hash table. If a hash collision occurs (different working conditions generate the same key), the conflicting template IDs are linked in the same bucket, and the best match is selected during retrieval using a weighted Euclidean distance quadratic check.

[0064] Index optimization: To accelerate nearest neighbor search when hash misses occur, a KD-tree or ball tree index is built on the historically stored set of reference condition feature vectors.

[0065] Online incremental update: When the system accumulates new high-confidence health condition data during long-term operation, extract its condition feature vector and spectrum template, insert them into the hash mapping table (if the hash key already exists, append it to the collision chain; otherwise, create a new entry), and synchronously update the historical feature vector set and tree index.

[0066] The operating condition spectrum structure knowledge base utilizes a hash mapping table to achieve millisecond-level template retrieval, while retaining a historically stored set of reference operating condition feature vectors to support nearest neighbor search and incremental updates. It is the core supporting component for achieving adaptive spectrum topology comparison based on operating conditions in this invention.

[0067] The composite operating condition feature vector generated in step S3.1, which includes paper type code, instantaneous value of wire mesh running speed and pressure gradient sequence of vacuum dehydration zone, is received as the input query object for high-dimensional space similarity retrieval.

[0068] Multidimensional data standardization preprocessing is performed on the composite working condition feature vector to eliminate the numerical scale differences between different physical dimensions (such as rotational speed r / min, pressure kPa, and coded discrete values) and construct a dimensionless standard working condition feature space.

[0069] The min-max normalization method is used to perform a linear mapping transformation on the instantaneous values ​​of the network operation speed and the continuous variables in the pressure gradient sequence of the vacuum dehydration zone, compressing their numerical range to the [0, 1] interval, so as to ensure that each dimension has an equal weight contribution in the distance calculation.

[0070] For the discrete categorical variable of paper type coding, the one-hot encoding technique is applied to convert it into a sparse binary vector, which is then concatenated with the standardized continuous variable vector to form a unified high-dimensional Euclidean space coordinate representation.

[0071] Based on a pre-built knowledge base of operating condition spectrum structure, all historically stored reference operating condition feature vector sets are extracted to construct a high-dimensional index tree structure for similarity comparison. KD tree or ball tree algorithms are preferred to accelerate the search process for neighboring nodes.

[0072] Define a weighted Euclidean distance metric function to quantify the geometric distance between the current real-time operating condition feature vector and the reference operating condition feature vectors in the knowledge base. This distance value directly reflects the similarity between the two in their operating states.

[0073] A working condition sensitivity weighting coefficient matrix is ​​introduced to assign different distance calculation weights to the three dimensions of vehicle speed, pressure, and paper type. Among them, the vehicle speed dimension is given the highest weight because it has a significant impact on the position of harmonic frequencies, followed by the pressure dimension, and then the paper type dimension.

[0074] The weighted Euclidean distance between the current operating condition feature vector and the i-th reference operating condition feature vector is calculated using the following formula: in, This represents the weighted Euclidean distance between the current operating condition and the i-th reference operating condition. The total dimension of the feature vectors. Let be the sensitivity weight coefficient of the j-th dimension feature. Let j be the value of the feature vector of the current working condition in the j-th dimension. Let be the value of the i-th reference working condition feature vector in the j-th dimension.

[0075] Traverse all reference working condition feature vectors in the knowledge base, calculate the distance value one by one using the weighted Euclidean distance formula mentioned above, and generate a distance sorted list containing all candidate reference templates.

[0076] The distance sorting list is sorted in ascending order, and the top K reference working condition feature vectors with the smallest distance values ​​are selected as the nearest neighbor candidate set. The value of K is usually set to 3 to 5 to balance matching accuracy and fault tolerance.

[0077] Perform consistency checks on the feature vectors of the K candidate reference operating conditions in the nearest neighbor candidate set, check whether the corresponding reference spectrum templates are comparable in the topological dimension, and remove invalid templates caused by missing or abnormal data.

[0078] The reciprocal of the distance to each candidate in the nearest neighbor candidate set is calculated as the similarity score, and the score is normalized so that the sum of the similarity scores of all candidates is 1, thereby quantifying the matching confidence of each candidate template.

[0079] The index identifier corresponding to the candidate reference working condition feature vector with the highest similarity score is selected as the candidate reference spectrum template index that best matches the current operating state.

[0080] If the highest similarity score is lower than the preset trust threshold, the current working condition is determined to be a rare or unmodeled working condition, triggering the knowledge base to update the flag, and temporarily using the global average reference template index as a fallback strategy to prevent matching failure.

[0081] By using a weighted Euclidean distance metric and a nearest neighbor search mechanism, the feature vector of high-dimensional composite operating conditions is transformed into a uniquely determined candidate reference spectrum template index, enabling rapid and accurate positioning from complex and ever-changing production operating conditions to a standardized spectrum topology benchmark, providing a structural reference with operating condition adaptability for the subsequent construction of measured spectrum maps.

[0082] S3.3: Use the candidate reference spectrum template index to retrieve the corresponding graph structure data definition, so as to parse out the original reference spectrum template containing the set of harmonic cluster center frequency nodes and the set of amplitude ratio and phase difference stability edges.

[0083] Receive the candidate reference spectrum template index from the output of step S3.2. This index uniquely identifies the pre-set knowledge base entry that is closest to the current composite condition feature vector in the multidimensional space.

[0084] Based on the candidate reference spectrum template index, a fast addressing operation is performed in the hash mapping table of the operating condition spectrum structure knowledge base to locate and read the serialized graph structure data block stored in the non-volatile memory.

[0085] The serialized graph structure data block read is deserialized and decoded to parse out the original data structure object containing the node attribute definition table and the adjacency matrix definition table, and restore its graph topology representation in memory.

[0086] Extract the initial nominal frequency value, node type identifier, and reference amplitude parameter under rated operating conditions of all harmonic cluster center frequency nodes from the node attribute definition table to construct the original reference node set.

[0087] The initial values ​​of edge weights, phase difference stability thresholds, and modulation envelope consistency coefficients connecting the center frequency nodes of each harmonic cluster are extracted from the adjacency matrix definition table to construct the original reference edge set.

[0088] Each node in the original reference node set is instantiated as a vertex object in graph theory, and each connection in the original reference edge set is instantiated as a directed edge object with weighted properties.

[0089] Perform integrity checks on the instantiated vertex and directed edge objects to ensure that the start and end nodes of all edges exist in the vertex set and that there are no isolated nodes or dangling edges.

[0090] The verified vertex and edge sets are encapsulated into a standard graph structure data object, which fully preserves the topological characteristics of the vibration spectrum of the paper machine under specific standard operating conditions.

[0091] Through the above decoding, parsing, instantiation, and verification processes, the index identifier from the previous step is transformed into an original reference spectrum template containing a set of harmonic cluster center frequency nodes and a set of amplitude ratio and phase difference stability edges. This achieves a precise mapping from abstract indexes to specific physical topological benchmarks, providing a structured data foundation for subsequent dynamic corrections based on changes in vehicle speed and pressure.

[0092] S3.4: Perform frequency scaling adaptive correction processing on the set of harmonic cluster center frequency nodes in the original reference spectrum template based on the instantaneous value of the network vehicle speed, so as to generate a frequency calibration reference spectrum template that eliminates the influence of vehicle speed fluctuations.

[0093] The set of harmonic cluster center frequency nodes in the original reference spectrum template parsed in step S3.3, and the instantaneous value of the network vehicle speed read in real time in step S1.2 are used as input data for frequency scaling adaptive correction processing.

[0094] Extract the reference order parameters corresponding to each harmonic cluster node in the original reference spectrum template. The reference order parameters include the fundamental frequency order of the dewatering roller rotation, the gear meshing order, and the bearing fault characteristic order. Establish a mapping table between node identifiers and physical orders.

[0095] Based on the mechanical structural parameters of the paper machine's transmission system, calculate the theoretical fundamental frequency corresponding to the instantaneous value of the current wire section's running speed.

[0096] Traverse each harmonic cluster center frequency node in the original reference spectrum template, read its preset standard operating condition reference vehicle speed, and calculate the reference rotating fundamental frequency under the standard operating condition as the reference anchor point for frequency scaling normalization.

[0097] Calculate the speed change ratio coefficient of the current actual working condition relative to the standard working condition, and determine the frequency scaling factor by the ratio of the current theoretical rotating fundamental frequency to the reference rotating fundamental frequency.

[0098] The frequency scaling factor is applied to the frequency coordinates of all harmonic cluster center frequency nodes in the original reference spectrum template, and a linear scaling transformation is performed to generate the corrected node frequency values, ensuring that the spectral features maintain a strict order alignment relationship as the vehicle speed changes.

[0099] Boundary constraint checks are performed on the corrected node frequency values ​​to remove frequency nodes that exceed the Nyquist limit of the sensor's effective sampling frequency, and the remaining effective nodes form a subset of the nodes in the frequency calibration reference spectrum template.

[0100] Keeping the topological connections and edge attribute definitions between nodes in the original reference spectrum template unchanged, only updating the frequency coordinate attributes in the node set, the frequency domain adaptive reconstruction of the graph structure is completed.

[0101] Through the above frequency scaling adaptive correction process, the static reference template obtained in the previous step is transformed into a frequency calibration reference spectrum template that is dynamically adapted to the current vehicle speed condition. This eliminates the frequency drift of the spectrum characteristics caused by vehicle speed fluctuations, ensuring that subsequent topology comparisons are performed in a unified order coordinate system, and significantly improving the recognition robustness under multiple speed conditions.

[0102] For example, in a large paper production line, the effective diameter D of the dewatering element support roller is set to 0.8 meters. Under standard operating conditions, the wire section running speed is 600 meters per minute, at which time the reference rotation frequency f... ref The calculated frequency is 3.98Hz. When the production scenario switches to high-speed paper, the instantaneous value of the wire section running speed v mesh When the speed reaches 900 m / min, the system calculates the current theoretical fundamental frequency f in real time. base The original frequency was 5.97 Hz. Based on this, the frequency scaling factor λ was calculated to be 1.5. In the original reference spectrum template, the original frequency value of the node representing the fundamental frequency of the dewatering roller was 3.98 Hz, the original frequency value of the node representing the second harmonic was 7.96 Hz, and the original frequency value of the node representing the gear meshing frequency (assuming an order of 20) was 79.6 Hz. After applying the frequency scaling factor, the fundamental frequency node frequency was corrected to 5.97 Hz, the second harmonic node to 11.94 Hz, and the gear meshing frequency node to 119.4 Hz. If the sensor sampling rate is 1024 Hz and the Nyquist frequency is 512 Hz, all the corrected frequencies are within the limits and are retained. If there is a higher harmonic node with an original frequency of 400 Hz, which becomes 600 Hz after correction, exceeding the Nyquist limit, then that node is removed. In the final frequency calibration reference spectrum template, all node frequencies accurately correspond to the theoretical order positions at a vehicle speed of 900 m / min, eliminating the spectral peak misalignment caused by a 50% increase in vehicle speed. This reduces the node matching error between the subsequently measured spectrum and the reference template from an average of 15 Hz to less than 0.5 Hz, significantly improving the accuracy of topology comparison.

[0103] S3.5: Based on the pressure gradient sequence of the vacuum dehydration zone, perform weighted dynamic reconstruction processing on the amplitude ratio and phase difference stability edge set in the frequency calibration reference spectrum template to output the final reference spectrum template adapted to the current vacuum dehydration condition.

[0104] The amplitude ratio and phase difference stability set in the received frequency calibration reference spectrum template, as well as the pressure gradient sequence in the vacuum dehydration region, are used as input data.

[0105] Normalization preprocessing is performed on the pressure gradient sequence in the vacuum dehydration zone to extract a scalar pressure factor characterizing the current dehydration intensity. This factor reflects the degree of contact tightness and frictional coupling state between the ceramic dehydration element and the forming mesh.

[0106] Traverse each edge in the frequency calibration reference spectrum template, identify the physical vibration source type corresponding to the two harmonic cluster nodes connected by the edge, and distinguish the fundamental frequency component, meshing frequency component and its modulation sideband component.

[0107] Based on the classification of the physical properties of the edges, the preset pressure-coupling sensitivity coefficient matrix is ​​called to obtain the amplitude attenuation rate and phase drift rate parameters of different vibration source combinations under pressure changes.

[0108] The exponential decay model is used to calculate the correction coefficient of the current pressure factor on the edge weight. For edges reflecting rigid structural connections, increased pressure leads to enhanced coupling, and the weight correction coefficient is greater than 1. For edges reflecting loose gaps, increased pressure inhibits relative motion, and the weight correction coefficient approaches a stable value.

[0109] Phase consistency verification is performed on the edge weights after pressure correction. The dynamic stability of the phase difference is judged by the pressure gradient change rate. If the pressure fluctuation exceeds the preset threshold, the phase difference stability weight of the corresponding edge is reduced to eliminate false phase shifts caused by transient pressure shocks.

[0110] The corrected amplitude ratio weight and the adjusted phase difference stability weight are weighted and fused to generate the final dynamic weight value of each edge, ensuring that the strength of the edges in the graph structure truly reflects the mechanical coupling state under the current vacuum pressure condition.

[0111] Through the above-mentioned weighted dynamic reconstruction processing based on the pressure gradient sequence of the vacuum dehydration zone, the frequency calibration reference spectrum template of the previous step is transformed into a final reference spectrum template adapted to the current vacuum dehydration condition. This enables the reference benchmark to adapt to the working pressure, eliminates spectral feature mismatch caused by pressure fluctuations, and improves the robustness of loosening identification under varying pressure conditions.

[0112] like Figure 3 As shown, step S4 involves clustering the energy density distribution of the initial spectrogram to generate measured nodes, and calculating the dynamic coupling strength between clusters using sliding window cross-correlation analysis to generate weighted edges, thereby constructing a measured spectrogram structure isomorphic to the reference spectrogram template. Specifically, this includes: S4.1: Based on the energy density distribution data of the initial spectrum, identify local energy maxima and divide the frequency-assigned regions, thereby generating a set of measured nodes that characterize the center frequency position of each harmonic cluster.

[0113] Receive the initial spectrum output from step S2, which includes frequency axis, energy axis and operating condition metadata. This spectrum characterizes the frequency domain distribution of vibration energy of the ceramic dehydration element under the current operating condition, and serves as the data basis for the actual measurement node extraction.

[0114] Local extremum search processing is performed on the power spectral density sequence in the initial spectrum. A sliding window mechanism is used to traverse the entire frequency band to identify candidate peak points with amplitudes significantly higher than the average level of the neighborhood, thus initially locking the potential harmonic cluster center frequency location.

[0115] The candidate peak points are filtered based on their amplitude and signal-to-noise ratio threshold. False peaks caused by random noise are removed, and significant frequency components with physical meaning are retained to generate a high-confidence set of candidate nodes, ensuring the quality of input data for subsequent clustering analysis.

[0116] For the selected candidate node set, the local density of each data point in the spectral space is calculated. The local density is defined as the number of other data points contained in a spherical region centered on the point and with a specific cutoff distance as the radius, thus quantifying the degree of clustering of each frequency point.

[0117] Calculate the local density of the i-th data point, and calculate the minimum distance from each data point to all other higher-density data points, which is defined as the decision distance. This distance measures the independence of the point as a cluster center. The larger the distance, the more likely the point is to be an independent cluster center rather than a member of other clusters.

[0118] Construct a decision graph with local density ρ as the horizontal axis and decision distance δ as the vertical axis, and draw a scatter plot of the distribution of all candidate nodes to intuitively show the topological relationship of each frequency point in the density-distance space.

[0119] The decision graph automatically identifies outliers located in the upper right corner. These points have both high local density and large decision distance, and are determined to be cluster centers, i.e. key nodes in the measured spectrum graph, corresponding to harmonic clusters with clear physical meaning such as fundamental frequency, harmonics, or modulation sidebands.

[0120] Based on the identified cluster centers, the remaining non-central data points are assigned to the clusters to which the nearest cluster center belongs, forming several frequency assignment regions, each representing a complete harmonic cluster structure.

[0121] A weighted average is calculated for all frequency points within each frequency region, with the weight being the power spectral density value of that frequency point. The centroid frequency of each cluster is then calculated and used as the measured value of the center frequency of that harmonic cluster.

[0122] Calculate the center frequency of the k-th harmonic cluster.

[0123] The frequency value, amplitude integral energy, and phase consistency index of each cluster center are extracted and encapsulated into a node attribute vector to generate a set of measured nodes that characterize the frequency position and energy characteristics of each harmonic cluster center.

[0124] By using an adaptive clustering method based on density peaks, the initial spectrum map from the previous step is transformed into a set of measured nodes with clear physical meaning, achieving accurate mapping from continuous spectrum data to discrete graph structure nodes, eliminating noise interference and highlighting key fault characteristics, and providing a stable vertex data foundation for constructing isomorphic measured spectrum maps.

[0125] For example, the initial spectrum of a vibration signal with a sampling rate of 10 kHz and a length of 1 s is processed, and the frequency resolution is set to 1 Hz. The cutoff distance d is set. c Representing 2% of the total number of points in the spectrum, the calculated frequency is approximately 20Hz. In local density calculations, points near 50Hz (fundamental frequency), 100Hz (second harmonic), and 485Hz (dewatering roller meshing frequency) were found to have extremely high local density values. In decision distance calculations, the δ values ​​corresponding to these three frequency points were significantly higher than those of surrounding points, at 15.2, 12.8, and 18.5 respectively, confirming them as three main cluster centers. The remaining frequency points were assigned to these three clusters based on the principle of proximity: the 50Hz cluster covers the 45-55Hz range, the 100Hz cluster covers the 95-105Hz range, and the 485Hz cluster covers the 480-490Hz range. Using the weighted average formula, the measured center frequencies were calculated to be 50.12Hz, 100.05Hz, and 485.32Hz, with minimal deviation from the theoretical values. The final generated set of measured nodes contains three nodes, each carrying frequency, energy and phase information. This successfully achieved the goal of extracting key feature nodes from a complex spectral background, significantly improving the accuracy of subsequent graph structure matching.

[0126] S4.2: Based on the frequency boundary range of each node in the measured node set, extract the corresponding time-frequency energy segment sequence from the initial spectrum to construct the inter-cluster signal pair to be processed for subsequent correlation analysis.

[0127] Receive the set of measured nodes output from step S4.1. The set of measured nodes includes the center frequency position of each harmonic cluster and the corresponding frequency boundary range parameters, which serves as the input data source for this step.

[0128] The upper and lower limits of the frequency boundary of each node in the measured node set are analyzed to construct a frequency mask interval sequence for the initial spectrum and clarify the physical coverage of the signal to be extracted in the frequency domain.

[0129] Based on the frequency mask interval sequence, a frequency band slicing operation is performed on the initial spectrum generated in step S2 to extract local power spectral density data fragments located within the frequency boundary range of each node, forming independent frequency domain energy subsets.

[0130] For each frequency domain energy subset, the inverse short-time Fourier transform or bandpass filtering reconstruction technique is used to reverse map the local energy distribution in the frequency domain back to the time domain space, thereby recovering the time-frequency energy segment sequence corresponding to a specific harmonic cluster.

[0131] The recovered time-frequency energy segment sequence is subjected to amplitude normalization to eliminate the dimensional influence caused by the difference in absolute energy between different frequency clusters, ensuring that subsequent cross-correlation analysis focuses only on waveform morphology and phase coupling characteristics rather than absolute amplitude.

[0132] Traverse all node pairs in the measured node set, combine the normalized time-frequency energy segment sequences corresponding to any two different nodes into inter-cluster signal pairs to be processed, and construct the original signal matrix to characterize the topological connectivity.

[0133] Through the above processing method, the discrete node frequency information of the previous step is transformed into a continuous time-frequency energy segment sequence pair with a time dimension, realizing the transformation from static spectrum points to dynamic coupling signal pairs, and providing a standardized input data basis for calculating the inter-cluster dynamic coupling strength in step S4.3.

[0134] S4.3: Perform sliding window cross-correlation analysis on the inter-cluster signal pairs to be processed to quantify the time lag characteristics and waveform similarity between clusters of different frequencies, thereby generating the original cross-correlation matrix characterizing the dynamic coupling strength between clusters.

[0135] Receive the inter-cluster signal pairs to be processed from the output of step S4.2. The signal pairs contain time-frequency energy segment sequences extracted from the initial spectrogram and corresponding to the center frequency nodes of different harmonic clusters, which serve as the input data source for cross-correlation analysis.

[0136] For each inter-cluster signal pair to be processed, the length and step size parameters of the sliding time window are set. The window length is determined based on an integer multiple of the fundamental frequency period corresponding to the paper machine wire section running speed, so as to cover at least two complete mechanical vibration cycles and ensure that stable phase coupling characteristics are captured.

[0137] The sliding window is applied sequentially to the time axis of the first cluster of signals and the second cluster of signals. At each window position, a signal segment of equal length is extracted and denoted as the reference signal segment x(t) and the signal segment to be measured y(t), respectively, where t represents the discrete sampling time point.

[0138] The truncated reference signal segment and the signal segment under test are subjected to mean-reduction preprocessing to eliminate the interference of DC component on correlation calculation, resulting in zero-mean signal sequences x'(t) and y'(t).

[0139] Based on a zero-mean signal sequence, the similarity coefficient between two signal segments at different time lags τ is calculated using the discrete cross-correlation function. The original cross-correlation coefficient R is then calculated using the following formula. xy (τ): Where N is the number of sampling points in the sliding window, τ is the time lag variable, whose value range covers the preset maximum allowable phase offset interval, x'(n) is the value of the reference signal at the nth sampling point, and y'(n+τ) is the value of the signal under test at the n+τth sampling point.

[0140] Iterate through all possible time lag values ​​τ to find the cross-correlation coefficient R. xy (τ) The lag τ in reaching the global maximum max This hysteresis characteristic represents the time delay of vibrational energy transfer between two frequency clusters.

[0141] Extract the global maximum value R xy (τ max As the peak cross-correlation coefficient of the current signal pair under specific operating conditions, this value reflects the maximum similarity in waveform morphology between the two harmonic clusters, that is, a direct measure of dynamic coupling strength.

[0142] Repeat the above sliding window cross-correlation calculation process for all node combinations within the current monitoring period of the paper machine to construct a symmetric matrix. The rows and columns of the matrix correspond to the node indices in the measured spectrum, and the element values ​​are the peak cross-correlation coefficients of the corresponding node pairs.

[0143] By using a sliding window cross-correlation analysis method, the time-frequency energy segments extracted in the previous step are transformed into the original cross-correlation matrix, which characterizes the time lag characteristics and waveform similarity between nodes. This enables the quantitative extraction of edge weight information in the spectral topology, providing an accurate data foundation for the subsequent construction of physically meaningful measured spectral graph structures.

[0144] S4.4: The original cross-correlation coefficient matrix is ​​numerically transformed using a normalized mapping function to eliminate differences in magnitude and retain information on relative correlation strength, thereby generating standardized weighted edge weight data.

[0145] S4.5: Based on the measured node set as vertices and the weighted edge weight data as connection relationships, perform graph structure assembly operation to construct a measured spectrum graph structure with the same topological dimension as the reference spectrum graph template.

[0146] Step S5: Perform a topological comparison calculation between the measured spectrogram structure and the reference spectrogram template to quantify the degree of structural difference between the two and output a graph editing distance value reflecting the relative topological mismatch. Specifically, this includes: S5.1: Perform node attribute mapping matching processing based on the measured node set and the reference node set to align the center frequency of the harmonic cluster using the frequency tolerance window, thereby generating a node mapping relationship table containing the frequency deviation and amplitude normalization coefficient.

[0147] S5.2: Perform a coupling strength consistency check on the measured weighted edge and the reference weighted edge according to the node mapping relationship table, and calculate the dynamic deviation of each corresponding edge weight through the difference of cross-correlation coefficients of the sliding window, thereby generating an edge weight difference matrix that characterizes the stability of local connection.

[0148] Based on the node mapping table generated in step S5.1, the weighted edge set corresponding to each node in the measured spectrum structure and the weighted edge set of the corresponding node in the reference spectrum template are extracted as input data objects for coupling strength consistency verification. The node mapping table clarifies the one-to-one correspondence or tolerance matching relationship between the measured harmonic cluster center frequency node and the reference template node, ensuring the topological isomorphism basis for subsequent edge weight comparison.

[0149] For each pair of matching nodes in the node mapping table, locate all adjacent edges connecting them in the measured spectrogram structure and the reference spectrogram template, and construct the edge weight pairing sequence to be verified. For each matching node pair, obtain its measured cross-correlation coefficient weight value and the reference cross-correlation coefficient weight value to form the original data pair used to calculate the dynamic deviation.

[0150] For each pair of edge weights to be verified, the local dynamic deviation between the measured edge weights and the reference edge weights is calculated using a sliding window cross-correlation coefficient difference processing method. This calculation process is not a simple numerical subtraction, but rather incorporates a time lag compensation mechanism to eliminate the phase asynchrony caused by minute fluctuations in vehicle speed. Specifically, a sliding time window of length L is selected, and cross-correlation calculations are performed on the measured signal segment and the reference signal segment within the window to obtain the maximum cross-correlation coefficient and its corresponding time lag.

[0151] Calculate the dynamic deviation index of the i-th edge.

[0152] The calculated dynamic deviation indices of each edge are filled into a pre-defined sparse matrix structure to generate an edge weight difference matrix characterizing the stability of local connections. The row and column indices of this matrix correspond to the node IDs in the spectrogram, and the matrix element values ​​are the dynamic deviations of the edges between the corresponding nodes. If there is no direct connection between two nodes, the matrix element is set to zero.

[0153] Threshold truncation is performed on the edge weight difference matrix to remove minor deviations caused by measurement noise, while retaining topological change information with significant physical meaning. By setting a dynamic deviation threshold, continuous values ​​in the matrix are converted into discrete state indicators reflecting the connection stability level, thereby enhancing the discriminability of loosening features at the topological level.

[0154] By calculating and normalizing the cross-correlation coefficient difference of the sliding window, the node mapping relationship of the previous step is transformed into a boundary weight difference matrix that quantifies the stability of local connections. This enables accurate verification of the consistency of coupling strength within the spectrogram structure and provides a high-precision boundary weight penalty basis for the minimum cost path search of the subsequent graph editing distance.

[0155] S5.3: Utilize the node mapping relationship table and edge weight difference matrix to perform graph structure editing operation sequence planning processing, and use a greedy search strategy to determine the minimum set of node insertion, deletion and edge weight modification operations required to transform the measured spectrum graph structure into a reference spectrum graph template, thereby generating the optimal graph editing path sequence.

[0156] The node mapping table and the edge weight difference matrix are received as input data. The node mapping table includes the frequency deviation and amplitude normalization coefficient between the measured spectrum nodes and the reference template nodes. The edge weight difference matrix represents the dynamic deviation of the coupling strength of the corresponding connection edge.

[0157] A cost space for graph editing operations is constructed, and three basic editing operation types are defined: node insertion operation, node deletion operation, and edge weight modification operation. An initial unit penalty factor is set for each operation. The unit penalty factor for node insertion and deletion is set to the same value to maintain topological symmetry, and the unit penalty factor for edge weight modification is dynamically calibrated based on the normalized deviation in the edge weight difference matrix.

[0158] Initialize the greedy search queue, set the current measured spectrum graph structure as the initial state, and calculate the local editing cost of all unmatched node pairs in the initial state. The local editing cost is obtained by weighted summation of the absolute value of the node frequency deviation and the weight deviation of the corresponding associated edge, forming an initial candidate operation set.

[0159] The single editing operation with the lowest local editing cost is selected from the initial candidate operation set as the current optimal step. If the operation is node insertion or deletion, the node set topology of the measured spectrum is updated, isolated nodes are removed or missing harmonic cluster center frequency nodes are added, and the edge weight connection relationship of the affected area is reset simultaneously.

[0160] If the optimal step selected is the edge weight modification operation, then the weight values ​​of the corresponding edges in the measured spectrum graph are directly corrected according to the target value in the edge weight difference matrix, so that the measured edge weights converge to the edge weights of the reference template. At the same time, the residual energy value generated by this modification is recorded as the basis for subsequent path evaluation.

[0161] An iterative greedy approach is employed, recalculating the local editing costs of the remaining unaligned nodes and edges based on the updated graph structure. The operation with the smallest global cost increment is then selected from the newly generated candidate operation set and added to the optimal graph editing path sequence until all nodes and edges of the measured spectrogram have completed structural mapping with the reference template or reached the preset maximum number of editing steps threshold.

[0162] Redundancy pruning is performed on the generated optimal graph editing path sequence. Consecutive minor adjustment operations on the same node attribute or the same connecting edge are identified and merged, and integrated into a single compound editing action, thereby simplifying path complexity and preserving the main topological transformation features.

[0163] Through the greedy search strategy and iterative optimization process described above, the node mapping relationship and edge weight difference obtained in the previous step are transformed into an ordered optimal graph editing path sequence, which realizes a quantitative description of the structural mismatch process between the measured spectrogram and the reference template, and provides an accurate operation sequence basis for subsequent calculation of the graph editing distance value that reflects the overall degree of topological mismatch.

[0164] For example, in a paper production line with a machine speed of 1200 m / min and a production basis of 80 g / m² cultural paper, the measured spectrum contains 15 harmonic cluster nodes, while the reference template contains 16 nodes. The initial node insertion / deletion penalty factor is 1.0, and the baseline value of the edge weight modification penalty factor is 0.5. After processing with S5.1 and S5.2, it is found that the measured spectrum lacks node number 8, which represents the "second harmonic of the dewatering roller meshing frequency" from the reference template, and the edge weight difference between node number 3 (fundamental frequency) and node number 4 (second harmonic) is 0.35. The first step of the greedy search calculation shows that the local cost of inserting node number 8 is 1.0 (node ​​penalty only), while the cost of correcting the edge weights of nodes 3 and 4 is 0.35 × 0.5 = 0.175. The system prioritizes correcting the edge weights of nodes 3 and 4 and adds them to the path sequence. In the second step, due to the absence of node 8, its three associated edges cannot be matched. The system calculates the total cost of inserting this node and initializing its associated edge weights as 1.0 + 3 × 0.2 (assuming the initial difference of the new edge is small) = 1.6, which is still the smallest compared to other nodes to be processed. Therefore, the node insertion operation is performed. After 12 iterations, all nodes are mapped, and the edge weight differences converge to within 0.05. The final generated optimal graph editing path sequence contains 1 node insertion, 0 node deletions, and 11 edge weight modification operations. This sequence clearly reflects that under the current operating conditions, the main mismatch originates from the slight lack of high-frequency harmonic energy and fluctuations in low-frequency coupling strength, rather than a large-scale structural topological collapse, significantly improving the interpretability of loosening identification.

[0165] S5.4: Based on the optimal graph editing path sequence, perform cumulative calculation of the cost function to combine the preset unit node topology change penalty factor and unit edge weight fluctuation penalty factor to perform weighted summation on each editing operation, thereby generating the original graph editing distance scalar value that reflects the overall degree of topology mismatch.

[0166] The system receives the optimal graph editing path sequence output from step S5.3. This sequence contains the minimum set of node insertion, deletion, and edge weight modification operations required to transform the measured spectrogram structure into a reference spectrogram template. Each independent editing operation unit in the optimal graph editing path sequence is extracted, and each operation unit undergoes type identification and attribute parsing to distinguish between node-level topology change operations and edge-level weight correction operations. For node-level topology change operations, a preset unit node topology change penalty factor library is retrieved, and the corresponding penalty coefficient value is matched according to the operation type. For node insertion operations, a higher penalty weight is assigned to characterize the abnormal occurrence of newly added harmonic clusters; for node deletion operations, an equal or slightly higher penalty weight is assigned to characterize the loss of key feature frequencies; for node position offset correction operations, a dynamic penalty value is calculated based on the frequency deviation. For edge-level weight correction operations, the absolute value of the difference between the measured edge weight and the reference edge weight is extracted from the optimal graph editing path sequence as an index of edge weight fluctuation amplitude. A preset unit edge weight fluctuation penalty factor is retrieved; this factor is used to quantify the degree of influence of coupling strength changes on overall topology stability. The edge weight fluctuation amplitude index is multiplied by the unit edge weight fluctuation penalty factor to generate the local cost value of a single edge editing operation. A graph editing distance cumulative cost function is constructed, defined as a linear weighted sum of the local costs of all editing operations. The original graph editing distance scalar value is calculated. All node editing operations in the optimal graph editing path sequence are traversed, and the penalty cost corresponding to each node operation is accumulated to form a node topology mismatch component. All edge editing operations in the optimal graph editing path sequence are traversed, and the local cost value corresponding to each edge operation is accumulated to form an edge weight coupling mismatch component. The node topology mismatch component and the edge weight coupling mismatch component are algebraically added to generate the original graph editing distance scalar value reflecting the degree of overall structural difference between the measured spectrum and the reference template. Through the above cumulative calculation processing of the cost function, the discrete graph editing operation sequence is transformed into a continuous numerical topology mismatch index, realizing a quantitative characterization of the complex changes in the vibration spectrum structure of ceramic dehydration elements, and providing basic data support for subsequent adaptive normalization under operating conditions.

[0167] For example, under the condition of a paper machine speed of 1200 m / min and a production basis of 80 g / m² for cultural paper, the system obtains a set of measured spectrum diagram structures and corresponding reference spectrum diagram templates. Through planning in step S5.3, the optimal graph editing path sequence is obtained, containing 3 node operations and 5 edge operations. Specifically, the node operations include: fine-tuning the position of one fundamental frequency node (frequency deviation 2 Hz), retaining one second harmonic node (no operation cost), and deleting one high-frequency noise node. In the preset unit node topology change penalty factor, the node position fine-tuning penalty coefficient is 0.5 / Hz, and the node deletion penalty coefficient is 10.0. The edge operations involve weight correction of 5 connecting edges. The absolute values ​​of the differences between the measured edge weights and the reference edge weights are 0.05, 0.12, 0.08, 0.03, and 0.15, respectively, and the preset unit edge weight fluctuation penalty factor Ce is 20.0. Calculate the node cost: the cost of fine-tuning the fundamental frequency node is 0.5 × 2 = 1.0, the cost of deleting the high-frequency noise node is 10.0, and the total node cost is 11.0. Calculate the edge cost: (0.05 + 0.12 + 0.08 + 0.03 + 0.15) × 20.0 = 0.43 × 20.0 = 8.6. The final original graph editing distance scalar value D = 11.0 + 8.6 = 19.6. This value accurately reflects the degree of deviation of the spectral topology from the standard state under the current operating conditions. Compared with the traditional single feature threshold judgment, this method can comprehensively consider the changes in frequency drift and coupling relationship, significantly improving the sensitivity to early features of minor loosening.

[0168] S5.5: Perform adaptive normalization processing based on the original map editing distance scalar value, and use the instantaneous value of the current network vehicle speed and the pressure gradient sequence of the vacuum dehydration zone as dynamic scaling factors to correct the scale of the original distance, thereby outputting the final map editing distance value that eliminates working condition interference.

[0169] The original graph editing distance scalar value output from step S5.4 is received. This value represents the degree of absolute difference between the measured spectrogram structure and the reference template in terms of topology, but it has not yet eliminated the background noise interference and feature scale drift caused by the drastic fluctuations in the paper machine's operating conditions.

[0170] Extract the instantaneous values ​​of the network vehicle speed and the pressure gradient sequence of the vacuum dehydration zone that are synchronously collected at the current moment. Input the above operating condition parameters as dynamic environmental factors into the operating condition adaptive normalization module to construct a scaling factor model that reflects the stability of the current physical field.

[0171] The vehicle speed fluctuation sensitivity factor is calculated based on the instantaneous value of the vehicle speed in the network operation. The degree of deviation of the vehicle speed from the reference value is mapped by the exponential decay function. The higher the vehicle speed or the greater the fluctuation, the more significant the high-frequency modulation component in the vibration signal. A larger normalization weight needs to be assigned to suppress the topological distortion caused by non-loosening.

[0172] The vehicle speed fluctuation sensitivity coefficient is calculated using the following formula: in, For vehicle speed fluctuation sensitivity coefficient, This represents the instantaneous operating speed of the vehicles within the network. σ represents the standard reference speed for this type of paper, and σ is the standard deviation constant of the allowable fluctuation of the speed.

[0173] The pressure stability factor is calculated based on the pressure gradient sequence in the vacuum dehydration zone. A sliding window variance analysis is performed on the pressure gradient sequence to quantify the dynamic fluctuation of the dehydration load. Pressure fluctuations will cause changes in the contact stiffness between the ceramic plate and the scraper, which in turn will cause non-faulty fluctuations in the spectral sideband energy.

[0174] The pressure stability correction factor is calculated using the following formula: in, Var is the pressure stability correction coefficient, k is the pressure sensitivity adjustment constant, and Var is the pressure stability correction coefficient. p This represents the variance of the pressure gradient sequence in the vacuum dehydration zone within a preset time window.

[0175] The vehicle speed fluctuation sensitivity coefficient and the pressure stability correction coefficient are linearly weighted and fused to generate a comprehensive operating condition scaling coefficient. The weight allocation is pre-calibrated based on the contribution of different operating conditions to the spectral topology, ensuring that the consistency of the measurement benchmark can still be maintained under extreme operating conditions such as high speed and low pressure or low speed and high pressure.

[0176] By using the comprehensive working condition scaling factor to perform division normalization on the original map editing distance scalar value, the effect of distance value expansion or contraction caused by drastic changes in working conditions is eliminated, so that the degree of topological mismatch under different working conditions is mapped to the same comparable dimension interval.

[0177] The final image editing distance value is calculated using the following formula: in, To eliminate operating condition interference, the final map editing distance values ​​are... Edit the distance scalar values ​​for the original graph generated in step S5.4.

[0178] The final calculated graph edit distance value is truncated to limit its value to between 0 and 1, preventing numerical overflow due to extreme abnormal conditions and ensuring the stability and validity of the input data for the subsequent fuzzy rule engine.

[0179] By introducing a dynamic scaling mechanism that combines vehicle speed and pressure, the original topological difference data from the previous step is transformed into a standardized distance index with robust operating conditions. This achieves uniformity and stability of the loosening feature identification benchmark under varying paper production environments, significantly reducing the false alarm rate caused by operating condition switching.

[0180] Step S6: Based on the graph editing distance values ​​and combined with the topological anomaly pattern sets defined for slightly loose, moderately loose, and severely loose states, a state inference logic is executed through a fuzzy rule engine. Simultaneously, operating parameters are used to dynamically weight the rule confidence levels to generate a loosening state discrimination result with confidence weights. Specifically, this includes: S6.1: Based on the graph editing distance values ​​and the set of topological anomaly patterns defined for micro-loose, medium-loose, and severely loose, a fuzzy rule engine is constructed, which includes an input membership function, a fuzzy inference rule base, and a defuzzified output interface, to generate a state deduction execution unit with the ability to fuse multi-source heterogeneous data.

[0181] The topological anomaly pattern set is a set of rules used in this invention to describe the graph structure distortion characteristics and constraints between the vibration spectrum structure of ceramic dehydration elements and a healthy reference template under different degrees of loosening (slightly loose, moderately loose, and severely loose). This pattern set defines typical topological distortion characteristics corresponding to each loosening level, including quantitative indicators such as node isolation threshold, edge weight attenuation rate range, and fundamental frequency offset tolerance, and specifies the combination logic between these characteristics. The pattern set provides logical constraints for the fuzzy rule engine, enabling the system to map the measured spectral topological mismatch characteristics into physically meaningful loosening state discrimination results, thereby significantly improving the interpretability and accuracy of the detection results.

[0182] The Topological Anomaly Pattern Set is a structured knowledge base containing pattern definitions for three main loosening levels. Each pattern consists of the following elements: Pattern identifier: A name that uniquely identifies the pattern, such as "M" MICRO (Slightly loose), "M" MEDIUM "(Nakamatsu),"M SEVERE (Seriously loose)

[0183] Node anomaly feature constraints: describe topological distortions at the node level, including: Node isolation threshold: refers to the degree to which the proportion of effective connections between a target harmonic cluster node and its neighboring nodes decreases relative to the theoretical maximum number of connections. For example, in the slightly loose mode, the isolation threshold for the meshing frequency cluster node is set to be greater than 0.7, indicating that the node has lost more than 70% of its normal connections; in the moderately loose mode, the isolation threshold for at least two harmonic cluster nodes is greater than 0.5; and in the severely loose mode, the isolation threshold for the fundamental frequency node is greater than 0.8. Fundamental frequency offset tolerance: refers to the absolute offset (unit: Hz) of the center frequency of the fundamental frequency node relative to the healthy reference value. In slightly loose mode, the offset should not exceed 2Hz; in moderately loose mode, the offset should be between 2Hz and 5Hz; and in severely loose mode, the offset should be greater than 5Hz. The offset tolerance for other harmonic clusters (such as harmonics and meshing frequencies) can be set proportionally to the fundamental frequency.

[0184] In addition, constraints on frequency offsets of other nodes or node missing / redundancy may also be included.

[0185] Edge anomaly feature constraints: describe topological distortions at the edge level, including: Edge weight decay rate range: The percentage decrease in measured edge weight (cross-correlation coefficient) relative to the reference edge weight. In the slightly loose mode, the edge weight decay rate is typically between 20% and 50%; in the moderately loose mode, it is between 50% and 80%; and in the severely loose mode, it is greater than 80%. Marginal weight volatility variance: used to quantify the stability of margin weights within a continuous time window. The Zhongsong model often requires the marginal weight volatility variance to be greater than 0.1. Critical edge breakage count: The number of breaks in important connections (such as between the fundamental frequency and the harmonics, or between the meshing frequency and the sideband). In severely loose mode, the critical edge breakage count is usually greater than 3.

[0186] Combinational logic constraints: Combine node anomalies and edge anomalies according to logical relationships, usually using an "AND" operation. For example, the micro-loose mode is defined as follows: the isolation degree of the meshing frequency cluster nodes is greater than 0.7, and the edge weight attenuation rate of at least two associated edges is between 20% and 50%, and the fundamental frequency offset does not exceed 2Hz.

[0187] Confidence weight: The prior confidence of each pattern in historical failure statistics, used as the initial assignment of rule strength during fuzzy inference.

[0188] The topology anomaly pattern set was constructed by combining offline fault simulation with on-site historical data mining. Fault Simulation and Data Acquisition: On a test bench or actual production line, the slight, moderate, and severe loosening states of the ceramic dehydration element are artificially simulated, and vibration signals and operating parameters for the corresponding states are collected. Short-time Fourier transform and spectrum structure construction are performed on the vibration signals under each fault state to obtain the measured spectrum structure, and a health reference template under the same operating condition is obtained simultaneously.

[0189] Feature extraction and statistical modeling: By comparing the fault state with the health reference template, the difference indicators of each node and edge are calculated, including node isolation degree, fundamental frequency offset, edge weight attenuation rate, etc. Statistical analysis is performed on multiple sets of sample data under the same loosening level to determine the typical value range and probability distribution of each indicator, and then a reasonable threshold interval is set (for example, taking ±1.5 times the standard deviation of the mean as the boundary).

[0190] Rule induction and validation: Decision trees or association rule-based machine learning methods (such as the Apriori algorithm) are used to automatically mine association patterns of node and edge anomalies from labeled data, forming combinatorial logical constraints. Domain experts review and fine-tune the automatically generated rules, eliminating physically unreasonable combinations to ensure the engineering credibility of the pattern set. Independent test sets are used to validate the detection rate and false positive rate of the pattern set, and thresholds are adjusted to achieve optimal performance.

[0191] Knowledge solidification and version management: The finalized pattern set is stored in non-volatile memory as structured data (such as JSON or XML format) and bound to the fuzzy rule engine. Version numbers are established to support incremental updates based on long-term operational feedback.

[0192] The topological anomaly pattern set provides the fuzzy rule engine with precise quantitative discrimination boundaries, ensuring the engineering interpretability and reliability of loose state identification.

[0193] The system receives the final graph editing distance value after adaptive normalization processing based on operating conditions. This value characterizes the relative topological mismatch between the measured spectrogram structure and the reference template, serving as the core input variable for the fuzzy rule engine. Simultaneously, a pre-set set of topological anomaly patterns is loaded. This set defines the graph structure distortion characteristic constraints corresponding to three loosening levels: slightly loose, moderately loose, and severely loose. These constraints include node isolation thresholds, edge weight attenuation rate ranges, and fundamental frequency offset tolerances.

[0194] A membership function library for input variables is constructed, and a three-segment fuzzy set is designed for the graph edit distance values, corresponding to the states of "normal," "slightly abnormal," and "severely abnormal." A Gaussian membership function is used to model the "normal" state, with its center point set to zero and the standard deviation determined based on the statistical distribution of historical normal operation data to ensure high confidence even under minor noise interference. For the "slightly abnormal" and "severely abnormal" states, a combination of Z-shaped and S-shaped membership functions is used. By setting overlapping regions, a smooth transition between states is achieved, avoiding decision jitter caused by sudden threshold changes.

[0195] A fuzzy inference rule base based on topological anomaly patterns is established, formalizing the mapping relationship between the fuzzy linguistic variable of graph edit distance and the loosening level. The antecedent of each rule includes the fuzzy value of the graph edit distance and the matching degree of specific topological features, while the consequent is the preliminary determination of the loosening level. For example, when the graph edit distance is "slightly anomaly" and the isolation degree of the meshing frequency cluster nodes exceeds a preset threshold, the "slightly loose" rule is triggered; when the graph edit distance is "severely anomaly" and the fundamental frequency node undergoes significant shift accompanied by the breakage of multiple critical edges, the "severely loose" rule is triggered. Each rule is assigned an initial confidence weight, reflecting the typicality of the topological pattern under a specific fault mechanism.

[0196] A defuzzification output interface is configured, employing the centroid method to transform the fuzzy set of loosening levels generated by fuzzy inference into a deterministic numerical index. This interface receives the trigger intensity of each loosening level from the fuzzy rule engine and calculates the final loosening state judgment value through weighted averaging. Simultaneously, the interface reserves a channel for inputting operating parameters, which is used in subsequent steps to dynamically adjust the rule confidence level based on paper type, machine speed, and pressure gradient, ensuring that the output results can adapt to changing production environments.

[0197] Through the above construction process, discrete graph editing distance values ​​and complex topological anomaly patterns are transformed into state inference execution units with the ability to fuse multi-source heterogeneous data. This achieves an interpretable mapping from quantitative topological differences to qualitative loosening states, providing a standardized logical framework for subsequent adaptive calibration combined with operating parameters.

[0198] S6.2: The state deduction execution unit is used to fuzzify the graph editing distance value and map it into a fuzzy linguistic variable that reflects the degree of topological mismatch, so as to generate a fuzzy input vector that characterizes the difference level between the current spectrogram structure and the reference template structure.

[0199] The final graph editing distance value for eliminating operating condition interference, output from step S5, is received. This value serves as a core quantitative indicator characterizing the degree of difference between the measured spectrum topology and the reference template structure, and is directly input into the fuzzification interface of the state deduction execution unit.

[0200] Based on the pre-configured fuzzy rule engine, the domain range of the graph edit distance value is defined as [0, D]. max ], where D max This is the maximum permissible topology mismatch threshold obtained based on historical fault data statistics, used to define the boundary conditions for a severely loose state.

[0201] A family of triangle membership functions is constructed for graph editing distance input, mapping continuous numerical distances to four fuzzy linguistic variable sets: "normal", "slightly loose", "moderately loose" and "severely loose", in order to achieve a semantic description of the degree of topological mismatch.

[0202] The peak of the "normal" membership function is set at the zero point, and its support set covers the interval from 0 to the first threshold, reflecting the state characteristics of the spectrum structure being highly consistent with the reference template and without significant topological changes.

[0203] The membership function of "slightly loose" is set as a symmetrical triangular distribution, with its center point corresponding to slight structural node offsets or edge weight fluctuations. The support set has a pre-defined overlapping area with the "normal" and "medium loose" sets to accommodate minor uncertainties caused by operating condition fluctuations.

[0204] The membership function of "Zhongsong" is shifted towards higher distance values, and its peak value corresponds to typical harmonic cluster decoupling or secondary sideband energy anomalous enhancement phenomenon, and the support set covers a moderate range of topological distortion.

[0205] The membership function of "severely loose" is set at the high end of the universe of discourse, with its starting point adjacent to the tail of the "medium loose" set. The peak value corresponds to the extreme case of a large drift of the fundamental frequency node or the breakage of multiple key connection edges, reflecting that the equipment is in a high-risk operating state.

[0206] Iterate through all defined fuzzy linguistic variables, calculate the membership value corresponding to the current graph edit distance value, and generate a multi-dimensional vector containing the confidence level of each state.

[0207] The calculated membership vector is normalized and verified to ensure that the sum of the membership degrees of all fuzzy sets logically conforms to the probability distribution constraints, thus eliminating numerical overflow anomalies caused by incorrect parameter configuration.

[0208] The normalized membership vector is encapsulated into a standardized fuzzy input vector, which fully represents the probability distribution of the deviation of the current spectral topology from the healthy baseline.

[0209] Through the above-mentioned triangle membership function mapping and normalization process, the single scalar graph edit distance value obtained in the previous step is transformed into a fuzzy input vector reflecting the possibility of loosening at multiple levels. This realizes the transformation from precise numerical values ​​to fuzzy semantic space, providing an input basis with uncertainty and fault tolerance for subsequent fuzzy inference combined with working condition parameters.

[0210] S6.3: Based on the fuzzy input vector and combined with the logical constraints corresponding to the slightly loose, moderately loose, and severely loose conditions defined in the topological anomaly pattern set, fuzzy inference operations are performed through the fuzzy rule engine to generate a preliminary fuzzy set of looseness levels and the corresponding initial trigger strength.

[0211] The fuzzy rule engine is the core inference component in this invention, used to combine quantitative indicators of spectral topology mismatch (graph edit distance, node isolation, edge weight attenuation rate, fundamental frequency offset, etc.) with expert knowledge from the topology anomaly pattern set to deduce the loosening state (slightly loose, moderately loose, severely loose) of ceramic dehydration elements. Based on fuzzy set theory and fuzzy inference mechanisms, this engine can handle the uncertainty and nonlinear relationships of the input quantities, outputting loosening discrimination results with confidence weights. The fuzzy rule engine consists of three parts: an input membership function library, a fuzzy inference rule library, and a defuzzified output interface. Through this engine, an interpretable and robust mapping from precise topology difference values ​​to loosening levels with physical semantics is achieved, significantly enhancing the system's adaptability under complex operating conditions.

[0212] The fuzzy rule engine consists of the following three core modules cascaded together: The input membership function library maps each input variable (e.g., edit distance D, node isolation I, edge weight attenuation rate R, fundamental frequency offset Δf, etc.) from precise numerical values ​​to membership vectors of fuzzy linguistic variables. Typically, three or more fuzzy sets (e.g., "small," "medium," "large," or "normal," "slightly abnormal," "severely abnormal") are defined for each input variable, using triangular, trapezoidal, or Gaussian membership functions. Membership function parameters (center point, width, inflection point) are calibrated offline based on historical normal operation data and fault data distribution.

[0213] The fuzzy inference rule base stores a set of expert rules expressed in "IF-THEN" format. Each rule's antecedent is a fuzzy proposition about the input variables (e.g., "graph edit distance is 'medium' and node isolation is 'high'"), and its consequent is a fuzzy proposition about the output looseness level (e.g., "looseness level is 'medium-loose'"). The rule base is built based on logical constraints from a set of topology anomaly patterns, combined with the experience of field engineers. Each rule is assigned an initial confidence weight reflecting its reliability in historical failure cases. Mamdani-type fuzzy inference is used during inference, calculating the premise satisfaction degree for each rule (usually using a minimum operation), and truncating or scaling the output fuzzy set of the consequent.

[0214] The defuzzification output interface converts the inference-derived fuzzy set (covering the comprehensive membership distribution of three levels: slightly loose, moderately loose, and severely loose) into a definite numerical index or discrete level identifier. Common methods include the centroid method or the maximum membership method. The output interface also receives operating condition parameters (paper type, vehicle speed, pressure gradient) to dynamically weight and correct the rule confidence level, achieving adaptive calibration based on operating conditions. The final output is a looseness state discrimination result with confidence weights (e.g., "moderately loose, confidence level 0.85").

[0215] The fuzzy rule engine is built using a strategy of "offline calibration + online adaptation": Input variable selection and data acquisition: Determine the input variables involved in the inference: final graph editing distance D (after working condition normalization), node isolation degree, edge weight attenuation rate, fundamental frequency offset, etc. Under healthy conditions and various degrees of loosening, collect a large number of vibration signals and calculate the above input variables, while recording the actual loosening level (label).

[0216] Membership function design: For each input variable, calculate its probability distribution under different loosening levels. Use fuzzy C-means clustering or expert experience to divide the number and intervals of fuzzy sets. For example, divide the graph edit distance into three fuzzy sets: "Normal" (0~0.25), "Slightly Abnormal" (0.15~0.55), and "Severely Abnormal" (0.45~1.0). Select a triangular or trapezoidal membership function, with parameters adjusted through grid search or manual adjustment to ensure appropriate overlap near the threshold (generally 20%~40%) for a smooth transition.

[0217] Rule Extraction and Validation: Initial rules are directly generated based on logical constraints (node ​​isolation threshold, edge weight decay rate range, fundamental frequency offset tolerance) in the topological anomaly pattern set. For example: IF Graph edit distance IS “Slight anomaly” AND Meshing frequency cluster node isolation IS “High” AND Edge weight decay rate IS “Medium” THEN Looseness level IS “Slightly loose”. Rules are supplemented from labeled data using decision trees or association rule mining algorithms. Domain experts are invited to review and remove redundant or contradictory rules, and an initial confidence weight is set for each rule (e.g., slightly loose rule weight 0.8, moderately loose rule weight 0.9, severely loose rule weight 0.95).

[0218] Defuzzification method selection and calibration: The centroid method is adopted as the default defuzzification strategy, and the centroid coordinates of the output fuzzy set are used as the numerical index of the loosening state. The numerical index is mapped to the discrete level: [0, 0.3) is defined as normal / slightly loose, [0.3, 0.6) as moderately loose, and [0.6, 1.0] as severely loose, and a hysteresis interval is set to avoid frequent state jumps.

[0219] Online adaptive weighting mechanism: An environmental fluctuation coefficient (synthesized from paper stiffness coefficient, vehicle speed fluctuation rate, and pressure impact intensity) is introduced to dynamically correct the rule confidence level. When environmental fluctuations are large, the output confidence level of all rules is reduced to avoid misjudgment; when environmental fluctuations are stable, the original confidence level is restored. The corrected confidence level is used for weighted calculation during defuzzification, achieving adaptive loosening detection based on environmental conditions.

[0220] Deployment and Storage: Membership function parameters, rule tables, and defuzzification coefficients are stored in non-volatile memory. The engine is embedded in the online monitoring program as a function library, and inference output is completed within milliseconds each time new graph edit distances and topological features are received.

[0221] Through the above-described structured and standardized construction, the fuzzy rule engine provides interpretable, robust, and condition-adaptive reasoning capabilities for detecting loosening of ceramic dehydration components, and is one of the core decision-making components of this invention.

[0222] The fuzzy input vector representing the degree of topological mismatch, which is output from step S6.2, is received. This vector contains the membership degrees of linguistic variables after numerical mapping of graph editing distance, and serves as the initial input data for the fuzzy inference engine.

[0223] The system calls a pre-set fuzzy rule base to retrieve logical constraints defined for three loosening levels: slightly loose, moderately loose, and severely loose. These logical constraints consist of a set of topological anomaly patterns, such as node isolation, edge weight attenuation rate, and fundamental frequency offset.

[0224] Each component in the fuzzy input vector is matched with the antecedent part in the rule base, and the premise satisfaction degree of each fuzzy rule is calculated. That is, the minimum membership degree or product value of each input variable in the corresponding fuzzy set is determined by taking the minimum or multiplying operation.

[0225] Based on the premise satisfaction, the output fuzzy set of each rule's consequent part is truncated or scaled to generate an activated rule output subset. Among them, the slightly loose rule corresponds to the low-graph edit distance and slight perturbation of local edge weights, the medium loose rule corresponds to the medium-graph edit distance and decoupling of specific harmonic cluster nodes, and the severely loose rule corresponds to the high-graph edit distance and global topology collapse.

[0226] The output subsets of all activated rules are combined into a comprehensive fuzzy set of loosening levels, which covers the membership distribution of all possible states from normal to severe loosening.

[0227] Calculate the maximum membership value or centroid position of each state level in the integrated fuzzy set, and define it as the initial trigger strength of each loosening level in that state. This is used to characterize the matching confidence level between the current spectral topology and each loosening mode set.

[0228] Through the aforementioned fuzzy inference mechanism, the single graph editing distance scalar is transformed into a multi-dimensional fuzzy set of loosening levels and the corresponding initial trigger intensity, thereby realizing a refined semantic description and preliminary quantitative assessment of the loosening state of ceramic dehydration components, providing a basic decision-making basis for subsequent adaptive weighted calculation under working conditions.

[0229] S6.4: Calculate the operating environment fluctuation coefficient based on the paper type code, the instantaneous value of the wire section running speed and the pressure gradient sequence of the vacuum dehydration zone, and use the operating environment fluctuation coefficient to dynamically weight and correct the initial trigger intensity to generate a rule confidence weight sequence that has been adaptively calibrated for operating conditions.

[0230] The process involves acquiring a fuzzy set of initial loosening levels and initial triggering strength, while simultaneously reading a multidimensional working condition parameter vector containing paper type codes, instantaneous values ​​of the wire mesh operating speed, and pressure gradient sequences in the vacuum dehydration zone. The paper type codes are discretized and mapped, then converted into paper type stiffness coefficients based on a paper type physical property database, reflecting the dynamic load of different paper types on ceramic components. Speed ​​fluctuation rate is calculated based on instantaneous speed values, and a sliding window is used to statistically analyze the ratio of the speed standard deviation to the mean, quantifying dynamic instability. Time-domain differentiation is performed on the pressure gradient sequence, extracting the maximum absolute value of the pressure change rate as the pressure impact strength index. A multidimensional fusion calculation model for the working condition environment fluctuation coefficient is constructed, combining the paper type stiffness coefficient, speed fluctuation rate, and pressure impact strength in a weighted linear combination, with weights determined by regression analysis of historical fault data. The initial triggering strength is dynamically weighted and corrected using the working condition environment fluctuation coefficient; when the coefficient exceeds a stability threshold, the fuzzy rule confidence weight is reduced. The rule confidence weights corresponding to each loosening level are normalized to ensure the sum of confidence values ​​is 1, forming a probability distribution sequence. By dynamically weighting based on operating conditions, the initial fuzzy inference results are transformed into a sequence of rule-based confidence weights that have been suppressed by environmental noise and compensated for operating condition interference. This enables adaptive adjustment of the loosening identification confidence under complex operating conditions, reduces the misjudgment rate caused by operating condition drift, and improves the robustness of the system.

[0231] S6.5: Based on the rule confidence weight sequence, perform defuzzification processing on the loosening level fuzzy set, transform the fuzzy inference result into a definite numerical index, so as to generate a loosening state discrimination result with confidence weight and complete the final mapping from topological difference to equipment health status.

[0232] Step S7: Continuously record the graph structure evolution trajectory corresponding to the loosening state discrimination result. If three or more sets of spectrograms with similar mismatch patterns appear consecutively at the same location, trigger a local spectrum resampling command and start the high-resolution order tracking analysis process. Specifically, this includes: S7.1: The loosening state discrimination result with confidence weight generated at the current moment and its corresponding measured spectrum graph structure are serialized and encapsulated to generate a graph structure evolution trajectory data unit containing timestamp, graph edit distance value and topological anomaly pattern identifier.

[0233] S7.2: Construct a sliding time window sequence based on the graph structure evolution trajectory data unit, and perform temporal alignment and feature extraction operations on the historical graph structure evolution trajectory data units within the window to generate a topological mismatch pattern sequence arranged in chronological order.

[0234] S7.3: Perform consistency comparison calculation on adjacent elements in the topological mismatch pattern sequence to identify similar mismatch pattern clusters that appear consecutively and have the same topological anomaly pattern identifier, and count the number of consecutive occurrences.

[0235] The system receives a sequence of topological mismatch patterns, containing graph structure evolution data units for each time window. Each unit has an anomaly pattern identifier, graph edit distance, and operating condition confidence weight. Feature vectors are extracted from adjacent units: node center frequency deviation, edge weight distribution histogram, and the top k features of the graph Laplacian are extracted to construct a high-dimensional feature vector. Cosine similarity is used to calculate the topological consistency of adjacent windows, obtaining the original similarity. Dynamic correction of the operating condition confidence weight is introduced: the fluctuation coefficients of the current and previous operating conditions are obtained, and the average confidence factor is calculated as a penalty term. The similarity threshold is increased during high fluctuations and maintained with high sensitivity during stable periods. A dynamic similarity threshold is set; if the corrected similarity is greater than the threshold and the topological anomaly pattern identifiers are completely identical, the pattern is considered continuous and classified into the same pattern cluster. Adjacent elements are traversed; a counter is incremented if the pattern is continuous, otherwise it is reset, and the number of consecutive occurrences is output. Through weighted cosine similarity comparison and cumulative counting, the discrete pattern sequence is transformed into a continuous occurrence index, filtering transient interference, locking persistent loosening features, and reducing the false trigger rate.

[0236] S7.4: Perform logical judgment processing based on the number of consecutive occurrences and the preset threshold. If it is determined that the number of consecutive occurrences of similar mismatch pattern clusters at the same position reaches three or more, a local spectrum resampling trigger command is generated; otherwise, the current monitoring state is maintained.

[0237] The system acquires the statistical values ​​of consecutive occurrences of similar mismatch pattern clusters in the topological mismatch pattern sequence and a preset loosening confirmation threshold parameter as input data for logical judgment. The consecutive occurrence count is compared with the loosening confirmation threshold to construct state maintenance and triggering decision logic. If the consecutive occurrence count is less than the threshold, a state maintenance instruction is executed, maintaining the current sampling frequency and processing flow unchanged, and marking the current graph structure evolution trajectory data unit as a transient state and storing it in a cache queue to filter out occasional spectral distortions. If the consecutive occurrence count reaches or exceeds the threshold, the topological anomaly is considered persistent and stable, confirming it as a genuine loosening sign. A local spectrum resampling trigger instruction is generated, containing the target device ID, the anomaly start timestamp, and the frequency range requiring focus, guiding subsequent high-resolution analysis. Logical judgment transforms the pattern matching statistics into control command signals, achieving a precise transition from probabilistic matching to deterministic fault triggering, suppressing false alarms caused by brief pressure fluctuations or paper type switching, and improving the robustness and reliability of the loosening detection system.

[0238] S7.5: In response to the local spectrum resampling trigger command, start the high-resolution order tracking analysis process, perform variable speed synchronous resampling and order spectrum refinement processing on the original vibration signal of the target area, so as to generate high-resolution order tracking analysis results for enhancing the loosening positioning accuracy.

[0239] Upon receiving a local spectrum resampling trigger command, the system extracts the target ceramic dehydration element location identifier, the instantaneous value sequence of the current network operating speed, and the time window index as initial input conditions. Based on the time window index, a time-domain data segment containing a complete rotation cycle is extracted from the original vibration signal buffer. Simultaneously, encoder pulse counts or speed sensor data are read to construct a time-angle domain mapping dataset. Angular domain resampling is used to perform equal-angle interpolation on the non-uniformly sampled time-domain vibration signal. A cubic spline function is used to map the time axis amplitude points to uniform points on the angle axis, eliminating spectral ambiguity caused by speed fluctuations and generating an angular domain synchronous vibration signal sequence. The instantaneous rotation frequency is calculated based on the network operating speed to determine the number of sampling points per revolution, ensuring a constant sampling rate for the angular domain signal and converting the non-stationary time-domain signal into a stationary angular domain signal. A fast Fourier transform is performed on the angular domain synchronous signal to obtain the order domain spectrum, with the horizontal axis representing the order multiple and the vertical axis representing the amplitude energy, forming an initial order spectrum. A Blackman window function is applied to suppress sidelobe leakage, improving resolution and amplitude accuracy, generating windowed order spectrum data. Based on a predefined set of loosening fault characteristic orders, including the fundamental frequency order, harmonic order, dewatering roller meshing order, and its sideband order, characteristic peaks are located in the order spectrum, and the amplitude, phase, and bandwidth parameters of each order are extracted to construct high-order feature vectors. An order slicing refinement technique is introduced, using zero-fill spread spectrum and FFT interpolation to refine the frequency bands near the characteristic orders, accurately estimating the center frequency and peak amplitude, and generating high-resolution order tracking analysis results. Through variable-speed synchronous resampling and order spectrum refinement, local monitoring requirements are transformed into high-precision order domain feature data, enabling accurate extraction and location of loosening fault characteristics under variable-speed conditions, enhancing the reliability of discrimination and anti-interference capabilities.

[0240] Step S8: Update the current loosening status judgment result according to the enhanced positioning information output by the high-resolution order tracking analysis process, and store the final loosening level identifier and working condition association log into the historical database to complete the detection loop. Specifically, this includes: S8.1: Obtain the enhanced positioning information output by the high-resolution order tracking analysis process and the loosening state discrimination result with confidence weight generated in the previous steps. Perform weighted fusion processing on the enhanced positioning information and the loosening state discrimination result to generate a corrected comprehensive judgment value of loosening state.

[0241] The process acquires the enhanced positioning information data stream output from the high-resolution order tracking analysis workflow. This enhanced positioning information includes the characteristic order amplitude, phase stability index, and local resonance band energy density of the target loosened component. Simultaneously, it retrieves the loosening state discrimination result with confidence weights generated in the preceding step S6. This discrimination result includes the initial loosening level identifier calculated based on graph editing distance and the corresponding topological mismatch confidence value. The enhanced positioning information undergoes physical meaning analysis and dimensional standardization, extracting the characteristic order amplitude normalization coefficient, phase jitter variance, and resonance band energy concentration index to construct a high-dimensional loosening feature vector. A pre-defined weighted fusion model maps the high-dimensional loosening feature vector to a loosening intensity correction factor. This correction factor quantifies the compensation effect of high-frequency order features on the low-frequency spectral topological mismatch criterion, eliminating the limitations of single-frequency domain analysis under complex operating conditions. The baseline score corresponding to the initial loosening level identifier is read, and a dynamic weight coefficient is calculated based on the topological mismatch confidence value. This dynamic weight coefficient reflects the reliability of the spectral topology comparison under the current operating conditions. Based on dynamic weighting coefficients and loosening intensity correction factors, a multi-source data weighted fusion operation is performed. Through a combination of linear combination and nonlinear correction, a corrected comprehensive judgment value for the loosening state is generated. By fusing high-resolution order information and low-frequency spectral topology discrimination results, the previous step is transformed into a more robust comprehensive judgment value for the loosening state, achieving multi-dimensional and accurate quantification and misjudgment suppression of the loosening state of ceramic dehydration elements.

[0242] S8.2: Based on the corrected comprehensive judgment value of the loosening state, perform quantitative grading processing using the preset loosening level mapping rule to convert the continuous judgment value into a discrete final loosening level identifier, so as to clarify the current specific loosening degree of the ceramic dehydration element.

[0243] The system receives a corrected comprehensive loosening status judgment value, which is a continuous scalar. Based on a preset loosening level mapping rule base, which defines threshold ranges and fuzzy boundary transition zones for three levels—slight loosening, moderate loosening, and severe loosening—based on historical faults and expert experience, the judgment value undergoes interval assignment verification: if it falls within a clear interval, the level is directly determined; if it falls within the fuzzy transition zone between two levels, linear interpolation or a membership function is used to calculate the probability weights of each level to achieve a smooth transition. A hysteresis comparison logic is introduced: if the currently calculated highest membership level differs from the previous level and the membership difference is less than a preset confidence switching threshold, the previous level identifier remains unchanged. When the level switching condition is met, the level corresponding to the maximum membership value is selected as the final loosening level identifier and bound with a confidence weight. Through quantization grading and hysteresis stabilization processing, continuous mismatch values ​​are transformed into discrete loosening level identifiers, eliminating false alarms caused by signal noise or operating condition fluctuations.

[0244] S8.3: Obtain the paper type code, the instantaneous value of the wire mesh running speed, and the pressure gradient sequence of the vacuum dehydration zone at the current moment as the original operating condition parameters. Based on the timestamp alignment mechanism, associate and encapsulate the original operating condition parameters with the final loosening level identifier to generate an operating condition association log containing complete context information.

[0245] S8.4: Based on the operating condition associated log, use the industrial real-time database write interface to perform persistent storage operation, store the operating condition associated log into the historical database to form a traceable detection record and complete the detection closed loop.

[0246] For those skilled in the art, various other corresponding changes and modifications can be made based on the technical solutions and concepts described above, and all such changes and modifications should fall within the protection scope of the claims of this invention.

[0247] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this application pertains. The terms “first,” “second,” “third,” and similar terms used in this patent application specification and claims do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms “an” or “a” and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms “comprising” or “including” and similar terms mean that the elements or objects preceding “comprising” or “including” encompass the elements or objects listed following “comprising” or “including” and their equivalents, and do not exclude other elements or objects. The “multiple” mentioned in the embodiments of this application refers to two or more. A and / or B indicate three possibilities: A; B; and A and B.

[0248] The above description is merely an exemplary embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and such modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for detecting loosening of ceramic dewatering elements used in papermaking based on vibration spectrum analysis, specifically including: S1: Obtain the original vibration signal and three key operating parameters of the ceramic dehydration element, and generate a composite monitoring dataset; S2: Perform a short-time Fourier transform on the time-domain waveforms in the composite monitoring dataset to convert the time-domain vibration signal into an initial spectrum. S3: Based on three types of key operating condition parameters, match the corresponding reference spectrum template from the operating condition spectrum structure knowledge base; S4: Cluster the energy density distribution of the initial spectrum to generate measured nodes, calculate the dynamic coupling strength between clusters to generate weighted edges, and construct a measured spectrum structure isomorphic to the reference spectrum template; S5: Perform topological comparison calculations between the measured spectrum structure and the reference spectrum template, quantify the degree of structural difference between the two, and output the graph editing distance value; S6: Based on graph editing distance values ​​and combined with topological anomaly pattern sets defined for slightly loose, moderately loose and severely loose, the state inference logic is executed through a fuzzy rule engine. The rule confidence is dynamically weighted using working condition parameters to generate loosening state discrimination results. S7: Continuously record the graph structure evolution trajectory corresponding to the loosening state discrimination result. If three or more sets of spectrum graphs with similar mismatch patterns appear consecutively at the same position, a local spectrum resampling command is triggered and a high-resolution order tracking analysis process is started. S8: Update the current loosening status judgment result based on the enhanced positioning information output by the high-resolution order tracking analysis process, and store the final loosening level identifier and working condition association log into the historical database.

2. The method for detecting looseness of ceramic dewatering elements for papermaking based on vibration spectrum analysis according to claim 1, characterized in that, The three key operating parameters include paper type code, instantaneous value of wire mesh running speed, and pressure gradient sequence of vacuum dehydration zone.

3. The method for detecting looseness of ceramic dewatering elements for papermaking based on vibration spectrum analysis according to claim 1, characterized in that, The composite monitoring dataset includes time-domain waveforms and operating condition labels.

4. The method for detecting looseness of ceramic dewatering elements for papermaking based on vibration spectrum analysis according to claim 1, characterized in that, The initial spectrum characterizes the frequency energy distribution.

5. The method for detecting looseness of ceramic dewatering elements for papermaking based on vibration spectrum analysis according to claim 1, characterized in that, The reference spectrum template is a graph structure where nodes represent the center frequencies of harmonic clusters and edges represent the amplitude ratio and phase difference stability.

6. The method for detecting looseness of ceramic dewatering elements for papermaking based on vibration spectrum analysis according to claim 1, characterized in that, The operating condition spectrum structure knowledge base includes a hash mapping table, a set of reference operating condition feature vectors, a reference spectrum template table, and a version and verification table.

7. The method for detecting looseness of ceramic dewatering elements for papermaking based on vibration spectrum analysis according to claim 1, characterized in that, The set of topological anomaly patterns includes pattern identifiers, node anomaly feature constraints, edge anomaly feature constraints, combinational logic constraints, and confidence weights.

8. The method for detecting looseness of ceramic dewatering elements for papermaking based on vibration spectrum analysis according to claim 1, characterized in that, The fuzzy rule engine includes an input membership function library, a fuzzy inference rule library, and a defuzzification output interface.

9. The method for detecting looseness of ceramic dewatering elements for papermaking based on vibration spectrum analysis according to claim 2, characterized in that, S3 specifically includes: The paper type encoding, the instantaneous value of the wire section running speed and the pressure gradient sequence of the vacuum dewatering zone are processed by multi-dimensional vector splicing to generate a composite working condition feature vector containing information on the current operating status of the paper machine; Based on the composite operating condition feature vector, the candidate reference spectrum template index that best matches the current operating state is located and extracted from the pre-set operating condition spectrum structure knowledge base; The corresponding graph structure data definition is retrieved using the candidate reference spectrum template index to parse out the original reference spectrum template containing the set of harmonic cluster center frequency nodes and the set of amplitude ratio and phase difference stability edges; Based on the instantaneous value of the network's operating vehicle speed, the set of harmonic cluster center frequency nodes in the original reference spectrum template is subjected to frequency scaling adaptive correction processing to generate a frequency calibration reference spectrum template that eliminates the influence of vehicle speed fluctuations; Based on the pressure gradient sequence in the vacuum dehydration zone, the amplitude ratio and phase difference stability edge set in the frequency calibration reference spectrum template are dynamically reconstructed with weights to output the final reference spectrum template adapted to the current vacuum dehydration condition.

10. The method for detecting looseness of ceramic dewatering elements for papermaking based on vibration spectrum analysis according to claim 1, characterized in that, S4 specifically includes: Based on the energy density distribution data of the initial spectrum, local energy maxima are identified and frequency-assigned regions are divided, thereby generating a set of measured nodes that characterize the central frequency position of each harmonic cluster. Based on the frequency boundary range of each node in the measured node set, the corresponding time-frequency energy segment sequence is extracted from the initial spectrum to construct the inter-cluster signal pair to be processed for subsequent correlation analysis; Sliding window cross-correlation analysis is performed on the inter-cluster signal pairs to be processed to quantify the time lag characteristics and waveform similarity between clusters of different frequencies, thereby generating the original cross-correlation matrix characterizing the dynamic coupling strength between clusters; The original cross-correlation matrix is ​​numerically transformed using a normalized mapping function to eliminate differences in magnitude and retain information on relative correlation strength, thereby generating standardized weighted edge weight data. Based on the measured node set as vertices and the weighted edge weights as connections, a graph structure assembly operation is performed to construct a measured spectrum graph structure with the same topological dimension as the reference spectrum graph template.

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