Robustness-oriented process parameter optimization method and device, electronic equipment and medium

Abstract

The invention provides a robustness-oriented process parameter optimization method and device, electronic equipment and a medium, and the method comprises the steps: carrying out the preprocessing of a pre-constructed multi-dimensional data tensor, and obtaining a disturbance feature template library; carrying out attribute marking processing on the process parameters to obtain a process parameter list; inputting the process parameter list into the double-target agent model, and outputting probability distribution of average performance and probability distribution of performance fluctuation; if it is monitored that the real-time disturbance characteristics are matched with the basic disturbance characteristics in the experiment process, process parameters marked with control force attributes are called for experimental feed-forward compensation, and an experimental data set carrying the real-time disturbance characteristics is fed back to the Bayesian optimizer to update the double-target agent model; and according to the probability distribution of the average performance and the probability distribution of the performance fluctuation, drawing a dual-target Pareto frontier to determine an optimal process window. According to the method, the robustness of the final process is improved, and the influence of disturbance on the product consistency is reduced.

Description

Technical Field

[0001] This application relates to the field of process parameter optimization technology, and more specifically, to a robust process parameter optimization method, apparatus, electronic device, and medium. Background Technology

[0002] In the industrial manufacturing sector, as product precision requirements increase and production processes become more complex, process parameter optimization has become a core element determining product quality stability and production efficiency. Whether it's semiconductor etching, bio-fermentation, automotive battery spot welding, or chemical polymerization, precise control of process parameters is essential to achieve product performance targets and consistency in mass production.

[0003] In industrial process optimization, traditional Design of Experiments (DOE) methods, such as Response Surface Methodology (RSM), select experimental points within a pre-defined process space, construct response surface models, and seek parameter combinations that maximize average performance. Meanwhile, existing process control methods, centered on Advanced Process Control (APC) and Statistical Process Control (SPC), monitor the deviation between the process output and the setpoint in real time after production starts, and compensate for the deviation by adjusting parameters through feedback.

[0004] However, existing technologies still have significant shortcomings in real-world industrial scenarios, making it difficult to meet the demands for high-precision and high-stability production. On one hand, traditional DOE methods suffer from a narrow process window: their optimization objective focuses solely on maximizing average performance, failing to adequately consider the prevalent non-stationary disturbances in the production process. This results in the optimal parameter combinations being effective only under ideal, disturbance-free conditions. Once actual disturbances occur, product performance is prone to drastic fluctuations, affecting batch production consistency. On the other hand, existing process control methods exhibit passive lag. Technologies such as APC and SPC can only compensate after detecting parameter deviations during production, leading to compensation operations often lagging behind the impact of disturbances. This results in weak disturbance resistance, increasing the risk of product scrap and potentially introducing new process fluctuations through frequent parameter adjustments, making it difficult to adapt to dynamic disturbance scenarios in actual production. Summary of the Invention

[0005] In view of this, the purpose of this application is to provide a robust process parameter optimization method, apparatus, electronic device and medium that can introduce quantitative evaluation of process disturbances in the experimental stage, solve the problems of narrow process window and weak disturbance resistance of traditional methods, improve the robustness of the final process, reduce the impact of disturbances on product consistency, and meet the production requirements of high precision and high stability.

[0006] In a first aspect, embodiments of this application provide a robust process parameter optimization method, including: The pre-constructed multidimensional data tensor is preprocessed to obtain a perturbation feature template library for quantifying basic perturbation features. The multidimensional data tensor represents the data set of process parameters in multiple dimensions. The process parameters are labeled with attributes to obtain a process parameter list. Some process parameters in the process parameter list are labeled with sensitivity attributes, some with controllability attributes, and some with robustness attributes. The process parameter list is input into the trained bi-objective surrogate model, which outputs the probability distribution of average performance and the probability distribution of performance fluctuation. If, during the experiment, a real-time perturbation feature is detected to match the basic perturbation feature in the perturbation feature template library, the process parameters marked with control force attributes are called for experimental feedforward compensation, and the experimental dataset carrying the real-time perturbation feature is fed back to the Bayesian optimizer to update the bi-objective surrogate model. Based on the probability distribution of the average performance and the probability distribution of the performance fluctuation, a bi-objective Pareto front is plotted to determine the optimal process window, which represents the range of values ​​for the optimal process parameters.

[0007] In one optional embodiment, the preprocessing of the pre-constructed multidimensional data tensor to obtain a perturbation feature template library for quantizing basic perturbation features includes: Construct a multidimensional data tensor based on the acquired historical production data; The multidimensional data tensor is subjected to Tucker decomposition to obtain a benchmark reference tensor that characterizes the stable interaction relationship between process parameters in each dimension and a perturbation feature factor matrix that captures non-stationary perturbation signals in each dimension. Statistical analysis is performed on the disturbance feature factor matrix to obtain the basic disturbance features and the disturbance intensity and disturbance occurrence frequency corresponding to the basic disturbance features; Based on the basic disturbance characteristics and the disturbance intensity and frequency of occurrence corresponding to the basic disturbance characteristics, a disturbance characteristic template library is constructed.

[0008] In one optional embodiment, the dimensions corresponding to the multidimensional data tensor include a batch dimension, a time dimension, and a sensor dimension, wherein the sensor dimension includes multiple process parameter dimensions. The Tucker decomposition process is performed on the multidimensional data tensor to obtain a reference tensor characterizing the stable interaction relationships between process parameters in each dimension and a perturbation feature factor matrix capturing non-stationary perturbation signals in each dimension, including: The multidimensional data tensor is subjected to Tucker decomposition to obtain a benchmark reference tensor that characterizes the stable interaction relationship between process parameters in each dimension, as well as batch dimension perturbation factor matrix, time dimension perturbation factor matrix and sensor dimension perturbation factor matrix that capture non-stationary perturbation signals in each dimension.

[0009] In one optional embodiment, the disturbance intensity and disturbance occurrence frequency corresponding to the basic disturbance characteristics are determined through the following steps: Based on the amplitude of the eigenvector in the disturbance characteristic factor matrix and in combination with the physical range of the sensor, the disturbance intensity corresponding to the basic disturbance characteristic is calculated. The frequency of occurrence of basic disturbance features in historical production data is calculated by statistically analyzing the occurrence frequency and combining it with the total production batches; wherein the frequency of occurrence represents the ratio between the occurrence frequency of basic disturbance features and the total production batches; or, the duration of disturbances of basic disturbance features in historical production data is calculated by statistically analyzing the duration of disturbances and combining it with the total production duration; wherein the frequency of occurrence represents the ratio between the duration of disturbances and the total production duration.

[0010] In one optional embodiment, the step of performing attribute tagging processing on the process parameters to obtain a process parameter list includes: Calculate the disturbance sensitivity index of each process parameter, wherein the disturbance sensitivity index characterizes the degree of correlation between the change of process parameters under disturbance scenario and the fluctuation range of product quality indicators; Based on the disturbance sensitivity index and the correlation between process parameters and basic disturbance characteristics, the process parameters are labeled with attributes to obtain a process parameter list. Process parameters whose disturbance sensitivity index is greater than the disturbance index threshold and positively correlated with the basic disturbance characteristics are labeled with a sensitivity attribute; process parameters whose disturbance sensitivity index is greater than the disturbance index threshold and negatively correlated with the basic disturbance characteristics are labeled with a controllability attribute; and process parameters whose disturbance sensitivity index is not greater than the disturbance index threshold are labeled with a robustness attribute. The disturbance index threshold is predetermined based on the statistical distribution of the disturbance sensitivity indices of all process parameters in historical production data.

[0011] In one optional embodiment, the disturbance sensitivity index is used to characterize the correlation between changes in process parameters and fluctuations in product quality indicators under disturbance scenarios.

[0012] In an optional embodiment, when the correlation is linear, the disturbance sensitivity index is calculated using the following formula: DSI=|Cov( X, KPI) / Var(Q)|; Wherein, DSI represents the disturbance sensitivity index. X represents the changes in process parameters. KPI represents the fluctuation range of product quality indicators, Cov represents covariance, Var represents variance, and Q represents the disturbance intensity corresponding to the basic disturbance characteristics.

[0013] In one optional embodiment, the dual-objective proxy model includes an average performance proxy model and a performance fluctuation proxy model. The step of inputting the process parameter list into the trained bi-objective surrogate model and outputting the probability distribution of average performance and the probability distribution of performance fluctuation includes: The process parameter list is input into the average performance proxy model and the performance fluctuation proxy model respectively to obtain the probability distribution of average performance and the probability distribution of performance fluctuation.

[0014] The average performance proxy model and the performance fluctuation proxy model are iterated through the following steps: Step S301: Select initial experimental points in the process parameter space using Latin hypercube sampling to perform physical experiments, obtain an initial dataset, and train the average performance proxy model and the performance fluctuation proxy model using the initial dataset; wherein, the initial dataset includes a list of process parameters corresponding to the experimental points, real-time perturbation features, and corresponding average performance and performance fluctuation; Step S302: During the iteration process, the average performance proxy model and the performance fluctuation proxy model are trained using the current dataset, respectively. Step S303: In the entire process parameter space, use numerical optimization methods to find the process parameters corresponding to the next experimental point that maximize the desired supervolume improvement acquisition function. Step S304: Perform a physical experiment using the process parameters corresponding to the next experimental point. During the experiment, monitor the average performance and performance fluctuations under disturbance scenarios in real time, and obtain the process parameters corresponding to the next experimental point, as well as the monitored average performance and performance fluctuations, to update the current dataset. Step S305: Return to step S302 and repeat steps S303 to S304 until the termination condition is met, thus completing the iteration of the average performance proxy model and the performance fluctuation proxy model.

[0015] In an optional embodiment, if a real-time perturbation feature is detected to match a basic perturbation feature in the perturbation feature template library during the experiment, then process parameters marked with control force attributes are invoked for experimental feedforward compensation, and the experimental dataset carrying the real-time perturbation feature is fed back to the Bayesian optimizer to update the bi-objective surrogate model, including: The online tensor monitoring system continuously compares real-time data with a benchmark reference tensor. If the deviation between the real-time data and the benchmark tensor is found to be greater than a preset deviation threshold, and the real-time perturbation features in the real-time data match the basic perturbation features in the perturbation feature template library, then the process parameters marked with control force attributes are adjusted for experimental feedforward compensation, and the experimental dataset carrying the real-time perturbation features is fed back to the Bayesian optimizer to update the bi-objective surrogate model; wherein, the experimental dataset includes the process parameters and performance results corresponding to the experimental points, the identifiers corresponding to the real-time perturbation features, the perturbation intensity, and the time of the experiment.

[0016] In one optional embodiment, determining the optimal process window based on the bi-objective Pareto front includes: Based on the characteristics of the scenario during the experimental phase, the optimal compromise operation point is selected from the Pareto front. Around the optimal compromise operation point, an optimal process window in the process parameter space is determined; wherein, the average performance of any process parameter within the optimal process window is greater than a first preset threshold and the robustness of any process parameter is greater than a second preset threshold.

[0017] Secondly, embodiments of this application also provide a robust process parameter optimization apparatus, comprising: The preprocessing module is used to preprocess the pre-constructed multidimensional data tensor to obtain a perturbation feature template library for quantifying basic perturbation features. The multidimensional data tensor represents the data set of process parameters in multiple dimensions. The attribute tagging module is used to perform attribute tagging processing on the process parameters to obtain a process parameter list. Some process parameters in the process parameter list are tagged with sensitivity attributes, some process parameters are tagged with controllability attributes, and some process parameters are tagged with robustness attributes. The performance output module is used to input the list of process parameters into the trained bi-objective surrogate model and output the probability distribution of average performance and the probability distribution of performance fluctuation. If, during the experiment, a real-time perturbation feature is detected to match the basic perturbation feature in the perturbation feature template library, then the process parameters marked with control force attributes are called for experimental feedforward compensation, and the experimental dataset carrying the real-time perturbation feature is fed back to the Bayesian optimizer to update the bi-objective surrogate model. The window generation module is used to draw a bi-objective Pareto front based on the probability distribution of the average performance and the probability distribution of the performance fluctuation, so as to determine the optimal process window based on the bi-objective Pareto front, wherein the optimal process window represents the range of values ​​of the optimal process parameters.

[0018] Thirdly, embodiments of this application also provide an electronic device, including: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, the steps of the robust process parameter optimization method described above are performed.

[0019] Fourthly, embodiments of this application also provide a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of the robust process parameter optimization method described above.

[0020] This application provides a robust process parameter optimization method, apparatus, electronic device, and medium. It constructs a perturbation feature template library through multidimensional data tensor preprocessing to achieve quantitative characterization of perturbations. Process parameter attribute labeling provides targeted objectives for subsequent optimization. A dual-objective surrogate model outputs the probability distribution of average performance and the probability distribution of performance fluctuations, and updates the dual-objective surrogate model in conjunction with real-time perturbation feedback to ensure dynamic adaptability of the optimization. Finally, based on the Pareto front, the optimal process window is determined, effectively identifying a range of process parameters that combines high performance and high stability. This solves the problems of narrow process windows and weak perturbation resistance in traditional methods, significantly improving the robustness of the final process, reducing the impact of perturbations on product consistency, meeting the production requirements of high precision and high stability, and shortening the R&D optimization cycle. To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 One of the flowcharts for a robust process parameter optimization method provided in this application embodiment; Figure 2 A second flowchart illustrating a robust process parameter optimization method provided in this application embodiment; Figure 3 Flowchart 3 of a robust process parameter optimization method provided in this application embodiment; Figure 4This is a schematic diagram of a robust process parameter optimization device provided in an embodiment of this application; Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. Based on the embodiments of this application, every other embodiment obtained by those skilled in the art without inventive effort falls within the scope of protection of this application.

[0024] Please see Figure 1 , Figure 1 This is a flowchart illustrating a robust process parameter optimization method provided in an embodiment of this application. Figure 1 As shown in the embodiments of this application, the method includes: S101. Preprocess the pre-constructed multidimensional data tensor to obtain a perturbation feature template library for quantifying basic perturbation features. The multidimensional data tensor represents the data set of process parameters in multiple dimensions. S102. Perform attribute marking processing on the process parameters to obtain a process parameter list. Some process parameters in the process parameter list are marked with sensitivity attributes, some process parameters are marked with controllability attributes, and some process parameters are marked with robustness attributes. S103. Input the list of process parameters into the trained bi-objective surrogate model and output the probability distribution of average performance and the probability distribution of performance fluctuation. If, during the experiment, a real-time disturbance feature is detected to match the basic disturbance feature in the disturbance feature template library, then the process parameters marked with control force attributes are called for experimental feedforward compensation, and the experimental dataset carrying the real-time disturbance feature is fed back to the Bayesian optimizer to update the bi-objective surrogate model. S104. Based on the probability distribution of average performance and the probability distribution of performance fluctuation, plot the bi-objective Pareto front to determine the optimal process window. The optimal process window represents the range of values ​​for the optimal process parameters.

[0025] Steps S101 to S104 above construct a perturbation feature template library by preprocessing multidimensional data tensors to achieve quantitative characterization of perturbations. By labeling process parameter attributes, targeted targets are provided for subsequent optimization. The probability distribution of average performance and the probability distribution of performance fluctuation are output through a dual-objective surrogate model. The dual-objective surrogate model is updated in conjunction with real-time perturbation feedback to ensure the dynamic adaptability of optimization. Finally, the optimal process window is determined based on the Pareto front, effectively identifying the process parameter range that combines high performance and high stability. This solves the problems of narrow process window and weak anti-perturbation ability of traditional methods, significantly improves the robustness of the final process, reduces the impact of perturbations on product consistency, and shortens the R&D optimization cycle. In other words, this application embodiment, through a perturbation feature template library, transforms fuzzy and random perturbations in production into structured knowledge that can be reused in the experimental stage for the first time; through process parameter attribute labeling, it endows the Bayesian optimizer with goal-oriented decision-making capabilities; most importantly, by embedding real-time feedforward compensation into the iterative loop of Bayesian optimization, the optimization process itself can actively learn from each successful or failed perturbation confrontation, dynamically correct the surrogate model, and thus obtain a process window with both high performance and high robustness that traditional separate optimization methods cannot achieve.

[0026] The above steps are illustrated by specific embodiments below: In step S101, the pre-constructed multidimensional data tensor is preprocessed to obtain a perturbation feature template library for quantifying basic perturbation features. The multidimensional data tensor represents the data set of process parameters in multiple dimensions. Multidimensional data tensors represent the data set of process parameters across multiple dimensions. Specifically, a multidimensional data tensor is a structured data carrier formed by integrating multidimensional process data from historical production. It can fully preserve the interaction relationships and dynamic changes of process parameters across different dimensions, providing a data foundation for subsequent separation of stable process patterns and non-stationary disturbance signals. This multidimensional data tensor typically includes three core dimensions: batch, time, and sensor. The sensor dimension directly corresponds to specific process parameters and can be extended to higher dimensions, such as equipment, depending on the industry scenario. Its data structure must meet the input requirements of Tucker decomposition for multidimensional data to ensure accurate extraction of disturbance features.

[0027] For example, in semiconductor plasma etching processes, a multidimensional data tensor can be constructed as a three-dimensional tensor of wafer batch × etching seconds × sensor parameters. Sensor parameters may include RF power, chamber pressure, gas flow rate, etc. This multidimensional data tensor records the changes of various process parameters over time during multiple batches of production.

[0028] Here, preprocessing refers to data processing operations performed on multidimensional data tensors. Its purpose is to separate the benchmark reference tensor representing the stability of the process and the perturbation feature factor matrix capturing non-stationary disturbances from complex multidimensional data. Then, through statistical analysis, the perturbation features are quantified, ultimately forming a perturbation feature template library. The preprocessing process may include key sub-steps such as tensor decomposition and perturbation feature statistics. For example, the Tucker decomposition algorithm is used for tensor decomposition to ensure the practicality of the output perturbation features. Furthermore, such as Figure 2 As shown, step S101 includes: Step S1011: Construct a multidimensional data tensor based on the acquired historical production data.

[0029] Historical production data refers to raw data recorded during the production process by devices such as sensors and data acquisition systems, containing temporal changes in process parameters and product quality indicators. It provides a data source for constructing multidimensional data tensors. Historical production data needs to cover sufficient production cycles and disturbance scenarios to ensure that representative basic disturbance features can be extracted. For example, historical production data may include fields such as parameter name, acquisition time, batch number, parameter value, quality indicator (KPI), and equipment number. Preliminary screening can be performed to remove obviously invalid data, such as outliers from when sensors are offline.

[0030] Here, the construction of multidimensional data tensors can be combined with the process characteristics of specific industries to ensure that the data dimensions match the actual production scenario. For example, in the semiconductor plasma etching process, historical production data comes from the real-time acquisition of the chamber sensor, which can cover n1 wafer etching batches (batch dimension), n2 seconds of time-series data for each batch (time dimension), and five key process parameters (sensor dimension) such as RF power, chamber pressure, C4F8 flow rate, O2 flow rate, and etching temperature. Finally, a three-dimensional data tensor of batch dimension (n1) × time dimension (n2) × sensor dimension (5) is constructed. This three-dimensional data tensor fully records the numerical changes of each process parameter under different batches and different time points, providing comprehensive data support for subsequent perturbation feature extraction.

[0031] It should be noted that the preferred implementation method in this application is to construct a multidimensional data tensor using historical production data. For a completely new process lacking historical production data, a multidimensional data tensor can be constructed in one or more of the following ways: (1) generating an initial dataset through limited, high-fidelity process simulations based on physical models; (2) performing a small-scale preliminary experimental design (such as orthogonal experiments or Latin hypercube sampling) to obtain a basic dataset; (3) using the idea of ​​transfer learning to borrow historical data from similar processes or equipment as an initial reference. The initial tensor constructed in these ways can also serve as the starting point for subsequent Bayesian optimization iterative learning.

[0032] Step S1012: Perform Tucker decomposition on the multidimensional data tensor to obtain the benchmark reference tensor characterizing the stable interaction relationship between process parameters in each dimension and the perturbation feature factor matrix for capturing non-stationary perturbation signals in each dimension.

[0033] Here, Tucker decomposition is applied to decompose the multidimensional data tensor, which can separate complex multidimensional data into a reference tensor and multiple perturbation eigenfactor matrices. The reference tensor represents the stable interaction relationship between process parameters in each dimension, while the perturbation eigenfactor matrices capture non-stationary perturbation signals in each dimension.

[0034] It should be noted that the Tucker decomposition method used in this application embodiment is applied in the process design and experimental stage. That is, before large-scale production begins, Tucker decomposition is applied to historical production data to systematically extract, classify, and quantify all the basic disturbance characteristics that have occurred in the past from massive amounts of historical data. By applying the Tucker decomposition method, a disturbance feature template library can be obtained. As a reusable and structured disturbance knowledge base, the disturbance feature template library labels each typical disturbance as a basic disturbance feature and quantifies the disturbance intensity and occurrence probability of the basic disturbance feature for subsequent use.

[0035] Optionally, the dimensions corresponding to the multidimensional data tensor include batch dimension, time dimension and sensor dimension, and the sensor dimension includes multiple process parameter dimensions; specifically, step S1012 includes: performing Tucker decomposition on the multidimensional data tensor to obtain a benchmark reference tensor characterizing the stable interaction relationship between process parameters in each dimension, as well as batch dimension perturbation factor matrix, time dimension perturbation factor matrix and sensor dimension perturbation factor matrix for capturing non-stationary perturbation signals in each dimension.

[0036] In the above steps, each process parameter corresponds to an independent sensor monitoring channel. The number of sensor dimensions equals the number of process parameters, ensuring that the dynamic changes of each process parameter can be accurately captured. For example, in semiconductor etching processes, the sensor dimensions include five process parameter dimensions: RF power, chamber pressure, C4F8 flow rate, O2 flow rate, and etching temperature. Each dimension corresponds to a dedicated sensor, and the sensor dimension has a size of 5.

[0037] Furthermore, when performing Tucker decomposition on the multidimensional data tensor, the output perturbation feature factor matrix corresponds one-to-one with the three dimensions of the multidimensional data tensor, namely the batch dimension perturbation factor matrix, the time dimension perturbation factor matrix, and the sensor dimension perturbation factor matrix.

[0038] Firstly, the batch-dimensional perturbation factor matrix has the dimension of batch number × core tensor rank. It can capture slow perturbations across batches, such as equipment aging and raw material batch differences. Each row in the batch-dimensional perturbation factor matrix corresponds to a perturbation feature vector for a batch. By analyzing the trend of the perturbation feature vector, the type of perturbation can be identified. For example, in the batch-dimensional perturbation factor matrix of a semiconductor etching process, the feature vector values ​​of batches 1-10 gradually increase, which indicates that chamber wall deposition causes cross-batch parameter drift.

[0039] Secondly, the time-dimensional perturbation factor matrix has the dimension of time steps × core tensor rank. It is used to capture temporal perturbations within a single batch, such as instantaneous voltage fluctuations and plasma oscillations. Each row in the time-dimensional perturbation factor matrix corresponds to a perturbation feature vector at a given time point. By analyzing the high-frequency fluctuations of the perturbation feature vector, instantaneous perturbations can be identified. For example, in the time-dimensional perturbation factor matrix of the automotive battery spot welding process, the jump in the feature vector value at time steps 20-30 (corresponding to 100-150 milliseconds of welding) can reveal the instantaneous voltage fluctuation.

[0040] Third, the sensor-dimensional perturbation factor matrix has a dimension of the number of process parameters multiplied by the core tensor rank. It is used to capture the differences in the response of different process parameters to perturbations. Each row in the sensor-dimensional perturbation factor matrix corresponds to the perturbation response coefficient of a parameter. The larger the coefficient, the more sensitive the parameter is to perturbations. For example, in the sensor-dimensional factor matrix of chemical polymerization processes, the row corresponding to the catalyst flow rate has the largest coefficient, indicating that this parameter is most sensitive to catalyst deactivation perturbations.

[0041] Step S1013: Perform statistical analysis on the disturbance feature factor matrix to obtain the basic disturbance features and the disturbance intensity and disturbance frequency corresponding to the basic disturbance features.

[0042] Specifically, the basic perturbation features with physical meaning are extracted from the perturbation feature factor matrix, and the perturbation intensity and perturbation frequency of each basic perturbation feature are calculated.

[0043] Specifically, the disturbance intensity and frequency of occurrence corresponding to the basic disturbance characteristics are determined through the following steps: Step S1013a: Calculate the disturbance intensity corresponding to the basic disturbance feature based on the amplitude of the eigenvector in the disturbance feature factor matrix and the physical range of the sensor.

[0044] Here, the calculation of disturbance intensity needs to be based on the eigenvector amplitude of the disturbance characteristic factor matrix, and combined with the physical range of the corresponding sensor, to transform the dimensionless mathematical amplitude into an actual disturbance magnitude with engineering significance, ensuring that the intensity value can directly reflect the degree of influence of the disturbance on the process. Specifically, the eigenvector amplitude is extracted from the disturbance factor matrix, and the amplitude needs to be normalized before being correlated and converted with the sensor range.

[0045] Step S1013b: Count the occurrence frequency of basic disturbance features in historical production data and calculate the disturbance occurrence frequency in combination with the total production batches; wherein, the disturbance occurrence frequency represents the ratio between the occurrence frequency of basic disturbance features and the total production batches; or, count the disturbance duration of basic disturbance features in historical production data and calculate the disturbance occurrence frequency in combination with the total production duration; wherein, the disturbance occurrence frequency represents the ratio between the disturbance duration and the total production duration.

[0046] Here, there are two statistical methods for determining the frequency of disturbance occurrence. The appropriate method can be selected based on the process type, such as discrete batch production or continuous production: Firstly, batch-based frequency calculation: This method is suitable for discrete batch production, such as semiconductor etching and battery spot welding. The frequency of disturbance occurrence is the ratio of the number of occurrences of the basic disturbance feature to the total number of production batches. For example, if the number of occurrences of plasma instability disturbances in the semiconductor etching process is 12, and the total number of production batches is 30, then the frequency of disturbance occurrence = (12 / 30) × 100% = 40%. Secondly, frequency calculation based on duration: This method is applicable to continuous production or long-cycle batch production, such as bio-fermentation and chemical polymerization. The frequency of disturbance occurrence is the ratio between the duration of the disturbance and the total production time. For example, in a bio-fermentation process, if a disturbance occurs due to uneven substrate concentration, and the total production time is 20 × 120 = 2400 hours, with a disturbance duration of 120 hours, the frequency of disturbance occurrence is (120 / 2400) × 100% = 5%.

[0047] Step S1014: Construct a disturbance feature template library based on the basic disturbance features and the disturbance intensity and disturbance occurrence frequency corresponding to the basic disturbance features.

[0048] The disturbance feature template library refers to a structured database that stores basic disturbance features and their quantification parameters (such as disturbance intensity and frequency of occurrence). It provides a reference standard for real-time disturbance identification during experiments and a disturbance data source for subsequent sensitivity analysis of process parameters. The disturbance feature template library can contain key information such as the unique identifier, type description, disturbance intensity, frequency of occurrence, and associated sensor dimension of the basic disturbance feature. The data format facilitates online monitoring system access and matching, ensuring the real-time performance and accuracy of disturbance identification.

[0049] It should be added that the disturbance feature template library in this application mainly serves the following functions: First, the disturbance feature template library is the direct basis for labeling process parameter attributes. The DSI index is calculated using this library to classify parameter attributes into three categories: sensitivity attributes, controllability attributes, and robustness attributes. Second, the disturbance feature template library is a reference standard for real-time feedforward compensation. During the experiment, it is by matching real-time disturbances with the disturbance feature template library that the system can identify the current disturbance and predictively call the corresponding process parameters carrying controllability attributes for cancellation. Third, the disturbance feature template library is a key information input for Bayesian optimization closed-loop learning. The data fed back to the Bayesian optimizer contains the identifiers of real-time disturbance features, enabling the bi-objective surrogate model to learn the process response under specific disturbances.

[0050] Optionally, the perturbation feature template library can be stored in a table or database format. Specifically, the perturbation feature template library can be stored in an SQL database, supporting real-time querying and feature matching by the online monitoring system. When the feature vector of the monitored real-time data has a high similarity to the basic perturbation features in the template library, it can be determined that the real-time data has plasma instability perturbations.

[0051] return Figure 1 In step S102, the process parameters are marked with attributes to obtain a process parameter list. Some process parameters in the process parameter list are marked with sensitivity attributes, some process parameters are marked with controllability attributes, and some process parameters are marked with robustness attributes.

[0052] Among them, attribute labeling refers to the operation of classifying each process parameter based on the correlation characteristics between process parameters and basic disturbance characteristics. Its purpose is to clarify the use of each process parameter in disturbance rejection optimization, such as sensitive parameters needing strict control, control parameters being used for compensation, and robust parameters not requiring special attention, so as to provide targeted guidance for subsequent adaptive experimental design and real-time disturbance compensation.

[0053] Specifically, step S102 includes: Step S1021: Calculate the disturbance sensitivity index of each process parameter. The disturbance sensitivity index characterizes the degree of correlation between the changes in process parameters and the fluctuation range of product quality indicators under disturbance scenarios.

[0054] Step S1022: Based on the disturbance sensitivity index and the correlation between process parameters and basic disturbance characteristics, perform attribute labeling on the process parameters to obtain a process parameter list; among them, process parameters whose disturbance sensitivity index is greater than the disturbance index threshold and is positively correlated with the basic disturbance characteristics are labeled with sensitivity attributes, process parameters whose disturbance sensitivity index is greater than the disturbance index threshold and is negatively correlated with the basic disturbance characteristics are labeled with controllability attributes, and process parameters whose disturbance sensitivity index is not greater than the disturbance index threshold are labeled with robustness attributes; wherein, the disturbance index threshold is predetermined based on the statistical distribution of the disturbance sensitivity index of all process parameters in historical production data.

[0055] In steps S1021 to S1022 above, the Disturbance Sensitivity Index (DSI) of each process parameter is first calculated, and then classified according to the correlation direction between the process parameter and the basic disturbance feature: when the DSI is greater than the disturbance index threshold and is positively correlated with the basic disturbance feature, the process parameter is labeled with a sensitivity attribute; when the DSI is greater than the disturbance index threshold and is negatively correlated with the basic disturbance feature, the process parameter is labeled with a controllability attribute; when the DSI is not greater than the disturbance index threshold, the process parameter is labeled with a robustness attribute.

[0056] The disturbance index threshold is predetermined based on the statistical distribution of the disturbance sensitivity indices of all process parameters in historical production data. Specifically, the steps for determining the disturbance index threshold may include: calculating the disturbance sensitivity index of all process parameters for one or more basic disturbance characteristics, and setting the threshold according to the statistical distribution of these index values ​​(such as the mean, median, or preset percentile). For example, the median or 75th percentile of all index values ​​can be set as the disturbance index threshold.

[0057] Taking the chemical polymerization reactor process as an example, the calculated DSI of catalyst flow rate is 0.8, which is greater than the disturbance index threshold and positively correlated with catalyst deactivation disturbance, indicating that catalyst flow rate is a sensitivity attribute; the DSI of reactor temperature is 0.7, which is greater than the disturbance index threshold and negatively correlated with the disturbance, indicating that reactor temperature is a control force attribute; and the DSI of stirring speed is 0.2, indicating that stirring speed is a robustness attribute.

[0058] The process parameter list is a structured document that records the names, attribute labels, and associated perturbation features of process parameters. It clearly presents the role of each process parameter, providing intuitive guidance for parameter input, experimental point selection, and real-time compensation operations in the subsequent bi-objective surrogate model. The process parameter list can include basic information about the process parameters, such as name, unit, value range, attribute label results, associated perturbation feature ID, and DSI value.

[0059] For example, the process parameter list exists in the form of an Excel spreadsheet or database table, containing fields such as process parameter name, parameter unit, attribute tag, DSI value, and related perturbation feature ID. For instance, in a semiconductor etching process, the process parameter list could record: Parameter name: RF power, unit: W, attribute: sensitivity attribute, DSI: 0.9, related perturbation ID: 002 (plasma oscillation); Parameter name: chamber pressure, unit: mTorr, attribute: control force attribute, DSI: 0.7, related perturbation ID: 002, providing clear guidance for subsequent model input and parameter adjustment.

[0060] In one optional embodiment, the disturbance sensitivity index is used to characterize the correlation between changes in process parameters and fluctuations in product quality indicators under disturbance scenarios.

[0061] For example, when the correlation is linear, the perturbation sensitivity index is calculated using the following formula: DSI=|Cov( X, KPI) / Var(Q)|; Wherein, DSI represents the disturbance sensitivity index. X represents the changes in process parameters. KPI represents the fluctuation range of product quality indicators, Cov represents covariance, Var represents variance, and Q represents the disturbance intensity corresponding to the basic disturbance characteristics.

[0062] The method of normalizing by using the variance Var(Q) of the disturbance strength corresponding to the basic disturbance characteristics aims to eliminate the influence of the difference in the fluctuation amplitude of different disturbance sources, so that the DSI can more purely reflect the sensitivity of process parameters to disturbance response.

[0063] It should be understood that the above DSI formula is a specific embodiment of this application, particularly suitable for scenarios where there is a strong linear relationship between process parameters and quality indicators. In other embodiments, to more accurately capture nonlinear relationships, the covariance Cov( X, KPIs can be replaced with other correlation metrics, such as mutual information, maximum information coefficient (MIC), or correlation metrics based on kernel functions (such as Gaussian kernels). These nonlinear metrics can more comprehensively assess the complex dependencies between parameters and quality fluctuations.

[0064] Specifically, X represents the change in process parameters, which refers to the actual change in process parameters under the influence of basic disturbance characteristics. It can be an absolute value or a relative change, and the unit is consistent with the process parameter. KPIs represent the fluctuation range of product quality indicators, indicating X causes changes in key product quality indicators, such as etching rate and protein expression levels, with units consistent with KPIs; Cov( X, KPIs represent X and The covariance of KPIs reflects the degree of linear correlation between the two; a positive covariance indicates a positive correlation, and a negative covariance indicates a negative correlation. Var(Q) represents the variance of the perturbation intensity Q corresponding to the basic perturbation feature, reflecting the dispersion of the perturbation intensity. The absolute value sign can eliminate the positive and negative effects of covariance, retaining only the magnitude of the sensitivity, and ensuring that DSI is non-negative.

[0065] Specifically, the Disturbance Sensitivity Index (DSI) is used as the quantitative basis to ensure that the attributes of each parameter have clear justification. For example, taking five process parameters of semiconductor etching: RF power, chamber pressure, C4F8 flow rate, O2 flow rate, and etching temperature as an example, firstly, based on the disturbance feature template library obtained in step S101, the DSI value of each process parameter is calculated: for plasma instability disturbances, the change data of each parameter when the disturbance occurs are collected, such as RF power change ±5W, chamber pressure change ±1mTorr, and the corresponding etching uniformity fluctuation data, such as ±2%, and the formula DSI=|Cov( X, The calculation of KPI / Var(Q) yielded DSI values ​​of 0.9 for RF power, 0.7 for chamber pressure, 0.3 for C4F8 flow rate, 0.5 for O2 flow rate, and 0.2 for etching temperature. The correlation between each process parameter and disturbance characteristics was then analyzed: RF power was positively correlated with plasma instability; as power fluctuations increased, the disturbance intensity increased. Chamber pressure was negatively correlated with the disturbance; as pressure increased appropriately, the disturbance intensity decreased. The correlation of other parameters was not significant. Finally, a disturbance index threshold of 0.6 was set, and attributes were assigned to the process parameters according to defined rules: RF power (DSI > 0.6 and positively correlated) was labeled with a sensitivity attribute; chamber pressure (DSI > 0.6 and negatively correlated) was labeled with a controllability attribute; and C4F8 flow rate, O2 flow rate, and etching temperature (DSI ≤ 0.6) were labeled with robustness attributes, forming a process parameter list.

[0066] return Figure 1In step S103, the list of process parameters is input into the trained bi-objective surrogate model, and the probability distribution of average performance and the probability distribution of performance fluctuation are output. If, during the experiment, a real-time disturbance feature is detected to match the basic disturbance feature in the disturbance feature template library, the process parameters marked with control force attributes are called for experimental feedforward compensation, and the experimental dataset carrying the real-time disturbance feature is fed back to the Bayesian optimizer to update the bi-objective surrogate model.

[0067] The dual-objective surrogate model refers to a combined model comprising an average performance surrogate model and a performance fluctuation surrogate model. It can predict the average performance and performance fluctuation of an experiment based on a list of process parameters, and output the prediction results in the form of a probability distribution, providing data support for subsequent Pareto front plotting. This dual-objective surrogate model is constructed using the Gaussian process (GP) algorithm, requiring separate training of sub-models for average performance and performance fluctuation to ensure the prediction accuracy of both objectives. It also supports dynamic updates based on new experimental data and possesses self-learning capabilities.

[0068] Optionally, the dual-objective proxy model includes an average performance proxy model and a performance fluctuation proxy model, and step S103 specifically includes: Step S1031: Input the process parameter list into the average performance proxy model and the performance fluctuation proxy model respectively to obtain the probability distribution of average performance and the probability distribution of performance fluctuation.

[0069] Here, the average performance surrogate model (GP_perf) and the performance fluctuation surrogate model (GP_robust) are two independent Gaussian process sub-models. They share the process parameter inputs but have different output targets. They fit the probability distributions of average performance and performance fluctuation respectively to ensure that the prediction accuracy of the two optimization targets is independent of each other and avoid the coupling error of a single model.

[0070] The average performance surrogate model (GP_perf) takes a list of process parameters as input and outputs a probability distribution of average performance. The mean of this probability distribution is the expected value of the average performance predicted by the model, while the variance represents the uncertainty of the prediction; a smaller variance indicates a more reliable prediction. This model focuses on fitting the positive correlation between process parameters and average performance, and the kernel function typically uses a squared exponential kernel (RBF).

[0071] The performance fluctuation surrogate model (GP_robust) takes a list of process parameters as input and outputs a probability distribution of performance fluctuations. The mean of the probability distribution represents the expected value of the fluctuation, and the variance represents the uncertainty in the fluctuation prediction. This model focuses on fitting the correlation between process parameters, disturbance intensity, and performance fluctuations. A Matern kernel can be used to improve the fitting accuracy of the disturbance response.

[0072] Furthermore, such as Figure 3 As shown, step S103 iterates the average performance proxy model and the performance fluctuation proxy model through the following steps: Step S301: Select initial experimental points in the process parameter space using Latin hypercube sampling to perform physical experiments, obtain the initial dataset, and train the average performance proxy model and the performance fluctuation proxy model using the initial dataset; wherein, the initial dataset includes the process parameter list corresponding to the experimental points, real-time perturbation features, and the corresponding average performance and performance fluctuation.

[0073] Latin hypercube sampling (LHS) is a space-filling sampling method used to uniformly select a small number of initial experimental points in a high-dimensional process parameter space. This ensures that the sampling points cover the entire range of parameter values, avoiding the problems of point concentration or omission of key regions caused by traditional sampling (such as random sampling). The number of initial experimental points is usually 1-2 times the parameter dimension; for example, 5-10 experimental points are selected for 5 parameters. This ensures the representativeness of the sampling while reducing the physical experimental cost.

[0074] Step S302: During the iteration process, using the current dataset, train the average performance proxy model and the performance fluctuation proxy model respectively.

[0075] Here, the current dataset is an experimental dataset that is continuously expanded during the iteration process, i.e., Dn = Dn-1 ∪ new experimental data (where n is the iteration number). It is used to provide more comprehensive parameter-perturbation-performance correlation data for model training, ensuring that the model continues to optimize with the number of iterations. The current dataset must contain a list of process parameters, real-time perturbation characteristics, average performance, and performance fluctuations for all historical experimental points. The data format must be consistent with the initial dataset for easy model access.

[0076] Step S303: In the entire process parameter space, use numerical optimization methods to find the process parameters corresponding to the next experimental point that maximize the desired supervolume improvement acquisition function.

[0077] Among them, the Expected Hypervolume Improvement Acquisition Function (EHVI) is the core criterion for evaluating the experimental value of candidate experimental sites. The larger the EHVI value, the higher the experimental value of that site. The EHVI needs to be calculated based on the performance probability distribution output by the bi-objective surrogate model, and the integral is solved numerically using the Monte Carlo method (there is no analytical solution).

[0078] Step S304: Perform a physical experiment using the process parameters corresponding to the next experimental point. During the experiment, monitor the average performance and performance fluctuations under disturbance scenarios in real time, and obtain the process parameters corresponding to the next experimental point, as well as the monitored average performance and performance fluctuations, to update the current dataset.

[0079] In this context, performance fluctuations under disturbance scenarios refer to the recorded fluctuation range of product quality indicators when known basic disturbances are actively introduced or naturally occurring disturbances are monitored during the experiment. Its core function is to provide realistic disturbance-fluctuation correlation data for the performance fluctuation surrogate model (GP_robust), ensuring that the model can accurately fit the disturbance resistance stability. This fluctuation needs to be monitored in real time using high-precision sensors, and the data sampling frequency must match the dynamic characteristics of the disturbance.

[0080] Step S305: Return to step S302 and repeat steps S303 to S304 until the termination condition is met, thus completing the iteration of the average performance proxy model and the performance fluctuation proxy model.

[0081] The termination condition is a preset criterion for determining whether the iteration process should stop. It ensures that the model accuracy meets the optimization requirements while avoiding the cost waste caused by excessive physical experiments. For example, common termination conditions include reaching a preset number of experiments, the maximum EHVI value falling below a threshold, or the model prediction error falling below a threshold. Single conditions or combinations of conditions can be selected according to actual needs.

[0082] In steps S301 to S305 above, the iterative process of the average performance proxy model and the performance fluctuation proxy model is defined. This iterative process is a closed-loop adaptive optimization, forming a loop from initial sampling to model update until the termination condition is met, ensuring that the model continuously improves its prediction accuracy as experimental data accumulates.

[0083] Optionally, step S103 further includes: Step S103a: Control the online tensor monitoring system to continuously compare real-time data with the benchmark reference tensor.

[0084] Here, the online tensor monitoring system is a hardware-software integrated system that collects process data in real time, compares it with the benchmark reference tensor, and identifies disturbances. It is used to capture the dynamic changes of process data in real time during the experimental execution process and compare it with the benchmark reference tensor (characterizing stable process laws) obtained in step S101 to determine whether there is a disturbance.

[0085] For example, this online tensor monitoring system may include a data acquisition module, a data processing module, and a comparison analysis module to ensure the real-time performance (delay ≤ 1 second) and accuracy of the monitoring. The data acquisition module connects to the sensor, the data processing module converts the real-time data into tensor form, and the comparison analysis module calculates the deviation between the real-time data and the reference tensor.

[0086] For example, the online tensor monitoring system for semiconductor etching processes works as follows: The data acquisition module connects to sensors such as RF power and pressure in the chamber via an industrial Ethernet network, acquiring real-time data at a frequency of 1 second / time; the data processing module assembles the real-time data into two-dimensional tensor segments according to the "time step-sensor" dimension; the comparison and analysis module calculates the Euclidean distance (deviation value) between this segment and the corresponding segment of the reference tensor. If the deviation value is greater than a preset deviation threshold, where the preset deviation threshold can be set based on the variance value of historical stable data, it is determined that the real-time data deviates significantly from the reference tensor, and there may be a disturbance.

[0087] Step S103b: If the deviation between the real-time data and the benchmark tensor is found to be greater than the preset deviation threshold, and the real-time disturbance features in the real-time data match the basic disturbance features in the disturbance feature template library, then the process parameters marked with control force attributes are adjusted to perform experimental feedforward compensation, and the experimental dataset carrying the real-time disturbance features is fed back to the Bayesian optimizer to update the bi-objective surrogate model.

[0088] The Bayesian optimizer can be driven by the acquisition function to explore the unknown space, or by identified perturbation events occurring in the real world to perform targeted learning and model correction. Thus, whenever a perturbation occurs and is successfully compensated, the bi-objective surrogate model learns from this perturbation event that, under the X parameter combination, encountering a Y-type perturbation, it can take Z compensation measures to obtain the performance fluctuation result W.

[0089] In this way, the Bayesian optimizer in this embodiment can learn, adapt, and find a robust process window in real time amidst disturbances. By deeply integrating real-time disturbance identification and feedforward control—concepts originally belonging to the field of process control—with Bayesian optimization, which belongs to the field of experimental design, an adaptive optimization framework capable of actively learning disturbance resistance strategies during the experimental phase is constructed.

[0090] Here, if the deviation between the real-time data and the reference tensor is found to be greater than a preset deviation threshold, it is considered that there is a disturbance feature in the real-time data. Furthermore, the cosine similarity between the real-time disturbance feature in the real-time data and the basic disturbance feature in the disturbance feature template library can be used to determine whether the real-time disturbance feature in the real-time data matches the basic disturbance feature in the disturbance feature template library. This confirms whether the real-time disturbance feature in the current real-time data that deviates from the reference tensor corresponds to the known basic disturbance feature, ensuring the pertinence of the feedforward compensation.

[0091] In an optional implementation, the disturbance matching and compensation process of the semiconductor etching process is as follows: When the online monitoring system calculates that the deviation between the real-time data and the reference tensor is greater than a preset deviation threshold, the real-time disturbance feature vector of the real-time data (e.g., [0.8, 0.2, 0.5, 0.3, 0.1]) is extracted; the cosine similarity between the real-time disturbance feature vector and the 001 "plasma instability" feature vector ([0.75, 0.25, 0.48, 0.32, 0.12]) in the disturbance feature template library is calculated to be 92% (≥90%), and the matching is determined to be successful; the system immediately calls the control force attribute parameter "chamber pressure" marked in step S102, and according to the "disturbance intensity-compensation amplitude" correlation model, the current disturbance intensity is 0.6, and the adjustment amplitude is calculated to be 0.3 mTorr, adjusting the chamber pressure from 11.5 mTorr to 11.8 mTorr; after compensation, the etching uniformity is continuously monitored, and the fluctuation decreases from 3.1% to 2.2%, indicating successful compensation.

[0092] The experimental dataset includes the process parameters and performance results corresponding to the experimental points, the identifiers corresponding to the real-time disturbance features, the disturbance intensity, and the time when the experiment occurred.

[0093] In other words, the inputs of the Bayesian optimizer in this embodiment include the process parameters and performance results corresponding to the experimental points, the identifiers corresponding to the real-time perturbation features, the perturbation intensity, and the time of the experiment.

[0094] Specifically, the process parameters corresponding to the experimental points refer to the specific parameter combinations used during the experiment, providing input parameters for the dual-objective surrogate model and ensuring that the model can correlate parameters with performance. The process parameter names, values, and units need to be recorded here. The identifier corresponding to the real-time disturbance feature refers to the unique ID of the basic disturbance feature matching the real-time disturbance, such as 001 or 002, providing disturbance type information for the dual-objective surrogate model and ensuring that the model can distinguish the impact of different disturbances on performance. The disturbance intensity refers to the quantified intensity value of the real-time disturbance, obtained based on the calculation method in step S101, providing disturbance degree information for the dual-objective surrogate model and ensuring that the model can fit the correlation between disturbance intensity and performance fluctuations. The intensity value and unit need to be recorded. The experiment occurrence time refers to the specific time the experiment was executed, accurate to the second or minute, providing time-series information for the dual-objective surrogate model and ensuring that the model can capture the changing patterns of disturbances over time. Year-month-day, hour:minute:second needs to be recorded, such as "Experiment occurrence time: 2024-05-20, 15:30:45".

[0095] For example, the experimental dataset can include process parameters corresponding to the experimental points, such as RF power: 400W, and identifiers corresponding to real-time perturbation features, such as real-time perturbation feature ID: 002, perturbation intensity: 0.6, and experimental occurrence time: 2025-09-20, 14:30. Furthermore, the experimental dataset can also include information such as: experimental point ID, average etching rate: 505nm / min, etching rate fluctuation: 6nm, etc. After being fed back to the Bayesian optimizer, the Bayesian optimizer can adjust the kernel function parameters of the GP model accordingly, improving the accuracy of subsequent predictions. return Figure 1 In step S104, a bi-objective Pareto front is plotted based on the probability distribution of average performance and the probability distribution of performance fluctuation, so as to determine the optimal process window based on the bi-objective Pareto front. The optimal process window represents the range of values ​​of the optimal process parameters.

[0096] The bi-objective Pareto front is a curve formed by the optimal experimental points in the bi-objective optimization space of average performance versus performance fluctuation, representing the points where both objectives cannot be improved simultaneously. It visually represents the trade-off between the two optimization objectives, providing a visual basis for selecting the optimal compromise point. The plotting of this bi-objective Pareto front requires a large number of experimental point performance distributions output by the bi-objective surrogate model. A non-dominated sorting algorithm is used to select the Pareto optimal solution, ensuring the completeness and accuracy of the bi-objective Pareto front curve.

[0097] The optimal process window is the optimal compromise point around the Pareto front. It is a range of parameter values ​​determined in the process parameter space that satisfies the condition that the average performance is ≥ the first preset threshold and the performance fluctuation is ≤ the second preset threshold. It provides a parameter range that can be directly used for large-scale production and has both high performance and high stability. It can overcome the vulnerability of single-point optima in traditional methods and ensure the fault tolerance of the production process to disturbances.

[0098] For example, the optimal process window can be determined by combining the actual needs of the production scenario, selecting the optimal compromise point through a multi-criteria decision-making method, and then determining the window boundary based on surrogate model prediction. In an optional implementation, the determination of the optimal process window can follow a process of compromise point selection, window boundary calculation, and verification to ensure the practicality and reliability of the window. The model prediction performance of any parameter combination within the optimal process window meets the threshold requirements and can be issued to the production line as a standard operating procedure (SOP).

[0099] In one optional embodiment, step S104 specifically includes: Step S1041: Based on the scenario characteristics of the experimental stage, select the optimal compromise operation point from the Pareto front.

[0100] In the experimental phase, scenario characteristics refer to the weighting of average performance and performance fluctuations based on production needs, providing a basis for selecting compromise points. For example, different scenarios have different weights; military products prioritize robustness and have a high weight for performance fluctuations, while consumer electronics prioritize efficiency and have a high weight for average performance. Scenario characteristics need to be transformed into weight coefficients using multi-criteria decision-making methods, such as linear weighting and analytic hierarchy process (AHP), to ensure that the selection of compromise points is objective and reasonable.

[0101] Step S1042: Determine the optimal process window in the process parameter space around the optimal compromise operation point; wherein, the average performance of any process parameter within the optimal process window is greater than a first preset threshold and the robustness of any process parameter is greater than a second preset threshold.

[0102] The first preset threshold is the minimum acceptable standard for average performance, and the second preset threshold is the minimum acceptable standard for robustness. Both thresholds need to be set based on industry standards, product requirements, or cutting-edge optimal solution performance to ensure that the parameter combination within the window can simultaneously meet high performance and high stability.

[0103] The method provided in this application has the following technical effects: First, by directly optimizing the reduction of sensitivity to disturbances, it finds flat process regions that are insensitive to disturbances, thereby improving product consistency (Cpk) from the traditional 1.25 to ≥1.67. Second, by utilizing process parameters marked with controllability attributes, it enables feedforward active cancellation in the early stages of disturbances, rather than delayed feedback compensation, significantly reducing disturbance recovery time from the traditional 3-5 minutes to <30 seconds, thus improving disturbance recovery efficiency. Third, by leveraging Bayesian-optimized adaptive sampling, it greatly reduces the number of physical experiments required, and closed-loop correction avoids invalid experiments due to disturbances, shortening the R&D / optimization cycle from the traditional 4-6 weeks to 1-2 weeks, significantly reducing the R&D / optimization cycle. Fourth, through the closed-loop correction mechanism, the model can continuously learn from real-world disturbances, dynamically adapting to equipment aging and environmental changes. The model lifecycle changes from traditional static and easily failed due to disturbances to continuously adaptive and never outdated, improving the applicability of the dual-objective proxy model.

[0104] Based on the same inventive concept, this application also provides a robust process parameter optimization device corresponding to the robust process parameter optimization method. Since the principle of the device in this application is similar to the process parameter optimization method in the experimental stage of this application, the implementation of the device can refer to the implementation of the method, and the repeated parts will not be described again.

[0105] Please see Figure 4 , Figure 4 This is a schematic diagram of a robust process parameter optimization device provided in an embodiment of this application. Figure 4As shown, the device 400 includes: Preprocessing module 401 is used to preprocess the pre-constructed multidimensional data tensor to obtain a perturbation feature template library for quantifying basic perturbation features. The multidimensional data tensor represents a data set of process parameters in multiple dimensions. The attribute marking module 402 is used to perform attribute marking processing on the process parameters to obtain a process parameter list. Some process parameters in the process parameter list are marked with sensitivity attributes, some process parameters are marked with controllability attributes, and some process parameters are marked with robustness attributes. The performance output module 403 is used to input the process parameter list into the trained bi-objective surrogate model and output the probability distribution of average performance and the probability distribution of performance fluctuation. If, during the experiment, a real-time perturbation feature is detected to match the basic perturbation feature in the perturbation feature template library, the process parameters marked with control force attributes are called for experimental feedforward compensation, and the experimental dataset carrying the real-time perturbation feature is fed back to the Bayesian optimizer to update the bi-objective surrogate model. The window generation module 404 is used to draw a bi-objective Pareto front based on the probability distribution of the average performance and the probability distribution of the performance fluctuation, so as to determine the optimal process window based on the bi-objective Pareto front, wherein the optimal process window represents the range of values ​​of the optimal process parameters.

[0106] In one optional embodiment, the preprocessing module 401 is specifically used for: Construct a multidimensional data tensor based on the acquired historical production data; The multidimensional data tensor is subjected to Tucker decomposition to obtain a benchmark reference tensor that characterizes the stable interaction relationship between process parameters in each dimension and a perturbation feature factor matrix that captures non-stationary perturbation signals in each dimension. Statistical analysis is performed on the disturbance feature factor matrix to obtain the basic disturbance features and the disturbance intensity and disturbance occurrence frequency corresponding to the basic disturbance features; Based on the basic disturbance characteristics and the disturbance intensity and frequency of occurrence corresponding to the basic disturbance characteristics, a disturbance characteristic template library is constructed.

[0107] In one optional embodiment, the dimensions corresponding to the multidimensional data tensor include a batch dimension, a time dimension, and a sensor dimension, wherein the sensor dimension includes multiple process parameter dimensions; the preprocessing module 401 is further configured to: The multidimensional data tensor is subjected to Tucker decomposition to obtain a benchmark reference tensor that characterizes the stable interaction relationship between process parameters in each dimension, as well as batch dimension perturbation factor matrix, time dimension perturbation factor matrix and sensor dimension perturbation factor matrix that capture non-stationary perturbation signals in each dimension.

[0108] In an optional embodiment, the preprocessing module 401 is further configured to determine the disturbance intensity and disturbance occurrence frequency corresponding to the basic disturbance characteristics through the following steps: Based on the amplitude of the eigenvector in the disturbance characteristic factor matrix and in combination with the physical range of the sensor, the disturbance intensity corresponding to the basic disturbance characteristic is calculated. The frequency of occurrence of basic disturbance features in historical production data is calculated by statistically analyzing the occurrence frequency and combining it with the total production batches; wherein the frequency of occurrence represents the ratio between the occurrence frequency of basic disturbance features and the total production batches; or, the duration of disturbances of basic disturbance features in historical production data is calculated by statistically analyzing the duration of disturbances and combining it with the total production duration; wherein the frequency of occurrence represents the ratio between the duration of disturbances and the total production duration.

[0109] In one optional embodiment, the attribute tagging module 402 is specifically used for: Calculate the disturbance sensitivity index of each process parameter, wherein the disturbance sensitivity index characterizes the degree of correlation between the change of process parameters under disturbance scenario and the fluctuation range of product quality indicators; Based on the disturbance sensitivity index and the correlation between process parameters and basic disturbance characteristics, the process parameters are labeled with attributes to obtain a process parameter list. Process parameters whose disturbance sensitivity index is greater than the disturbance index threshold and positively correlated with the basic disturbance characteristics are labeled with a sensitivity attribute; process parameters whose disturbance sensitivity index is greater than the disturbance index threshold and negatively correlated with the basic disturbance characteristics are labeled with a controllability attribute; and process parameters whose disturbance sensitivity index is not greater than the disturbance index threshold are labeled with a robustness attribute. The disturbance index threshold is predetermined based on the statistical distribution of the disturbance sensitivity indices of all process parameters in historical production data.

[0110] In one optional embodiment, the disturbance sensitivity index is used to characterize the correlation between changes in process parameters and fluctuations in product quality indicators under disturbance scenarios.

[0111] In an optional embodiment, when the correlation is linear, the disturbance sensitivity index is calculated using the following formula: DSI=|Cov( X, KPI) / Var(Q)|; Wherein, DSI represents the disturbance sensitivity index. X represents the changes in process parameters. KPI represents the fluctuation range of product quality indicators, Cov represents covariance, Var represents variance, and Q represents the disturbance intensity corresponding to the basic disturbance characteristics.

[0112] In one optional embodiment, the dual-objective proxy model includes an average performance proxy model and a performance fluctuation proxy model, and the performance output module 403 is specifically used for: The process parameter list is input into the average performance proxy model and the performance fluctuation proxy model respectively to obtain the probability distribution of average performance and the probability distribution of performance fluctuation. Specifically, the performance output module 403 is further used to iterate the average performance proxy model and the performance fluctuation proxy model through the following steps: Step S301: Select initial experimental points in the process parameter space using Latin hypercube sampling to perform physical experiments, obtain an initial dataset, and train the average performance proxy model and the performance fluctuation proxy model using the initial dataset; wherein, the initial dataset includes a list of process parameters corresponding to the experimental points, real-time perturbation features, and corresponding average performance and performance fluctuation; Step S302: During the iteration process, the average performance proxy model and the performance fluctuation proxy model are trained using the current dataset, respectively. Step S303: In the entire process parameter space, use numerical optimization methods to find the process parameters corresponding to the next experimental point that maximize the desired supervolume improvement acquisition function. Step S304: Perform a physical experiment using the process parameters corresponding to the next experimental point. During the experiment, monitor the average performance and performance fluctuations under disturbance scenarios in real time, and obtain the process parameters corresponding to the next experimental point, as well as the monitored average performance and performance fluctuations, to update the current dataset. Step S305: Return to step S302 and repeat steps S303 to S304 until the termination condition is met, thus completing the iteration of the average performance proxy model and the performance fluctuation proxy model.

[0113] In one optional embodiment, the performance output module 403 is further configured to: The online tensor monitoring system continuously compares real-time data with a benchmark reference tensor. If the deviation between the real-time data and the benchmark tensor is found to be greater than a preset deviation threshold, and the real-time perturbation features in the real-time data match the basic perturbation features in the perturbation feature template library, then the process parameters marked with control force attributes are adjusted for experimental feedforward compensation, and the experimental dataset carrying the real-time perturbation features is fed back to the Bayesian optimizer to update the bi-objective surrogate model; wherein, the experimental dataset includes the process parameters and performance results corresponding to the experimental points, the identifiers corresponding to the real-time perturbation features, the perturbation intensity, and the time of the experiment.

[0114] In one optional embodiment, the window generation module 404 is specifically used for: Based on the characteristics of the scenario during the experimental phase, the optimal compromise operation point is selected from the Pareto front. Around the optimal compromise operation point, an optimal process window in the process parameter space is determined; wherein, the average performance of any process parameter within the optimal process window is greater than a first preset threshold and the robustness of any process parameter is greater than a second preset threshold.

[0115] The apparatus provided in this application solves the problems of narrow process window and weak anti-disturbance capability of traditional methods, significantly improves the robustness of the final process, reduces the impact of disturbances on product consistency, and shortens the R&D optimization cycle. Please see Figure 5 , Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 5 As shown, the electronic device 500 includes a processor 510, a memory 520, and a bus 530.

[0116] The memory 520 stores machine-readable instructions executable by the processor 510. When the electronic device 500 is running, the processor 510 and the memory 520 communicate via the bus 530. When the machine-readable instructions are executed by the processor 510, they can perform the operations described above. Figure 1 So much so Figure 3 The steps of the robust process parameter optimization method in the illustrated method embodiment can be found in the method embodiment for specific implementation, and will not be repeated here.

[0117] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, can perform the above-described actions. Figures 1 to 3 The steps of the robust process parameter optimization method in the illustrated method embodiment can be found in the method embodiment for specific implementation, and will not be repeated here.

[0118] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0119] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. The apparatus 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. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the shown or discussed mutual couplings, direct couplings, or communication connections may be through some communication interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.

[0120] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0121] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0122] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0123] Finally, it should be noted that the above-described embodiments are merely specific implementations of this application, used to illustrate the technical solutions of this application, and not to limit them. The scope of protection of this application is not limited thereto. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the scope of the technology disclosed in this application. Such modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and 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 robust process parameter optimization method, characterized in that, include: The pre-constructed multidimensional data tensor is preprocessed to obtain a perturbation feature template library for quantifying basic perturbation features. The multidimensional data tensor represents the data set of process parameters in multiple dimensions. The process parameters are labeled with attributes to obtain a process parameter list. Some process parameters in the process parameter list are labeled with sensitivity attributes, some with controllability attributes, and some with robustness attributes. The process parameter list is input into the trained bi-objective surrogate model, which outputs the probability distribution of average performance and the probability distribution of performance fluctuation. If, during the experiment, a real-time perturbation feature is detected to match the basic perturbation feature in the perturbation feature template library, the process parameters marked with control force attributes are called for experimental feedforward compensation, and the experimental dataset carrying the real-time perturbation feature is fed back to the Bayesian optimizer to update the bi-objective surrogate model. Based on the probability distribution of the average performance and the probability distribution of the performance fluctuation, a bi-objective Pareto front is plotted to determine the optimal process window, which represents the range of values ​​for the optimal process parameters.

2. The method according to claim 1, characterized in that, The preprocessing of the pre-constructed multidimensional data tensor to obtain a perturbation feature template library for quantizing basic perturbation features includes: Construct a multidimensional data tensor based on the acquired historical production data; The multidimensional data tensor is subjected to Tucker decomposition to obtain a benchmark reference tensor that characterizes the stable interaction relationship between process parameters in each dimension and a perturbation feature factor matrix that captures non-stationary perturbation signals in each dimension. Statistical analysis is performed on the disturbance feature factor matrix to obtain the basic disturbance features and the disturbance intensity and disturbance occurrence frequency corresponding to the basic disturbance features; Based on the basic disturbance characteristics and the disturbance intensity and frequency of occurrence corresponding to the basic disturbance characteristics, a disturbance characteristic template library is constructed.

3. The method according to claim 2, characterized in that, The dimensions corresponding to the multidimensional data tensor include batch dimension, time dimension and sensor dimension, and the sensor dimension includes multiple process parameter dimensions. The Tucker decomposition process is performed on the multidimensional data tensor to obtain a reference tensor characterizing the stable interaction relationships between process parameters in each dimension and a perturbation feature factor matrix capturing non-stationary perturbation signals in each dimension, including: The multidimensional data tensor is subjected to Tucker decomposition to obtain a benchmark reference tensor that characterizes the stable interaction relationship between process parameters in each dimension, as well as batch dimension perturbation factor matrix, time dimension perturbation factor matrix and sensor dimension perturbation factor matrix that capture non-stationary perturbation signals in each dimension.

4. The method according to claim 2, characterized in that, The following steps are used to determine the disturbance intensity and frequency of occurrence corresponding to the basic disturbance characteristics: Based on the amplitude of the eigenvector in the disturbance characteristic factor matrix and in combination with the physical range of the sensor, the disturbance intensity corresponding to the basic disturbance characteristic is calculated. The frequency of occurrence of basic disturbance features in historical production data is calculated by statistically analyzing the occurrence frequency and combining it with the total production batches; wherein the frequency of occurrence represents the ratio between the occurrence frequency of basic disturbance features and the total production batches; or, the duration of disturbances of basic disturbance features in historical production data is calculated by statistically analyzing the duration of disturbances and combining it with the total production duration; wherein the frequency of occurrence represents the ratio between the duration of disturbances and the total production duration.

5. The method according to claim 1, characterized in that, The process parameters are then subjected to attribute tagging to obtain a process parameter list, including: Calculate the disturbance sensitivity index of each process parameter, wherein the disturbance sensitivity index characterizes the degree of correlation between the change of process parameters under disturbance scenario and the fluctuation range of product quality indicators; Based on the disturbance sensitivity index and the correlation between process parameters and basic disturbance characteristics, the process parameters are labeled with attributes to obtain a process parameter list. Process parameters whose disturbance sensitivity index is greater than the disturbance index threshold and positively correlated with the basic disturbance characteristics are labeled with a sensitivity attribute; process parameters whose disturbance sensitivity index is greater than the disturbance index threshold and negatively correlated with the basic disturbance characteristics are labeled with a controllability attribute; and process parameters whose disturbance sensitivity index is not greater than the disturbance index threshold are labeled with a robustness attribute. The disturbance index threshold is predetermined based on the statistical distribution of the disturbance sensitivity indices of all process parameters in historical production data.

6. The method according to claim 5, characterized in that, The disturbance sensitivity index is used to characterize the correlation between changes in process parameters and fluctuations in product quality indicators under disturbance scenarios.

7. The method according to claim 6, characterized in that, When the correlation is linear, the disturbance sensitivity index is calculated using the following formula: DSI=|Cov( X, KPI) / Var(Q)|; Wherein, DSI represents the disturbance sensitivity index. X represents the changes in process parameters. KPI represents the fluctuation range of product quality indicators, Cov represents covariance, Var represents variance, and Q represents the disturbance intensity corresponding to the basic disturbance characteristics.

8. The method according to claim 1, characterized in that, The dual-objective proxy model includes an average performance proxy model and a performance fluctuation proxy model. The step of inputting the process parameter list into the trained bi-objective surrogate model and outputting the probability distribution of average performance and the probability distribution of performance fluctuation includes: The process parameter list is input into the average performance proxy model and the performance fluctuation proxy model respectively to obtain the probability distribution of average performance and the probability distribution of performance fluctuation. The average performance proxy model and the performance fluctuation proxy model are iterated through the following steps: Step S301: Select initial experimental points in the process parameter space using Latin hypercube sampling to perform physical experiments, obtain an initial dataset, and train the average performance proxy model and the performance fluctuation proxy model using the initial dataset; wherein, the initial dataset includes a list of process parameters corresponding to the experimental points, real-time perturbation features, and corresponding average performance and performance fluctuation; Step S302: During the iteration process, the average performance proxy model and the performance fluctuation proxy model are trained using the current dataset, respectively. Step S303: In the entire process parameter space, use numerical optimization methods to find the process parameters corresponding to the next experimental point that maximize the desired supervolume improvement acquisition function. Step S304: Perform a physical experiment using the process parameters corresponding to the next experimental point. During the experiment, monitor the average performance and performance fluctuations under disturbance scenarios in real time, and obtain the process parameters corresponding to the next experimental point, as well as the monitored average performance and performance fluctuations, to update the current dataset. Step S305: Return to step S302 and repeat steps S303 to S304 until the termination condition is met, thus completing the iteration of the average performance proxy model and the performance fluctuation proxy model.

9. The method according to claim 2, characterized in that, If, during the experiment, a real-time disturbance feature is detected to match a basic disturbance feature in the disturbance feature template library, then experimental feedforward compensation is performed using process parameters labeled with control force attributes, and the experimental dataset carrying the real-time disturbance feature is fed back to the Bayesian optimizer to update the bi-objective surrogate model, including: The online tensor monitoring system continuously compares real-time data with a benchmark reference tensor. If the deviation between the real-time data and the benchmark tensor is found to be greater than a preset deviation threshold, and the real-time perturbation features in the real-time data match the basic perturbation features in the perturbation feature template library, then the process parameters marked with control force attributes are adjusted for experimental feedforward compensation, and the experimental dataset carrying the real-time perturbation features is fed back to the Bayesian optimizer to update the bi-objective surrogate model; wherein, the experimental dataset includes the process parameters and performance results corresponding to the experimental points, the identifiers corresponding to the real-time perturbation features, the perturbation intensity, and the time of the experiment.

10. The method according to claim 1, characterized in that, The step of determining the optimal process window based on the dual-objective Pareto front includes: Based on the characteristics of the scenario during the experimental phase, the optimal compromise operation point is selected from the Pareto front. Around the optimal compromise operation point, an optimal process window in the process parameter space is determined; wherein, the average performance of any process parameter within the optimal process window is greater than a first preset threshold and the robustness of any process parameter is greater than a second preset threshold.

11. A robust process parameter optimization device, characterized in that, include: The preprocessing module is used to preprocess the pre-constructed multidimensional data tensor to obtain a perturbation feature template library for quantifying basic perturbation features. The multidimensional data tensor represents the data set of process parameters in multiple dimensions. The attribute tagging module is used to perform attribute tagging processing on the process parameters to obtain a process parameter list. Some process parameters in the process parameter list are tagged with sensitivity attributes, some process parameters are tagged with controllability attributes, and some process parameters are tagged with robustness attributes. The performance output module is used to input the list of process parameters into the trained bi-objective surrogate model and output the probability distribution of average performance and the probability distribution of performance fluctuation. If, during the experiment, a real-time perturbation feature is detected to match the basic perturbation feature in the perturbation feature template library, then the process parameters marked with control force attributes are called for experimental feedforward compensation, and the experimental dataset carrying the real-time perturbation feature is fed back to the Bayesian optimizer to update the bi-objective surrogate model. The window generation module is used to draw a bi-objective Pareto front based on the probability distribution of the average performance and the probability distribution of the performance fluctuation, so as to determine the optimal process window based on the bi-objective Pareto front, wherein the optimal process window represents the range of values ​​of the optimal process parameters.

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