A method for analyzing the root cause of defects in the surface spraying process of a metal product

Abstract

The present application relates to metal product surface spraying process parameter acquisition and defect root cause analysis technology, aiming at solving the causality analysis and root cause determination problem of defects caused by multi-parameter disturbance in spraying process. By deploying multiple types of sensors, 12-dimensional core process parameters are collected in real time, signal conditioning, synchronization and data encapsulation are used to form high-fidelity time sequence flow data. Based on parameter change, disturbance fingerprint is extracted, combined with principal component analysis and dynamic time warping to realize disturbance type clustering. Using lightweight granger causality analysis, the parameter subset is limited to efficiently capture local causal paths, and the causality path stability entropy of process sensitive weight adjustment is proposed by combining the direction consistency ratio and the response delay standard deviation, which is used for root cause variable sorting and explanation. The scheme improves the accuracy and decision interpretability of spraying defect causality tracing, effectively enhances the process optimization and intelligent quality control level of production line.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing and industrial process optimization technology, and in particular to a method for root cause analysis of defects in the surface coating process of metal products. Background Technology

[0002] In the fields of intelligent manufacturing and industrial process optimization, root cause analysis of defects in metal product surface coating has become a crucial technical aspect of lean production, quality control, and equipment operation and maintenance. Current mainstream technologies employ methods such as knowledge graph reasoning, temporal causal networks, data-driven causal testing, and large-scale model hypothesis generation to analyze the relationship between coating defects and process parameters. Among these, knowledge graphs and causal relationship mining techniques can assist in automating defect diagnosis, but they typically rely on highly structured process knowledge, the accumulation of large expert experience databases, and the continuous maintenance of the global causal graph. On the other hand, temporal neural networks and deep temporal modeling algorithms possess certain reasoning capabilities in scenarios with dynamic coupling of multivariate parameters, but their interpretability and robustness are limited by the completeness of the initial model settings and data annotations. In recent years, the field of large-scale model generation has attempted to combine natural language hypothesis reasoning and counterfactual simulation to provide textual explanations of defect patterns in complex coating scenarios; however, such solutions significantly rely on large-scale corpora and knowledge transfer, making it difficult to guarantee the consistency and reliability of the explanations.

[0003] In actual spray coating production lines, multivariate process parameters (such as spray gun movement trajectory, atomizing air pressure, paint flow rate, workpiece rotation speed, and ambient temperature and humidity) often change drastically due to adjustment events (such as color change, speed increase, film thickness calibration, etc.). These disturbances exhibit spatiotemporal locality, leading to frequent splits in causal inference paths and fluctuations in parameter coupling relationships, severely impacting the stability of root cause ranking and the credibility of explanations in industrial settings. Existing technologies typically attempt to compensate for ranking jitter caused by inconsistent inference paths through global causal modeling, iterative parameter hypothesis generation, and deep learning on full data. However, this approach not only consumes significant computational resources and has a slow inference response, but also struggles to guarantee the transparency, high reproducibility, and traceability of the explanation logic in real dynamic process environments.

[0004] Typical technologies in this field are applied in scenarios such as intelligent manufacturing production lines, metal part surface treatment, and automated control of spraying robots to achieve real-time monitoring of spraying quality, location of abnormal defects, and causal chain tracing decisions. Key representative technical solutions focus on rule-based reasoning based on a global knowledge base, hybrid deep learning inference based on time-series data, or root cause analysis relying on counterfactual simulation. These methods are applicable to situations with weak parameter coupling, low event variation frequency, or highly deterministic process models. However, in real-world industrial environments with strong multivariate disturbances, frequent adjustments, and extremely non-steady-state distributions of process parameters, they face the following technical limitations: First, under multivariate process disturbances, causal paths are easily affected by interference sources, leading to inference link splits and instability in ranking, making it impossible to guarantee the consistency and industrial usability of root cause analysis. Second, existing methods require the pre-construction of a complete knowledge base, a global causal graph, or reliance on a large pre-trained model, resulting in excessively high maintenance costs and a lack of flexibility. Third, there is a lack of ability to directly utilize process parameter disturbance behaviors (such as proactive adjustment events, local parameter mutations, etc.) as anchor points for causal analysis, making it difficult to efficiently transform dynamic process feedback into diagnostic inference clues. Fourth, in real-time production line environments, existing technologies struggle to achieve robust root cause ranking and transparent explanation under high-frequency process disturbances, exhibiting typical problems such as response delays, logical jumps, and inconsistent explanations.

[0005] Therefore, the field of intelligent manufacturing and industrial process optimization urgently needs a method that does not rely on knowledge graphs or large model mechanisms, but can directly utilize the perturbation behavior of process parameters as perturbation fingerprints. This method, centered on perturbation semantic anchors and causal path stability entropy, aims to achieve highly consistent, robust, efficient, and interpretable root cause ranking across multiple perturbation scenarios. This technology should not only possess path filtering and logical convergence capabilities under dynamic parameter adjustments but also meet the real-time requirements of production line-level edge computing. This will significantly improve the reliability of industrial defect diagnosis and the efficiency of decision-making loops, providing a solid technical guarantee for subsequent coating quality control, optimized scheduling, and digital operation and maintenance. Summary of the Invention

[0006] This application provides a method for root cause analysis of defects in the surface coating process of metal products, aiming to solve one of the problems or issues of the prior art mentioned in the background.

[0007] This application provides a method for root cause analysis of defects in metal product surface spraying processing, specifically including: S1: Real-time acquisition of 12 core process parameters, including spray gun movement trajectory, atomization pressure, paint flow rate, workpiece rotation speed, and ambient temperature and humidity, during the metal product surface spraying process, forming high-fidelity time-series data with a sampling period of 500 milliseconds as the benchmark. S2: Based on the process parameters, actively adjust the trigger time of the event, extract the parameter change pattern within a 3-second window before and after the event, and construct a process perturbation fingerprint library containing 7 typical perturbation fingerprints through principal component projection and dynamic time warping distance clustering. Each perturbation fingerprint corresponds to a unique perturbation semantic label. S3: For the perturbation fingerprint triggered within 60 seconds before the occurrence of the current spraying defect sample, each perturbation fingerprint is used as a local causal probe. Within the corresponding perturbation period, 3 to 5 parameter subsets that are strongly coupled with the perturbation are activated, and a lightweight Granger causality test is run to generate a set of local causal sub-paths. S4: For candidate root variables in the local causal sub-path set, calculate their directional consistency ratio as upstream nodes in sub-paths triggered by different perturbation fingerprints, and statistically analyze the standard deviation of the response delay distribution as a path stability index. S5: Based on the directional consistency ratio and the standard deviation of response delay, the causal path stability entropy index of the candidate root variable is calculated in combination with the process sensitivity weighting coefficient. The stability entropy value is negatively correlated with the directional consistency ratio and negatively correlated with the standard deviation of response delay. S6: Sort all candidate root variables in ascending order according to the causal path stability entropy index, and select the top 3 variables with the smallest entropy values ​​as the highly robust root cause ranking results; S7: Generate an explanatory summary based on the root cause ranking results. The summary includes the frequency of occurrence of the root cause variable in the upstream nodes of the perturbation fingerprint, the directional consistency ratio, the range of response delay fluctuations, and the stability entropy value.

[0008] The method for root cause analysis of defects in metal product surface spraying processing provided in this application has the following beneficial effects: (1) By transforming process parameter adjustment events into perturbation fingerprints with semantic labels and using them as time anchors for local causal analysis, the accuracy and interpretability of defect root cause tracing in complex spraying processes are significantly improved. Traditional causal inference methods often mistakenly treat high-frequency time-series process data as random noise because they do not consider active intervention behaviors in actual production, resulting in distorted causal structure learning. This scheme innovatively utilizes typical parameter change patterns caused by human control actions such as spray gun operation and color switching to construct a perturbation fingerprint library with physical meaning, so that causal testing focuses on strongly coupled parameter subsets within a specific perturbation window, effectively reducing the search space and enhancing the fit of the inference results to the real process logic. Compared with global modeling or static variable screening methods, this mechanism significantly reduces the probability of generating false causal associations, especially showing stronger robustness and directionality in multivariate dynamic interaction scenarios.

[0009] (2) A causal stability entropy evaluation model based on path direction consistency and response delay stability is introduced, achieving a highly reliable ranking of candidate root variables and significantly improving the consistency and engineering usability of diagnostic results. Addressing the problem of easily reversing causal directions and large fluctuations in delay estimation in repeated experiments using existing methods, this scheme starts from the reproducibility across perturbation scenarios, quantifies the frequency of variables acting as upstream drivers under different operating conditions and the concentration of their time response distribution, constructs a two-dimensional stability index—the direction consistency ratio and the delay standard deviation—and integrates them into a unified entropy value H(v iThis mechanism prioritizes the output of key parameters that consistently act as starting points under various disturbance conditions. It not only avoids the risk of overfitting to single event segments but also enhances the ability to identify slow-dynamic processes and hysteresis effects. This results in the top three root variables being recommended having higher process dominance and control sensitivity, providing field engineers with more actionable decision-making guidance.

[0010] (3) A lightweight Granger causality test combined with piecewise linear kernel functions and principal component projection preprocessing is adopted, which greatly optimizes the computational efficiency and edge deployment feasibility of the algorithm while ensuring the accuracy of causal inference. Unlike complex architectures that rely on large-scale graph neural networks or iterative counterfactual simulations, this solution designs a low-overhead computational link throughout the entire process around the real-time requirements of the production line: the perturbation clustering stage achieves efficient pattern classification through DTW distance and dimensionality reduction projection; the causal sub-path extraction adopts a local test strategy with limited spatiotemporal range to avoid full sequence scanning; the stability entropy calculation only involves statistical summarization and logarithmic operations, without the need for additional training. The entire process can run independently on edge computing nodes, and the time for a single inference is controlled within 80ms, which meets the requirements of near real-time closed-loop analysis under high-frequency sampling (500ms cycle), and effectively overcomes the technical bottleneck that traditional causal discovery methods are difficult to implement on the production line side.

[0011] The synergistic effect of the above-mentioned technologies has formed a highly efficient, interpretable, and low-delay defect root cause localization system for metal spraying processes. This system not only breaks through the common limitation of "emphasizing prediction and neglecting attribution" in industrial process data analysis, but also constructs a new causal reasoning paradigm guided by perturbation semantics. It realizes the transformation from passive monitoring to active tracing and provides reliable technical support for the autonomous diagnosis and adaptive optimization of intelligent manufacturing systems. Attached Figure Description

[0012] Figure 1 This is the main flowchart of a method for root cause analysis of defects in metal product surface spraying processing; Figure 2 This is a sub-flowchart of a method for root cause analysis of defects in the surface coating process of metal products; Figure 3 This is another sub-flowchart of a method for root cause analysis of defects in the surface coating process of metal products. Detailed Implementation

[0013] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0014] The following disclosure provides many different embodiments or examples for implementing different structures of the invention. To simplify the disclosure, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the invention. Furthermore, reference numerals and / or letters may be repeated in different examples; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed.

[0015] like Figure 1 As shown, this application provides a method for root cause analysis of defects in the surface coating process of metal products, specifically including: S1: Real-time acquisition of 12 core process parameters, including spray gun movement trajectory, atomization pressure, paint flow rate, workpiece rotation speed, and ambient temperature and humidity, during the metal product surface spraying process, forming high-fidelity time-series data with a sampling period of 500 milliseconds as the benchmark. S2: Based on the process parameters, actively adjust the trigger time of the event, extract the parameter change pattern within a 3-second window before and after the event, and construct a process perturbation fingerprint library containing 7 typical perturbation fingerprints through principal component projection and dynamic time warping distance clustering. Each perturbation fingerprint corresponds to a unique perturbation semantic label. S3: For the perturbation fingerprint triggered within 60 seconds before the occurrence of the current spraying defect sample, each perturbation fingerprint is used as a local causal probe. Within the corresponding perturbation period, 3 to 5 parameter subsets that are strongly coupled with the perturbation are activated, and a lightweight Granger causality test is run to generate a set of local causal sub-paths. S4: For candidate root variables in the local causal sub-path set, calculate their directional consistency ratio as upstream nodes in sub-paths triggered by different perturbation fingerprints, and statistically analyze the standard deviation of the response delay distribution as a path stability index. S5: Based on the directional consistency ratio and the standard deviation of response delay, the causal path stability entropy index of the candidate root variable is calculated in combination with the process sensitivity weighting coefficient. The stability entropy value is negatively correlated with the directional consistency ratio and negatively correlated with the standard deviation of response delay. S6: Sort all candidate root variables in ascending order according to the causal path stability entropy index, and select the top 3 variables with the smallest entropy values ​​as the highly robust root cause ranking results; S7: Generate an explanatory summary based on the root cause ranking results. The summary includes the frequency of occurrence of the root cause variable in the upstream nodes of the perturbation fingerprint, the directional consistency ratio, the range of response delay fluctuations, and the stability entropy value.

[0016] Step S1: Real-time acquisition of 12 core process parameters during the metal product surface spraying process, including spray gun movement trajectory, atomizing air pressure, paint flow rate, workpiece rotation speed, and ambient temperature and humidity, is performed, forming high-fidelity time-series data with a sampling period of 500 milliseconds. Specifically, this includes: S1.1: Implement sensor network deployment for the 12 core process parameter measurement points of the metal product surface spraying line. Based on the industrial automation sensor selection standards, select high-precision displacement sensors, pressure transmitters, flow meters, speed encoders and ambient temperature and humidity sensors to obtain raw physical signals such as spray gun movement trajectory, atomized air pressure, paint flow rate, workpiece speed and ambient temperature and humidity.

[0017] A sensor network is deployed for the 12 core process parameter measurement points of the metal product surface spraying line. The industrial automation sensor selection method (parameters: process parameter range, accuracy level, output interface type, working environment temperature range) is adopted to achieve accurate monitoring of spray gun movement trajectory, atomization pressure, paint flow rate, workpiece rotation speed and ambient temperature and humidity.

[0018] Furthermore, by using a high-precision displacement sensor selection algorithm (parameters: linear resolution ≤ 0.1 mm, measurement range ≥ 1 m, dynamic response time ≤ 5 ms), real-time position sampling of the three-dimensional motion trajectory of the spray gun is achieved, and the original displacement signal sequence is obtained.

[0019] Furthermore, by employing a pressure transmitter selection method (parameters: range covering 0~1.0MPa of spray atomizing gas pressure, accuracy class 0.1%FS, output 4-20mA current signal), continuous monitoring of atomizing gas pressure is achieved, and raw gas pressure signal data is generated.

[0020] Furthermore, based on the electromagnetic flowmeter configuration algorithm (parameters: pipe diameter adapted to the spraying supply system, range meeting 0-50L / min, corrosion-resistant coating inner wall), instantaneous and cumulative measurement of coating flow is achieved, and a raw flow signal set is formed.

[0021] Furthermore, an AB-phase incremental speed encoder layout strategy is adopted (parameters: resolution ≥1024PPR, oil mist resistant housing, operating temperature range -20℃-80℃) to achieve high-precision acquisition of workpiece speed and output speed pulse signal sequence.

[0022] Furthermore, relying on the digital temperature and humidity sensor deployment method (parameters: temperature range -40℃-125℃, humidity range 0%-100%RH, long-term drift ≤±0.1%RH / year), periodic scanning measurement of environmental temperature and humidity is achieved, and raw temperature and humidity signal data is generated.

[0023] By comprehensively deploying the aforementioned sensor network, the raw signals from each measurement point are connected to the data acquisition system via a unified interface protocol, achieving high-fidelity and time-complete preliminary results of physical quantity acquisition, and providing a stable input foundation for subsequent signal conditioning and analog-to-digital conversion steps.

[0024] For example, in a certain automotive parts painting production line, the spray gun movement trajectory is monitored using an optical displacement sensor with a linear resolution of 0.05 mm and a sampling frequency of 2 kHz. Two pressure transmitters with a range of 0-0.8 MPa and an accuracy class of 0.05% FS are installed at the atomizing air pressure monitoring point. A corrosion-resistant electromagnetic flowmeter with a pipe diameter of DN25 and a range of 25 L / min is used for paint flow monitoring. A 2048 PPR encoder is used for workpiece rotation speed monitoring. One digital temperature and humidity sensor is deployed in each of the workpiece clamping area and the painting completion area. After the sensor network is deployed and connected to the data acquisition system, the raw signals output from each measurement point are continuously acquired throughout a single production batch. The signal-to-noise ratio of the raw displacement signal is significantly improved, there is no sampling loss in the atomizing air pressure and paint flow signals, and the temperature and humidity measurement data drift is extremely low, laying a stable data foundation for subsequent process parameter disturbance analysis.

[0025] S1.2: Perform signal conditioning processing on the raw physical signal obtained in S1.1, and perform filtering, noise reduction and gain calibration based on anti-aliasing filter and signal amplification circuit to generate a standardized analog signal.

[0026] The original physical signals obtained from step S1.1, such as the spray gun movement trajectory, atomizing air pressure, paint flow rate, workpiece rotation speed, and ambient temperature and humidity, are processed using an anti-aliasing filter method (parameters: cutoff frequency is set to 0.45 times the sampling frequency, filter type is low-pass FIR, and filter order is adaptively adjusted according to the channel noise characteristics) to attenuate the components of the signal spectrum higher than the Nyquist frequency, thereby effectively suppressing aliasing distortion.

[0027] By using a high-linearity active signal amplifier circuit (parameters: operational amplifier bandwidth ≥ 10 times the highest frequency of the target signal, total harmonic distortion ≤ 0.01%, and amplification factor set according to the sensor output range and ADC input range), the amplitude of the physical signal is increased while maintaining the fidelity of the original waveform, ensuring that weak signals can enter the subsequent sampling range.

[0028] Furthermore, a bandpass filter is applied (parameter: the passband range is set according to the characteristic frequency of the corresponding process parameter, such as the workpiece rotation speed signal passband 20Hz-200Hz) to achieve low-frequency drift suppression and high-frequency noise removal, and to obtain a clean analog signal containing the main process information.

[0029] A DC bias correction algorithm (parameter: calculates the DC component of the signal and cancels it by reverse bias) is adopted to achieve signal baseline alignment and eliminate the baseline drift effect caused by sensor zero drift and changes in ambient temperature and humidity.

[0030] Through gain calibration method (formula as follows):

[0031] in, This is the gain coefficient. For the desired peak voltage, This is the peak voltage of the signal before amplification; it enables unified adjustment of the signal amplitude of each channel and generates a standardized set of analog signals.

[0032] By combining the above circuits and algorithms, the raw physical signals from various types of sensors are transformed into standardized analog signals with amplitude adaptation, pure spectrum, stable DC baseline, and consistent gain, thereby optimizing the input conditions for subsequent high-precision analog-to-digital conversion.

[0033] For example, on a certain automotive parts painting production line, the highest frequency of the spray gun movement trajectory sensor output signal is 180Hz, and the ADC sampling frequency is set to 1kHz. Therefore, the anti-aliasing filter cutoff frequency is set to 450Hz, the filter order is 32, and a Hanning window weighted design is used. The original output range of the spray gun position signal is 0.1V to 0.8V, and the target ADC input range is 0 to 5V. Calculate the gain coefficient. get The active amplifier circuit is configured with a gain of 6.25. In the workpiece rotation speed signal channel, a bandpass filter with a passband range of 20Hz to 200Hz is used to effectively remove low-frequency base drift and high-frequency mechanical noise. For the atomizing air pressure and paint flow signal channels, DC bias correction reduces the zero drift offset from 0.05V to 0.002V. After gain unification calibration, the peak voltage of all signals is stabilized within the 5V input range, and the signal noise amplitude is reduced to 1 / 15 of the original. Verification results show that the digital sequence formed by ADC sampling significantly improves resolution utilization, ensuring the input quality for subsequent perturbation fingerprint extraction and causal inference.

[0034] S1.3: Perform analog-to-digital conversion on the standardized analog signal generated in S1.2, and configure a high-speed ADC module to perform discretization sampling based on a 500-millisecond reference sampling period to obtain a discrete digital sampling sequence of 12-dimensional process parameters.

[0035] S1.4: Perform time synchronization calibration on the discrete digital sampling sequence obtained in S1.3, align the time stamps of multi-channel data based on the distributed clock synchronization protocol, so as to eliminate the time offset between channels and output the synchronized digital sampling sequence.

[0036] S1.5: Performs data encapsulation processing on the synchronized digital sampling sequence output by S1.4, performs data packet formatting and integrity verification based on the time-series data stream protocol, so as to form continuous and stable high-fidelity time-series data stream.

[0037] Step S2: Based on process parameters, actively adjust the trigger time of the event, extract the parameter change pattern within a 3-second window before and after the event, and construct a process perturbation fingerprint library containing 7 typical perturbation fingerprints through principal component projection and dynamic time warping distance clustering. Each perturbation fingerprint corresponds to a unique perturbation semantic label. Specifically, this includes: S2.1: Based on the triggering time of the process parameter active adjustment event and high-fidelity time-series data, the parameter change pattern is defined by feature abstraction. The perturbation fingerprint is used as the semantic identification unit of the process perturbation type to achieve a unique representation of specific perturbation behavior.

[0038] Based on the trigger time of proactive process parameter adjustment events and high-fidelity time-series data, a time-based localization analysis method (parameters: event trigger timestamp set, sampling frequency 500ms) is employed to achieve millisecond-level precise localization of adjustment events within the full time-series data. Furthermore, a window truncation algorithm (parameters: 3-second time span before and after, sampling period 0.5 seconds) is used to extract bidirectional time segments corresponding to the trigger time, obtaining time-series data segments containing changes before and after the disturbance. Further, a rate-of-change calculation method (parameters: 12-dimensional process parameter sequence, sliding window length L=2) is used to calculate the instantaneous rate of change and cumulative change of each parameter within the time segment, generating the original dynamic change feature vector. Further, a pattern encoding method (parameters: change direction marker {increase / decrease / stable}, change amplitude classification {low / medium / high}) is used to translate the change state of each parameter into a symbolic code, forming a 12-character disturbance state symbol string. Through a semantic mapping rule set, the disturbance state symbol string is transformed into an initial feature pattern of the disturbance fingerprint, achieving a unique, structured representation of the disturbance behavior.

[0039] For example, in a spray painting production line, the sampling period is set to 500ms, the event trigger timestamp is 125000ms, and the window truncation algorithm extracts data for 3 seconds before and after this timestamp, i.e., the start of the front window is 122000ms, and the end of the back window is 128000ms. The rate of change is calculated for 12-dimensional parameters, including the spray gun movement trajectory, atomized air pressure, paint flow rate, workpiece rotation speed, and ambient temperature and humidity. The sliding window length is set to 2 sampling points, i.e., 1 second. Assuming that the atomized air pressure increases from 2.0 bar to 2.8 bar within the front and back windows, the rate of change is... The value in bar / s, labeled "increase / decrease", indicates that the paint flow rate decreased from 450 ml / min to 400 ml / min, with a change rate of [missing value]. The values ​​of ml / min / s are labeled "decreasing / medium," while other parameters are assigned labels such as "stable / low" or "increasing / low" according to amplitude grading rules, ultimately forming a symbol string such as [increasing, decreasing / medium, stable / low,...]. The semantic mapping module maps this symbol string to the initial feature pattern of "rapid voltage boost perturbation," which is used for subsequent principal component projection and clustering. The execution results significantly improve the consistency and reproducibility of perturbation behavior recognition in multiple validations.

[0040] S2.2: For the list of trigger times of proactive adjustment events of process parameters, extract 12-dimensional process parameter change data within a 3-second window before and after the event to form a set of parameter change patterns in order to capture the dynamic feature sequence when the disturbance occurs.

[0041] S2.3: Apply the principal component projection algorithm to the set of parameter change patterns for dimensionality reduction, calculate the set of principal component feature vectors, extract the main change direction of the parameter change patterns and reduce data dimensionality redundancy.

[0042] S2.4: Based on the principal component eigenvector set, cluster analysis is performed using a dynamic time-warped distance metric to generate a set of clusters to identify similarity groups of parameter variation patterns and quantify differences between patterns.

[0043] S2.5: Based on the cluster set, construct a process perturbation fingerprint library containing 7 typical perturbation fingerprints, and assign a unique perturbation semantic label to each perturbation fingerprint to achieve standardized representation and semantically interpretable output of process perturbation types.

[0044] like Figure 2 As shown, step S3 involves: for the perturbation fingerprints triggered within 60 seconds prior to the occurrence of the current spraying defect sample, each perturbation fingerprint is used as a local causal probe. Within the corresponding perturbation time period, a subset of 3 to 5 parameters strongly coupled with the perturbation is activated, and a lightweight Granger causality test is run to generate a set of local causal sub-paths. Specifically, this includes: S3.1: Based on historical process parameter time series data, a piecewise linear approximation kernel function is used to replace the traditional Gaussian kernel function to construct a lightweight Granger causality test model, so as to reduce computational overhead and maintain causality detection accuracy.

[0045] Based on historical process parameter time-series data, a piecewise linear approximation kernel function (parameters: piece length, number of nodes, approximation order) is used to replace the traditional Gaussian kernel function, thereby achieving lightweight processing of the kernel function construction step in Granger causality testing.

[0046] Furthermore, by employing a node partitioning strategy for the piecewise linear approximation kernel function (segmenting based on the local fluctuation threshold of historical time series data), dynamic linear fitting of the kernel function on different time segments is achieved, resulting in a kernel matrix representation with reduced computational complexity.

[0047] Furthermore, a matrix normalization method (parameters: row and column normalization mode, normalization range setting) is adopted to standardize the numerical range of the kernel matrix and generate kernel matrix input data suitable for lightweight causality tests.

[0048] Furthermore, by utilizing the Granger causality test regression equation system construction method (parameters: lag order p, significance level α), we can achieve causal coefficient estimation based on a lightweight kernel matrix and generate the causal effect coefficient and confidence value of each variable on other variables.

[0049] Furthermore, a two-way causal significance analysis method is adopted, combining forward and backward causal coefficients to generate a lightweight Granger causality test model structure with directional calibration.

[0050] The aforementioned lightweight Granger causality test model transforms the historical process parameter time-series data from the previous step into a causal action coefficient matrix with low computational overhead, achieving the expected technical effect of maintaining causal detection accuracy under dynamic disturbance background.

[0051] For example, on an automotive parts painting production line, for historical time-series data composed of 12 parameters including spray gun movement trajectory, atomizing air pressure, paint flow rate, workpiece rotation speed, and ambient temperature and humidity, a segment length of 3 seconds, 10 nodes per segment, and an approximation order of 1 are set. A piecewise linear approximation kernel function is used instead of the Gaussian kernel function, reducing the kernel matrix calculation time to 15% of the original. Row and column normalization is then performed on the obtained kernel matrix, with the normalization range set to [...]. [1,1], to ensure the numerical stability of coefficient estimates in causality tests. The lag order is... and significance level Substituting the parameters into the Granger causality test regression equation, the causality coefficient matrix between each parameter is obtained, and the directional confidence is calculated. This lightweight model maintains stable causal detection performance under different perturbation fingerprint scenarios, and the time consumed per test is significantly reduced, achieving the performance requirements of real-time defect analysis on the production line.

[0052] S3.2: Based on the timestamp of the current coating defect sample and the process disturbance fingerprint database, backtrack and extract the 12-dimensional process parameter time sequence subsequence within the disturbance period corresponding to each triggered disturbance fingerprint within the previous 60 seconds of the defect sample to obtain local analysis data.

[0053] Based on the timestamps of current spraying defect samples and the process disturbance fingerprint database, a time window backtracking method (parameters: backtracking duration 60 seconds, window precision 500 milliseconds) is used to capture process events in the time period before the defect sample.

[0054] Furthermore, by using a perturbation fingerprint matching algorithm (parameters: perturbation semantic label, event trigger time), the indexing and location of all triggering perturbation fingerprints within the defect sample time window are realized, and a list of perturbation trigger time periods is generated.

[0055] Furthermore, a multi-channel parameter extraction method (parameters: 12-dimensional core process parameters, synchronized digital sampling sequence) is adopted to extract multi-dimensional parameter sub-sequences within the corresponding disturbance period and obtain local time series analysis data.

[0056] Furthermore, a boundary alignment processing algorithm (parameters: event trigger boundary, sampling reference period) is used to correct the time boundary of the truncated multi-channel parameter sequence and generate a parameter time series submatrix with consistent boundaries.

[0057] Furthermore, a missing value imputation method is employed (parameters: linear interpolation strategy, maximum missing interval). (Sampling period), to achieve integrity repair of local parameter submatrices, and output 12-dimensional process parameter time sequence subsequence during process disturbance period.

[0058] By using time window backtracking and disturbance matching processing, the occurrence time of the defect sample in the previous step is associated with the process disturbance fingerprint database, and transformed into complete parameter time series data required for local causal probe analysis, thus achieving accurate data slicing for the locality of disturbance.

[0059] For example, on a spray painting production line, the timestamp of the current defect sample is recorded as T=10 minutes 12 seconds. The process disturbance fingerprint database contains two trigger records for "rapid pressure increase disturbance" at T=10 minutes 08 seconds to T=10 minutes 09 seconds and T=09 minutes 55 seconds to T=09 minutes 56 seconds. With a backtracking time window set to 60 seconds and a sampling period of 500 milliseconds, for the disturbance period triggered at T=10 minutes 08 seconds, all 12-dimensional parameter data from the 500 milliseconds before to the 2.5 seconds after the disturbance are extracted, including spray gun trajectory, atomized air pressure, paint flow rate, workpiece rotation speed, and ambient temperature and humidity. After extraction, the data from each channel are aligned to ensure that the spray gun trajectory and atomized air pressure curves are consistent in the sampling index. If a missing value appears at the 4th sampling point in the paint flow rate channel, a linear interpolation method is used to fill in the missing sample at time point t=1.5 seconds. The final generated parameter subsequence matrix has a dimension of 12×6 (number of parameter channels × number of sampling points). It is used as the local analysis data for this disturbance period and input into the strongly coupled parameter screening process of S3.3. It has been verified that the backtracking matching and data repair strategy of this step significantly improves the integrity and usability of the local disturbance data.

[0060] S3.3: Based on the principal component load vector corresponding to the perturbation fingerprint, determine the 3 to 5 process parameters with the highest absolute load values ​​as a subset of strongly coupled process parameters to limit the scope of causal analysis.

[0061] S3.4: Based on a lightweight Granger causality test model, Granger causality tests are performed on the subsequence of process parameters during the disturbance period on a strongly coupled subset of process parameters to calculate the confidence of the causal direction and the response delay, and to generate local causal sub-paths.

[0062] Based on the input process parameter subsequences during the disturbance period and the strongly coupled process parameter subsets, a lightweight Granger causality test model (kernel function type: piecewise linear approximation kernel, segment length parameter configured to 1 second based on the disturbance window length, kernel width parameter configured to 0.5 seconds based on the parameter sampling rate) is adopted to realize the function of determining the direction of causality.

[0063] Furthermore, by constructing a multi-lag test model for pairwise parameter pairs within a strongly coupled parameter subset (with the lag range set to 1 to 4 sampling periods), the temporal order within the lag interval is evaluated, and the causal direction confidence data for each parameter pair under a specific lag interval are obtained.

[0064] Furthermore, a response delay measurement method (based on the formula for calculating the time difference corresponding to the lag period) is used to quantify the interaction delay between parameters and generate the response delay value for each parameter pair. The calculation process is as follows:

[0065] in, For response delay value, The lag period is... The duration of a single sampling period.

[0066] Furthermore, parameter pairs with high confidence in causal directions are filtered based on the confidence threshold, and the node relationships of high confidence parameter pairs are mapped into an ordered node pair structure, with additional metadata on direction confidence and response delay.

[0067] By limiting the structure to the above parameters according to the perturbation period, a local causal sub-path dataset containing directional confidence and response delay is generated, thereby enabling the characterization of causal patterns within a single perturbation period.

[0068] For example, during the "rapid pressure rise disturbance" period of a certain metal spraying production line, the strongly coupled process parameter subset consists of atomizing gas pressure (P), paint flow rate (F), and spray gun speed (V). A lightweight Granger causality test model is configured with a midpoint length of 1 second, a kernel width of 0.5 seconds, and a lag period ranging from 1 to 4 sampling periods. In pairwise parameter tests of P and F, the directional confidence level is measured to be 0.87 when the lag period L=2, and the corresponding response delay value is calculated as follows:

[0069] get The delay value in seconds. In the test of P and V, the direction confidence level is 0.91 when the lag period L=3, and the response delay value is... Seconds. After filtering with a direction confidence threshold of 0.85, two local causal sub-paths, P→F and P→V, are retained, and their direction confidence and delay values ​​are recorded respectively. The local causal sub-path dataset output by this embodiment during the perturbation period can significantly improve the temporal matching accuracy and reliability assessment effect of subsequent root cause stability analysis.

[0070] S3.5: Aggregate all local causal sub-paths generated by perturbation fingerprints to form a set of local causal sub-paths to support subsequent root cause stability assessment.

[0071] Based on the local causal sub-paths of each perturbation fingerprint output by S3.4, a path metadata aggregation method (parameters: perturbation semantic label, causal direction confidence, response delay value) is adopted to realize the construction of a centralized storage structure for causal paths in multi-perturbation scenarios.

[0072] Furthermore, a path discrimination merging algorithm (parameter: causal direction threshold τ) is used. dir Response delay threshold τ delay This enables the redundancy merging of similar sub-paths with the same candidate variable under multiple perturbation fingerprints, and obtains structured causal path matrix data.

[0073] Furthermore, by using an index mapping generation method (parameters: perturbation fingerprint ID, node index table), a fast retrieval mapping of local sub-paths in the global path set is achieved, and a causal path index set with unified node encoding and time labeling is generated.

[0074] Furthermore, a path metadata consistency verification algorithm is adopted (parameter: mean confidence score in causal direction μ). dir Response delay standard deviation σ delay This enables quality screening of the aggregated path set and generates a valid path set that satisfies consistency constraints.

[0075] By aggregating multiple perturbation paths and performing consistency screening, the single perturbation causal sub-path results from the previous step are transformed into a set of local causal sub-paths with full perturbation coverage, thus achieving unified analytical data input required for causal stability assessment.

[0076] For example, for four types of disturbance fingerprints occurring during the spraying process, such as rapid voltage boost disturbance, low-flow steady-state entry, film thickness calibration disturbance, and cycle speed-up disturbance, each is processed by S3.4 to generate five local causal sub-paths. The path metadata includes disturbance semantic labels, causal direction confidence (range 0.65~0.92), and response delay (1.2s~2.5s). A path discrimination and merging algorithm is used, setting τ... dir =0.6、τdelay =0.5s, merge paths with the same candidate variable that have consistent direction and delay difference less than the threshold under different perturbations, reducing the total number of paths from 20 to 14. Establish a bidirectional mapping between perturbation fingerprint IDs and node index tables, encoded as v1 to v 12 Corresponding to 12-dimensional process parameters, a global index set is generated to support rapid localization. During the consistency verification phase, the mean confidence value μ of the causal direction for each path after merging is calculated. dir With response delay standard deviation σ delay , screen out μ dir Below 0.6 or σ delay Paths with latency longer than 1.0 seconds were ultimately selected, resulting in a set of 11 valid paths. The standard deviation of response latency was calculated using the following formula to support the selection:

[0077] in, For response delay sample values, Given the sample size, the delay volatility can be quantified using the standard deviation formula. This processing ensures that the output set of local causal pathways meets the input requirements for S4 stability assessment in terms of structure, indexing, and consistency, significantly improving the efficiency and reliability of subsequent root cause ranking analysis.

[0078] like Figure 3 As shown, step S4 involves calculating the directional consistency ratio of candidate root dependent variables in the local causal sub-path set as upstream nodes in sub-paths triggered by different perturbation fingerprints, and statistically analyzing the standard deviation of the response delay distribution as a path stability index. Specifically, this includes: S4.1: Perform candidate root variable extraction processing on the set of local causal sub-paths from step S3 to obtain a list of all unique candidate root variables, ensuring that subsequent analysis covers all potential defect-driving variables in the spraying process.

[0079] S4.2: Based on the extracted candidate root dependent variable list, traverse each perturbation fingerprint triggering sub-path in the local causal sub-path set, extract the candidate root dependent variable as the binary indicator state of the upstream node in the sub-path, and form the upstream node state sequence.

[0080] Based on the input of the candidate root dependent variable list, the perturbation fingerprint index traversal method (parameters: candidate variable identifier, perturbation fingerprint ID, path set reference) is used to realize the systematic scanning of all perturbation fingerprint triggered sub-paths in the local causal sub-path set.

[0081] Furthermore, a path node matching algorithm (parameters: candidate variable node labels, path structure array) is used to retrieve the position of nodes within the sub-path, and an upstream node determination is generated when the matching node matches the candidate variable.

[0082] Furthermore, a binary state coding method is adopted (parameter: 1 indicates that the variable is an upstream node in the sub-path, and 0 indicates that it is not an upstream node) to realize the encoding and storage of the judgment result and construct the binary indicator value of the corresponding sub-path.

[0083] Furthermore, by using a time series construction method (parameters: perturbation triggering order, binary indicator value serialization rule), the binary indicator values ​​on multiple perturbation fingerprint triggering sub-paths are arranged in chronological order to generate a complete upstream node state sequence.

[0084] By encapsulating the results of the previous step into a binary state list, the results are transformed into structured state data of candidate root variables triggered by perturbations, thus providing accurate input for subsequent directional consistency ratio statistics.

[0085] For example, in a defect analysis scenario of a certain spraying production line, the candidate root variable list includes three variables: paint flow rate, atomizing air pressure, and spray gun moving speed. The disturbance fingerprint database contains two types of disturbances: "rapid pressure increase disturbance" and "low flow steady state cut-in". The set of local causal sub-paths triggered by the perturbation fingerprint totals 8. Among them, the paint flow is the first node in 5 sub-paths and has a causal impact on downstream variables. It is determined to be an upstream node by the matching algorithm, and its binary state code is as follows. In the remaining three sub-paths, no upstream causal relationship is established, and the encoding is as follows: ; Align all encoded results according to the perturbation trigger time to form a state sequence. , , , , , , , This sequence is passed as a standardized input to the directional consistency ratio calculation module to generate the basic data for directional consistency assessment. It has been verified that under the selected production line conditions, the state sequence structure is complete and without missing parts, which can significantly improve the robustness and interpretability of subsequent ratio calculations.

[0086] S4.3: Perform frequency statistics and ratio calculation on the state sequence of upstream nodes to determine the candidate root dependent variable as the ratio of the number of sub-paths of upstream nodes to the total number of sub-paths, and obtain the directional consistency ratio index.

[0087] S4.4: For each sub-path in the local causal sub-path set, collect the response delay values ​​corresponding to the candidate root dependent variables and generate a list of response delay values ​​as the basic data for quantifying time dynamic characteristics.

[0088] Based on the overall objective of step S4, the input data consists of the set of local causal sub-paths aggregated in step S3.5, and the list of candidate root variables extracted in step S4.1.

[0089] The path traversal method (parameters: local causal sub-path set, candidate root dependent variable identifier) ​​is adopted to traverse each perturbation fingerprint triggering sub-path in the set, so as to locate all instances of candidate root dependent variable nodes in the sub-path and retrieve their associated response delay record data.

[0090] Furthermore, by using the node attribute matching method (parameters: node type = candidate root dependent variable, path attribute = response delay), the function of accurately extracting response delay values ​​is realized, and the original response delay data corresponding to each sub-path is obtained.

[0091] Furthermore, a numerical normalization algorithm (parameters: delay unit conversion coefficient = seconds, time resolution = 500 milliseconds) is adopted to realize the unified dimension and accuracy calibration function of delay data, and generate a normalized sequence of delay values.

[0092] Furthermore, by using a list generation method (parameters: normalized delay value sequence, candidate root dependent variable identifier), the function of summarizing delay values ​​for the same candidate root dependent variable is realized, and a complete list of response delay values ​​is generated.

[0093] By encapsulating the results of the previous step into a list of response delay values ​​that can be directly used for statistical analysis, the input data structure required for path stability quantification based on time dynamic characteristics is realized.

[0094] For example, in the causal analysis of a metal spraying production line, the local causal sub-path set contains 120 path records, and the candidate root dependent variable list has a size of 8. For a candidate root dependent variable v3, all paths are traversed, and path entries with node attribute v3 and a response delay record are matched, totaling 35 matches. The delay values ​​are extracted, ranging from 0.4 seconds to 3.2 seconds. After processing with a numerical normalization algorithm, all delay values ​​are uniformly converted to seconds with a precision of 0.0001 seconds, forming a normalized sequence of delay values ​​of length 35. This sequence is encapsulated as a response delay value list for S4.5 to perform dispersion calculation, where the dispersion calculation uses the standard deviation formula: The weighted sum of squared mean differences ensures that the final output standard deviation accurately reflects the dynamic fluctuation range over time. In this embodiment, the subsequent standard deviation calculation step significantly improves the accuracy and reliability of the path stability entropy evaluation.

[0095] S4.5: Perform dispersion calculation on the list of response delay values ​​to quantify the fluctuation characteristics of the response delay distribution and output the standard deviation index of the response delay distribution.

[0096] Step S5: Based on the directional consistency ratio and the standard deviation of response delay, and combined with the process sensitivity weighting coefficient, calculate the causal path stability entropy index of the candidate root cause variable. The stability entropy value is negatively correlated with the directional consistency ratio and negatively correlated with the standard deviation of response delay. Specifically, this includes: S5.1: Analyze the path stability assessment requirements of candidate root dependent variables. Based on the statistical differences between the directional consistency ratio and the standard deviation of response delay, define the causal path stability entropy index. This index adjusts the contribution weights of the directional consistency ratio and the standard deviation of response delay through the process sensitivity weight coefficient to ensure that the entropy value is negatively correlated with the directional consistency ratio and negatively correlated with the standard deviation of response delay, so as to form a quantifiable path stability assessment benchmark.

[0097] Based on the candidate root dependent variables directional consistency ratio and response delay standard deviation output by step S4, a path stability requirement analysis method (parameters: directional consistency ratio list, response delay standard deviation list, spraying process characteristic library) is adopted to achieve quantitative normalization of different path stability characteristics under a unified evaluation system.

[0098] Furthermore, by using a feature statistical modeling method (parameters: sample distribution of directional consistency ratio and sample distribution of response delay standard deviation), the statistical characteristics of the two types of indicators are characterized, and the relative sensitivity coefficients of directional consistency ratio and delay variability under different process scenarios are obtained.

[0099] Furthermore, by using a weighting coefficient adjustment algorithm (parameters: process sensitivity weight α, process sensitivity weight β), the weighted contribution balance between the directional consistency ratio and the response delay standard deviation is achieved, ensuring that the stability entropy value is negatively correlated with the directional consistency ratio and negatively correlated with the response delay standard deviation.

[0100] Furthermore, the causal path stability entropy index is defined using a mathematical formula, expressed as follows:

[0101] in, It is an entropy index for the stability of causal paths. Let i be the i-th candidate root dependent variable. The directional consistency ratio, The standard deviation of response delay, and This is the process sensitivity weighting coefficient. This is the smoothing constant.

[0102] Furthermore, the monotonicity of the above expression is verified by using the formula symbol constraint analysis method, and the negative correlation between entropy value and direction consistency ratio and negative correlation with response delay standard deviation are verified.

[0103] Through the above weight adjustment and formula definition, the directional consistency ratio and response delay fluctuation data of the previous step are transformed into quantifiable stability entropy indicators, achieving the technical effect of root cause robustness comparability under dynamic process disturbance environment.

[0104] For example, when evaluating the stability of candidate variable v5 on a painting line, the directional consistency ratio is 0.92, the standard deviation of response delay is 0.8 seconds, the process sensitivity weighting coefficients α and β are selected as 1.5 and 1.0, and the smoothing constant ε is set to 0.05. The calculation is performed using the formula:

[0105] The calculated stability entropy value is 0.13. Under this parameter setting, the stability entropy value is in the lowest range among all candidate variables, indicating that the causal path direction of this variable is highly stable and the delay fluctuation is extremely low under multiple perturbations, making it suitable as a priority output object in highly robust root cause ranking.

[0106] S5.2: Based on the set of local causal sub-paths output by the defect identification module, obtain the directional consistency ratio, response delay standard deviation and preset process sensitivity weight coefficient corresponding to each candidate root dependent variable, and use them as the input parameter set for calculating the causal path stability entropy index to ensure the process context adaptability of subsequent calculations.

[0107] Based on the local causal sub-path set data transmitted by the defect identification module, a structured data parsing method (parameters: path node identifier, perturbation semantic label, node time stamp) is used to separate and extract the node attributes and corresponding causal indicators of each sub-path in the set.

[0108] Furthermore, by using the directional consistency ratio index retrieval method (parameters: candidate variable identifier list, upstream node state sequence), the directional consistency ratio of each candidate root variable can be quickly located and its value read, and the original data matrix of directional consistency ratio can be obtained.

[0109] Furthermore, a response delay standard deviation calculation method (parameters: delay data list, statistical window range) is adopted to quantify the response delay volatility of each candidate root dependent variable in different perturbation fingerprint triggering paths and generate a response delay standard deviation vector.

[0110] Furthermore, by using a process context adaptability retrieval method (parameters: process parameter type, sensitivity grading rule base), the process sensitivity weight coefficients of each candidate root dependent variable are matched and read, generating a weight coefficient sequence, which is used to adjust the contribution ratio of each part of the subsequent entropy calculation.

[0111] By assembling the input parameter set, the original data matrix of directional consistency ratio, the standard deviation vector of response delay, and the sequence of process sensitivity weight coefficients are combined into a unified format of input parameter set for calculating causal path stability entropy, thereby ensuring the consistency of the process environment and the integrity of data in subsequent calculations.

[0112] For example, in an automotive parts painting production line scenario, the local causal sub-path set contains 28 sub-paths triggered by 4 types of disturbance fingerprints, and the candidate root dependent variable identifier list has a length of 6. The original data matrix of the directional consistency ratio is retrieved through indexing, yielding values ​​such as 0.92 and 0.87; the response delay standard deviation vector is statistically calculated, yielding values ​​such as 0.8 and 1.1; the process sensitivity weight coefficient sequence is derived from the process parameter type library, with values ​​such as 1.5 and 0.8. When constructing the entropy calculation input set, the directional consistency ratio of candidate variable v5 (0.92) is encapsulated as... The response latency standard deviation is 0.8, and the package is... The process weighting factor is 1.5 for the packaged product. These parameters are combined into a parameter triplet for subsequent formula calculations. This embodiment, in field verification, ensures zero-loss input during the causal path stability entropy calculation process, significantly improving the stability of the calculation results in real-time analysis.

[0113] S5.3: Apply the natural logarithm function to the obtained directional consistency ratio to generate the directional consistency logarithm index; at the same time, apply the natural logarithm function to the reciprocal of the response delay standard deviation plus a smoothing constant to generate the delay stability logarithm index; then, perform a weighted linear combination operation on the above two logarithm indices based on the process sensitivity weighting coefficient to calculate the preliminary value of the causal path stability entropy index.

[0114] The directional consistency ratio obtained based on step S5.2 With response delay standard deviation The natural logarithm transformation method is used (parameter: base). This enables the construction of a logarithmic index for directional consistency.

[0115] Furthermore, through the natural logarithm function Process the directional consistency ratio to generate the directional consistency logarithm index. And obtained scaled data results that reflect directional stability.

[0116] Furthermore, the standard deviation of the response delay is transformed into a stability measure by adding the reciprocal to the smoothing constant, using the formula...

[0117] Achieve logarithmic index of delay stability The calculation is performed to generate standardized data that reflects the degree of suppression of response delay fluctuations.

[0118] Furthermore, based on preset process sensitivity weighting coefficients A weighted linear combination operation is performed on the logarithmic index of directional consistency and the logarithmic index of delay stability, using the formula...

[0119] A preliminary value of the causal path stability entropy index is calculated to form a comprehensive path stability measure by combining the weighted characteristics of two types of logarithmic indices.

[0120] By combining the above weighted linear combinations, the characteristic information of both directional consistency and delay fluctuation is integrated into a single index, thereby achieving an integrated preliminary assessment of the path stability of candidate root variables.

[0121] For example, in the scenario of defect analysis in spray painting, the directional consistency ratio of a candidate variable. = standard deviation of response delay = seconds, smoothing constant = Process sensitivity weighting coefficient = , = The logarithmic index of directional consistency is calculated as follows: = The logarithmic index of delay stability is calculated as follows: = The initial value of entropy is calculated as follows: = The output shows that the variable has high directional consistency and low latency fluctuation, and the overall stability index is at a high level, which helps to maintain the consistency of causal reasoning path logic under multivariate disturbances.

[0122] S5.4: Numerical stability optimization is performed on the preliminary value of the calculated causal path stability entropy index. By introducing a smoothing constant to handle the sensitivity of the logarithmic function in the low-value region, a stable value of the causal path stability entropy index with anti-interference ability is generated to eliminate calculation anomalies caused by process parameter fluctuations.

[0123] Based on the initial value of the causal path stability entropy index, a numerical stability optimization method (parameters: smoothing constant ε, directional consistency logarithmic index, and delay stability logarithmic index) is adopted to achieve the function of suppressing the sensitivity of the logarithmic function in the low-value region.

[0124] Furthermore, through the numerical scaling normalization method (parameter: minimum value mapping threshold μ) minMaximum value mapping threshold μ max This achieves a unified amplitude range for the causal path stability entropy index across different candidate root variables, and yields a normalized entropy value sequence.

[0125] Furthermore, a smoothing function reconstruction method (parameters: B-spline smoothing order 3, smoothing window length w=5) is adopted to realize the high-order continuity enhancement function of the entropy value sequence and generate a smoothed stability entropy curve.

[0126] Furthermore, by using an interval weighted compensation method (parameters: sensitive interval [ε,τ], compensation weight γ), the numerical output of the low entropy range is improved, and a stable entropy correction index with anti-interference capability is generated.

[0127] By using anti-interference optimization processing, the preliminary entropy value result of the previous step is transformed into a stability entropy technical index that adapts to multivariate disturbance scenarios, thereby achieving the expected technical effect of eliminating calculation anomalies under the fluctuating conditions of the spraying process.

[0128] For example, in the spraying process of a certain production batch, the directional consistency ratio of candidate root variable v5 is 0.92, the standard deviation of response delay is 0.8 seconds, the process sensitivity weighting coefficients are set to α=0.7, β=0.3, and the smoothing constant ε=0.001. Applying the natural logarithm function to the directional consistency ratio yields the directional consistency logarithm index:

[0129] Adding the smoothing constant to the reciprocal of the standard deviation of the response delay and then applying the natural logarithm yields the logarithmic index of delay stability:

[0130] Calculate the initial entropy value based on a weighted linear combination:

[0131] A smoothing constant was applied to the initial entropy value, and interval weighted compensation was performed in the low-value range to obtain a final stability entropy value of 0.13. Verification showed that this value exhibited significant adaptability to process fluctuations in subsequent root cause sorting operations, resulting in a significant improvement in sorting stability.

[0132] S5.5: Output the stable value of the generated causal path stability entropy index to the root cause ranking module as the core basis for evaluating the robustness of candidate root cause variables, and use it to support the decision-making closed loop of subsequent ascending sorting operation and selection of highly robust root causes.

[0133] Step S6: Sort all candidate root cause variables in ascending order according to the causal path stability entropy index, and select the top 3 variables with the smallest entropy values ​​as the highly robust root cause ranking results. Specifically, this includes: S6.1: Load the output data from the causal path stability entropy calculation module to obtain the causal path stability entropy value corresponding to each candidate root dependent variable; perform a vectorization transformation operation based on the obtained causal path stability entropy value to generate a causal path stability entropy vector as the sorting input dataset.

[0134] S6.2: Perform ascending sorting on the causal path stability entropy vector using the quicksort algorithm: First, select the pivot element to divide the entropy vector into low-entropy subvectors and high-entropy subvectors; second, recursively sort the low-entropy subvectors in ascending order; then recursively sort the high-entropy subvectors in ascending order; finally, merge the ordered low-entropy subvectors, the pivot element, and the ordered high-entropy subvectors to generate an ordered sequence of causal path stability entropy.

[0135] Based on the causal path stability entropy vector dataset output by step S6.1, the quicksort algorithm (parameters: pivot selection rule is median of three, sorting method is ascending) is used to achieve ordered processing of the vector set.

[0136] Furthermore, by using the pivot partitioning sub-process of quicksort (parameters: low index start position, high index end position), the entropy vector is split into two parts: a low-entropy sub-vector and a high-entropy sub-vector, and the partition index result is obtained.

[0137] Furthermore, by recursively calling the quicksort subprocess on the low-entropy subvectors (parameter: recursion depth limited to log2n), ascending sorting is achieved within the low-entropy subvectors, and sorted low-entropy subvector data is generated.

[0138] Furthermore, by recursively calling the quicksort subprocess (with the same parameters as before) on the high-entropy subvectors, ascending sorting is achieved within the high-entropy subvectors, and sorted high-entropy subvector data is generated.

[0139] Furthermore, an ordered vector merging algorithm (parameter: merging order is low-entropy sub-vector, pivot element, high-entropy sub-vector) is used to sequentially concatenate the three data segments and generate an ordered sequence of causal path stability entropy to support subsequent root variable selection.

[0140] By using the quicksort algorithm to process the data into an ordered sequence, the stability entropy vector from the previous step is transformed into an ordered sequence with entropy values ​​arranged in ascending order, thereby optimizing the data structure and improving the retrieval efficiency of the root cause sorting process.

[0141] For example, in a certain spraying production batch, the stability entropy vector of the candidate root dependent variable is denoted as [0.21, 0.05, 0.18, 0.07, 0.15]. The quicksort algorithm is used to process it. The pivot element is chosen as the median of three numbers, 0.15, and the vector is divided into a low-entropy subvector [0.05, 0.07] and a high-entropy subvector [0.21, 0.18].

[0142] Recursively sorting the low-entropy subvectors maintains [0.05, 0.07], while recursively sorting the high-entropy subvectors yields [0.18, 0.21].

[0143] Perform a merge operation to generate an ordered sequence of causal path stability entropy [0.05, 0.07, 0.15, 0.18, 0.21].

[0144] Among them, the entropy value ascending order significantly improves the indexing efficiency of subsequent root cause screening, and achieves a sorting calculation time of less than 50ms in actual production, meeting the performance requirements of real-time root cause sorting on the production line.

[0145] S6.3: Extract the top 3 candidate root variables with the smallest entropy values ​​from the ordered sequence of causal path stability entropy; perform a root cause ranking list generation operation based on the extraction results to output a highly robust root cause ranking result to the decision support module.

[0146] Step S7: Generate an explanatory summary based on the root cause ranking results. The summary includes the frequency of occurrence of the root cause variable in the upstream nodes of the perturbed fingerprint, the directional consistency ratio, the range of response delay fluctuations, and the stability entropy value. Specifically, it includes: S7.1: Parse the robust root cause ranking list output by S6 to identify the top 3 root cause variables with the smallest entropy values ​​and obtain a root cause variable identifier list; based on the root cause variable identifier list, query the upstream node occurrence frequency records in the system causal analysis storage unit and extract the upstream node occurrence frequency values.

[0147] S7.2: Based on the root dependent variable identifier list, query the directional consistency ratio record in the system's causal analysis storage unit and extract the directional consistency ratio value; perform numerical standardization on the directional consistency ratio value to adapt to the semantic expression specification of the interpretive summary, and obtain the standardized directional consistency ratio value.

[0148] S7.3: Based on the root dependent variable identifier list, query the response delay fluctuation range record in the system causal analysis storage unit, extract the response delay fluctuation range value; perform fluctuation amplitude quantization conversion on the response delay fluctuation range value to generate a natural language readable fluctuation description text, and obtain the response delay fluctuation description text.

[0149] S7.4: Based on the root dependent variable identifier list, query the stability entropy value records in the system causal analysis storage unit and extract the stability entropy value; perform entropy level classification processing on the stability entropy value to map it to a predefined stability level label and obtain the stability level label.

[0150] S7.5: Perform multi-source data fusion processing on the frequency value of upstream nodes, the standardization direction consistency ratio value, the response delay fluctuation description text, and the stability level label, and substitute it into a predefined explanatory summary template to generate a structured analytical summary containing specific numerical values ​​and logical connections; perform natural language optimization processing based on the structured analytical summary to output a final explanatory summary that conforms to the terminology specifications of the industrial control field.

[0151] Based on the upstream node occurrence frequency value, standardized directional consistency ratio value, response delay fluctuation description text and stability level label generated in steps S7.1 to S7.4, a multi-source data fusion algorithm (parameters: data source type = four types of indicators, fusion strategy = weight factor method) is used to construct multi-indicator feature vectors for parameter injection into the interpretive summary template.

[0152] Furthermore, through the template mapping method (parameter: template field binding rule = one-to-one correspondence between indicator name and semantic field), the automatic matching of the four types of indicator values ​​with template semantic placeholders is realized, and a structured analytical summary draft containing technical quantitative indicators and logical relationships is generated.

[0153] Furthermore, through a natural language optimization algorithm (parameters: terminology library = standard terms in the field of industrial control, syntactic optimization rules = simplification of subject-verb-object structure + postposition of attributive clauses), the text of the structured analytical abstract is optimized from the initial draft to the final abstract, and a natural language version conforming to the terminology standards of the field of industrial control is obtained.

[0154] Furthermore, a consistency check algorithm (parameters: logical relationship verification = indicator-factual relationship, numerical range verification = industry standard allowable range) is used to verify the indicators and descriptive logic in the final summary, and generate a final summary draft that meets semantic and numerical reasonableness requirements.

[0155] Through the above-mentioned multi-source fusion and natural language optimization processing methods, the various indicators in the previous step are transformed into explanatory summaries with a unified expression format that can directly support the decision-making module, thereby realizing the intuitive presentation and improved interpretability of the root cause ranking results.

[0156] For example, in the quality control scenario of a metal surface spraying production line, the system obtains the upstream node occurrence frequency value corresponding to the highly robust root cause variable v5 as 46 times, the standardized directional consistency ratio value as 0.92, the response delay fluctuation range as ±0.8s, and the stability level label as "high stability". The multi-source data fusion algorithm sets the weights of the four types of indicators to 0.25, 0.35, 0.2, and 0.2 respectively, and generates a fusion vector. <fuse vectorThe template mapping method accurately fills the above indicators into predefined template fields, such as "Variable {ID} frequently exhibits upstream driving behavior in {disturbance type} (occurrence frequency {freq} times), directional consistency ratio is {ratio}, response delay fluctuation range {delay}, and stability level {level}". The natural language optimization algorithm processes the mapped text as: "Variable v5 frequently exhibits upstream driving behavior in multiple disturbance fingerprints, directional consistency ratio 0.92, response delay fluctuation range ±0.8 seconds, and high stability level". Consistency checks confirm that all values ​​are within the allowable range of the production line painting process, and the logical relationship is consistent with the analyzed data. The final output summary is used for real-time calling by the production line management system, achieving a clear, quantitative, and interpretable presentation of the root causes of painting defects.

[0157] For those skilled in the art, various other corresponding changes and modifications can be made based on the technical solutions and concepts described above, and all such changes and modifications should fall within the protection scope of the claims of this invention.

[0158] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this application pertains. The terms “first,” “second,” “third,” and similar terms used in this patent application specification and claims do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms “an” or “a” and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms “comprising” or “including” and similar terms mean that the elements or objects preceding “comprising” or “including” encompass the elements or objects listed following “comprising” or “including” and their equivalents, and do not exclude other elements or objects. The “multiple” mentioned in the embodiments of this application refers to two or more. A and / or B indicate three possibilities: A; B; and A and B.

[0159] The above description is merely an exemplary embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and such modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for root cause analysis of defects in surface coating processing of metal products, characterized in that, include: S1: Real-time acquisition of 12 core process parameters, including spray gun movement trajectory, atomization pressure, paint flow rate, workpiece rotation speed, and ambient temperature and humidity, during the metal product surface spraying process, forming high-fidelity time-series data with a sampling period of 500 milliseconds as the benchmark. S2: Based on the process parameters, actively adjust the trigger time of the event, extract the parameter change pattern within a 3-second window before and after the event, and construct a process perturbation fingerprint library containing 7 typical perturbation fingerprints through principal component projection and dynamic time warping distance clustering. Each perturbation fingerprint corresponds to a unique perturbation semantic label. S3: For the perturbation fingerprint triggered within 60 seconds before the occurrence of the current spraying defect sample, each perturbation fingerprint is used as a local causal probe. Within the corresponding perturbation period, 3 to 5 parameter subsets that are strongly coupled with the perturbation are activated, and a lightweight Granger causality test is run to generate a set of local causal sub-paths. S4: For candidate root variables in the local causal sub-path set, calculate their directional consistency ratio as upstream nodes in sub-paths triggered by different perturbation fingerprints, and statistically analyze the standard deviation of the response delay distribution as a path stability index. S5: Based on the directional consistency ratio and the standard deviation of response delay, the causal path stability entropy index of the candidate root variable is calculated in combination with the process sensitivity weighting coefficient. The stability entropy value is negatively correlated with the directional consistency ratio and negatively correlated with the standard deviation of response delay. S6: Sort all candidate root variables in ascending order according to the causal path stability entropy index, and select the top 3 variables with the smallest entropy values ​​as the highly robust root cause ranking results; S7: Generate an explanatory summary based on the root cause ranking results. The summary includes the frequency of occurrence of the root cause variable in the upstream nodes of the perturbation fingerprint, the directional consistency ratio, the range of response delay fluctuations, and the stability entropy value.

2. The method for root cause analysis of defects in surface spraying of metal products according to claim 1, characterized in that, Step S1 specifically includes: S1.1: Deploy a sensor network for the 12 core process parameter measurement points of the metal product surface spraying line. Based on the industrial automation sensor selection standards, select high-precision displacement sensors, pressure transmitters, flow meters, speed encoders and ambient temperature and humidity sensors to obtain raw physical signals such as spray gun movement trajectory, atomized air pressure, paint flow rate, workpiece speed and ambient temperature and humidity. S1.2: Perform signal conditioning processing on the raw physical signal obtained in S1.1, and perform filtering, noise reduction and gain calibration based on anti-aliasing filter and signal amplification circuit to generate a standardized analog signal; S1.3: Perform analog-to-digital conversion on the standardized analog signal generated in S1.2, and configure a high-speed ADC module to perform discretization sampling based on a 500-millisecond reference sampling period to obtain a discrete digital sampling sequence of 12-dimensional process parameters; S1.4: Perform time synchronization calibration on the discrete digital sampling sequence obtained in S1.3, align the time stamps of multi-channel data based on the distributed clock synchronization protocol to eliminate time offset between channels and output synchronized digital sampling sequence; S1.5: Performs data encapsulation processing on the synchronized digital sampling sequence output by S1.4, performs data packet formatting and integrity verification based on the time-series data stream protocol, so as to form continuous and stable high-fidelity time-series data stream.

3. The method for root cause analysis of defects in surface spraying processing of metal products according to claim 1, characterized in that, Step S2 specifically includes: S2.1: Based on the triggering time of the process parameter active adjustment event and high-fidelity time-series data, the parameter change pattern is defined by feature abstraction. The perturbation fingerprint is used as the semantic identification unit of the process perturbation type to achieve a unique representation of specific perturbation behavior. S2.2: For the list of trigger times of proactive adjustment events of process parameters, extract 12-dimensional process parameter change data within a 3-second window before and after the event to form a set of parameter change patterns in order to capture the dynamic feature sequence when the disturbance occurs; S2.3: Apply the principal component projection algorithm to the set of parameter change patterns for dimensionality reduction, calculate the set of principal component feature vectors, extract the main change direction of the parameter change patterns and reduce data dimensionality redundancy; S2.4: Based on the principal component eigenvector set, cluster analysis is performed using dynamic time-warped distance metric to generate a set of clusters to identify similarity groupings of parameter variation patterns and quantify differences between patterns; S2.5: Based on the cluster set, construct a process perturbation fingerprint library containing 7 typical perturbation fingerprints, and assign a unique perturbation semantic label to each perturbation fingerprint to achieve standardized representation and semantically interpretable output of process perturbation types.

4. The method for root cause analysis of defects in surface spraying processing of metal products according to claim 1, characterized in that, Step S3 specifically includes: S3.1: Based on historical process parameter time series data, a piecewise linear approximation kernel function is used to replace the traditional Gaussian kernel function to construct a lightweight Granger causality test model, so as to reduce computational overhead and maintain causality detection accuracy. S3.2: Based on the timestamp of the current coating defect sample and the process disturbance fingerprint database, backtrack and extract the 12-dimensional process parameter time sequence subsequence within the disturbance period corresponding to each triggered disturbance fingerprint within the previous 60 seconds of the defect sample to obtain local analysis data; S3.3: Based on the principal component load vector corresponding to the perturbation fingerprint, determine the 3 to 5 process parameters with the highest absolute load values ​​as a subset of strongly coupled process parameters to limit the scope of causal analysis; S3.4: Based on a lightweight Granger causality test model, Granger causality tests are performed on the subsequence of process parameters during the disturbance period on a strongly coupled subset of process parameters to calculate the confidence of the causal direction and the response delay, and to generate local causal sub-paths. S3.5: Aggregate all local causal sub-paths generated by perturbation fingerprints to form a set of local causal sub-paths to support subsequent root cause stability assessment.

5. The method for root cause analysis of defects in surface spraying processing of metal products according to claim 1, characterized in that, Step S4 specifically includes: S4.1: Perform candidate root variable extraction processing on the set of local causal sub-paths from step S3 to obtain a list of all unique candidate root variables, ensuring that subsequent analysis covers all potential defect-driving variables in the spraying process; S4.2: Based on the extracted candidate root dependent variable list, traverse each perturbation fingerprint triggering sub-path in the local causal sub-path set, extract the candidate root dependent variable in the sub-path as the binary indicator state of the upstream node, and form the upstream node state sequence. S4.3: Perform frequency statistics and ratio calculation on the state sequence of upstream nodes to determine the candidate root dependent variable as the ratio of the number of sub-paths of upstream nodes to the total number of sub-paths, and obtain the directional consistency ratio index. S4.4: For each sub-path in the local causal sub-path set, collect the response delay values ​​corresponding to the candidate root dependent variables and generate a list of response delay values ​​as the basic data for quantifying time dynamic characteristics; S4.5: Perform dispersion calculation on the list of response delay values ​​to quantify the fluctuation characteristics of the response delay distribution and output the standard deviation index of the response delay distribution.

6. The method for root cause analysis of defects in surface spraying of metal products according to claim 1, characterized in that, Step S5 specifically includes: S5.1: Analyze the path stability assessment requirements for candidate root dependent variables, and define the causal path stability entropy index based on the statistical differences between the directional consistency ratio and the standard deviation of response delay. S5.2: Based on the set of local causal sub-paths output by the defect identification module, obtain the directional consistency ratio, response delay standard deviation and preset process sensitivity weight coefficient corresponding to each candidate root dependent variable, and use them as the input parameter set for calculating the causal path stability entropy index; S5.3: Apply the natural logarithm function to the obtained directional consistency ratio to generate the directional consistency logarithm index; at the same time, apply the natural logarithm function to the reciprocal of the response delay standard deviation plus a smoothing constant to generate the delay stability logarithm index; then, perform a weighted linear combination operation on the above two logarithm indices based on the process sensitivity weighting coefficient to calculate the preliminary value of the causal path stability entropy index. S5.4: Perform numerical stability optimization on the initial value of the calculated causal path stability entropy index. By introducing a smoothing constant, the sensitivity of the logarithmic function in the low-value region is addressed, and a stable value of the causal path stability entropy index with anti-interference capability is generated. S5.5: Output the stable value of the generated causal path stability entropy index to the root cause ranking module as the core basis for evaluating the robustness of candidate root variables.

7. The method for root cause analysis of defects in surface spraying of metal products according to claim 1, characterized in that, The high-precision displacement sensor used for acquiring process parameters has a linear resolution of 0.1 mm or less, a measurement range of not less than 1 meter, and a dynamic response time of not more than 5 milliseconds.

8. The method for root cause analysis of defects in surface spraying of metal products according to claim 1, characterized in that, The pressure transmitter used for atomized air pressure monitoring has a range of 0 to 1.0 MPa, preferably 0 to 0.8 MPa, an accuracy class of 0.1%FS or preferably 0.05%FS, and an output interface of 4-20 mA current signal.

9. The method for root cause analysis of defects in surface spraying of metal products according to claim 1, characterized in that, The paint flow measurement uses an electromagnetic flow meter with a corrosion-resistant coating. The pipe diameter is adapted to the spraying supply system, and the range is 0 to 50 liters per minute, preferably 25 liters per minute.

10. The method for root cause analysis of defects in surface spraying of metal products according to claim 1, characterized in that, The workpiece rotation speed monitoring uses an AB phase incremental encoder with a resolution of no less than 1024 PPR, preferably 2048 PPR. The housing is resistant to oil mist contamination and the operating temperature range is -20 degrees Celsius to 80 degrees Celsius.

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