A method for optimizing parameters of methylal three-tower rectification

Abstract

The application provides a method for optimizing parameters of methylal three-tower rectification, which comprises the following steps: collecting rectification parameters to be optimized, sampling and constructing an initial candidate set, obtaining corresponding product purity and total energy consumption, and constructing a statistical covariance matrix; combining parameter comprehensive sensitivity to generate a weight matrix, and obtaining a corrected covariance matrix through element-by-element multiplication; performing matrix eigenvalue decomposition, estimating dimensionless gradients of two groups of performance indexes, solving characteristic vector gradient projection, comprehensive contribution degree and target synergy index, and completing descending order sorting of the characteristic vectors; selecting front characteristic vectors to build a dimension reduction mapping matrix, iteratively optimizing along a compliance synergy direction in a low-dimensional orthogonal space, mapping back to the original parameter space, and outputting a rectification optimal parameter combination.

Description

Technical Field

[0001] This application belongs to the field of methyl acetal, and particularly relates to a method for optimizing the parameters of a three-tower distillation of methyl acetal. Background Technology

[0002] Methylal is an important chemical solvent and intermediate. Its separation and purification after industrial synthesis typically rely on a three-tower distillation process. In the three-tower distillation of methylal, product purity and total system energy consumption are key indicators for evaluating production efficiency. These two indicators are influenced by various process parameters, including feed flow rate, reflux ratio, operating pressure, and reboiler heating, and complex nonlinear coupling relationships exist between these parameters. Due to the high dimensionality of the parameters to be optimized, traditional optimization algorithms incur significant computational overhead and are prone to getting trapped in local optima when searching in high-dimensional parameter spaces. To improve optimization efficiency, dimensionality reduction methods are commonly used in engineering, mapping the high-dimensional parameter space to a lower-dimensional space before iterative solving, thereby reducing computational complexity and improving convergence speed.

[0003] However, traditional orthogonal dimensionality reduction methods typically extract principal components based on the variance distribution characteristics of sample data, failing to fully consider the varying impacts of different process parameters on product purity and energy consumption. This type of dimensionality reduction, which is detached from parameter sensitivity, easily weakens or even omits key parameters that significantly affect the target indicators but have relatively small fluctuations. Furthermore, in the distillation process, improving product purity and reducing energy consumption are often mutually restrictive. Existing methods, when iteratively optimizing in low-dimensional space, struggle to accurately characterize the co-evolutionary relationship between different target gradient directions. Without targeted search guidance, the optimization process struggles to identify effective paths that balance improving product purity and controlling energy consumption, easily leading to optimization results that deviate from actual industrial production needs and making it difficult to obtain better parameter combinations. Summary of the Invention

[0004] According to a first aspect of the present invention, a method for optimizing parameters in a three-tower distillation system for methyl acetal is proposed to address the problem that existing methods lack the ability to accurately calculate the co-evolution relationship between different target gradient directions, comprising the following steps:

[0005] The parameters to be optimized in the three-tower distillation process of methyl acetal are obtained, an initial candidate parameter set is generated by sampling, and the product purity and total energy consumption corresponding to each parameter are obtained. The parameters to be optimized in each dimension of the initial candidate parameter set are dimensionless. A statistical covariance matrix is ​​constructed based on the dimensionless initial candidate parameter set. A preset weight matrix is ​​established based on the comprehensive sensitivity of the parameters to be optimized. The statistical covariance matrix and the preset weight matrix are multiplied element by element to obtain the modified covariance matrix. The modified covariance matrix is ​​decomposed into eigenvalues ​​and eigenvectors. Based on the initial candidate parameter set, the dimensionless gradient vectors of product purity and total energy consumption relative to the parameters to be optimized are estimated. The projection of each eigenvector onto the two dimensionless gradient vectors is calculated. When the projection of the eigenvector onto the dimensionless gradient vector of product purity is less than zero, the eigenvector is reversed and the two projections corresponding to the eigenvector are updated synchronously. The comprehensive contribution is calculated based on the projection and eigenvalue. The two projections are multiplied to obtain the target synergy index. The eigenvectors are sorted in descending order according to the comprehensive contribution. The first N eigenvectors are selected to form a dimension reduction mapping matrix. In the low-dimensional orthogonal space, the low-dimensional optimal solution is obtained by iteratively searching along the synergistic optimization direction where the target synergistic index is less than 0 and the projection of the eigenvector onto the dimensionless gradient vector of product purity is greater than 0. The low-dimensional optimal solution is then reconstructed to the original parameter space through the dimension reduction mapping matrix to obtain the optimal parameter combination.

[0006] Optionally, the step of dimensionlessly transforming the parameters to be optimized in each dimension of the initial candidate parameter set, and constructing a statistical covariance matrix based on the dimensionless initial candidate parameter set, includes: The parameters to be optimized in each dimension of the initial candidate parameter set are dimensionless, and the mean of each parameter sample after dimensionless processing is calculated to obtain the parameter mean vector. Calculate the deviation vector of each dimensionless parameter sample relative to the parameter mean vector, and multiply the deviation vector by its transpose to obtain the corresponding sample covariance matrix; The statistical covariance matrix is ​​obtained by summing the covariance matrices of all samples and dividing by the total number of samples in the initial candidate parameter set minus one.

[0007] Optionally, establishing a preset weight matrix based on the comprehensive sensitivity of the parameters to be optimized includes: The product purity, total energy consumption, and each parameter to be optimized are dimensionless. The absolute value of the first partial derivative of the i-th dimensionless parameter to be optimized with respect to the dimensionless product purity and the absolute value of the second partial derivative with respect to the dimensionless total energy consumption are calculated respectively. The absolute values ​​of the first and second partial derivatives are summed to obtain the sensitivity value of the i-th parameter to be optimized. Multiply the sensitivity value of the i-th parameter to be optimized by the sensitivity value of the j-th parameter to be optimized, and assign the resulting product to the element in the i-th row and j-th column of the preset weight matrix.

[0008] Optionally, estimating the dimensionless gradient vectors of product purity and total energy consumption relative to the parameters to be optimized based on the initial candidate parameter set includes: Based on the initial candidate parameter set, construct the independent variable matrix, and perform least squares regression with the product purity measurement vector and the total energy consumption measurement vector as the dependent variable vector respectively to obtain the partial regression coefficient vector corresponding to product purity and the partial regression coefficient vector corresponding to total energy consumption. Extract the coefficients of the linearly correlated variables from the partial regression coefficient vector corresponding to the product purity and the partial regression coefficient vector corresponding to the total energy consumption, respectively, and construct the gradient vector of product purity relative to the parameter to be optimized and the gradient vector of total energy consumption relative to the parameter to be optimized. The gradient vectors of product purity and total energy consumption relative to the parameters to be optimized are made dimensionless to obtain dimensionless gradient vectors of product purity and total energy consumption relative to the parameters to be optimized.

[0009] Optionally, the calculation of the projection of each feature vector onto the two dimensionless gradient vectors, when the projection of a feature vector onto the dimensionless gradient vector of product purity is less than zero, involves reverse processing of the feature vector and synchronously updating the two projections corresponding to the feature vector. The comprehensive contribution is calculated based on the projections and eigenvalues, including: The projections of the normalized eigenvectors onto the dimensionless gradient vector of product purity and the dimensionless gradient vector of total energy consumption are calculated to obtain the first projection and the second projection. When the first projection is less than zero, the feature vector is reversed and the corresponding first and second projections are recalculated. The square of the first projection is multiplied by a preset product purity weight constant to obtain a first product, and the square of the second projection is multiplied by a preset total energy consumption weight constant to obtain a second product. The sum of the first product and the second product is multiplied by the eigenvalue corresponding to the eigenvector to obtain the comprehensive contribution.

[0010] Optionally, selecting the first N feature vectors to construct the dimensionality reduction mapping matrix includes: The top N feature vectors, sorted in descending order of comprehensive contribution, are used as column vectors and horizontally concatenated in sequence to construct a two-dimensional matrix as a dimension reduction mapping matrix. The number of rows in the two-dimensional matrix is ​​the number of the original spatial dimensions of the parameters to be optimized, and the number of columns in the two-dimensional matrix is ​​the number of the orthogonal spatial dimensions after dimension reduction.

[0011] Optionally, the step of reconstructing the low-dimensional optimal solution to the original parameter space through a dimensionality-reduction mapping matrix to obtain the optimal parameter combination includes: The low-dimensional optimal solution is mapped to the dimensionless parameter space through a dimension reduction mapping matrix, and then added to the parameter mean vector of the dimensionless initial candidate parameter set to obtain the dimensionless parameter vector. According to the dimensionless transformation rules of the parameters to be optimized in each dimension, the dimensionless parameter vector is mapped back to the original parameter space. When the parameters obtained by reverse mapping are discrete parameters, they are rounded or mapped according to the preset discrete value set to obtain the optimal parameter combination.

[0012] Optionally, the step of obtaining the parameters to be optimized in the three-tower distillation process of methyl acetal and sampling to generate an initial candidate parameter set includes: Obtain the constraint boundary of the three-tower distillation process of methyl acetal, and generate an initial candidate parameter set based on Latin hypercube sampling.

[0013] Optionally, the step of iteratively searching for the low-dimensional optimal solution in the low-dimensional orthogonal space along the collaborative optimization direction corresponding to the target collaborative index being less than 0 and the projection of the feature vector onto the dimensionless gradient vector of product purity being greater than 0 includes: The initial search step size is set according to the comprehensive contribution of the eigenvectors corresponding to each orthogonal axis, and the initial search step size is decreased with the number of iterations. Iterative search is performed along the collaborative optimization direction where the target collaborative index is less than 0 and the projection of the feature vector onto the dimensionless gradient vector of product purity is greater than 0. When the change in coordinates of a search point on a certain orthogonal axis is less than the convergence threshold, the coordinate value of that orthogonal axis is locked, and the search continues for the remaining unlocked orthogonal axes until a low-dimensional optimal solution is obtained.

[0014] According to a second aspect of the present invention, a three-tower distillation parameter optimization system for methyl acetal is provided, comprising the following modules: The module is used to obtain the parameters to be optimized in the three-tower distillation process of methyl acetal, sample and generate an initial candidate parameter set, and obtain the product purity and total energy consumption corresponding to each parameter. The parameters to be optimized in each dimension of the initial candidate parameter set are dimensionless. A statistical covariance matrix is ​​constructed based on the dimensionless initial candidate parameter set. A preset weight matrix is ​​established based on the comprehensive sensitivity of the parameters to be optimized. The statistical covariance matrix and the preset weight matrix are multiplied element by element to obtain the modified covariance matrix. The calculation module is used to perform eigenvalue decomposition on the modified covariance matrix to obtain eigenvalues ​​and eigenvectors. Based on the initial candidate parameter set, it estimates the dimensionless gradient vectors of product purity and total energy consumption relative to the parameters to be optimized. It calculates the projection of each eigenvector onto the two dimensionless gradient vectors. When the projection of an eigenvector onto the dimensionless gradient vector of product purity is less than zero, the eigenvector is reversed and the two projections corresponding to the eigenvector are updated synchronously. The comprehensive contribution is calculated based on the projection and eigenvalue. The two projections are multiplied to obtain the target synergy index. The eigenvectors are sorted in descending order based on the comprehensive contribution. The reconstruction module is used to select the first N feature vectors to form a dimension reduction mapping matrix. In the low-dimensional orthogonal space, it iteratively searches along the collaborative optimization direction corresponding to the target collaborative index being less than 0 and the projection of the feature vector onto the dimensionless gradient vector of product purity being greater than 0 to obtain the low-dimensional optimal solution. The low-dimensional optimal solution is then reconstructed to the original parameter space through the dimension reduction mapping matrix to obtain the optimal parameter combination.

[0015] Preferably, the step of dimensionlessly transforming the parameters to be optimized in each dimension of the initial candidate parameter set, and constructing a statistical covariance matrix based on the dimensionlessly transformed initial candidate parameter set, includes: The parameters to be optimized in each dimension of the initial candidate parameter set are dimensionless, and the mean of each parameter sample after dimensionless processing is calculated to obtain the parameter mean vector. Calculate the deviation vector of each dimensionless parameter sample relative to the parameter mean vector, and multiply the deviation vector by its transpose to obtain the corresponding sample covariance matrix; The statistical covariance matrix is ​​obtained by summing the covariance matrices of all samples and dividing by the total number of samples in the initial candidate parameter set minus one.

[0016] Preferably, the step of establishing a preset weight matrix based on the comprehensive sensitivity of the parameters to be optimized includes: The product purity, total energy consumption, and each parameter to be optimized are dimensionless. The absolute value of the first partial derivative of the i-th dimensionless parameter to be optimized with respect to the dimensionless product purity and the absolute value of the second partial derivative with respect to the dimensionless total energy consumption are calculated respectively. The absolute values ​​of the first and second partial derivatives are summed to obtain the sensitivity value of the i-th parameter to be optimized. Multiply the sensitivity value of the i-th parameter to be optimized by the sensitivity value of the j-th parameter to be optimized, and assign the resulting product to the element in the i-th row and j-th column of the preset weight matrix.

[0017] Preferably, estimating the dimensionless gradient vectors of product purity and total energy consumption relative to the parameters to be optimized based on the initial candidate parameter set includes: Based on the initial candidate parameter set, construct the independent variable matrix, and perform least squares regression with the product purity measurement vector and the total energy consumption measurement vector as the dependent variable vector respectively to obtain the partial regression coefficient vector corresponding to product purity and the partial regression coefficient vector corresponding to total energy consumption. Extract the coefficients of the linearly correlated variables from the partial regression coefficient vector corresponding to the product purity and the partial regression coefficient vector corresponding to the total energy consumption, respectively, and construct the gradient vector of product purity relative to the parameter to be optimized and the gradient vector of total energy consumption relative to the parameter to be optimized. The gradient vectors of product purity and total energy consumption relative to the parameters to be optimized are made dimensionless to obtain dimensionless gradient vectors of product purity and total energy consumption relative to the parameters to be optimized.

[0018] Preferably, the calculation of the projection of each feature vector onto the two dimensionless gradient vectors, when the projection of the feature vector onto the dimensionless gradient vector of product purity is less than zero, involves reverse processing of the feature vector and synchronously updating the two projections corresponding to the feature vector. The comprehensive contribution is calculated based on the projections and eigenvalues, including: The projections of the normalized eigenvectors onto the dimensionless gradient vector of product purity and the dimensionless gradient vector of total energy consumption are calculated to obtain the first projection and the second projection. When the first projection is less than zero, the feature vector is reversed and the corresponding first and second projections are recalculated. The square of the first projection is multiplied by a preset product purity weight constant to obtain a first product, and the square of the second projection is multiplied by a preset total energy consumption weight constant to obtain a second product. The sum of the first product and the second product is multiplied by the eigenvalue corresponding to the eigenvector to obtain the comprehensive contribution.

[0019] Preferably, the step of selecting the first N feature vectors to construct the dimensionality reduction mapping matrix includes: The top N feature vectors, sorted in descending order of comprehensive contribution, are used as column vectors and horizontally concatenated in sequence to construct a two-dimensional matrix as a dimension reduction mapping matrix. The number of rows in the two-dimensional matrix is ​​the number of the original spatial dimensions of the parameters to be optimized, and the number of columns in the two-dimensional matrix is ​​the number of the orthogonal spatial dimensions after dimension reduction.

[0020] Preferably, the step of reconstructing the low-dimensional optimal solution to the original parameter space through a dimension reduction mapping matrix to obtain the optimal parameter combination includes: The low-dimensional optimal solution is mapped to the dimensionless parameter space through a dimension reduction mapping matrix, and then added to the parameter mean vector of the dimensionless initial candidate parameter set to obtain the dimensionless parameter vector. According to the dimensionless transformation rules of the parameters to be optimized in each dimension, the dimensionless parameter vector is mapped back to the original parameter space. When the parameters obtained by reverse mapping are discrete parameters, they are rounded or mapped according to the preset discrete value set to obtain the optimal parameter combination.

[0021] Preferably, the step of obtaining the parameters to be optimized in the three-tower distillation process of methyl acetal and sampling to generate an initial candidate parameter set includes: Obtain the constraint boundary of the three-tower distillation process of methyl acetal, and generate an initial candidate parameter set based on Latin hypercube sampling.

[0022] Preferably, the step of iteratively searching for the low-dimensional optimal solution in the low-dimensional orthogonal space along the collaborative optimization direction corresponding to a target collaborative index less than 0 and a projection of the feature vector onto the dimensionless gradient vector of product purity greater than 0 includes: The initial search step size is set according to the comprehensive contribution of the eigenvectors corresponding to each orthogonal axis, and the initial search step size is decreased with the number of iterations. Iterative search is performed along the collaborative optimization direction where the target collaborative index is less than 0 and the projection of the feature vector onto the dimensionless gradient vector of product purity is greater than 0. When the change in coordinates of a search point on a certain orthogonal axis is less than the convergence threshold, the coordinate value of that orthogonal axis is locked, and the search continues for the remaining unlocked orthogonal axes until a low-dimensional optimal solution is obtained.

[0023] This invention constructs a modified covariance matrix by combining the comprehensive sensitivity and statistical covariance matrix of the parameters to be optimized, representing the fusion relationship between various parameters in the distillation process and their degree of influence on key indicators. Utilizing eigenvalue decomposition technology, and combining the dimensionless gradient vectors of product purity and total energy consumption, the projection of eigenvectors is calculated to obtain the comprehensive contribution and target synergy index, identifying the synergistic change patterns among multiple objectives and achieving the extraction and scientific ranking of high-dimensional parameter features. By selecting high-quality eigenvectors to construct a dimensionality-reduced mapping matrix, iterative searches are performed along specific synergistic optimization directions in a low-dimensional orthogonal space, solving the curse of dimensionality problem faced by traditional high-dimensional optimization and improving the search efficiency and solution accuracy of parameter optimization. The reconstructed optimal parameter combination can reduce the total energy consumption of the system while ensuring the purity of the methylal product, improving the overall economic efficiency and operational performance of the distillation process. Attached Figure Description

[0024] Figure 1 A flowchart of the first embodiment; Figure 2 This is a scatter plot of Latin hypercube sampling. Detailed Implementation

[0025] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0026] In the first embodiment, the present invention proposes a method for optimizing the parameters of a three-tower distillation system for methyl acetal, such as... Figure 1 It includes the following steps: S1. Obtain the parameters to be optimized in the three-tower distillation process of methyl acetal, sample and generate an initial candidate parameter set, and obtain the product purity and total energy consumption corresponding to each parameter. Perform dimensionless processing on the parameters to be optimized in each dimension of the initial candidate parameter set. Construct a statistical covariance matrix based on the dimensionless initial candidate parameter set. Establish a preset weight matrix based on the comprehensive sensitivity of the parameters to be optimized. Multiply the statistical covariance matrix and the preset weight matrix element by element to obtain the corrected covariance matrix.

[0027] A steady-state simulation system for three-tower distillation of methylal was established using chemical process simulation software. The three towers include a light component removal tower, a methylal product tower, and a heavy component removal tower. Multiple parameters related to each tower, such as feed location, reflux ratio, top pressure, and reboiler heating, were selected as parameters to be optimized, and corresponding upper and lower limits were set. Spatially uniform sampling was performed within these limits to generate an initial candidate parameter set containing multiple parameter combinations. Each parameter combination from the initial candidate parameter set was input into the steady-state simulation system and run until convergence. The methylal mass fraction in the simulation results was extracted as the product purity. The sum of the absolute values ​​of the condenser heat load and the reboiler heat load of the three distillation towers was extracted as the total energy consumption. When the condenser heat load output by the chemical process simulation software was negative, its absolute value was taken before being added to the total energy consumption. The parameters to be optimized in each dimension of the initial candidate parameter set are dimensionless, and the column mean is subtracted from each column to achieve zero mean. The covariance between each pair of the dimensionless parameter sequences is calculated to generate a statistical covariance matrix. For each parameter to be optimized, small positive and negative perturbation steps are applied to the initial set value, and the simulation is run again, recording the changes in product purity and total energy consumption. The absolute values ​​of the rate of change of product purity and the rate of change of total energy consumption are weighted and summed to obtain the comprehensive sensitivity of each parameter to be optimized. The comprehensive sensitivities of each parameter to be optimized are multiplied pairwise to construct a preset weight matrix with the same dimensions as the statistical covariance matrix. The elements in the same position of the statistical covariance matrix and the preset weight matrix are multiplied element-wise to complete the Hadamard product operation, resulting in a modified covariance matrix that enhances the characteristics of the high-sensitivity parameters.

[0028] In an optional embodiment, the step of dimensionlessly transforming the parameters to be optimized in each dimension of the initial candidate parameter set, and constructing a statistical covariance matrix based on the dimensionless initial candidate parameter set, includes: The parameters to be optimized in each dimension of the initial candidate parameter set are dimensionless, and the mean of each parameter sample after dimensionless processing is calculated to obtain the parameter mean vector. Calculate the deviation vector of each dimensionless parameter sample relative to the parameter mean vector, and multiply the deviation vector by its transpose to obtain the corresponding sample covariance matrix; The statistical covariance matrix is ​​obtained by summing the covariance matrices of all samples and dividing by the total number of samples in the initial candidate parameter set minus one.

[0029] The optimization parameters for the three-column distillation process of methylal are defined as having dimension D, for example, D=6, including the reflux ratio of the first column and the reboiler heating amount of the second column. The initial candidate parameter set generated by sampling contains M samples, for example, M=100. The arithmetic mean of these 100 D-dimensional column vectors is calculated, i.e., the sum of the values ​​of all samples in each dimension is divided by 100, resulting in a 6×1 parameter mean vector. For each initial candidate parameter sample, the parameter mean vector is subtracted from the sample, resulting in a 6×1 difference vector. This difference vector is multiplied by its transpose, resulting in a 1×6 row vector, and matrix multiplication yields a 6×6 sample covariance matrix.

[0030] The 6×6 sample covariance matrices corresponding to all 100 samples are summed element-wise to obtain a total deviation matrix. Each element in this deviation matrix is ​​then divided by the total number of samples minus one, i.e., M-1=99, to obtain a 6×6 statistical covariance matrix. The diagonal elements of this matrix represent the variance of each parameter, while the off-diagonal elements measure the degree of linear correlation between, for example, the reflux ratio of one tower and the heating amount of the second tower.

[0031] In an optional embodiment, establishing a preset weight matrix based on the comprehensive sensitivity of the parameters to be optimized includes: The product purity, total energy consumption, and each parameter to be optimized are dimensionless. The absolute value of the first partial derivative of the i-th dimensionless parameter to be optimized with respect to the dimensionless product purity and the absolute value of the second partial derivative with respect to the dimensionless total energy consumption are calculated respectively. The absolute values ​​of the first and second partial derivatives are summed to obtain the sensitivity value of the i-th parameter to be optimized. Multiply the sensitivity value of the i-th parameter to be optimized by the sensitivity value of the j-th parameter to be optimized, and assign the resulting product to the element in the i-th row and j-th column of the preset weight matrix.

[0032] The Min-Max normalization method is used to map product purity (e.g., from 99.5% to 99.9%) to 0 to 1, total energy consumption (e.g., from 500kW to 800kW) to 0 to 1, and various parameters to be optimized (e.g., the reflux ratio of the first distillation column from 1.2 to 2.5) to 0 to 1, scaling them to the [0,1] interval to remove dimension differences. The ratio of the change in dimensionless product purity to the amount of the disturbance when the dimensionless i-th parameter experiences a small perturbation (e.g., an increment of 0.01) is calculated. The absolute value of this ratio is taken as the absolute value of the first partial derivative, for example, 0.45. Similarly, the absolute value of the second partial derivative with respect to total energy consumption is calculated, for example, 0.35.

[0033] Adding the two absolute values ​​gives the sensitivity value of the i-th parameter, for example, 0.80. Repeating this calculation for all parameters to be optimized, multiply the sensitivity value of the i-th parameter (e.g., 0.80) by the sensitivity value of the j-th parameter (e.g., 0.60 for the second parameter). The product, 0.48, is assigned to the i-th row and j-th column of the preset weight matrix. This process is repeated to construct a 6×6 symmetric preset weight matrix. This matrix integrates the influence of parameters on product quality and energy consumption, ensuring that parameters with high sensitivity have a higher weight in the subsequent corrected covariance matrix.

[0034] In an optional embodiment, the step of obtaining the parameters to be optimized in the three-tower distillation process of methyl acetal and sampling to generate an initial candidate parameter set includes: Obtain the constraint boundary of the three-tower distillation process of methyl acetal, and generate an initial candidate parameter set based on Latin hypercube sampling.

[0035] Obtain the constraint boundaries of the three-tower distillation process of methylal, and define the upper and lower limits of the six parameters to be optimized. For example, the reflux ratio of the first tower is constrained in the range of [1.0, 3.0], and the reboiler heating capacity of the second tower is constrained in the range of [400kW, 600kW]. Set the required total number of sampling samples M, such as M=100. Based on the Latin hypercube sampling algorithm, divide the constraint interval of each parameter to be optimized into 100 non-overlapping equal probability sub-intervals.

[0036] Within each sub-interval of each parameter, a value is randomly selected. For discrete parameters such as feed location, the selection result is rounded or mapped according to a preset tray number set, and the mapped integer tray number is used as the candidate parameter value. The 100 sampled value sequences generated for each of these six parameter dimensions are randomly shuffled and combined to generate an initial candidate parameter set matrix of size 100×6, containing 100 independent samples, each with 6-dimensional features. The Latin hypercube sampling results of the first column reflux ratio - the second column reboiler heat are shown below. Figure 2 As shown.

[0037] S2, perform eigenvalue decomposition on the modified covariance matrix to obtain eigenvalues ​​and eigenvectors. Estimate the dimensionless gradient vectors of product purity and total energy consumption relative to the parameters to be optimized based on the initial candidate parameter set. Calculate the projection of each eigenvector onto the two dimensionless gradient vectors. When the projection of an eigenvector onto the dimensionless gradient vector of product purity is less than zero, reverse the processing of the eigenvector and update the two projections corresponding to the eigenvector simultaneously. Calculate the comprehensive contribution based on the projection and eigenvalue. Multiply the two projections to obtain the target synergy index. Sort the eigenvectors in descending order based on the comprehensive contribution.

[0038] An eigenvalue decomposition algorithm is applied to the modified covariance matrix to obtain its non-negative eigenvalues ​​and mutually orthogonal eigenvectors. Linear surrogate fitting is performed based on the initial candidate parameter set and its corresponding product purity and total energy consumption sample data to establish surrogate expressions for product purity and total energy consumption, respectively. The first-order partial derivatives of these two surrogate expressions are calculated with respect to each parameter to be optimized, and the results are scaled using the upper and lower limits of each parameter to remove dimensional differences, generating dimensionless gradient vectors for product purity and total energy consumption. Each eigenvector is then multiplied by the dimensionless gradient vectors for product purity and total energy consumption to obtain the first and second projections corresponding to that eigenvector. Before calculating the target synergy index, the eigenvectors are standardized in sign and direction: when the first projection of a eigenvector is less than 0, the eigenvector is multiplied by -1, and the corresponding first and second projections are recalculated to ensure the eigenvector direction aligns with the product purity improvement direction; when the first projection is equal to 0, the eigenvector direction remains unchanged. The square of the first projection is multiplied by the preset product purity weight constant to obtain the first product. The square of the second projection is multiplied by the preset total energy consumption weight constant to obtain the second product. The sum of the first and second products is multiplied by the eigenvalue corresponding to the current eigenvector to obtain the comprehensive contribution. The first and second projections corresponding to each eigenvector are multiplied by the second projection to obtain the target synergy index of the eigenvector. All eigenvectors are sorted in descending order according to the comprehensive contribution.

[0039] In an optional embodiment, estimating the dimensionless gradient vectors of product purity and total energy consumption relative to the parameters to be optimized based on the initial candidate parameter set includes: Based on the initial candidate parameter set, construct the independent variable matrix, and perform least squares regression with the product purity measurement vector and the total energy consumption measurement vector as the dependent variable vector respectively to obtain the partial regression coefficient vector corresponding to product purity and the partial regression coefficient vector corresponding to total energy consumption. Extract the coefficients of the linearly correlated variables from the partial regression coefficient vector corresponding to the product purity and the partial regression coefficient vector corresponding to the total energy consumption, respectively, and construct the gradient vector of product purity relative to the parameter to be optimized and the gradient vector of total energy consumption relative to the parameter to be optimized. The gradient vectors of product purity and total energy consumption relative to the parameters to be optimized are made dimensionless to obtain dimensionless gradient vectors of product purity and total energy consumption relative to the parameters to be optimized.

[0040] The initial candidate parameter set contains 100 samples, and there are 6 parameters to be optimized. A constant term "1" is added to the beginning of each sample to construct a 100×7 independent variable matrix X. Using the least squares analytical solution formula of multiple linear regression, the transpose of X (7×100) is first calculated, and then multiplied by X (100×7) to obtain a 7×7 square matrix. The inverse matrix of this square matrix is ​​then calculated and multiplied by the transpose of X to obtain a 7×100 pseudo-inverse matrix.

[0041] The pseudo-inverse matrix is ​​multiplied by the 100×1 product purity measurement vector and the 100×1 total energy consumption measurement vector, respectively, to calculate the 7×1 partial regression coefficient vectors for product purity and total energy consumption, including the intercept term. After removing the coefficient of the first intercept term, the coefficients of the last six linearly correlated variables are extracted to form the 6×1 gradient vectors for purity and energy consumption, respectively. The dimensions of these two gradient vectors are then scaled according to the width of the range of the parameters to be optimized, i.e., dimensionless processing, such as multiplying by the range of the independent variable and dividing by the range of the dependent variable, to generate the dimensionless gradient vectors for purity and energy consumption.

[0042] In an optional embodiment, the calculation of the projection of each feature vector onto two dimensionless gradient vectors, wherein when the projection of a feature vector onto the dimensionless gradient vector of product purity is less than zero, the feature vector is reverse-processed, and the two projections corresponding to the feature vector are updated synchronously, and the comprehensive contribution is calculated based on the projections and feature values, including: The projections of the normalized eigenvectors onto the dimensionless gradient vector of product purity and the dimensionless gradient vector of total energy consumption are calculated to obtain the first projection and the second projection. When the first projection is less than zero, the feature vector is reversed and the corresponding first and second projections are recalculated. The square of the first projection is multiplied by a preset product purity weight constant to obtain a first product, and the square of the second projection is multiplied by a preset total energy consumption weight constant to obtain a second product. The sum of the first product and the second product is multiplied by the eigenvalue corresponding to the eigenvector to obtain the comprehensive contribution.

[0043] Suppose that an eigenvector obtained through eigenvalue decomposition has been normalized to a unit column vector with a magnitude of 1. Multiply the transpose of this normalized eigenvector by the dimensionless gradient vector of product purity to calculate the first projection value, for example, 0.65. Calculate the inner product of this eigenvector and the dimensionless gradient vector of total energy consumption to obtain the second projection value, for example, -0.42. If the calculated first projection is negative, for example -0.65, multiply the corresponding eigenvector by -1 and recalculate the first projection 0.65 and the corresponding second projection, thereby eliminating the influence of the arbitrary sign of the eigenvector on the determination of the collaborative optimization direction.

[0044] Set process control preference parameters, such as a product purity weight constant of 0.6 and a total energy consumption weight constant of 0.4. Squaring the first projection 0.65 yields 0.4225, multiplying by the weight 0.6 gives a first product of 0.2535; squaring the second projection -0.42 yields 0.1764, multiplying by the weight 0.4 gives a second product of 0.07056. Summing the first and second products gives 0.32406. Multiplying this sum by the eigenvalue corresponding to this eigenvector (assumed to be 2.15) yields a comprehensive contribution of 0.6967 for this eigenvector.

[0045] S3. Select the first N eigenvectors to form a dimension reduction mapping matrix. In the low-dimensional orthogonal space, iteratively search along the synergistic optimization direction corresponding to the target synergistic index being less than 0 and the projection of the eigenvector onto the dimensionless gradient vector of product purity being greater than 0 to obtain the low-dimensional optimal solution. Reconstruct the low-dimensional optimal solution to the original parameter space through the dimension reduction mapping matrix to obtain the optimal parameter combination.

[0046] The comprehensive contribution of each feature vector after descending sorting is accumulated. When the cumulative comprehensive contribution ratio first reaches a set threshold of 85%, the total number N of feature vectors accumulated at this point is recorded. The top N feature vectors are extracted and concatenated column-wise to generate a dimension-reduced mapping matrix. The mean vector of the dimensionless initial candidate parameter set is defined as the baseline parameter combination. For any dimensionless parameter vector, the mean vector is subtracted for centering, and then multiplied by the transpose of the dimension-reduced mapping matrix, projecting it into an N-dimensional low-dimensional orthogonal space. The particle position in the particle swarm optimization algorithm represents the low-dimensional coordinate increment relative to the mean vector of the parameters, and the particle swarm is initialized in this N-dimensional low-dimensional orthogonal space.

[0047] The search points or search population of the iterative search algorithm are initialized in a low-dimensional orthogonal space. The target synergy index and the first projection corresponding to each eigenvector in the dimensionality reduction mapping matrix are examined. If the target synergy index is less than 0 and the first projection is greater than 0, it indicates that moving along the positive direction of the low-dimensional coordinate axis corresponding to that eigenvector can improve product purity while reducing total energy consumption, and this is determined to be a synergistic optimization direction. In the position update mechanism of the iterative search algorithm, the initial momentum of the particle optimization velocity and the iteration step size scaling factor are added to the low-dimensional coordinate dimension corresponding to the synergistic optimization direction. A penalty function constraint is applied when the product purity is lower than the preset qualified index, and multi-generation heuristic iterative solution is performed with the minimization of total energy consumption as the fitness evaluation objective.

[0048] After each generation or update of the low-dimensional particle position, a temporary dimensionless parameter vector is first obtained through the dimensionality reduction mapping matrix and the dimensionless mean vector of the parameters. Then, according to the dimensionless rules of each dimension of the parameters to be optimized, the temporary dimensionless parameter vector is back-mapped to the original parameter space. Next, based on the pre-set upper and lower limits of each parameter to be optimized, it is determined whether the temporary parameter combination is out of bounds. If out-of-bounds parameters exist, constraint correction is performed through boundary truncation or resampling to ensure that all parameter combinations participating in the fitness evaluation are within the allowable range of the process. When the fitness of the globally optimal particle changes less than the convergence tolerance within ten consecutive generations, the search stops, and the position coordinates of that particle at this point are output as the low-dimensional optimal solution.

[0049] The column vector corresponding to the low-dimensional optimal solution is multiplied by the dimension reduction mapping matrix on the left, and the column mean translation vector of the dimensionless initial candidate parameter set is added to obtain the dimensionless reconstructed parameter vector. Then, according to the dimensionless rules of each dimension of the parameter to be optimized, the dimensionless reconstructed parameter vector is back-mapped to the original high-dimensional operating parameter value. Then, according to the constraint boundary of the three-tower distillation process of methyl acetal, the reconstructed parameters of each dimension are finally checked for out-of-bounds and the boundary is corrected. For discrete parameters to be optimized such as feed position, the continuous reconstructed values ​​after boundary correction are rounded or mapped according to the preset tray number set. The output parameter set is the optimal parameter combination of the three-tower distillation of methyl acetal.

[0050] In an optional embodiment, selecting the first N feature vectors to construct the dimensionality reduction mapping matrix includes: The top N feature vectors, sorted in descending order of comprehensive contribution, are used as column vectors and horizontally concatenated in sequence to construct a two-dimensional matrix as a dimension reduction mapping matrix. The number of rows in the two-dimensional matrix is ​​the number of the original spatial dimensions of the parameters to be optimized, and the number of columns in the two-dimensional matrix is ​​the number of the orthogonal spatial dimensions after dimension reduction.

[0051] Assuming the original spatial dimension D of the parameters to be optimized in the three-tower distillation system of methyl acetal is 6, and the cumulative comprehensive contribution threshold is set to be above 85%, all 6 calculated eigenvectors and their corresponding comprehensive contributions are obtained, and these 6 eigenvectors are reordered according to their comprehensive contribution values ​​from largest to smallest. Calculations show that the sum of the comprehensive contributions of the top 3 eigenvectors reaches the set threshold, thus determining the number of orthogonal spatial dimensions N after dimensionality reduction to be 3.

[0052] The top three feature vectors with the largest overall contribution are extracted sequentially. Each feature vector is a 6x1 column vector. These feature vectors are then horizontally concatenated from left to right to construct a 6x3 two-dimensional real matrix, which is the dimensionality reduction mapping matrix. In this dimensionality reduction mapping matrix, row 6 corresponds to the dimensions of the six original process parameters, such as the reflux ratio of each tower and the feed position, while column 3 represents the three extracted independent orthogonal principal component variables.

[0053] In an optional embodiment, the step of reconstructing the low-dimensional optimal solution to the original parameter space through a dimensionality-reduction mapping matrix to obtain the optimal parameter combination includes: The low-dimensional optimal solution is mapped to the dimensionless parameter space through a dimension reduction mapping matrix, and then added to the parameter mean vector of the dimensionless initial candidate parameter set to obtain the dimensionless parameter vector. According to the dimensionless transformation rules of the parameters to be optimized in each dimension, the dimensionless parameter vector is mapped back to the original parameter space. When the parameters obtained by reverse mapping are discrete parameters, they are rounded or mapped according to the preset discrete value set to obtain the optimal parameter combination.

[0054] Assume the algorithm completes the iterative search in the 3D orthogonal space after dimensionality reduction, obtaining a 3x1 low-dimensional optimal solution vector. The previously constructed dimensionality reduction mapping matrix is ​​known to be a 6x3 two-dimensional matrix. Performing matrix multiplication, multiplying the 6x3 dimensionality reduction mapping matrix by the 3x1 low-dimensional optimal solution column vector, yields a 6x1 reconstruction change vector, representing the relative changes in each process parameter.

[0055] The dimensionless initial candidate parameter set mean vector, pre-calculated and saved during covariance matrix construction, is extracted and is also 6 rows and 1 column. The calculated reconstructed change vector is added element-wise to this parameter mean vector to complete the coordinate system translation and restoration, resulting in a dimensionless 6-dimensional reconstructed parameter vector. Then, according to the upper and lower limits or normalization mapping relationship of each dimension parameter, de-dimensionization is performed to map it back to the original 6-dimensional parameter space of the three-tower distillation of methylal. Subsequently, each mapped parameter is compared with the preset upper and lower limits of that dimension. If a parameter is below the lower limit, the lower limit is used; if it is above the upper limit, the upper limit is used; if it is within the range of the upper and lower limits, it remains unchanged. For the elements of discrete parameters in the output 6-row, 1-column result vector, after rounding or mapping according to the preset discrete value set, the optimal combination of process parameters is obtained.

[0056] In an optional embodiment, the step of iteratively searching for the low-dimensional optimal solution in the low-dimensional orthogonal space along the collaborative optimization direction corresponding to the target collaborative index being less than 0 and the projection of the feature vector onto the dimensionless gradient vector of product purity being greater than 0 includes: The initial search step size is set according to the comprehensive contribution of the eigenvectors corresponding to each orthogonal axis, and the initial search step size is decreased with the number of iterations. Iterative search is performed along the collaborative optimization direction where the target collaborative index is less than 0 and the projection of the feature vector onto the dimensionless gradient vector of product purity is greater than 0. When the change in coordinates of a search point on a certain orthogonal axis is less than the convergence threshold, the coordinate value of that orthogonal axis is locked, and the search continues for the remaining unlocked orthogonal axes until a low-dimensional optimal solution is obtained.

[0057] The optimization begins in an N-dimensional low-dimensional orthogonal space. An initial search step size is assigned to each orthogonal axis, which is equal to the combined contribution of the corresponding eigenvector multiplied by a base step size coefficient, such as 0.1. The step size decay mechanism is set to multiply by a decay factor after each iteration, such as 0.95. In each iteration, each orthogonal axis direction is checked: if the target cooperability index of the axis, i.e., the product of purity projection and energy consumption projection, is less than 0, and the projection on the purity gradient is greater than 0, then the search point coordinates are added to the current step size to update the state.

[0058] As the iteration continues, each step calculates the coordinate displacement of the search point on each orthogonal axis, which is the current step size multiplied by the direction sign. When the absolute value of the coordinate change on a certain orthogonal axis is less than the set convergence threshold (e.g., 0.001) three consecutive times, the coordinate value on that orthogonal axis is locked. The other unlocked orthogonal axes continue to be determined and searched according to the decay step size rule. This process continues until all N orthogonal axes meet the convergence condition and are locked, and the coordinate components of the search point constitute the final N-dimensional low-dimensional optimal solution vector.

[0059] In the second embodiment, the present invention also proposes a three-tower distillation parameter optimization system for methyl acetal, comprising the following modules: The module is used to obtain the parameters to be optimized in the three-tower distillation process of methyl acetal, sample and generate an initial candidate parameter set, and obtain the product purity and total energy consumption corresponding to each parameter. The parameters to be optimized in each dimension of the initial candidate parameter set are dimensionless. A statistical covariance matrix is ​​constructed based on the dimensionless initial candidate parameter set. A preset weight matrix is ​​established based on the comprehensive sensitivity of the parameters to be optimized. The statistical covariance matrix and the preset weight matrix are multiplied element by element to obtain the modified covariance matrix. The calculation module is used to perform eigenvalue decomposition on the modified covariance matrix to obtain eigenvalues ​​and eigenvectors. Based on the initial candidate parameter set, it estimates the dimensionless gradient vectors of product purity and total energy consumption relative to the parameters to be optimized. It calculates the projection of each eigenvector onto the two dimensionless gradient vectors. When the projection of an eigenvector onto the dimensionless gradient vector of product purity is less than zero, the eigenvector is reversed and the two projections corresponding to the eigenvector are updated synchronously. The comprehensive contribution is calculated based on the projection and eigenvalue. The two projections are multiplied to obtain the target synergy index. The eigenvectors are sorted in descending order based on the comprehensive contribution. The reconstruction module is used to select the first N feature vectors to form a dimension reduction mapping matrix. In the low-dimensional orthogonal space, it iteratively searches along the collaborative optimization direction corresponding to the target collaborative index being less than 0 and the projection of the feature vector onto the dimensionless gradient vector of product purity being greater than 0 to obtain the low-dimensional optimal solution. The low-dimensional optimal solution is then reconstructed to the original parameter space through the dimension reduction mapping matrix to obtain the optimal parameter combination.

[0060] The above description represents the preferred embodiments of the present invention. It should be noted that, for those skilled in the art, various improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for optimizing parameters in a three-tower distillation process for methyl acetal, characterized in that, include: The parameters to be optimized in the three-tower distillation process of methyl acetal are obtained, an initial candidate parameter set is generated by sampling, and the product purity and total energy consumption corresponding to each parameter are obtained. The parameters to be optimized in each dimension of the initial candidate parameter set are dimensionless. A statistical covariance matrix is ​​constructed based on the dimensionless initial candidate parameter set. A preset weight matrix is ​​established based on the comprehensive sensitivity of the parameters to be optimized. The statistical covariance matrix and the preset weight matrix are multiplied element by element to obtain the modified covariance matrix. The modified covariance matrix is ​​decomposed into eigenvalues ​​and eigenvectors. Based on the initial candidate parameter set, the dimensionless gradient vectors of product purity and total energy consumption relative to the parameters to be optimized are estimated. The projection of each eigenvector onto the two dimensionless gradient vectors is calculated. When the projection of the eigenvector onto the dimensionless gradient vector of product purity is less than zero, the eigenvector is reversed and the two projections corresponding to the eigenvector are updated synchronously. The comprehensive contribution is calculated based on the projection and eigenvalue. The two projections are multiplied to obtain the target synergy index. The eigenvectors are sorted in descending order according to the comprehensive contribution. The first N eigenvectors are selected to form a dimension reduction mapping matrix. In the low-dimensional orthogonal space, the low-dimensional optimal solution is obtained by iteratively searching along the synergistic optimization direction where the target synergistic index is less than 0 and the projection of the eigenvector onto the dimensionless gradient vector of product purity is greater than 0. The low-dimensional optimal solution is then reconstructed to the original parameter space through the dimension reduction mapping matrix to obtain the optimal parameter combination.

2. The method according to claim 1, characterized in that, The step of dimensionlessly transforming the parameters to be optimized in each dimension of the initial candidate parameter set, and constructing a statistical covariance matrix based on the dimensionless initial candidate parameter set, includes: The parameters to be optimized in each dimension of the initial candidate parameter set are dimensionless, and the mean of each parameter sample after dimensionless processing is calculated to obtain the parameter mean vector. Calculate the deviation vector of each dimensionless parameter sample relative to the parameter mean vector, and multiply the deviation vector by its transpose to obtain the corresponding sample covariance matrix; The statistical covariance matrix is ​​obtained by summing the covariance matrices of all samples and dividing by the total number of samples in the initial candidate parameter set minus one.

3. The method according to claim 1 or 2, characterized in that, The establishment of a preset weight matrix based on the comprehensive sensitivity of the parameters to be optimized includes: The product purity, total energy consumption, and each parameter to be optimized are dimensionless. The absolute value of the first partial derivative of the i-th dimensionless parameter to be optimized with respect to the dimensionless product purity and the absolute value of the second partial derivative with respect to the dimensionless total energy consumption are calculated respectively. The absolute values ​​of the first and second partial derivatives are summed to obtain the sensitivity value of the i-th parameter to be optimized. Multiply the sensitivity value of the i-th parameter to be optimized by the sensitivity value of the j-th parameter to be optimized, and assign the product to the element position of the i-th row and j-th column of the preset weight matrix.

4. The method according to claim 1, characterized in that, The estimation of the dimensionless gradient vectors of product purity and total energy consumption relative to the parameters to be optimized based on the initial candidate parameter set includes: Based on the initial candidate parameter set, construct the independent variable matrix, and perform least squares regression with the product purity measurement vector and the total energy consumption measurement vector as the dependent variable vector respectively to obtain the partial regression coefficient vector corresponding to product purity and the partial regression coefficient vector corresponding to total energy consumption. Extract the coefficients of the linearly correlated variables from the partial regression coefficient vector corresponding to the product purity and the partial regression coefficient vector corresponding to the total energy consumption, respectively, and construct the gradient vector of product purity relative to the parameter to be optimized and the gradient vector of total energy consumption relative to the parameter to be optimized. The gradient vectors of product purity and total energy consumption relative to the parameters to be optimized are made dimensionless to obtain dimensionless gradient vectors of product purity and total energy consumption relative to the parameters to be optimized.

5. The method according to claim 1, characterized in that, The calculation of the projection of each feature vector onto two dimensionless gradient vectors is performed. When the projection of a feature vector onto the dimensionless gradient vector of product purity is less than zero, the feature vector is reversed, and the two projections corresponding to the feature vector are updated synchronously. The comprehensive contribution is calculated based on the projections and eigenvalues, including: The projections of the normalized eigenvectors onto the dimensionless gradient vector of product purity and the dimensionless gradient vector of total energy consumption are calculated to obtain the first projection and the second projection. When the first projection is less than zero, the feature vector is reversed and the corresponding first and second projections are recalculated. The square of the first projection is multiplied by a preset product purity weight constant to obtain a first product, and the square of the second projection is multiplied by a preset total energy consumption weight constant to obtain a second product. The sum of the first product and the second product is multiplied by the eigenvalue corresponding to the eigenvector to obtain the comprehensive contribution.

6. The method according to claim 1, characterized in that, The step of selecting the first N feature vectors to construct the dimensionality reduction mapping matrix includes: The top N feature vectors, sorted in descending order of comprehensive contribution, are used as column vectors and horizontally concatenated in sequence to construct a two-dimensional matrix as a dimension reduction mapping matrix. The number of rows in the two-dimensional matrix is ​​the number of the original spatial dimensions of the parameters to be optimized, and the number of columns in the two-dimensional matrix is ​​the number of the orthogonal spatial dimensions after dimension reduction.

7. The method according to claim 1, characterized in that, The process of reconstructing the low-dimensional optimal solution back to the original parameter space using a dimension reduction mapping matrix to obtain the optimal parameter combination includes: The low-dimensional optimal solution is mapped to the dimensionless parameter space through a dimension reduction mapping matrix, and then added to the parameter mean vector of the dimensionless initial candidate parameter set to obtain the dimensionless parameter vector. According to the dimensionless transformation rules of the parameters to be optimized in each dimension, the dimensionless parameter vector is mapped back to the original parameter space. When the parameters obtained by reverse mapping are discrete parameters, they are rounded or mapped according to the preset discrete value set to obtain the optimal parameter combination.

8. The method according to claim 1, characterized in that, The process of obtaining the parameters to be optimized in the three-tower distillation process of methyl acetal, and sampling to generate an initial candidate parameter set, includes: Obtain the constraint boundary of the three-tower distillation process of methyl acetal, and generate an initial candidate parameter set based on Latin hypercube sampling.

9. The method according to claim 1, characterized in that, The step of iteratively searching for the low-dimensional optimal solution within a low-dimensional orthogonal space along the collaborative optimization direction where the target collaborative index is less than 0 and the projection of the feature vector onto the dimensionless gradient vector of product purity is greater than 0 includes: The initial search step size is set according to the comprehensive contribution of the eigenvectors corresponding to each orthogonal axis, and the initial search step size is decreased with the number of iterations. Iterative search is performed along the collaborative optimization direction where the target collaborative index is less than 0 and the projection of the feature vector onto the dimensionless gradient vector of product purity is greater than 0. When the change in coordinates of a search point on a certain orthogonal axis is less than the convergence threshold, the coordinate value of that orthogonal axis is locked, and the search continues for the remaining unlocked orthogonal axes until a low-dimensional optimal solution is obtained.

10. A parameter optimization system for a three-tower distillation of methyl acetal, characterized in that, include: The module is used to obtain the parameters to be optimized in the three-tower distillation process of methyl acetal, sample and generate an initial candidate parameter set, and obtain the product purity and total energy consumption corresponding to each parameter. The parameters to be optimized in each dimension of the initial candidate parameter set are dimensionless. A statistical covariance matrix is ​​constructed based on the dimensionless initial candidate parameter set. A preset weight matrix is ​​established based on the comprehensive sensitivity of the parameters to be optimized. The statistical covariance matrix and the preset weight matrix are multiplied element by element to obtain the modified covariance matrix. The calculation module is used to perform eigenvalue decomposition on the modified covariance matrix to obtain eigenvalues ​​and eigenvectors. Based on the initial candidate parameter set, it estimates the dimensionless gradient vectors of product purity and total energy consumption relative to the parameters to be optimized. It calculates the projection of each eigenvector onto the two dimensionless gradient vectors. When the projection of an eigenvector onto the dimensionless gradient vector of product purity is less than zero, the eigenvector is reversed and the two projections corresponding to the eigenvector are updated synchronously. The comprehensive contribution is calculated based on the projection and eigenvalue. The two projections are multiplied to obtain the target synergy index. The eigenvectors are sorted in descending order based on the comprehensive contribution. The reconstruction module is used to select the first N feature vectors to form a dimension reduction mapping matrix. In the low-dimensional orthogonal space, it iteratively searches along the collaborative optimization direction corresponding to the target collaborative index being less than 0 and the projection of the feature vector onto the dimensionless gradient vector of product purity being greater than 0 to obtain the low-dimensional optimal solution. The low-dimensional optimal solution is then reconstructed to the original parameter space through the dimension reduction mapping matrix to obtain the optimal parameter combination.

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