Preparation control method based on residual twin space projection

Abstract

The application relates to the technical field of ceramic matrix composite material preparation, and discloses a preparation control method based on residual double subspace projection. The process first constructs a time-varying process-performance double subspace containing a process parameter subspace and a performance residual subspace, then constructs a residual solving model based on the double subspace, and calculates the performance residual of each time sequence node in the preparation process by using the model; the process parameter adjustment direction is determined through double subspace projection operation, the parameters are adjusted according to the direction, and the material is prepared, the residual calculation, parameter adjustment and preparation steps are repeated after the actual performance is detected, until the performance residual meets the preset condition, and the process parameter combination for stably preparing the material is obtained. The process improves the control accuracy and stability of the ceramic matrix composite material preparation, and provides effective guarantee for the stable control of the material performance.

Description

Technical Field

[0001] This application relates to the field of ceramic matrix composite material preparation technology, specifically to a preparation control method based on residual biplane projection. Background Technology

[0002] The performance stability of stable ceramic matrix composites is influenced by multiple factors during preparation, including raw material ratios, sintering processes, and post-treatment parameters. Traditional processes often rely on empirical parameter adjustments, optimizing the preparation process through trial and error. This approach struggles to establish a precise correlation between process parameters and performance indicators (such as mechanical strength, thermal stability, and microstructure uniformity), resulting in numerous iterations, low efficiency, and significant batch-to-batch performance variations due to parameter fluctuations, making it difficult to simultaneously meet multi-dimensional stability requirements. Existing control methods lack dynamic tracking and feedback of performance deviations (residual weight), failing to systematically link process parameter adjustments with residual weight optimization, hindering efficient parameter convergence and restricting the large-scale stable preparation of stable ceramic matrix composites. Summary of the Invention

[0003] To solve, or at least partially solve, the above-mentioned technical problems, this application provides a preparation and control method based on residual bispace projection.

[0004] This application provides a method for preparing and controlling residual bispace projection, including the following steps:

[0005] S1: Construct a time-varying process-performance bispace, which includes a process parameter subspace and a performance residual quantum space. The process parameter subspace consists of key process parameters that affect the stability of ceramic matrix composites, and the performance residual quantum space consists of the deviation between the actual performance of ceramic matrix composites and the target stability index.

[0006] S2: Based on the time-varying process-performance bispace, a residual solution model is constructed, which is used to solve for the performance residual in the performance residual quantum space;

[0007] S3: Using the residual solution model, calculate the performance residuals at each time point in the preparation process of ceramic matrix composites;

[0008] S4: Based on the performance residual, determine the adjustment direction of key process parameters in the process parameter subspace through dual subspace projection calculation;

[0009] S5: Adjust the key process parameters according to the adjustment direction to prepare ceramic matrix composite materials, and test the actual performance of the prepared ceramic matrix composite materials;

[0010] S6: Repeat steps S3 to S5 until the performance residual meets the preset conditions, obtain a stable combination of process parameters for preparing ceramic matrix composite materials, and complete the regulation.

[0011] Optionally, in step S1,

[0012] The process parameter subspace is constructed as follows: key process parameters that affect the stability of ceramic matrix composites are selected, including raw material ratio parameters, sintering process parameters and post-treatment process parameters. The key process parameters are constructed into a process parameter subspace that dynamically changes with the preparation stage according to the preparation sequence.

[0013] The residual quantum space of the performance is constructed as follows: a target stability index for the ceramic matrix composite material is set, which includes a mechanical stability index, a thermal stability index, and a microstructure stability index; the deviation between the actual performance of the ceramic matrix composite material and the target stability index is calculated; and the residual quantum space of the performance is constructed based on the deviation.

[0014] Optionally, in step S2, the residual solution model is a residual nullification neural network model, and the residual nullification neural network model is constructed as follows:

[0015] Using the combination of key process parameters in the process parameter subspace as input and the performance residual vector in the performance residual quantum space as output, an error function is constructed. ,in This is the predicted residual vector of the residual nullification neural network model. The actual performance residual vector is obtained by driving the error function to converge to zero.

[0016] Optionally, in step S4, the specific implementation of the bi-subspace projection operation is as follows:

[0017] S41: Project the performance residual vector onto the process parameter subspace to construct a projection matrix. ,in This is the parameter matrix of the process parameter subspace;

[0018] S42: Calculate the projection vector of the performance residual in the process parameter subspace using the projection matrix, and determine the adjustment direction of the key process parameter based on the projection vector. The adjustment direction is the parameter change direction that minimizes the performance residual.

[0019] Optionally, when determining the adjustment direction of key process parameters based on the projection vector, a composite scoring function is constructed. ,in This is the normalized value of the performance residual. The deviation between the parameter adjustment direction and the target direction for optimal performance. This is the deviation weighting coefficient;

[0020] Calculate the score value corresponding to each candidate adjustment direction, and select the candidate adjustment direction with the smallest score value as the final adjustment direction of the key process parameter.

[0021] Optionally, when the process parameter subspace is a high-dimensional parameter space, a random sketch matrix is ​​introduced before performing the bi-subspace projection operation. The process parameter subspace is subjected to dimensionality reduction processing;

[0022] High-dimensional process parameter matrix Through the random sketch matrix Projecting to a lower-dimensional space yields a lower-dimensional parameter matrix. ;

[0023] Based on the low-dimensional parameter matrix A low-dimensional projection matrix is ​​constructed, and the projection operation of the performance residual is performed in the low-dimensional space. Then, the projection result in the low-dimensional space is mapped back to the original high-dimensional space to determine the adjustment direction of the key process parameters.

[0024] Optionally, in step S6, the method for determining whether the performance residual meets the preset conditions is as follows:

[0025] The rate of change of residual properties of ceramic matrix composites prepared in multiple consecutive preparations is calculated. If the rate of change of residual properties is less than a preset threshold and each residual property is within a preset allowable range, the residual properties are determined to meet the preset conditions. If not, the parameter adjustment and preparation process is continued, and the current residual properties and the corresponding combination of process parameters are recorded.

[0026] Optionally, if the performance residual continues to increase or there is no effective parameter adjustment direction during the execution of steps S5 to S6, the backtracking correction mechanism is activated.

[0027] Revert to the last valid combination of process parameters and mark the current range of process parameters as invalid.

[0028] Based on the effective combination of process parameters after the return, steps S3 to S4 are repeated to determine the new direction of adjustment of key process parameters, and then the ceramic matrix composite material is prepared according to the new adjustment direction.

[0029] Optionally, when constructing the time-varying process-performance bipartite space, a time-varying correlation model is established using matrix equations, wherein the matrix equations are: ,in This is a time-varying correlation matrix of process parameters, where each element corresponds to the correlation strength of different key process parameters in the preparation time sequence. This is a vector of process parameters for each time node, where each element represents the specific value of the key process parameter at the corresponding time node. This is the performance residual vector corresponding to the time node, and its elements are the specific values ​​of each performance deviation in the performance residual quantum space at the corresponding time node;

[0030] By solving the matrix equation, a quantitative correlation is obtained between the changes in key process parameters with the preparation time and the changes in performance residuals. Based on this quantitative correlation, the time-varying process-performance bipartite space is constructed.

[0031] Optionally, during the iteration process of steps S3 to S6, the linear convergence of the performance residual is achieved through the bi-subspace projection operation;

[0032] After each iteration, the performance residual satisfies ,in For the first Performance residuals of the next iteration For the first Performance residual of the next iteration is the convergence factor and ;

[0033] The performance residual is continuously decayed through multiple iterations until a preset condition is met. The iteration is then stopped, and the combination of process parameters at this point is used as the combination of process parameters for the stable preparation of ceramic matrix composite materials.

[0034] The preparation and control method based on residual bispace projection provided in this application has the following beneficial effects:

[0035] The fabrication control method based on residual bispace projection provided in this application, by constructing a time-varying process-performance bispace, can capture the relationship between the temporal changes of key process parameters and the deviation of the actual material performance from the target stability index during the fabrication of ceramic matrix composites. This breaks through the limitation of traditional static parameter control being difficult to adapt to dynamic fabrication processes, providing a basic framework for subsequent precise control that fits the actual production scenario. Based on this bispace, a residual solution model is constructed and the performance residual at each time node is calculated. This allows for real-time monitoring of the deviation of material performance during fabrication, avoiding the control lag problem caused by only detecting performance after fabrication, and enabling timely response to performance changes. Determining the adjustment direction of key process parameters through bispace projection calculations allows parameter adjustments to be specifically aimed at reducing performance residuals, avoiding resource waste and performance fluctuations caused by blind adjustments, and improving the accuracy of process control. By iteratively adjusting process parameters and detecting performance until the performance residual meets the preset conditions, the combination of process parameters can be gradually optimized, ultimately obtaining process parameters that can stably fabricate ceramic matrix composites that meet the requirements, effectively improving the stability and consistency of material fabrication.

[0036] By clarifying the specific categories of key process parameters and target stability indicators, the compositional dimensions of the time-varying process-performance bi-subspace are further refined, making the correlation between process parameters and performance indicators more targeted. This reduces control deviations caused by ambiguity in parameter or indicator definitions and improves the accuracy of bi-subspace modeling. A residual zeroing neural network model is used to solve for performance residuals. Leveraging the convergence of the error function to zero, the performance residual vector can be obtained more quickly and accurately. Compared to traditional iterative solutions, this improves the efficiency and accuracy of residual calculation, providing efficient data support for real-time control. By constructing a projection matrix and calculating the projection vector to determine the parameter adjustment direction, the determination of the adjustment direction is based on quantitative analysis, ensuring that parameter adjustments efficiently target performance optimization goals and further enhancing the scientific nature of control. Introducing a composite scoring function to consider the deviation between performance residuals and adjustment direction comprehensively balances the performance optimization effect and the rationality of the adjustment direction, avoiding local optima problems caused by solely considering performance residuals and improving the overall applicability of the parameter adjustment scheme. To address the dimensionality reduction of high-dimensional process parameter spaces, a stochastic sketch matrix is ​​introduced, effectively reducing the computational complexity of projection operations under high-dimensional parameters and minimizing computational resource consumption. This allows the controlled process to adapt to complex fabrication scenarios with multiple coupled parameters. By judging whether preset conditions are met through the rate of change of performance residuals and the allowable range, the stability of process parameter combinations can be determined more scientifically, avoiding performance fluctuations caused by premature iteration termination or efficiency waste due to excessive iteration. A backtracking correction mechanism can promptly revert to effective parameter combinations and replan the adjustment direction when performance residuals continue to increase or there is no effective adjustment direction, preventing deadlock in the control process and ensuring smooth progress. A time-varying correlation model is established through matrix equations, clarifying the quantitative correlation between the time-series changes of process parameters and the changes of performance residuals, improving the accuracy and reliability of time-varying bi-subspace modeling, and providing a more solid theoretical support for parameter adjustment. By achieving linear convergence of performance residuals, continuous and efficient decay of performance residuals is ensured during iteration, shortening the iteration cycle of parameter optimization, improving overall control efficiency, and enabling process parameters to converge to a stable state more quickly. Attached Figure Description

[0037] Figure 1 A schematic diagram of a preparation and control method based on residual bispace projection provided for an embodiment of this application;

[0038] Figure 2 A schematic diagram of another preparation and control method based on residual bispace projection provided in this application embodiment;

[0039] Figure 3 This is a schematic diagram comparing the convergence curves of a random overdetermined matrix provided in an embodiment of this application. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this application clearer, specific embodiments of this application will be described in further detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely for explaining this application and not for limiting it. It should also be noted that, for ease of description, only the parts relevant to this application are shown in the drawings, not all of them. Before discussing exemplary embodiments in more detail, it should be mentioned that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe operations (or steps) as sequential processes, many of these operations can be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the operations can be rearranged. The process can be terminated when its operation is completed, but may also have additional steps not included in the drawings. The process can correspond to a method, function, procedure, subroutine, subprogram, etc.

[0041] The technical solutions of the embodiments of this application will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application are within the scope of protection of this application.

[0042] See Figure 1 This application provides a method for preparing and controlling data based on residual bispace projection, including the following steps:

[0043] S1: Construct a time-varying process-performance bispace, which includes a process parameter subspace and a performance residual quantum space. The process parameter subspace consists of key process parameters that affect the stability of ceramic matrix composites, and the performance residual quantum space consists of the deviation between the actual performance of ceramic matrix composites and the target stability index.

[0044] S2: Based on the time-varying process-performance bispace, a residual solution model is constructed. The residual solution model is used to solve the performance residual in the performance residual quantum space.

[0045] S3: Using the residual solution model, calculate the performance residuals at each time node during the preparation of ceramic matrix composites;

[0046] S4: Based on the performance residual, the adjustment direction of key process parameters in the process parameter subspace is determined through dual subspace projection calculation;

[0047] S5: Adjust the key process parameters according to the adjustment direction, prepare ceramic matrix composites, and test the actual performance of the prepared ceramic matrix composites;

[0048] S6: Repeat steps S3 to S5 until the performance residual meets the preset conditions, obtain a stable combination of process parameters for preparing ceramic matrix composites, and complete the control.

[0049] To achieve precise control over the preparation of stable ceramic matrix composites, a complete control process needs to be constructed based on the dynamic correlation between process parameters and material properties. First, a time-varying process-performance bi-subspace needs to be constructed, comprising two core subspaces: the process parameter subspace and the performance residual quantum space. The process parameter subspace consists of key process parameters affecting the stability of ceramic matrix composites, including raw material ratios, sintering temperature, holding time, and post-treatment conditions, which exhibit temporal changes as the preparation stage progresses. The performance residual quantum space consists of the deviation between the actual properties of the ceramic matrix composite and the preset target stability indicators, including mechanical strength, thermal stability, and microstructure uniformity. The calculation of the deviation corresponds to different time nodes in the preparation process.

[0050] Based on the aforementioned time-varying process-performance bispace, a residual solution model needs to be further constructed. This model is built upon the solution logic of linear equations, transforming the relationship between process parameters and performance residuals into the form of… A linear system, in which This is a process parameter matrix, where each element corresponds to the value of a key process parameter at different time points. Adjust the coefficient vector for the parameters to be determined. Let this be the target performance vector. The core of the residual solution model is calculating the residual vector. To quantify the overall deviation of the residual, the 2-norm of the residual is introduced for calculation. The norm directly reflects the overall gap between the material performance and the target under the current combination of process parameters. By solving the residual vector and its norm, the specific dimensions and degree of performance deviation can be accurately captured.

[0051] In the preparation of ceramic matrix composites, the aforementioned residual solution model is needed to calculate the performance residuals at each time step. Specifically, real-time performance data of the material is collected at each key preparation stage, such as raw material mixing, molding, sintering, and post-processing. This includes data such as porosity at different temperatures during sintering and flexural strength after cooling. These data are compared with the target performance at the corresponding stage, and then substituted into the residual solution model to obtain the residual values ​​at each time step. ( (as time sequence nodes), forming a complete residual time sequence { }( (This represents the total number of time-series nodes).

[0052] After obtaining the performance residuals, the direction for adjusting the process parameters needs to be determined through bi-subspace projection operations. The core of the projection operation is to orthogonally project the residual vector in the performance residual quantum space onto the process parameter subspace; this process can be achieved by constructing a projection matrix. Projection matrix The expression is (Superscript in this article) (represents transpose), where Let be the parameter matrix of the process parameter subspace. To derive the rationality of this projection matrix, consider the residual vector. Projection vector in the process parameter subspace The orthogonality condition must be met, that is , combined It can be deduced For any It is established, and thus we can solve it. ,in For the process parameter matrix An identity matrix of the same dimension has all 1s on its main diagonal and all other elements as 0. This projection matrix can be used to map the residual vector to an adjustment vector in the process parameter space. The direction of this adjustment vector is the direction of process parameter changes that can minimize performance residuals.

[0053] After adjusting the key process parameters according to the determined adjustment direction, ceramic matrix composite materials are prepared, and the actual performance of the prepared materials is comprehensively tested. The testing items include, but are not limited to, mechanical property testing, thermal stability analysis, and microstructure characterization, in order to obtain new performance data.

[0054] The newly acquired performance data is substituted into the residual solution model to recalculate the performance residual, and the above process of parameter adjustment, preparation, and testing is repeated. In each iteration, the norm of the residual vector satisfies the linear convergence property, i.e. (in (where is the convergence factor), this convergence relation can be obtained through residual decomposition after projection. The derivation of the norm inequality shows that the performance residual continuously decreases with the increase of the number of iterations. When the residual meets the preset allowable range, the iteration stops. The combination of process parameters at this point is the combination of process parameters that can stably prepare ceramic matrix composite materials that meet the target stability index, thus completing the entire control process.

[0055] This process allows for full utilization of the dynamic correlation information between process parameters and performance residuals, enabling precise control of the ceramic matrix composite material preparation process. This effectively improves the stability and consistency of material properties, avoids the blindness of traditional trial-and-error adjustments, and provides a reliable method for the efficient preparation of stable ceramic matrix composite materials.

[0056] In some implementations, in step S1,

[0057] The process parameter subspace is constructed as follows: key process parameters that affect the stability of ceramic matrix composites are selected. These key process parameters include raw material ratio parameters, sintering process parameters, and post-treatment process parameters. The key process parameters are then constructed into a process parameter subspace that dynamically changes with the preparation stage according to the preparation sequence.

[0058] The residual quantum space of performance is constructed as follows: a target stability index for the ceramic matrix composite material is set, which includes mechanical stability index, thermal stability index and microstructure stability index. The deviation between the actual performance of the ceramic matrix composite material and the target stability index is calculated, and the residual quantum space of performance is constructed based on the deviation.

[0059] When constructing a time-varying process-performance bispace, the composition of the process parameter subspace must first be clarified. The selection of key process parameters needs to cover the entire process of ceramic matrix composite material preparation. Raw material proportioning parameters include the ratio of ceramic particles to reinforcing phases, the type and proportion of additives, etc., which directly affect the initial composition and microstructure of the material. Sintering process parameters encompass heating rate, sintering temperature, holding time, sintering atmosphere, etc., whose changes alter the grain growth, pore evolution, and interfacial bonding state within the material. Post-processing parameters include annealing temperature, surface treatment method, etc., used to adjust the residual stress and surface properties of the material. Arranging these parameters according to the preparation sequence forms a dynamic vector of process parameters that changes with each stage. ,in Indicates the first Key process parameters at timing nodes The specific values, This represents the total number of key process parameters. For example, in the raw material mixing stage, the focus is on recording and adjusting the raw material ratio parameters, while in the sintering stage, the focus is on tracking changes in temperature and time. This allows the process parameter subspace to be visualized through vector sequences. ( (Total number of timing nodes) reflects the parameter characteristics of different preparation stages.

[0060] The construction of the performance residual quantum space requires a clear foundation of target stability indices. Mechanical stability indices mainly include flexural strength and fracture toughness, reflecting the material's ability to resist external forces; thermal stability indices encompass strength retention at high temperatures and coefficient of thermal expansion, reflecting the material's performance stability in temperature-changing environments; microstructural stability indices involve grain size distribution, porosity, and interfacial bonding states, determining the material's macroscopic properties at the microscopic level. During the fabrication process, the actual performance of the material is detected at different time points, defining the performance residual components. ( , (This represents the total number of performance indicators), such as testing the density of the billet during the initial sintering stage and testing the mechanical strength after cooling. The residual components at each time node are integrated into a performance residual vector. These performance residual vectors are arranged according to the detection time sequence, forming a performance residual quantum space, allowing the residuals to pass through the vector sequence. It dynamically reflects the gap between material properties and targets at each stage.

[0061] The process parameter subspace and performance residual quantum space constructed in the above manner can comprehensively characterize the preparation process of ceramic matrix composites. The process parameter subspace captures the dynamic changes of parameters throughout the entire process through parameter vector sequences, while the performance residual quantum space tracks performance deviations at each stage through residual vector sequences. The time-varying process-performance dual subspace jointly constituted by the two can be represented in matrix form. Integrating time-series correlation information provides a precise analytical basis for subsequent residual calculation and parameter adjustment, enabling the control process to closely follow the actual situation of material preparation and ensuring that the direction of parameter adjustment is consistent with the performance optimization goal.

[0062] In some implementations, in step S2, the residual solution model is a residual nullification neural network model, and the residual nullification neural network model is constructed as follows:

[0063] Using the combination of key process parameters in the process parameter subspace as input and the performance residual vector in the performance residual quantum space as output, an error function is constructed. ,in This represents the predicted residual vector of the residual-zeroing neural network model. The actual performance residual vector is solved by driving the error function to converge to zero.

[0064] The core purpose of constructing the residual solution model is to accurately obtain the performance residual vector in the performance residual quantum space. This model adopts the form of a residual zeroing neural network model, and its design and solution process strictly follows the mathematical logic of linear system optimization. The input of the model is set as the combination of key process parameters in the process parameter subspace, covering key parameters of the entire process such as raw material ratio, sintering conditions, and post-processing parameters. The output is the performance residual vector under the corresponding parameter combination, which directly reflects the dimension and degree of deviation between the actual material performance and the target index.

[0065] To achieve accurate residual calculation, an error function is first constructed to quantify the difference between the model's predicted residual and the actual residual. Based on the accuracy requirements of residual calculation, the error function is defined as follows: ,in This represents the predicted residual vector of the residual-zeroing neural network model. This represents the actual performance residual vector. The error function is constructed based on the least squares principle, amplifying the impact of residual bias through the square norm to ensure that model optimization focuses on reducing the gap between predicted and actual values. To further clarify the mathematical properties of the error function, its expansion yields... When unfolded, it becomes Among them, the cross terms It directly reflects the correlation between the predicted value and the actual value.

[0066] To drive the error function to converge to zero, an iterative update rule needs to be designed based on the core principle of nullable neural networks. The derivation of the partial derivative of the error function with respect to the network weight parameters is as follows: [From...] According to the matrix differentiation rule, ,in These are the weight parameters of the neural network. Assume that the prediction residual and the weights satisfy a linear mapping relationship. ( (For the input process parameter matrix), then Substituting the values, we obtain the gradient expression. After transposition, it becomes Based on this, design the weight update formula. ,in The learning rate is achieved by continuously adjusting the weight parameters to gradually reduce the error function.

[0067] To prove the error convergence property, the Lyapunov function is introduced. Taking its derivative, we get Due to the actual residual amount It changes slowly over time and can be approximated as , combined Substituting into .because It is a positive semi-definite matrix, and its quadratic form is non-negative, therefore And only if hour Prove that the error function converges exponentially, i.e. ( (This is the convergence rate coefficient), ensuring that the model can converge quickly and accurately to the actual residual value.

[0068] In practical applications, historical data from the preparation of ceramic matrix composites is used to train a residual zeroing neural network model. Through multiple rounds of iterative optimization of weight parameters, the model acquires the ability to accurately predict performance residuals under different combinations of process parameters. After training, real-time collected process parameter combinations are input into the model, which quickly outputs the corresponding performance residual vector. This provides accurate residual data support for subsequent bi-space projection calculations, ensuring the accuracy of parameter adjustment and laying the foundation for the efficient implementation of the entire control process.

[0069] See Figure 2 In some implementations, the specific implementation of the bi-subspace projection operation in step S4 is as follows:

[0070] S41: Project the performance residual vector onto the process parameter subspace to construct the projection matrix. ,in The parameter matrix is ​​the subspace of process parameters;

[0071] S42: The projection vector of the performance residual in the process parameter subspace is obtained by calculating the projection matrix. Based on the projection vector, the adjustment direction of the key process parameters is determined. The adjustment direction is the parameter change direction that minimizes the performance residual.

[0072] The core of bi-subspace projection computation is to establish a quantitative mapping relationship between performance residuals and process parameters. By projecting the performance residual vector onto the process parameter subspace, the specific direction of parameter adjustment is clarified. This process requires using the parameter matrix of the process parameter subspace as a foundation, constructing a projection matrix through mathematical operations, and then using this matrix to complete the spatial mapping of the residual vector.

[0073] Process parameter matrix It consists of the values ​​of each key process parameter at different time nodes. The number of rows corresponds to the number of time nodes in the manufacturing process, and the number of columns corresponds to the types of key process parameters. To achieve orthogonal projection of the performance residual vector onto the process parameter subspace, a projection matrix needs to be constructed. Its expression is The derivation of this matrix stems from the geometric principle of orthogonal projection: to transform the residual vector... Projected to The subspace spanned by the column vectors, and the projection vectors The error vector must be satisfied. Orthogonal to all vectors in the subspace, i.e. Combining Substituting, we can get ,Right now (in To and (identity matrix of the same dimension) for any It is established, and from this it can be deduced that Further deformation yields Multiply both sides by the right. Finally, the solution was obtained. Ensure the projection vector Residual vector The best approximation in the process parameter subspace.

[0074] To quantify the optimization effect of the residual after projection, a relationship regarding the variation of the residual norm is introduced. Decomposed into projection components within subspace Components orthogonal to the subspace ,because and Orthogonal, according to the Pythagorean theorem, the norm relationship can be obtained. , This indicates that the norm of the projected error vector is smaller than the norm of the original residual, verifying the effectiveness of the projection operation for residual optimization.

[0075] Through projection matrix Calculate the projection vector of the performance residual in the process parameter subspace. By combining the linear correlation between process parameter adjustment and residual change, the parameter adjustment vector can be further derived. Each element of this vector corresponds to the adjustment amount of different process parameters. The direction of the vector indicates the direction of change of the process parameter required to minimize the performance residual: if an element of the projection vector is positive, it means that the corresponding process parameter needs to be increased; if it is negative, it needs to be decreased; the larger the absolute value of the element, the more significant the influence of the parameter on the residual, and the higher the adjustment priority.

[0076] In practice, a matrix is ​​first constructed based on the process parameters of the current preparation stage. Substitute into the formula to calculate the projection matrix. Then, the real-time acquired performance residual vector Substitute to obtain the projection vector. With parameter adjustment vector .in accordance with By adjusting the direction and magnitude of key process parameters, the adjusted parameter combinations can specifically reduce performance residuals and push material properties closer to target indicators. This parameter adjustment method based on projection calculations can accurately correlate performance deviations with changes in process parameters, avoiding blind adjustments and making the entire control process more scientific and efficient.

[0077] In some implementations, when determining the adjustment direction of key process parameters based on projection vectors, a composite scoring function is constructed. ,in This is the normalized value of the performance residual. The deviation between the parameter adjustment direction and the target direction for optimal performance. This is the deviation weighting coefficient;

[0078] Calculate the score value corresponding to each candidate adjustment direction, and select the candidate adjustment direction with the smallest score value as the final adjustment direction of the key process parameter.

[0079] When determining the adjustment direction of key process parameters based on projection vectors, it is necessary to comprehensively consider both the magnitude of the performance residual and the rationality of the adjustment direction to avoid adjustment deviations caused by a single indicator. This process is achieved by constructing a composite scoring function, which can simultaneously reflect the optimization degree of the performance residual and the accuracy of the adjustment direction, providing a quantitative basis for parameter adjustment.

[0080] The expression for the composite scoring function is: The selection and construction of each item are based on the logic of multi-objective optimization. The normalized value representing the performance residual is calculated using the following formula: ,in Let 2 be the norm of the current residual vector. The 2-norm of the initial residual vector is used to eliminate the influence of differences in the dimensions of different performance indices through normalization. The value range of is stable in the [0,1] interval. The smaller the value, the closer the performance of the current parameter combination is to the target index.

[0081] The deviation between the parameter adjustment direction and the target direction for optimal performance is deduced based on the cosine theorem of the angle between vectors. Let the current adjustment direction vector be... The theoretically optimal direction vector is (Determined by the ideal parameter-residual correlation model), the angle between the two vectors is Then the cosine value is The deviation value is defined as ,make Similarly, if the deviation falls within the [0,2] interval, the smaller the deviation value, the closer the adjustment direction is to the theoretical optimal path.

[0082] This is the deviation weighting coefficient, used to balance the influence of residual magnitude and directional accuracy. Mathematically, The value of must satisfy By constructing the Lagrange function ( , (where is the Lagrange multiplier) Solving for the constrained extrema, we know that when When the value is too small, the function may overemphasize reducing the residual value while neglecting the rationality of the direction, causing the adjustment to fall into a local optimum; when... If the value is too large, excessive focus on direction may slow down the rate of residual quantity reduction. Therefore, a small number of preliminary experiments are needed to determine the adjustment efficiency. The value is usually between 0.3 and 0.7.

[0083] In practical applications, calculations are performed separately for each candidate adjustment direction. , Substitute the value of into the composite scoring function to obtain the corresponding score value. The scores of all candidate directions are compared, and the direction with the lowest score is selected as the final adjustment direction for the key process parameters. This process balances residual optimization and directional accuracy through quantitative evaluation, enabling parameter adjustments to effectively reduce performance deviations while progressing along the optimal path, avoiding ineffective adjustments, and further improving the stability control efficiency of ceramic matrix composite material preparation.

[0084] In some implementations, when the process parameter subspace is a high-dimensional parameter space, a random sketch matrix is ​​introduced before performing the bi-subspace projection operation. Dimensionality reduction is performed on the process parameter subspace;

[0085] High-dimensional process parameter matrix Through random sketch matrix Projecting onto a lower-dimensional space yields a lower-dimensional parameter matrix. ;

[0086] Based on low-dimensional parameter matrix A low-dimensional projection matrix is ​​constructed, and the projection calculation of the performance residual is performed in the low-dimensional space. Then, the projection result in the low-dimensional space is mapped back to the original high-dimensional space to determine the adjustment direction of key process parameters.

[0087] When the process parameter subspace contains many types of parameters or has dense time-series nodes, the parameter matrix will exhibit high-dimensionality. Directly performing bi-subspace projection operations may significantly increase computational complexity and even lead to matrix invertibility. To address this issue, a random sketch matrix needs to be introduced before the projection operation to reduce the dimensionality of the high-dimensional process parameter subspace, simplifying the calculation process while preserving key information.

[0088] The selection of the random sketch matrix must satisfy the interval preservation condition. Typically, Gaussian random matrices or sparse random matrices are used, whose elements take values ​​according to a specific probability distribution. For example, the elements of a Gaussian random matrix have a mean of 0 and a variance of 1 / 2. normal distribution ( (where is the dimension of the low-dimensional space), ensuring that the matrix can establish a stable mapping relationship between the high-dimensional and low-dimensional spaces. According to the Johnson-Lindenstrauss lemma, for any given Given n points in a high-dimensional space, does there exist a path from the high-dimensional space to... A linear mapping in low-dimensional space (implemented by a random sketch matrix) such that the Euclidean distance between any two points is approximately preserved in low-dimensional space, i.e., it satisfies... ,in A random sketch matrix, , is an arbitrary vector in a high-dimensional space. The core derivation of this lemma is based on the concentration inequality of random variables. By calculating the expectation and variance of the distance after mapping, it can be proved that when , the distance-preserving property holds with high probability, ensuring that the low-dimensional space approximately preserves the geometric structure of the high-dimensional space.

[0089] The high-dimensional process parameter matrix (with dimensions n×d, where n is the number of timing nodes and d is the number of parameter types) is projected through a random sketch matrix (with dimensions ×n, and <<n, where "<< " means much less than) to obtain a low-dimensional parameter matrix with dimensions ×d. To verify the retention effect of the projection process on the parameter correlation information, the inner product relationship of the parameter vectors in the high-dimensional and low-dimensional spaces can be deduced by calculating: , when is a Gaussian random matrix, is approximately an identity matrix (the deviation term decreases as increases), so , indicating that the low-dimensional matrix can approximately retain the inner product information of the high-dimensional matrix, that is, the correlation characteristics between parameters are not significantly damaged.

[0090] Based on the low-dimensional parameter matrix , a low-dimensional projection matrix is constructed. The construction logic of this matrix is the same as that of the high-dimensional projection matrix . Its derivation also follows the geometric principle of orthogonal projection: the low-dimensional projection vector needs to satisfy that the error vector is orthogonal to the low-dimensional process parameter subspace, that is, . Combining can deduce . Due to the reduction of the dimension of the low-dimensional matrix, the calculation process is more efficient, and 's condition number is usually less than , and it is not easy to have matrix singularity problems.

[0091] The performance residual vector is projected onto the low-dimensional process parameter subspace to obtain a low-dimensional projection vector , which reflects the direction of parameter adjustment in the low-dimensional space. To obtain the adjustment direction in the high-dimensional space, the linear correspondence between the low-dimensional projection and the high-dimensional adjustment needs to be used: Let the high-dimensional adjustment vector be , and the low-dimensional adjustment vector be . From can deduce , when , Therefore, high-dimensional adjustment vectors can be obtained through Solve (when) (When it is a square matrix) or calculated through pseudo-inverse This ensures that it can accurately respond to changes in the original process parameters.

[0092] In practice, the dimensions of the low-dimensional space are first determined based on the dimensions of the high-dimensional parameter matrix. (Typically, 1 / 5 to 1 / 3 of the original dimension is taken) to generate the corresponding random sketch matrix. Substituting the high-dimensional process parameters collected in real time into the equation yields... The process involves calculating the low-dimensional projection matrix and completing the residual projection; then, the high-dimensional adjustment direction is obtained through the mapping relationship, and the process parameters are adjusted according to this direction. This dimensionality reduction process significantly reduces the computational load while effectively preserving the core correlation information between parameters and residuals, ensuring the accuracy of the adjustment direction, and enabling the control process in the high-dimensional parameter space to proceed efficiently.

[0093] In some implementations, the method for determining whether the performance residual meets the preset conditions in step S6 is as follows:

[0094] Calculate the residual performance change rate of the ceramic matrix composite material prepared in multiple consecutive preparations. If the residual performance change rate is less than the preset threshold and each residual performance is within the preset allowable range, the residual performance is determined to meet the preset conditions. If not, continue to execute the parameter adjustment and preparation process, and record the current residual performance and the corresponding process parameter combination.

[0095] Determining whether the performance residual meets the preset conditions requires considering both the dynamic trend and absolute value range of the residual to avoid bias caused by accidental fluctuations in a single test result. This process is based on performance residual data obtained from multiple consecutive preparations, and multi-dimensional analysis ensures that the final determined combination of process parameters can stably produce ceramic matrix composite materials that meet the target.

[0096] First, the number of consecutive tests used for judgment needs to be determined. The selection of the number of tests should cover the typical fluctuation cycle of ceramic matrix composite material preparation, such as batch differences in raw materials and minor changes in equipment operating status, which may affect performance. Typically, performance data from 3 to 5 consecutive preparations are selected to balance judgment accuracy and control efficiency. This continuous... The performance residual of the sequence is denoted as the sequence. ,in For the first The performance residual vectors are prepared in this way. The rate of change of performance residuals is calculated for these continuous data. Specifically, the 2-norm difference between two adjacent residual vectors is compared with the 2-norm of the previous residual vector to obtain the rate of change for each iteration. (Take the absolute value), where This is the 2-norm of the residual vector, reflecting the overall size of the residual. The rate of change for each consecutive iteration must be less than a preset threshold. That is, satisfying , , ..., The threshold The threshold is set based on the stability requirements of the material properties. If the material is used in high-precision scenarios, the threshold needs to be set smaller in order to strictly control performance fluctuations.

[0097] Simultaneously, it is necessary to check whether the absolute values ​​of the performance residuals for each iteration are within the preset allowable range. The determination of the allowable range is directly related to the target stability index, using the upper limit threshold of the residual norm. This means that it must meet the following requirements. ( For example, the allowable range of residual mechanical strength. The allowable range of residual thermal stability must correspond to the acceptable strength fluctuation range in practical applications, and must match the temperature change requirements of the operating environment. The allowable range of residual microstructural parameters must ensure that there are no significant defects within the material. Only when continuous... The residual change rate was less than the threshold for each time. and all residual norms All fell into Only when the interval is reached can it be determined that the performance residual meets the preset conditions.

[0098] If the above conditions are not met, the parameter adjustment and preparation process must continue. After each adjustment, the current performance residual vector, the corresponding combination of process parameters, and environmental variables during the preparation process (such as room temperature, humidity, and other factors that may affect the results) must be recorded in detail. This recorded data is not only used for the next residual calculation but also for subsequent optimization of threshold judgment. With the permitted range This provides a basis for judgment, allowing the entire judgment process to be continuously improved as preparation experience accumulates.

[0099] This judgment method based on continuous data can effectively filter out accidental interference in a single preparation, accurately capture the stable trend of performance residuals, ensure that the final determined combination of process parameters has continuous stability, avoid performance rebound caused by premature termination of control, and provide a reliable guarantee for the stable batch preparation of ceramic matrix composites.

[0100] In some implementations, if the performance residual continues to increase or there is no effective parameter adjustment direction during the execution of steps S5 to S6, a backtracking correction mechanism is initiated.

[0101] Revert to the last valid combination of process parameters and mark the current range of process parameters as invalid.

[0102] Based on the effective combination of process parameters after the return, steps S3 to S4 are repeated to determine the new direction of adjustment of key process parameters, and then the ceramic matrix composite material is prepared according to the new adjustment direction.

[0103] During the iterative process of parameter adjustment and fabrication, abnormal changes in performance residuals may occur. In such cases, a backtracking correction mechanism needs to be activated to prevent the control process from falling into an invalid loop. A continuous increase in performance residuals is typically manifested as an increasing trend in the 2-norm of the residual vector after multiple consecutive fabrications. This can be defined using quantitative standards: assuming continuous... The residual norm of the second preparation is , ,..., If satisfied (in The preset increase threshold is determined based on the maximum increase in normal fluctuations in historical data, typically ranging from 0.1 to 0.3. If the residual value continues to increase, it is determined that the residual value is continuously increasing. This situation indicates that the current parameter adjustment direction deviates from the performance optimization target. If the adjustment continues in this direction, the material performance will deviate further from the target index.

[0104] The absence of effective parameter adjustment direction is manifested in the extremely small magnitude of the projection vector obtained through the bispace projection operation, i.e. ( This is a minimum threshold, set based on the minimum effective amount of parameter adjustment (such as the minimum adjustable ratio of raw material proportions, the minimum controllable precision of temperature, etc.), or the score values ​​of multiple candidate adjustment directions differ only slightly and are all at a high level. ( The difference threshold (reflecting the resolution accuracy of the scoring function) indicates that adjustments within the current process parameter subspace cannot effectively reduce performance residuals, and the parameter search range needs to be replanned.

[0105] When initiating the backtracking correction mechanism, the first step is to determine the previous effective combination of process parameters. This combination must satisfy the condition that, during its corresponding preparation process, the residual performance is either declining or stable within a reasonable range, meaning there exists a specific time point. , making and ( (This refers to the upper limit of the allowable residual amount), and the material properties show a clear improvement after parameter adjustment. The current process parameter range is marked as an invalid region, which can be represented as... ,in , The first The minimum and maximum values ​​of key process parameters within the invalid range, such as the ratio range of raw material proportions and the fluctuation range of sintering temperature, are used to avoid re-entering this range during subsequent adjustments and reduce invalid attempts.

[0106] Based on the returned effective process parameter combination, material property data under this combination is re-acquired and substituted into the residual solution model to calculate the performance residual. This ensures that the residual data accurately reflects the gap between the current parameters and the target. Subsequently, the bi-space projection calculation is re-executed, utilizing the updated process parameter matrix. Constructing the projection matrix , to the new residual vector Projecting onto the process parameter subspace to determine the direction of adjustment for new key process parameters. The determination of new directions needs to be combined with the marking results of invalid regions, and the search range of parameter adjustment should be appropriately expanded. For example, when adjusting the raw material ratio, try ratio combinations that exceed the original range, or when adjusting the sintering temperature, change auxiliary parameters such as the heating rate to break through the limitations of the original invalid region.

[0107] After preparing the ceramic matrix composite material according to the newly determined adjustment direction, the material properties were tested again and the residual weight was calculated to observe the trend of residual weight change. If the residual weight begins to decrease and the adjustment direction is effective, that is... If an anomaly persists, the iteration continues; if anomalies still occur, the backtracking correction process is repeated until an effective parameter adjustment path is found. This mechanism can promptly correct deviations in the control process, ensuring that the entire preparation process always progresses towards the goal of performance optimization by avoiding invalid parameter ranges and replanning the adjustment direction, thus maintaining the effectiveness and stability of the control.

[0108] In some implementations, when constructing the time-varying process-performance bipartite space, a time-varying correlation model is established using matrix equations, where the matrix equations are: ,in This is a time-varying correlation matrix of process parameters, where each element corresponds to the correlation strength of different key process parameters in the preparation time sequence. This is a vector of process parameters for each time node, where each element represents the specific value of a key process parameter at the corresponding time node. This is the performance residual vector corresponding to the time node, and its elements are the specific values ​​of each performance deviation in the performance residual quantum space at the corresponding time node;

[0109] By solving the matrix equations, the quantitative correlation between the changes in key process parameters with the preparation time and the changes in performance residuals is obtained. Based on this quantitative correlation, a time-varying process-performance bi-subspace is constructed.

[0110] When constructing a time-varying process-performance bipartite space, it is necessary to fully reflect the dynamic correlation between process parameters and performance residuals as the fabrication time sequence changes. Matrix equations are an effective tool for modeling this correlation. This process requires first clarifying the composition of each matrix in the equation, and then establishing quantitative relationships through data fitting and solving, so that the bipartite space can accurately reflect the parameter-performance interaction patterns at different fabrication stages.

[0111] Matrix equations In this context, the elements of each matrix must correspond to specific physical meanings and be determined through quantitative derivation. (Time-varying correlation matrix) elements Indicates the first Class of process parameters and the first Class performance residual at time-series nodes The correlation strength is derived by calculating the time-series correlation between the two: Let the process parameters... In time sequence The value sequence is , performance residual The sequence is ,but Covariance ,variance , , These are the mean values ​​of process parameters and performance residuals, respectively. This derivation is based on the principle of linear regression, making... This is precisely the regression coefficient of performance residual on process parameters, quantifying the influence of a single process parameter on performance residual.

[0112] Process parameter vector elements For the first Key process parameters at timing nodes The actual values, encompassing parameters such as raw material ratios and sintering temperature that change over time, must be recorded sequentially according to the preparation stage (e.g., mixing, sintering, cooling). Performance residual vector elements Then it is the first Performance indicators (such as flexural strength and porosity) at time nodes The residual value is determined by the difference between the actual detected value and the target value, i.e. .

[0113] To solve the matrix equations and establish a global quantitative correlation, an overdetermined system of equations needs to be constructed based on multiple sets of time-series data. Assuming N time-series data points are collected, then... , , ..., The system of equations is solved using the least squares method, i.e., minimizing the sum of squared residuals. .right about Taking the partial derivative and setting it to zero, the derivation process is as follows: Organized Finally, the optimal estimate of the time-varying correlation matrix is ​​obtained. .

[0114] This solution ensures that at each time node... Above, the local correlation between parameters and residuals satisfies At its minimum, by integrating these local relationships, the time-varying correlation law of the entire domain can be obtained, and the changes of key process parameters at different stages can be clearly identified (such as the sintering temperature from...). arrive The increase value ) and the change in performance residual (such as the decrease in strength residual) Quantitative correspondence between ) for example, when When, it indicates the parameter For every unit change, the residual The corresponding change is 0.8 units, that is .

[0115] In practical applications, process parameters and performance data need to be continuously collected according to the preparation sequence, and the element values ​​in the matrix equation need to be updated periodically so that the correlation model can adapt to the dynamic changes in the material preparation process. Through this time-varying matrix modeling method, the constructed process-performance bipartite space can reflect the influence weight of parameters at different stages in real time, providing a more accurate temporal correlation basis for subsequent projection calculations and parameter adjustments. This ensures that appropriate adjustment strategies can be adopted at different stages such as raw material reaction and grain growth, further improving the timing control accuracy of ceramic matrix composite material preparation.

[0116] In some implementations, during the iteration process of steps S3 to S6, linear convergence of the performance residual is achieved through bi-subspace projection operations;

[0117] After each iteration, the performance residual satisfies ,in For the first Performance residual of the next iteration For the first Performance residual of the next iteration is the convergence factor and ;

[0118] Through multiple iterations, the performance residual is continuously reduced until the preset conditions are met. The iteration is then stopped, and the combination of process parameters at this point is used as the combination of process parameters for the stable preparation of ceramic matrix composites.

[0119] In the iterative process of preparing ceramic matrix composites, bispace projection operations provide clear mathematical support for the convergence of performance residuals, enabling the residuals to gradually decrease according to a linear law and eventually approach the ideal range. Each iteration follows the process of parameter adjustment, material preparation, performance testing, and residual calculation. The projection operation ensures that each round of adjustment can specifically reduce performance deviations and form a stable convergence trend.

[0120] The linear convergence characteristic of the performance residual can be verified through mathematical derivation, based on the orthogonality principle of projection operations and the residual decomposition law. Let the th... The performance residual of the next iteration is The process parameter matrix is The projection matrix is .Will Decomposed into projected components within the process parameter subspace Components orthogonal to the subspace Because orthogonality is satisfied According to the Pythagorean theorem, the norm relationship can be obtained as follows: .

[0121] After determining the parameter adjustment direction through bispace projection calculation, the parameters are adjusted and the first... The residual of the next iteration Due to the adjustment of direction and Consistency can be proven Orthogonal to the process parameter subspace, i.e. ,therefore It belongs to the orthogonal component space and satisfies ( As a correction term, its norm is much smaller than Approximately .

[0122] To derive the linear convergence relation, a convergence factor is introduced. From the norm relation, we know that ,and Combining the eigenvalue properties of the projection matrix (whose eigenvalues ​​are either 0 or 1), we can obtain ,in , They are respectively Minimum and maximum eigenvalues ​​(condition numbers) Substituting into the norm relation, we get: After taking the square root, we can obtain ,make ,but And it satisfies the linear convergence relation: .

[0123] To verify the practical effectiveness of the above linear convergence properties, combined with Figure 3 (Comparison of convergence curves for random overdetermined matrices) It can be seen that: the vertical axis In the trend of the logarithm of the residual squared error as a function of the number of iterations (IT) on the horizontal axis, our method (corresponding to the iterative logic of bi-subspace projection) shows a stable linear decay trend in the residuals for matrix sizes of 40000×30000 and 100000×30000, and the convergence rate is significantly better than that of PRTK (different... This experimental result directly demonstrates that the theoretically derived linear convergence characteristics of iterative control based on bi-space projection have practical engineering effectiveness in the residual optimization process, ensuring that multiple iterations can efficiently reduce the performance residual and promote the stable convergence of material properties towards the target index.

[0124] During multiple iterations, each parameter adjustment is based on the direction determined by the projection operation, ensuring that the residual continuously converges to zero. As the number of iterations increases, the norm of the performance residual gradually decreases, i.e. ( (As the initial residual), the gap between the actual material properties and the target stability index continues to narrow. When the residual meets the preset conditions (such as...) , When the allowable residual threshold is reached, the iteration process is stopped. At this point, the combination of process parameters has been optimized through multiple rounds, and the material properties are now stably aligned with the target indicators.

[0125] This iterative control method based on linear convergence can orderly reduce performance deviations, avoid repeated fluctuations during the adjustment process, and ensure that the final determined combination of process parameters has the ability to stably prepare ceramic matrix composites, thus providing a reliable guarantee for the consistency of material properties.

[0126] The above description is merely a preferred embodiment and the technical principles employed in this application. This application is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions that can be made by those skilled in the art will not depart from the scope of protection of this application. Therefore, although this application has been described in detail through the above embodiments, this application is not limited to the above embodiments, and may include more other equivalent embodiments without departing from the concept of this application, the scope of which is determined by the scope of the claims.

Claims

1. A method for preparing and controlling residual biplane projection, characterized in that, Includes the following steps: S1: Construct a time-varying process-performance bispace, which includes a process parameter subspace and a performance residual quantum space. The process parameter subspace consists of key process parameters that affect the stability of ceramic matrix composites, and the performance residual quantum space consists of the deviation between the actual performance of ceramic matrix composites and the target stability index. S2: Based on the time-varying process-performance bispace, a residual solution model is constructed, which is used to solve for the performance residual in the performance residual quantum space; S3: Using the residual solution model, calculate the performance residuals at each time point in the preparation process of ceramic matrix composites; S4: Based on the performance residual, determine the adjustment direction of key process parameters in the process parameter subspace through dual subspace projection calculation; S5: Adjust the key process parameters according to the adjustment direction to prepare ceramic matrix composite materials, and test the actual performance of the prepared ceramic matrix composite materials; S6: Repeat steps S3 to S5 until the performance residual meets the preset conditions, obtain a stable combination of process parameters for preparing ceramic matrix composite materials, and complete the regulation.

2. The preparation and control method based on residual binary space projection according to claim 1, characterized in that, In step S1, The process parameter subspace is constructed as follows: key process parameters that affect the stability of ceramic matrix composites are selected, including raw material ratio parameters, sintering process parameters and post-treatment process parameters. The key process parameters are constructed into a process parameter subspace that dynamically changes with the preparation stage according to the preparation sequence. The residual quantum space of the performance is constructed as follows: a target stability index for the ceramic matrix composite material is set, which includes a mechanical stability index, a thermal stability index, and a microstructure stability index; the deviation between the actual performance of the ceramic matrix composite material and the target stability index is calculated; and the residual quantum space of the performance is constructed based on the deviation.

3. The preparation and control method based on residual binary space projection according to claim 1, characterized in that, In step S2, the residual solution model is a residual nullification neural network model, and the residual nullification neural network model is constructed as follows: Using the combination of key process parameters in the process parameter subspace as input and the performance residual vector in the performance residual quantum space as output, an error function is constructed. ,in This is the predicted residual vector of the residual nullification neural network model. The actual performance residual vector is obtained by driving the error function to converge to zero.

4. The preparation and control method based on residual binary space projection according to claim 3, characterized in that, In step S4, the specific implementation of the bi-subspace projection operation is as follows: S41: Project the performance residual vector onto the process parameter subspace to construct a projection matrix. ,in This is the parameter matrix of the process parameter subspace; S42: Calculate the projection vector of the performance residual in the process parameter subspace using the projection matrix, and determine the adjustment direction of the key process parameter based on the projection vector. The adjustment direction is the parameter change direction that minimizes the performance residual.

5. The preparation and control method based on residual binary space projection according to claim 4, characterized in that, When determining the adjustment direction of key process parameters based on the projection vector, a composite scoring function is constructed. ,in This is the normalized value of the performance residual. The deviation between the parameter adjustment direction and the target direction for optimal performance. This is the deviation weighting coefficient; Calculate the score value corresponding to each candidate adjustment direction, and select the candidate adjustment direction with the smallest score value as the final adjustment direction of the key process parameter.

6. The preparation and control method based on residual binary space projection according to claim 4, characterized in that, When the process parameter subspace is a high-dimensional parameter space, a random sketch matrix is ​​introduced before performing the bi-subspace projection operation. The process parameter subspace is subjected to dimensionality reduction processing; High-dimensional process parameter matrix Through the random sketch matrix Projecting onto a lower-dimensional space yields a lower-dimensional parameter matrix. ; Based on the low-dimensional parameter matrix A low-dimensional projection matrix is ​​constructed, and the projection operation of the performance residual is performed in the low-dimensional space. Then, the projection result in the low-dimensional space is mapped back to the original high-dimensional space to determine the adjustment direction of the key process parameters.

7. The preparation and control method based on residual binary space projection according to claim 1, characterized in that, In step S6, the method for determining whether the performance residual meets the preset conditions is as follows: Calculate the residual performance change rate of the ceramic matrix composite material prepared in multiple consecutive preparations. If the residual performance change rate is less than a preset threshold and each residual performance is within a preset allowable range, then the residual performance is determined to meet the preset condition. If the requirements are not met, continue with the parameter adjustment and preparation process, and record the current performance residual and the corresponding combination of process parameters.

8. The preparation and control method based on residual biplane projection according to claim 1, characterized in that, If, during the execution of steps S5 to S6, the performance residual continues to increase or there is no effective parameter adjustment direction, the backtracking correction mechanism will be activated. Revert to the last valid combination of process parameters and mark the current range of process parameters as invalid. Based on the effective combination of process parameters after the return, steps S3 to S4 are repeated to determine the new direction of adjustment of key process parameters, and then the ceramic matrix composite material is prepared according to the new adjustment direction.

9. The preparation and control method based on residual binary space projection according to claim 2, characterized in that, When constructing the time-varying process-performance bipartite space, a time-varying correlation model is established using matrix equations, wherein the matrix equations are as follows: ,in This is a time-varying correlation matrix of process parameters, where each element corresponds to the correlation strength of different key process parameters in the preparation time sequence. This is a vector of process parameters for each time node, where each element represents the specific value of the key process parameter at the corresponding time node. This is the performance residual vector corresponding to the time node, and its elements are the specific values ​​of each performance deviation in the performance residual quantum space at the corresponding time node; By solving the matrix equation, a quantitative correlation is obtained between the changes in key process parameters with the preparation time and the changes in performance residuals. Based on this quantitative correlation, the time-varying process-performance bipartite space is constructed.

10. The preparation and control method based on residual binary space projection according to claim 1, characterized in that, During the iteration process from steps S3 to S6, the linear convergence of the performance residual is achieved through the bi-subspace projection operation; After each iteration, the performance residual satisfies ,in For the first Performance residual of the next iteration For the first Performance residual of the next iteration is the convergence factor and ; The performance residual is continuously decayed through multiple iterations until a preset condition is met. The iteration is then stopped, and the combination of process parameters at this point is used as the combination of process parameters for the stable preparation of ceramic matrix composite materials.

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