A method and system for optimizing a manufacturing process of a thermistor chip

Abstract

The present application relates to the technical field of resistance chip, and particularly relates to a manufacturing process optimization method and system of a thermistor chip. The method performs multi-scale process entropy analysis on a process parameter dynamic flow, analyzes coupling strength between key processes, and identifies a process parameter cluster with strong non-monotonic correlation and an entropy increase path of a process system thereof, so as to construct a cooperative stability domain boundary model. According to transient fluctuation characteristics extracted from the process parameter dynamic flow, in combination with the cooperative stability domain boundary model, a parameter subset exceeding a cooperative stability operation interval is determined as a drift parameter cluster, an optimization instruction set is executed for trial production, cooperative trajectory data of the process parameter cluster is synchronously collected, the cooperative stability is verified by calculating an entropy change rate of the process system, and the cooperative stability domain boundary model is fed back for boundary toughness reinforcement, so as to realize dynamic cooperative convergence of associated parameters such as sintering gradient and electrode pressure, and improve product consistency and yield stability.

Description

Technical Field

[0001] This invention relates to the field of resistor chip technology, and in particular to a method and system for optimizing the manufacturing process of a thermistor chip. Background Technology

[0002] The manufacturing of thermistor chips involves a complex process involving multiple coupled steps, such as material sintering and electrode formation. Their performance consistency is highly dependent on the synergistic stability of process parameters. Traditional methods primarily employ statistical process control (SPC) or single-parameter feedback regulation, which have significant limitations: Firstly, there is a strong non-monotonic correlation between parameters such as sintering temperature gradient, atmosphere concentration, electrode printing pressure, and slurry viscosity, making linear compensation of a single parameter insufficient to suppress cross-process disturbance propagation. Secondly, the time-varying characteristics of transient fluctuations (such as the dominant fluctuation frequency and extreme values ​​of the rise slope) make it difficult to quantify parameter drift paths, easily leading to entropy increases in the process system (such as thermal stress accumulation and electrode interface defects). Existing technologies lack the analytical capability to determine the dynamic coupling strength of multi-scale parameter clusters, making it impossible to construct a synergistic stability domain boundary model to suppress entropy increases. This results in frequent process instability and bottlenecks in product yield and consistency control. Therefore, there is an urgent need to develop a manufacturing process optimization method that can capture the dynamic flow of process parameters in real time, identify entropy increase paths, and dynamically optimize drift parameter clusters through synergistic stability domain boundaries to overcome the technical barriers to high-consistency manufacturing of thermistor chips. Summary of the Invention

[0003] This invention overcomes the shortcomings of the prior art and provides a method and system for optimizing the manufacturing process of a thermistor chip.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] The first aspect of this invention discloses a method for optimizing the manufacturing process of a thermistor chip, comprising the following steps:

[0006] S1: Real-time acquisition of dynamic flow of process parameters for each key step in the entire manufacturing process of thermistor chip, including set values, actual values ​​and their transient fluctuation characteristics;

[0007] S2: Perform multi-scale process entropy analysis on the dynamic flow of the process parameters, analyze the coupling strength between key processes, and identify process parameter clusters with strong non-monotonic correlations and the process system entropy increase paths dominated by the process parameter clusters.

[0008] S3: Based on the process parameter cluster and its process system entropy increase path, a collaborative stability domain boundary model that suppresses the entropy increase of the process system is constructed in the multidimensional process parameter space to characterize the collaborative stability operation range of the parameter cluster.

[0009] S4: Based on the transient fluctuation characteristics extracted from the dynamic flow of process parameters acquired in real time, and combined with the collaborative stability domain boundary model, determine the parameter subset that exceeds the collaborative stability operation range as the drift parameter cluster, and generate an optimized instruction set to converge the drift parameter cluster to the collaborative stability operation range.

[0010] S5: Execute the optimized instruction set for trial production, synchronously collect the collaborative trajectory data of the process parameter cluster, verify the collaborative stability by calculating the entropy change rate of the process system, and feed it back to the collaborative stability domain boundary model for boundary toughness enhancement.

[0011] Preferably, S1 specifically includes:

[0012] The original process timing signals of the material sintering process and electrode formation process are captured in real time through an embedded sensor network, and the process gait labels of each data point are marked synchronously.

[0013] The original process timing signal is divided into sliding windows, and the following steps are performed in parallel within each window: extracting the set command value sequence of the current process equipment control system; eliminating environmental noise interference through signal filtering to generate the actual physical quantity measurement value sequence; performing Fourier transform and Hilbert transform on the actual physical quantity measurement value sequence to separate the frequency domain envelope features and time domain transient features, and merging them to form a transient fluctuation feature set;

[0014] The sequence of set command values, the sequence of actual physical quantity measurements, and the corresponding transient fluctuation feature sets within the same time window are spatiotemporally aligned and bound according to the process step label to generate a dynamic flow unit of process parameters with multi-dimensional attributes.

[0015] By sequentially connecting the dynamic flow units of each process parameter according to the process sequence, a dynamic flow of process parameters covering the entire manufacturing process is formed. Each dynamic flow unit of process parameter inherits the process gait label of the preceding unit to achieve cross-process correlation and traceability.

[0016] Preferably, S2 specifically includes:

[0017] Empirical mode decomposition is performed on the sequence of actual physical quantity measurements in the dynamic flow of process parameters to extract the intrinsic mode components that characterize the dynamic response of different processes, and obtain a multi-scale time-domain feature set including short-term fluctuations, medium-range oscillations and long-range trends.

[0018] Based on the multi-scale time-domain feature set, the mutual information entropy of key process parameter pairs at the same time scale is calculated to generate a cross-process coupling strength matrix, wherein the matrix element values ​​characterize the degree of nonlinear dependence of parameter pairs at a specific scale.

[0019] In the coupling strength matrix, parameter pairs whose mutual information entropy values ​​exceed a set threshold but whose absolute Pearson correlation coefficient values ​​are lower than a monotonicity threshold are selected and marked as strongly non-monotonic correlation pairs; strong non-monotonic correlation pairs with cross-correlation are aggregated into process parameter clusters through cluster analysis.

[0020] For each cluster of process parameters, a conditional entropy transfer network of its multi-scale time-domain characteristics is constructed: the parameter features within the cluster are used as nodes, and the transfer entropy between nodes is used as edge weights. A directed weighted graph model is used to characterize the transfer path of process disturbances among multiple parameters. The longest entropy increase path in the network is identified by a graph search algorithm and defined as the entropy increase path of the process system. The entropy increase path of the process system has the largest cumulative edge weight and the transfer direction conforms to the time sequence of the process steps.

[0021] Preferably, S3 specifically includes:

[0022] For each process parameter cluster, the entropy increase path of the process system is defined, and the key transfer node with the maximum sum of in-degree and out-degree is extracted from the corresponding directed weighted graph. The key transfer node corresponds to the multi-scale temporal features of a specific process stage.

[0023] The actual physical quantity measurement sequence of all process parameters and their transient fluctuation characteristics within the process parameter cluster associated with the key transmission node are organized into a multidimensional time series according to the process time sequence; the higher-order cross-cumulative quantity of the multidimensional series within the sliding time window is calculated to generate a parameter coupling tensor characterizing the nonlinear coupling strength between parameters.

[0024] The parameter coupling tensor is decomposed into a nonnegative tensor, and its dominant load factor vector is extracted as the principal co-variation vector; the principal co-variation vector represents the covariation mode of the multidimensional fluctuation characteristics of the parameter cluster in the steady state.

[0025] Using the main cooperative vector as the normal vector, a reference hyperplane is defined in a multidimensional space composed of the actual values ​​of cluster parameters; the Euclidean projection distance from each data point in the real-time process parameter dynamic flow to the hyperplane is calculated, and the toughness margin threshold range of the projection distance distribution is determined by kernel density estimation in combination with the transient fluctuation characteristics at the corresponding time.

[0026] The toughness margin threshold range is mapped back to the original process parameter space, and a convex envelope boundary is fitted around the corresponding mapping point set; the convex envelope boundary is the collaborative stability domain boundary model that characterizes the collaborative stable operation range of the parameter cluster, and its geometry is jointly determined by the covariation mode of the main collaborative vector and the dynamic toughness margin threshold.

[0027] Specifically, mapping the toughness margin threshold range back to the original process parameter space and fitting a convex hull boundary surrounding the corresponding mapped point set is as follows:

[0028] A subset of data points whose Euclidean projection distance falls within the toughness margin threshold range is selected from the real-time dynamic flow of process parameters to form a mapping point set;

[0029] Extract the multidimensional coordinate values ​​of the mapping point set from the original process parameter space, and determine the spatial distribution characteristics of the mapping point set based on the multidimensional coordinate values;

[0030] Using the aforementioned spatial distribution characteristics, the mapping point set is fitted to the boundary to generate the minimum convex hull boundary surface that surrounds all points;

[0031] The minimum convex hull boundary surface is defined as the cooperative stable domain boundary model, whose geometry is dynamically constrained by the covariation mode of the principal cooperative vector and the dynamic toughness margin threshold.

[0032] Preferably, S4 specifically includes:

[0033] For the actual physical quantity measurement sequence in the current process parameter dynamic flow unit, extract its multidimensional coordinate values; based on the main cooperative vector in the cooperative stability domain boundary model, calculate the second Euclidean projection distance from the corresponding multidimensional coordinate values ​​to the reference hyperplane, and synchronously associate the transient fluctuation characteristics recorded by the unit.

[0034] The second Euclidean projection distance is compared with the toughness margin threshold range in the cooperative stability domain boundary model. Data points whose second Euclidean projection distance is not within the preset range are selected as drift points, and the process stage identifier and timestamp in their process gait label are recorded.

[0035] Based on the continuity of timestamps and the correlation of process stages of process gait tags, the drift points are spatiotemporally clustered to form several drift parameter clusters. The drift parameter clusters include the actual value offset of the associated parameters and the transient fluctuation feature anomalies.

[0036] For the entropy increase path of the process system dominated by the drift parameter cluster, the entropy increase transmission direction in its directed weighted graph is extracted; the reverse direction of the entropy increase transmission direction is used as the adjustment benchmark, and a negative feedback adjustment amount is generated according to the product of the actual value offset of each parameter in the cluster and the transient fluctuation characteristic anomaly value.

[0037] Based on the negative feedback adjustment, gradient compensation values ​​are generated for continuous parameters of the sintering temperature gradient, and pulse correction waveforms based on the extreme values ​​of the rising slope are generated for transient parameters of the electrode printing pressure. Finally, an optimized instruction set containing parameter adjustment target values ​​and execution timing is output, driving the drift parameter cluster to converge to the boundary of the cooperative stability domain.

[0038] Specifically, based on the continuity of timestamps and the correlation of process stages of the process gait tags, the drift points are spatiotemporally clustered to form several drift parameter clusters, as follows:

[0039] Based on the timestamps in the process gait tags carried by the drift points, the time difference between adjacent drift points is calculated; at the same time, the process stage identifiers are extracted to generate a spatiotemporal neighborhood group that includes time continuity and process correlation.

[0040] Extract the actual value offset and transient fluctuation feature anomaly value of each drift point recorded in the spatiotemporal neighborhood group, and fuse the two according to a preset weight to generate the feature fusion vector of the corresponding drift point;

[0041] Using spatiotemporal neighborhood groups as initial clustering units, the process coupling distance between the feature fusion vectors of each drift point within the group is calculated; density clustering algorithm is used, with process coupling distance as the metric, to aggregate spatially adjacent drift points with process correlation higher than a preset correlation threshold into candidate drift clusters;

[0042] Backtrack the entropy increase propagation direction of all drift points in each candidate drift cluster in the entropy increase path of the process system; if the propagation direction of all points in the cluster is consistent in the entropy increase path of the process system, mark the candidate cluster as a valid drift parameter cluster; otherwise, split it into sub-clusters for re-verification.

[0043] For the finally confirmed drift parameter cluster, the average actual value offset of all drift points within it is calculated as the actual value offset of the cluster, and the extreme values ​​of transient fluctuation feature outliers are calculated as transient fluctuation feature outliers of the cluster. These outliers are then bound to the associated process stage identifier and timestamp interval for output.

[0044] Preferably, S5 specifically includes:

[0045] During the process of executing the optimized instruction set to drive the adjustment of equipment parameters, the actual physical quantity measurement sequence of all parameters in the process parameter cluster and their transient fluctuation characteristics are captured in real time through the embedded sensor network. At the same time, the process phase angle difference of each parameter in the process sequence is recorded to form a multi-dimensional collaborative trajectory data stream.

[0046] Based on the cooperative trajectory data stream, multi-scale time-domain features of parameter clusters are extracted within the sliding time window. Taking the entropy transfer direction in the entropy increase path of the process system as the reference axis, the divergence rate of multi-dimensional feature vectors between adjacent windows is calculated to generate the Lyapunov exponent characterizing the stability of the system.

[0047] The Lyapunov exponent is input into a pre-constructed entropy rate mapping table. If the exponent exceeds the stable range, cooperative instability is determined. At the same time, the transient fluctuation feature combination that causes the exponent to exceed the limit is extracted from the cooperative trajectory data stream and marked as a weak point cloud.

[0048] Project the spatial coordinates of the weak point cloud into the reference hyperplane in the cooperative stability domain boundary model, and calculate the Euclidean offset vector of the spatial coordinates to the boundary of the original toughness margin threshold interval.

[0049] The toughness margin threshold range of the boundary model is adjusted based on the Euclidean offset vector: the threshold range boundary is expanded along the offset direction so that the weak point cloud falls into the new range, and the fitting parameters of the convex envelope boundary are updated to achieve boundary toughness enhancement.

[0050] The second aspect of this invention discloses a manufacturing process optimization system for a thermistor chip. The manufacturing process optimization system for the thermistor chip includes a memory and a processor. The memory stores a manufacturing process optimization method program for the thermistor chip. When the manufacturing process optimization method program for the thermistor chip is executed by the processor, the steps of the manufacturing process optimization method for the thermistor chip described in any one of the claims are implemented.

[0051] This invention addresses the technical deficiencies in the prior art and offers the following advantages: It performs multi-scale process entropy analysis on the dynamic flow of process parameters, analyzes the coupling strength between key processes, and identifies process parameter clusters with strong non-monotonic correlations and their entropy increase paths in the process system. This allows for the construction of a collaborative stability domain boundary model in a multi-dimensional process parameter space to suppress entropy increase in the process system. Furthermore, based on the transient fluctuation characteristics extracted from the real-time dynamic flow of process parameters, combined with the collaborative stability domain boundary model, it identifies a subset of parameters exceeding the collaborative stability operating range as drift parameter clusters, generates an optimized instruction set, executes the optimized instruction set for trial production, simultaneously collects collaborative trajectory data of the process parameter clusters, and finally verifies collaborative stability by calculating the entropy change rate of the process system, feeding this data back to the collaborative stability domain boundary model for boundary toughness enhancement. This achieves dynamic collaborative convergence of related parameters such as sintering gradient and electrode pressure, improving product consistency and yield stability. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other embodiments can be obtained from these drawings without creative effort.

[0053] Figure 1 This is a flowchart illustrating the overall method for optimizing the manufacturing process of this thermistor chip.

[0054] Figure 2 This is a working framework diagram of the thermistor chip manufacturing process optimization method;

[0055] Figure 3 This is a system block diagram of the thermistor chip manufacturing process optimization system. Detailed Implementation

[0056] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0057] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0058] like Figure 1 , 2 As shown, the first aspect of this invention discloses a method for optimizing the manufacturing process of a thermistor chip, comprising the following steps:

[0059] S1: Real-time acquisition of dynamic flow of process parameters for each key step in the entire manufacturing process of thermistor chip, including set values, actual values ​​and their transient fluctuation characteristics;

[0060] S2: Perform multi-scale process entropy analysis on the dynamic flow of the process parameters, analyze the coupling strength between key processes, and identify process parameter clusters with strong non-monotonic correlations and the process system entropy increase paths dominated by the process parameter clusters.

[0061] S3: Based on the process parameter cluster and its process system entropy increase path, a collaborative stability domain boundary model that suppresses the entropy increase of the process system is constructed in the multidimensional process parameter space to characterize the collaborative stability operation range of the parameter cluster.

[0062] S4: Based on the transient fluctuation characteristics extracted from the dynamic flow of process parameters acquired in real time, and combined with the collaborative stability domain boundary model, determine the parameter subset that exceeds the collaborative stability operation range as the drift parameter cluster, and generate an optimized instruction set to converge the drift parameter cluster to the collaborative stability operation range.

[0063] S5: Execute the optimized instruction set for trial production, synchronously collect the collaborative trajectory data of the process parameter cluster, verify the collaborative stability by calculating the entropy change rate of the process system, and feed it back to the collaborative stability domain boundary model for boundary toughness enhancement.

[0064] It should be noted that this invention constructs a parameter cluster to coordinate the stable domain boundary, identifies drift clusters in real time, and generates optimization instructions in reverse along the entropy increase path, thereby achieving dynamic coordinated convergence of related parameters such as sintering gradient and electrode pressure, thus improving product consistency and yield stability.

[0065] Specifically, S1 is:

[0066] The original process timing signals of the material sintering process (such as temperature gradient and atmosphere concentration) and the electrode formation process (such as printing pressure and slurry viscosity) are captured in real time by an embedded sensor network, and the process gait labels (including process stage identifiers and timestamps) of each data point are marked synchronously.

[0067] The original process timing signal is divided into sliding windows, and the following parallel operations are performed within each window: The sequence of set command values ​​from the current process equipment control system is extracted; environmental noise interference is eliminated through signal filtering to generate a sequence of actual physical quantity measurements; Fourier transform and Hilbert transform are performed on the actual physical quantity measurement sequence to separate the frequency domain envelope features and time domain transient features, which are then merged to form a transient fluctuation feature set; wherein, the frequency domain envelope features include the dominant fluctuation frequency and harmonic energy ratio; and the time domain transient features include the extreme values ​​of the rise slope and the decay time constant.

[0068] The sequence of set command values, the sequence of actual physical quantity measurements, and the corresponding transient fluctuation feature sets within the same time window are spatiotemporally aligned and bound according to the process step label to generate a dynamic flow unit of process parameters with multi-dimensional attributes.

[0069] By sequentially connecting the dynamic flow units of each process parameter according to the process sequence, a dynamic flow of process parameters covering the entire manufacturing process is formed. Each dynamic flow unit of process parameter inherits the process gait label of the preceding unit to achieve cross-process correlation and traceability.

[0070] It should be noted that this step binds the set values, actual values, and transient feature sets within the same window into dynamic flow units according to the process step labels, and strings them together into a complete process chain according to the process sequence, which serves as the underlying data architecture for process entropy increase analysis.

[0071] Specifically, S2 is:

[0072] Empirical mode decomposition is performed on the sequence of actual physical quantity measurements in the dynamic flow of process parameters to extract the intrinsic mode components that characterize the dynamic response of different processes, and obtain a multi-scale time-domain feature set including short-term fluctuations, medium-range oscillations and long-range trends.

[0073] It should be noted that short-term fluctuations refer to signal changes lasting in milliseconds (1ms-100ms), medium-range oscillations refer to periodic signal changes lasting in seconds (100ms-10s), and long-range trends refer to signal evolution characteristics lasting in minutes (10s-10min) or longer.

[0074] Based on the multi-scale time-domain feature set, the mutual information entropy of key process parameter pairs (such as sintering temperature gradient and electrode printing pressure) on the same time scale is calculated, and a cross-process coupling strength matrix is ​​generated, where the matrix element values ​​characterize the degree of nonlinear dependence of parameter pairs at a specific scale.

[0075] Further explanation is needed: for the three scales of short-term fluctuations, medium-term oscillations, and long-term trends, feature sequences of parameter pairs within the same time window are extracted respectively. Then, the joint probability distribution and marginal probability distribution of parameter pairs at each scale are constructed by kernel density estimation, thereby calculating the normalized mutual information entropy to quantify the nonlinear statistical dependence strength of parameter pairs at a specific scale. Finally, the mutual information entropy values ​​at the three scales are arranged into a 3×3 coupling strength matrix according to the scale dimension.

[0076] In the coupling strength matrix, parameter pairs whose mutual information entropy values ​​exceed a set threshold but whose absolute Pearson correlation coefficient values ​​are lower than a monotonicity threshold are selected and marked as strongly non-monotonic correlation pairs; strong non-monotonic correlation pairs with cross-correlation are aggregated into process parameter clusters through cluster analysis.

[0077] In a preferred embodiment of the present invention, the set threshold (i.e., mutual information entropy threshold) is set to 0.35; the monotonicity threshold (i.e., Pearson correlation coefficient threshold) is set to 0.25 (a value lower than this indicates that the linear correlation between parameters can be ignored, ensuring that the true non-monotonic relationship is screened out).

[0078] For each cluster of process parameters, a conditional entropy transfer network of its multi-scale time-domain characteristics is constructed: the parameter features within the cluster are used as nodes, and the transfer entropy between nodes is used as edge weights. A directed weighted graph model is used to characterize the transfer path of process disturbances among multiple parameters. The longest entropy increase path in the network is identified by a graph search algorithm and defined as the entropy increase path of the process system. The entropy increase path of the process system has the largest cumulative edge weight and the transfer direction conforms to the time sequence of the process steps.

[0079] It should be noted that by constructing a conditional entropy transfer network for a cluster of process parameters, interactive parameter features are used as nodes, and transfer entropy is used as directed edge weights to form a weighted directed graph that reflects the propagation path of process disturbances. A time-constrained graph search algorithm is used to identify the path with the largest cumulative edge weight as the entropy increase path of the process system. This satisfies the process sequence constraints and reveals the key links of energy dissipation and information transmission in the process, thus providing clear intervention targets for process optimization.

[0080] Specifically, S3 is:

[0081] For each process parameter cluster, the entropy increase path of the process system is extracted, and the key transfer node with the maximum sum of in-degree and out-degree is extracted in the corresponding directed weighted graph. The key transfer node corresponds to the multi-scale time-domain features of a specific process stage (e.g., the long-range trend features of the sintering temperature gradient or the short-term fluctuation features of the electrode printing pressure).

[0082] The actual physical quantity measurement sequence of all process parameters in the process parameter cluster associated with the key transmission node and their transient fluctuation characteristics (such as main fluctuation frequency and extreme value of rising slope) are organized into a multidimensional time series according to the process time sequence; the higher-order cross-cumulative quantity of the multidimensional series within the sliding time window is calculated to generate a parameter coupling tensor characterizing the nonlinear coupling strength between parameters.

[0083] It should be noted that the actual physical quantity measurement sequence and transient fluctuation characteristics of each parameter in the process parameter cluster are extracted within the sliding time window and aligned according to the process time sequence to form a multidimensional time series matrix. For each three parameter combination of this multidimensional time series matrix (such as sintering temperature gradient, slurry viscosity, and printing pressure), its third-order cross-cumulative is calculated: the steady-state offset is eliminated by de-meaning, and then the synchronous fluctuation values ​​of the parameters at all times within the window are summed by triple product and normalized by dividing by the window length. Finally, the third-order cross-cumulative of different parameter combinations is organized into a three-dimensional tensor according to the input parameter dimension, output parameter dimension, and time window dimension. The tensor element values ​​are the nonlinear coupling strength of the corresponding parameter combination within a specific time window, thereby generating the parameter coupling tensor.

[0084] The parameter coupling tensor is decomposed into a nonnegative tensor, and its dominant load factor vector is extracted as the principal co-variation vector. The principal co-variation vector represents the covariation mode of the multidimensional fluctuation characteristics of the parameter cluster in a steady state (e.g., the synchronous change ratio of the slurry viscosity harmonic energy ratio and the printing pressure decay time constant).

[0085] Using the main cooperative vector as the normal vector, a reference hyperplane is defined in a multidimensional space composed of the actual values ​​of cluster parameters; the Euclidean projection distance from each data point in the real-time process parameter dynamic flow to the hyperplane is calculated, and the toughness margin threshold range of the projection distance distribution is determined by kernel density estimation in combination with the transient fluctuation characteristics at the corresponding time.

[0086] More specifically, the principal cooperative vector is normalized to a unit normal vector. In a multidimensional space composed of the actual physical quantity measurements of all parameters within the process parameter cluster (e.g., temperature gradient values ​​and printing pressure values), a reference hyperplane is established with the origin as the reference point. This hyperplane satisfies the geometric constraint that the spatial coordinates of the unit normal dot product are equal to zero. Then, for each data point in the real-time process parameter dynamic stream (including the actual measurements of each parameter at a specific timestamp), the dot product of its spatial coordinate vector and the unit normal vector is calculated. The absolute value is then divided by the magnitude of the unit normal vector to obtain the vertical Euclidean projection distance from that point to the reference hyperplane, and the transient fluctuation characteristics corresponding to that data point are synchronously associated. Finally, Gaussian kernel density estimation is applied to the projection distance sequence of all data points to obtain the probability density distribution curve of the projection distance. The boundary values ​​of the intervals with a cumulative probability of 95% on both sides of the density peak are selected as the upper and lower limits of the toughness margin threshold, thus forming a dynamic threshold interval.

[0087] The toughness margin threshold range is mapped back to the original process parameter space, and a convex envelope boundary is fitted around the corresponding mapping point set; the convex envelope boundary is the collaborative stability domain boundary model that characterizes the collaborative stable operation range of the parameter cluster, and its geometry is jointly determined by the covariation mode of the main collaborative vector and the dynamic toughness margin threshold.

[0088] Specifically, mapping the toughness margin threshold interval back to the original process parameter space and fitting a convex hull boundary surrounding the corresponding mapped point set involves: selecting a subset of data points whose Euclidean projection distance falls within the toughness margin threshold interval from the real-time process parameter dynamic flow to form a mapped point set; extracting multidimensional coordinate values ​​of the mapped point set from the original process parameter space (these coordinate values ​​originate from the actual physical quantity measurement sequence in the process parameter dynamic flow unit), and determining the spatial distribution characteristics of the mapped point set based on the multidimensional coordinate values; using the spatial distribution characteristics, performing boundary fitting on the mapped point set to generate a minimum convex hull boundary surface surrounding all points; the minimum convex hull boundary surface is defined as the cooperative stability domain boundary model, whose geometry is dynamically constrained by the covariance mode of the main cooperative vector and the dynamic toughness margin threshold.

[0089] In summary, this invention adaptively generates convex hull boundaries by combining dynamic toughness margin thresholds, enabling the stable domain to respond in real time to transient fluctuation characteristics. This effectively suppresses entropy increase in the process system and transforms the drift risk of strongly correlated parameters such as sintering temperature gradient and electrode printing pressure into quantifiable and monitorable boundary over-limit events, providing early warning for process instability.

[0090] Specifically, S4 is:

[0091] Extract the multi-dimensional coordinate values for the sequence of actual physical quantity measurement values in the current process parameter dynamic flow unit; calculate the second Euclidean projection distance from the corresponding multi-dimensional coordinate values to the reference hyperplane based on the main co-vector in the co-stable domain boundary model, and synchronously associate the transient fluctuation characteristics recorded in this unit;

[0092] Compare the second Euclidean projection distance with the toughness margin threshold interval in the co-stable domain boundary model, screen out the data points whose second Euclidean projection distance is not within the preset range interval as drift points, and record the process stage identifier and time stamp in their process gait labels;

[0093] It should be noted that reading the pre-stored toughness margin threshold interval in the co-stable domain boundary model includes the upper limit value Dmax and the lower limit value Dmin, and obtaining the second Euclidean projection distance values of all data points in the current process parameter dynamic flow unit (calculating the projection result of the multi-dimensional coordinate values and the main co-vector through dot product operation). Then, compare the corresponding distance values with the threshold interval point by point: if the second Euclidean projection distance of a certain point satisfies D > Dmax (exceeding the upper limit) or D < Dmin (exceeding the lower limit), then mark this point as a drift point. Finally, extract the process stage identifier and accurate time stamp in the process gait label corresponding to this drift point, and bind and store them as a drift point record set.

[0094] Based on the time stamp continuity and process stage relevance of the process gait label, perform spatio-temporal clustering on the drift points to form several drift parameter clusters, and the drift parameter clusters include the actual value offset of the associated parameters and the outlier of the transient fluctuation characteristics;

[0095] Extract the entropy increase transfer direction in the directed weighted graph for the process system entropy increase path dominated by the drift parameter cluster; take the reverse of the entropy increase transfer direction as the adjustment reference, and generate a negative feedback adjustment amount according to the product of the actual value offset of each parameter in the cluster and the outlier of the transient fluctuation characteristics;

[0096] It should be noted that load the directed weighted graph of the process system entropy increase path corresponding to the drift parameter cluster, use the Dijkstra algorithm to search for the maximum edge weight cumulative path from the starting node (the characteristics of the earliest stage of the process) to the ending node (the characteristics of the latest stage of the process), define the node transfer direction of this path as the entropy increase transfer direction, and take the reverse of the entropy increase transfer direction as the adjustment reference direction to determine the negative feedback adjustment amount of each parameter in the cluster: take the difference between the current actual physical quantity measurement value of the parameter and the co-stable domain boundary reference value, calculate the deviation of the current value relative to the steady-state reference value, and multiply the two after dimension normalization to generate a signed adjustment amount. For example: adjustment amount = sign(direction) × (temperature zone gradient offset × viscosity increase slope outlier), where the sign sign(direction) is determined by the adjustment reference direction (+1 for the positive direction, -1 for the negative direction).

[0097] Based on the negative feedback adjustment, gradient compensation values ​​are generated for continuous parameters of the sintering temperature gradient, and pulse correction waveforms based on the extreme values ​​of the rising slope are generated for transient parameters of the electrode printing pressure. Finally, an optimized instruction set containing parameter adjustment target values ​​and execution timing is output, driving the drift parameter cluster to converge to the boundary of the cooperative stability domain.

[0098] It should be noted that for continuous parameters of gradient type in sintering temperature zone: a smooth gradient compensation value sequence is generated based on the negative feedback adjustment amount (compensation value = negative feedback amount × reciprocal of process time constant), and it is divided into compensation segments of equal duration according to the process sequence to generate a segmented linearly increasing / decreasing target temperature curve.

[0099] For transient parameters such as electrode printing pressure: extract the extreme value component of the rising slope in the negative feedback adjustment amount and design a pulse correction waveform: take 120% of the current extreme value of the rising slope as the pulse amplitude reference, set the pulse phase according to the reverse direction of entropy increase transmission (positive entropy increase corresponds to 180° phase reversal), and determine the pulse width according to the rheological characteristics of the slurry, where pulse width = 2 × viscosity relaxation time.

[0100] Finally, an optimized instruction set is constructed: the gradient compensation value sequence is converted into executable instructions for the temperature controller (including the target temperature zone value and arrival timestamp), the pulse correction waveform is encoded into a step instruction for the pressure controller (including amplitude-phase-width triplet), and then the execution sequence of the two types of instructions is aligned according to the process stage identifier, and encapsulated into a JSON structured instruction set with process gait tags.

[0101] Specifically, based on the continuity of timestamps and the correlation of process stages of the process gait tags, the drift points are spatiotemporally clustered to form several drift parameter clusters, as follows:

[0102] Based on the timestamps in the process gait tags carried by the drift points, the time difference between adjacent drift points is calculated; at the same time, the process stage identifiers are extracted to generate a spatiotemporal neighborhood group that includes time continuity and process correlation.

[0103] It should be noted that drift points with a time difference less than a preset time difference threshold and whose process identifiers belong to the same process chain are grouped into the same spatiotemporal neighborhood group. The preset time difference threshold can be defined as follows: the time interval between adjacent drift points does not exceed 20% of the current process's standard processing cycle, and the absolute value is controlled within the range of 0.5-5 seconds. The specific value is dynamically adjusted based on the dynamic response characteristics of different process stages in the thermistor chip manufacturing process.

[0104] Extract the actual value offset (i.e., the difference between the actual physical quantity measurement value and the benchmark value of the cooperative stability domain boundary) and transient fluctuation feature anomalies (including the main fluctuation frequency deviation and the extreme value offset of the rising slope) recorded for each drift point in the spatiotemporal neighborhood group, and fuse the two according to the preset weight to generate the feature fusion vector of the corresponding drift point.

[0105] It should be noted that the weighting coefficient for the actual value offset is 0.6-0.8, and the weighting coefficient for the transient fluctuation characteristic outlier is 0.2-0.4, and the sum of the two is strictly equal to 1. The specific values ​​are dynamically allocated according to the type of process parameter (e.g., 0.7:0.3 for sintering parameters and 0.6:0.4 for printing parameters).

[0106] Using spatiotemporal neighborhood groups as initial clustering units, the process coupling distance between the feature fusion vectors of each drift point within the group is calculated (this distance simultaneously measures the Euclidean distance of the actual value offset, the Manhattan distance of the transient fluctuation feature outlier, and the process correlation degree of the process stage identifier). Using density clustering algorithm, with process coupling distance as the metric, drift points that are spatially adjacent and have a process correlation degree higher than a preset correlation degree threshold are aggregated into candidate drift clusters.

[0107] It should be noted that for each drift point within the spatiotemporal neighborhood group, its feature fusion vector is calculated according to a preset weight fusion rule, and then the process coupling distance is calculated according to the following formula:

[0108] ;

[0109] In the formula, The process coupling distance between drift points i and j; The weighting coefficient for the actual value offset (preset 0.6). This represents the actual offset of drift point i. This represents the actual offset of the drift point j. The weighting coefficient for transient feature outliers (preset 0.3); Let i be the vector of transient fluctuation characteristic anomalies at drift point i; Let be the vector of transient fluctuation characteristic anomalies at drift point j; This is the weighting coefficient for the degree of correlation between processes (preset 0.1). The degree of similarity in process relevance is used to identify the process stages.

[0110] Next, using process coupling distance as the metric, spatial adjacency conditions (Euclidean distance of feature fusion vectors less than or equal to twice the standard deviation within the group) and process correlation threshold (greater than 0.85) are set. Finally, the DBSCAN density clustering algorithm is used, with the average process coupling distance within the group as the neighborhood radius, and drift points that simultaneously meet the spatial adjacency and correlation thresholds are aggregated into candidate drift clusters.

[0111] Backtrack the entropy increase propagation direction of all drift points in each candidate drift cluster in the entropy increase path of the process system; if the propagation direction of all points in the cluster is consistent in the entropy increase path of the process system, mark the candidate cluster as a valid drift parameter cluster; otherwise, split it into sub-clusters for re-verification.

[0112] For the finally confirmed drift parameter cluster, the average actual value offset of all drift points within it is calculated as the actual value offset of the cluster, and the extreme values ​​of transient fluctuation feature outliers are calculated as transient fluctuation feature outliers of the cluster. These outliers are then bound to the associated process stage identifier and timestamp interval for output.

[0113] It should be noted that during the thermistor manufacturing process, there is a strong nonlinear coupling between parameters such as the sintering temperature gradient and electrode printing pressure. Traditional single-point threshold alarms (such as monitoring only the upper limit of the temperature gradient) cannot identify cluster drift of related parameters (such as sudden changes in slurry viscosity caused by gradual changes in the temperature gradient). Furthermore, conventional PID control can exacerbate system instability by ignoring the direction of entropy increase path. To address this, this invention extracts the multidimensional coordinate values ​​of the actual physical quantities measured in the real-time process parameter dynamic flow unit (such as temperature gradient values ​​and printing pressure values). Based on the principal co-variation vector of the co-stability domain boundary model (representing the steady-state co-variation mode between parameters), the second Euclidean projection distance from each point to the reference hyperplane is calculated and associated with transient fluctuation characteristics (such as the principal fluctuation frequency). Then, the projection distance is compared with the toughness margin threshold range, and points exceeding the limit are selected as drift points. Their process gait labels are recorded, and then the discrete drift points are aggregated into drift parameter clusters using a spatiotemporal clustering algorithm (constrained by time continuity and process correlation). The system quantifies the actual value offset of parameters within the cluster (such as the cumulative deviation of temperature gradient) and transient characteristic anomalies (such as sudden changes in the slope of slurry viscosity rise). Finally, for the entropy increase path dominated by the cluster, the direction of entropy increase transmission in the directed weighted graph is extracted, and its reverse direction is used as the adjustment benchmark: for continuous parameters (such as temperature gradient), gradient compensation values ​​proportional to the actual value offset are generated; for transient parameters (such as printing pressure), pulse correction waveforms are designed based on the extreme value of the rising slope (such as reverse peak suppression of overshoot), and a time-series optimized instruction set is output, thereby effectively reducing the process instability rate in the thermistor manufacturing process and improving the product qualification rate.

[0114] Specifically, S5 is:

[0115] During the process of executing the optimized instruction set to drive the adjustment of equipment parameters, the actual physical quantity measurement sequence of all parameters in the process parameter cluster and their transient fluctuation characteristics are captured in real time through the embedded sensor network. At the same time, the process phase angle difference of each parameter in the process sequence (i.e., the cross-parameter phase offset extracted based on Hilbert transform) is recorded to form a multi-dimensional collaborative trajectory data stream.

[0116] It should be noted that while executing the optimized instruction set, the actual physical quantity measurement sequence and transient fluctuation characteristics of all parameters in the parameter cluster are collected in real time through the embedded sensor network. Based on the Hilbert transform, the cross-parameter process phase angle difference is extracted to form a collaborative trajectory data stream that integrates physical quantities, transient characteristics and phase relationships.

[0117] Based on the cooperative trajectory data stream, multi-scale time-domain features of parameter clusters (including short-term fluctuation energy and long-term trend slope) are extracted within the sliding time window. Taking the entropy transfer direction in the entropy increase path of the process system as the reference axis, the divergence rate of multi-dimensional feature vectors between adjacent windows is calculated to generate the Lyapunov exponent characterizing the stability of the system.

[0118] It should be noted that multi-scale time-domain features are extracted within the sliding window: short-term fluctuation energy (wavelet packet decomposition frequency band energy integral) and long-term trend slope (linear fitting derivative). The divergence rate (i.e., Lyapunov exponent) of the feature vectors of adjacent windows is calculated with the entropy increase path direction as the reference axis.

[0119] ;

[0120] In the formula, The Lyapunov index; Let be the feature vector of the window at time t; The feature vector of the window at time t+1; This represents the window step size.

[0121] The Lyapunov exponent is input into a pre-constructed entropy rate mapping table. If the exponent exceeds the stable range, cooperative instability is determined. Simultaneously, transient fluctuation feature combinations that cause the exponent to exceed the limit are extracted from the cooperative trajectory data stream and marked as weak point clouds. The entropy rate mapping table is obtained by training with historical trial production data and associates the exponent value with the entropy rate threshold range of the entropy increase path of the process system. The transient fluctuation feature combinations include the co-occurrence pattern of specific main fluctuation frequencies and extreme values ​​of rising slopes.

[0122] It should be noted that a pre-built entropy rate mapping table (structured as a hash table, with the key being the Lyapunov exponent range and the value being the corresponding entropy rate state label and stability flag) is loaded. Then, the real-time calculated Lyapunov exponent is compared item by item with the key value range of the mapping table: it is determined whether the value of the Lyapunov exponent falls between the lower limit and the upper limit of the predefined exponent range in the entropy rate mapping table. If it falls within this range, then cooperative instability is determined.

[0123] If it is determined to be a cooperative instability, feature extraction is triggered synchronously: all transient fluctuation feature data points within the Lyapunov exponent overlimit time window are extracted from the current cooperative trajectory data stream, and feature combinations that meet the co-occurrence conditions are selected (for example, points with main fluctuation frequency ∈ [100Hz, 150Hz] and extreme values ​​of rising slope greater than 0.4kV / s). Their actual physical quantity measurements (such as temperature gradient values) are combined with transient feature values ​​(frequency + slope) to form three-dimensional spatial coordinates, which are then aggregated to form a set of resilient weak point clouds.

[0124] The spatial coordinates of the weak point cloud (composed of actual physical quantity measurements and transient fluctuation characteristics) are projected onto the reference hyperplane in the cooperative stability domain boundary model, and the Euclidean offset vector from the spatial coordinates to the boundary of the original toughness margin threshold interval is calculated.

[0125] The toughness margin threshold range of the boundary model is adjusted based on the Euclidean offset vector: the threshold range boundary is expanded along the offset direction so that the weak point cloud falls into the new range, and the fitting parameters of the convex envelope boundary are updated to achieve boundary toughness enhancement.

[0126] It should be noted that the weak point cloud is projected onto the reference hyperplane of the cooperative stability domain boundary model, the Euclidean offset vector to the original toughness margin threshold boundary is calculated, the threshold interval is then extended along the direction of the Euclidean offset vector, and the convex hull boundary is refitted, thereby achieving boundary toughness enhancement.

[0127] In addition, the thermistor chip manufacturing process optimization method may also include the following steps:

[0128] Based on the real-time acquired temperature data of the thermocouple array in the sintering process, an initial temperature distribution matrix of the sintering temperature zone in the spatiotemporal dimension is constructed.

[0129] The initial temperature distribution matrix is ​​mapped to a non-Euclidean geometric space with adjustable fractal dimensions, the metric of which is defined by a competing energy function of lattice growth and oxygen vacancy diffusion;

[0130] Using the Koch curve generation algorithm as the iterative kernel, fractal iterative operations are performed on the mapped temperature distribution matrix to generate a set of candidate gradient sintering paths with self-similar structures, where the fractal dimension parameter of each path is unique.

[0131] Calculate the local Lyapunov characteristic exponent spectrum of each candidate gradient sintering path, and select the path that can simultaneously suppress abnormal grain growth and oxygen vacancy accumulation as a feasible solution based on the convergence of the exponent spectrum.

[0132] Extract the fractal dimension parameters of the feasible solution path as control variables, and define the optimal fractal dimension setting value based on the control variables;

[0133] The recursion depth and scaling factor of the Koch curve iterative algorithm are adjusted in reverse using the optimal fractal dimension setting value, and the final optimal gradient sintering path instruction sequence is output to the sintering equipment control system.

[0134] It should be noted that during the sintering process of thermistor chips, there is usually a competitive relationship between grain growth and oxygen vacancy diffusion. Existing technologies often employ linear or step-type sintering temperature curves, making it difficult to simultaneously coordinate the two physical processes—rapid grain boundary migration and orderly annihilation of oxygen vacancies—at the microscale, which have different rates and conflicting mechanisms. This results in poor uniformity of the product's microstructure and inconsistent electrical performance. Therefore, this embodiment uses a thermocouple array embedded in each temperature zone of the sintering furnace to collect continuous spatiotemporal temperature data in real time and construct an initial temperature distribution matrix. This matrix accurately characterizes the macroscopic thermal field state of the current sintering environment. Subsequently, the thermal field matrix is ​​mapped to a specially constructed non-Euclidean geometric space. After mapping, the classic Koch curve generation algorithm is used as the iterative kernel to perform fractal iteration operations on the mapped matrix. Each iteration introduces more subtle, self-similar structural fluctuations into the original temperature distribution, thereby generating a set of candidate gradient sintering paths containing multiple paths with different complexities and fine structures. Each candidate path corresponds to a unique fractal dimension parameter.

[0135] To select the optimal path from the candidate set, this embodiment introduces a stability criterion from nonlinear dynamics. By calculating the local Lyapunov characteristic index spectrum of each candidate path, this index spectrum can accurately predict the sensitivity of the microstructure evolution system to initial conditions and its divergence or convergence trend under the perturbation of the corresponding temperature path. By identifying whether the modes characterizing grain size divergence (abnormal growth) and oxygen vacancy concentration divergence (aggregation) in the index spectrum converge, paths that can simultaneously suppress these two instability phenomena can be selected and marked as feasible solutions.

[0136] Subsequently, key features are extracted from the selected feasible solution paths: fractal dimension parameters, which are the control variables for achieving stable sintering. Based on the process database or theoretical model, the optimal value of this control variable, i.e., the optimal fractal dimension setting, can be determined. Finally, this optimal setting value is used to adjust the key parameters of the Koch curve iterative algorithm (such as recursion depth and scaling factor), enabling the algorithm to generate a unique optimal gradient sintering path. This path instruction sequence is output to the control system of the sintering equipment, thereby precisely controlling the furnace temperature to operate according to this optimized curve with fractal self-similarity characteristics. Ultimately, in the physical manufacturing process, the synergistic goals of uniform grain refinement and effective oxygen vacancy control are achieved, thereby improving the performance consistency and reliability of the thermistor chip.

[0137] In addition, the thermistor chip manufacturing process optimization method may also include the following steps:

[0138] The original optimized instruction set generated by the process optimization method is loaded into the virtual twin system, and the instruction set is deconstructed into a multi-dimensional instruction vector sequence according to the process timing.

[0139] A preset spatiotemporal stress field is applied to the multidimensional instruction vector sequence. This stress field includes a nonlinear compression transformation of the instruction execution time axis and a bicontinuous topological deformation of the device parameter space, generating a series of perturbed test instruction sequences.

[0140] All test instruction sequences are executed in parallel within the twin, and the collaborative trajectory response of the process parameter cluster under the action of each sequence is collected synchronously. The Lyapunov exponent spectrum and transient fluctuation entropy in the response trajectory are extracted as stability feature vectors.

[0141] Calculate the Friesian distance between the stability eigenvector of each test instruction sequence and the corresponding vector of the baseline instruction sequence, and use this distance as the spatiotemporal invariance strength of the test sequence;

[0142] All test instruction sequences are sorted according to the strength of spatiotemporal invariance, and sequences with strengths higher than the robustness threshold are selected and classified as a subset of candidate robust instructions.

[0143] Common features are extracted from the candidate robust instruction subsets, and then mapped back to the time-parameter domain of the original optimized instruction set. Finally, a robust instruction subset with time-space invariance and its corresponding tolerance range are output.

[0144] Specifically, the generated original optimized instruction set is first loaded into the existing virtual twin system for the entire thermistor chip manufacturing process. This instruction set is then deconstructed according to the dimensions of the controlled device parameters and the order of their execution, forming a multi-dimensional instruction vector sequence, where each vector represents the set state of all controlled parameters at a specific moment.

[0145] Subsequently, to simulate the temporal asynchrony and parameter drift that may occur in real production, a preset spatiotemporal stress field is applied to the above vector sequence. This stress field contains two core perturbations: one is a nonlinear compression transformation of the instruction execution time axis (e.g., simulating device response delay or acceleration), and the other is a bicontinuous topological deformation of the device parameter space (e.g., simulating sensor calibration error or actuator nonlinearity). By applying this stress field, a series of test instruction sequences can be generated that both retain the original instruction intent and contain perturbations of different degrees and types, thereby greatly expanding the test coverage.

[0146] Next, all these generated test instruction sequences are executed in parallel within the virtual twin. Simultaneously, high-frequency acquisition is used to capture the dynamic response of the process parameter clusters (such as sintering temperature, pressure, and atmosphere concentration) driven by each test sequence, i.e., the cooperative trajectory response. From these response trajectories, two key nonlinear dynamic indices are quantitatively extracted: the Lyapunov exponent spectrum (used to quantify the system's sensitivity to initial conditions and long-term predictability) and the transient fluctuation entropy (used to quantify the randomness and disorder of process disturbances), which together constitute a stability feature vector for evaluating the stability of each test sequence.

[0147] Then, the Fraser distance between the stability feature vector corresponding to each test instruction sequence and the stability feature vector of the baseline instruction sequence executed under ideal, undisturbed conditions is calculated. The reciprocal or negative value of the Fraser distance is defined as the spatiotemporal invariance strength of the test instruction sequence. The higher the strength, the closer the behavior of the test sequence under perturbation is to the ideal baseline, i.e., the more robust it is. All test instruction sequences are sorted according to the calculated spatiotemporal invariance strength, and sequences with strengths higher than a preset robustness threshold are selected and classified into a subset of candidate robust instructions.

[0148] Finally, common features are extracted from the selected candidate robust instruction subset to analyze the common patterns that maintain the invariance of their instruction structure under spatiotemporal stress fields (e.g., the cooperative relationships between certain parameters remain unchanged). These common features are then mapped back to the time-parameter domain of the original optimized instruction set, ultimately outputting a robust instruction subset that not only contains specific instructions but also clearly defines its tolerable parameter and timing deviation tolerance ranges, possessing spatiotemporal invariance. This subset provides a highly reliable and robust control guideline for actual production, fundamentally improving the resilience and consistency of the manufacturing process.

[0149] like Figure 3 As shown, the second aspect of the present invention discloses a manufacturing process optimization system for a thermistor chip. The manufacturing process optimization system for the thermistor chip includes a memory and a processor. The memory stores a manufacturing process optimization method program for the thermistor chip. When the manufacturing process optimization method program for the thermistor chip is executed by the processor, the steps of the manufacturing process optimization method for the thermistor chip described in any one of the claims are implemented.

[0150] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0151] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units. They may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs.

[0152] In addition, in the various embodiments of the present invention, each functional unit can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0153] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0154] Alternatively, if the integrated units of this invention are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0155] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the manufacturing process of a thermistor chip, characterized in that, Includes the following steps: S1: Real-time acquisition of dynamic flow of process parameters for each key step in the entire manufacturing process of thermistor chip, including set values, actual values ​​and their transient fluctuation characteristics; S2: Perform multi-scale process entropy analysis on the dynamic flow of the process parameters, analyze the coupling strength between key processes, and identify process parameter clusters with strong non-monotonic correlations and the process system entropy increase paths dominated by the process parameter clusters. S3: Based on the process parameter cluster and its process system entropy increase path, a collaborative stability domain boundary model that suppresses the entropy increase of the process system is constructed in the multidimensional process parameter space to characterize the collaborative stability operation range of the parameter cluster. S4: Based on the transient fluctuation characteristics extracted from the dynamic flow of process parameters acquired in real time, and combined with the collaborative stability domain boundary model, determine the parameter subset that exceeds the collaborative stability operation range as the drift parameter cluster, and generate an optimized instruction set to converge the drift parameter cluster to the collaborative stability operation range. S5: Execute the optimized instruction set to conduct trial production, synchronously collect the collaborative trajectory data of the process parameter cluster, verify the collaborative stability by calculating the entropy change rate of the process system, and feed it back to the collaborative stability domain boundary model for boundary toughness reinforcement. Specifically, S3 is: For each process parameter cluster, the entropy increase path of the process system is defined, and the key transfer node with the maximum sum of in-degree and out-degree is extracted from the corresponding directed weighted graph. The key transfer node corresponds to the multi-scale temporal features of a specific process stage. The actual physical quantity measurement sequence of all process parameters and their transient fluctuation characteristics within the process parameter cluster associated with the key transmission node are organized into a multidimensional time series according to the process time sequence; the higher-order cross-cumulative quantity of the multidimensional series within the sliding time window is calculated to generate a parameter coupling tensor characterizing the nonlinear coupling strength between parameters. The parameter coupling tensor is decomposed into a nonnegative tensor, and its dominant load factor vector is extracted as the principal co-variation vector; the principal co-variation vector represents the covariation mode of the multidimensional fluctuation characteristics of the parameter cluster in the steady state. Using the main cooperative vector as the normal vector, a reference hyperplane is defined in a multidimensional space composed of the actual values ​​of cluster parameters; the Euclidean projection distance from each data point in the real-time process parameter dynamic flow to the hyperplane is calculated, and the toughness margin threshold range of the projection distance distribution is determined by kernel density estimation in combination with the transient fluctuation characteristics at the corresponding time. The toughness margin threshold range is mapped back to the original process parameter space, and a convex envelope boundary is fitted around the corresponding mapping point set; the convex envelope boundary is the collaborative stability domain boundary model that characterizes the collaborative stable operation range of the parameter cluster, and its geometry is jointly determined by the covariation mode of the main collaborative vector and the dynamic toughness margin threshold.

2. The method for optimizing the manufacturing process of a thermistor chip according to claim 1, characterized in that, Specifically, S1 is: The original process timing signals of the material sintering process and electrode formation process are captured in real time through an embedded sensor network, and the process gait labels of each data point are marked synchronously. The original process timing signal is divided into sliding windows, and the following is executed in parallel within each window: extract the sequence of set command values ​​of the current process equipment control system; Environmental noise interference is eliminated by signal filtering to generate a sequence of actual physical quantity measurements; Fourier transform and Hilbert transform are performed on the actual physical quantity measurement sequence to separate the frequency domain envelope features and time domain transient features, which are then combined to form a transient fluctuation feature set; The sequence of set command values, the sequence of actual physical quantity measurements, and the corresponding transient fluctuation feature sets within the same time window are spatiotemporally aligned and bound according to the process step label to generate a dynamic flow unit of process parameters with multi-dimensional attributes. By sequentially connecting the dynamic flow units of each process parameter according to the process sequence, a dynamic flow of process parameters covering the entire manufacturing process is formed. Each dynamic flow unit of process parameter inherits the process gait label of the preceding unit to achieve cross-process correlation and traceability.

3. The method for optimizing the manufacturing process of a thermistor chip according to claim 1, characterized in that, Specifically, S2 is: Empirical mode decomposition is performed on the sequence of actual physical quantity measurements in the dynamic flow of process parameters to extract the intrinsic mode components that characterize the dynamic response of different processes, and obtain a multi-scale time-domain feature set including short-term fluctuations, medium-range oscillations and long-range trends. Based on the multi-scale time-domain feature set, the mutual information entropy of key process parameter pairs at the same time scale is calculated to generate a cross-process coupling strength matrix, wherein the matrix element values ​​characterize the degree of nonlinear dependence of parameter pairs at a specific scale. In the coupling strength matrix, parameter pairs whose mutual information entropy values ​​exceed a set threshold but whose absolute Pearson correlation coefficient values ​​are lower than a monotonicity threshold are selected and marked as strongly non-monotonic correlation pairs; strong non-monotonic correlation pairs with cross-correlation are aggregated into process parameter clusters through cluster analysis. For each cluster of process parameters, a conditional entropy transfer network with multi-scale time-domain characteristics is constructed: the parameter features within the cluster are used as nodes, and the transfer entropy between nodes is used as edge weights. A directed weighted graph model is used to characterize the transfer path of process disturbances between multiple parameters. The longest entropy increase path in the network is identified by a graph search algorithm and defined as the entropy increase path of the process system. Among them, the edge weight accumulation value of the entropy increase path of the process system is the largest and the transmission direction conforms to the process sequence.

4. The method for optimizing the manufacturing process of a thermistor chip according to claim 1, characterized in that, The toughness margin threshold range is mapped back to the original process parameter space, and a convex hull boundary enclosing the corresponding mapped point set is fitted, specifically as follows: A subset of data points whose Euclidean projection distance falls within the toughness margin threshold range is selected from the real-time dynamic flow of process parameters to form a mapping point set; Extract the multidimensional coordinate values ​​of the mapping point set from the original process parameter space, and determine the spatial distribution characteristics of the mapping point set based on the multidimensional coordinate values; Using the aforementioned spatial distribution characteristics, the mapping point set is fitted to the boundary to generate the minimum convex hull boundary surface that surrounds all points; The minimum convex hull boundary surface is defined as the cooperative stable domain boundary model, whose geometry is dynamically constrained by the covariation mode of the principal cooperative vector and the dynamic toughness margin threshold.

5. The method for optimizing the manufacturing process of a thermistor chip according to claim 1, characterized in that, Specifically, S4 is: For the sequence of actual physical quantity measurements in the dynamic flow unit of the current process parameters, extract its multidimensional coordinate values; Based on the principal cooperative vector in the cooperative stable domain boundary model, the second Euclidean projection distance from the corresponding multidimensional coordinate value to the reference hyperplane is calculated, and the transient fluctuation characteristics recorded by the unit are synchronously associated. The second Euclidean projection distance is compared with the toughness margin threshold range in the cooperative stability domain boundary model. Data points whose second Euclidean projection distance is not within the preset range are selected as drift points, and the process stage identifier and timestamp in their process gait label are recorded. Based on the continuity of timestamps and the correlation of process stages of process gait tags, the drift points are spatiotemporally clustered to form several drift parameter clusters. The drift parameter clusters include the actual value offset of the associated parameters and the transient fluctuation feature anomalies. For the entropy increase path of the process system dominated by the drift parameter cluster, the entropy increase transmission direction in its directed weighted graph is extracted; the reverse direction of the entropy increase transmission direction is used as the adjustment benchmark, and a negative feedback adjustment amount is generated according to the product of the actual value offset of each parameter in the cluster and the transient fluctuation characteristic anomaly value. Based on the negative feedback adjustment, gradient compensation values ​​are generated for continuous parameters of the sintering temperature gradient, and pulse correction waveforms based on the extreme values ​​of the rising slope are generated for transient parameters of the electrode printing pressure. Finally, an optimized instruction set containing parameter adjustment target values ​​and execution timing is output, driving the drift parameter cluster to converge to the boundary of the cooperative stability domain.

6. The method for optimizing the manufacturing process of a thermistor chip according to claim 5, characterized in that, Based on the continuity of timestamps and the correlation of process stages of the process gait tags, the drift points are spatiotemporally clustered to form several drift parameter clusters, specifically: Based on the timestamps in the process gait tags carried by the drift points, the time difference between adjacent drift points is calculated; at the same time, the process stage identifiers are extracted to generate a spatiotemporal neighborhood group that includes time continuity and process correlation. Extract the actual value offset and transient fluctuation feature anomaly value of each drift point recorded in the spatiotemporal neighborhood group, and fuse the two according to a preset weight to generate the feature fusion vector of the corresponding drift point; Using spatiotemporal neighborhood groups as initial clustering units, the process coupling distance between the feature fusion vectors of each drift point within the group is calculated; density clustering algorithm is used, with process coupling distance as the metric, to aggregate spatially adjacent drift points with process correlation higher than a preset correlation threshold into candidate drift clusters; Tracing back the entropy increase propagation direction of all drift points within each candidate drift cluster in the entropy increase path of the process system; If all points within a cluster have the same direction of propagation on the entropy increase path of the process system, then the candidate cluster is marked as a valid drift parameter cluster. Otherwise, split into sub-clusters and re-verify; For the finally confirmed drift parameter cluster, the average actual value offset of all drift points within it is calculated as the actual value offset of the cluster, and the extreme values ​​of transient fluctuation feature outliers are calculated as transient fluctuation feature outliers of the cluster. These outliers are then bound to the associated process stage identifier and timestamp interval for output.

7. The method for optimizing the manufacturing process of a thermistor chip according to claim 1, characterized in that, Specifically, S5 is: During the process of executing the optimized instruction set to drive the adjustment of equipment parameters, the actual physical quantity measurement sequence of all parameters in the process parameter cluster and their transient fluctuation characteristics are captured in real time through the embedded sensor network. At the same time, the process phase angle difference of each parameter in the process sequence is recorded to form a multi-dimensional collaborative trajectory data stream. Based on the cooperative trajectory data stream, multi-scale time-domain features of parameter clusters are extracted within the sliding time window. Taking the entropy transfer direction in the entropy increase path of the process system as the reference axis, the divergence rate of multi-dimensional feature vectors between adjacent windows is calculated to generate the Lyapunov exponent characterizing the stability of the system. The Lyapunov exponent is input into a pre-constructed entropy rate mapping table. If the exponent exceeds the stable range, cooperative instability is determined. At the same time, the transient fluctuation feature combination that causes the exponent to exceed the limit is extracted from the cooperative trajectory data stream and marked as a weak point cloud. Project the spatial coordinates of the weak point cloud into the reference hyperplane in the cooperative stability domain boundary model, and calculate the Euclidean offset vector of the spatial coordinates to the boundary of the original toughness margin threshold interval. The toughness margin threshold range of the boundary model is adjusted based on the Euclidean offset vector: the threshold range boundary is expanded along the offset direction so that the weak point cloud falls into the new range, and the fitting parameters of the convex envelope boundary are updated to achieve boundary toughness enhancement.

8. A manufacturing process optimization system for a thermistor chip, characterized in that, The thermistor chip manufacturing process optimization system includes a memory and a processor. The memory stores a thermistor chip manufacturing process optimization method program. When the thermistor chip manufacturing process optimization method program is executed by the processor, the steps of the thermistor chip manufacturing process optimization method as described in any one of claims 1 to 7 are implemented.

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