A coal preparation plant equipment fault detection method based on a graph domain and an electronic device

Abstract

The application discloses a coal preparation plant equipment fault detection method based on a graph domain and electronic equipment, and belongs to the technical field of equipment fault detection. The method comprises the following steps: pre-processing multi-source operation data to obtain a characteristic vector; mapping the characteristic vector into a device state symbol sequence based on symbolic dynamic filtering, and constructing a probability finite state automaton transition matrix; constructing a device operation graph model; extracting a graph residual error and a graph wavelet decomposition component; and matching the graph wavelet decomposition component with a fault reference feature to determine the maximum similarity. The application solves the technical problem that the coal preparation plant washing capacity, coal quality, start-stop state and production system can cause normal data distribution drift. The application is used for coal preparation plant equipment fault detection. The application converts continuous time series data into a limited symbol state and a state transition matrix through symbolic dynamic filtering, reduces the influence of sensor noise, coal quality fluctuation and washing capacity change on fault discrimination, and improves the robustness under non-stationary working conditions.

Description

Technical Field

[0001] This invention belongs to the field of equipment fault detection technology, specifically relating to a method and electronic equipment for fault detection in coal preparation plants based on a graph domain. Background Technology

[0002] Coal preparation plants typically involve continuous processes such as crushing, screening, separation, media circulation, dewatering, and conveying. There are clear upstream and downstream coupling relationships between equipment such as crushers, vibrating screens, jigs, heavy media hydrocyclones, media circulation pumps, centrifugal dewatering machines, scraper conveyors, and belt conveyors: fluctuations in upstream feed volume and coal quality affect the load on downstream equipment; fluctuations in media density and flow rate alter the separation effect; and local equipment failures can propagate to adjacent equipment through material flow, media flow, and energy flow. Therefore, relying solely on a single vibration or current threshold for a single piece of equipment is prone to missed alarms, false alarms, or inaccurate fault location under conditions of fluctuating operating conditions, noise disturbances, and multi-equipment coupling.

[0003] Traditional fault diagnosis methods primarily extract features from single-channel signals in the time domain, frequency domain, or time-frequency domain. For example, they extract root mean square, kurtosis, and envelope spectrum peak values ​​from vibration signals, current harmonics from current signals, and fluctuation amplitude from flow and pressure signals. While these methods can reflect the status of local equipment, they struggle to represent the complex process topology, physical conservation relationships, and irregular connections between multiple sensor sources in coal preparation plants.

[0004] Graph signal processing can represent equipment, sensors, or process elements as graph nodes, and process connections, material transfer, media circulation, signal similarity, and state transition relationships as edge weights. It can then analyze signal variations in the global structure and local branches within the graph domain. Low-frequency components in the graph domain typically reflect globally consistent changes or overall load variations, while high-frequency components typically reflect local abrupt changes, branch anomalies, or equipment-level faults. Therefore, converting coal preparation plant equipment operating data to the graph domain for processing is beneficial for enhancing the characteristics of local weak faults and improving fault location capabilities under complex operating conditions.

[0005] The existing related graph domain fault diagnosis research shows that the discrete time sequence signal is converted into a path graph or a device graph, and the weak fault component is extracted through graph Fourier transform, spectral graph wavelet transform and reference signal matching, which can improve the fault feature recognition effect. But there are still the following problems if this kind of method is directly used for the equipment of the coal preparation plant: first, the coal preparation plant process has material flow conservation, medium circulation balance and equipment rated capacity constraint, if only the data similarity is constructed, the edge connection and non-physical graph pattern which do not conform to the process mechanism are easy to be generated; second, the washing amount, coal quality, start-stop state and production system will cause the distribution drift of normal data; third, the fault types of the coal preparation plant are complex, including pump cavitation, screen mesh blockage, belt deviation, bearing deterioration, medium density imbalance and crusher impact anomaly, etc., which need to fuse the device structure reference frequency, process residual template and graph domain abnormal characteristics. SUMMARY

[0006] An object of the present application is to provide a coal preparation plant equipment fault detection method and electronic equipment based on a graph domain, which can solve the above technical problems in the prior art.

[0007] According to a first aspect of the present application, a coal preparation plant equipment fault detection method based on a graph domain is provided, comprising:

[0008] Obtaining multi-source operation data of the coal preparation plant, wherein the multi-source operation data comprises operation data of a plurality of key equipment nodes and process data;

[0009] Preprocessing the multi-source operation data to obtain a feature vector of each key equipment node in each time window;

[0010] Mapping the feature vector into a device state symbol sequence based on symbolic dynamic filtering, and constructing a probabilistic finite state automaton transition matrix according to the device state symbol sequence;

[0011] Constructing a device operation graph model according to the feature vector, the probabilistic finite state automaton transition matrix and physical constraints;

[0012] Extracting a graph residual and a spectral graph wavelet decomposition component in the graph domain according to the device operation graph model;

[0013] Matching the spectral graph wavelet decomposition component with a plurality of preset fault reference features to determine a maximum similarity with the plurality of fault reference features;

[0014] Determining a fault detection result according to the graph residual, the spectral graph wavelet decomposition component, the probabilistic finite state automaton transition matrix, the physical constraints and the maximum similarity.

[0015] Optionally, the mapping of the feature vector into the device state symbol sequence based on the symbolic dynamic filtering comprises:

[0016] The sign division boundary is determined based on historical normal data, expert thresholds, and quantile thresholds;

[0017] Based on the symbol division boundary and the feature vector of each key device node in each time window, determine the symbol corresponding to each feature of each key device node in each time window;

[0018] The device status symbol sequence is determined based on the symbol corresponding to each feature of each key device node within each time window.

[0019] Optionally, constructing the device operation graph model based on the feature vector, the probabilistic finite automaton transition matrix, and physical constraints includes:

[0020] Construct an initial graph model, which includes a set of device nodes, a set of edges, and an adjacency matrix;

[0021] The adjacency matrix is ​​determined based on the eigenvector and the transition matrix of the finite probability automaton.

[0022] Calculate the degree matrix and the initial graph Laplacian matrix based on the adjacency matrix;

[0023] The initial graph Laplacian matrix is ​​modified according to the physical constraints to obtain the physical constraint graph Laplacian matrix.

[0024] Optionally, determining the adjacency matrix based on the eigenvector and the transition matrix of the probabilistic finite automaton includes:

[0025] The adjacency matrix is ​​calculated using the following formula:

[0026] ;

[0027] ;

[0028] in, It is an adjacency matrix. Indicates the first The device node and the first Edge weights between device nodes The process connection masking matrix is ​​used to represent the first... The device node and the first Do the individual equipment nodes have direct or indirect coupling relationships in the coal preparation process? For the first The feature vector of each device node For the first The feature vector of each device node For feature scale parameters, a path distance between the first device node and the second device node in the process flow graph, is a path scale parameter, is a transition similarity weight, is a probability finite state automaton transition matrix of the first device node, is a probability finite state automaton transition matrix of the first device node, represents a similarity of the probability finite state automaton transition matrix of the first device node and the probability finite state automaton transition matrix of the second device node. represents a similarity of the probability finite state automaton transition matrix of the first device node and the probability finite state automaton transition matrix of the second device node.

[0029] Optionally, the similarity of the probability finite state automaton transition matrix of the first device node and the probability finite state automaton transition matrix of the second device node is:

[0030] ;

[0031] wherein, is a probability finite state automaton transition matrix of the first device node, is a probability finite state automaton transition matrix of the first device node, represents a similarity of the probability finite state automaton transition matrix of the first device node and the probability finite state automaton transition matrix of the second device node, is a Frobenius norm, is a transition matrix similarity scale parameter. Optionally, the physical constraints include a material conservation constraint, a medium circulation balance constraint, a power boundary constraint, and a pressure-flow matching constraint. The modifying the initial graph Laplacian matrix according to the physical constraints to obtain a physical constraint graph Laplacian matrix comprises:

[0032] constructing a physical constraint matrix and a boundary constraint matrix according to the physical constraints;

[0033] calculating the physical constraint graph Laplacian matrix according to the physical constraint matrix, the boundary constraint matrix, and the initial graph Laplacian matrix;

[0034]

[0035]

[0036] ​​​​​​​​​​​ ;

[0037] wherein, is a physical constraint graph Laplacian matrix, is an initial graph Laplacian matrix, and is a non-negative penalty coefficient, is a physical constraint matrix, is a boundary constraint matrix.

[0038] Optionally, the manner of calculating the graph residual comprises:

[0039] performing eigen-decomposition on the physical constraint graph Laplacian matrix to obtain graph Fourier basis vectors;

[0040] performing graph Fourier transform on the graph Fourier basis vectors and a graph signal to obtain graph spectrum coefficients, the graph signal representing device node state quantities or window feature quantities;

[0041] calculating the graph residual according to the graph spectrum coefficients and graph spectrum mean and standard deviation of a historical normal operation phase.

[0042] Optionally, the manner of calculating the spectral graph wavelet decomposition component comprises:

[0043] performing multi-scale decomposition on the graph signal by using a spectral graph wavelet kernel to obtain multi-scale components;

[0044] calculating a root mean square-kurtosis combined index of the multi-scale components;

[0045] determining the component with the maximum root mean square-kurtosis combined index as the spectral graph wavelet decomposition component.

[0046] Optionally, the determining the fault detection result according to the graph residual, the spectral graph wavelet decomposition component, the probabilistic finite state automaton transition matrix, the physical constraint, and the maximum similarity comprises:

[0047] calculating a graph Fourier residual score according to the graph residual;

[0048] calculating a spectral graph wavelet impact score according to the spectral graph wavelet decomposition component;

[0049] calculating a state transition difference according to the probabilistic finite state automaton transition matrix;

[0050] calculating a physical constraint residual according to the physical constraint;

[0051] calculating a fault comprehensive score according to the graph Fourier residual score, the spectral graph wavelet impact score, the state transition difference, the physical constraint residual, and the maximum similarity;

[0052] The fault detection result is determined by comparing the comprehensive fault score with an adaptive threshold determined based on historical normal operation phases.

[0053] According to a second aspect of the present invention, an electronic device is provided, including a processor and a memory, the memory storing a program or instructions executable on the processor, the program or instructions, when executed by the processor, implementing the steps of a graph domain-based coal preparation plant equipment fault detection method as described in the first aspect of the present invention.

[0054] The beneficial effects of this invention are as follows: This invention converts continuous time-series data into finite symbolic states and state transition matrices through symbolic dynamic filtering, reducing the impact of sensor noise, coal quality fluctuations, and changes in feed volume on fault identification, and improving robustness under non-stationary operating conditions. This invention expresses the process topology, upstream and downstream coupling, and state similarity among multiple devices in a coal preparation plant through an equipment operation diagram model, extending single-device monitoring to full-process collaborative diagnosis. This invention distinguishes between low-frequency global load fluctuations and high-frequency local branch anomalies through graphical Fourier transform, helping to avoid misjudging normal feed volume changes as equipment failures. This invention adaptively selects fault-related components through spectral wavelet decomposition and root mean square-kurtosis combination indices, enhancing weak fault characteristics such as pump cavitation, bearing deterioration, crushing impact, and screen blockage. This invention uses fault reference signals, reference templates, envelope spectra, and PFSA transition difference fusion discrimination to simultaneously output fault determination, type identification, equipment-level location, contribution, and confidence, facilitating rapid troubleshooting by on-site maintenance personnel. Attached Figure Description

[0055] Figure 1 This is a flowchart of a coal preparation plant equipment fault detection method based on the spectral domain according to the present invention. Detailed Implementation

[0056] Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention.

[0057] The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the invention or its application or use.

[0058] Techniques, methods, and apparatus known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and apparatus should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0059] It should be noted that similar labels and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be discussed further in subsequent figures.

[0060] In the specification of this invention, the terms "first" and "second" may explicitly or implicitly include one or more of the same feature. In the description of this invention, unless otherwise stated, "multiple" means two or more. Furthermore, in the specification, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0061] like Figure 1 As shown in the figure, this embodiment introduces a method for detecting equipment faults in coal preparation plants based on the spectral domain, including steps 1100-1700.

[0062] Step 1100: Obtain multi-source operation data of the coal preparation plant, which includes operation data and process data of multiple key equipment nodes.

[0063] The coal preparation plant has a total of There are one equipment node and one process node, and the node set is as follows:

[0064] ;

[0065] in, For a set of nodes, Indicates the first Each node.

[0066] For the i-th node, collect data from R-type sensors or process variables, i.e., the aforementioned multi-source operational data:

[0067] ;

[0068] in, This represents the multi-source operational data vector of the i-th device node at time t. This represents the sampled value of the Rth channel, where R represents the number of sensor or process variable channels. Collectible data includes, but is not limited to: motor current, electrical power, triaxial vibration, sound pressure, speed, flow rate, pressure, medium density, temperature, feed rate, product flow rate, load rate, and start / stop status.

[0069] Step 1200: Preprocess the multi-source operating data to obtain the feature vector of each key device node in each time window.

[0070] The multi-source operational data undergoes time synchronization, missing value imputation, outlier removal, filtering, detrending, and normalization. For the i-th device node and r-th channel, the normalization process can be expressed as:

[0071] ;

[0072] in, For the normalized data, This represents the average value of the r-th channel at the i-th node during the historical normal operation phase. Let $\frac{i}{r}$ be the standard deviation of the $i$-th node and $r$-th channel during the historical normal operation phase. To prevent extremely small positive values ​​from being divided by zero.

[0073] The normalized data is then processed according to the window length. and step length Divided into sliding windows , The starting time of the sliding window is defined, and feature vectors are extracted within each sliding window:

[0074] ;

[0075] in, This represents the feature vector of the i-th node within the k-th window, where M is the feature dimension. This represents the M-th dimension feature of the i-th node within the k-th window. Features can include mean, root mean square, peak value, peak-to-peak value, variance, kurtosis, skewness, frequency band energy, envelope peak value, power fluctuation rate, pressure-flow residual, medium density deviation, and temperature rise rate, etc.

[0076] Step 1300: Map the feature vector to a sequence of device state symbols based on symbolic dynamic filtering, and construct a transition matrix of a probabilistic finite state automaton based on the sequence of device state symbols.

[0077] Specifically, the step of mapping the feature vector to a device status symbol sequence based on symbolic dynamic filtering includes: determining the symbol division boundary based on historical normal data, expert thresholds, and quantile thresholds; determining the symbol corresponding to each feature of each key device node in each time window based on the symbol division boundary and the feature vector of each key device node in each time window; and determining the device status symbol sequence based on the symbol corresponding to each feature of each key device node in each time window.

[0078] To reduce the impact of coal quality fluctuations, changes in washing volume, and measurement noise on continuous numerical characteristics, this application employs symbolic dynamic filtering to map continuous features into a finite set of symbols. The equipment state symbol sequence transforms continuously changing features into a discrete string of state labels arranged in chronological order according to a preset threshold boundary. The equipment state symbol sequence provides a standardized and discretized description of the equipment's operating trajectory. For example, instead of recording the specific numerical value of vibration velocity, it records the vibration velocity state as "high" within one time window and "low" in the next time window.

[0079] Define the set of symbols as:

[0080] ;

[0081] in, For a set of symbols, This is the Qth symbol.

[0082] The symbolic boundary contains multiple thresholds, which can be represented as follows: , The Qth threshold can be determined by historical normal data quantiles, cluster centers, the maximum information gain criterion, or expert experience.

[0083] The symbol of the m-th feature of the i-th node within the k-th window is:

[0084] ;

[0085] in, Let m be the symbol of the m-th feature of the i-th node within the k-th window. Let m be the m-th feature of the i-th node within the k-th window.

[0086] For multidimensional features, the symbols of each dimension are combined to form a joint symbol. Within a time window of length T, construct a sequence of device state symbols:

[0087] ;

[0088] in, This is a sequence of device status symbols.

[0089] Further, establish the transition matrix for the Probabilistic Finite State Automaton (PFSA):

[0090] ;

[0091] ;

[0092] in, Let be the transition matrix of the probabilistic finite state automaton at the i-th node. This indicates that the i-th node has a symbolic state. Transition to symbolic state The probability, This indicates that the i-th node within the time window has a symbol state. Transition to symbolic state Number of times, The smoothing coefficient is used to avoid zero probability. The PFSA transition matrix can describe the equipment state evolution pattern and is more suitable for fault detection under non-stationary operating conditions than single-point thresholds.

[0093] Step 1400: Construct a device operation diagram model based on the feature vector, the probabilistic finite state automaton transition matrix, and physical constraints.

[0094] Specifically, step 1400 includes steps 1410-1440.

[0095] Step 1410: Construct an initial graph model, which includes a set of device nodes, a set of edges, and an adjacency matrix.

[0096] Initial graph model Represented as:

[0097] ;

[0098] in, For a set of nodes, Let be the set of edges. This is the adjacency matrix. The adjacency matrix represents the edge weights, which comprehensively consider process topology, feature similarity, symbolic state transition similarity, and upstream and downstream path distances.

[0099] Step 1420: Determine the adjacency matrix based on the eigenvector and the transition matrix of the finite state automaton.

[0100] The adjacency matrix is ​​calculated using the following formula:

[0101] ;

[0102] ;

[0103] in, It is an adjacency matrix. Indicates the first The device node and the first Edge weights between device nodes The process connection masking matrix is ​​used to represent the first... The device node and the first Do the individual equipment nodes have direct or indirect coupling relationships in the coal preparation process? For the first The feature vector of each device node For the first The feature vector of each device node For feature scale parameters, Indicates the first The device node and the first The path distance of each equipment node in the process flow diagram. For path scale parameters, To transfer similarity weights, For the first The transition matrix of a probabilistic finite state automaton for each device node. For the first The transition matrix of a probabilistic finite state automaton for each device node. Indicates the first The transition matrix of the probabilistic finite state automaton of the nth device node and the nth device node Similarity of the transition matrices of a finite-probability state automaton for each device node.

[0104] If the first The device node and the first If individual equipment nodes have direct or indirect coupling relationships in the coal preparation process, then... . No. The device node and the first If there is no direct or indirect coupling relationship between the equipment nodes in the coal preparation process, then... .

[0105] ;

[0106] in, For the first The transition matrix of a probabilistic finite state automaton for each device node. For the first The transition matrix of a probabilistic finite state automaton for each device node. Indicates the first The transition matrix of the probabilistic finite state automaton of the nth device node and the nth device node The similarity of the transition matrices of the probabilistic finite state automata of each device node. It is the Frobenius norm. This is the similarity scale parameter for the transition matrix.

[0107] Step 1430: Calculate the degree matrix and the initial graph Laplacian matrix based on the adjacency matrix.

[0108] Calculate the weighted degree of the i-th node based on the adjacency matrix:

[0109] ;

[0110] in, This represents the weighted degree of the i-th node. A degree matrix is ​​constructed based on the weighted degrees of all nodes.

[0111] The initial graph Laplacian matrix is:

[0112] ;

[0113] in, Let the initial graph be the Laplace matrix. For degree matrix, This is the adjacency matrix. The initial graph Laplacian matrix is ​​used to describe the difference and smoothness of the graph structure.

[0114] Step 1440: Correct the initial graph Laplacian matrix according to the physical constraints to obtain the physical constraint graph Laplacian matrix.

[0115] The physical constraints include material conservation constraints, medium circulation balance constraints, power boundary constraints, and pressure-flow matching constraints.

[0116] Graph construction based solely on data similarity may result in edge connections that do not conform to the coal preparation process mechanism. To improve the interpretability of the graph model, this application uses material conservation constraints, medium circulation balance constraints, power boundary constraints, and pressure-flow matching constraints as physical priors.

[0117] Material conservation constraint: For a given splitting or merging process node, set For the first Inlet material flow rate For the export material flow rate of item b, To allow for losses or moisture content correction factors, the material conservation constraints are expressed as follows:

[0118] ;

[0119] in, Let be the set of entries for node i. Let i be the set of exits from node i. This represents the measurement error or disturbance term. When... When the volume continues to increase, it may correspond to blockage, leakage, metering abnormalities, or material distribution abnormalities.

[0120] Medium cyclic balance constraint: For heavy medium systems, assume For medium flow rate, Given the density of the medium, it can be constructed as follows:

[0121] ;

[0122] in, To balance the residuals of the medium circulation, For the medium feed flow rate, For the medium feed density, For the return flow of the medium, Return density for the medium. If Deviations from the normal range may correspond to media density imbalance, abnormal magnetic separation and recovery, abnormal replenishment media, or abnormal hydrocyclone separation status.

[0123] Power boundary constraints: Let Let be the actual power of the i-th device. Let i be the rated power of the i-th device. If the start / stop state of the i-th device is given, then the power boundary constraint is expressed as:

[0124] ;

[0125] in, To allow for margin. When the equipment is in a stopped state. At that time, the actual power should be close to zero when the equipment is in operation. At that time, the actual power should not continuously exceed the rated power limit.

[0126] Pressure-flow matching constraint: For media circulation pumps or pipeline branches, pressure difference With traffic It can be approximately satisfied as follows:

[0127] ;

[0128] in, This is the branch resistance coefficient. This is the pressure-flow residual. If pump cavitation, pipeline blockage, or valve malfunction occurs, It will continue to deviate or fluctuate at high frequency.

[0129] Step 1440 includes steps 1441-1442.

[0130] Step 1441: Construct the physical constraint matrix and the boundary constraint matrix based on the physical constraints.

[0131] The above-mentioned various physical constraints can be uniformly represented as:

[0132] ;

[0133] in, The physical constraint matrix, It is a state vector composed of device node diagram signals, flow rate, pressure, density, and power, etc. These are boundary terms or balance terms.

[0134] Step 1442: Calculate the physical constraint graph Laplacian matrix based on the physical constraint matrix, the boundary constraint matrix, and the initial graph Laplacian matrix.

[0135] To ensure that the spectral domain features conform to the process mechanism, a quadratic penalized modified Laplace matrix is ​​adopted:

[0136] ;

[0137] in, The Laplace matrix of the physical constraint graph. Let the initial graph be the Laplace matrix. and The non-negative penalty coefficient is... The physical constraint matrix, This is the boundary constraint matrix. Graph patterns that violate physical conservation and equilibrium relationships are penalized. Boundary constraint matrices are used to constrain rated power, start / stop logic, and permissible operating range. Through correction, non-physical patterns that do not conform to material flow, medium flow, and power boundaries during graph decomposition are suppressed.

[0138] Step 1500: Extract the spectral residual and spectral wavelet decomposition components in the spectral domain according to the equipment operation graph model.

[0139] The calculation method for the spectrum residuals includes steps 1510-1530.

[0140] Step 1510: Perform eigenvalue decomposition on the Laplace matrix of the physical constraint graph to obtain the graph Fourier basis vectors.

[0141] Laplace matrix of physical constraint graph Perform eigenvalue decomposition:

[0142] ;

[0143] in, For the first Spectral frequencies, These are the corresponding graph Fourier basis vectors. Smaller ones. Corresponding to the low-frequency smoothing pattern in the graph, the larger This corresponds to the high-frequency local mutation patterns on the diagram.

[0144] Step 1520: Perform a graph Fourier transform based on the graph Fourier basis vectors and the graph signal to obtain graph spectral coefficients, where the graph signal represents the device node state quantity or window feature quantity.

[0145] Suppose a graph signal within a certain time window for:

[0146] ;

[0147] in, It can be the first The comprehensive status of a device node, a health indicator based on a single feature or the fusion of multiple features.

[0148] The graphical Fourier transform includes a forward transform and an inverse transform, where the forward transform is represented as:

[0149] ;

[0150] The inverse transform is represented as:

[0151] ;

[0152] in, For the first The first window Spectral coefficients, For the first The Fourier basis vectors of the graph are at the th... Components on each node.

[0153] Step 1530: Calculate the spectrum residuals based on the spectrum coefficients and the spectrum mean and standard deviation during the historical normal operation phase.

[0154] Calculate the residuals of the graphs based on the mean and standard deviation of the graphs during the historical normal operation phase:

[0155] ;

[0156] in, The first stage of normal historical operation The mean of each spectral coefficient, The first stage of normal historical operation The standard deviation of each spectral coefficient For the disturbance term, The standardized spectral residuals.

[0157] Define low-frequency energy, high-frequency energy, and the high-low frequency energy ratio:

[0158] ;

[0159] ;

[0160] ;

[0161] in, This is a collection of low-frequency spectra, reflecting consistent changes across the entire plant or multiple pieces of equipment. For the first Low-frequency energy in each window; This is a collection of high-frequency spectra, reflecting anomalies in local equipment or local branches. For the first High-frequency energy in each window; Used to distinguish between global load fluctuations and local faults. It is a very small positive number, used to prevent division by zero.

[0162] In the actual operation of a coal preparation plant, changes in the amount of coal washed will cause synchronous changes in the power of all equipment, which will be represented by low-frequency energy in the spectral domain. The energy increases rapidly at this point. The change is very small, therefore Keeping it at a low level will not trigger false alarms.

[0163] The calculation method for the wavelet decomposition components of the spectral graph includes steps 1540-1560.

[0164] Step 1540: Use the spectral wavelet kernel to perform multi-scale decomposition on the graph signal to obtain multi-scale components.

[0165] Spectral wavelet operator Represented as:

[0166] ;

[0167] in, For the bandpass spectrum wavelet kernel function, For scale parameters, The Laplace matrix is ​​the physical constraint graph.

[0168] The bandpass wavelet kernel function is a pre-designed mathematical function that acts on the physical constraint graph Laplacian matrix to determine which frequency components are allowed to pass through. The scaling parameter directly controls the passband position of the wavelet kernel; when the scaling parameter is small, Larger values ​​in the high-frequency band can capture localized instantaneous impacts, such as bearing pitting. When the scale parameter is large... Larger values ​​in the low-frequency range can capture slow trends over a wide range, such as load increases or decreases across the entire plant.

[0169] The wavelet coefficients of the spectral graph are:

[0170] ;

[0171] in, Representing scale Next node The wavelet coefficients of the spectral plot at that location, Indicates the frequency in the spectrum The filter response at that point, Indicates the first Fourier coefficients of the graph For the first The Fourier basis vectors of the graph are at the th... Components on each node.

[0172] It is a value between 0 and 1, when the spectral frequency Falling on the current scale When within the passband range, A value of 1 indicates that passage is permitted. When falling within the stopband, A value of 0 indicates that the code has been filtered out.

[0173] Scaling function coefficients for:

[0174] ;

[0175] in, It is the kernel of the low-pass scaling function. Used to preserve the low-frequency smoothing components of the graph signal. Indicates the first Fourier coefficients of the graph For the first The Fourier basis vectors of the graph are at the th... Components on each node.

[0176] The graph signal is decomposed into multiple components using low-pass and band-pass filters of different scales. .

[0177] Step 1550: Calculate the root mean square-kurtosis combination index of the multi-scale components.

[0178] To avoid under-decomposition or over-decomposition due to manually specifying the number of decomposition layers, this invention constructs a root mean square-kurtosis combination index:

[0179] ;

[0180] ;

[0181] ;

[0182] in, Indicates the first Each spectral wavelet decomposition component The combined impact indicators. Indicates the first Each spectral wavelet decomposition component In the The amplitude at each device node represents the degree of concentration of anomalous energy at that scale on a specific device. Indicates the first Each spectral wavelet decomposition component The energy of this component reflects the total energy level of the anomalous signal at this scale. The larger the value, the stronger the vibrational or state change energy carried by this component. This represents the mean of the components. Indicates the standard deviation of the components. Let be the mathematical expectation. Indicates the first Each spectral wavelet decomposition component The impact factor is the kurtosis value of this component in the spatial dimension, reflecting the degree of concentration of abnormal energy distribution in the equipment group. If the kurtosis value is large, it indicates that the energy is highly concentrated on a very few equipment nodes, while other equipment nodes are close to zero, which is the typical spatial characteristic of local equipment failure. On the other hand, a small kurtosis value indicates that the energy is evenly distributed on most equipment, which corresponds to plant-wide public fluctuations and is not a failure.

[0183] When equipment experiences abnormalities such as bearing spalling, pump cavitation, screen impact, or breakage, the relevant components typically possess high energy and impact characteristics. Increase.

[0184] Step 1560: The component with the largest root mean square-kurtosis combination index is determined as the wavelet decomposition component of the spectrum.

[0185] Adaptive selection of the optimal decomposition level or target component can be expressed as:

[0186] ;

[0187] in, Number the relevant components of the target fault. To determine the optimal number of decomposition layers, The minimum allowed number of decomposition levels, This represents the maximum allowed number of decomposition levels.

[0188] Step 1600: Match the wavelet decomposition components of the spectrum with a variety of preset fault reference features to determine the maximum similarity with the variety of fault reference features.

[0189] Fault reference features include fault reference signals and fault reference templates. Fault reference signals or templates are constructed based on the structural parameters and technological mechanisms of different equipment. For equipment with rotating parts, such as crushers, media circulation pumps, centrifugal dewatering machines, scraper conveyor drives, and belt conveyor rollers, rotation-related fault reference signals can be constructed.

[0190] ;

[0191] in, For the first Class of fault reference signals, The fault characteristic frequency, The harmonic order is... For the first First harmonic weights, For phase.

[0192] For bearing-related failures, let the number of rolling elements be... Frequency conversion The diameter of the rolling element is The pitch circle diameter is The contact angle is The commonly used characteristic frequencies are:

[0193] ;

[0194] ;

[0195] ;

[0196] ;

[0197] in, The characteristic frequency of the outer ring fault. The characteristic frequency of inner ring faults, The characteristic frequency of rolling element failure, These frequencies are characteristic frequencies of cage failure. These frequencies can serve as the base frequencies for reference signals of bearing deterioration, spalling, or pitting faults.

[0198] For belt misalignment faults, a template for the difference between the left and right side sensors can be constructed:

[0199] ;

[0200] in, For the first The larger the value of the comprehensive residual of belt misalignment in each window, the more severe the asymmetry of the physical state on both sides of the belt, and the higher the risk of belt misalignment or impending misalignment.

[0201] Temperature characteristics on the left side of the belt. This describes the temperature characteristics on the right side of the belt. When the belt runs off-center, the belt edge rubs violently against the frame or sidewall, generating a large amount of heat and causing the temperature on the off-center side to rise significantly. The temperature difference between the left and right sides can serve as thermodynamic evidence of belt misalignment.

[0202] The vibration characteristics are those of the left side of the belt. The vibration characteristics on the right side of the belt can be, for example, the vibration amplitude or the root mean square value. These are the weighting coefficients corresponding to the vibration characteristics. Belt misalignment leads to uneven distribution of belt tension; the misaligned side experiences significantly greater vibration energy due to friction and impact compared to the normal side. Vibration differences are an important dimension reflecting mechanical dynamic imbalance.

[0203] This refers to the current or load characteristics on the left side of the belt. This refers to the current or load characteristics on the right side of the belt. This refers to the weighting coefficient corresponding to the current or load characteristics. When the belt runs off-center, the resistance on the off-center side increases, and the load current of the drive motor on that side will increase, causing a significant deviation in the current on both sides.

[0204] For cavitation failure in media circulation pumps, pressure-flow and high-frequency vibration and acoustic templates can be constructed:

[0205] ;

[0206] in, For the first The overall residual of pump cavitation in each window. The larger the value, the more severe the cavitation phenomenon in the pump, and the higher the risk of cavitation failure.

[0207] The pressure difference between the pump inlet and outlet, i.e., the first The average difference between the pump outlet pressure and the inlet pressure within each window. This represents the actual operating flow rate of the pump. This is the pipeline resistance coefficient.

[0208] The absolute value of the pressure-flow matching residual measures whether the current pump operating point deviates from the theoretical pipeline resistance curve. When cavitation occurs in the pump, a large number of bubbles are generated inside the impeller and block the flow channel, causing a sharp drop in pressure differential, making it impossible to maintain normal operation. and The relationship between them means that this value will increase significantly.

[0209] For high-frequency vibrational energy, representing the first The amplitude or band-limited root mean square value of the high-frequency spectral energy in the pump body vibration signal within a window. The impact energy generated when cavitation bubbles collapse is extremely large, which can excite high-frequency structural resonance in the pump casing and pipeline. This value directly quantifies the mechanical impact intensity of bubble collapse. This represents the weighting coefficient corresponding to the high-frequency energy of the vibration.

[0210] For acoustic high-frequency energy, representing the first The acoustic energy amplitude in the high-frequency band is collected by a sound pressure sensor near the pump body within a window. Cavitation produces specific high-frequency noise, such as a "hissing" or "crackling" sound. This value quantifies the intensity of the radiated acoustic energy generated by cavitation. In situations with strong electrical interference or complex vibration transmission paths, high-frequency acoustic energy is an important complement to high-frequency vibration energy. This represents the weighting coefficient corresponding to the high-frequency acoustic energy.

[0211] For media density imbalance faults, density deviation and media balance residual templates can be constructed:

[0212] ;

[0213] in, For the first The comprehensive residual of medium density imbalance in each window. The larger this value, the more ineffective the density control of the heavy medium suspension is, and the higher the risk of medium imbalance failure.

[0214] For the first The measured medium density of each window is measured in real time by a density meter installed on the medium pipeline. To set the media density, i.e. the process target value, the separation density target value is preset by the coal preparation plant process engineer based on the properties of the raw coal.

[0215] This is the absolute value of the instantaneous density deviation, which directly measures the degree to which the current actual sorting environment deviates from the target. Higher density (positive deviation) leads to contamination of clean coal by gangue (reduced recovery rate); lower density (negative deviation) leads to coal inclusion in the gangue (loss of clean coal). This is the most crucial process quality indicator for heavy media coal preparation.

[0216] To return the volumetric flow rate of the medium suspension in the system, This is the density of the medium suspension returned to the system. The volumetric flow rate of the medium suspension entering the system. This represents the density of the medium suspension entering the system. If the returned mass is less than the input mass, it indicates that a large amount of medium has been lost with the product, which may correspond to a damaged screen on the desliming screen or low efficiency of the magnetic separator. If the returned mass is greater than the input mass, it indicates that excess medium has unexpectedly accumulated in the system, which may correspond to a blockage in the distribution box. These are the weighting coefficients.

[0217] Spectral wavelet decomposition components With fault reference signal Or troubleshooting reference template Perform similarity calculations. For time series components, normalized cross-correlation can be used:

[0218] ;

[0219] in, For the first The wavelet decomposition component of the graph and the first Maximum similarity of reference signals for similar faults This is a time delay.

[0220] For graph node templates, cosine similarity can be used:

[0221] ;

[0222] in, For the first Reference templates for similar faults on equipment diagrams, such as pump cavitation templates mainly focusing on media circulation pumps and their adjacent pipeline nodes, and screen blockage templates mainly focusing on screening equipment and upstream and downstream material flow nodes.

[0223] If the actual abnormal energy The high incidence point is precisely... If a high-weight node is set, then The inner product will yield a large positive value. Conversely, if the exception occurs on a node for which the template is not defined, the inner product will be close to 0.

[0224] for The L2 norm represents the total energy of the actual anomalous components. for The L2 norm represents the baseline energy calibration value of the fault template. It should be a very small positive number to prevent the denominator from being zero.

[0225] For periodic impact-type faults, Hilbert (Hilbert transform) envelope spectrum analysis is performed on the target component:

[0226] ;

[0227] ;

[0228] in, For the first Time-domain signal of wavelet decomposition components of the spectrum For Hilbert transform, This is the envelope signal. In traditional vibration analysis, fault impact signals typically manifest as a high-frequency oscillating decaying wave (carrier wave) modulated by a low-frequency pulse sequence (modulation wave). Let's look directly at the original waveform. The high-frequency oscillations are so dense that it is difficult to discern the frequency of the pulses with the naked eye. By constructing an analytical signal using the Hilbert transform and taking its modulus, a smooth envelope is obtained. The fluctuations in this envelope accurately reflect the timing and intensity of the fault impact on the timeline.

[0229] To perform a Fast Fourier Transform, the time-domain envelope signal is transformed. Transform from the time domain to the frequency domain. The envelope spectrum amplitude represents the repetition frequency and energy distribution of the impulse pulse sequence in the original signal. Envelope signal Although periodic "bumps" are observed, directly measuring the time intervals between these "bumps" may not be accurate enough under noise interference. However, after performing a Fast Fourier Transform to convert it to the frequency domain, if these "bumps" are strictly uniform (with a period of...), the accuracy will be improved. ), then at frequency A clear peak spectral line will form at that point.

[0230] Step 1700: Determine the fault detection result based on the spectrum residual, the spectrum wavelet decomposition components, the probabilistic finite state automaton transition matrix, the physical constraints, and the maximum similarity.

[0231] Specifically, step 1700 includes steps 1710-1760.

[0232] Step 1710: Calculate the Fourier residual score based on the graph residual.

[0233] The graph Fourier residual score is obtained by aggregating the high-frequency energy of the graph residuals. The graph Fourier residual score is typically the L2 norm of the high-frequency graph residuals. It measures the overall deviation strength of the entire equipment group after removing fluctuations under normal operating conditions, indicating abrupt changes in local branches. A higher value indicates a higher probability of local anomalies.

[0234] Step 1720: Calculate the spectral wavelet impact score based on the spectral wavelet decomposition components.

[0235] Based on the spectral wavelet decomposition components, the product of the root mean square and the kurtosis is used as a combination index, and the optimal component is adaptively selected. The spectral wavelet impulse score is the combination index of this optimal component.

[0236] Step 1730: Calculate the state transition difference based on the probabilistic finite state automaton transition matrix.

[0237] PFSA difference is used to measure the change in the current state transition pattern relative to the normal state:

[0238] ;

[0239] in, This refers to the state transition difference. The first stage of normal historical operation State transition matrix of each device node Denotes the Frobenius norm. For the first The device node at the ... The transition matrix of a finite probability state automaton with windows.

[0240] Step 1740: Calculate the physical constraint residuals based on the physical constraints.

[0241] Based on the physical constraints established in the preceding steps, calculate the physical deviation values ​​of each actual measurement from the theoretical values. The physical constraint residual is a weighted linear combination of multiple physical deviation values. The physical constraint residual reflects the severity of the violation of physical constraints by the current operating state. For example, when cavitation occurs in a pump, the pressure no longer increases with the square of the flow rate, and the physical constraint residual increases sharply.

[0242] Step 1750: Calculate the comprehensive fault score based on the graph Fourier residual score, the spectral wavelet impact score, the state transition difference, the physical constraint residual, and the maximum similarity.

[0243] The overall fault score is expressed as follows:

[0244] ;

[0245] in, Indicates the first Comprehensive fault score for each device node. For the Fourier residual score, For wavelet impact scoring of the spectral graph, For state transition differences, For physical constraint residuals, To achieve the maximum similarity, , , , , These are the weighting coefficients.

[0246] Step 1760: Compare the comprehensive fault score with the adaptive threshold determined based on historical normal operation phases to determine the fault detection result.

[0247] The adaptive threshold is determined by statistics from historical normal operation phases:

[0248] ;

[0249] in, For adaptive threshold, This is the average score of the overall evaluation during the historical normal operation phase. The standard deviation of the overall score during the historical normal operation phase. This is the threshold coefficient.

[0250] The fault detection results include the location of the faulty equipment, the confidence level, and the fault type.

[0251] The confidence level output is:

[0252] ;

[0253] in, Indicates the first The confidence level of an anomaly or failure occurring in a device node. This is the scale parameter.

[0254] The location of the faulty device is determined by the node contribution:

[0255] ;

[0256] in, Indicates the first The contribution of each device node to the overall plant anomaly. The node with the highest contribution and exceeding the location threshold is identified as a faulty device or a primary device to investigate.

[0257] The fault type can be determined by the maximum a posteriori score:

[0258] ;

[0259] in, The index for the final fault type is a discrete label, such as... The fault type is pump cavitation. This indicates that the fault type is bearing deterioration. Indicates the first The first window The device node is for the first The type-specific comprehensive score for fault classes is jointly determined by reference template similarity, envelope spectrum peak value, physical residual type, and PFSA difference. For example, it can be obtained by weighted fusion of reference template similarity, envelope spectrum peak value, physical residual type, and PFSA difference. .

[0260] This invention converts continuous time-series data into finite symbol states and state transition matrices through symbolic dynamic filtering, thereby reducing the impact of sensor noise, coal quality fluctuations, and changes in the amount of coal washed on fault identification and improving robustness under non-stationary operating conditions.

[0261] This invention uses an equipment operation diagram model to express the process topology, upstream and downstream coupling, and state similarity among multiple devices in a coal preparation plant, thus extending single-device monitoring to full-process collaborative diagnosis.

[0262] This invention distinguishes between low-frequency global load fluctuations and high-frequency local branch anomalies using graphical Fourier transform, which helps to avoid misjudging normal changes in wash volume as equipment failure.

[0263] This invention adaptively selects fault-related components through spectral wavelet decomposition and root mean square-kurtosis combination index, thereby enhancing the characteristics of weak faults such as pump cavitation, bearing deterioration, crushing impact, and screen blockage.

[0264] This invention uses fault reference signal, reference template, envelope spectrum and PFSA transfer difference fusion discrimination to simultaneously output fault determination, type identification, equipment-level location, contribution and confidence, which facilitates quick troubleshooting by on-site maintenance personnel.

[0265] This embodiment introduces an electronic device, including a processor and a memory. The memory stores programs or instructions that can run on the processor. When the program or instructions are executed by the processor, they implement the steps of a coal preparation plant equipment fault detection method based on a spectral domain as described in any embodiment of the present invention.

[0266] While specific embodiments of the present invention have been described in detail by way of examples, those skilled in the art should understand that the above examples are for illustrative purposes only and are not intended to limit the scope of the invention. Those skilled in the art should understand that modifications can be made to the above embodiments without departing from the scope and spirit of the invention.

[0267] Those skilled in the art will recognize that the modules and algorithm steps described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0268] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the above-described apparatus and equipment can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0269] In the embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or modules may be electrical, mechanical, or other forms.

[0270] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical modules; that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of the embodiments of the present invention, depending on actual needs.

[0271] In addition, the functional modules in the embodiments of the present invention can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0272] If the aforementioned functions are implemented as software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, ROM, RAM, magnetic disks, or optical disks.

[0273] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

[0274] It should be understood that the sequence number of each step in the invention and embodiments of this invention does not absolutely imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this invention. The foregoing description of embodiments of this disclosure has been provided for illustrative and descriptive purposes. The foregoing description is not exhaustive and is not intended to limit this disclosure to the exact form disclosed. Various modifications and variations may exist based on the foregoing teachings, or various modifications and variations may be derived from the practice of this disclosure. These embodiments were chosen and described to illustrate the principles of this disclosure and its practical application, so that those skilled in the art can utilize this disclosure in various implementations and modifications suitable for the specific purpose of the concept.

Claims

1. A method for fault detection in coal preparation plant equipment based on graph domain, characterized in that, include: Acquire multi-source operational data of the coal preparation plant, including operational data and process data of multiple key equipment nodes; The multi-source operational data is preprocessed to obtain the feature vector of each key device node in each time window; The feature vector is mapped to a sequence of device state symbols based on symbolic dynamic filtering, and a transition matrix of a probabilistic finite state automaton is constructed based on the sequence of device state symbols. A device operation diagram model is constructed based on the feature vectors, the probabilistic finite state automaton transition matrix, and physical constraints. Based on the equipment operation diagram model, extract the spectral residual and spectral wavelet decomposition components in the spectral domain; The wavelet decomposition components of the spectrum are matched with a variety of preset fault reference features to determine the maximum similarity with the various fault reference features; The fault detection result is determined based on the spectrum residual, the spectrum wavelet decomposition components, the probability finite state automaton transition matrix, the physical constraints, and the maximum similarity.

2. The method for fault detection of coal preparation plant equipment based on graph domain according to claim 1, characterized in that, The step of mapping the feature vector to a device status symbol sequence based on symbolic dynamic filtering includes: The sign division boundary is determined based on historical normal data, expert thresholds, and quantile thresholds; Based on the symbol division boundary and the feature vector of each key device node in each time window, determine the symbol corresponding to each feature of each key device node in each time window; The device status symbol sequence is determined based on the symbol corresponding to each feature of each key device node within each time window.

3. The method for fault detection of coal preparation plant equipment based on graph domain as described in claim 1, characterized in that, The step of constructing the device operation graph model based on the feature vector, the probabilistic finite automaton transition matrix, and physical constraints includes: Construct an initial graph model, which includes a set of device nodes, a set of edges, and an adjacency matrix; The adjacency matrix is ​​determined based on the eigenvector and the transition matrix of the finite probability automaton. Calculate the degree matrix and the initial graph Laplacian matrix based on the adjacency matrix; The initial graph Laplacian matrix is ​​modified according to the physical constraints to obtain the physical constraint graph Laplacian matrix.

4. The method for fault detection of coal preparation plant equipment based on the spectral domain according to claim 3, characterized in that, Determining the adjacency matrix based on the eigenvector and the transition matrix of the finite-probability automaton includes: The adjacency matrix is ​​calculated using the following formula: ； ； in, It is an adjacency matrix. Indicates the first The device node and the first Edge weights between device nodes The process connection masking matrix is ​​used to represent the first... The device node and the first Do the individual equipment nodes have direct or indirect coupling relationships in the coal preparation process? For the first Feature vectors of each device node For the first Feature vectors of each device node For feature scale parameters, Indicates the first The device node and the first The path distance of each equipment node in the process flow diagram. For path scale parameters, To transfer similarity weights, For the first The transition matrix of a probabilistic finite state automaton for each device node. For the first The transition matrix of a probabilistic finite state automaton for each device node. Indicates the first The transition matrix of the probabilistic finite state automaton of the nth device node and the nth device node Similarity of the transition matrices of a finite-probability state automaton for each device node.

5. The method for fault detection of coal preparation plant equipment based on graph domain according to claim 4, characterized in that, The first The transition matrix of the probabilistic finite state automaton of the nth device node and the nth device node The similarity of the transition matrices of the probabilistic finite state automata of the device nodes is: ； in, For the first The transition matrix of a probabilistic finite state automaton for each device node. For the first The transition matrix of a probabilistic finite state automaton for each device node. Indicates the first The transition matrix of the probabilistic finite state automaton of the nth device node and the nth device node The similarity of the transition matrices of the probabilistic finite state automata of each device node. It is the Frobenius norm. This is the similarity scale parameter for the transition matrix.

6. The method for fault detection of coal preparation plant equipment based on the spectral domain according to claim 3, characterized in that, The physical constraints include material conservation constraints, medium circulation balance constraints, power boundary constraints, and pressure-flow matching constraints. The step of correcting the initial graph Laplacian matrix according to the physical constraints to obtain the physical constraint graph Laplacian matrix includes: Construct the physical constraint matrix and boundary constraint matrix based on the physical constraints; Calculate the physical constraint graph Laplacian matrix based on the physical constraint matrix, the boundary constraint matrix, and the initial graph Laplacian matrix; ； in, The Laplace matrix of the physical constraint graph. Let the initial graph be the Laplace matrix. and The non-negative penalty coefficient is... The physical constraint matrix, This is the boundary constraint matrix.

7. The method for fault detection of coal preparation plant equipment based on graph domain according to claim 6, characterized in that, The calculation method for the spectrum residuals includes: The physical constraint graph Laplace matrix is ​​subjected to eigenvalue decomposition to obtain the graph Fourier basis vectors; A graph Fourier transform is performed based on the graph Fourier basis vectors and the graph signal to obtain graph spectral coefficients, wherein the graph signal represents the device node state quantity or window feature quantity; The residuals of the spectrum are calculated based on the spectrum coefficients and the mean and standard deviation of the spectrum during the historical normal operation phase.

8. The method for fault detection of coal preparation plant equipment based on the spectral domain according to claim 7, characterized in that, The calculation methods for the wavelet decomposition components of the spectral graph include: The graph signal is decomposed into multi-scale components using a spectral wavelet kernel. Calculate the root mean square-kurtosis combination index of the multi-scale components; The component with the largest root mean square-kurtosis combination index is determined as the wavelet decomposition component of the spectrum.

9. The method for fault detection of coal preparation plant equipment based on graph domain according to claim 1, characterized in that, The step of determining the fault detection result based on the spectral residual, the spectral wavelet decomposition components, the probabilistic finite automaton transition matrix, the physical constraints, and the maximum similarity includes: Calculate the Fourier residual score based on the graph residuals; Calculate the spectral wavelet impact score based on the spectral wavelet decomposition components; Calculate the state transition difference based on the probabilistic finite automaton transition matrix; Calculate the physical constraint residuals based on the physical constraints; A comprehensive fault score is calculated based on the graph Fourier residual score, the spectral wavelet impact score, the state transition difference, the physical constraint residual, and the maximum similarity. The fault detection result is determined by comparing the comprehensive fault score with an adaptive threshold determined based on historical normal operation phases.

10. An electronic device, characterized in that, It includes a processor and a memory, the memory storing programs or instructions that can run on the processor, the programs or instructions being executed by the processor to implement the steps of a graph domain-based coal preparation plant equipment fault detection method as described in any one of claims 1 to 9.

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