Mesoporous carbon electrode slurry dispersion state monitoring method and system based on data fusion

Abstract

This invention relates to the field of electro-digital data processing technology, specifically to a method and system for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion. The method includes: performing Granger causality tests on time-series monitoring data to identify target sensor pairs and their causal directions, determining the causal and consequential sensors; performing multi-scale decomposition; performing cross-scale correspondence analysis to determine the cross-scale correspondence layer; setting a prediction window and verifying cross-scale response during real-time monitoring; and calculating the dispersion state index of the mesoporous carbon electrode slurry. This invention establishes a causal correlation and transfer parameter model between monitoring data at the micro-particle scale and macro-flow behavior scale of mesoporous carbon electrode slurry through the coupling of Granger causality tests and multi-scale decomposition, enabling the dispersion state assessment to reflect cross-scale dynamic evolution rather than local information at a single scale.

Description

Technical Field

[0001] This invention relates to the field of electro-digital data processing technology, specifically to a method and system for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion. Background Technology

[0002] The dispersion state of mesoporous carbon electrode slurries directly affects the construction quality, coating uniformity, and final electrochemical performance of the electrode's conductive network. To effectively monitor the dispersion state, existing technologies typically employ two main approaches: offline sampling and detection, and online single-parameter detection. Offline detection includes laser particle size analyzers, scanning electron microscopes (SEM), and transmission electron microscopes (TEM) to acquire microstructural information such as the geometric dimensions and surface morphology of particles or aggregates. Online detection includes methods such as viscometry and resistivity analysis to acquire macroscopic response information such as the overall flow behavior of the slurry or the characteristics of the conductive network. Furthermore, pH meters reflect the chemical environment determined by the ionization of functional groups on the particle surface, and densitometers reflect the overall solid-liquid ratio of the slurry. These detection methods correspond to different monitoring scales, from the molecular level, nanometer to micrometer level, mesoscopic scale to macroscopic average and overall macroscopic behavior, collectively covering a complete cross-scale information space of the dispersion state of mesoporous carbon electrode slurries.

[0003] However, existing monitoring methods generally fail to establish an intrinsic correlation mechanism between monitoring data at different scales, resulting in the inability to form a traceable causal transmission path between changes at the micro-particle scale and macro-flow behavior responses. The dispersed state assessment results can only reflect local information at a single scale, making it difficult to comprehensively and accurately characterize the overall evolution law of slurry from micro-particle morphology to macro-flow behavior. Summary of the Invention

[0004] This invention provides a method and system for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion, in order to solve existing problems.

[0005] The present invention provides a method and system for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion, which adopts the following technical solution: In a first aspect, one embodiment of the present invention provides a method for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion. The method includes: acquiring time-series monitoring data of mesoporous carbon electrode slurry at multiple different monitoring scales; performing Granger causality tests on the time-series monitoring data at multiple different monitoring scales to screen out the target sensor pairs with the strongest cross-scale driving relationship and their causal directions, and determining the cause sensor and the result sensor; performing multi-scale decomposition on the time-series monitoring data of the target sensor pairs to obtain multi-scale hierarchical representations; performing cross-scale correspondence analysis based on the multi-scale hierarchical representations to determine the cross-scale correspondence layers and extracting the cross-scale transfer parameters of the cross-scale correspondence layers; in the real-time monitoring stage, setting a prediction window based on the cross-scale correspondence layers and the cross-scale transfer parameters to perform cross-scale response verification on the cross-scale correspondence layers of the result sensor; and calculating the dispersion state index of the mesoporous carbon electrode slurry based on the cross-scale response verification results and the cross-scale transfer parameters.

[0006] Furthermore, the step of performing cross-scale correspondence analysis based on the multi-scale hierarchical representation to determine the cross-scale correspondence layer includes: performing a layer-to-layer Granger causality test on each layer in the multi-scale hierarchical representation of the cause sensor and the multi-scale hierarchical representation of the result sensor to determine the preliminary correspondence layer; and refining and verifying the preliminary correspondence layer based on the matching of change nodes to determine the final correspondence layer, thereby obtaining the cross-scale correspondence layer.

[0007] Further, the step of performing a layer-by-layer Granger causality test on each layer of the multi-scale hierarchical representation of the causal sensor and the multi-scale hierarchical representation of the result sensor to determine the preliminary corresponding layer includes: performing full combination pairing of each layer in the multi-scale hierarchical representation of the causal sensor and each layer in the multi-scale hierarchical representation of the result sensor to obtain multiple layer pairs; performing a Granger causality test on each layer pair to determine the optimal lag order of each layer pair, and obtaining the statistic and significance probability value of each layer pair; retaining the layer pairs whose significance probability value is less than a preset significance level to obtain significant layer pairs; and determining the preliminary corresponding layer among the significant layer pairs; wherein the preliminary corresponding layer is the layer pair with the largest statistic among the significant layer pairs.

[0008] Further, the refinement and verification of the preliminary corresponding layer based on change node matching to determine the final corresponding layer includes: extracting the reconstruction signals of the cause sensor and the result sensor corresponding to the preliminary corresponding layer based on the multi-scale hierarchical representation; performing change node detection on the reconstruction signals of the cause sensor and the result sensor respectively to obtain the change node set of the cause sensor and the change node set of the result sensor; wherein, the information of each change node includes the occurrence time, change magnitude, and change direction; for each change node in the change node set of the cause sensor, searching for candidate nodes that meet preset matching conditions in the change node set of the result sensor, and selecting the node with the smallest delay time as the matching node among the candidate nodes. The process involves recording the delay time of successfully matched node pairs; wherein the preset matching conditions include time lag constraints, maximum delay threshold constraints, and consistency constraints in the direction of change; based on the successfully matched node pairs, calculating the matching rate, delay statistics parameters, and amplitude propagation parameters between the node pairs; when the preliminary matching layer meets the preset refinement conditions, the preliminary matching layer is determined as the final matching layer; wherein the preset refinement conditions include the matching rate being no less than a preset matching rate threshold and the coefficient of variation of the delay statistics parameters not exceeding a preset coefficient of variation threshold; when the preliminary matching layer does not meet the preset refinement conditions, other layer pairs are selected sequentially as new preliminary matching layers in descending order of statistical quantity for refinement verification until a final matching layer that meets the preset refinement conditions is determined.

[0009] Further, the step of setting a prediction window based on the cross-scale correspondence layer and the cross-scale transfer parameters to perform cross-scale response verification on the cross-scale correspondence layer of the result sensor includes: acquiring monitoring data from the cause sensor and the result sensor in real time, and reconstructing them into real-time reconstructed signals of the cross-scale correspondence layer respectively; detecting change nodes in the real-time reconstructed signal of the cause sensor; when a change node of the cause sensor is detected, setting a prediction window based on the cross-scale transfer parameters; within the prediction window, detecting change nodes in the real-time reconstructed signal of the result sensor to verify whether there are change nodes with the same direction as the change nodes of the cause sensor; if there are change nodes with the same direction, the cross-scale response verification is determined to be successful, and the cross-scale transfer parameters are updated based on the successfully verified nodes; if no change nodes with the same direction are detected within the prediction window, the cross-scale response verification is determined to be unsuccessful and an anomaly warning is triggered.

[0010] Furthermore, the step of setting a prediction window based on the cross-scale transfer parameters includes: setting a time boundary for the prediction window based on the occurrence time of the change node of the cause sensor and the delay statistics parameter in the cross-scale transfer parameters; wherein, the time boundary is used to limit the time observation interval in the cross-scale corresponding layer of the result sensor that is expected to generate a cross-scale response.

[0011] Further, the step of detecting change nodes in the real-time reconstructed signal of the result sensor within the prediction window and verifying whether there are change nodes with the same change node direction as the cause sensor includes: detecting change nodes in the real-time reconstructed signal of the result sensor within the prediction window to obtain a set of change nodes in the result sensor; filtering candidate change nodes whose change direction is consistent with the change node of the cause sensor from the set of change nodes; when there are multiple candidate change nodes, determining a target matching node from the candidate change nodes based on a preset matching strategy to obtain cross-scale response verification results.

[0012] Furthermore, the step of calculating the dispersion state index of the mesoporous carbon electrode slurry based on the cross-scale response verification results and the cross-scale transfer parameters includes: within a sliding window, calculating the matching success rate, delay consistency, and amplitude consistency based on the cross-scale response verification results and the cross-scale transfer parameters, respectively; and weighting and summing the matching success rate, the delay consistency, and the amplitude consistency to obtain the dispersion state index of the mesoporous carbon electrode slurry.

[0013] Furthermore, the step of performing Granger causality tests on the time-series monitoring data at multiple different monitoring scales to screen out the target sensor pairs with the strongest cross-scale driving relationship and their causal directions, and to determine the causal sensors and result sensors, includes: preprocessing the time-series monitoring data at multiple different monitoring scales to obtain stationary time-series data; performing pairwise causal directionality tests on the stationary time-series data at each monitoring scale to obtain the causal driving strength and significance level of each sensor pair in different directions; based on the causal driving strength and the significance level, screening out the target sensor pairs with the strongest cross-scale driving relationship and their causal directions; and based on the target sensor pairs and the causal directions, determining the causal sensors and result sensors.

[0014] Secondly, another embodiment of the present invention provides a data fusion-based system for monitoring the dispersion state of mesoporous carbon electrode slurry, including a host computer and a multi-scale sensor communicatively connected to the host computer, wherein: The multi-scale sensor is installed in the mixing tank or transmission pipeline of the mesoporous carbon electrode slurry, and is used to collect time-series monitoring data of the mesoporous carbon electrode slurry at multiple different monitoring scales, and send the time-series monitoring data to the host computer. The host computer is used to acquire the time-series monitoring data; perform Granger causality tests on the time-series monitoring data at multiple different monitoring scales to screen out the target sensor pairs with the strongest cross-scale driving relationship and their causal directions, and determine the cause sensor and the result sensor; perform multi-scale decomposition on the time-series monitoring data of the target sensor pairs to obtain multi-scale hierarchical representations; perform cross-scale correspondence analysis based on the multi-scale hierarchical representations to determine the cross-scale correspondence layers and extract the cross-scale transfer parameters of the cross-scale correspondence layers; in the real-time monitoring stage, set a prediction window based on the cross-scale correspondence layers and the cross-scale transfer parameters, and perform cross-scale response verification on the cross-scale correspondence layers of the result sensor; calculate the dispersion state index of the mesoporous carbon electrode slurry based on the cross-scale response verification results and the cross-scale transfer parameters.

[0015] The beneficial effects of the technical solution of the present invention are: In this embodiment of the invention, time-series monitoring data of mesoporous carbon electrode slurry at multiple different monitoring scales are acquired; Granger causality tests are performed on the time-series monitoring data at multiple different monitoring scales to screen out the target sensor pairs with the strongest cross-scale driving relationship and their causal directions, and to determine the causal sensor and the result sensor; multi-scale decomposition is performed on the time-series monitoring data of the target sensor pairs to obtain multi-scale hierarchical representations; cross-scale correspondence analysis is performed based on the multi-scale hierarchical representations to determine the cross-scale correspondence layers and extract the cross-scale transfer parameters of the cross-scale correspondence layers; in the real-time monitoring stage, a prediction window is set based on the cross-scale correspondence layers and the cross-scale transfer parameters to verify the cross-scale response of the result sensor's cross-scale correspondence layers; based on the cross-scale response verification results and the cross-scale transfer parameters, the dispersion state index of the mesoporous carbon electrode slurry is calculated.

[0016] This invention establishes a causal relationship and transfer parameter model between monitoring data of the micro-particle scale and macro-flow behavior scale of mesoporous carbon electrode slurry by coupling Granger causality test and multi-scale decomposition. This enables the dispersion state assessment to reflect the dynamic evolution law across scales rather than local information of a single scale. On the other hand, based on Granger causality test, the target sensor pair with the strongest cross-scale driving relationship is screened from multi-scale sensors to avoid interference from redundant sensor data on fusion analysis. A hierarchical tree is constructed through multi-resolution decomposition to capture the evolution characteristics at different time scales. Furthermore, the initial corresponding layer is refined and verified by using change node matching, and delay statistics and amplitude transfer parameters are extracted to quantitatively characterize the time lag characteristics and amplitude transfer relationship of cross-scale response, providing a quantifiable physical basis for real-time prediction. Finally, based on the cross-scale transfer parameters, a prediction window is set for online response verification, and a dispersion state index is generated by comprehensively considering the matching success rate, delay consistency, and amplitude consistency. This enables real-time quantitative assessment and anomaly warning of the dispersion state of mesoporous carbon electrode slurry. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A flowchart illustrating the data fusion-based method for monitoring the dispersion state of mesoporous carbon electrode slurry provided in this application embodiment; Figure 2 A flowchart illustrating a data fusion-based method for monitoring the dispersion state of mesoporous carbon electrode slurry in an application scenario provided in this application embodiment; Figure 3 This is a schematic diagram of the architecture of a data fusion-based mesoporous carbon electrode slurry dispersion state monitoring system provided in an embodiment of this application. Detailed Implementation

[0019] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following detailed description, in conjunction with the accompanying drawings and preferred embodiments, provides a detailed account of the specific implementation methods, structures, features, and effects of the method proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0020] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0021] The following description, in conjunction with the accompanying drawings, details a specific scheme for a data fusion-based method for monitoring the dispersion state of mesoporous carbon electrode slurry provided by this invention.

[0022] Please see Figure 1 This illustrates an embodiment of the present invention providing a method for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion, comprising: Step S110: Obtain time-series monitoring data of mesoporous carbon electrode slurry at multiple different monitoring scales.

[0023] The aforementioned mesoporous carbon electrode is an electrochemical electrode with mesoporous carbon material as its core functional component. Mesoporous carbon refers to porous carbon materials with a pore size distribution between 2 nm and 50 nm, possessing a highly developed pore structure and a large specific surface area. These materials exhibit excellent electrochemical activity and conductivity due to the rapid ion transport pathways provided by mesoporous channels and abundant surface active sites. In electrode construction, mesoporous carbon is typically used as an active energy storage material or a highly conductive additive, combined with binders, conductive agents, and current collectors to form an electrode sheet with a three-dimensional porous network structure. It is widely used in electrochemical energy storage and conversion devices such as supercapacitors, lithium-ion batteries, and fuel cells. The electrode slurry is a key intermediate material in the preparation of the aforementioned mesoporous carbon electrode. Essentially, it is a multiphase dispersion system with specific rheological properties formed by uniformly mixing mesoporous carbon active material, conductive agent, polymer binder, and dispersing solvent. In industrial coating processes, electrode slurry is precisely coated onto the surface of a metal current collector and then dried and rolled to form a solid electrode sheet. Therefore, the uniformity of dispersion, agglomeration, and suspension stability of the components within the slurry directly determine the final electrode coating thickness consistency, pore structure integrity, and interfacial electrochemical performance. If the slurry dispersion is poor, mesoporous carbon particles are prone to agglomeration and sedimentation or the formation of local concentration gradients, leading to defects such as cracks, pinholes, or uneven thickness in the electrode coating. Ultimately, this deteriorates the capacity utilization, rate performance, and cycle life of the electrochemical device. Therefore, real-time monitoring and control of the electrode slurry dispersion is a core element in ensuring the quality of mass production of mesoporous carbon electrodes.

[0024] Mesoporous carbon electrode slurry, as a complex multiphase dispersion system composed of mesoporous carbon active particles, conductive additives, polymer binders, and solvents, exhibits significant multi-scale heterogeneity in its dispersion state. At the microscale, this involves the aggregation and dispersion equilibrium of nanoscale mesoporous carbon particles; at the mesoscale, it reflects the evolution of the local concentration field and rheological structure of the slurry; and at the macroscale, it manifests as changes in overall mixing homogeneity and transport stability. Because the physicochemical processes at different scales have vastly different time constants and spatial characteristics, a single monitoring scale can only capture state information within a specific frequency band or spatial range, failing to comprehensively characterize the entire slurry's internal structure from particle-level dispersion to the overall phase state. Therefore, collaborative observation at multiple different monitoring scales can overcome the inherent information limitations and spectral blind spots of single-scale monitoring. Furthermore, mesoporous carbon electrode slurry is not independent across different monitoring scales but exhibits complex cross-scale driving and response relationships. Microscale particle aggregation often induces parameter drift at the mesoscale and even macroscale through mechanisms such as rheological transfer or diffusion mass transfer; conversely, macroscale shear field changes also have a reaction effect on the microscale dispersion equilibrium. Relying solely on data from a single scale makes it difficult to identify such cross-scale causal chains, which can easily lead to missed detections or false alarms of dispersed anomalies. However, by simultaneously acquiring time-series data from multiple different monitoring scales, it is possible to establish the driving direction and transmission law between scales based on cross-scale causal tests. This allows for the fusion and extraction of the essential characteristics of dispersed states from multi-source heterogeneous information, thereby improving the sensitivity and robustness of the aforementioned dispersed state monitoring methods.

[0025] An optional implementation of step S110 above includes: deploying a multi-scale sensor array at key process nodes in the slurry mixing tank or transfer pipeline. This sensor array consists of sensors oriented towards different physical quantities and possessing different spatial resolutions. Each sensor sets its sampling frequency according to its corresponding scale characteristics and response bandwidth to ensure complete capture of the dynamic process at its respective scale. Each sensing unit synchronously acquires continuous state signals of the slurry during mixing or transport using a unified time reference. The acquired raw physical signals are then converted from analog to digital and transmitted to an electronic device executing the aforementioned decentralized state monitoring method. The time-series data from each channel are then preprocessed with timestamp alignment, sampling rate normalization, and noise reduction to construct a time-series monitoring dataset covering multiple monitoring scales and synchronized in time. The time-series monitoring dataset is stored in the form of a multi-channel time series, where each channel corresponds to the output of a sensing unit at a specific monitoring scale. The data from each channel are arranged on a unified discrete time axis, providing a structured data foundation for subsequent cross-scale Granger causality tests and multi-scale decomposition analysis.

[0026] Step S120: Perform Granger causality test on time-series monitoring data at multiple different monitoring scales, screen out the target sensor pairs with the strongest cross-scale driving relationship and their causal direction, and determine the causal sensor and the result sensor.

[0027] Granger causality testing is a statistical hypothesis testing method based on time series forecasting. Its core idea is that if incorporating historical information from sequence A into the prediction model of sequence B significantly reduces the prediction error of sequence B (usually tested for significance using the F-statistic), then statistically, a Granger causal relationship exists between sequence A and sequence B. This means that changes in sequence A precede changes in sequence B and provide additional predictive information, thus revealing the dynamic dependence and information transmission direction between variables with a temporal order. In the above scheme, Granger causality testing is performed on time-series monitoring data covering multiple monitoring scales from micro-particle scales to macro-flow behavior. The aim is to quantitatively screen target sensor pairs with the strongest cross-scale driving relationship and clear causal direction from multi-source sensor data. This determines the causal and consequent sensors that can stably drive responses at larger monitoring scales, thus providing a physically interpretable causal structure for subsequent multi-scale decomposition, cross-scale corresponding layer determination, and prediction window setting. This avoids the lack of a stable driving path in cross-scale fusion analysis due to sensor data redundancy or weak inter-scale causal relationships.

[0028] Step S120 above can quantify the causal driving strength and statistical significance of each sensor pair in different directions by performing stationarity preprocessing and pairwise causal directionality tests on multi-scale time-series monitoring data, thereby screening out the target sensor pair with the strongest cross-scale driving relationship and its causal direction, and determining the causal sensor and result sensor that drive the response at a smaller monitoring scale to a larger monitoring scale. Specifically, step S120 may include: preprocessing time-series monitoring data at multiple different monitoring scales to obtain stationary time-series data; performing pairwise causal directionality tests on the stationary time-series data at each monitoring scale to obtain the causal driving strength and significance level of each sensor pair in different directions; screening out the target sensor pair with the strongest cross-scale driving relationship and its causal direction based on the causal driving strength and significance level; and determining the causal sensor and result sensor based on the target sensor pair and causal direction.

[0029] Granger causality tests require time series to satisfy the stationarity assumption to avoid spurious regressions or false causal relationships arising from non-stationary series during the test. This ensures that the statistical test result and significance probability accurately reflect the dynamic dependencies between variables rather than spurious correlations caused by time trends. Therefore, before conducting Granger causality tests on time series monitoring data at multiple different monitoring scales, preprocessing is necessary to obtain stationary time series data. Preprocessing methods may include: removing outliers caused by instantaneous sensor malfunctions or environmental disturbances; using linear interpolation to fill in blank data points caused by communication interruptions or missing sampling; and removing the overall trend term from the original series through first-order differencing, ensuring that the time series data at each monitoring scale statistically meet the stationarity requirement.

[0030] When conducting pairwise causal directionality tests on stationary time-series data at various monitoring scales, stationary time-series data from any two sensors are combined into sensor pairs. A bidirectional Granger causality test is then performed on each sensor pair. This involves constructing a vector autoregressive model with one sensor as the candidate cause and the other as the outcome, while simultaneously exchanging the causal directions for a reverse test. The statistics and significance probabilities for each direction are recorded. Within the Granger causality test framework, the statistic typically refers to the F-statistic constructed based on the sum of squared residuals from the vector autoregressive model. Its magnitude reflects the reduction in prediction error resulting from incorporating historical information from the candidate cause sequence into the outcome sequence prediction model, i.e., the strength of the causal driving relationship. The significance probability is the probability corresponding to the current or more extreme F-statistic, assuming the null hypothesis (that the candidate cause sequence has no Granger causal influence on the outcome sequence) holds. The smaller the probability, the stronger the evidence for rejecting the null hypothesis, thus determining that the causal direction is statistically significant.

[0031] After obtaining the causal driving strength and significance level of the bidirectional causal directionality test for each sensor pair, the target sensor pair with the strongest cross-scale driving relationship and its causal direction can be screened. This screening process uses statistical significance as a prerequisite threshold, retaining only causal directions whose significance level meets a preset threshold to exclude spurious correlations caused by random fluctuations. Based on this, the causal driving strength of the retained causal directions is compared, and the sensor pair corresponding to the maximum driving strength is determined as the target sensor pair with the strongest cross-scale driving relationship, and its corresponding causal direction is taken as the inherent driving direction of the sensor pair. If there are cases where both bidirectional causal relationships meet the significance requirement and the driving strengths are similar, then based on the physical principle that the monitoring scale increases from micro to macro, the direction from the micro scale to the macro scale is selected as the final causal direction of the sensor pair, thereby ensuring that the screened target sensor pairs have a clear and stable cross-scale information transmission path. After determining the target sensor pair and its causal direction, the roles of the two sensors are assigned according to the information transmission direction of the causal direction: the initiating end of the causal direction, that is, the sensor that can drive a response at a larger monitoring scale after a change at a smaller monitoring scale, is determined as the causal sensor; the receiving end of the causal direction, that is, the sensor whose response change is triggered by the cross-scale drive of the causal sensor, is determined as the result sensor.

[0032] Step S130: Perform multi-scale decomposition on the time-series monitoring data of the target sensor pair to obtain a multi-scale hierarchical representation.

[0033] The aforementioned multi-scale decomposition is a signal processing technique that separates time-series signals layer by layer according to different time or frequency scales. It aims to extract multi-level representations reflecting low-frequency trends, high-frequency fluctuations, and intermediate-scale features from the original signal, allowing the dynamic evolution patterns at different scales to be presented independently. Multi-scale decomposition can be implemented using one of several multi-resolution time-frequency analysis methods, such as wavelet transform, empirical mode decomposition, variational mode decomposition, and ensemble empirical mode decomposition. Specifically, wavelet transform uses discrete wavelet transform or maximum overlap discrete wavelet transform, employing iterative low-pass and high-pass filters to decompose the signal into approximate and detail components. Empirical mode decomposition adaptively decomposes the signal into a finite number of eigenmode functions based on its local characteristics. Variational mode decomposition decomposes the signal into modal components with specific center frequencies and finite bandwidths by solving constrained optimization problems within a variational framework. Ensemble empirical mode decomposition introduces Gaussian white noise to aid analysis and overcome mode aliasing, obtaining a stable set of eigenmode functions through multiple averaging.

[0034] Taking wavelet transform as an example, in multi-scale decomposition, low-pass and high-pass filters can be applied to the time-series monitoring data of the target sensor pair for iterative decomposition layer by layer. Starting from the original signal, after low-pass filtering, the first-level approximate signal reflecting the low-frequency trend of the signal is obtained. After high-pass filtering, the first-level detail signal reflecting the high-frequency fluctuation of the signal is obtained. Then, the first-level approximate signal is used as input to apply low-pass and high-pass filters again to obtain the second-level approximate signal and the second-level detail signal, and so on until the preset number of decomposition layers is reached, so that the original time-series data is decomposed into components at multiple different frequency scales. The wavelet coefficients generated by the above decomposition process need to be reconstructed back to the time domain through inverse transform to obtain the time-series node data corresponding to each layer component. During reconstruction, only the approximate coefficients or detail coefficients of the target layer are retained, while the coefficients of the other layers are set to zero. After inverse wavelet transform, the time series of the node is obtained, and the length of all reconstructed sequences is consistent with the original signal, thereby ensuring the alignment and comparability of each layer node in the time dimension in subsequent cross-scale correspondence analysis. Based on the reconstruction results, a wavelet hierarchical tree structure is constructed. The original signal is used as the root node (level zero). The first level contains approximate node 1 and detail node 1, with both having the root node as their parent. The second level consists of approximate node 2 and detail node 2, obtained by further decomposing the approximate node 1, with approximate node 1 as their parent. This process continues until level L, forming approximate node L and detail node L. Each sensor thus obtains a hierarchical tree containing 2×L nodes (L levels of approximate and detail nodes). Each node is assigned a unique identifier to represent its sensor, component type, and level number. For example, the format of the unique identifier is "sensor name_type_level number". For instance, "particle size_detail_two" represents the second level detail signal of a particle size sensor, and "viscosity_approximate_four" represents the fourth level approximate signal of a viscosity sensor. In the hierarchical tree, the frequency of approximate signal nodes decreases and the time scale increases with the layer number, reflecting the slow evolution trend of the slurry state on a larger time scale. Detail signal nodes, on the other hand, reflect the rapid fluctuation characteristics of the corresponding layer on the time scale. This allows the cross-scale dynamic information of mesoporous carbon electrode slurry from the micro-particle scale to the macro-flow behavior scale to be organized in an orderly manner in each node of the hierarchical tree, providing a structured multi-scale representation that can be compared layer by layer for subsequent Granger causality tests.

[0035] Step S140: Perform cross-scale correspondence analysis based on multi-scale hierarchical representation, determine the cross-scale correspondence layer, and extract the cross-scale transfer parameters of the cross-scale correspondence layer.

[0036] The aforementioned cross-scale correspondence layer refers to the layer-by-layer mapping relationship with statistical causal correlation established between the multi-scale hierarchical representations of causal sensors and result sensors. Specifically, it represents the cross-scale pairing formed between a node in the causal sensor hierarchical tree reflecting dynamic characteristics at a specific timescale and a node in the result sensor hierarchical tree that stably responds to changes at that level. The cross-scale correspondence layer characterizes the timescale matching position with the strongest causal driving correlation within the multi-resolution decomposition framework during the transmission of microscale state changes to macroscale responses in mesoporous carbon electrode slurries. It not only identifies the hierarchical nodes where two sensors generate causal coupling after multi-scale decomposition but also implicitly contains the time lag characteristics and amplitude response relationship of cross-scale information transmission. It serves as a bridging structure connecting microscale particle-scale dynamics with macroscale flow behavior-scale responses.

[0037] The necessity of determining the cross-scale correspondence layer stems from the inherent cross-scale cumulative effect of the dispersion state evolution of mesoporous carbon electrode slurry. Specifically, the particle breakage or agglomeration changes captured by microscale sensors do not act instantaneously and directly on macroscale sensors, but rather gradually alter the internal structure of the slurry through the accumulation of multiple microscale changes, ultimately triggering a hysteresis response at the macroscale. If this cross-scale correspondence is not located through multi-scale hierarchical representation, and a holistic correlation analysis is performed directly on the original sensor time-series data, the cumulative transmission path of microscale changes will be unidentifiable due to the overlapping of dynamic information at different time scales. This results in the inaccurate extraction of cross-scale delay parameters and amplitude transmission characteristics. Only by determining the cross-scale correspondence layer can irrelevant fluctuation interference be removed from the pure scale space after multi-resolution decomposition, focusing on the hierarchical nodes that truly carry cross-scale causal transmission. This provides a quantifiable basis for cross-scale transmission parameters for subsequent real-time dispersion state monitoring based on delay prediction windows.

[0038] The above step S140 can determine the cross-scale corresponding layer through one of the following methods: The first method of determination: determining the corresponding layer across scales based on cross-correlation analysis; This method identifies layer pairs with the highest correlation and significant time lag as cross-scale corresponding layers by calculating the cross-correlation coefficients between the time series of nodes in the multi-scale hierarchical representation of cause and effect sensors. Each node in the cause sensor hierarchical tree is paired with each node in the effect sensor hierarchical tree, and the Pearson cross-correlation coefficients or normalized cross-correlation coefficients of each pair under different time lags are calculated. The peak correlation coefficients and corresponding lag times of each pair are compared, and the layer pairs with the highest peak correlation coefficients and passing the significance test are identified as cross-scale corresponding layers. In this pair, the node changes in the cause sensor layer and the node changes in the effect sensor layer show the strongest linear covariance relationship statistically, and the corresponding lag time is the time delay feature of cross-scale transmission.

[0039] The second method of determination: determining the corresponding layer across scales based on frequency domain coherence analysis; This approach utilizes frequency domain coherence metrics to analyze the linear dependence of nodes at specific frequency components in a multi-scale hierarchical representation. The layer pairs with the strongest coherence and highest frequency matching are identified as the corresponding cross-scale layers. Spectral analysis or wavelet coherence analysis is performed on the time series of nodes at each layer in the multi-scale hierarchical tree of the cause and effect sensors. The amplitude squared coherence coefficient of each layer pair within the common frequency range is calculated, and the peak value and frequency concentration of the coherence spectrum of each layer pair are evaluated. Layer pairs with significant coherence at the dominant frequency component and a stable phase lag relationship are selected. This indicates that the fluctuation energy of the cause sensor at a specific frequency scale can be stably transmitted to the corresponding frequency scale of the effect sensor, and its phase lag corresponds to the time delay of cross-scale transmission.

[0040] The third method of determination: determining the corresponding layer across scales based on transitive entropy; This method uses the transfer entropy from information theory to measure the amount of directed information transferred from each layer of the cause sensor hierarchical tree to each layer of the result sensor hierarchical tree. The layer pair with the largest and statistically significant transfer entropy is determined as the cross-scale corresponding layer. The nodes of each layer in the multi-scale hierarchical representation of the cause and result sensors are paired, and the transfer entropy value of each layer pair under different lag orders is estimated. The transfer entropy quantifies the incremental contribution of the historical state of the cause node to the predictive ability of the current state of the result node through conditional mutual information, which can capture the nonlinear cross-scale driving relationship. The transfer entropy value of each layer pair is statistically significant, and the layer pair with the largest transfer entropy value and the significance level meeting the preset threshold is selected as the cross-scale corresponding layer. This layer pair represents the cross-scale channel with the least information loss in the process of transferring the dynamic from the microscale to the macroscale response.

[0041] The fourth determination method: determining the corresponding layer across scales based on dynamic time warping; This approach utilizes a dynamic time warping algorithm to measure the similarity of time series of nodes at each level in the multi-scale hierarchical representation of cause and effect sensors. It identifies cross-scale corresponding layers by finding the optimal nonlinear time alignment path. Each node in the cause sensor hierarchical tree is paired with each node in the effect sensor hierarchical tree, and the dynamic time warping distance and optimal warping path between the time series of each pair are calculated. Dynamic time warping minimizes the morphological differences between the two sequences by locally stretching or compressing the time axis, and can adapt to the nonlinear time deformation caused by process drift during cross-scale transmission. The layer pair with the smallest warping distance and the warping path exhibiting a stable monotonic lag mode is selected as the cross-scale corresponding layer. The morphological evolution of the cause node and the effect node in this layer pair has the highest similarity under the condition of allowing nonlinear time distortion. The cumulative offset of the warping path reflects the cumulative time delay characteristics of cross-scale transmission.

[0042] The fifth method of determination: determining the corresponding layer across scales based on Granger causality tests and matching of change nodes; Optionally, the above-mentioned cross-scale correspondence analysis based on multi-scale hierarchical representation to determine the cross-scale correspondence layer includes: performing layer-to-layer Granger causality tests on each layer in the multi-scale hierarchical representation of the cause sensor and the multi-scale hierarchical representation of the result sensor to determine the preliminary correspondence layer; and refining and verifying the preliminary correspondence layer based on the matching of change nodes to determine the final correspondence layer, so as to obtain the cross-scale correspondence layer.

[0043] After multi-scale decomposition, each layer of the hierarchical tree corresponds to the dynamic evolution characteristics at different time scales. Particle breakage or surface charge changes captured by microscale sensors typically alter the internal structure of the slurry through multiple cumulative effects, ultimately triggering the viscosity or resistivity response reflected by macroscale sensors. However, this cross-scale information transmission does not occur uniformly at any given time scale. The Granger causality test of layers identifies the pair of layer nodes with the strongest statistical causal drive between the multi-scale hierarchical representations of cause and effect sensors, serving as candidate channels for cross-scale information transmission. This test evaluates the reduction in prediction error of the current state of another layer node by the historical time-series information of a certain layer node, screening for layer pairs with significant causal relationships. This focuses the cross-scale analysis on the scale nodes most likely to carry the transmission relationship from micro-dynamics to macro-response. The initial correspondence layer only reflects the statistical correlation of the overall time-series data and may contain spurious correlations due to long-term trend covariance or environmental noise coupling, and may not physically correspond to stable cross-scale event-level transmission paths. Change node matching captures abrupt events in time-series signals to verify whether abrupt changes in small-scale nodes can statistically stably trigger hysteresis responses in large-scale nodes. This verification not only examines the significance of causal relationships between corresponding layers but also analyzes the matching patterns of the occurrence time, direction of change, and response amplitude of abrupt events to examine the stability and consistency of cross-scale causal transmission, thereby eliminating layer pairs that only possess overall statistical correlation but lack event-level transmission patterns. After refined verification, layer pairs that meet the preset stability conditions are determined as the final corresponding layers. These layer pairs characterize the most stable channel for the transmission of microscale dynamics to macroscale responses during the evolution of the dispersion state of mesoporous carbon electrode slurry. Simultaneously, the delay statistical parameters and amplitude transmission parameters extracted from the successfully verified node pairs are solidified as cross-scale transmission parameters. These parameters quantify the time lag characteristics and amplitude response ratios of cross-scale responses, providing a quantifiable physical benchmark for cross-scale response verification based on prediction windows during the real-time monitoring phase.

[0044] In the above scheme, a full combination Granger causality test can be performed on the multi-scale hierarchical representations of the causal sensor and the result sensor. Under the constraint of statistical significance, the layer pairs with the strongest causal driving strength are selected as the preliminary corresponding layers. This is to locate the strongest candidate channel for the transmission of micro-dynamics to macro-response in the hierarchical tree after multi-scale decomposition. Specifically, the above-mentioned Granger causality test on each layer in the multi-scale hierarchical representations of the causal sensor and the result sensor to determine the preliminary corresponding layers includes: performing a full combination pairing of each layer in the multi-scale hierarchical representations of the causal sensor and the result sensor to obtain multiple layer pairs; performing a Granger causality test on each layer pair to determine the optimal lag order of each layer pair and obtaining the statistic and significance probability value of each layer pair; retaining layer pairs with significance probability values ​​less than a preset significance level to obtain significant layer pairs; and determining the preliminary corresponding layers among the significant layer pairs. The preliminary corresponding layers are the layer pairs with the largest statistic among the significant layer pairs.

[0045] The full combination pairing of multi-scale hierarchical representations of causal and consequential sensors involves exhaustively pairing each node in the causal sensor hierarchy with each node in the consequential sensor hierarchy, forming a set of layer pairs covering all possible scale matching relationships. The necessity of this full combination strategy lies in the fact that cross-scale causal transmission can occur between nodes at any time scale. Rapid fluctuations at the microscale can directly drive immediate responses at the macroscale, or they can induce slow trend changes over larger time scales through cumulative effects. If only specific layers or adjacent layers are locally paired, the optimal scale matching position that truly carries cross-scale information transmission may be missed, leading to subsequent analyses based on suboptimal or erroneous correspondences. After obtaining the full combination set of layer pairs, a Granger causality test is performed on each layer pair to quantitatively evaluate the predictive contribution of the historical time-series information of a specific layer node in the causal sensor to the current state of the corresponding layer node in the consequent sensor. Compared with directly performing causal tests on the raw sensor time-series data, performing layer-by-layer tests on the hierarchical tree after multi-scale decomposition has the advantage of scale isolation: different frequency components in the raw signal are mixed with each other, and it is difficult to separate the micro-rapid fluctuations and macro-slow trends. However, each layer node in the hierarchical tree corresponds to the dynamic characteristics of a specific frequency scale or time resolution, which allows causal tests to be performed in a pure single-scale space, thereby identifying the scale channel that truly plays a dominant role in the transmission of micro-dynamics to macro-response.

[0046] In layer-to-Granger causality tests, the optimal lag order characterizes the optimal time backtracking length for the statistical impact of historical information from causal layer nodes on outcome layer nodes. The optimal lag order can be determined based on information criteria, such as by comparing the Akaike information criterion or Bayesian information criterion values ​​of vector autoregressive models with different lag orders, selecting the order that achieves the best balance between model goodness of fit and parameter complexity. Alternatively, a sequential test method can be used, starting with a lag of one order and gradually expanding until the joint significance of the regression coefficients of newly added lag terms no longer meets a preset threshold. Determining the optimal lag order not only ensures the statistical reliability of the causal test model, avoiding the omission of causal information due to an excessively short lag order or model redundancy due to an excessively long lag order, but its value itself also provides an initial scale reference for the time delay characteristics of cross-scale transmission.

[0047] The statistical statistic and significance probability are the core statistical measures of the Granger causality test output for each layer. The statistical statistic is usually the F-statistic, which is constructed based on the sum of squared residuals of the restricted and unrestricted models. Its value quantifies the degree of reduction in prediction error brought about by incorporating the lag terms of the causal layer nodes into the prediction model of the outcome layer nodes, i.e., the strength of the cross-scale causal driving relationship. The significance probability, under the premise that the null hypothesis is true, represents the probability of observing the current or more extreme F-statistic. The smaller the probability value, the more sufficient the evidence to reject the null hypothesis, thus determining that the causal direction of the layer at that lag order is more statistically significant. Together, they constitute the quantitative basis for screening the corresponding layer across scales.

[0048] Since the full combination of pairings generates a large number of stratified pairs, the multiple comparison problem may lead to false positive causal relationships. Therefore, it is necessary to statistically screen the stratified pairs by setting a preset significance level. This preset significance level can be an uncorrected fixed threshold, or it can be achieved by dividing the original significance level by the total number of comparisons using Bonferroni correction, or by using permutation tests to generate an empirical distribution by shuffling the time series to control the Type I error rate. Only stratified pairs with significance probabilities lower than the preset significance level are retained as significant stratified pairs, thereby limiting the analysis to cross-scale causal associations with statistical confidence and excluding spurious correlation stratified pairs caused by random fluctuations or noise coupling.

[0049] After obtaining the set of significant layer pairs, the layer pair with the largest statistical value is determined as the preliminary corresponding layer. The principle behind this operation is that the statistical value directly reflects the strength of the cross-scale causal driving relationship. The larger the statistical value, the more prominent the predictive contribution of the causal layer node to the result layer node, and the more stable the cross-scale information transmission. Therefore, under the premise that statistical significance has been guaranteed, selecting the layer pair with the largest causal driving strength as the preliminary corresponding layer can ensure that subsequent refinement and verification focus on the cross-scale channels that are most likely to stably carry the micro-dynamics of mesoporous carbon electrode slurry to the macro-response, thereby improving the efficiency and reliability of cross-scale correspondence analysis.

[0050] In addition to the statistical inference method based on Granger causality test mentioned above, a time-domain correlation method based on cross-correlation analysis can also be used. This involves calculating the cross-correlation coefficients of the time series of each layer node in the multi-scale hierarchical representation of the cause and effect sensors at different time lags, and identifying the layer pairs exhibiting the highest correlation and passing the significance test as the preliminary corresponding layers. Alternatively, a frequency-domain correlation method based on frequency-domain coherence analysis can be used. This involves evaluating the linear dependence strength and phase lag relationship of each layer pair on the common frequency component using wavelet coherence spectrum or amplitude-squared coherence coefficient, and selecting the pair with the strongest coherence and phase lag at the dominant frequency. Stable layer pairs can be used as initial corresponding layers; alternatively, a transfer entropy analysis based on information theory can be adopted, by estimating the directed information transfer between each layer pair, and determining the layer pair with the largest and statistically significant transfer entropy as the initial corresponding layer to capture nonlinear cross-scale driving relationships; or a similarity measurement based on dynamic time warping can be used, by finding the optimal nonlinear time alignment path between the time series of each layer pair, and determining the layer pair with the smallest warping distance and the warping path exhibiting a stable monotonous lag mode as the initial corresponding layer to adapt to the nonlinear time deformation caused by process drift during cross-scale transfer.

[0051] In the above scheme, the preliminary correspondence layer can be refined and verified based on change node matching. The physical authenticity of the overall statistical causal relationship is verified by the consistency of response at the abrupt event level, and the delay statistical parameters and amplitude transfer parameters of cross-scale transmission are extracted. When the preliminary correspondence layer does not meet the preset matching stability conditions, other candidate layer pairs are iteratively verified by sorting them according to causal driving strength until the final correspondence layer that meets the refinement conditions is determined. Specifically, the preliminary correspondence layer is refined and verified based on change node matching to determine the final correspondence layer, including: extracting the reconstructed signals of the cause sensor and the result sensor corresponding to the preliminary correspondence layer based on multi-scale hierarchical representation; performing change node detection on the reconstructed signals of the cause sensor and the result sensor respectively to obtain the change node sets of the cause sensor and the result sensor; wherein, the information of each change node includes the occurrence time, change amplitude, and change direction; for each change node in the change node set of the cause sensor, candidate nodes that meet the preset matching conditions are searched in the change node set of the result sensor, and the node with the smallest delay time is selected as the matching node from the candidate nodes. Record the delay time of successfully matched node pairs; the preset matching conditions include time lag constraints, maximum delay threshold constraints, and consistency constraints of change direction; based on the successfully matched node pairs, calculate the matching rate, delay statistics parameters, and amplitude propagation parameters between the node pairs; when the preliminary matching layer meets the preset refinement conditions, the preliminary matching layer is determined as the final matching layer; the preset refinement conditions include a matching rate not lower than a preset matching rate threshold and a coefficient of variation of the delay statistics parameter not exceeding a preset coefficient of variation threshold; when the preliminary matching layer does not meet the preset refinement conditions, other layer pairs are selected as new preliminary matching layers in descending order of statistical quantity for refinement verification until the final matching layer that meets the preset refinement conditions is determined.

[0052] The reconstructed signal mentioned above refers to the time-domain signal recovered by inverse transforming the wavelet coefficients of a specific layer obtained after multi-scale decomposition. Its sequence length remains consistent with the original sensor time-series data, but only the dynamic characteristics at the corresponding frequency scale or time resolution of that layer are retained; other scale information has been filtered out by zeroing the coefficients. By extracting the reconstructed signals of the cause sensor and the result sensor corresponding to the initial corresponding layer, the dynamic correlation between the two can be examined in a pure single-scale space, avoiding interference from the aliasing of multiple frequency components in the original signal on the detection of abrupt events. This provides a scale-aligned and time-aligned signal basis for subsequent change node matching. A change node refers to the moment point in the time-series signal where a significant abrupt change occurs, characterizing the local state transition caused by particle breakage, agglomeration, or surface charge changes during the dispersion process of the mesoporous carbon electrode slurry. When detecting change nodes on the reconstructed signal, the sliding window variance ratio method can be used, comparing the ratio of signal variances within adjacent sliding windows to identify the abrupt change location; alternatively, the cumulative sum method can be used, accumulating the deviation of the signal from the reference value to detect persistent mean shifts or variance changes. Each detected change node records three attributes: occurrence time, change amplitude, and change direction. The occurrence time represents the instantaneous moment of the state transition; the change amplitude represents the difference in signal before and after that moment; and the change direction represents whether the signal shows an upward or downward trend. To suppress false detections caused by noise, changes with amplitudes less than a preset multiple of the standard deviation of the signal at that layer (e.g., 1.5 times or based on 3) must be removed. In principle, tiny nodes (three times the standard deviation of signal noise in the stable segment) are selected, and only statistically significant change nodes are retained for subsequent matching.

[0053] For each change node in the set of cause sensor change nodes, a candidate node satisfying preset matching conditions needs to be found in the set of result sensor change nodes. The preset matching conditions include three constraints: a time lag constraint, requiring the occurrence time of the result node to be strictly greater than that of the cause node, to reflect the causal temporal relationship of cross-scale responses; a maximum delay threshold constraint, requiring the time difference between the result node and the cause node to not exceed a preset upper limit (this upper limit can be set according to slurry characteristics and process cycle time, for example, taking the 95th percentile of the successful matching delay in the pre-experiment or 1.5 times the process cycle time), to exclude spurious correlations caused by accidental events or external disturbances; and a change direction consistency constraint, requiring the change direction of the result node to be the same as that of the cause node (both rising or both falling), to reflect the physical consistency of the transmission from microscale changes to macroscale responses. Among the candidate nodes satisfying the above three constraints, the node with the smallest delay time is selected as the matching node. This selection strategy is based on the shortest path principle of cross-scale physical transmission, that is, the most direct path for microscale changes to trigger macroscale responses should exhibit the smallest time delay.

[0054] Based on successfully matched node pairs, the matching rate, delay statistics, and amplitude transfer parameters are calculated. The matching rate is defined as the ratio of the number of successfully matched cause nodes to the total number of cause nodes. It is dimensionless and ranges from 0 to 1, representing the proportion of cause nodes in the initial correspondence layer that can stably trigger the response of result nodes. Delay statistics include the delay mean and delay standard deviation. The delay mean is the arithmetic mean of the differences between the occurrence time of the result node and the occurrence time of the cause node in all successfully matched node pairs, measured in time units (e.g., seconds), representing the average lag time of the cross-scale response. The delay standard deviation is the sample standard deviation of the aforementioned delay times, also measured in time units, representing the dispersion of the cross-scale response lag time. Amplitude transfer parameters include the amplitude ratio mean and amplitude ratio standard deviation. The amplitude ratio of a single node pair is defined as the change amplitude of the result node divided by the change amplitude of the cause node, dimensionless, representing the amplitude gain or attenuation ratio when microscale changes are transferred to macroscale responses. The amplitude ratio mean is the arithmetic mean of the amplitude ratios of all successfully matched node pairs, and the amplitude ratio standard deviation is its sample standard deviation. Both together characterize the stability of cross-scale amplitude transfer.

[0055] The calculated matching rate and delay statistics are compared with preset refinement conditions to determine whether the preliminary correspondence layer possesses a stable cross-scale event-level transmission pattern. The preset refinement conditions include two indicators: the matching rate is not lower than a preset matching rate threshold (e.g., 80%, which can be determined based on the mean matching rate of qualified batches minus two standard deviations), ensuring a sufficiently high proportion of stable response relationships between cause nodes and result nodes; the coefficient of variation of the delay statistics does not exceed a preset coefficient of variation threshold (e.g., 0.3 or 0.5, which can be the smaller of the 90th percentile of the coefficient of variation of qualified batches and 0.5), ensuring sufficient statistical stability of the cross-scale delay time. If the preliminary correspondence layer simultaneously meets the above refinement conditions, it is determined as the final correspondence layer; if not, other candidate layer pairs are selected sequentially in descending order of statistical magnitude as new preliminary correspondence layers, and the process of reconstructed signal extraction, change node detection, matching verification, and parameter calculation is repeated until a final correspondence layer that meets the refinement conditions is determined. If no matching pair is found after traversing all candidate layer pairs, the layer pair with the highest matching rate and the smallest delay standard deviation is selected as the final corresponding layer to ensure the completeness of cross-scale correspondence analysis in the statistically optimal sense.

[0056] The physical essence of refined verification of change node matching lies in verifying the physical authenticity of the overall statistical correlation identified by the Granger causality test down to the level of abrupt events. The Granger causality test can only indicate a predictive dependency between two nodes in the overall time series, but this dependency may stem from long-term common trends or environmental noise coupling, and may not correspond to the physical transmission path from micro-changes to macro-scale responses. By detecting and matching abrupt events, it is possible to directly verify whether each micro-state transition can statistically stably trigger a macro-scale hysteresis response, thereby eliminating pseudo-correspondence layers that only have overall correlation but lack event-level causal transmission. Simultaneously, the delay statistical parameters and amplitude transmission parameters extracted from successful matches provide a quantifiable physical benchmark for setting prediction windows and evaluating cross-scale response consistency in the real-time monitoring phase, elevating decentralized state monitoring from qualitative judgment to quantitative assessment based on cross-scale dynamic parameters.

[0057] In addition to the aforementioned refined verification method based on changing node matching, another method can be adopted: a refined verification method based on time-domain cross-correlation coefficients. This method calculates the normalized cross-correlation coefficients of the reconstructed signals of the preliminary corresponding layers under different time lags, and selects the layer pairs with the largest correlation coefficient peaks and stable corresponding lag times as the final corresponding layers. Alternatively, a refined verification method based on frequency-domain coherence analysis can be used. This method evaluates the coherence intensity and phase lag stability of the preliminary corresponding layers on common frequency components using wavelet coherence spectra or amplitude-squared coherence coefficients, and determines the layer pairs with significant coherence and monotonically lag-mode phase spectra as the final corresponding layers. Another method can be adopted based on dynamic time warping. This method finds the optimal nonlinear time alignment path between the reconstructed signals of the preliminary corresponding layers, and determines the layer pairs with the smallest warping distance and stable monotonically lag-mode warping path as the final corresponding layers. Yet another method can be adopted based on information theory transfer entropy. This method estimates the directed information transfer between the preliminary corresponding layers and performs statistical significance tests, determining the layer pairs with the largest transfer entropy and meeting the significance level as the final corresponding layers.

[0058] The aforementioned cross-scale transfer parameters are a set of statistical parameters characterizing the relationship between time lag and amplitude response during the transfer of dynamic changes at the microscale to the macroscale response of mesoporous carbon electrode slurry. These parameters typically include delay statistical parameters and amplitude transfer parameters. The delay statistical parameters include the delay mean and delay standard deviation, while the amplitude transfer parameters include the amplitude ratio mean and amplitude ratio standard deviation. After determining the corresponding cross-scale layer, the reconstructed signals of the corresponding layers of the cause sensor and the result sensor are extracted and change node detection is performed to obtain a set of change nodes containing occurrence time, change amplitude, and change direction. Then, for each change node in the change node set of the cause sensor, matching nodes satisfying the time lag constraint, maximum delay threshold constraint, and change direction consistency constraint are searched in the change node set of the result sensor, and relevant information of successfully matched node pairs is recorded. Based on the successfully matched node pairs, the arithmetic mean of the difference between the occurrence time of the result node and the occurrence time of the cause node is used as the delay mean, and the sample standard deviation is used as the delay standard deviation. Similarly, the arithmetic mean of the ratio of the change amplitude of the result node to the change amplitude of the cause node is used as the amplitude ratio mean, and the sample standard deviation is used as the amplitude ratio standard deviation. This completes the extraction of the cross-scale transfer parameters for the corresponding cross-scale layer.

[0059] Step S150: In the real-time monitoring phase, a prediction window is set based on the cross-scale correspondence layer and cross-scale transfer parameters, and the cross-scale response of the result sensor's cross-scale correspondence layer is verified.

[0060] In the real-time monitoring phase, the cross-scale response of the cross-scale corresponding layer of the result sensor is verified based on the cross-scale corresponding layer determined in the offline learning phase and the extracted cross-scale transfer parameters. The purpose is to apply the micro-macro cross-scale causal transfer law established in the stable dispersion state of mesoporous carbon electrode slurry to online process monitoring. By determining whether the macro-scale sensor produces a corresponding change with expected time lag and amplitude response to micro-scale changes according to historical statistical laws, it is possible to determine in real time whether the current dispersion state of the slurry deviates from the normal cross-scale dynamic evolution path. If the result sensor does not produce a response that meets the expected cross-scale transfer parameters within the prediction window, it indicates that the changes at the micro-particle scale have failed to be stably transferred to the macro-flow behavior scale, suggesting that the dispersion state may be deteriorated due to agglomeration, sedimentation, or damage to the conductive network inside the slurry, or that the sensor system is malfunctioning. This enables real-time anomaly identification and early warning of the dispersion state of the mesoporous carbon electrode slurry.

[0061] The above step S150 can verify the cross-scale response of the resulting sensor's cross-scale corresponding layer through at least one of the following verification methods: The first verification method: cross-scale response verification based on statistical hypothesis testing; This approach transforms the question of whether the result sensor produces the expected response within the prediction window into a statistical decision problem. It uses the cross-scale transfer parameters extracted in the offline phase to establish a statistical distribution model of the result sensor response characteristics. The null hypothesis is set as the result sensor does not produce a cross-scale response driven by the change node of the cause sensor within the prediction window. Then, a test statistic is calculated on the real-time observation data within the prediction window. This statistic is compared with a statistical threshold determined based on historical cross-scale transfer parameters. If the test statistic falls into the rejection region, the cross-scale response is deemed to have been successfully verified; otherwise, the verification is deemed to have failed and an anomaly warning is triggered.

[0062] The second verification method: cross-scale response verification based on Bayesian probability inference; This approach utilizes historical cross-scale transfer parameters to construct a prior probability distribution of the existence of cross-scale responses, and updates the posterior probability by combining it with real-time observation data within the prediction window. By using delay statistics and amplitude transfer parameters obtained in the offline phase as hyperparameters of the prior distribution, a conditional probability model of the resulting sensor response characteristics is established. During real-time monitoring, the likelihood function is calculated based on the observation data within the prediction window, and then the posterior probability of the existence of cross-scale responses is obtained using Bayes' theorem. If this posterior probability exceeds a preset confidence threshold, the response is considered successfully verified; otherwise, the verification is considered to have failed. This approach integrates historical statistical patterns with real-time observation uncertainties, providing a probabilistic quantitative basis for decentralized state assessment.

[0063] The third verification method: cross-scale response verification based on state-space models; This approach models the cross-scale transfer process as a dynamic system with hidden state transitions and observed outputs. A state transition equation is constructed using the delay statistics parameter in the cross-scale transfer parameters to describe the evolution of the result sensor's response state driven by changes in the cause sensor node. The real-time reconstructed signal is used as the output of the observation equation. Kalman filtering or particle filtering algorithms are employed to recursively estimate and update the hidden state within the prediction window. By analyzing whether the observation residual or state estimation covariance exceeds the confidence interval set based on historical statistics, it is determined whether the result sensor has produced a response consistent with the expected cross-scale transfer parameters, thereby achieving adaptive verification against nonlinear and noise-interference process environments.

[0064] The fourth verification method: cross-scale response verification based on dynamic time warping similarity measurement; This method determines the response by comparing the morphological similarity between the real-time signal of the resulting sensor and the expected response template within the prediction window. It constructs the time series morphology of the expected response template based on the delay statistics and amplitude transfer parameters in the cross-scale transfer parameters. A dynamic time warping algorithm is used to find the optimal nonlinear time alignment path between the real-time signal of the resulting sensor and the expected template within the prediction window. The warping distance or warping similarity coefficient is calculated. If the warping distance is less than the similarity threshold determined based on historical data, it indicates that the real-time signal morphology and the expected response template have a sufficient degree of matching, and the cross-scale response verification is considered successful; otherwise, the verification is considered unsuccessful. This method is robust to time deformation caused by process drift.

[0065] The fifth verification method: cross-scale response verification based on changing node detection and orientation consistency determination; Optionally, step S150 includes: acquiring monitoring data from the cause sensor and the result sensor in real time, and reconstructing them into real-time reconstructed signals for the corresponding cross-scale layers; detecting change nodes in the real-time reconstructed signal of the cause sensor, and setting a prediction window based on the cross-scale transfer parameters when a change node of the cause sensor is detected; within the prediction window, detecting change nodes in the real-time reconstructed signal of the result sensor to verify whether there are change nodes with the same direction as the change nodes of the cause sensor; if there are change nodes with the same direction, the cross-scale response verification is determined to be successful, and the cross-scale transfer parameters are updated based on the successfully verified nodes; if no change nodes with the same direction are detected within the prediction window, the cross-scale response verification is determined to be unsuccessful and an anomaly warning is triggered.

[0066] The core of the real-time monitoring phase lies in applying the cross-scale corresponding layer and extracted cross-scale transfer parameters determined in the offline phase to online process monitoring. This requires mapping the raw monitoring data collected in real-time by cause and result sensors to the cross-scale corresponding layer to obtain a real-time reconstructed signal consistent with the scale space of the offline modeling. This real-time reconstructed signal retains only the dynamic characteristics at the frequency scale represented by the cross-scale corresponding layer, filtering out irrelevant fluctuations and interference from other scales. This provides a scale-aligned and time-aligned signal foundation for subsequent detection of change nodes and verification of cross-scale responses. The calculation of the real-time reconstructed signal can use the same wavelet basis functions and decomposition levels as in the offline phase, while also considering the real-time requirements of online calculation. This can be achieved using a sliding window approach, where a fixed length of recent time-series monitoring data is truncated for batch wavelet decomposition and corresponding layer coefficient reconstruction. The window is updated over time to ensure signal timeliness. Alternatively, online filtering algorithms such as recursive wavelet transform can be used to achieve low-latency reconstruction point-by-point or segment-by-segment by recursively updating wavelet coefficients, avoiding the time lag caused by batch calculations and thus meeting the real-time requirements of industrial sites for monitoring response speed. The purpose of detecting change nodes in real-time reconstructed signals is to identify abrupt events in the dispersion process of mesoporous carbon electrode slurry online. The detection method can be a lightweight exponentially weighted moving average cumulative sum control chart, which can sensitively detect small mean shifts by accumulating and calculating weighted residuals. Alternatively, the sliding window variance ratio method or the cumulative sum method can be used. When a new change node is detected in the corresponding layer of the cause sensor across the scale, the occurrence time and direction of change of the node are recorded as the cross-scale driving event that triggers the setting of the subsequent prediction window.

[0067] When a change node is detected in the causal sensor, a prediction window is set based on the delay statistics parameter in the cross-scale transfer parameters extracted in the offline stage. This window delineates the time observation interval expected to generate a cross-scale response in the corresponding cross-scale layer of the result sensor. Within the prediction window, change node detection is performed on the real-time reconstructed signal of the result sensor to verify whether there are any change nodes with the same change direction as the change nodes in the causal sensor. The change direction consistency constraint requires that the change direction of the change nodes in the result sensor and the change direction of the change nodes in the causal sensor both have an upward trend or both have a downward trend, reflecting the physical unidirectionality of the transfer of microscale dynamics to macroscale response. If a change node satisfying the direction consistency is detected within the prediction window, the cross-scale response verification is considered successful, indicating that the cross-scale causal transfer path of the current mesoporous carbon electrode slurry is in a normal state. If no change node satisfying the direction consistency is detected at the end of the prediction window, the cross-scale response verification is considered to have failed and an anomaly warning is triggered, indicating that small-scale changes have not caused the expected large-scale response, which may indicate agglomeration or sensor failure.

[0068] After successful cross-scale response verification, the actual delay time and actual amplitude ratio of this verification can be included in the offline sample library for subsequent adaptive updates of cross-scale transfer parameters. The actual delay time is the difference between the occurrence time of the result sensor matching node and the occurrence time of the cause sensor change node, measured in units of time. The actual amplitude ratio is the ratio of the change amplitude of the result sensor matching node to the change amplitude of the cause sensor change node, and is dimensionless. After each preset number of successful matches, the average delay, standard deviation of delay, average amplitude ratio, and standard deviation of amplitude ratio are recalculated based on the expanded sample library. The updated cross-scale transfer parameters replace the original parameters for setting the subsequent prediction window, thus enabling the time boundary of the prediction window to adapt to the evolution of cross-scale dynamic characteristics caused by process drift.

[0069] When multiple result sensor change nodes appear within the prediction window, the node with the same direction as the cause sensor change node and the shortest delay time is selected as the matching node to follow the shortest path principle of cross-scale physical transfer. If no change node with the same direction is detected in multiple consecutive prediction windows, but the slurry state is confirmed to be normal by manual verification, it indicates that the cross-scale transfer parameters established in the offline stage may be invalid due to process condition drift. At this time, the warning level should be temporarily reduced and the model retraining process should be triggered to re-execute the offline learning stage of cross-scale corresponding layer determination and cross-scale transfer parameter extraction. If the matching rate of the current cross-scale corresponding layer is consistently lower than the preset threshold during long-term operation, it will automatically switch to the second-best corresponding layer sorted by statistics and relearn the delay statistics parameters and amplitude transfer parameters of this layer to maintain the continuous effectiveness of the cross-scale response verification mechanism.

[0070] It is understood that the accuracy of the aforementioned cross-scale response verification depends on the degree of matching between the prediction window time boundary and the cross-scale delay dynamics characteristics. This time boundary should be set based on the delay statistical parameters extracted in the offline stage to delineate a reasonable cross-scale response observation interval in the corresponding layer of the result sensor. Specifically, the aforementioned setting of the prediction window based on cross-scale transfer parameters includes: setting the time boundary of the prediction window based on the occurrence time of the change node of the cause sensor and the delay statistical parameters in the cross-scale transfer parameters; wherein, the time boundary is used to limit the time observation interval in the cross-scale corresponding layer of the result sensor where the expected cross-scale response is generated.

[0071] The setting of the prediction window directly determines the sensitivity and false alarm rate of cross-scale response verification. If the window is too wide, it will introduce too much irrelevant fluctuation, leading to a decrease in verification specificity. If the window is too narrow, it may miss legitimate delayed responses caused by process drift. The delay statistics parameter is the core basis for setting the prediction window. It consists of the delay average and delay standard deviation extracted from the offline stage based on successfully matched node pairs. The delay average characterizes the average lag time in the process of transferring microscale changes in mesoporous carbon electrode slurry to macroscale responses, reflecting the reference time scale of cross-scale causal transmission under steady-state process conditions. The delay standard deviation characterizes the dispersion of this lag time caused by local non-uniformity of the slurry, fluctuations in stirring intensity, or sensor sampling noise. Together, they characterize the statistical distribution characteristics of cross-scale response delay. The time boundary of the prediction window is determined by the following formula: Window start point = Occurrence time of causal node + (Delay average) The window endpoint is calculated as follows: Cause node occurrence time + (mean delay + twice the standard deviation of delay). The cause node occurrence time is the instant when the cause sensor change node is detected, measured in units of time. The mean delay is the average lag time of the cross-scale response statistically analyzed during the offline phase, measured in units of time. The standard deviation of delay represents the dispersion of the cross-scale response lag time statistically analyzed during the offline phase, measured in units of time. If the calculated window start point is less than or equal to the cause node occurrence time, the window start point is corrected to the cause node occurrence time plus the minimum physical delay. This minimum physical delay is the sum of the sensor's inherent response time and the fluid transport time of the slurry in the pipeline or mixing tank, rounded up, measured in units of time. This ensures that the prediction window has a physically achievable time lag.

[0072] If the starting point of the window calculated by the above formula is less than or equal to the occurrence time of the causal node, it indicates that the lower bound of the statistically estimated delay is physically unrealizable. In this case, the starting point of the window needs to be corrected to the occurrence time of the causal node plus the minimum physical delay. The minimum physical delay is the sum of the inherent response time of the sensor and the fluid transport time of the slurry in the mixing tank or transfer pipeline, rounded up. The dimension is time unit, and its value depends on the sensor hardware characteristics and process pipeline geometry parameters. This correction ensures the rationality of the prediction window in terms of physical causal timing and avoids the logical paradox caused by setting the starting point of the window before or at the same time as the occurrence of the causal node.

[0073] Besides the ±2 standard deviation method based on the assumption of normal distribution, the time boundary of the prediction window can also be set using other statistical criteria. When historical delay data does not conform to a normal distribution after testing, a quantile method based on empirical distribution can be used, taking the 2.5% and 97.5% quantiles of historical successful matching delay times as the offsets for the start and end points of the window, respectively, to cover approximately 95% of the sample interval without being constrained by the distribution shape. Alternatively, an adaptive exponential weighted moving average method can be used, assigning higher weight to the delay times of recent successful matching to update the delay average and delay standard deviation online, so that the time boundary of the prediction window can adapt to the gradual drift of process conditions more quickly. A variable window method based on information criteria can also be used, dynamically adjusting the window width according to the magnitude of the change in the cause node during the real-time monitoring stage, using a wider window for nodes with large changes to accommodate possible nonlinear delay expansion, and using a narrower window for nodes with small changes to improve verification accuracy.

[0074] It is understandable that, in addition to the above-mentioned scheme of setting the prediction window time boundary based on delay statistical parameters, the prediction window can also be set using the quantile method based on the historical delay experience distribution. That is, the low quantile and high quantile of the successful matching delay time in the offline stage are taken as the offset of the window start and end points, respectively, to cover a preset proportion of the sample interval without being constrained by the normal distribution assumption. Alternatively, a dynamic update method based on adaptive exponential weighted moving average can be used to give higher weight to the recently successfully matched delay time to update the delay statistical parameters online, so that the time boundary of the prediction window is adaptively adjusted with process drift. Or, a variable window method based on the change amplitude classification can be used to dynamically adjust the window width according to the magnitude of the change in the cause sensor node. A wider window is used for nodes with large value changes to accommodate nonlinear delay expansion, and a narrower window is used for nodes with small value changes to improve verification accuracy. Or, a method based on fixed physical delay superimposed with statistical tolerance can be used, with the minimum physical delay as the benchmark start point and a preset multiple of the delay standard deviation as the end point, to ensure that the prediction window achieves a balance between physical feasibility and statistical coverage.

[0075] It is understandable that the aforementioned cross-scale response verification may detect multiple change nodes satisfying the directional consistency constraint within the prediction window. To clarify the true attribution of the result sensor's response to the change nodes of the cause sensor, a preset matching strategy needs to be established to determine a unique target matching node from multiple candidate nodes. Specifically, the aforementioned change node detection of the real-time reconstructed signal of the result sensor to verify whether there are change nodes with the same direction as the change nodes of the cause sensor includes: within the prediction window, performing change node detection on the real-time reconstructed signal of the result sensor to obtain a set of change nodes of the result sensor; filtering candidate change nodes whose change direction is consistent with the change nodes of the cause sensor from the set of change nodes; when there are multiple candidate change nodes, determining the target matching node from the candidate change nodes based on the preset matching strategy to obtain the cross-scale response verification result.

[0076] The purpose of detecting change nodes in the real-time reconstructed signal of the result sensor within the prediction window is to focus cross-scale response verification on the expected response arrival time driven by the change nodes of the causal sensor, avoiding indiscriminate scanning of the result sensor signal throughout the entire time period and introducing irrelevant fluctuations or noise pseudo-nodes outside the prediction window, thereby improving the specificity and signal-to-noise ratio of cross-scale response verification. This detection is only performed within the time observation interval defined by offline delay statistics, ensuring that the detection results have a direct causal relationship with the cross-scale driving event of the causal node in time. Change node detection can employ lightweight algorithms suitable for online scenarios to meet real-time requirements, such as the exponentially weighted moving average cumulative sum control chart, which sensitively detects small mean shifts in the signal by accumulating weighted residuals, has low computational complexity, and is suitable for point-by-point updates; alternatively, the sliding window variance ratio method can be used to identify state transition moments by comparing the degree of abrupt change in signal variance within adjacent windows; or the cumulative sum method can be used to detect persistent mean drift by continuously accumulating the deviation of the signal from the benchmark value. The detected change nodes record three attributes: occurrence time, change amplitude, and change direction. The occurrence time is the instant the node is detected, measured in units of time. The change amplitude is the difference in signal level before and after the node, measured in the same units as the original sensor signal. The change direction indicates whether the signal shows an upward or downward trend. Screening candidate change nodes whose change direction matches the cause sensor's change node from the detection results is based on the physical unidirectional constraint of cross-scale causal transmission. Microscopic particle breakage in mesoporous carbon electrode slurry leads to a reduction in particle size, usually accompanied by increased exposure of surface functional groups and a decrease in overall slurry viscosity. This physical process should show a unidirectional trend in both the cause and result sensors. If the result sensor produces a reverse change node within the prediction window, the change is more likely to originate from external disturbances or local noise independent of the cause node, rather than a cross-scale response driven by the cause node. Therefore, directional consistency constraints can effectively eliminate spurious correlations. When multiple candidate change nodes satisfying directional consistency constraints exist within the prediction window, a unique target matching node is determined based on a preset matching strategy. This strategy prioritizes the candidate node with the smallest delay time as the target matching node. The delay time is defined as the difference between the occurrence time of the candidate change node and the occurrence time of the causal sensor change node, measured in units of time. This minimum delay priority strategy follows the shortest path principle of cross-scale physical transmission, meaning that the response directly driven by microscopic changes at the macroscopic scale should exhibit the smallest time lag. Candidate nodes with larger delays may correspond to other independent disturbance events or indirect transmission paths, rather than the most direct cross-scale response triggered by the causal node.

[0077] The cross-scale response verification results are obtained based on the determination of the target matching node: If the target matching node is successfully determined within the prediction window, it indicates that the result sensor has generated a response with the same direction as the change node of the cause sensor and the minimum delay within the expected time interval. The cross-scale response verification is judged to be successful, and the actual delay time of this verification is included in the online update sample library of cross-scale transfer parameters. If no candidate change node is obtained after directional consistency screening within the prediction window, or if the candidate nodes do not meet the selection conditions of the preset matching strategy, the cross-scale response verification is judged to be unsuccessful. This indicates that the microscale change failed to cause a corresponding macroscale response within the statistically expected time window, suggesting that the cross-scale causal transfer path of the mesoporous carbon electrode slurry may have been interrupted.

[0078] It is understandable that, in addition to the matching strategy based on minimum delay priority mentioned above, a matching method based on amplitude propagation consistency can also be adopted within the prediction window. This involves calculating the deviation between the actual amplitude ratio of each candidate change node and the average historical amplitude ratio extracted during the offline phase, selecting the candidate node with the smallest deviation as the target matching node, thus prioritizing the retention of responses most consistent with historical cross-scale amplitude propagation patterns. Alternatively, a matching method based on multi-attribute comprehensive scoring can be adopted. This involves constructing a weighted scoring function that integrates delay deviation, amplitude deviation, and direction consistency, calculating a comprehensive score for each candidate node, and selecting the one with the highest score as the target matching node, thereby achieving matching across multiple dimensions. The rationality of cross-scale responses can be evaluated in a balanced way; alternatively, a matching method based on dynamic time warping similarity can be used to compare the real-time signal segments in the neighborhood of each candidate node with the expected response template constructed based on historical transmission parameters, and select the candidate node with the smallest warping distance as the target matching node to adapt to nonlinear time deformation caused by process drift; or, a matching method based on Bayesian probability inference can be adopted, which uses historical cross-scale transmission parameters to establish a prior distribution of candidate nodes as the true response and combines real-time observations to calculate the posterior probability, and selects the candidate node with the largest posterior probability as the target matching node, providing a probabilistic quantitative decision basis for the attribution of cross-scale responses.

[0079] Step S160: Based on the cross-scale response verification results and cross-scale transfer parameters, calculate the dispersion state index of the mesoporous carbon electrode slurry.

[0080] The aforementioned dispersion state index of mesoporous carbon electrode slurry is a single comprehensive evaluation index used to quantitatively characterize the dispersion quality of mesoporous carbon electrode slurry in real time. A higher value indicates that the dynamic changes at the microscopic particle scale can be stably and consistently transmitted to the macroscopic flow behavior scale, meaning that the cross-scale causal transmission path is smooth and the dispersion state is good. Conversely, a lower value indicates that microscopic changes have failed to trigger the expected macroscopic response according to historical statistical patterns, suggesting possible dispersion state deterioration such as agglomeration, sedimentation, or damage to the conductive network within the slurry. This index, by integrating the degree of conformity between cross-scale response verification results and historical cross-scale transmission parameters, transforms the inherent correlation between multi-source, multi-scale sensor monitoring data into a discrete value that can be output in real time. This provides a direct and quantitative basis for the classification and determination of dispersion state and process intervention decisions during the production process of mesoporous carbon electrode slurry.

[0081] Optionally, step S160 includes: within a sliding window, calculating the matching success rate, delay consistency, and amplitude consistency based on the cross-scale response verification results and cross-scale transfer parameters; and weighting and summing the matching success rate, delay consistency, and amplitude consistency to obtain the dispersion state index of the mesoporous carbon electrode slurry.

[0082] The aforementioned sliding window is a time-localized mechanism for online evaluation of the dispersion state of mesoporous carbon electrode slurry. It constructs a dynamic data subset using the nodes of recent causal sensor changes as boundaries, ensuring both the sensitivity of the dispersion state evaluation to recent process fluctuations and maintaining the statistical stability of the evaluation benchmark through a fixed window length. The window contains the total number of causal sensor change nodes and the number of nodes that successfully trigger the cross-scale response verification of the result sensor. This provides a unified sample basis for calculating the three sub-indicators: matching success rate, delay consistency, and amplitude consistency. The window length can be set according to the average node interval to ensure that the window typically contains a preset number of nodes. The matching success rate characterizes the proportion of causal sensor change nodes that can stably drive the result sensor to produce the expected cross-scale response within the sliding window time range. It is calculated as the ratio of the number of successfully matched causal sensor change nodes within the window to the total number of causal sensor change nodes within the window. If the actual number of nodes within the window is less than the preset length, it is calculated based on the actual number of nodes. This indicator is dimensionless, ranging from 0 to 1. A higher value indicates a better degree of smoothness of the cross-scale causal transmission path within the current process period.

[0083] Delay consistency characterizes the degree of agreement between the actual delay time of each successfully matched node pair within the sliding window and the historical cross-scale transmission pattern. It transforms the actual delay deviation into a probabilistic score using a Gaussian scoring function. For each successfully matched node pair within the window, when the delay standard deviation is greater than zero, the delay score of a single node is calculated using the following formula: Delay score of a single node = exp(-(actual delay)) The delay score is calculated as the square of the average delay / (the square of twice the standard deviation of the delay). If the standard deviation of the delay is zero, and the actual delay equals the average delay, the delay score is set to 1; otherwise, it is set to 0. Here, the actual delay is the difference between the time when the node matches the result sensor and the time when the node changes due to the cause sensor, measured in units of time. The average delay is the average lag time of the cross-scale response statistically based on historical successfully matched node pairs during the offline phase, measured in units of time. The standard deviation of the delay is the sample standard deviation of the cross-scale response lag time statistically based on the offline phase, measured in units of time. The delay consistency is obtained by taking the arithmetic mean of the delay scores of all successfully matched nodes within the window. If there are no successfully matched nodes within the window, the delay consistency is zero. This indicator is dimensionless and ranges from 0 to 1.

[0084] Amplitude consistency characterizes the degree of agreement between the actual amplitude ratio of each successfully matched node pair within the sliding window and the historical cross-scale amplitude propagation pattern. It also uses a Gaussian scoring function for deviation measurement. For each successfully matched node pair within the window, when the standard deviation of the amplitude ratio is greater than zero, the amplitude score of a single node is calculated using the following formula: Amplitude score of a single node = exp(-(actual amplitude ratio)) The amplitude consistency is calculated as the square of the amplitude ratio (mean) / (square of twice the standard deviation of the amplitude ratio). When the standard deviation of the amplitude ratio is zero, if the actual amplitude ratio equals the mean amplitude ratio, the amplitude score is set to 1; otherwise, the amplitude score is set to 0. Here, the actual amplitude ratio is the ratio of the change amplitude of the result sensor matching node to the change amplitude of the cause sensor matching node in the node pairing, and is dimensionless; the mean amplitude ratio is the mean of the cross-scale amplitude transmission ratio statistically analyzed based on historical successful matching node pairs during the offline phase, and is dimensionless; the standard deviation of the amplitude ratio is the sample standard deviation of the cross-scale amplitude transmission ratio statistically analyzed during the offline phase, and is dimensionless. The arithmetic mean of the amplitude scores of all successfully matched nodes within the window is used to obtain the amplitude consistency. If there are no successfully matched nodes within the window, the amplitude consistency is zero. This indicator is dimensionless and ranges from 0 to 1.

[0085] After obtaining the three sub-indicators of matching success rate, delay consistency, and amplitude consistency, they are weighted and synthesized to obtain the dispersion state index of the mesoporous carbon electrode slurry. The calculation formula is as follows: Final dispersion state index = 100 × (matching success rate × weight 1 + delay consistency × weight 2 + amplitude consistency × weight 3). Wherein, weight 1, weight 2, and weight 3 are the contribution weights of matching success rate, delay consistency, and amplitude consistency in the comprehensive evaluation, respectively. All three are dimensionless and satisfy weight 1 + weight 2 + weight 3 = 1. The dispersion state index is dimensionless, ranging from 0 to 100. A higher value indicates a better dispersion state of the mesoporous carbon electrode slurry. The three sub-indicators characterize dispersion quality from three orthogonal dimensions: the existence of cross-scale response, time lag stability, and amplitude propagation stability. Matching success rate reflects the smoothness of the propagation from micro-changes to macro-response; delay consistency reflects the stability of the cross-scale propagation time pattern; and amplitude consistency reflects the stability of the cross-scale response intensity ratio. The Gaussian scoring function maps the deviation between the actual observed value and the historical average to an exponentially decaying probability score, so that small deviations receive higher scores while large deviations decay rapidly. This balances the tolerance for normal process fluctuations and the sensitivity to abnormal deviations in the comprehensive evaluation.

[0086] After calculating the dispersion state index of the mesoporous carbon electrode slurry, the dispersion state of the current slurry is classified according to the numerical range of the index to support graded process decisions. When the dispersion state index is greater than the first preset threshold, the dispersion state is judged to be excellent, indicating that the dynamic changes at the microscale can be stably and consistently transmitted to the macroscale response, and the cross-scale causal transmission path is in good condition. When the dispersion state index is between the first and second preset thresholds, the dispersion state is judged to be average, indicating that the stability of cross-scale transmission has slightly deteriorated, and process attention needs to be strengthened. When the dispersion state index is lower than the second preset threshold, the dispersion state is judged to be poor, indicating that the microscale changes have failed to effectively trigger the expected macroscale response, suggesting that agglomeration, sedimentation or damage to the conductive network may occur inside the slurry, and process intervention should be implemented immediately.

[0087] Furthermore, the calculation and output of the dispersion state index adopts a real-time update mechanism that combines event-driven or period-driven approaches. Each time a new cause sensor change node is detected, the dispersion state index is recalculated based on the updated sliding window and output immediately, or recalculated at preset fixed time intervals when no change node is detected, to ensure the timeliness of the monitoring results. The index is output to the process control system or human-machine interface in real time in the form of a single numerical value, providing operators with an intuitive quantitative basis for dispersion quality and serving as an input signal to trigger automatic control or alarm interlocking. During long-term operation, if multiple cross-scale response verifications fail to match within the prediction window but the slurry condition is manually confirmed to be normal, it indicates that the cross-scale transfer parameters established in the offline stage may become invalid due to sensor sensitivity drift or gradual changes in process conditions. In this case, the abnormal warning level should be temporarily reduced and the model retraining process should be triggered to re-execute the offline learning stage of cross-scale corresponding layer determination and cross-scale transfer parameter extraction. If the matching rate of the current cross-scale corresponding layer continues to be lower than the preset switching threshold during long-term operation, it will automatically switch to the second-best corresponding layer ranked by statistics as the new primary corresponding layer, and relearn the delay statistics parameters and amplitude transfer parameters of this layer to maintain the continuous effectiveness of the cross-scale response verification mechanism.

[0088] To facilitate understanding of the working principle of the above-described data fusion-based method for monitoring the dispersion state of mesoporous carbon electrode slurry, this application also provides an application example of this method in a specific scenario. For example... Figure 2 As shown, in this application scenario, the above-mentioned data fusion-based method for monitoring the dispersion state of mesoporous carbon electrode slurry mainly includes: Step 1: Data collection; Based on the monitoring requirements, sensors with suitable accuracy and response speed are selected. For this application scenario, the following five sensors are chosen: ultrasonic particle size analyzer, pH meter, resistivity meter, density meter, and rheometer. From ultrasonic particle size analyzer (particle size), pH meter (surface charge), resistivity meter (conductive network), density meter (solid content) to rheometer (flow behavior), the monitoring scale increases sequentially from microscopic to macroscopic. Specifically, the ultrasonic particle size analyzer reflects the geometric size of individual particles or aggregates (nanometer to micrometer scale), the pH meter reflects the chemical environment determined by the ionization of functional groups on the particle surface (molecular level), the resistivity meter reflects the network structure formed by the contact between conductive particles (mesoscopic scale), the density meter reflects the overall solid-liquid ratio of the slurry (macroscopic average), and the rheometer reflects the flow and deformation of the slurry under external forces (macroscopic overall behavior). Therefore, the data collected by these five sensors covers the complete cross-scale range from particle scale to macroscopic flow behavior.

[0089] Then, according to process requirements, install the sensors in appropriate locations within the slurry mixing tank or pipeline to ensure representative measurements. Simultaneously, establish a unified data acquisition platform to achieve synchronous triggering and recording of the five sensors, ensuring all data have the same time reference, setting a uniform sampling frequency (usually the highest sampling rate among all sensors), and configuring data storage and transmission interfaces.

[0090] Step 2: Integrate data from multiple sensors to perform anomaly monitoring; Based on the inherent differences in monitoring scale among different detection methods—from ultrasonic particle size analyzers (particle size), pH meters (surface charge), resistivity meters (conductive network), density meters (solid content) to rheometers (flow behavior)—the monitoring scale gradually increases from microscopic to macroscopic. By utilizing the inherent correlation between these monitoring data at different scales, a comprehensive assessment and monitoring of the electrode slurry dispersion state can be achieved. Step two mainly includes: Step 2.1, Sensor Screening: Obtain the strongest causal pairs and directions through pairwise Granger causality tests.

[0091] Step 2.2, Hierarchical Decomposition: Obtain the multi-scale hierarchical tree of the target sensor through wavelet packet decomposition.

[0092] Step 2.3, Granger correspondence layer: Obtain the preliminary correspondence layer through the layer-to-Granger test.

[0093] Step 2.4, Change Node Refinement: Obtain the final corresponding layer and delay parameters through change node matching calculation.

[0094] Step 2.5 Real-time monitoring: Obtain matching success or failure alarms through online reconstruction and delayed window prediction.

[0095] The following sections will describe each of the above steps in detail: Step 2.1: Screening of target sensor pairs; Among the five types of sensors (ultrasonic particle size analyzer, pH meter, resistivity meter, density meter, and rheometer), the pair with the clearest influence relationship at the monitoring scale, that is, the strongest causal relationship (for example, the greater the probability that a change at a small scale can cause a change at a larger scale, the stronger the causal relationship), is identified as the focus of subsequent cross-scale analysis.

[0096] The specific steps include: (1) Synchronously collect time series data from five sensors and unify the sampling frequency (e.g., one data point per second). Preprocess each sequence: remove outliers, fill missing data with linear interpolation, and remove the overall trend (first-order difference) to make the sequence stable. (2) For any two sensor combinations (ten pairs in total), test two directions (e.g., from sensor A to sensor B, and from sensor B to sensor A). Record the statistics (F-value) and significance probability (p-value) for each direction. Only retain causal relationships with a significance probability less than 5% (i.e., p < 0.05). (3) Compare the statistics (F-value) of all significant causal relationships, and take the sensor pair and direction corresponding to the maximum value. This direction is considered to be the smaller-scale sensor (cause) driving the larger-scale sensor (effect). For example, obtain "ultrasonic particle size analyzer → rheometer". If the strongest causal pair is significant in both directions and has similar intensity, then according to physical common sense (particle size and acidity / alkalinity belong to the microscopic, while resistivity, density, and viscosity belong to the macroscopic), choose the direction from microscopic to macroscopic. The final output is the target sensor pair, denoted as "cause sensor" and "result sensor", along with the causal direction (cause drives result).

[0097] Step 2.2: Multi-resolution decomposition and hierarchical tree construction; The number of decomposition layers is determined based on the length of the original sequence and the sampling frequency. Generally, five to eight layers are chosen; for example, six layers can be used when the sampling frequency is one point per second and the data length is one thousand points. The number of decomposition layers can also be determined based on the signal length and the lowest frequency period, stopping decomposition when the energy of the approximation layer is lower than two percent of the original signal. Discrete wavelet transform or maximum overlap discrete wavelet transform is used to decompose the original sequences of the two sensors in the target sensor alignment layer by layer: starting with the original signal, a low-pass filter and a high-pass filter are applied to obtain the first-layer approximation signal and the first-layer detail signal, respectively; then, the above operation is repeated for the first-layer approximation signal to obtain the second-layer approximation signal and the second-layer detail signal; and so on, until the preset number of decomposition layers is reached. The decomposition yields wavelet coefficients, which need to be reconstructed back to the time domain: for each layer's approximation signal, only the approximation coefficients of that layer are retained, and the rest are set to zero; an inverse transform is then performed to obtain the time series of that node; for each layer's detail signal, only the detail coefficients of that layer are retained, and the rest are set to zero; an inverse transform is then performed to obtain the time series of that node. The length of all reconstructed sequences is the same as the original signal. Each reconstructed signal is treated as a node, and a hierarchical tree is constructed: the original signal is the root node (level 0); the first level contains approximation 1 and detail 1, with the root node as the parent node; the second level further decomposes approximation 1 to obtain approximation 2 and detail 2, with approximation 1 as the parent node; and so on, until the Lth level yields approximation L and detail L. Each sensor obtains a hierarchical tree containing 2×L nodes (L levels of approximation and L levels of detail). The approximation signal reflects low-frequency trends, while the detail signal reflects high-frequency fluctuations, and the higher the level number, the lower the frequency and the larger the time scale. Each node is assigned a unique name in the format sensor name_type_level number, for example, "particle size_detail_two" represents the second level detail signal of the particle size sensor, and "viscosity_approximation_four" represents the fourth level approximation signal of the viscosity sensor.

[0098] Step 2.3: Determine the initial corresponding layer; Pair all nodes (2×L in total) of the cause sensor with all nodes (2×L in total) of the result sensor one-to-one, resulting in (2×L)×(2×L) layer pairs. For each layer pair, using the layer of the cause sensor as the candidate cause and the layer of the result sensor as the result, perform a Granger causality test to determine the optimal lag order (based on the information criterion), and record the F-statistic and the significance probability value p-value. Only layer pairs with p-values ​​less than the preset significance level are retained; if there are no significant layer pairs, the number of decomposition layers needs to be increased or the data quality needs to be checked. Among the significant layer pairs, sort them in descending order of the F-statistic, and take the layer pair with the largest F-value as the initial corresponding layer, denoted as a layer of the cause sensor and a layer of the result sensor, for example, "particle size_details_two → viscosity_details_one".

[0099] Step 2.4: Refined Validation and Cross-Scale Transfer Parameter Extraction; Reconstructed signals from the cause and result sensors corresponding to the initial corresponding layers are extracted separately. Significantly changing nodes are detected using the sliding window variance ratio method or the cumulative sum method. For each node, the occurrence time, magnitude of change, and direction of change are recorded. To suppress false detections caused by noise, the magnitude threshold for changing nodes can be set to three times the standard deviation of the signal noise in the stable segment (3σ principle), eliminating tiny nodes with magnitudes smaller than this threshold. In practical applications, nodes with magnitudes smaller than 1.5 times the standard deviation of the signal in that layer can also be used as a screening criterion. For each changing node in the cause sensor layer, a matching node satisfying the following conditions is searched among the changing nodes in the result sensor layer: the time of the result node is greater than the time of the cause node; the maximum delay does not exceed a preset time limit (e.g., thirty seconds, which can be taken as the 95th percentile of the successful matching delay in the pre-experiment, or calculated by multiplying the process cycle time by 1.5); and the direction of change is the same. Among the candidate nodes that meet the conditions, the one with the smallest delay is selected as the match, and the delay time of this match is recorded. If no match is found, the cause node is marked as unmatched. Wherein, the matching rate = number of successfully matched cause nodes / total number of cause nodes; the average delay = arithmetic mean of the delay times of all successfully matched nodes; the standard deviation of delay = sample standard deviation of the delay times of all successfully matched nodes. Determine whether the preliminary corresponding layer meets the preset refinement conditions. The preset refinement conditions include a matching rate not lower than a preset matching rate threshold and a delay standard deviation not exceeding a preset proportion of the average delay. The matching rate threshold can be determined based on the average matching rate of qualified batches minus twice the standard deviation (e.g., 80%), and the delay coefficient of variation threshold can be the smaller of the 90th percentile of the coefficient of variation of qualified batches and 0.5 (e.g., delay standard deviation not exceeding 30% of the average delay). If the matching rate of the preliminary corresponding layer is lower than the preset threshold, or the delay standard deviation is greater than the preset proportion of the average delay, it indicates that the layer pair is not optimal. In this case, take the next layer pair from the candidate layer pairs in step 2.3 (sorted by F-value from largest to smallest), and repeat the refinement verification in this stage until a layer pair that meets the matching rate and delay coefficient of variation requirements is found as the final corresponding layer (i.e., the cross-scale corresponding layer). If none of the candidate layer pairs meet the requirements, the one with the highest matching rate and the smallest delay standard deviation is selected as the final corresponding layer (i.e., the cross-scale corresponding layer).

[0100] Output: The final matching layer (cross-scale matching layer), and the mean delay, standard deviation of delay, and matching rate for each pair of nodes in this layer. Additionally, the amplitude ratio parameters should also be recorded. For each successfully matched node pair in the final matching layer (cross-scale matching layer), calculate the amplitude ratio as the change in amplitude of the result node divided by the change in amplitude of the cause node. Then calculate the mean amplitude ratio and standard deviation of the amplitude ratio for all matched node pairs, used for subsequent real-time amplitude consistency evaluation. The mean delay, standard deviation of delay, mean amplitude ratio, and standard deviation of amplitude ratio together constitute the cross-scale transfer parameters.

[0101] Step 2.5: Real-time cross-scale fusion and anomaly monitoring; Data from the cause and result sensors are acquired in real time and preprocessed using the same methods as in the offline phase (detrending and denoising). Stationarity is updated online using a sliding window approach. Using the same wavelet basis functions and decomposition levels as in the offline phase, the cross-scale corresponding layer reconstruction signals of the cause and result sensors are calculated in real time. Low-latency reconstruction can be achieved using a sliding window or online filtering algorithm (such as recursive wavelet transform).

[0102] Lightweight change node detection (such as the cumulative sum of exponentially weighted moving average) is performed on the two reconstructed signals respectively. When a new change node is detected in the corresponding layer of the cause sensor across the scale, its occurrence time and change direction are recorded.

[0103] The prediction window is set based on the offline statistical mean delay and standard deviation delay. The time boundary of the prediction window is determined by the following formula: Window start point = Occurrence time of the cause node + (Mean delay) The window endpoint is calculated as: (twice the standard deviation of the delay). The window endpoint is calculated as: (cause node occurrence time + (delay average + twice the standard deviation of the delay)). If the calculated starting point is less than or equal to the cause node occurrence time, the starting point is set to the cause node occurrence time plus a minimum physical delay. If historical delay data is found to be non-normally distributed, the prediction window width can be replaced by using the 2.5% and 97.5% quantiles of historical successful match delay times as boundaries, instead of the standard deviation-based calculation method. The cross-scale corresponding layers of the sensor are continuously observed within the prediction window. If a node with a consistent direction of change is detected within the window, it is considered a normal response, and the actual delay time and actual amplitude ratio are added to the offline sample library for subsequent updates of the delay average, delay standard deviation, amplitude ratio average, and amplitude ratio standard deviation. If no node with a consistent direction of change is detected at the end of the window, an anomaly warning is triggered. Every ten new successful matches are accumulated, the delay average, delay standard deviation, amplitude ratio average, and amplitude ratio standard deviation are recalculated to make the prediction window adapt to process drift.

[0104] Step 3: Output the comprehensive evaluation index of the distributed state; The distributed state comprehensive evaluation index is based on a sliding window (the window length is determined according to the average node interval, so that the window usually contains ten nodes, for example, twenty minutes; if there are fewer than ten nodes in the window, the actual number of nodes is taken), and the following three sub-indicators are calculated respectively: (1) Matching success rate = number of nodes successfully matched in the window divided by the total number of nodes in the window. (2) Delay consistency: For each successfully matched node in the window, the deviation between its actual delay time and the historical delay average is calculated. When the delay standard deviation is greater than zero, a Gaussian scoring function is used: Delay score of a single node = exp(-(actual delay) The square of the average delay / (the square of twice the standard deviation of the delay); when the standard deviation of the delay is zero, if the actual delay is equal to the average delay, the delay score is set to 1, otherwise the delay score is set to 0; then take the average score of all successfully matched nodes. If there is no successful match in the window, the delay consistency score is zero. (3) Amplitude consistency: For each successfully matched node in the window, calculate the deviation between its actual amplitude ratio and the historical average amplitude ratio. When the standard deviation of the amplitude ratio is greater than zero, the Gaussian scoring function is also used: Amplitude score of a single node = exp(-(actual amplitude ratio)) / (the square of twice the standard deviation of the delay ... The amplitude consistency score is calculated as the square of the amplitude ratio to the mean, divided by the square of twice the amplitude ratio to the standard deviation. When the amplitude ratio to the standard deviation is zero, if the actual amplitude ratio equals the amplitude ratio to the mean, the amplitude score is set to 1; otherwise, the amplitude score is set to 0. Then, the average score of all successfully matched nodes is taken. If there is no successful match within the window, the amplitude consistency score is zero.

[0105] The final dispersion index = 100 × (matching success rate × weight 1 + delay consistency × weight 2 + amplitude consistency × weight 3). Weights can be obtained through the analytic hierarchy process (pairwise comparisons by experts) or regression coefficient normalization. Recommended weights: matching success rate 50%, delay consistency 30%, amplitude consistency 20%.

[0106] The status grading threshold can be determined based on the maximum Yangen index of the ROC curves for acceptable and unacceptable batches. The status grading is as follows: A dispersion index greater than 85 indicates excellent dispersion, with microscopic changes being stably transmitted to macroscopic responses.

[0107] A dispersion index between 60 and 85 indicates a generally low level of dispersion, which warrants attention.

[0108] A dispersion index of less than 60 indicates poor dispersion, requiring immediate intervention.

[0109] Real-time updates: Each time a new cause sensor change node is detected (or after a fixed time interval, such as thirty seconds), the dispersion state index within the sliding window is recalculated and output.

[0110] Special Case Handling: If multiple result sensor layer nodes appear within the prediction window, prioritize the one with the same direction as the cause node and the smallest delay as the match. If multiple nodes with the same direction exist, take the first one. If no match is found within three consecutive prediction windows, but the slurry status is subsequently confirmed to be normal, it may be due to decreased sensor sensitivity or offline parameter failure. The tolerance for consecutive non-matches can be taken as the 95th percentile of the number of consecutive non-matches under normal process conditions (e.g., three). In this case, the warning level should be temporarily lowered, and model retraining should be triggered (re-execute steps 2.3 to 2.5). If the matching rate of the corresponding layer across scales remains below 60% during long-term operation, automatically switch to the second-best corresponding layer (the next candidate layer pair sorted by F-value), and relearn the delay parameter and amplitude ratio parameter. The threshold for switching the backup layer can be set to trigger when the main layer matching rate is lower than the historical average minus two standard deviations and remains lower than the backup layer.

[0111] like Figure 3 As shown, based on the same inventive concept, this application also provides a data fusion-based mesoporous carbon electrode slurry dispersion state monitoring system 200, including a host computer 210 and a multi-scale sensor 220 communicatively connected to the host computer, wherein: The multi-scale sensor 220 is installed in the mixing tank or transmission pipeline of the mesoporous carbon electrode slurry to collect time-series monitoring data of the mesoporous carbon electrode slurry at multiple different monitoring scales and send the time-series monitoring data to the host computer. The host computer 210 is used to acquire time-series monitoring data; Granger causality tests are performed on time-series monitoring data at multiple different monitoring scales to screen out the target sensor pairs with the strongest cross-scale driving relationship and their causal directions, and to determine the cause sensor and the result sensor; multi-scale decomposition is performed on the time-series monitoring data of the target sensor pairs to obtain multi-scale hierarchical representations; cross-scale correspondence analysis is performed based on the multi-scale hierarchical representations to determine the cross-scale correspondence layers and extract the cross-scale transfer parameters of the cross-scale correspondence layers; in the real-time monitoring stage, a prediction window is set based on the cross-scale correspondence layers and the cross-scale transfer parameters to verify the cross-scale response of the result sensor's cross-scale correspondence layers; based on the cross-scale response verification results and the cross-scale transfer parameters, the dispersion state index of the mesoporous carbon electrode slurry is calculated.

[0112] It is understood that the host computer 210 described above can realize any one of the functions of the data fusion-based mesoporous carbon electrode slurry dispersion state monitoring method provided in the embodiments of this application. The method embodiment section describes the way each function is realized and the working principle. The system embodiment section will not repeat the description.

[0113] This invention is now complete.

[0114] In summary, in this embodiment of the invention, time-series monitoring data of mesoporous carbon electrode slurry at multiple different monitoring scales are acquired; Granger causality tests are performed on the time-series monitoring data at multiple different monitoring scales to screen out the target sensor pairs with the strongest cross-scale driving relationship and their causal directions, thus determining the causal sensor and the result sensor; multi-scale decomposition is performed on the time-series monitoring data of the target sensor pairs to obtain multi-scale hierarchical representations; cross-scale correspondence analysis is performed based on the multi-scale hierarchical representations to determine the cross-scale correspondence layers and extract the cross-scale transfer parameters of the cross-scale correspondence layers; during the real-time monitoring stage, a prediction window is set based on the cross-scale correspondence layers and the cross-scale transfer parameters to verify the cross-scale response of the result sensor's cross-scale correspondence layers; based on the cross-scale response verification results and the cross-scale transfer parameters, the dispersion state index of the mesoporous carbon electrode slurry is calculated. This invention establishes a causal relationship and transfer parameter model between monitoring data of mesoporous carbon electrode slurry at the micro-particle scale and macro-flow behavior scale by coupling Granger causality test and multi-scale decomposition. This enables the dispersion state assessment to reflect the dynamic evolution law across scales rather than local information at a single scale. On the other hand, based on Granger causality test, the target sensor pair with the strongest cross-scale driving relationship is screened from multi-scale sensors to avoid interference from redundant sensor data on fusion analysis. A hierarchical tree is constructed through multi-resolution decomposition to capture the evolution characteristics at different time scales. Furthermore, the initial corresponding layer is refined and verified by using change node matching, and delay statistics parameters and amplitude transfer parameters are extracted. This allows for a quantitative characterization of the time lag characteristics and amplitude transfer relationship of the cross-scale response, providing a quantifiable physical basis for real-time prediction. Finally, based on the cross-scale transfer parameters, a prediction window is set for online response verification. The dispersion state index is generated by comprehensively considering the matching success rate, delay consistency, and amplitude consistency, thereby realizing real-time quantitative assessment and anomaly warning of the dispersion state of mesoporous carbon electrode slurry.

[0115] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion, characterized in that, The method includes: Acquire time-series monitoring data of mesoporous carbon electrode slurry at multiple different monitoring scales; Granger causality test was performed on the time-series monitoring data at multiple different monitoring scales to screen out the target sensor pairs with the strongest cross-scale driving relationship and their causal direction, and to determine the causal sensor and the result sensor. The time-series monitoring data of the target sensor pair are decomposed into multi-scale data to obtain a multi-scale hierarchical representation. Cross-scale correspondence analysis is performed based on the multi-scale hierarchical representation to determine the cross-scale correspondence layer and extract the cross-scale transfer parameters of the cross-scale correspondence layer. During the real-time monitoring phase, a prediction window is set based on the cross-scale correspondence layer and the cross-scale transfer parameters to verify the cross-scale response of the result sensor's cross-scale correspondence layer. Based on the cross-scale response verification results and the cross-scale transfer parameters, the dispersion state index of the mesoporous carbon electrode slurry was calculated.

2. The method for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion according to claim 1, characterized in that, The cross-scale correspondence analysis based on the multi-scale hierarchical representation to determine the cross-scale correspondence layer includes: Perform a layer-to-layer Granger causality test on each layer of the multi-scale hierarchical representation of the cause sensor and the multi-scale hierarchical representation of the result sensor to determine the preliminary corresponding layers; Based on the matching of changing nodes, the preliminary corresponding layer is refined and verified to determine the final corresponding layer, so as to obtain the cross-scale corresponding layer.

3. The method for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion according to claim 2, characterized in that, The process of performing a layer-by-layer Granger causality test on each layer of the multi-scale hierarchical representation of the cause sensor and the multi-scale hierarchical representation of the result sensor to determine the preliminary corresponding layers includes: The layers in the multi-scale hierarchical representation of the cause sensor and the layers in the multi-scale hierarchical representation of the result sensor are fully combined and paired to obtain multiple layer pairs; Granger causality test is performed on each of the layer pairs to determine the optimal lag order for each layer pair, and the statistics and significance probability values ​​of each layer pair are obtained. Retain the layer pairs whose significance probability values ​​are less than a preset significance level to obtain significant layer pairs; A preliminary corresponding layer is determined from the salient layer pairs; wherein the preliminary corresponding layer is the layer pair with the largest statistic among the salient layer pairs.

4. The method for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion according to claim 2, characterized in that, The step of refining and verifying the preliminary corresponding layer based on changing node matching to determine the final corresponding layer includes: Based on the multi-scale hierarchical representation, the reconstructed signals of the cause sensor and the result sensor corresponding to the preliminary corresponding layer are extracted respectively; Change node detection is performed on the reconstructed signals of the cause sensor and the result sensor respectively to obtain the change node set of the cause sensor and the change node set of the result sensor; wherein, the information of each change node includes the occurrence time, change magnitude and change direction; For each of the change nodes in the set of change nodes of the cause sensor, a candidate node that meets the preset matching conditions is found in the set of change nodes of the result sensor, and the node with the smallest delay time is selected as the matching node from the candidate nodes. The delay time of the successfully matched node pair is recorded. The preset matching conditions include time lag constraints, maximum delay threshold constraints, and change direction consistency constraints. Based on the successfully matched node pairs, calculate the matching rate, delay statistics parameters, and amplitude transmission parameters between the node pairs; When the preliminary matching layer meets the preset refinement conditions, the preliminary matching layer is determined as the final matching layer; wherein, the preset refinement conditions include the matching rate being not lower than a preset matching rate threshold and the coefficient of variation of the delay statistics parameter not exceeding a preset coefficient of variation threshold; If the preliminary corresponding layer does not meet the preset refinement conditions, other layers are selected in descending order of statistical quantity as new preliminary corresponding layers for refinement verification until the final corresponding layer that meets the preset refinement conditions is determined.

5. The method for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion according to claim 1, characterized in that, The step of setting a prediction window based on the cross-scale correspondence layer and the cross-scale transfer parameters, and performing cross-scale response verification on the cross-scale correspondence layer of the result sensor, includes: The monitoring data from the cause sensor and the result sensor are acquired in real time and reconstructed into real-time reconstructed signals for the corresponding cross-scale layers, respectively. Change nodes are detected in the real-time reconstructed signal of the cause sensor. When a change node of the cause sensor is detected, a prediction window is set based on the cross-scale transfer parameters. Within the prediction window, change nodes are detected in the real-time reconstructed signal of the result sensor to verify whether there are change nodes whose change nodes are consistent with the change nodes of the cause sensor. If there are nodes with consistent direction of change, the cross-scale response verification is deemed successful, and the cross-scale transfer parameters are updated based on the successfully verified node pairs. If no nodes with consistent direction of change are detected within the prediction window, the cross-scale response verification is deemed to have failed and an anomaly warning is triggered.

6. The method for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion according to claim 5, characterized in that, The step of setting the prediction window based on the cross-scale transfer parameters includes: Based on the occurrence time of the change node of the cause sensor and the delay statistics parameter in the cross-scale transfer parameter, the time boundary of the prediction window is set; wherein, the time boundary is used to limit the time observation interval in the cross-scale corresponding layer of the result sensor that is expected to generate a cross-scale response.

7. The method for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion according to claim 5, characterized in that, Within the prediction window, the process of detecting change nodes in the real-time reconstructed signal of the result sensor and verifying whether there are change nodes with the same direction as the change nodes of the cause sensor includes: Within the prediction window, change nodes are detected on the real-time reconstructed signal of the result sensor to obtain the set of change nodes of the result sensor; From the set of change nodes, candidate change nodes whose change direction is consistent with the change nodes of the cause sensor are selected; When there are multiple candidate change nodes, a target matching node is determined from the candidate change nodes based on a preset matching strategy to obtain cross-scale response verification results.

8. The method for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion according to any one of claims 1-7, characterized in that, The calculation of the dispersion state index of the mesoporous carbon electrode slurry based on the cross-scale response verification results and the cross-scale transfer parameters includes: Within the sliding window, the matching success rate, delay consistency, and amplitude consistency are calculated based on the cross-scale response verification results and the cross-scale transfer parameters, respectively. The dispersion state index of the mesoporous carbon electrode slurry is obtained by weighting and synthesizing the matching success rate, the delay consistency, and the amplitude consistency.

9. The method for monitoring the dispersion state of mesoporous carbon electrode slurry based on data fusion according to any one of claims 1-7, characterized in that, The Granger causality test is performed on the time-series monitoring data at multiple different monitoring scales to screen out the target sensor pairs with the strongest cross-scale driving relationship and their causal direction, and to determine the causal sensor and the result sensor, including: Preprocessing is performed on the time-series monitoring data at multiple different monitoring scales to obtain stationary time-series data; The causal directionality test is performed on the stationary time series data at each monitoring scale in pairs to obtain the causal driving strength and significance level of each sensor pair in different directions. Based on the causal driving strength and the significance level, the target sensor pair with the strongest cross-scale driving relationship and its causal direction are selected. Based on the target sensor pair and the causal direction, the cause sensor and the result sensor are determined.

10. A data fusion-based system for monitoring the dispersion state of mesoporous carbon electrode slurry, characterized in that, It includes a host computer and a multi-scale sensor that is communicatively connected to the host computer, wherein: The multi-scale sensor is installed in the mixing tank or transmission pipeline of the mesoporous carbon electrode slurry, and is used to collect time-series monitoring data of the mesoporous carbon electrode slurry at multiple different monitoring scales, and send the time-series monitoring data to the host computer. The host computer is used to acquire the time-series monitoring data; perform Granger causality tests on the time-series monitoring data at multiple different monitoring scales to screen out the target sensor pairs with the strongest cross-scale driving relationship and their causal directions, and determine the cause sensor and the result sensor; perform multi-scale decomposition on the time-series monitoring data of the target sensor pairs to obtain multi-scale hierarchical representations; perform cross-scale correspondence analysis based on the multi-scale hierarchical representations to determine the cross-scale correspondence layers and extract the cross-scale transfer parameters of the cross-scale correspondence layers; in the real-time monitoring stage, set a prediction window based on the cross-scale correspondence layers and the cross-scale transfer parameters, and perform cross-scale response verification on the cross-scale correspondence layers of the result sensor; calculate the dispersion state index of the mesoporous carbon electrode slurry based on the cross-scale response verification results and the cross-scale transfer parameters.

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