A method for optimizing the formulation of a high color interior polypropylene material

Abstract

The application provides a formula optimization method of high-color interior polypropylene material, and belongs to the technical field of polypropylene. The application constructs a double-path variational self-encoder morphology-process collaborative optimization model, encodes scanning electron microscope images and formula-process time sequence data into pigment dispersion morphology potential representation and formula-process potential representation, embeds a mixing rule equation and a rheological equation into a loss function through a physical information neural network to inhibit overfitting under high-dimensional sparse data, covers a key formula space with the least number of experiments by using an active learning framework, collects pigment particle dispersion information in real time by means of an online laser backscattering probe and an ultrasonic attenuation spectrometer, drives a model predictive controller to dynamically adjust extrusion process parameters, and realizes reverse formula solving through an artificial intelligence model, thereby solving the technical problem that it is difficult to establish a causal relationship between pigment dispersion morphology and formula-process parameters in a high-dimensional sparse formula space of high-color interior polypropylene material.

Description

Technical Field

[0001] This invention belongs to the field of polypropylene technology, and more specifically, relates to a method for optimizing the formulation of high-color interior polypropylene materials. Background Technology

[0002] High-color polypropylene materials for automotive interior trim are widely used in the production of automotive interior parts, and their color consistency and pigment dispersion uniformity are core indicators for evaluating product quality. Traditional formulation optimization methods rely on trial and error based on experience and orthogonal experimental design, iteratively adjusting the formulation components by manually adjusting extrusion process parameters such as screw speed and melt temperature, combined with colorimeter test results. In current high-color polypropylene production for interior trim, due to the presence of more than ten formulation components, high dimensionality of process parameters, and extremely sparse experimental data, traditional surrogate models struggle to accurately fit the nonlinear relationship between pigment dispersion morphology and formulation-process parameters in high-dimensional space.

[0003] The drawback of traditional methods is that the microscopic dispersion morphology information of pigments reflected in scanning electron microscope images and the formulation-process time series data are heterogeneous and multimodal data, and the causal relationship between the two cannot be effectively captured by linear regression or shallow machine learning models. At the same time, the combinatorial explosion problem in the discrete high-dimensional formulation space makes the convergence efficiency of optimization algorithms based on global search extremely low, and it is impossible to locate the optimal formulation region within a limited number of experiments.

[0004] In the current development of high-color polypropylene formulations for interior decoration, due to the inherent heterogeneity between pigment dispersion morphology image features and formulation-process parameter features in semantic space, existing technologies cannot align these two heterogeneous features in a unified latent space. Consequently, it is impossible to establish a causal mapping between the microscopic dispersion state of pigments and macroscopic formulation-process decisions, resulting in a severe deficiency in the generalization ability of formulation optimization results in regions without known formulations. In other words, existing technologies suffer from the technical problem of difficulty in establishing a causal relationship between pigment dispersion morphology and formulation-process parameters in high-dimensional sparse formulation spaces for high-color polypropylene interior decoration materials. Summary of the Invention

[0005] In view of this, the present invention provides a formulation optimization method for high-color interior polypropylene materials, which can solve the technical problem in the prior art that it is difficult to establish the causal relationship between pigment dispersion morphology and formulation-process parameters in high-color interior polypropylene materials in a high-dimensional sparse formulation space.

[0006] This invention is achieved as follows: This invention provides a method for optimizing the formulation of a high-color interior polypropylene material, comprising the following steps:

[0007] Historical formula parameters, extrusion process parameter time-series curves, scanning electron microscope images, and color difference batch data were collected to construct a training dataset for the morphology-process co-optimization model. The training dataset was preprocessed and then input into the morphology-process co-optimization model for training.

[0008] A matrix of interaction between formulation components is constructed. The negative value of the formulation performance index is used as the system Hamiltonian. The parallel tempering Monte Carlo algorithm is used to run Metropolis sampling in parallel at multiple virtual temperatures. The phase separation critical point is identified by the peak detection of the specific heat capacity curve and the critical region is marked as the formulation forbidden zone. The formulation phase diagram and the optimal region boundary are output.

[0009] Within the optimal region boundary, a physical information neural network is used to embed the hybrid rule equation and rheological equation into the loss function, and an active learning framework is combined to improve the acquisition function and dynamically select the next experimental point.

[0010] Calculate the dispersion state evaluation function value, and adjust the screw speed and melt temperature parameters according to the interval to which the dispersion state evaluation function value belongs;

[0011] After the extruder melt pump, the chord length distribution and particle size information of pigment particles are collected in real time by an online laser backscattering probe and an ultrasonic attenuation spectrometer. The chord length distribution and particle size information of pigment particles are input into the morphology-process co-optimization model to reconstruct the dispersion state field of the entire screw section and drive the model prediction controller to dynamically adjust the screw speed and melt temperature.

[0012] Using the target spectral reflectance curve as input, the color matching decoding path in the morphology-process co-optimization model outputs the concentration vector of each pigment, thus completing the reverse formulation solution;

[0013] Among them, the morphology-process co-optimization model adopts a dual-path variational autoencoder architecture and is coupled with a differentiable extrusion physical simulator. Path A is a convolutional encoder and path B is a graph variational encoder. The latent representation of pigment dispersion morphology and the latent representation of formulation-process are subject to mutual information maximization constraints in the latent space through Barlow Twins loss variants. The decoder includes dispersion state decoding path and color matching decoding path.

[0014] The training dataset for the morphology-process co-optimization model was established by collecting historical formula experimental records of no less than a threshold number of historical experimental records, expanding the color matching training samples using Monte Carlo multiple scattering simulation, performing random flipping and brightness perturbation data enhancement processing on scanning electron microscope images, performing maximum-minimum normalization on continuous numerical parameters, performing one-thermal encoding on discrete formula components, and dividing the training set and validation set according to the training-validation ratio threshold.

[0015] The morphology-process co-optimization model training specifically employs the Adam optimizer. The loss function consists of a weighted sum of four parts: reconstruction loss, Kullback-Leibler divergence regularization term, Barlow Twins loss variant, and the constraint residual of the differentiable extrusion physical simulator. The constraint residual weight of the differentiable extrusion physical simulator is linearly increased to the constraint weight threshold through a course learning strategy. An early stopping strategy is adopted, and training stops when the validation set loss does not decrease for the threshold number of consecutive rounds.

[0016] Specifically, the convolutional encoder in path A takes a scanning electron microscope image as input and consists of four stacked 2D convolutional layers. Each 2D convolutional layer is followed by a batch normalization layer and a linear rectified function activation layer. The output of the 4th 2D convolutional layer is compressed into a vector by a global average pooling layer, and then outputs the latent mean vector of pigment dispersion morphology through two parallel fully connected layers. With the latent log-variance vector of pigment dispersion morphology The latent representation of pigment dispersion morphology is obtained through reparameterized sampling. .

[0017] Specifically, the graph variational encoder for path B extracts the inter-component relationships from the node feature matrix using a 3-layer graph convolutional network, followed by global mean pooling to obtain a formulation component relationship representation vector. The extrusion process parameter time-series curve is processed by a bidirectional long short-term memory network, and the latent state at the last moment is taken as the process time-series representation vector. The two vectors are concatenated and then output as formulation-process latent mean vectors through two parallel fully connected layers. With the latent log-variance vector of formulation and process The latent representation of the formulation-process is obtained through reparameterized sampling. .

[0018] Specifically, the Barlow Twins loss variant minimizes the latent representation of pigment dispersion morphology. Potential representation of formulation-process The Frobenius norm of the difference between the cross-correlation matrix and the identity matrix forces the two-path encoder to learn a causal relationship between morphology and formulation-process.

[0019] Specifically, the dispersed state decoding path is based on the latent representation of the formulation and process. As input, the pigment dispersion parameter vector is output through the fully connected layer. The pigment dispersion parameter vector is input to the differentiable extrusion physics simulator, which is built based on the Herschel-Bulkley rheological model and outputs the reconstructed dispersion state field of the entire screw segment.

[0020] Specifically, the color matching decoding path is based on the recipe-process latent representation. The input is processed by the Transformer decoder, which outputs the pigment concentration vectors. The Transformer decoder consists of multiple Transformer decoding layers, each containing a multi-head self-attention mechanism sublayer and a feedforward network sublayer.

[0021] Among them, the elements of the interaction matrix of the formulation components Specifically, it is composed of the formula components With formulation components The Flory-Huggins interaction parameters between the components were estimated by calculating the difference in solubility parameters of each component. These solubility parameters were obtained from the technical manuals of each component supplier or determined by the Hansen solubility sphere method.

[0022] Specifically, the parallel tempering Monte Carlo algorithm runs Metropolis sampling simultaneously on multiple virtual temperature replicas. The high-temperature replicas achieve global unbiased exploration of the recipe space, while the low-temperature replicas converge to the performance extremum region. The replicas periodically exchange configurations so that the low-temperature replicas can escape local extrema and achieve cross-temperature information transfer.

[0023] The active learning framework is based on the surrogate model's prediction mean and prediction uncertainty for unexperimented points. It calculates the information gain for each candidate experimental point by improving the acquisition function. The value of the improved acquisition function is determined by the surrogate model's prediction mean and prediction standard deviation for the candidate points. Numerically, it is equal to the expectation that the candidate point's performance exceeds the current best value. It is obtained by analytically integrating the Gaussian distribution.

[0024] Among them, the value of the distributed state evaluation function The calculation formula is ,in This represents the median chord length of the pigment particles. The median chord length of the target pigment particles is the baseline value. The standard deviation of the pigment particle chord length distribution. The standard deviation of the chord length distribution of the target pigment particles is the baseline value. and The weighting coefficients are and satisfy the following conditions: .

[0025] Specifically, the target spectral reflectance curve is for the wavelength range of 400–700 nm. The discrete vector of spectral reflectance, containing 31 wavelength points, is obtained by measuring the target color sample with a spectrophotometer.

[0026] Among these, latent space optimization specifically refers to the direct representation of the latent space by the pigment dispersion morphology. Potential representation of formulation-process Within the latent space, continuous walking is performed along the direction of the formulation performance gradient. At each step, the dispersion state decoding path is used to decode the pigment dispersion parameter vector and evaluate the formulation performance, thereby realizing continuous formulation search within the latent space.

[0027] Among these, the thresholds are: 200 sets of historical experimental records, 8:2 training-to-validation ratio, at least 5000 sets of color matching training samples, 0.5 constraint weights, 20 early stopping rounds, and at least 300 training rounds; and the value of the dispersed state evaluation function. The threshold for upward adjustment is 1.3, and the threshold for downward adjustment is 0.9; when When the temperature is not lower than the upper threshold, increasing the screw speed by 5% increases the melt temperature by 3°C; when When the temperature is between the upper and lower thresholds, maintain the current screw speed and melt temperature unchanged; when... When the temperature drops below the lowering threshold, the screw speed decreases by 3% and the melt temperature decreases by 2°C.

[0028] This invention employs a dual-path variational autoencoder architecture, which maps scanning electron microscope images and formulation-process time-series data to independent latent spaces via a convolutional encoder and a graph variational encoder, respectively. Then, a Barlow Twins loss variant is used to implement mutual information maximization constraints in the latent space, forcing the two-path encoders to learn the causal relationship between pigment dispersion morphology and formulation-process parameters. This solves the technical problem of establishing causal relationships between two types of heterogeneous features in a high-dimensional sparse formulation space.

[0029] This invention embeds a differentiable extrusion physics simulator into the decoding process, using Herschel-Bulkley rheological physics as an implicit regularization term to limit the model's predictions from deviating from physical laws in data-free regions. This allows the model to maintain physically feasible predictions even in a high-dimensional recipe space with extremely sparse experimental data, effectively suppressing overfitting under high-dimensional sparse data conditions. The synergistic effect of the physical information neural network and the active learning framework ensures that each experiment targets the recipe region with the scarcest information and the highest probability of performance extrema, covering the key recipe space with the fewest possible experiments.

[0030] In summary, this invention solves the technical problem mentioned in the background art of the difficulty in establishing a causal relationship between pigment dispersion morphology and formulation-process parameters in high-color interior polypropylene materials. Attached Figure Description

[0031] Figure 1 This is a flowchart of the method of the present invention.

[0032] Figure 2 Phase diagram and optimal region boundary distribution diagram of polypropylene formulation for high-color interior trim.

[0033] Figure 3 A comparison chart of the target spectral reflectance curve and the predicted spectral reflectance curve obtained by reverse formulation. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0035] like Figure 1 The diagram shown is a flowchart of a method for optimizing the formulation of a high-color interior polypropylene material provided by the present invention. This method includes the following steps:

[0036] S01. Collect historical formula parameters, extrusion process parameter time-series curves, scanning electron microscope images, and color difference batch data to construct a training dataset for the morphology-process co-optimization model. After preprocessing the training dataset, input it into the morphology-process co-optimization model for training.

[0037] S02. Construct the interaction matrix of the formulation components, use the negative value of the formulation performance index as the system Hamiltonian, and use the parallel tempering Monte Carlo algorithm to run Metropolis sampling in parallel at multiple virtual temperatures. Identify the phase separation critical point by the peak detection of the specific heat capacity curve and mark the critical region as the formulation forbidden zone. Output the formulation phase diagram and the optimal region boundary.

[0038] S03. Within the boundary of the optimal region, a physical information neural network is used to embed the hybrid rule equation and rheological equation into the loss function. An active learning framework is combined to dynamically select the next experimental point in order to improve the acquisition function and cover the key formula space region with the fewest number of experiments.

[0039] S04. Calculate the dispersion state evaluation function value, and adjust the screw speed and melt temperature parameters according to the interval to which the dispersion state evaluation function value belongs;

[0040] S05. After the melt pump of the extruder, the chord length distribution and particle size information of pigment particles are collected in real time by an online laser backscattering probe and an ultrasonic attenuation spectrometer. The chord length distribution and particle size information of pigment particles are input into the morphology-process co-optimization model to reconstruct the dispersion state field of the entire screw section and drive the model prediction controller to dynamically adjust the screw speed and melt temperature.

[0041] S06. Using the target spectral reflectance curve as input, output the concentration vector of each pigment through the color matching decoding path in the morphology-process co-optimization model to complete the reverse formulation solution;

[0042] The specific structure of the morphology-process co-optimization model is as follows: the morphology-process co-optimization model adopts a dual-path variational autoencoder architecture and is coupled with a differentiable extrusion physical simulator.

[0043] Path A is a convolutional encoder, and the input is a scanning electron microscope image with a resolution of at least [resolution value missing]. The image has 1 pixel and 1 image channel. The convolutional encoder consists of 4 stacked two-dimensional convolutional layers, with each of the 4 layers having a kernel size of 1. The stride is 2, and the number of output channels is 32, 64, 128, and 256 respectively. Each 2D convolutional layer is followed by a batch normalization layer and a linear rectified function activation layer. The output of the 4th 2D convolutional layer is compressed into a vector of length 256 by a global average pooling layer. The vector of length 256 is then passed through two parallel fully connected layers to output the latent mean vector of pigment dispersion morphology. With the latent log-variance vector of pigment dispersion morphology All dimensions are 128; the latent representation of pigment dispersion morphology is obtained through reparameterized sampling. The dimension is 128.

[0044] Path B is a graph variational encoder. The input consists of two parts: the first part is the feature matrix of the formulation parameters nodes, where each node represents a formulation component, and the node feature dimension is 20; the second part is the time-series curve of the extrusion process parameters, with a time-series length of [missing information]. Each step has a feature dimension of 8. The node feature matrix is ​​processed by a 3-layer graph convolutional network to extract the inter-component relationships. The hidden layer of each graph convolutional network has a dimension of 128, and the activation function is a linear rectified function. The output of the 3rd layer graph convolutional network is processed by global mean pooling to obtain a formulation component relationship representation vector with a dimension of 128. The extrusion process parameter time series curve is processed by a bidirectional long short-term memory network with a hidden layer dimension of 64. After bidirectional concatenation, the output dimension is 128. The hidden state at the last moment is taken as the process time series representation vector with a dimension of 128. The formulation component relationship representation vector and the process time series representation vector are concatenated to obtain a concatenated vector with a dimension of 256. The concatenated vector is processed by two parallel fully connected layers to output the formulation-process latent mean vector. With the latent log-variance vector of formulation and process All dimensions are 128; the latent representation of the formulation-process is obtained through reparameterized sampling. The dimension is 128.

[0045] Potential representation of pigment dispersion morphology Potential representation of formulation-process The mutual information maximization constraint is implemented in the latent space using a Barlow Twins loss variant, which minimizes... and The Frobenius norm of the difference between the cross-correlation matrix and the identity matrix forces the two-path encoder to learn a causal relationship between morphology and formulation-process.

[0046] The decoder contains two decoding paths: the first decoding path is a distributed state decoding path, using the recipe-process latent representation. As input, a pigment dispersion parameter vector with a dimension of 16 is output after passing through three fully connected layers (hidden layer dimensions are 256, 128, and 64 respectively). This pigment dispersion parameter vector is input to a differentiable extrusion physics simulator, which is based on the Herschel-Bulkley rheological model and outputs a reconstructed dispersion state field across the entire screw section. The second decoding path is a color matching decoding path, using the latent representation of the formulation and process. The input is processed by the Transformer decoder, which outputs the concentration vectors of each pigment. The Transformer decoder consists of four Transformer decoding layers, each containing an eight-head self-attention mechanism sublayer and a feedforward network sublayer, with a hidden layer dimension of 512. The dimension of each pigment concentration vector is consistent with the number of formulation components and is used for reverse formulation solution in step S06. The reconstructed dispersed state field of the entire screw segment is used to drive the model predictive controller to dynamically adjust the screw speed and melt temperature in step S05.

[0047] The optimization stage directly represents the potential of pigment dispersion morphology. Potential representation of formulation-process Within the latent space, continuous walking is performed along the formula performance gradient direction. At each step, the dispersed state decoding path is used to decode the pigment dispersion parameter vector and evaluate the formula performance, thereby realizing continuous formula search within the latent space and bypassing the combinatorial explosion problem of the discrete formula space.

[0048] The technical effects of the morphology-process co-optimization model are as follows: the dual-path encoder maximizes mutual information to align pigment dispersion morphology features with formulation-process features in the latent space, enabling the model to establish a causal relationship between pigment dispersion morphology and formulation-process even in a high-dimensional formulation space with extremely sparse experimental data, thus suppressing overfitting under high-dimensional sparse data; the embedding of the differentiable extrusion physics simulator introduces Herschel-Bulkley rheological physics laws into the decoding process, making the model prediction results conform to physical constraints and improving the generalization ability in regions where no formulation has been seen; the latent space gradient walk transforms discrete high-dimensional formulation search into continuous low-dimensional latent space optimization, fundamentally eliminating the combinatorial explosion problem and significantly improving the convergence efficiency of formulation optimization.

[0049] The steps for establishing the training dataset for the morphology-process co-optimization model specifically include: collecting no fewer than 200 sets of historical formulation experimental records, each set containing no fewer than 20-dimensional formulation parameters, extrusion process parameter time-series curves, scanning electron microscope images, and color difference batch data; expanding the color matching training samples to no fewer than 5000 sets using Monte Carlo multiple scattering simulation; performing random flipping and brightness perturbation data enhancement processing on the scanning electron microscope images; performing maximum-minimum normalization processing on continuous numerical parameters and one-thermal encoding on discrete formulation components; and dividing the training set and validation set into an 8:2 ratio.

[0050] The specific steps for training the morphology-process co-optimization model include: using the Adam optimizer with an initial learning rate of 0.001 and a batch size of 32; the loss function is composed of a weighted sum of four parts: reconstruction loss, Kullback-Leibler divergence regularization term, BarlowTwins loss variant, and the constraint residual of the differentiable extrusion physical simulator; the weight of the constraint residual of the differentiable extrusion physical simulator is linearly increased from 0 to 0.5 through a course learning strategy; the number of training rounds is no less than 300 rounds, and an early stopping strategy is adopted, stopping training when the validation set loss does not decrease for 20 consecutive rounds; after training, the color difference prediction error and dispersion state prediction error are evaluated on the validation set respectively, and if the accuracy requirements are not met, training data is supplemented and retraining is performed.

[0051] The calculation formula for the dispersed state evaluation function is expressed as follows: ;in The value of the distributed state evaluation function is dimensionless. The median chord length of pigment particles measured in real time by an online laser backscattering probe, in units of The median chord length of the target pigment particles is the reference value, in units of The standard deviation of the pigment particle chord length distribution is given by . The standard deviation of the target pigment particle chord length distribution is the benchmark value, in units of and Let be the weighting coefficient, satisfying Both are dimensionless; when When the screw speed increases by 5%, the melt temperature increases by 3°C; when At that time, maintain the current screw speed and melt temperature unchanged; when At that time, the screw speed decreased by 3%, and the melt temperature decreased by 2°C; , , , The thresholds of 1.3 and 0.9 were obtained through no fewer than 30 sets of comparative experiments, with color uniformity and mechanical properties as evaluation indicators, and were fitted using response surface methodology.

[0052] Among them, the elements of the interaction matrix of the formulation components From the formulation components With formulation components The Flory-Huggins interaction parameters between components were estimated; the Flory-Huggins interaction parameters were calculated by the difference in solubility parameters of each component, which were obtained from the technical manuals of each component supplier or determined by the Hansen solubility sphere method; the sensitivity parameter for phase separation critical point detection was calibrated by no less than 20 sets of formulation compatibility experiments.

[0053] The scanning electron microscope (SEM) image was obtained by using a field emission scanning electron microscope to image the cross-section of the extruded sample after gold sputtering, under an accelerating voltage of 5. Grayscale images acquired at a magnification of 5000x with a resolution of no less than [missing information]. Pixel.

[0054] The principle and technical effects of the parallel tempering Monte Carlo algorithm are as follows: The parallel tempering Monte Carlo algorithm runs Metropolis sampling simultaneously on multiple virtual temperature replicas. The high-temperature replica achieves global unbiased exploration of the formulation space through a higher acceptance probability, while the low-temperature replica converges to the performance extremum region through a lower acceptance probability. The periodic exchange of configurations between replicas allows the low-temperature replica to escape local extrema and achieve cross-temperature information transfer. The compatibility state of formulation components is analogized to the Ising spin, and the interaction energy between components is estimated through the Flory-Huggins interaction parameters. The negative value of the formulation performance index is used as the system Hamiltonian, transforming the formulation optimization problem into an energy minimization problem. The phase transition criterion automatically identifies the phase separation critical point by detecting the peak of the specific heat capacity curve and marks the critical region as a formulation forbidden zone, thereby excluding physically incompatible formulation combinations in the initial stage of the search. This allows subsequent experimental resources to be concentrated on physically feasible high-performance formulation regions, improving the overall formulation optimization efficiency.

[0055] The principle and technical effects of the active learning framework are as follows: Based on the surrogate model's prediction mean and prediction uncertainty for unexperimented points, the active learning framework calculates the information gain of each candidate experimental point through the expected improvement acquisition function, and prioritizes points with high prediction uncertainty and excellent prediction performance as the next experimental point; the value of the expected improvement acquisition function is jointly determined by the surrogate model's prediction mean and prediction standard deviation for candidate points, and is numerically equal to the expectation that the candidate point's performance exceeds the current optimal value, which is obtained by analytical integration of the Gaussian distribution; the strategy ensures that each experiment points to the recipe region with the scarcest information and the highest probability of performance extrema, covering the key recipe space region with the fewest number of experiments, overcoming the problem of insufficient generalization of the surrogate model caused by the sparsity of experimental data in high-dimensional space.

[0056] The principle and technical effect of the physical information neural network are as follows: The physical information neural network incorporates the mixed rule equation and rheological equation into the loss function in the form of residuals, so that the neural network can satisfy the physical equation constraints while fitting the experimental data; In the high-dimensional recipe space where the experimental data is extremely sparse, the physical constraints act as implicit regularization terms, limiting the model's predictions in the data-free region from deviating from the physical laws, thereby suppressing overfitting, improving the reliability of the surrogate model's predictions in the blank recipe region, and reducing the dependence on a large amount of experimental data.

[0057] The Herschel-Bulkley rheological model is a constitutive equation describing the relationship between shear stress and shear rate in non-Newtonian fluids. It is applicable to describing the rheological behavior of polypropylene melts filled with pigments. The model parameters were obtained by measuring the temperature range of 180–220°C using a rotational rheometer.

[0058] The target spectral reflectance curve is in the wavelength range of 400–700 nm. The discrete vector of spectral reflectance containing 31 wavelength points is obtained by measuring the target color sample with a spectrophotometer. The output pigment concentration vectors are used for the reverse formulation solution in step S06.

[0059] The color difference batch data refers to the color difference calculated according to the CIE 1976 standard. Batch statistics, calculated by measuring the extruded samples with a spectrophotometer, are used to establish the training dataset for the morphology-process co-optimization model.

[0060] The extrusion process parameter timing curve includes screw speed timing data and melt temperature timing data, with a timing length of [missing information]. Each step has 8 feature dimensions and is collected and stored in real time by the extruder control system for use as input to the path B-graph variational encoder.

[0061] The pigment particle chord length distribution is a histogram of pigment particle chord length frequency distribution acquired in real time by an online laser backscattering probe, and the pigment particle size information is a volume-weighted particle size distribution of pigment particles acquired in real time by an ultrasonic attenuation spectrometer. Both are input into the morphology-process co-optimization model with an update cycle of 100ms, and are used to reconstruct the dispersed state field of the entire screw section and the predictive controller of the driving model.

[0062] The dispersion state field of the entire screw section is the spatial distribution of pigment dispersion along the screw axis of each section reconstructed by the morphology-process co-optimization model through a differentiable extrusion physical simulator. It is output with an update cycle of 100ms and is used to drive the model prediction controller to dynamically adjust the screw speed and melt temperature.

[0063] The formulation performance indicators include color uniformity and mechanical performance indicators. The color uniformity indicator is determined by color difference. Batch statistical values ​​characterize the mechanical properties, which are characterized by tensile strength and impact strength, both of which are obtained by laboratory testing. These values ​​are used to construct the system Hamiltonian in step S02 and to evaluate the desired improvement of the acquisition function in step S03.

[0064] The following are three sets of specific data collected during different implementation processes.

[0065] First set of data examples (typical conditions of poor dispersion and high color difference):

[0066] In the first set of data, the historical formulation parameters included 85% high-impact polypropylene (MFI=15), 5% rutile titanium dioxide, 1% phthalocyanine blue pigment, 8% talc, and 1% POE toughening agent. The extrusion process parameters showed that during a continuous 2-hour production process, the barrel melting zone temperature was set at 190℃, but the actual melt temperature time-series curve oscillated violently between 185℃ and 195℃. The screw speed was set at 300 rpm, and the main engine torque time-series curve showed multiple abnormal peaks as high as 85%, indicating extremely uneven material plasticization. The scanning electron microscope (SEM) images extracted at this time showed: obvious titanium dioxide and pigment agglomerates with a size of approximately 5-8 μm in the polypropylene matrix, and micropores at the interface between the inorganic powder and the resin matrix, exhibiting typical phase separation and poor bonding phenomena. The corresponding color difference batch data record showed that the brightness of this batch of products ( ) and yellow-blue axis ( The color value fluctuates greatly, with the total color difference between 15 consecutive batches ( The data set is distributed between 1.5 and 2.4, with obvious color unevenness and color difference defects visible to the naked eye, and is considered an unqualified dataset.

[0067] Second set of data examples (good dispersion and stable state after process optimization):

[0068] In the second set of data, the historical formulation parameters were adjusted to 83.5% homopolymer polypropylene, 4% titanium dioxide, 1.5% phthalocyanine green, and 8% ultrafine talc. 2% maleic anhydride-grafted polypropylene (PP-g-MAH) was specifically added as a compatibilizer, and 1% EBS dispersant was added. The extrusion process parameters showed a highly stable time-series curve. Within a 45-minute recording period, the melt temperature curve closely adhered to 200±0.5℃. The screw speed was increased to 400 rpm, and the feed rate curve and the main engine torque curve (stable at 65%) were highly correlated, with no significant fluctuations. Corresponding scanning electron microscopy (SEM) images showed that the pigment particles and talc were very uniformly dispersed in the PP matrix, with the average particle size significantly reduced to 1-2 μm. No large agglomerates were observed, and the addition of the compatibilizer blurred the interface between the powder and the matrix, indicating good resin coating of the pigment. Extracted batch data on color difference showed a qualitative leap in color stability, with 20 consecutive batches showing... and The standard deviation of the value is extremely small, and the total color difference is ( The value is stably controlled within the range of 0.6 to 0.8, which meets the conventional factory standards for high-end automotive interior parts.

[0069] The third set of data examples (ultimate high-color performance and nanoscale dispersion):

[0070] In the third set of data, the historical formulation parameters used 86.5% high-crystallinity polypropylene, 2% high-pigment carbon black, 1% high-scintillation pearlescent pigment, 10% nano-barium sulfate, and 0.5% high-molecular-weight superdispersant. The extrusion process parameter time-series curves reflect a stable and efficient high-shear state. The barrel high-temperature zone was set at 215℃, and the high screw speed time-series data at 500 rpm presented a perfect straight line. The die melt pressure curve remained at 12.5 MPa, fluctuating within a very small range (±0.1 MPa). The high-frequency micro-oscillation indicates that the material is extremely uniformly mixed within the screw. Scanning electron microscopy (SEM) images at this stage reveal an exceptionally high level of microstructure, with carbon black and pearlescent pigments achieving uniform dispersion at the submicron or even nanometer scale (200-500 nm). This forms a complete optical reflection network structure within the polypropylene matrix, without any visible agglomeration or critical phase separation regions. The final batch color difference data demonstrates exceptional color consistency and high chroma, exhibiting not only extremely high blackness and strong pearlescent texture, but also consistent overall color difference across 50 consecutive production batches. The color difference was strictly controlled within an extremely narrow range of 0.2 to 0.3, achieving the high-end quality requirement of "zero color difference" between batches.

[0071] The specific implementation of step S01 is as follows: Collect no less than 200 sets of historical formula experimental records. Each set of records includes no less than 20 dimensions of formula parameters, extrusion process parameter time-series curves, scanning electron microscope images, and color difference batch data. The scanning electron microscope images are obtained by sputtering gold onto the cross-section of the extruded sample using a field emission scanning electron microscope at an accelerating voltage of 5... Data was collected at a magnification of 5000x with a resolution of at least 1024×1024 pixels. Color difference batch data was calculated according to the CIE 1976 standard. Batch statistics. To expand the color matching training samples, the Monte Carlo multiple scattering simulation method was used to expand the color matching samples to no less than 5000 sets. The Monte Carlo method simulates the multiple scattering process of photons between pigment particles through random sampling, making the simulated color matching data statistically close to the real optical measurement results. In the preprocessing stage, the scanning electron microscope images were randomly flipped and brightness perturbed to enhance the data, thereby improving the robustness of the path A convolutional encoder to different image acquisition conditions. Continuous numerical parameters were normalized to maximum and minimum, and discrete formulation components were encoded using one-heat encoding. The training and validation sets were divided in an 8:2 ratio. The Adam optimizer was used during the training phase with an initial learning rate of 0.001 and a batch size of 32. The loss function consisted of a weighted sum of four parts: reconstruction loss, Kullback-Leibler divergence regularization term, BarlowTwins loss variant, and differentiable extrusion physics simulator constraint residuals. The weights of the differentiable extrusion physics simulator constraint residuals were linearly increased from 0 to 0.5 through a course learning strategy. The number of training epochs was no less than 300. An early stopping mechanism was triggered when the validation set loss did not decrease for 20 consecutive epochs.

[0072] The specific implementation of step S02 is: the elements of the interaction matrix of the formulation components. The Flory-Huggins interaction parameters were estimated by calculating the difference in solubility parameters of each component. These solubility parameters were obtained from supplier technical manuals or experimentally determined using the Hansen solubility sphere method. The compatibility state of the formulation components was analogized to the Ising spin, and the interaction energy between components was determined by... Parameterization is employed, using negative values ​​of formulation performance indicators to construct the system Hamiltonian, transforming the formulation optimization problem into an energy minimization problem. A parallel tempering Monte Carlo algorithm simultaneously runs Metropolis sampling on multiple virtual temperature replicas. The high-temperature replica achieves globally unbiased exploration with a higher acceptance probability, while the low-temperature replica converges to the performance extremum region. Periodic configuration exchanges between replicas facilitate cross-temperature information transfer, enabling the algorithm to escape local optima. Phase separation critical points are automatically identified by detecting peaks in the specific heat capacity curve. The critical point detection sensitivity parameter is calibrated through at least 20 sets of formulation compatibility experiments, marking critical regions as formulation forbidden zones. Finally, the formulation phase diagram and the optimal region boundary are output.

[0073] The specific implementation of step S03 is as follows: Within the optimal region boundary, the physical information neural network incorporates the hybrid rule equation and the rheological equation into the loss function in the form of residuals. The hybrid rule equation describes the weighted relationship between the macroscopic performance of the multi-component system and the performance of each component. The rheological equation, based on the Herschel-Bulkley constitutive equation, describes the relationship between shear stress and shear rate in pigment-filled polypropylene melt. The physical constraint gradient acts directly on the surrogate model parameters through backpropagation, ensuring that the surrogate model's predictions in sparse data regions conform to physical laws. The active learning framework is based on the surrogate model's prediction mean and prediction uncertainty for unexperimented points. It aims to improve the value of the acquisition function to be numerically equal to the expectation that the candidate point performance exceeds the current optimal value. This is obtained by analytical integration of the Gaussian distribution. Candidate points with high prediction uncertainty and excellent prediction performance are preferentially selected as the next experimental points, covering the key formulation space region with the fewest number of experiments.

[0074] The specific implementation of step S04 is: Distributed state evaluation function value The calculation input is the median of the pigment particle chord length measured in real time by an online laser backscattering probe. Standard deviation of pigment particle chord length distribution benchmark value , and weighting coefficients , The results were obtained through no fewer than 30 sets of comparative experiments, using color uniformity and mechanical properties as evaluation indicators, and fitted using response surface methodology. and satisfy Calculations yielded After the value, based on The process adjustment strategy is executed within the range to which the value belongs: when When the value is not lower than the upper threshold of 1.3, increasing the screw speed by 5% will increase the melt temperature by 3℃; when When the value is between 0.9 and 1.3, keep the current parameter unchanged; when... When the value is below the lowering threshold of 0.9, the screw speed decreases by 3% and the melt temperature decreases by 2℃.

[0075] The specific implementation of step S05 is as follows: both the online laser backscatter probe and the ultrasonic attenuation spectrometer are arranged after the melt pump of the extruder, and the two are connected at a ratio of 100... To update the periodic data, the histogram of pigment particle chord length distribution and the volume-weighted particle size distribution are collected in real time and simultaneously input into the morphology-process co-optimization model. The dispersion state decoding path is represented by the formulation-process latent representation. As input, a pigment dispersion parameter vector is output through a fully connected layer. This vector is then input to a differentiable extrusion physics simulator. Based on the Herschel-Bulkley rheological model, the spatial distribution of pigment dispersion along the screw axis is reconstructed, representing the dispersion state field of the entire screw section. Similarly, with a 100... To update the cycle output, a model predictive controller is used to drive the dispersed state field of the entire screw section. The model predictive controller takes minimizing the prediction error of the dispersed state field of the entire screw section in the prediction time domain as the objective function, and solves for the optimal screw speed and melt temperature adjustment sequence to achieve closed-loop dynamic control.

[0076] The specific implementation of step S06 is as follows: the target spectral reflectance curve is in the wavelength range of 400-700 nm. A discrete vector of spectral reflectance containing 31 wavelength points was obtained by spectrophotometer measurement of the target color sample. The color matching decoding path is represented by a formulation-process latent representation. The input is processed by a 4-layer Transformer decoder, each layer containing an 8-head self-attention mechanism sublayer and a feedforward network sublayer, with a hidden layer dimension of 512. The output is a vector of pigment concentration, with the vector dimension matching the number of formulation components. The Transformer decoder captures the optical interactions between pigment components through a multi-head self-attention mechanism, enabling the inverse formulation solution to consider the overlapping of covering forces and tinting force interference effects between pigments, thus improving the accuracy of the inverse solution.

[0077] It should be noted that the key technologies of this invention include: a dual-path variational autoencoder maximizes mutual information in the latent space through a Barlow Twins loss variant, geometrically aligning pigment dispersion morphology image features with formulation-process time-series features, enabling two fundamentally heterogeneous data types to establish a causal relationship in a unified low-dimensional continuous space, which is impossible for traditional multimodal fusion methods; a differentiable extrusion physics simulator embeds the Herschel-Bulkley rheological equation in a backpropagable form into the decoding process, with physical constraint gradients directly acting on model parameter updates, allowing the model's predictions in data-free regions to automatically satisfy rheological physical laws and suppress overfitting under high-dimensional sparse data; and a parallel tempering Monte Carlo algorithm and an active learning framework work together, with the former eliminating physically incompatible formulation combinations through phase separation critical point detection at the beginning of the search, and the latter guiding experimental resources to concentrate on the least information-scarce regions within the feasible formulation space using expected improvement criteria. The two form a two-stage collaborative mechanism of coarse screening and fine search, making the overall formulation optimization efficiency significantly higher than using either method alone. The synergy of three key technologies enables the model to establish a reliable pigment dispersion morphology and formulation-process causal model in a physically feasible high-dimensional formulation space with minimal experimental data, and achieves efficient convergence through continuous latent space gradient walks.

[0078] It should be noted that this invention also solves the following technical problem: In the production process of high-color interior polypropylene materials, disturbances in the extrusion process parameters will change the dispersion state of pigment particles in real time. Traditional offline detection methods cannot detect changes in the dispersion state and adjust process parameters in a timely manner during production, leading to difficulty in maintaining stable color difference between batches. This invention utilizes an online laser backscattering probe and an ultrasonic attenuation spectrometer at 100... To update the real-time acquisition of pigment particle chord length distribution and particle size information, and to combine the dispersion state field reconstruction and model prediction controller of the entire screw section, a closed-loop real-time control loop for pigment dispersion state is formed. This allows process parameter adjustment to intervene in the early stage when the pigment dispersion state deviates from the target range, preventing the degradation of dispersion state from being transmitted to batch color difference shift. This solves the technical problem that offline detection methods cannot achieve real-time closed-loop control of pigment dispersion state.

[0079] Specifically, the principle of this invention is:

[0080] The fundamental reason why this invention can solve the above-mentioned technical problems is that the dual-path variational autoencoder compresses two types of heterogeneous features into the same latent space by maximizing mutual information, so that the latent representation of pigment dispersion morphology and the latent representation of formulation-process are aligned in geometric distance, thereby establishing a causal mapping relationship between the two in a unified low-dimensional continuous space.

[0081] The logical rationale behind this design lies in the following: the reparameterization mechanism of the variational autoencoder enables continuous differentiability of the latent space, supporting continuous walks along the recipe performance gradient direction, transforming discrete high-dimensional recipe search into low-dimensional continuous optimization, fundamentally resolving the combinatorial explosion problem. The Barlow Twins loss variant, by minimizing the Frobenius norm of the difference between the cross-correlation matrix and the identity matrix of the two latent representations, forces the two features to align in direction and prevents the latent representations from collapsing into identical vectors through redundancy removal constraints, ensuring the effectiveness of causal association learning. The differentiable extrusion physics simulator embeds the Herschel-Bulkley rheological equations into the loss function in a backpropagable form, allowing the physical constraint gradients to directly affect encoder parameter updates, ensuring that model predictions are physically self-consistent—something traditional data-driven models cannot achieve.

[0082] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0083] The specific implementation of step S01 involves collecting no fewer than 200 sets of historical formula experimental records. Each set of records includes no fewer than 20 dimensions of formula parameters, extrusion process parameter time-series curves, scanning electron microscope (SEM) images, and color difference batch data. The SEM images are acquired using a field emission scanning electron microscope (FET) after gold sputtering of the extruded sample cross-section, under conditions of an accelerating voltage of 5 kV and a magnification of 5000x, with a resolution no lower than [missing information]. Pixels. Color difference batch data is calculated according to CIE 1976 standard. Batch statistics were calculated after measurement using a spectrophotometer. Monte Carlo multiple scattering simulation was used to expand the color matching training samples to at least 5000 sets. Scanning electron microscope images were subjected to random flipping and brightness perturbation data enhancement processing. Continuous numerical parameters were subjected to maximum-minimum normalization, and discrete formulation components were uniquely thermally encoded. The training and validation sets were divided in an 8:2 ratio.

[0084] The specific implementation of step S02 is to construct the interaction matrix of the formulation components. , for Square array The total number of components in the formula is expressed by the following formula:

[0085] ;

[0086] In the formula, For the matrix of the first Line number Column elements, i.e., components With components The Florey-Hutchins interaction parameters between the two are dimensionless and diagonal. The experience value is set to 0. The solubility parameters of each component are calculated based on the differences in their respective solubility parameters. These parameters are derived from the supplier's technical manual or determined experimentally using the Hansen solubility sphere method. The formula is expressed as follows:

[0087] ;

[0088] In the formula, Reference molar volume, in units of Experience value: 100 and Components With components The solubility parameter, in units of is the molar gas constant, with a value of 8.314. The absolute temperature of the formulation system, in units of Units are ,Right now , divided by back Dimensionless. The negative value of the formulation performance index is used as the system Hamiltonian. The formula is expressed as follows:

[0089] ;

[0090] In the formula, The system's Hamiltonian is dimensionless. and The ingredients are respectively the formulation components With components The Ising spin state takes the value or Dimensionless. The parallel tempering Monte Carlo algorithm simultaneously runs Metropolis sampling on multiple virtual temperature replicas. The high-temperature replicas achieve global exploration of the recipe space through a higher acceptance probability, while the low-temperature replicas converge to the performance extremum region. The replicas periodically exchange configurations to escape local optima, and the acceptance probability of configuration exchange is... The formula is expressed as follows:

[0091] ;

[0092] In the formula, For copy With copies The probability of accepting configurational exchanges between them is dimensionless. and Each is a copy With copies The inverse temperature, in units of Boltzmann constant, with values ​​ranging from 1 to 10. and Each is a copy With copies Virtual temperature, in units of and Each is a copy With copies The system Hamiltonian, in units of ,make Dimensionless. Specific heat capacity curve. The formula used to detect the critical point of phase separation is as follows:

[0093] ;

[0094] In the formula, The specific heat capacity of the system is expressed in units of 1. The ensemble mean of the squares of the Hamiltonian, in units of The square of the ensemble mean of the Hamiltonian, in units of The virtual temperature of the current copy, in units of ,and , The meaning is the same, but here it is used as... Mark to distinguish the current copy. By detection The curve spikes identify the critical points of phase separation, the critical regions are marked as formulation forbidden zones, and the formulation phase diagram and the boundary of the optimal region are output.

[0095] The specific implementation of step S03 involves embedding the hybrid rule equation and rheological equation into the loss function using a physical information neural network within the optimal region boundary. The physical constraint residuals of the hybrid rule equations are then considered. The formula is expressed as follows:

[0096] ;

[0097] In the formula, The physical constraint residuals of the mixed rule equations are dimensionless. The viscosity of the mixed system predicted by the neural network is expressed in units of... For the first Volume fraction of components, dimensionless For the first The intrinsic viscosity of the component, in units of Both the numerator and denominator are dimensionless. After division Dimensionless. Expected improvement of the acquisition function in the surrogate model. The formula is expressed as follows:

[0098] ;

[0099] In the formula, Candidate experimental points The expected improvement value at the point is consistent with the dimensions of the formulation performance index. For the surrogate model to select candidate points The predicted mean, with dimensions consistent with the formulation performance indicators. For the surrogate model to select candidate points The predictive standard deviation has dimensions consistent with the formulation performance indicators. This represents the currently known optimal formulation performance value, with dimensions consistent with the formulation performance index. Dimensionless standardized deviation The cumulative distribution function of the standard normal distribution is dimensionless. Let be the probability density function of the standard normal distribution, dimensionless; the first term... With the second item The dimensions are consistent with the performance indicators of the formulation. Each experiment selected... The largest candidate point is used as the next experimental point to cover the key formulation space region with the fewest number of experiments.

[0100] The specific implementation of step S04 involves calculating the value of the dispersed state evaluation function, expressed by the following formula:

[0101] ;

[0102] In the formula, The value of the distributed state evaluation function is dimensionless. The median chord length of pigment particles measured in real time by an online laser backscattering probe, in units of The median chord length of the target pigment particles is the reference value, in units of , Dimensionless The standard deviation of the pigment particle chord length distribution is given by . The standard deviation of the target pigment particle chord length distribution is the benchmark value, in units of , Dimensionless and Let be the weighting coefficient, satisfying Both are dimensionless. When When the screw speed increases by 5%, the melt temperature increases by 3°C; when When, keep the current parameters unchanged; when At that time, the screw speed decreased by 3%, and the melt temperature decreased by 2℃. , , , The thresholds of 1.3 and 0.9 were obtained through no fewer than 30 sets of comparative experiments, with color uniformity and mechanical properties as evaluation indicators, and were fitted using response surface methodology.

[0103] The specific implementation of step S05 involves acquiring real-time information on pigment particle chord length distribution and particle size using an online laser backscatter probe and an ultrasonic attenuation spectrometer with an update cycle of 100ms after the melt pump in the extruder. This information is then input into a morphology-process co-optimization model. A differentiable extrusion physics simulator reconstructs the dispersion state field across the entire screw section, driving the model prediction controller to dynamically adjust the screw speed and melt temperature. The differentiable extrusion physics simulator is based on the Herschel-Barkley rheological model, and its constitutive equation is expressed as follows:

[0104] ;

[0105] In the formula, Shear stress of pigmented polypropylene melt, in units of The yield stress is expressed in units of 1. This is the consistency coefficient, in units of... Shear rate, in units of Reference shear rate, in units of The experience value is 1. Dimensionless Units are The flow index is dimensionless; the molecule... With denominator All units are The right side of the equation represents the dimensionless 1. Model parameters. , , The results were obtained by measuring the temperature range of 180–220 °C using a rotational rheometer.

[0106] The specific implementation of step S06 involves taking the target spectral reflectance curve as input. The target spectral reflectance curve is a discrete vector of spectral reflectance with a wavelength range of 400–700 nm, containing 31 wavelength points. It is obtained by measuring the target color sample with a spectrophotometer. The color matching decoding path in the morphology-process co-optimization model outputs the concentration vectors of each pigment, thus completing the reverse formulation solution. The color matching decoding path uses a 4-layer transformer decoding layer, each layer containing an 8-head self-attention mechanism sublayer and a feedforward network sublayer. The hidden layer dimension is 512, and the dimension of the output pigment concentration vector is consistent with the number of formulation components.

[0107] Training loss function of morphology-process co-optimization model The formula is expressed as follows:

[0108] ;

[0109] In the formula, The total loss function value is dimensionless. For reconstruction losses, dimensionless The Korbeck-Leibler divergence regularity term is dimensionless. For Barlow twin loss variant, dimensionless The constraint residuals of the differentiable extrusion physics simulator are dimensionless. and The corresponding dimensionless weighting coefficients The weights for course learning strategies are dimensionless and increase linearly from 0 to 0.5. This is the current training round. The formula is expressed as follows:

[0110] ;

[0111] In the formula, For matrix The square of the Frobenius norm, dimensionless identity matrix The square of the Frobenius norm, dimensionless, takes a value equal to the latent representation dimension 128. for and The cross-correlation matrix, with dimensions of Dimensionless for The identity matrix is ​​dimensionless. The calculation formula is expressed as follows:

[0112] ;

[0113] In the formula, Cross-correlation matrix No. Line number Column elements, dimensionless For the first Pigment dispersion morphology latent representation vector for each sample No. Dimensionless components For the first The latent representation vector of the formulation-process for each sample No. Dimensionless components and The values ​​range from 1 to 128. The Adam optimizer is used for training, with an initial learning rate of 0.001, a batch size of 32, and a training epoch of no less than 300 epochs. An early stopping strategy is triggered when the validation set loss does not decrease for 20 consecutive epochs.

[0114] To better understand and implement this invention, the following is a specific application scenario of the invention, Example 2: To verify the effect of the invention, technicians set up a test environment and, by simulating the production process of high-color interior polypropylene automotive dashboard trim panels, conducted a full-process test of formula optimization and online process control on a batch of high-color blue interior polypropylene materials using the technical solution of this invention.

[0115] The basic composition of the test formulation is high-impact polypropylene (melt index 15). / 10 The ingredients included rutile titanium dioxide, phthalocyanine blue pigment, ultrafine talc, maleic anhydride-grafted polypropylene compatibilizer, and EBS dispersant. Technicians first collected 240 sets of historical formulation experimental records. Each record included 20-dimensional formulation parameters, a 480-step extrusion process parameter time-series curve, a 1024×1024 pixel scanning electron microscope image, and color difference data under the CIE 1976 standard. Batch statistics. The color matching training samples were expanded to 5200 groups using the Monte Carlo multiple scattering simulation method. After random flipping and brightness perturbation enhancement processing of the scanning electron microscope images, the training set and validation set were divided in an 8:2 ratio to complete the construction of the training dataset for the morphology-process co-optimization model.

[0116] In step S02, technicians calculate the Flory-Huggins interaction parameters based on the Hansen solubility parameters of each formulation component, construct the formulation component interaction matrix, and calibrate the phase separation critical point detection sensitivity parameters through 24 sets of formulation compatibility experiments. The parallel tempering Monte Carlo algorithm runs in parallel on 12 virtual temperature replicas, identifies three phase separation critical regions through specific heat capacity curve peak detection and marks them as formulation forbidden zones, finally outputting the formulation phase diagram and optimal region boundaries, as shown below. Figure 2 As shown, the distribution of high-performance formulation areas and the boundaries of restricted areas can be seen intuitively.

[0117] In step S03, the physical information neural network uses the hybrid rule equation and Herschel-Bulkley rheological equation as physical constraints within the optimal region boundary. Combined with the active learning framework, it dynamically selects the next experimental point to improve the acquisition function. After 18 rounds of active learning iterations, the prediction uncertainty of the surrogate model in the key formulation region converges to the target level, completing the spatial coverage of the key formulation.

[0118] Technicians obtained the parameters of the dispersed state evaluation function by fitting a response surface methodology through no fewer than 30 sets of comparative experiments. It is 2.0. , It is 0.4 , It is 0.6. The threshold is 0.4, with an upward threshold of 1.3 and a downward threshold of 0.9. In actual extrusion production, the online laser backscatter probe and ultrasonic attenuation spectrometer are used at 100... To update the real-time acquisition of pigment particle chord length distribution and particle size information, a morphology-process co-optimization model reconstructs the dispersion state field of the entire screw section. The model predictive controller dynamically adjusts the screw speed and melt temperature based on the dispersion state evaluation function value.

[0119] Table 1 records the typical decentralized state evaluation function values ​​and corresponding process adjustment strategies during the online process control of 50 consecutive production batches in this test, as shown in Table 1:

[0120] Table 1. Record of Distributed State Evaluation Function Values ​​and Process Adjustment Strategies

[0121]

[0122] As can be seen from Table 1, driven by the closed-loop process control mechanism, the median chord length of pigment particles... With the standard deviation of the chord length distribution After initial fluctuations, the value of the dispersed state evaluation function gradually converges to near the target baseline. It remains stable within the acceptable range between the lower and upper thresholds.

[0123] Table 2 records the color difference of 50 consecutive production batches. The distribution of batch statistics is shown in Table 2:

[0124] Table 2 Color Difference of 50 Consecutive Batches Statistical distribution table

[0125]

[0126] In step S06, the technician uses a spectrophotometer to measure the target color sample to obtain 400-700. The target spectral reflectance curves at 31 wavelength points within the range are input into the color matching decoding path of the morphology-process co-optimization model. After processing by the Transformer decoder, the output is the concentration vector of each pigment, thus completing the reverse formulation solution. Figure 3 As shown, a comparison is given between the target spectral reflectance curve and the spectral reflectance curve predicted by the formula after inverse solving. The two curves are in the range of 400-700. Highly compatible across all frequency bands.

[0127] The technological advancements of this invention compared to traditional methods are reflected in the following aspects. Traditional methods rely on trial and error based on experience. The causal relationship between pigment dispersion morphology information and formulation-process parameters exists as tacit knowledge in the experience of technicians, which cannot be quantitatively modeled, resulting in extremely poor repeatability and transferability of formulation optimization. This invention, through the mutual information maximization mechanism of a dual-path variational autoencoder, explicitly encodes the above causal relationship into a computable latent space structure, transforming the formulation optimization process from experience-driven to model-driven, fundamentally improving the transferability of formulation knowledge. The introduction of a differentiable extrusion physics simulator allows model predictions to operate within a physically constrained framework, avoiding physically infeasible predictions from purely data-driven models in sparse data regions. This is a fundamental improvement that traditional machine learning proxy models cannot achieve. The online closed-loop control mechanism, by sensing the dispersion state of pigment particles in real time and immediately adjusting process parameters, moves the source of batch-to-batch color difference from the end of the process disturbance transmission chain to the source for control. This proactive intervention mechanism has a fundamental advantage in logic compared to the traditional offline detection-post-adjustment process.

[0128] It should be noted that the variables involved in this invention are explained in detail in Tables 3 and 4.

[0129] Table 3. Variable Explanation Table (Part 1)

[0130]

[0131] Table 4. Variable Explanation Table (Part Two)

[0132]

[0133] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the formulation of a high-color interior polypropylene material, characterized in that, Includes the following steps: Historical formula parameters, extrusion process parameter time-series curves, scanning electron microscope images, and color difference batch data were collected to construct a training dataset for the morphology-process co-optimization model. The training dataset was preprocessed and then input into the morphology-process co-optimization model for training. A matrix of interaction between formulation components is constructed. The negative value of the formulation performance index is used as the system Hamiltonian. The parallel tempering Monte Carlo algorithm is used to run Metropolis sampling in parallel at multiple virtual temperatures. The phase separation critical point is identified by the peak detection of the specific heat capacity curve and the critical region is marked as the formulation forbidden zone. The formulation phase diagram and the optimal region boundary are output. Within the optimal region boundary, a physical information neural network is used to embed the hybrid rule equation and rheological equation into the loss function, and an active learning framework is combined to improve the acquisition function and dynamically select the next experimental point. Calculate the dispersion state evaluation function value, and adjust the screw speed and melt temperature parameters according to the interval to which the dispersion state evaluation function value belongs; After the extruder melt pump, the chord length distribution and particle size information of pigment particles are collected in real time by an online laser backscattering probe and an ultrasonic attenuation spectrometer. The chord length distribution and particle size information of pigment particles are input into the morphology-process co-optimization model to reconstruct the dispersion state field of the entire screw section and drive the model prediction controller to dynamically adjust the screw speed and melt temperature. Using the target spectral reflectance curve as input, the color matching decoding path in the morphology-process co-optimization model outputs the concentration vector of each pigment, thus completing the reverse formulation solution; Among them, the morphology-process co-optimization model adopts a dual-path variational autoencoder architecture and is coupled with a differentiable extrusion physical simulator. Path A is a convolutional encoder and path B is a graph variational encoder. The latent representation of pigment dispersion morphology and the latent representation of formulation-process are subject to mutual information maximization constraints in the latent space through Barlow Twins loss variants. The decoder includes dispersion state decoding path and color matching decoding path.

2. The formulation optimization method for high-color interior polypropylene material according to claim 1, characterized in that, The training dataset for the morphology-process co-optimization model was established by collecting historical formula experimental records of no less than a threshold number of historical experimental records. Monte Carlo multiple scattering simulation was used to expand the color matching training samples. Scanning electron microscope images were subjected to random flipping and brightness perturbation data enhancement processing. Continuous numerical parameters were normalized to maximum and minimum. Discrete formula components were encoded using one-heat encoding. The training set and validation set were divided according to the training-validation ratio threshold.

3. The formulation optimization method for high-color interior polypropylene material according to claim 2, characterized in that, The morphology-process co-optimization model training specifically employs the Adam optimizer. The loss function consists of a weighted sum of four parts: reconstruction loss, Kullback-Leibler divergence regularization term, Barlow Twins loss variant, and the constraint residuals of the differentiable extrusion physical simulator. The weights of the constraint residuals of the differentiable extrusion physical simulator are linearly increased to the constraint weight threshold through a course learning strategy. An early stopping strategy is adopted, and training stops when the validation set loss does not decrease for the threshold number of consecutive rounds.

4. The formulation optimization method for the high-color interior polypropylene material according to claim 3, characterized in that, The convolutional encoder for path A, specifically taking a scanning electron microscope image as input, consists of four sequentially stacked 2D convolutional layers. Each 2D convolutional layer is followed by a batch normalization layer and a linear rectified function activation layer. The output of the 4th 2D convolutional layer is compressed into a vector by a global average pooling layer, and then outputs the latent mean vector of pigment dispersion morphology through two parallel fully connected layers. With the latent log-variance vector of pigment dispersion morphology The latent representation of pigment dispersion morphology is obtained through reparameterized sampling. .

5. The formulation optimization method for the high-color interior polypropylene material according to claim 4, characterized in that, The graph variational encoder for path B specifically involves extracting the inter-component relationships from the node feature matrix using a 3-layer graph convolutional network, followed by global mean pooling to obtain a vector representing the formulation component relationships. The extrusion process parameter time-series curve is processed by a bidirectional long short-term memory network, and the hidden state at the last moment is taken as the process time-series representation vector. The two vectors are concatenated and then passed through two parallel fully connected layers to output the latent mean vector and the latent log-variance vector of the formulation and process, respectively. The latent representation of the formulation and process is obtained through reparameterized sampling.

6. The formulation optimization method for the high-color interior polypropylene material according to claim 5, characterized in that, The BarlowTwins loss variant specifically forces two-path encoders to learn a causal relationship between morphology and formulation-process by minimizing the Frobenius norm of the difference between the cross-correlation matrix and the identity matrix of the latent representation of pigment dispersion morphology and the latent representation of formulation-process.

7. The formulation optimization method for the high-color interior polypropylene material according to claim 6, characterized in that, The dispersion state decoding path takes the latent representation of the formulation and process as input, outputs a pigment dispersion parameter vector through a fully connected layer, inputs the pigment dispersion parameter vector into a differentiable extrusion physics simulator, and the differentiable extrusion physics simulator is built based on the Herschel-Bulkley rheological model, outputting a reconstructed dispersion state field across the entire screw section.

8. The method for optimizing the formulation of high-color interior polypropylene material according to claim 7, characterized in that, The color matching decoding path takes the latent representation of the recipe-process as input, and outputs the pigment concentration vectors after processing by the Transformer decoder. The Transformer decoder consists of multiple Transformer decoding layers, each of which contains a multi-head self-attention mechanism sublayer and a feedforward network sublayer.

9. The formulation optimization method for the high-color interior polypropylene material according to claim 8, characterized in that, Elements of the interaction matrix of formulation components Specifically, it is composed of the formula components With formulation components The Flory-Huggins interaction parameters between the components were estimated by calculating the difference in solubility parameters of each component. These solubility parameters were obtained from the technical manuals of each component supplier or determined by the Hansen solubility sphere method.

10. The method for optimizing the formulation of high-color interior polypropylene material according to claim 9, characterized in that, The parallel tempering Monte Carlo algorithm specifically runs Metropolis sampling simultaneously on multiple virtual temperature replicas. The high-temperature replicas achieve global unbiased exploration of the recipe space, while the low-temperature replicas converge to the performance extremum region. The replicas periodically exchange configurations so that the low-temperature replicas can escape local extrema and achieve cross-temperature information transfer.

Images