Process optimization method and system based on Bayesian modeling and multi-objective function
By employing Bayesian modeling and multi-objective function-based process optimization methods, the problem of low efficiency in traditional process optimization is solved. This approach achieves efficient and systematic multi-objective optimization, finds the optimal combination of process parameters, provides a stable process range, and quantifies the influence of parameters. It is applicable to fields such as textile dyeing.
Patent Information
- Application Number
- CN202511024246.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-24
- Publication Date
- 2025-11-11
AI Technical Summary
Existing process optimization methods are inefficient, time-consuming, and labor-intensive, making it difficult to effectively balance multiple conflicting performance objectives and lacking a systematic guiding approach to make the optimal trade-off between contradictory goals.
A process optimization method based on Bayesian modeling and multi-objective functions is adopted. By defining the experimental space, calculating the aggregate score, and iteratively optimizing Bayesianly, the optimal combination of process parameters is found. Combined with user-defined importance weights, a flexible trade-off between multiple objectives is achieved.
It significantly improves optimization efficiency, reduces the number of experiments, effectively balances conflicts among multiple objectives, provides the best combination of process parameters and a stable process range, quantifies the impact of parameters, and guides large-scale production.
Smart Images
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Abstract
Description
Technical Field
[0001] This invention relates to the field of industrial data analysis and process control technology, specifically to a process optimization method and system based on Bayesian modeling and multi-objective functions. Background Technology
[0002] In numerous practical engineering and production scenarios, process optimization is a key step in improving product quality, reducing costs, and increasing production efficiency. In advanced manufacturing, particularly in the textile industry, optimizing process parameters to achieve ideal product performance has always been a core challenge. Taking the development of new fabrics as an example, engineers need to find the optimal combination of numerous process parameters, such as temperature, pressure, time, and auxiliary agent concentration, to simultaneously meet the requirements of multiple performance indicators, including tensile strength, color fastness, production cost, and durability.
[0003] Traditional process optimization methods have many limitations. For example, single-factor experimental design (OFAT) observes the effect by changing only one parameter at a time, which is extremely inefficient, time-consuming, and labor-intensive. Furthermore, because it ignores the interaction between parameters, it often fails to find the true optimum. While statistical methods such as Design of Experiments (DoE) are more systematic, they require numerous experiments to explore the entire parameter space when dealing with multi-objective problems, resulting in high costs and complex processes.
[0004] The key challenge these methods face is the difficulty in effectively balancing multiple conflicting performance objectives. For example, process adjustments made to improve fabric strength may lead to increased production costs or color degradation. There is a lack of systematic guidance for making optimal trade-offs among these conflicting goals.
[0005] This demonstrates the industry's urgent need for a data-driven, efficient optimization method that can intelligently search within a complex parameter space to find the optimal process solution that meets multiple objectives. Summary of the Invention
[0006] The technical problem to be solved by this invention is that existing process optimization methods are inefficient, time-consuming and labor-intensive, difficult to balance multiple conflicting performance objectives, and lack a systematic guiding method to make the optimal trade-off between contradictory objectives.
[0007] To solve the above problems, the technical solution adopted by the present invention is as follows:
[0008] On the one hand, this invention provides a process optimization method based on Bayesian modeling and multi-objective functions, including the following steps:
[0009] S1 defines the experimental space: The user defines the experimental space according to the actual process problem. The experimental space includes input parameters and multi-parameter objectives (MPOs). The input parameters are the process variables that need to be optimized, and the multi-parameter objectives are the product performance indicators that need to be measured in each experiment.
[0010] S2 calculates the aggregate score: The measurement results of multiple performance indicators in each experiment are converted into a single aggregate score through target normalization transformation, importance weighting, and geometric mean aggregation.
[0011] S3 Iterative Bayesian Optimization: It adopts a Bayesian optimization framework, builds a surrogate model based on existing experimental data, uses a collection function to recommend the next most valuable experimental point, and finds the optimal combination of process parameters that maximizes the aggregation score through iterative experiments until the expected performance is achieved or the experimental budget is exhausted.
[0012] S4 Analysis and Output Results: After the optimization cycle is completed, the best optimization results are provided, including the optimal combination of process parameters, the stable process range, and the degree of influence of each input parameter on the final result.
[0013] Preferably, the types of the input parameters include continuous, ordinal, and categorical. The continuous type is a variable that can take any value within a given range. The ordinal type is a numerical variable that can only take values at preset, ordered discrete points. The categorical type is a non-numerical, discrete classification variable.
[0014] Preferably, the target normalization transformation employs piecewise linear interpolation for the original measured value x. j Locate its interval [x] j,i x j,i+1 The corresponding evaluation value d is calculated using a linear interpolation formula. j ,
[0015]
[0016] Where, x j For a certain performance index, [x] represents the original measured value. j,i x j,i+1 ] is x j The preset interval, d j,i d j,i+1 The endpoints of the interval are x j,i x j,i+1 The corresponding normalized evaluation value, the evaluation value d j The range is [0,1].
[0017] Preferably, the importance weighting adopts a weighting function s = d + (1-d) × (1-w), where w is the importance weight, ranging from [0,1], and the higher the weight, the more important the target is; d is the evaluation value of the target after normalization (range [0,1]); and s is the final score of the target.
[0018] Preferably, in the geometric mean aggregation, the aggregation score of a single experiment is the geometric mean of the final scores si of all targets, i.e., the final score si = (s1 × s2 × ... × sn). (1 / n) , where si is the final score of the i-th performance objective, and n is the number of performance objectives.
[0019] Preferably, the surrogate model is a Gaussian process model, and the acquisition function is a q-expected boosting function, the expression of which is:
[0020] EI(x)=(μ(x)-f(x + )-ξ)Φ(Z)+σ(x)φ(Z)
[0021] Where EI(x) is the expected improvement value of point x, used to measure the value of this point as the next experimental point; μ(x) is the mean prediction of the surrogate model (such as the Gaussian process model) at point x; f(x+) is the best aggregate score observed so far (i.e., the highest aggregate score in the existing experiments); ξ is the exploration parameter, the larger the value, the more inclined it is to explore unknown regions; σ(x) is the standard deviation of the surrogate model's prediction at point x, reflecting the model's uncertainty about this point; Z is the standardized variable, calculated by the following formula:
[0022]
[0023] Where Z = 0 when σ(x) = 0; Φ(*) is the cumulative distribution function (CDF) of the standard normal distribution; φ(*) is the probability density function (PDF) of the standard normal distribution.
[0024] Preferably, the initial experimental data for the iterative Bayesian optimization comes from historical production records or is generated through a space-filling algorithm.
[0025] On the other hand, the present invention also provides a process optimization system based on Bayesian modeling and multi-objective functions, comprising:
[0026] Experimental Space Definition Module: This module allows users to define the experimental space based on actual process problems, including input parameters and multi-parameter objectives (MPOs).
[0027] Aggregated score calculation module: used to aggregate the measurement results of multiple performance indicators for each completed experiment into a single aggregate score;
[0028] Bayesian Optimization Module: This module uses a Bayesian optimization framework to build a surrogate model based on existing experimental data, recommends the next most valuable experimental point using a collection function, and finds the optimal combination of process parameters that maximizes the aggregate score through iterative experiments.
[0029] The results analysis and output module is used to provide the optimal combination of process parameters, the stable process range, and to quantitatively analyze the impact of each input parameter on the final result after the optimization cycle is completed.
[0030] Preferably, the aggregated score calculation module includes a target normalization unit, an importance weighting unit, and a geometric mean aggregation unit. The target normalization unit uses piecewise linear interpolation to perform target normalization transformation. The importance weighting unit uses a weighting function s = d + (1-d) × (1-w) to perform importance weighting. The geometric mean aggregation unit obtains the aggregated score by calculating the geometric mean of the final scores of all targets.
[0031] Preferably, the surrogate model in the Bayesian optimization module is a Gaussian process model, and the acquisition function is a q-expected boosting function.
[0032] The beneficial effects achieved by the present invention using the above solution are as follows:
[0033] 1. The Bayesian optimization framework can efficiently find the optimal combination of process parameters with the fewest experiments. Compared with traditional single-factor experiments and experimental design, this significantly reduces the number of experiments, saving time and costs. For example, in the textile dyeing process optimization example, the optimal process parameters were found in only 25 experiments, greatly improving optimization efficiency.
[0034] 2. By using a multi-objective aggregation method, multiple discrete performance objectives with different units are aggregated into a single comprehensive evaluation index. Combined with user-defined importance weights, it is possible to flexibly weigh different objectives, solving the problem that traditional methods have difficulty balancing conflicting performance objectives and effectively balancing multi-objective conflicts.
[0035] 3. It can not only provide the optimal combination of process parameters, but also define the stable process range and quantify the impact of each input parameter, providing strong guidance for large-scale production. Detailed Implementation
[0036] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.
[0037] Example 1
[0038] This invention proposes a process optimization method based on Bayesian modeling and multi-objective functions, comprising the following steps:
[0039] Step 1: Define the experimental space
[0040] The user first defines the boundary conditions of the experiment based on the actual process problem:
[0041] Input Parameters: The process variables that need to be optimized. Each parameter must have its type defined.
[0042] Continuous: A variable that can take any value within a given range (e.g., temperature: 80.0℃-120.0℃).
[0043] Ordinal: Numerical variables that can only take values at preset, ordered discrete points (e.g., stirring speed: 100, 200, 300 RPM).
[0044] Categorical: Non-numerical, discrete categorical variables (e.g., dye suppliers: 'Factory A', 'Factory B', 'Factory C').
[0045] Multi-parameter objectives (MPOs): Product performance indicators that need to be measured in each experiment (e.g., color fastness, breaking strength, unit cost, etc.).
[0046] Step 2: Calculate the uniform aggregate score
[0047] For each completed experiment, the measurement results of its multiple performance indicators will be aggregated into a single aggregate score.
[0048] A. Target value normalization transformation: Define a target normalization function d = f(x) for each performance index (MPO). Piecewise linear interpolation is used to implement the target normalization function for any new input original measurement value x. j The system first locates its interval [x] j,i x j,i+1 ], its corresponding evaluation value d j Specifically, the calculation is performed using a linear interpolation formula:
[0049]
[0050] Where, x j For a certain performance index, [x] represents the original measured value. j,i x j,i+1 ] is x j The preset interval, dj,i d j,i+1 The endpoints of the interval are x j,i x j,i+1 The corresponding normalized evaluation value, the evaluation value d j The range is [0,1]. This function converts the original measurement value x into a standardized, dimensionless evaluation value d.
[0051] B. Importance Weighting: Assign an "importance weight" w (ranging from 0 to 1) to each performance indicator, and use the weighting function s = d + (1-d) × (1-w) to adjust the normalized evaluation value d to the final score s of the target.
[0052] C. Geometric Mean Aggregation: The final "aggregate score" of a single experiment is the geometric mean of the final scores si of all n objectives: final score si = (s1 × s2 × ... × sn). (1 / n) , where si is the final score of the i-th performance objective, and n is the number of performance objectives.
[0053] Step 3: Iterative Bayesian Optimization
[0054] The system iterates and continuously recommends new experimental schemes in order to find the maximum value of the aggregate score.
[0055] A. Initial data collection: The optimization process can begin with a set of initial experimental data, which can come from historical production records or be generated using space-filling algorithms such as "Latin hypercube sampling".
[0056] B. Proxy Model Training: Based on all known experimental data (process parameters and corresponding aggregate scores), a statistical proxy model (e.g., Gaussian process model) is systematically trained. The selection of the covariance function and related methods are involved in the Gaussian process model.
[0057] C. Acquisition Function Calculation: The system calculates the value of the "acquisition function" over the entire parameter space (e.g., the "q-expected improvement" function, whose expression is:
[0058] EI(x)=(μ(x)-f(x + )-ξ)Φ(Z)+σ(x)φ(Z)
[0059] Identify the next or next batch of most worthwhile experimental points. Here, EI(x) is the expected improvement value of point x, used to measure the value of this point as the next experimental point; μ(x) is the mean prediction of the surrogate model (such as a Gaussian process model) at point x; f(x+) is the currently observed best aggregate score (i.e., the highest aggregate score among existing experiments); ξ is the exploration parameter (usually a small positive number, such as 0.01), used to balance "exploration" and "exploitation," with a larger value indicating a greater tendency to explore unknown areas; σ(x) is the standard deviation of the surrogate model's prediction at point x, reflecting the model's uncertainty about that point (a larger value indicates higher uncertainty); Z is the standardized variable, calculated using the following formula:
[0060]
[0061] Where Z = 0 when σ(x) = 0; Φ(*) is the cumulative distribution function (CDF) of the standard normal distribution; φ(*) is the probability density function (PDF) of the standard normal distribution.
[0062] D. Iterative Loop: The user conducts a new experiment based on the system's recommended parameter combination, measures various performance indicators, and the system calculates a new aggregate score. This new data point is added to the database, and then the process returns to step B to update the surrogate model. This loop repeats continuously until the expected performance is achieved or the experiment budget is exhausted.
[0063] Step 4: Analysis and Final Output
[0064] After the optimization loop is completed, the system provides a comprehensive analysis report.
[0065] A. Optimal parameter combination: The system identifies the best combination of input parameters that yields the highest predicted aggregate score.
[0066] B. Determination of stable process range: The system determines a stable process range around the optimal point. Within this range, the process parameters can fluctuate to a certain extent, while the overall performance of the final product can still be maintained at a high percentage above the optimal value.
[0067] C. Parameter Importance Analysis: Using model-independent analysis techniques (such as SHAP value analysis) or gradient information from surrogate models, quantitatively calculate the specific impact of each input parameter on the aggregate score.
[0068] Example 2
[0069] The following explanation uses the optimization of textile dyeing processes as an example:
[0070] (1) Objective: To find the best dyeing process for a new type of synthetic fiber fabric.
[0071] (2) Input parameters:
[0072] Temperature (°C): Continuous, [80, 120]
[0073] pH value: Category, ['Low', 'Medium', 'High']
[0074] Dye concentration (g / L): Sequential type, [5, 10, 15, 20]
[0075] (3) Performance Objectives (MPOs) and Normalization Rules:
[0076] Colorfastness (grades 1-5): Grade 5, the evaluation value d = 1; Grade 1, d = 0.
[0077] Fabric strength (N): When it is greater than 150N, the evaluation value d = 1; when it is less than 80N, d = 0.
[0078] Cost ($ / m): When it is below $0.50 / m, the evaluation value d = 1; when it is above $1.00 / m, d = 0.
[0079] Importance weights: color fastness (w=1.0), strength (w=0.8), cost (w=0.6).
[0080] (4) Optimize the process:
[0081] 0. The system uses Latin hypercube sampling to initially recommend 10 experimental groups.
[0082] 1. The laboratory completes the experiment and enters the results. The system calculates the corresponding aggregate score for each group of experiments.
[0083] 2. The system trains the agent model and recommends three new sets of experiments for the next batch through the acquisition function.
[0084] 3. The above iteration cycle is repeated 5 times (a total of 10 + 3 × 5 = 25 experiments).
[0085] (5) Final output result:
[0086] Optimal process parameters: temperature = 98℃, pH = 'medium', dye concentration = 15g / L. The predicted highest polymerization score is 0.92.
[0087] Stable process range: temperature [95℃-102℃], pH value [medium], dye concentration [15-20g / L].
[0088] Parameter importance ranking: 1. pH value (influence 0.55), 2. Temperature (influence 0.35), 3. Dye concentration (influence 0.10).
[0089] The present invention and its embodiments have been described above. This description is not restrictive, and actual embodiments are not limited thereto. In conclusion, if those skilled in the art are inspired by this description and, without departing from the spirit of the invention, design similar structures and embodiments to this technical solution, such designs should fall within the protection scope of the present invention.
Claims
1. A process optimization method based on Bayesian modeling and multi-objective functions, characterized in that, Includes the following steps: S1 defines the experimental space: The user defines the experimental space according to the actual process problem. The experimental space includes input parameters and multi-parameter objectives. The input parameters are the process variables that need to be optimized, and the multi-parameter objectives are the product performance indicators that need to be measured in each experiment. S2 calculates the aggregate score: The measurement results of multiple performance indicators in each experiment are converted into a single aggregate score through target normalization transformation, importance weighting, and geometric mean aggregation. S3 Iterative Bayesian Optimization: It adopts a Bayesian optimization framework, builds a surrogate model based on existing experimental data, uses a collection function to recommend the next most valuable experimental point, and finds the optimal combination of process parameters that maximizes the aggregation score through iterative experiments until the expected performance is achieved or the experimental budget is exhausted. S4 Analysis and Output Results: After the optimization cycle is completed, the best optimization results are provided, including the optimal combination of process parameters, the stable process range, and the degree of influence of each input parameter on the final result.
2. The process optimization method based on Bayesian modeling and multi-objective functions according to claim 1, characterized in that: The types of input parameters include continuous, ordinal, and categorical. Continuous variables are variables that can take any value within a given range. Ordinal variables are numerical variables that can only take values at preset, ordered discrete points. Categorical variables are non-numerical, discrete categorical variables.
3. The process optimization method based on Bayesian modeling and multi-objective functions according to claim 1, characterized in that: The target normalization transformation employs piecewise linear interpolation for the original measured value x. j Locate its interval [x] j,i x j,i+1 The corresponding evaluation value d is calculated using a linear interpolation formula. j , Where, x j For a certain performance index, [x] represents the original measured value. j,i x j,i+1 ] is x j The preset interval, d j,i d j,i+1 The endpoints of the interval are x j,i x j,i+1 The corresponding normalized evaluation value, the evaluation value d j The range is [0,1].
4. The process optimization method based on Bayesian modeling and multi-objective functions according to claim 3, characterized in that: The importance weighting adopts the weighting function s=d+(1-d)×(1-w), where w is the importance weight, ranging from [0,1]; d is the evaluation value after target normalization transformation, ranging from [0,1]; and s is the final score of the target.
5. The process optimization method based on Bayesian modeling and multi-objective functions according to claim 4, characterized in that: In the geometric mean aggregation, the aggregation score of a single experiment is the geometric mean of the final scores si of all targets, i.e., the final score si = (s1 × s2 × ... × sn). (1 / n) , where si is the final score of the i-th performance objective, and n is the number of performance objectives.
6. The process optimization method based on Bayesian modeling and multi-objective functions according to claim 5, characterized in that: The surrogate model is a Gaussian process model, and the acquisition function is a q-expected boosting function, the expression of which is: EI(x)=(μ(x)-f(x + )-ξ)Φ(Z)+σ(x)φ(Z) Where EI(x) is the expected improvement at point x, used to measure the value of this point as the next experimental point; μ(x) is the mean prediction of the surrogate model at point x; f(x+) is the best aggregate score observed so far (i.e., the highest aggregate score in the existing experiments); ξ is the exploration parameter; σ(x) is the standard deviation of the surrogate model's prediction at point x, reflecting the model's uncertainty at that point; Z is the standardized variable, calculated using the following formula: When σ(x) = 0, Z = 0; Φ(*) is the cumulative distribution function of the standard normal distribution; φ(*) is the probability density function of the standard normal distribution.
7. The process optimization method based on Bayesian modeling and multi-objective functions according to claim 6, characterized in that: The initial experimental data for the iterative Bayesian optimization comes from historical production records or is generated through a space-filling algorithm.
8. A process optimization system based on Bayesian modeling and multi-objective functions, used to implement the process optimization method according to any one of claims 1-7, characterized in that, include: Experimental Space Definition Module: This module allows users to define experimental spaces based on actual process problems, including input parameters and multi-parameter objectives. Aggregated score calculation module: used to aggregate the measurement results of multiple performance indicators for each completed experiment into a single aggregate score; Bayesian Optimization Module: This module uses a Bayesian optimization framework to build a surrogate model based on existing experimental data, recommends the next most valuable experimental point using a collection function, and finds the optimal combination of process parameters that maximizes the aggregate score through iterative experiments. The results analysis and output module is used to provide the optimal combination of process parameters, the stable process range, and to quantitatively analyze the impact of each input parameter on the final result after the optimization cycle is completed.
9. The process optimization system based on Bayesian modeling and multi-objective functions according to claim 8, characterized in that: The aggregated score calculation module includes a target normalization unit, an importance weighting unit, and a geometric mean aggregation unit. The target normalization unit uses piecewise linear interpolation to perform target normalization transformation. The importance weighting unit uses a weighting function s = d + (1-d) × (1-w) to perform importance weighting. The geometric mean aggregation unit obtains the aggregated score by calculating the geometric mean of the final scores of all targets.
10. A process optimization system based on Bayesian modeling and multi-objective functions according to claim 8, characterized in that: The surrogate model in the Bayesian optimization module is a Gaussian process model, and the acquisition function is the q-expected boosting function.