Intelligent rubber production detection control method based on microwave technology

Abstract

The invention discloses a rubber intelligent production detection control method based on a microwave technology, and relates to the technical field of rubber product intelligent production, and the method comprises the steps: loading a three-dimensional digital model of a target rubber product, initializing a digital twin, controlling a microwave antenna array to execute scanning, and collecting an S parameter of the rubber product; based on the S parameter, calculating a three-dimensional dielectric constant distribution field in the rubber through an electromagnetic inverse scattering reconstruction algorithm, and converting the three-dimensional dielectric constant distribution field into a three-dimensional vulcanization degree distribution field and a three-dimensional temperature distribution field according to a pre-stored calibration curve; and performing feature extraction on the three-dimensional vulcanization degree distribution field and the three-dimensional temperature distribution field, inputting the digital twinborn body, and updating activation energy parameters in the digital twinborn body. According to the invention, omnibearing and high-resolution perception of the internal vulcanization state of the rubber product with a complex structure is realized.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing technology for rubber products, and in particular to an intelligent manufacturing detection and control method for rubber based on microwave technology. Background Technology

[0002] Rubber vulcanization is a core process in rubber product manufacturing, and the accuracy of its process control directly determines the physical and mechanical properties, service life, and quality consistency of the final product. Traditional vulcanization control technologies mainly rely on pre-set time-temperature process curves or feedback control based on thermocouple temperature monitoring at limited points. In recent years, with the development of sensing technology, non-destructive testing methods, represented by dielectric analysis, have been introduced into vulcanization process monitoring. These methods indirectly reflect the degree of vulcanization by measuring changes in the dielectric constant or loss factor of the rubber during vulcanization. Microwave technology, in particular, exhibits unique advantages such as online, non-contact, and high penetration due to its high sensitivity to changes in polar molecular motion and material dielectric properties, making it a research hotspot for vulcanization status monitoring. Existing technologies utilize single-point or multi-point microwave sensors to measure signal amplitude or phase changes. By comparing these changes with pre-stored empirical models or calibration curves, the overall or local average degree of vulcanization is estimated, allowing for coarse adjustment of vulcanization time or heating power. While this has improved the sensing capability of the rubber vulcanization process to some extent, a closed-loop industrial control system has not yet been formed.

[0003] Despite advancements in rubber vulcanization monitoring, two core bottlenecks remain when dealing with complex, multi-layered products like tires. First, insufficient spatial state perception. Current microwave detection relies heavily on single-point or limited sensors, yielding signals that are essentially integral effects of medium properties along the path. This only allows for the inversion of the overall average degree of vulcanization, failing to analyze the fine distribution and evolutionary differences in vulcanization states at various points within the internal three-dimensional space (especially between different material layers). Second, the control model lacks adaptability. Existing strategies rely on vulcanization kinetic models whose key parameters (such as activation energy) are largely derived from laboratory calibration and considered fixed values. These parameters cannot adapt to the reactivity drift caused by raw material fluctuations and minor process variations in actual production. Static parameters introduce errors into the forward-looking simulations of digital twins, leading to deviations in optimized control commands and hindering the achievement of stable industrial control systems. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides a method for intelligent production detection and control of rubber based on microwave technology to solve the problems of insufficient perception of the internal state of complex structure products and lack of adaptive capability of control models in existing technologies.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] This invention provides a method for intelligent production detection and control of rubber based on microwave technology. The method includes: loading a three-dimensional digital model of the target rubber product and initializing a digital twin; simultaneously controlling a microwave antenna array to perform scanning and acquire the S-parameters of the rubber product; based on the S-parameters, calculating the three-dimensional dielectric constant distribution field inside the rubber using an electromagnetic inverse scattering reconstruction algorithm, and converting the three-dimensional dielectric constant distribution field into a three-dimensional vulcanizability distribution field and a three-dimensional temperature distribution field according to a pre-stored calibration curve; extracting features from the three-dimensional vulcanizability distribution field and the three-dimensional temperature distribution field, inputting them into the digital twin, and updating the activation energy parameters in the digital twin; using the updated activation energy parameters in the digital twin to construct coupled spatiotemporal stochastic partial differential equations, and predicting the three-dimensional spatial evolution and prediction uncertainty of the future vulcanization process; transforming the three-dimensional spatial evolution and prediction uncertainty of the future vulcanization process into a distributed bar stochastic programming problem, and generating spatially differentiated temperature control commands through a distributed solution algorithm; executing the spatially differentiated temperature control commands, adjusting the zoned heating power, and regulating the vulcanization process of the rubber product, while simultaneously performing scanning and control for the next cycle.

[0008] As a preferred embodiment of the intelligent rubber production detection and control method based on microwave technology described in this invention, the steps of loading a three-dimensional digital model of the target rubber product and initializing a digital twin, while simultaneously controlling the microwave antenna array to perform scanning and acquire the S-parameters of the rubber product, are as follows.

[0009] Load the three-dimensional digital model of the target rubber product and establish the posterior probability distribution of the digital twin based on the three-dimensional digital model;

[0010] The optimal scanning parameters are dynamically obtained based on the posterior probability distribution of the digital twin.

[0011] Based on the optimal scanning parameters, the microwave antenna array is controlled to perform scanning and acquire the S-parameters of the rubber product.

[0012] As a preferred embodiment of the intelligent rubber production detection and control method based on microwave technology described in this invention, the specific steps for calculating the three-dimensional dielectric constant distribution field inside the rubber based on S-parameters and using an electromagnetic inverse scattering reconstruction algorithm are as follows:

[0013] The S-parameters are preprocessed to obtain the frequency domain scattering data matrix;

[0014] Based on the frequency domain scattering data matrix and prior probability distribution, an electromagnetic inversion objective function is constructed.

[0015] A multi-resolution solution strategy is used to solve the electromagnetic inversion objective function to obtain the three-dimensional dielectric constant distribution field inside the rubber.

[0016] As a preferred embodiment of the intelligent rubber production detection and control method based on microwave technology described in this invention, the specific steps for converting the three-dimensional dielectric constant distribution field into a three-dimensional vulcanizability distribution field and a three-dimensional temperature distribution field according to the pre-stored calibration curve are as follows.

[0017] Dielectric relaxation spectrum features are extracted from the three-dimensional complex permittivity distribution field to generate a three-dimensional dielectric response feature field.

[0018] By performing bilinear interpolation mapping on the three-dimensional dielectric response characteristic field point by point through pre-stored calibration curves, a three-dimensional sulfidation distribution field and a three-dimensional temperature distribution field are generated.

[0019] As a preferred embodiment of the intelligent rubber production detection and control method based on microwave technology described in this invention, the specific steps for extracting features from the three-dimensional vulcanizate distribution field and the three-dimensional temperature distribution field, inputting them into a digital twin, and updating the activation energy parameters in the digital twin are as follows.

[0020] The spatiotemporal evolution sequence of each spatial location is extracted from the three-dimensional sulfurity distribution field and the three-dimensional temperature distribution field, and the local spatiotemporal derivative field is obtained.

[0021] Based on the local spatiotemporal derivative field and the current activation energy parameters of the digital twin, the process inconsistency index at each spatial location is calculated.

[0022] Using process inconsistency indices as observations, the activation energy parameters in the digital twin are updated using an ensemble Kalman filter algorithm.

[0023] As a preferred embodiment of the intelligent rubber production detection and control method based on microwave technology described in this invention, the specific steps for constructing coupled spatiotemporal stochastic partial differential equations using the activation energy parameters in the updated digital twin are as follows.

[0024] The activation energy parameters, three-dimensional sulfidation distribution field, and three-dimensional temperature distribution field in the updated digital twin are used as the initial conditions for the prospective simulation.

[0025] Based on the initial conditions, a coupled spatiotemporal stochastic partial differential equation for parameter uncertainty and process disturbance is constructed.

[0026] As a preferred embodiment of the intelligent rubber production detection and control method based on microwave technology described in this invention, the specific steps for predicting the three-dimensional spatial evolution and uncertainty of the future vulcanization process are as follows:

[0027] The stochastic spectrum method is used to solve the coupled spatiotemporal stochastic partial differential equations and calculate the probabilistic expansion coefficients of the sulfidation field and temperature field at multiple future time points.

[0028] Basis function synthesis and statistical moment extraction are performed on the probabilistic expansion coefficients to predict the three-dimensional spatial evolution of the future sulfurization process and predict uncertainty.

[0029] As a preferred embodiment of the intelligent rubber production detection and control method based on microwave technology described in this invention, the step of transforming the three-dimensional spatial evolution and prediction uncertainty of the future vulcanization process into a distributed Bruker stochastic programming problem includes the following specific steps.

[0030] Based on the three-dimensional spatial evolution and prediction uncertainty of the future vulcanization process, an optimization problem is defined with the objectives of controlling energy, tracking accuracy and spatial uniformity.

[0031] By utilizing the uncertainty of prediction, the optimization problem is transformed into a distributive bar stochastic programming problem.

[0032] As a preferred embodiment of the intelligent rubber production detection and control method based on microwave technology described in this invention, the specific steps for generating spatially differentiated temperature control commands through a distributed solution algorithm are as follows:

[0033] A distributed solution algorithm is used to optimize the bibliometric stochastic programming problem to obtain the globally optimal set of temperature control decision variables;

[0034] Extract the spatially differentiated temperature control command issued at the current moment from the set of globally optimal temperature control decision variables.

[0035] As a preferred embodiment of the intelligent rubber production detection and control method based on microwave technology described in this invention, the specific steps of executing spatially differentiated temperature control commands, adjusting zone heating power, regulating the vulcanization process of rubber products, and simultaneously performing scanning and control for the next cycle are as follows:

[0036] The spatially differentiated temperature control command is sent to the heaters in each zone, the heating power of the corresponding zone is adjusted, and the current temperature control command field is recorded.

[0037] Based on the spatial gradient of the temperature control command field and the spatial uncertainty of the current three-dimensional state field, the optimal scanning parameters for the next scanning cycle are obtained.

[0038] Based on the optimal scanning parameters, the microwave antenna array is driven to perform scanning, triggering and initiating a new round of detection and control.

[0039] The beneficial effects of this invention are as follows: By integrating microwave tomography and digital twins, it achieves comprehensive and high-resolution perception of the internal vulcanization state of complex rubber products, solving the "black box" problem that single-point detection cannot identify differences in vulcanization between internal layers; by using digital twins to perform forward-looking probabilistic simulation of coupled uncertainties, it achieves accurate prediction and adaptive control of the vulcanization process, improving vulcanization uniformity, stabilizing product quality, and reducing energy consumption, thereby constructing a high-precision and highly adaptable intelligent industrial control system for rubber production. Attached Figure Description

[0040] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a flowchart of a rubber intelligent production detection and control method based on microwave technology.

[0042] Figure 2 This is a flowchart for collecting S-parameters.

[0043] Figure 3 The graph shows the relationship between S-parameters and frequency.

[0044] Figure 4 This is a three-dimensional sulfur distribution map. Detailed Implementation

[0045] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0046] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0047] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0048] Reference Figures 1-4This is one embodiment of the present invention, which provides a method for intelligent production detection and control of rubber based on microwave technology, comprising the following steps:

[0049] S1. Load the three-dimensional digital model of the target rubber product and initialize the digital twin. At the same time, control the microwave antenna array to perform scanning and collect the S-parameters of the rubber product.

[0050] Load the three-dimensional digital model of the target rubber product and establish the posterior probability distribution of the digital twin based on the three-dimensional digital model.

[0051] The specific process includes: after loading the three-dimensional digital model of the target rubber product, based on the prior information contained in the three-dimensional digital model of the target rubber product, such as the spatial geometry, material distribution, and initial conditions of the vulcanization reaction, the state variables inside the digital twin are regarded as random variables with uncertainty, and a corresponding prior probability distribution is assigned to the state variables inside the digital twin; on this basis, according to the basic principles of Bayesian statistical inference, the probabilistic descriptions of each state variable in the digital twin are conditionally processed using the deterministic constraints and physical relationships provided by the three-dimensional digital model of the target rubber product, and the posterior probability distribution of the digital twin is established.

[0052] The optimal scanning parameters are dynamically obtained based on the posterior probability distribution of the digital twin.

[0053] The specific process includes: using the posterior probability distribution of the digital twin to probabilistically characterize the uncertainty of the internal state of the rubber product; evaluating the impact of different scanning parameters on the amount of information acquired by the microwave antenna array; quantifying the observation efficiency of each candidate scanning parameter through statistical criteria such as information entropy or expected information gain; and selecting the scanning parameter that maximizes the information acquisition efficiency or minimizes the uncertainty of state estimation as the optimal scanning parameter.

[0054] Based on the optimal scanning parameters, the microwave antenna array is controlled to perform scanning and acquire the S-parameters of the rubber product.

[0055] The specific process includes controlling the microwave antenna array to perform spatial scanning of the rubber product based on the optimal scanning parameters, according to the microwave frequency range, antenna position configuration and excitation timing determined by the optimal scanning parameters. The microwave antenna array applies microwave signals at the transmitting end and records the transmission and reflection responses between each antenna element at the receiving end, thereby acquiring the S-parameters of the rubber product.

[0056] It should be noted that the S-parameters of rubber products, also known as scattering parameters, are complex parameters that describe the relationship between incident, reflected, and transmitted waves between ports of a microwave network. When performing microwave scanning on rubber products, the S-parameters include the transmission coefficients and reflection coefficients between all combinations of transmitting and receiving antennas. Specifically, they cover the complex responses measured by each antenna as a transmitter and by the other antennas (including itself) as receivers, forming a complete S-parameter. The diagonal elements represent the reflection coefficients of each antenna, and the off-diagonal elements represent the transmission coefficients between different antennas.

[0057] S2. Based on the S-parameters, the three-dimensional dielectric constant distribution field inside the rubber is calculated by the electromagnetic inverse scattering reconstruction algorithm, and the three-dimensional dielectric constant distribution field is converted into a three-dimensional vulcanization distribution field and a three-dimensional temperature distribution field according to the pre-stored calibration curve.

[0058] The S-parameters are preprocessed to obtain the frequency domain scattering data matrix.

[0059] The specific process includes preprocessing the S-parameters, including removing noise interference, calibrating antenna coupling effects, and aligning the multi-channel phase reference. The S-parameters are then converted into complex scattering responses under a unified reference plane and organized into a structured frequency domain scattering data matrix according to the frequency dimension.

[0060] An electromagnetic inversion objective function is constructed based on the frequency domain scattering data matrix and prior probability distribution.

[0061] The specific process includes: based on the frequency domain scattering data matrix and the prior probability distribution, the physical relationship between the measured electromagnetic response characterized by the frequency domain scattering data matrix and the internal dielectric properties of the rubber product described by the prior probability distribution is modeled using Maxwell's equations. The least squares criterion or the maximum a posteriori estimation method is used to construct an error term that measures the difference between the simulated scattering field and the measured frequency domain scattering data matrix. A regularization term derived from the prior probability distribution is added to constrain the physical rationality of the solution, thereby constructing the electromagnetic inversion objective function.

[0062] It should be noted that the measured frequency domain scattering data matrix is ​​a structured complex data array formed by preprocessing the full matrix S-parameters obtained by microwave scanning of the rubber product. The matrix is ​​organized according to the frequency dimension, and each frequency point corresponds to a complete complex scattering response between the transmit and receive antenna pairs. The acquisition process is as follows: the microwave antenna array is controlled to scan the rubber product based on the optimal scanning parameters to collect the full matrix S-parameters. Then, the full matrix S-parameters are preprocessed to remove noise interference, calibrate antenna coupling effects, and perform phase alignment, and finally form the measured frequency domain scattering data matrix.

[0063] A multi-resolution solution strategy is used to solve the electromagnetic inversion objective function to obtain the three-dimensional dielectric constant distribution field inside the rubber, expressed as:

[0064] ;

[0065] in, Indicates the spatial location inside a rubber product. The three-dimensional dielectric constant distribution field at that location, Indicates the number is The internal spatial location of rubber products Indicates the index of a discrete point in space. Indicates the spatial location inside a rubber product. The relative permittivity distribution field to be optimized. This indicates the total number of resolution levels. An index representing the resolution level. Indicates the first The weight coefficients corresponding to each resolution level Indicates the first Frequency domain scattering data at each resolution level, Indicates the first The relative permittivity distribution field to be optimized at each resolution level Simulated frequency domain scattering data, This represents the weight coefficient of the prior regularization term. Let represent the prior probability density function of the relative permittivity distribution field to be optimized.

[0066] It should be noted that all physical quantities in this formula are expressed in the International System of Units (SI). The rate of change of sulfide, the predicted rate of change of sulfide, and the reference rate of change of sulfide are all expressed in terms of the change of sulfide per unit time. The smallest positive number has the same dimension as the numerator to ensure that the denominator is non-zero and there is no problem of dimension inconsistency. Therefore, the entire expression achieves dimension uniformity in the calculation process.

[0067] The weighting coefficients of the prior regularization term are used to balance the relative importance between the data fitting term and the regularization term corresponding to the prior probability distribution in the electromagnetic inversion objective function, based on... Methods such as the curve method, generalized cross-validation, or Bayesian evidence maximization are used to determine the frequency domain scattering data matrix by combining the noise level and the confidence level of the prior probability distribution. Frequency domain scattering data refers to the scattering response of rubber products to incident electromagnetic waves measured by the microwave antenna array at multiple frequency points during microwave scanning. Specifically, it is manifested as the complex transmission coefficient and reflection coefficient between each transmitting antenna and receiving antenna at each frequency point. These data completely record the amplitude and phase changes in the frequency domain after the interaction between electromagnetic waves and the internal dielectric properties of rubber, forming the basic observation information for reconstructing the internal three-dimensional dielectric constant distribution field.

[0068] The prior probability density function of the relative permittivity distribution field to be optimized describes the statistical understanding of the relative permittivity distribution field inside the rubber product before using the frequency domain scattering data matrix. The prior probability density function is provided by the three-dimensional digital model of the target rubber product. Specifically, it is derived from the physical constraints and empirical knowledge set in the initial stage of the digital twin based on information such as material type, initial vulcanization state and geometric structure. It is formalized into a probability distribution through a Bayesian inference framework and used to guide the physical rationality of the solution during the electromagnetic inversion process.

[0069] The weighting coefficients corresponding to the resolution levels are parameters used to balance the contributions of data fitting terms at different resolution levels during multi-resolution inversion. These weighting coefficients are set according to the importance of each resolution level in the overall inversion and are determined through prior knowledge of the relationship between frequency response characteristics and spatial resolution, so as to ensure that low-resolution layers provide global structure guidance and high-resolution layers realize fine detail restoration.

[0070] The specific process includes solving the electromagnetic inversion objective function using a multi-resolution solution strategy. Specifically, the three-dimensional dielectric constant distribution field to be determined is gradually optimized at different resolution levels. The relative dielectric constant values ​​at spatial discrete points are adjusted from coarse to fine. Combining the response of the frequency domain scattering data matrix at each resolution level with the regularization constraints provided by the prior probability distribution, the difference between the simulated scattering field and the measured frequency domain scattering data matrix is ​​minimized in each iteration while taking into account the degree of conformity with the prior information, thereby obtaining the three-dimensional dielectric constant distribution field inside the rubber product.

[0071] It should be noted that the degree of conformity with prior information refers to the level of consistency between the three-dimensional dielectric constant distribution field obtained by electromagnetic inversion and the prior probability distribution set by the three-dimensional digital model of the target rubber product during the initialization stage of the digital twin. This degree of conformity is calculated by substituting the currently estimated three-dimensional dielectric constant distribution field into the probability density function of the prior probability distribution, or equivalently quantified by the magnitude of the regularization term. The smaller the value, the closer the reconstruction result is to the physical constraints and statistical characteristics described by the prior information.

[0072] Dielectric relaxation spectrum features are extracted from the three-dimensional complex permittivity distribution field to generate a three-dimensional dielectric response feature field.

[0073] The specific process includes extracting dielectric relaxation spectrum features from the three-dimensional complex dielectric constant distribution field, analyzing the relationship between the real and imaginary parts of the three-dimensional complex dielectric constant distribution field in the frequency dimension, identifying the relaxation behavior of the dielectric response with frequency evolution at each spatial location, using spectral analysis methods such as multi-pole relaxation fitting to quantify characteristic parameters such as local dielectric loss peak position, relaxation time and intensity, and organizing the characteristic parameters according to spatial coordinates to form a three-dimensional dielectric response characteristic field.

[0074] It should be noted that dielectric relaxation spectrum characteristics refer to the relaxation behavior characteristics of a material under the action of an alternating electric field, which are shown by the change of its complex permittivity with frequency. Specifically, these characteristics include the position of the dielectric loss peak (corresponding to the relaxation time), the peak size (reflecting the polarization intensity or degree of loss), the peak width (characterizing the distribution width or non-uniformity of the relaxation process), and the dispersion curve shape of the real and imaginary parts.

[0075] By performing bilinear interpolation mapping on the three-dimensional dielectric response characteristic field point by point through pre-stored calibration curves, a three-dimensional sulfidation distribution field and a three-dimensional temperature distribution field are generated.

[0076] The specific process includes: performing bilinear interpolation mapping on the three-dimensional dielectric response feature field point by point through a pre-stored calibration curve; using the correspondence between the dielectric response features recorded in the pre-stored calibration curve and the degree of sulfidation and temperature; at each spatial location, based on the value of the three-dimensional dielectric response feature field at that point, finding adjacent nodes on the two-dimensional parameter grid of the pre-stored calibration curve; and obtaining the corresponding degree of sulfidation and temperature values ​​according to the bilinear interpolation method; and combining the interpolation results of all spatial points to form a three-dimensional degree of sulfidation distribution field and a three-dimensional temperature distribution field.

[0077] It should be noted that the pre-stored calibration curve is a pre-established curve showing the correspondence between dielectric response characteristics and vulcanization degree and temperature. The pre-stored calibration curve is constructed based on data obtained from microwave measurements of rubber samples with known vulcanization degree and temperature under controlled conditions. During the pre-stored process, the same microwave excitation as the actual test is applied to a series of rubber samples with different vulcanization degrees and temperatures. S-parameters are collected and the corresponding three-dimensional complex dielectric constant distribution field is reconstructed. The dielectric relaxation spectrum characteristics are recorded one-to-one with the actual vulcanization degree and temperature of the samples to form a multi-dimensional mapping table. The pre-stored calibration curve is then organized into a queryable pre-stored calibration curve through interpolation or fitting methods.

[0078] like Figure 3 This diagram illustrates the relationship between S-parameters and frequency. The top image is an overview plot, showing the trend of S-parameter variation across different frequency ranges. The X-axis represents frequency, ranging from 2.4 GHz to 2.5 GHz; the Y-axis represents the S-parameter value. The overview plot shows the general trend of S-parameter variation with frequency, revealing significant fluctuations within a certain frequency range, reflecting the specific response of rubber products under the influence of microwave technology. A magnified view, located below the image, enlarges the area marked by the red dashed box in the overview plot. This magnification clearly shows the variation of S-parameters between 2.44 GHz and 2.46 GHz. The variation curves in the local plot are prominently displayed, showing the peaks and troughs of the S-parameter. The plot marks the point of maximum difference at a specific frequency, demonstrating the fluctuation of the S-parameter in this frequency band. This fluctuation reflects a significant change in the microwave response characteristics of rubber products within a specific frequency range, possibly related to internal physical or chemical changes in the material.

[0079] S3. Extract features from the three-dimensional sulfurity distribution field and the three-dimensional temperature distribution field, input them into the digital twin, and update the activation energy parameters in the digital twin.

[0080] The spatiotemporal evolution sequence of each spatial location is extracted from the three-dimensional sulfurity distribution field and the three-dimensional temperature distribution field, and the local spatiotemporal derivative field is obtained.

[0081] The specific process includes extracting the spatiotemporal evolution sequence of each spatial location from the three-dimensional sulfurity distribution field and the three-dimensional temperature distribution field; arranging the sulfurity and temperature values ​​of each spatial location at multiple consecutive sampling times in chronological order to form their respective time series data; obtaining the rate of change of the time series data in the time dimension using numerical differentiation methods such as finite difference method or local polynomial fitting; and simultaneously performing gradient calculations on the values ​​of adjacent spatial locations in the spatial dimension to obtain the local spatiotemporal derivative field describing the local variation characteristics of sulfurity and temperature in time and space.

[0082] Based on the local spatiotemporal derivative field and the current activation energy parameters of the digital twin, the process inconsistency index at each spatial location is calculated, expressed as:

[0083] ;

[0084] in, Indicates the internal spatial location of a rubber product Location, at the number sampling time Inconsistency indicators in the process Indicates the number is Sampling time, Indicates the index of the sampling time.

[0085] Indicates the spatial location inside a rubber product. Location, at the number sampling time The rate of change of sulfidation Indicates the spatial location inside a rubber product. Location, at the number sampling time The predicted rate of change in sulfidation Indicates the rate of change of reference sulfidation. It represents a very small positive number.

[0086] It should be noted that the vulcanizability change rate refers to the rate at which the vulcanizability of a local spatial location changes over time during the vulcanization process of a rubber product. The vulcanizability change rate is obtained by performing a time-difference operation on the values ​​of the three-dimensional vulcanizability distribution field at multiple consecutive sampling times.

[0087] The predicted rate of change of sulfidation is the rate of change of sulfidation at each spatial location in the future, obtained by the digital twin based on the current activation energy parameters and the current three-dimensional temperature distribution field through the sulfidation reaction kinetic equation.

[0088] The reference sulfidation change rate is a benchmark value used to normalize or stabilize values ​​in the calculation of process inconsistency indicators. The reference sulfidation change rate is determined by the sulfidation change rate obtained by the digital twin under standard sulfidation conditions or typical process parameters, and is used to reflect the expected rate of change level in the normal sulfidation process.

[0089] The specific process includes calculating the process inconsistency index for each spatial location based on the local spatiotemporal derivative field and the current activation energy parameters of the digital twin. By comparing the difference between the rate of change of sulfide at each spatial point in the local spatiotemporal derivative field of the three-dimensional sulfide distribution field at the actual observation time and the predicted rate of change of sulfide at the corresponding spatial point predicted by the digital twin based on the current activation energy parameters, this difference is used as the numerator, and the sum of the maximum value of the two absolute values ​​of the rate of change and a very small positive number is used as the denominator to form a ratio. This quantifies the degree of deviation between the actual evolution process and the model prediction at each spatial location, thus obtaining the process inconsistency index for each spatial location.

[0090] Using process inconsistency indices as observations, the activation energy parameters in the digital twin are updated using an ensemble Kalman filter algorithm.

[0091] The specific process includes establishing a sample set representing the possible values ​​of the activation energy parameters in the digital twin by using random sampling methods such as Monte Carlo sampling or Latin hypercube sampling from the prior probability distribution of activation energy parameters set in the initialization stage of the digital twin. Based on the difference between the process inconsistency index and the inconsistency index of the sample set generation process, and combined with the statistical covariance information of the sample set, the correction weight is obtained, and the activation energy parameter sample set is weighted and adjusted to obtain the updated activation energy parameters in the digital twin.

[0092] It should be noted that the ensemble Kalman filter algorithm is a data assimilation method for parameter or state estimation that uses a set of samples to approximate the probability distribution of parameters or states and performs synchronous linear updates on all samples based on the difference between the observed values ​​and the sample predictions.

[0093] like Figure 4A three-dimensional vulcanizate distribution map illustrates the distribution of vulcanizate under different X and Y coordinates. The X and Y axes represent different spatial coordinate positions of the rubber product during microwave treatment, while the Z-axis represents the corresponding vulcanizate value. The chart uses different shades of color to represent the range of vulcanizate variation; the color bars at the bottom of the chart indicate the vulcanizate value ranges corresponding to different colors. The colors range from purple to yellow, with purple representing lower vulcanizate values ​​and yellow representing higher vulcanizate values, showing the differences in the degree of vulcanization of the rubber material in different regions. The spatial distribution characteristics of vulcanizate in the material are clearly visible, especially the trends in different regions.

[0094] S4. Using the activation energy parameters in the updated digital twin, a coupled spatiotemporal stochastic partial differential equation is constructed to predict the three-dimensional spatial evolution of the future sulfurization process and the prediction uncertainty.

[0095] The activation energy parameters, three-dimensional sulfidation distribution field, and three-dimensional temperature distribution field in the updated digital twin are used as the initial conditions for the prospective simulation.

[0096] The specific process includes using the activation energy parameters, three-dimensional sulfidation distribution field, and three-dimensional temperature distribution field in the updated digital twin as the initial conditions for the forward simulation. The activation energy parameters in the updated digital twin are substituted into the sulfidation reaction kinetic equation. At the same time, the three-dimensional sulfidation distribution field and the three-dimensional temperature distribution field at the current moment are used as the initial values ​​of sulfidation and temperature at each point in space, respectively, to jointly constitute the complete initial state required for the forward simulation at the start of time progression.

[0097] Based on the initial conditions, a coupled spatiotemporal stochastic partial differential equation for parameter uncertainty and process disturbance is constructed.

[0098] The specific process includes, based on the initial conditions, modeling the uncertainty carried by the activation energy parameter in the updated digital twin as a random variable, and representing the material inhomogeneity, heat conduction fluctuations and other disturbances in the sulfurization process as spatiotemporal random terms, and embedding both into the partial differential equation describing the evolution of sulfurization degree and temperature, forming a coupled spatiotemporal random partial differential equation that simultaneously contains parameter uncertainty and process disturbance.

[0099] The coupled spatiotemporal stochastic partial differential equations are solved using the stochastic spectral method. The probabilistic expansion coefficients of the sulfidation and temperature fields at multiple future time points are calculated, and their expressions are as follows:

[0100] ;

[0101] in, Indicates the spatial location inside a rubber product. Time nodes and physical field The The probabilistic expansion coefficients of a random spectral orthogonal basis function Represents a physical quantity field. The basis function number represents the random spectral expansion. This represents the discrete time points in the future forecast. Represents random variables The sample space, Indicates the spatial location inside a rubber product. Time nodes and the values ​​of random variables The values ​​of the sulfidation field and temperature field under the given conditions. Indicates the value taken by a random variable The next The function values ​​of a random spectral orthogonal basis function Represents random variables The joint probability density function.

[0102] It should be noted that the probabilistic expansion coefficients are the deterministic weighting coefficients corresponding to the expansion of the three-dimensional sulfidation distribution field and the three-dimensional temperature distribution field in the space of random variables using polynomial basis functions. They are used to describe the probabilistic evolution characteristics of these two fields under the influence of parameter uncertainty and process disturbance.

[0103] The specific process includes: constructing a set of polynomial basis functions orthogonal to the probability distribution of the random variables corresponding to the process perturbation, based on the uncertainty of the activation energy parameters in the updated digital twin; representing the stochastic evolution of the three-dimensional sulfidation distribution field and the three-dimensional temperature distribution field in time and space as a linear combination of polynomial basis functions, with the coefficients of the linear combination being deterministic spatiotemporal functions; substituting the expansion forms of the three-dimensional sulfidation distribution field and the three-dimensional temperature distribution field into the coupled spatiotemporal stochastic partial differential equations; and projecting the coupled spatiotemporal stochastic partial differential equations onto each polynomial basis function through Galerkin projection, thereby obtaining a set of deterministic partial differential equations about the expansion coefficients; and solving the deterministic partial differential equations to obtain the expansion coefficients of the three-dimensional sulfidation distribution field and the three-dimensional temperature distribution field on the polynomial basis functions of each order at multiple future time points, i.e., the probabilistic expansion coefficients.

[0104] Basis function synthesis and statistical moment extraction are performed on the probabilistic expansion coefficients to predict the three-dimensional spatial evolution of the future sulfurization process and predict uncertainty.

[0105] The specific process includes: performing basis function synthesis and statistical moment extraction on the probabilistic expansion coefficients; multiplying and summing the probabilistic expansion coefficients of the three-dimensional sulfurity distribution field and the three-dimensional temperature distribution field at multiple future time points with the corresponding polynomial basis functions to reconstruct the complete expressions for the stochastic sulfurity field and temperature field; and then obtaining the first-order statistical moments (i.e., mathematical expectation) and second-order statistical moments (i.e., variance) of the stochastic sulfurity field and temperature field expressions to obtain the three-dimensional spatial evolution of the future sulfurization process and its prediction uncertainty.

[0106] S5. The three-dimensional spatial evolution and prediction uncertainty of the future vulcanization process are transformed into a distributed bar stochastic programming problem, and spatially differentiated temperature control commands are generated through a distributed solution algorithm.

[0107] Based on the three-dimensional spatial evolution and prediction uncertainty of the future vulcanization process, an optimization problem is defined with the objectives of controlling energy, tracking accuracy, and spatial uniformity.

[0108] The specific process includes quantifying control energy, tracking accuracy, and spatial uniformity as cost terms in the optimization objective based on the three-dimensional spatial evolution and prediction uncertainty of the future vulcanization process. Control energy represents the total consumption of heating power in the partition, tracking accuracy represents the deviation between the three-dimensional spatial evolution of the future vulcanization process and the target vulcanization trajectory, and spatial uniformity represents the spatial consistency of the vulcanization degree distribution inside the rubber product. These three terms constitute the objective function of the multi-objective optimization problem, and are combined with physical constraints and equipment limitations to form a complete optimization problem.

[0109] By utilizing the uncertainty of prediction, the optimization problem is transformed into a distributive bar stochastic programming problem.

[0110] The specific process includes transforming the optimization problem into a sub-Bruker stochastic programming problem by utilizing the uncertainty of prediction. This involves modeling the probabilistic information of the future vulcanization process in three-dimensional space as a set of probability distributions of uncertain parameters, and optimizing the expected value of the objective function on the set of probability distributions in the worst case. This ensures that the generated temperature control command can guarantee control performance in all possible probability distributions, thereby transforming the original multi-objective optimization problem into a sub-Bruker stochastic programming problem that considers distribution uncertainty.

[0111] A distributed solution algorithm is used to optimize the bibliometric stochastic programming problem, resulting in the globally optimal set of temperature control decision variables.

[0112] The specific process includes optimizing the bibliometric stochastic programming problem using a distributed solution algorithm. Specifically, the global optimization task is decomposed into multiple interrelated sub-problems and assigned to different computing units. Each computing unit iteratively updates the temperature control decision variables based on local information. By exchanging boundary variables and coordinating constraints, the feasible region is gradually narrowed. Under the premise of satisfying the comprehensive objectives of control energy, tracking accuracy and spatial uniformity, the system finally converges to the globally optimal set of temperature control decision variables.

[0113] Extract the spatially differentiated temperature control command issued at the current moment from the set of globally optimal temperature control decision variables.

[0114] The specific process includes extracting the spatially differentiated temperature control command issued at the current moment from the globally optimal temperature control decision variable set, and selecting the control quantity that matches the current moment point by point according to the geometric partitioning structure of the rubber product based on the heating power set value of each spatial region contained in the globally optimal temperature control decision variable set at the current moment, forming a spatially differentiated temperature control command that covers the entire product space and whose values ​​can be different in each region.

[0115] S6. Execute the spatially differentiated temperature control command, adjust the zone heating power, regulate the vulcanization process of rubber products, and simultaneously perform scanning and control for the next cycle.

[0116] The spatially differentiated temperature control command is sent to the heaters in each zone, the heating power of the corresponding zone is adjusted, and the current temperature control command field is recorded.

[0117] The specific process includes: issuing spatially differentiated temperature control commands to each zone heater; adjusting the output power of each zone heater according to the control value corresponding to each spatial region in the spatially differentiated temperature control command, so that the heating power of each region is consistent with the temperature control command requirements; and organizing the spatially differentiated temperature control commands into a field form according to spatial location and recording it as the current temperature control command field.

[0118] Based on the spatial gradient of the temperature control command field and the spatial uncertainty of the current three-dimensional state field, the optimal scanning parameters for the next scanning cycle are obtained.

[0119] The specific process includes obtaining the rate of change of the temperature control command field in various spatial directions based on the spatial gradient of the temperature control command field and the spatial uncertainty of the current three-dimensional state field to identify areas of uneven heating or sensitive control. At the same time, combining the spatial uncertainty characterized by the posterior probability distribution of the digital twin in the current three-dimensional sulfidation distribution field and the current three-dimensional temperature distribution field, the information gain criterion is used to evaluate the observation value of different scanning configurations for key areas, thereby determining the microwave antenna array operating frequency, spatial coverage, and sampling density that can minimize the uncertainty of state estimation, and obtaining the optimal scanning parameters for the next scanning cycle.

[0120] It should be noted that the information gain criterion quantifies the observational value by obtaining the degree to which the expected observational data reduces the uncertainty of the current state under different scanning configurations. This information gain criterion is obtained based on the entropy change or covariance reduction of the posterior probability distribution of the digital twin.

[0121] Based on the optimal scanning parameters, the microwave antenna array is driven to perform scanning, triggering and initiating a new round of detection and control.

[0122] The specific process includes configuring the operating frequency, antenna element activation sequence, and signal transmission timing of the microwave antenna array according to the optimal scanning parameters, driving the microwave antenna array to perform a new round of spatial scanning on the rubber product, collecting S-parameters reflecting the current internal state, thereby triggering and starting a new round of detection and control.

[0123] In summary, this invention achieves comprehensive, high-resolution perception of the internal vulcanization state of complex rubber products by integrating microwave tomography and digital twins, solving the "black box" problem of single-point detection being unable to identify differences in vulcanization between internal layers; and utilizes digital twins for forward-looking probabilistic simulation of coupled uncertainties, enabling accurate prediction and adaptive control of the vulcanization process, improving vulcanization uniformity, stabilizing product quality, and reducing energy consumption, thereby constructing a high-precision, highly adaptable intelligent industrial control system for rubber production.

[0124] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for intelligent production detection and control of rubber based on microwave technology, characterized in that: include, Load the three-dimensional digital model of the target rubber product and initialize the digital twin, while controlling the microwave antenna array to perform scanning and collect the S-parameters of the rubber product; Based on the S-parameters, the three-dimensional dielectric constant distribution field inside the rubber is calculated by the electromagnetic inverse scattering reconstruction algorithm, and the three-dimensional dielectric constant distribution field is converted into a three-dimensional vulcanizability distribution field and a three-dimensional temperature distribution field according to the pre-stored calibration curve. Feature extraction is performed on the three-dimensional sulfurity distribution field and the three-dimensional temperature distribution field, and the input is used to update the activation energy parameters in the digital twin. Using the activation energy parameters in the updated digital twin, coupled spatiotemporal stochastic partial differential equations are constructed to predict the three-dimensional spatial evolution of the future sulfidation process and the prediction uncertainty. The three-dimensional spatial evolution and prediction uncertainty of the future vulcanization process are transformed into a distributed bar stochastic programming problem, and spatially differentiated temperature control commands are generated through a distributed solution algorithm. The system executes spatially differentiated temperature control commands, adjusts the heating power of different zones, regulates the vulcanization process of rubber products, and simultaneously scans and controls the next cycle.

2. The intelligent rubber production detection and control method based on microwave technology as described in claim 1, characterized in that: The process involves loading a three-dimensional digital model of the target rubber product and initializing its digital twin, while simultaneously controlling a microwave antenna array to perform scanning and acquire the S-parameters of the rubber product. The specific steps are as follows: Load the three-dimensional digital model of the target rubber product and establish the posterior probability distribution of the digital twin based on the three-dimensional digital model; The optimal scanning parameters are dynamically obtained based on the posterior probability distribution of the digital twin. Based on the optimal scanning parameters, the microwave antenna array is controlled to perform scanning and acquire the S-parameters of the rubber product.

3. The intelligent rubber production detection and control method based on microwave technology as described in claim 2, characterized in that: The specific steps for calculating the three-dimensional dielectric constant distribution field inside the rubber based on S-parameters and using an electromagnetic inverse scattering reconstruction algorithm are as follows: The S-parameters are preprocessed to obtain the frequency domain scattering data matrix; Based on the frequency domain scattering data matrix and prior probability distribution, an electromagnetic inversion objective function is constructed. A multi-resolution solution strategy is used to solve the electromagnetic inversion objective function to obtain the three-dimensional dielectric constant distribution field inside the rubber.

4. The intelligent rubber production detection and control method based on microwave technology as described in claim 3, characterized in that: The specific steps for converting the three-dimensional dielectric constant distribution field into a three-dimensional sulfidation degree distribution field and a three-dimensional temperature distribution field based on the pre-stored calibration curve are as follows. Dielectric relaxation spectrum features are extracted from the three-dimensional complex permittivity distribution field to generate a three-dimensional dielectric response feature field. By performing bilinear interpolation mapping on the three-dimensional dielectric response characteristic field point by point through pre-stored calibration curves, a three-dimensional sulfidation distribution field and a three-dimensional temperature distribution field are generated.

5. The intelligent rubber production detection and control method based on microwave technology as described in claim 4, characterized in that: The specific steps for extracting features from the three-dimensional sulfidation distribution field and the three-dimensional temperature distribution field, inputting them into the digital twin, and updating the activation energy parameters in the digital twin are as follows: The spatiotemporal evolution sequence of each spatial location is extracted from the three-dimensional sulfurity distribution field and the three-dimensional temperature distribution field, and the local spatiotemporal derivative field is obtained. Based on the local spatiotemporal derivative field and the current activation energy parameters of the digital twin, the process inconsistency index at each spatial location is calculated. Using process inconsistency indices as observations, the activation energy parameters in the digital twin are updated using an ensemble Kalman filter algorithm.

6. The intelligent rubber production detection and control method based on microwave technology as described in claim 5, characterized in that: The specific steps for constructing coupled spatiotemporal stochastic partial differential equations using the updated activation energy parameters in the digital twin are as follows. The activation energy parameters, three-dimensional sulfidation distribution field, and three-dimensional temperature distribution field in the updated digital twin are used as the initial conditions for the prospective simulation. Based on the initial conditions, a coupled spatiotemporal stochastic partial differential equation for parameter uncertainty and process disturbance is constructed.

7. The intelligent rubber production detection and control method based on microwave technology as described in claim 6, characterized in that: The specific steps for predicting the three-dimensional spatial evolution and uncertainty of the future vulcanization process are as follows. The stochastic spectrum method is used to solve the coupled spatiotemporal stochastic partial differential equations and calculate the probabilistic expansion coefficients of the sulfidation field and temperature field at multiple future time points. Basis function synthesis and statistical moment extraction are performed on the probabilistic expansion coefficients to predict the three-dimensional spatial evolution of the future sulfurization process and predict uncertainty.

8. The intelligent rubber production detection and control method based on microwave technology as described in claim 7, characterized in that: The process of transforming the three-dimensional spatial evolution and prediction uncertainty of the future vulcanization process into a dispersive bar stochastic programming problem involves the following steps: Based on the three-dimensional spatial evolution and prediction uncertainty of the future vulcanization process, an optimization problem is defined with the objectives of controlling energy, tracking accuracy and spatial uniformity. By utilizing the uncertainty of prediction, the optimization problem is transformed into a distributive bar stochastic programming problem.

9. The intelligent rubber production detection and control method based on microwave technology as described in claim 8, characterized in that: The specific steps for generating spatially differentiated temperature control commands using a distributed solution algorithm are as follows. A distributed solution algorithm is used to optimize the bibliometric stochastic programming problem to obtain the globally optimal set of temperature control decision variables; Extract the spatially differentiated temperature control command issued at the current moment from the set of globally optimal temperature control decision variables.

10. The intelligent rubber production detection and control method based on microwave technology as described in claim 9, characterized in that: The execution of spatially differentiated temperature control commands adjusts the zone heating power and regulates the vulcanization process of the rubber products, while simultaneously scanning and controlling the next cycle. The specific steps are as follows: The spatially differentiated temperature control command is sent to the heaters of each zone of the vulcanizing equipment to adjust the heating power of the corresponding zone, and at the same time, the vulcanization process of rubber products is controlled. Based on the changes in the internal state of the rubber product after regulation and the requirements of the next cycle of testing, the optimal scanning parameters for the next scanning cycle are obtained. Based on the optimal scanning parameters, the microwave antenna array is driven to perform scanning, triggering and initiating a new round of detection and control.

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