Optimization method of EPP foaming process parameters

Abstract

This invention relates to the technical field of EPP (expanded polypropylene) production and manufacturing, and discloses a method for optimizing EPP foaming process parameters. The method includes: real-time monitoring of temperature and pressure changes to determine whether the thermodynamic state deviates from a preset window; constructing a multi-physics field coupling model to assess the risk of dynamic imbalance in bubble growth when deviation occurs; identifying the characteristics of non-uniform micropore distribution through multi-source sensor data fusion and frequency domain analysis; determining whether to globally coordinate and control process parameters based on risk and characteristics; analyzing the effects of heat transfer and thermal radiation from temperature control units; quantifying parameter adjustment sensitivity; and determining control priorities. The system includes modules such as thermodynamic monitoring and dynamic coupling analysis. This invention enables real-time monitoring, precise analysis, and intelligent control of the EPP foaming process, improving process stability and product quality, and is suitable for the field of EPP production and manufacturing.

Description

Technical Field

[0001] The present invention relates to the technical field of EPP (expanded polypropylene) production and manufacturing, and in particular to an EPP foaming process parameter optimization method. Background Art

[0002] EPP (expanded polypropylene), a high-performance foam material, is widely used in the automotive industry, packaging logistics, building insulation, aerospace, and other fields due to its lightweight, high-strength, shock-absorbing, high-temperature resistance, and recyclability. As the performance requirements of EPP materials continue to increase across various industries, the precise control of foaming process parameters to achieve stable and efficient production has become a key technical challenge that needs to be addressed.

[0003] In traditional EPP foaming processes, the adjustment of process parameters relies primarily on operator experience, lacking real-time, accurate monitoring and analysis of the thermodynamic state during the foaming process. Because the foaming process involves the complex interaction of multiple physical fields, including temperature, pressure, foaming agent diffusion, and polymer melt flow, relying solely on empirical control makes it difficult to capture the dynamic changes within the molding cavity in real time. This can easily lead to problems such as uneven bubble growth and non-uniform distribution of micropore structures, which in turn affect the mechanical properties, dimensional accuracy, and appearance quality of EPP products.

[0004] The traditional process has the following technical bottlenecks:

[0005] Thermodynamic state monitoring is delayed, and it is impossible to obtain the temperature field distribution and pressure change data of each partition in the molding cavity in real time and comprehensively. There is a delay in judging whether the thermodynamic state deviates from the preset process window, making it difficult to detect process abnormalities in the first place.

[0006] There is insufficient analysis of multi-physical field coupling and a lack of a systematic analysis model for the interaction between foaming agent diffusion and polymer melt flow. This makes it impossible to accurately assess the risk of dynamic imbalance in the bubble growth process, resulting in a lack of scientific basis for process adjustments.

[0007] It is difficult to control the micropore structure, and it is difficult to identify the non-uniform distribution characteristics of the micropore structure during the material expansion process through effective data processing methods. It is impossible to accurately control high-risk areas, which affects the uniformity and stability of the product.

[0008] The process parameter control lacks coordination. When adjusting the process parameters, the heat transfer efficiency and thermal radiation effects between the temperature control units are not fully considered, resulting in inaccurate quantification of the sensitivity of parameter adjustment, unclear control execution priority, and difficulty in achieving global collaborative optimization.

[0009] With the development of intelligent manufacturing and industrial automation technology, higher requirements are being placed on the intelligent and precise control of EPP foaming processes. Although there are some sensor-based monitoring systems and simple process parameter adjustment methods in the existing technology, a complete process parameter optimization system based on multi-physics field coupling analysis and multi-source data fusion has not yet been formed, which cannot meet the modern industry's demand for high-quality and high-efficiency production of EPP materials. Therefore, it is urgent to develop an EPP foaming process parameter optimization method and system that can perform real-time monitoring, precise analysis, and intelligent control to solve the technical difficulties existing in traditional processes and improve the production quality and efficiency of EPP materials. Summary of the Invention

[0010] The object of the present invention is to provide a method for optimizing EPP foaming process parameters to solve the problems raised in the above background technology.

[0011] To achieve the above object, the present invention provides the following technical solution: an EPP foaming process parameter optimization method, the method comprising:

[0012] Real-time monitoring of temperature field distribution and pressure change data during the foaming process to determine whether the thermodynamic state in the molding cavity deviates from the preset process window;

[0013] When the thermodynamic state deviates from the preset process window, a multi-physics coupling model is constructed to analyze the interaction between foaming agent diffusion and polymer melt flow, and to assess the risk of dynamic imbalance in the bubble growth process within the molding cavity.

[0014] By combining multi-source sensor data fusion with frequency domain analysis to process density gradient signals in different areas of the molding cavity, the non-uniform distribution characteristics of the microscopic pore structure during the material expansion process can be identified.

[0015] Based on the dynamic imbalance risk of the bubble growth process and the non-uniform distribution characteristics of the micropore structure, it is determined whether to conduct global coordinated control of the molding process parameters;

[0016] When global coordinated control of molding process parameters is required, the heat transfer efficiency of each temperature control unit and the thermal radiation impact of adjacent units are correlated and analyzed to quantify the parameter adjustment sensitivity of each temperature control node;

[0017] The control execution priority of each temperature control node is determined according to the parameter adjustment sensitivity.

[0018] Preferably, the method monitors the temperature field distribution and pressure change data during the foaming process in real time to determine whether the thermodynamic state in the molding cavity deviates from the preset process window, specifically:

[0019] Synchronously collect temperature gradient data and pressure fluctuation data of each partition of the molding cavity;

[0020] Generate a thermodynamic state determination matrix based on the temperature distribution curve and pressure change threshold of the preset process window;

[0021] The real-time collected temperature gradient data and pressure fluctuation data are input into the judgment matrix for pattern matching to detect the deviation amplitude of thermodynamic parameters;

[0022] When the deviation amplitude of the parameters of any partition exceeds the corresponding threshold, it is determined that the thermodynamic state of the molding cavity deviates from the preset process window.

[0023] Preferably, the method analyzes the interaction between the diffusion of the blowing agent and the flow of the polymer melt by constructing a multi-physics field coupling model to evaluate the dynamic imbalance risk of the bubble growth process in the molding cavity, specifically:

[0024] Obtaining foaming agent concentration distribution data and melt viscosity real-time data as model input parameters;

[0025] Establish a multi-physics coupling equation to describe the mutual constraints between the diffusion rate of the foaming agent and the melt flow velocity;

[0026] The iterative calculation method is used to solve the spatial distribution relationship between the foaming agent concentration gradient field and the melt shear stress field;

[0027] By simulating the migration trend of bubble nucleation positions and the discreteness of size distribution, the dynamic imbalance risk level is output.

[0028] Preferably, the method combines multi-source sensor data fusion with frequency domain analysis to process density gradient signals in different regions within the molding cavity, thereby identifying the non-uniform distribution characteristics of the microscopic pore structure during the material expansion process, specifically:

[0029] Collect density detection signals and ultrasonic attenuation coefficient data in the axial and radial directions of the molding cavity;

[0030] Perform time-frequency conversion on multi-source sensor data and extract the spectral feature vector of density fluctuation;

[0031] The spectral feature vectors were processed by principal component analysis to reduce the dimension and build a mapping model between density distribution and pore structure.

[0032] Based on the spatial correlation index output by the mapping relationship model, high-risk areas with uneven pore distribution are marked.

[0033] Preferably, the method determines whether to perform global coordinated regulation of molding process parameters based on the dynamic imbalance risk of the bubble growth process and the non-uniform distribution characteristics of the microscopic pore structure, specifically:

[0034] When the dynamic imbalance risk level is lower than the first threshold and the spatial correlation index is lower than the second threshold, the current process parameters are maintained;

[0035] When the dynamic imbalance risk level reaches a first threshold or the spatial correlation index reaches a second threshold, a global coordinated control instruction is triggered.

[0036] Preferably, when the method needs to perform global coordinated control of molding process parameters, the heat transfer efficiency of each temperature control unit and the thermal radiation influence of adjacent units are correlated and analyzed to quantify the parameter adjustment sensitivity of each temperature control node, specifically:

[0037] Calculate the heat flux conductivity coefficient of each temperature control unit and the thermal radiation superposition effect value between adjacent units;

[0038] Establish a correlation index matrix between temperature fluctuations and heat conduction paths to identify the intensity of thermal radiation coupling;

[0039] According to the distribution range of the element values ​​in the correlation index matrix, the parameter adjustment sensitivity sequence of each node is generated.

[0040] Preferably, the method determines the control execution priority of each temperature control node according to the parameter adjustment sensitivity, specifically:

[0041] Set a sensitivity threshold and filter out the set of temperature control nodes that are higher than the threshold;

[0042] In the filtered set of nodes, a priority queue is generated by arranging them in descending order of sensitivity values;

[0043] The first N nodes in the queue are given the highest control priority, and the remaining nodes are assigned secondary priorities according to their sensitivity ratio.

[0044] Preferably, the method generates a priority queue by arranging the sensitivity values ​​in descending order, specifically:

[0045] The sensitivity value of each node is weighted with its corresponding spatial position weight;

[0046] The final priority queue is generated by reordering according to the weighted calculation results, and nodes with weight values ​​lower than the critical threshold are eliminated.

[0047] Preferably, the present invention further includes an EPP foaming process parameter optimization system for implementing the above-mentioned EPP foaming process parameter optimization method, wherein the system includes a thermodynamic monitoring module, a dynamic coupling analysis module, a pore feature recognition module, a process control decision module, a sensitivity quantification module, and a priority allocation module;

[0048] Thermodynamic monitoring module: real-time monitoring of temperature field distribution and pressure change data during the foaming process to determine whether the thermodynamic state in the molding cavity deviates from the preset process window;

[0049] Dynamic Coupling Analysis Module: When the thermodynamic state deviates from the preset process window, a multi-physics coupling model is constructed to analyze the interaction between foaming agent diffusion and polymer melt flow, and to assess the risk of dynamic imbalance in the bubble growth process within the molding cavity.

[0050] Pore ​​Feature Recognition Module: When the thermodynamic state deviates from the preset process window, the module processes the density gradient signals of different regions within the molding cavity through multi-source sensor data fusion and frequency domain analysis to identify the non-uniform distribution characteristics of the microscopic pore structure during the material expansion process.

[0051] Process control decision module: Based on the dynamic imbalance risk of the bubble growth process and the non-uniform distribution characteristics of the micropore structure, it determines whether to perform global coordinated control of the molding process parameters;

[0052] Sensitivity Quantification Module: When global coordinated control of molding process parameters is required, the heat transfer efficiency of each temperature control unit and the thermal radiation impact of adjacent units are correlated and analyzed to quantify the parameter adjustment sensitivity of each temperature control node.

[0053] Priority allocation module: determines the control execution priority of each temperature control node according to the parameter adjustment sensitivity.

[0054] Preferably, the sensitivity quantification module includes a heat conduction calculation unit, a radiation coupling analysis unit and a weighted sorting unit, which are respectively used to perform heat flux conduction coefficient calculation, heat radiation superposition effect analysis and sensitivity weighted value sorting operations.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] By collecting real-time temperature gradient and pressure fluctuation data from each zone of the molding cavity and performing pattern matching with the temperature distribution curve and pressure change threshold of a preset process window, this method can quickly and accurately determine whether the thermodynamic state deviates from the preset process window. This real-time monitoring and dynamic judgment mechanism overcomes the monitoring lag problem in traditional processes, ensuring that the control mechanism is triggered immediately when a process anomaly occurs, laying the foundation for subsequent precise control.

[0057] When the thermodynamic state deviates from the preset process window, a multi-physics field coupling model is constructed to deeply analyze the interaction between foaming agent diffusion and polymer melt flow. This model uses foaming agent concentration distribution data and real-time melt viscosity data as input parameters. By establishing coupling equations and iterative calculation methods, it accurately solves the spatial distribution relationship between the foaming agent concentration gradient field and the melt shear stress field. It also simulates the migration trend of bubble nucleation positions and the discreteness of size distribution, thereby outputting the dynamic imbalance risk level. This analytical method enables a quantitative assessment of the complex physical field interactions in the foaming process, providing a scientific theoretical basis for process parameter adjustments and effectively reducing the risk of dynamic imbalance during bubble growth.

[0058] Through multi-source sensor data fusion and frequency domain analysis technology, the density gradient signals of different areas within the molding cavity are processed. Axial and radial density detection signals and ultrasonic attenuation coefficient data are collected. After time-frequency conversion and principal component analysis, a mapping model between density distribution and pore structure is constructed, and high-risk areas of non-uniform pore distribution are marked. This technology can deeply identify the non-uniform distribution characteristics of the microscopic pore structure during the material expansion process, enabling refined monitoring of the internal structure of the product. It provides key data support for targeted adjustment of process parameters and optimization of pore structure, significantly improving the uniformity and stability of EPP products.

[0059] Based on the dynamic imbalance risk of the bubble growth process and the non-uniform distribution characteristics of the micropore structure, a scientific process control decision-making mechanism has been established. By setting clear threshold conditions to determine whether to trigger the global collaborative control instruction, the problem of blindly adjusting parameters in traditional processes is avoided. When control is required, the heat transfer efficiency of each temperature control unit and the thermal radiation effect of adjacent units are further analyzed, the sensitivity of parameter adjustment is quantified, and the control execution priority is determined based on the sensitivity. This global collaborative control strategy fully considers the interaction between each temperature control node. Through weighted calculation and priority sorting, it realizes the orderly and efficient adjustment of process parameters, improves the accuracy and effectiveness of control, shortens process adjustment time, and improves production efficiency.

[0060] The EPP foaming process parameter optimization system constructed by this invention integrates functional modules such as thermodynamic monitoring, dynamic coupling analysis, pore feature identification, process control decision-making, sensitivity quantification, and priority allocation, forming a complete intelligent process optimization system. This system not only enables full-process monitoring and analysis of the foaming process, but also automatically makes control decisions based on real-time data, reducing reliance on manual experience and the risk of process fluctuations caused by human factors, improving the automation level and stability of the production process, and providing reliable technical support for the large-scale industrial production of EPP materials.

[0061] Through the comprehensive application of the above-mentioned technical means, the present invention effectively solves the technical difficulties existing in the traditional EPP foaming process, such as the lag in thermodynamic state monitoring, insufficient multi-physical field coupling analysis, difficulty in controlling the micropore structure, and lack of coordination in process parameter control. It significantly improves the quality consistency and performance stability of EPP products, reduces production costs, and improves production efficiency. It has significant economic and social benefits, and promotes the development of EPP production and manufacturing technology towards intelligence and precision. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a working principle diagram of the EPP foaming process parameter optimization method of the present invention;

[0063] Figure 2 Flow chart for determining the deviation of thermodynamic state;

[0064] Figure 3 Flowchart for multi-physics coupled model analysis;

[0065] Figure 4 Flowchart for identification of heterogeneous distribution of pore structure;

[0066] Figure 5 Flowchart for determining the control priority of temperature control nodes. DETAILED DESCRIPTION

[0067] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0068] See also Figure 1-Figure 5 The EPP foaming process parameter optimization method of the present invention is specifically implemented as follows:

[0069] Real-time temperature gradient and pressure fluctuation data are collected for each zone of the molding cavity. The temperature distribution curve and pressure change threshold within the preset process window are simultaneously obtained to generate a thermodynamic state judgment matrix. The real-time temperature gradient and pressure fluctuation data are input into the judgment matrix for pattern matching, detecting the deviation of the thermodynamic parameters. If the deviation of the parameters in any zone exceeds the corresponding threshold, the thermodynamic state of the molding cavity is determined to have deviated from the preset process window.

[0070] When the thermodynamic state deviates from the preset process window, the foaming agent concentration distribution data and the real-time data of the melt viscosity are obtained as model input parameters, and a multi-physics field coupling equation is established to describe the mutual constraint relationship between the foaming agent diffusion rate and the melt flow velocity. The iterative calculation method is used to solve the spatial distribution relationship between the foaming agent concentration gradient field and the melt shear stress field. By simulating the migration trend of the bubble nucleation position and the discreteness of the size distribution, the dynamic imbalance risk level is output.

[0071] The density gradient signals of different areas in the molding cavity are processed by combining multi-source sensor data fusion with frequency domain analysis. Specifically, the axial and radial density detection signals and ultrasonic attenuation coefficient data of the molding cavity are collected, and the multi-source sensor data are subjected to time-frequency conversion processing. The spectral feature vectors of density fluctuations are extracted, and the dimensionality reduction of the spectral feature vectors is performed through principal component analysis. A mapping relationship model between density distribution and pore structure is constructed. According to the spatial correlation index output by the mapping relationship model, high-risk areas with uneven pore distribution are marked.

[0072] Process Control Decision Judgment: Based on the dynamic imbalance risk of the bubble growth process and the non-uniform distribution characteristics of the micropore structure, it is determined whether to perform global coordinated control of the molding process parameters. When the dynamic imbalance risk level is below the first threshold and the spatial correlation index is below the second threshold, the current process parameters are maintained. When the dynamic imbalance risk level reaches the first threshold or the spatial correlation index reaches the second threshold, the global coordinated control instruction is triggered.

[0073] Heat transfer analysis and parameter adjustment sensitivity quantification of temperature control units: When global coordinated control of molding process parameters is required, the heat transfer efficiency of each temperature control unit and the thermal radiation influence of adjacent units are correlated and analyzed. The heat flow conduction coefficient of each temperature control unit and the thermal radiation superposition effect value between adjacent units are calculated. The correlation index matrix between temperature fluctuation and heat conduction path is established, and the intensity of thermal radiation coupling is identified. According to the distribution range of the element values ​​in the correlation index matrix, the parameter adjustment sensitivity sequence of each node is generated.

[0074] Determination of control execution priority: Determine the control execution priority of each temperature control node according to the parameter adjustment sensitivity, set the sensitivity threshold and filter out the set of temperature control nodes above the threshold, and perform weighted calculation on the sensitivity value of each node and its corresponding spatial position weight in the filtered node set. Reorder the nodes according to the weighted calculation results to generate the final priority queue, and eliminate the nodes with weighted values ​​below the critical threshold. Arrange the nodes in descending order according to the weighted sensitivity values ​​to generate the priority queue. Give the first N nodes in the queue the highest control priority, and the remaining nodes are assigned secondary priorities according to the sensitivity ratio.

[0075] The present invention will be further described below in conjunction with Examples 1 to 5:

[0076] Example 1:

[0077] In the process of real-time monitoring of the temperature field distribution and pressure change data during the foaming process, determining whether the thermodynamic state in the molding cavity deviates from the preset process window is achieved through the following steps:

[0078] The data collection process relies on a network of sensors distributed in different areas of the molding cavity. The collection of temperature gradient data is achieved by evenly distributing thermocouples or thermistor sensors in the axial, radial and circumferential directions of the molding cavity. The density of the sensor layout is determined according to the cavity size and the requirements of the foaming process. For example, for a large cavity, a temperature detection point can be set every 5-10 cm to ensure that subtle temperature changes can be captured. The pressure fluctuation data is obtained through a pressure transmitter installed on the cavity wall. The pressure transmitter has a range that covers the pressure range that may occur during the foaming process, and the accuracy must reach ±0.1% FS to ensure the accuracy of the pressure data. All sensors are connected to the data acquisition system through signal cables or wireless transmission to achieve synchronous collection of temperature and pressure data. The sampling frequency is set to 5-20Hz to ensure real-time performance.

[0079] The preset process window is established based on the characteristics of the foaming material and product quality requirements. The temperature distribution curve is developed based on the EPP material's foaming temperature range (typically 120-180°C) and the thermodynamic requirements of each cavity zone. For example, due to slower heat dissipation in the center of the cavity, the preset temperature may be slightly lower than that of the edge zones, resulting in a gradient distribution. The pressure change threshold is determined based on the decomposition pressure of the blowing agent and the critical pressure required for bubble growth, typically set within a ±5% fluctuation range. The thermodynamic state determination matrix is ​​generated as follows: the molding cavity is divided into several independent zones (e.g., upper, middle, and lower zones along the axial direction, and center, transition, and edge zones radially). Each zone is assigned a set of preset temperature and pressure parameter ranges and deviation thresholds. The matrix is ​​structured as a multidimensional table, with rows representing different zones and columns representing temperature and pressure parameters. Cells contain preset upper and lower temperature limits, upper and lower pressure limits, and deviation thresholds. For example, a zone's preset temperature range is 140-150°C with a deviation threshold of ±5°C; a preset pressure range is 0.8-1.2 MPa with a deviation threshold of ±0.1 MPa.

[0080] During the data processing and pattern matching phase, the real-time temperature gradient and pressure fluctuation data are first preprocessed, including denoising, filtering, and normalization. Denoising uses a median filter algorithm to eliminate random noise; filtering is performed using a low-pass filter to remove high-frequency interference signals; and normalization maps the data to the [0, 1] interval to facilitate subsequent matrix matching operations. The preprocessed data is then input into the thermodynamic state determination matrix. Using a row-by-column pattern matching algorithm, the real-time temperature and pressure data for each partition are compared with the preset parameters in the matrix. Specifically, the comparison is performed by calculating the deviation between the real-time temperature and the preset temperature range: (real-time temperature - preset temperature mean) / preset temperature range span. If the absolute value of the deviation exceeds a preset deviation threshold (e.g., 5%), the temperature parameter is considered to have deviated. Similarly, the pressure parameter deviation is calculated. If the deviation of the temperature or pressure parameter in any partition exceeds the corresponding threshold, the deviation determination logic is triggered, and the system generates a thermodynamic state deviation alarm, recording the deviating partition, parameter type, and deviation magnitude.

[0081] It's worth noting that sensor calibration and maintenance are critical to ensuring data accuracy. Before the foaming process begins, all temperature and pressure sensors must be calibrated. Sensor accuracy is verified using standard heat and pressure sources. Calibration is performed weekly or after every 50 foaming batches. If a sensor malfunctions or measurement deviations exceed the allowable range, the system automatically issues a fault alarm and switches to a backup sensor to continue collecting data, ensuring continuous monitoring.

[0082] Furthermore, the data acquisition and processing system must be highly reliable and real-time. The hardware utilizes industrial-grade data acquisition cards that support multi-channel simultaneous acquisition and exhibit strong anti-interference capabilities. The software is developed based on real-time control platforms such as LabVIEW or MATLAB, and the data processing algorithms utilize parallel computing technology to ensure millisecond-level data preprocessing and pattern matching. The system must also provide data storage and traceability capabilities, with real-time temperature and pressure data stored in a database for at least six months to facilitate process traceability and problem analysis.

[0083] In practical applications, deviations from the thermodynamic state of a molding cavity can manifest in various forms. For example, if the temperature of a certain edge zone of a cavity suddenly rises to 160°C, exceeding the preset upper limit of 150°C for that zone, and the deviation reaches 10°C (exceeding the preset threshold of 5°C), while the pressure fluctuation is within the normal range, the temperature parameter of that zone is considered to have deviated, and the system issues a temperature anomaly alarm. Another example is when the pressure of the center zone of the cavity suddenly drops to 0.7MPa, below the preset lower limit of 0.8MPa, with a deviation of 0.1MPa (reaching the preset threshold), while the temperature parameters are normal, the pressure parameter of that zone is considered to have deviated. Regardless of whether a single parameter deviates or multiple parameters deviate simultaneously, as long as the deviation of the parameters of any zone exceeds the corresponding threshold, the thermodynamic state of the molding cavity is determined to have deviated from the preset process window, providing trigger conditions for subsequent multi-physics field coupling analysis and process control.

[0084] The entire monitoring and judgment process strictly follows a pre-set logical flow. Through high-precision sensors, a scientific matrix model, and efficient data processing algorithms, it achieves real-time, accurate monitoring and judgment of the thermodynamic state within the molding cavity, providing reliable basic data support for the optimization of EPP foaming process parameters. This method avoids the subjectivity and lag inherent in relying on human experience and judgment, and can promptly capture subtle changes in the thermodynamic state, laying the foundation for subsequent dynamic imbalance risk assessment and process parameter control.

[0085] Example 2:

[0086] In the process of analyzing the interaction between blowing agent diffusion and polymer melt flow by building a multi-physics coupling model and evaluating the dynamic imbalance risk of bubble growth in the molding cavity, the specific implementation method is as follows:

[0087] Real-time data on blowing agent concentration distribution and melt viscosity are collected as model input parameters. This data is collected in real time using spectral detection equipment. Near-infrared spectrometer probes are placed at different depths and radial positions within the molding cavity. These probes use optical fiber transmission to transmit the melt's absorption signal of light of a specific wavelength to a spectrum analyzer. The spectrometer then calculates the concentration value at each location in real time based on predefined characteristic absorption peaks of the blowing agent (e.g., the linear relationship between the absorption intensity of the blowing agent at 850 nm and concentration in a certain polymer system). To ensure data reliability, each spectrometer is equipped with a built-in calibration module that automatically performs a blank correction upon startup and performs single-point calibration using a standard concentration solution every hour during production. Real-time melt viscosity data is acquired using an online rheological monitoring device. This device consists of a rotating measuring head that is inserted into the melt at a constant angular velocity (e.g., 10 rad / s). A torque sensor measures the rotational resistance in real time and converts it into a viscosity value based on a fluid dynamics model. A temperature-controlled jacket surrounds the measuring head, which is maintained at the same temperature as the cavity by circulating hot oil to prevent viscosity measurement errors caused by temperature differences. The two types of data are transmitted to the control computer in real time at a frequency of 20 Hz through a synchronous acquisition card to form a time series data set.

[0088] A multi-physics coupling model was established to describe the interaction between blowing agent diffusion and melt flow. The model is based on the spatial distribution characteristics of the physical fields. The molding cavity is abstracted as a three-dimensional geometric entity and discretized into thousands of computational units using the finite volume method. Each unit corresponds to a tiny spatial region of the cavity (e.g., a cube with a side length of 2 mm). In the model, the blowing agent diffusion process follows Fick's law, while also considering the convective transport caused by the melt flow. That is, the diffusion flux is determined by both molecular diffusion driven by the concentration gradient and the macroscopic flow of the fluid. The melt flow is described using the modified Navier-Stokes equations, and a viscoelastic constitutive relation is introduced to accommodate the non-Newtonian characteristics of the EPP polymer melt. The model implements physical field interaction through coupling terms: the blowing agent concentration affects the melt viscosity (increased concentration leads to decreased viscosity), while the melt flow velocity distribution changes the diffusion path of the blowing agent. The model parameters are obtained through material property experiments. For example, the shear viscosity curve of the melt at different foaming agent concentrations is measured by a rotational rheometer, and the diffusion coefficient test device is used to measure the temperature variation data of the foaming agent in the melt. These parameters are embedded in the model as input boundary conditions.

[0089] When solving the physical field distribution using an iterative calculation method, initial conditions are first set: the concentration distribution at the moment of foaming agent injection (e.g., highest concentration at the center of the cavity, decreasing at the edges) and the melt's static state are used as the starting point for the calculation. Boundary conditions are set based on process parameters (e.g., a constant cavity wall temperature of 150°C and a melt velocity of 0.05 m / s at the inlet). The calculation process consists of two coupled steps. The first step solves the melt flow field, calculating the velocity and pressure distribution for each cell using a pressure-velocity coupling algorithm (such as the SIMPLE algorithm). The second step uses the velocity field as input to solve the foaming agent diffusion equation, calculating the concentration change for each cell using the finite difference method. This two-step calculation forms a closed-loop iteration. After each flow-diffusion calculation, convergence is determined by comparing the differences in physical quantities between adjacent iterations (e.g., the maximum relative change in velocity and concentration). The calculation terminates when the differences are less than 1% for all cells, and the concentration gradient field and melt shear stress field distribution at the current moment are output. The entire calculation process is completed under the acceleration of the graphics processing unit (GPU), and the time consumption of a single iteration is controlled within 50ms to ensure real-time performance.

[0090] The simulation of bubble nucleation site migration and size distribution dispersion is based on statistical physics models and interfacial dynamics theory. The prediction of bubble nucleation locations is based on a local supersaturation criterion: nucleation is triggered when the blowing agent concentration in a cell exceeds its saturation concentration in the melt. The saturation concentration changes dynamically with temperature and pressure (decreases with increasing temperature and decreasing pressure), and is queried in real time via a built-in thermodynamic database. Nucleation site migration is tracked by tracking the spatial distribution of supersaturated cells at each moment. For example, at time t1, a cell meets the nucleation conditions and forms an initial nucleus. At time t2, melt flow causes the cell to move and its concentration to change. Tracking stops if the supersaturation conditions are no longer met; otherwise, the position trajectory is continuously recorded. The simulation of bubble size distribution utilizes a population equilibrium model, dividing bubbles into multiple size bins (e.g., 10-20 μm, 20-30 μm, etc.) based on radius. The temporal variation of the bubble population within each bin is determined by the nucleation rate, growth rate, and coalescence / rupture events. The growth rate is calculated using the gas diffusion governing equation, taking into account the pressure difference inside and outside the bubble and the influence of the melt viscous resistance; the coalescence / rupture events are determined based on the relative velocity and spacing probability statistics of adjacent bubbles.

[0091] When assessing dynamic imbalance risk, a comprehensive analysis is conducted on the migration characteristics of nucleation sites and bubble size distribution parameters. Nucleation site migration trends are quantified using the average migration rate (the average distance traveled by the nucleation site per unit time) and the migration range (the maximum axial / radial displacement of the nucleation site within the cavity). For example, a nucleation site in a certain area moves an average of 4 mm in 5 seconds, with a maximum displacement of 12 mm, indicating active migration. The dispersion of the bubble size distribution is measured using the coefficient of variation (the ratio of the standard deviation to the mean). A coefficient of variation of 0.4 for a size range indicates significant bubble size variability. Risk levels are categorized into three levels: low risk when the average migration rate is <2 mm / s and the coefficient of variation is <0.3; medium risk when 2 mm / s ≤ average migration rate <5 mm / s or 0.3 ≤ coefficient of variation <0.6; and high risk when the average migration rate is ≥5 mm / s or the coefficient of variation is ≥0.6. Risk assessment results are visualized using a dynamic heat map generated on the monitoring interface, with the risk level of each area indicated by different colors. A list of risk parameters (such as migration rate and coefficient of variation values ​​for each area) is also displayed.

[0092] The actual application of the model needs to be combined with process debugging and data verification. When a new formula or new process is introduced, visual verification is carried out through a transparent experimental mold: the mold is made of high-temperature resistant glass, and has a built-in high-speed camera (frame rate 1000fps) to record the bubble growth process and simultaneously collect the nucleation position and size data predicted by the model. The operator compares the real-time image with the model output. If there is a significant deviation (such as the predicted nucleation area does not match the actual image), the input parameters (such as diffusion coefficient, viscosity curve) are checked for accuracy, or calculation parameters such as model grid density and iteration tolerance are adjusted. In addition, the system regularly conducts retrospective analysis of historical data, and by comparing product quality data at different risk levels (such as density uniformity, bubble structure parameters), it optimizes the weight distribution of risk assessment indicators to ensure that the model always adapts to changes in actual production conditions.

[0093] The entire multi-physics coupling analysis process achieves full automation from data acquisition and model building to risk assessment, avoiding the limitations of manual experience and judgment. By tracking the interaction between the foaming agent and the melt in real time, the system can identify potential imbalance risks in bubble growth in advance, providing a precise basis for subsequent process parameter control. For example, when the model detects that the risk level in a certain area has risen to medium, it can automatically trigger an early warning prompt. The operator can choose to adjust the temperature distribution, optimize the foaming agent injection rate, and other control strategies based on the risk type (such as active nucleation migration or high size dispersion), thereby achieving dynamic optimization control of the foaming process.

[0094] Example 3:

[0095] When multi-source sensor data fusion and frequency domain analysis are combined to process density gradient signals in different areas of the molding cavity to identify the non-uniform distribution characteristics of the microscopic pore structure during the material expansion process, the specific implementation method is as follows:

[0096] The acquisition of density gradient signals and ultrasonic attenuation coefficient data is accomplished through the coordinated use of multiple sensor types. Density sensor arrays are evenly arranged in the axial direction (perpendicular to the foaming direction) and radial direction (along the radius) of the molding cavity. Each array contains 10-20 sensor nodes, and the node spacing is set at 3-5 cm depending on the cavity size. The density sensor uses the gamma ray transmission principle, calculating the local density by measuring the intensity attenuation of the ray after it passes through the melt. The formula is: in, is the density of the melt being measured, is the path length of the ray through the melt, is the incident ray intensity, The ultrasonic attenuation coefficient data is obtained through piezoelectric ultrasonic probes. The probes are arranged in pairs on both sides of the cavity. The transmitting probe emits ultrasonic waves with a frequency of 1-5MHz, and the receiving probe detects the signal amplitude. The attenuation coefficient is obtained through the formula Calculation (where is the ultrasonic wave propagation distance, is the transmitted signal amplitude, The two types of sensors collect data synchronously, with a sampling frequency of 10 Hz to ensure that dynamic changes in density and acoustic properties are captured.

[0097] During the data preprocessing phase, multi-source sensor data is first aligned in time and space. The spatial positions of the density sensor and ultrasonic probe are calibrated using a three-dimensional coordinate system to ensure a one-to-one correspondence between different types of data at the same physical location. Time synchronization is achieved through hardware triggering, with all sensors driven by the same clock signal, and acquisition latency is controlled to less than 1ms. Preprocessing includes denoising and normalization: density data uses a median filter to remove impulse noise, and ultrasonic attenuation data uses a moving average filter to smooth the curve. Normalization maps density values ​​to the [0, 1] interval (based on the material's theoretical density and the measured minimum value), and the ultrasonic attenuation coefficient to the [0, 1] interval (based on the experimentally measured maximum attenuation range).

[0098] Time-frequency conversion is achieved through short-time Fourier transform (STFT). For each sensor node's time series data (e.g., the density fluctuation signal at a radial node), a window function length of 2 seconds and an overlap rate of 50% are set to convert the time domain signal into a frequency domain distribution. The mathematical expression of STFT is:

[0099] in, is the original time domain signal, is the window function, is the time displacement, After the conversion, a time-frequency matrix is ​​obtained, in which the matrix elements correspond to the amplitudes of the frequency components at different moments. For example, a high amplitude at 5 Hz at a certain moment indicates that there is a significant low-frequency density fluctuation at that moment.

[0100] Spectral feature vectors are extracted based on the statistical properties of the time-frequency matrix. For each node's time-frequency matrix, the following characteristic parameters are calculated: dominant frequency (the frequency component with the highest energy), bandwidth (the span of the frequency range that accounts for 80% of the energy), low-frequency energy fraction (the ratio of the sum of the energy of frequency components between 0 and 2 Hz to the total energy), and high-frequency energy fraction (the ratio of the sum of the energy of frequency components above 5 Hz to the total energy). These parameters form a 1×4-dimensional spectral feature vector. For example, a node's feature vector is [3.2 Hz, 2.5 Hz, 0.6, 0.1], indicating a dominant frequency of 3.2 Hz, a bandwidth of 2.5 Hz, a low-frequency energy fraction of 60%, and a high-frequency energy fraction of 10%.

[0101] The goal of principal component analysis (PCA) dimensionality reduction is to reduce the dimensionality of the eigenvector while retaining the key information. Assuming there are N sensor nodes, each generating an M-dimensional eigenvector (e.g., M = 4), an N × M dimensional eigenmatrix is ​​constructed. The covariance matrix of the matrix is ​​calculated, and the eigenvalues ​​and eigenvectors are solved. The top K principal components (K ≤ M) are selected based on the eigenvalue contribution (cumulative contribution exceeding 90%). For example, when M = 4, the cumulative contribution of the first two principal components reaches 92%. Therefore, the original 4-dimensional eigenvector is reduced to 2 dimensions. The reduced vector contains the main spectral characteristics of density fluctuations.

[0102] The mapping relationship model between density distribution and pore structure is constructed using a machine learning algorithm. The neural network model is trained using historical data, with the input being the spectral feature vector after dimension reduction, and the output being the corresponding pore structure parameters (such as average pore size, porosity, and pore size distribution standard deviation). The training data is obtained through destructive experiments: after foaming is completed, samples are taken from different locations in the cavity, and the pore structure is reconstructed using micro-CT scanning to measure the average pore size ( ), porosity (%), pore size distribution standard deviation ( ) and other parameters, and simultaneously extracts the spectral feature vector at the sampling moment to form the input-output dataset. The neural network adopts a three-layer structure (input layer with K nodes, hidden layer with 10 nodes, and output layer with 3 nodes), uses the ReLU activation function, the Adam optimizer, and a training cycle of 100 epochs with a batch size of 32.

[0103] The calculation of the spatial correlation index is based on Gaussian process regression (GPR). The spatial coordinates (x, y, z) of all sensor nodes and the spectral feature vector after dimension reduction are used as input to construct a spatial interpolation model to predict the spectral characteristics of any position in the cavity. For each predicted point, the Euclidean distance between its feature vector and the feature vector of all measured nodes within a radius R (e.g., 5 cm) is calculated, and the spatial correlation index is obtained by weighted summation using the Gaussian kernel function.

[0104] , the formula is: in, is the weight of the i-th measured node (related to the data confidence), is the spatial distance between the predicted point and the i-th node, is the kernel function bandwidth (1.5 times the average node spacing). Spatial correlation index The value range of is [0,1]. The larger the value, the more significant the difference between the pore structure of the area and the surrounding area, that is, the higher the risk of non-uniform distribution.

[0105] In practical applications, when the spatial correlation index of a region When the preset threshold (such as 0.7) is exceeded, the system automatically marks the area as a high-risk area for non-uniform pore distribution and highlights it in red in the three-dimensional model. The operator can view the spectral characteristic vector, predicted pore structure parameters and spatial position information of the area through the interactive interface, and judge whether the process parameters need to be adjusted (such as increasing the cooling rate of the area or adjusting the foaming agent injection amount). For example, if the spatial correlation index of a radial edge area reaches 0.8, the corresponding spectral characteristic vector shows a significant increase in the proportion of high-frequency energy (indicating the presence of rapid density fluctuations). The mapping model predicts that the standard deviation of the average pore size in this area is 30% higher than the normal value, indicating that there may be a problem of uneven pore size and that targeted regulation is required.

[0106] Throughout the entire process, regular sensor calibration and continuous model optimization are crucial. Density sensors undergo zero and span calibration every two weeks using standard density blocks, and ultrasonic probes undergo sound velocity calibration monthly (using calibration components made of known materials). The mapping model automatically triggers incremental training after accumulating 50 sets of new data, preventing model drift caused by material batch variations or equipment aging. Furthermore, the system supports manual intervention, allowing operators to manually mark anomalous data points to eliminate misjudgments caused by temporary sensor failures or process disturbances, ensuring accurate feature recognition.

[0107] Through multi-source data fusion and frequency domain analysis, this method enables non-invasive, real-time monitoring of the microscopic pore structure within the molding cavity, overcoming the lag inherent in traditional destructive testing. Combined with spatial correlation analysis, it can accurately locate high-risk areas of uneven distribution, providing an intuitive basis for the dynamic adjustment of foaming process parameters, thereby improving the uniformity of the pore structure and the stability of the mechanical properties of EPP products.

[0108] Example 4:

[0109] In the implementation process of determining whether to perform global coordinated control of molding process parameters based on the dynamic imbalance risk of the bubble growth process and the non-uniform distribution characteristics of the micropore structure, the following logic and operations are used:

[0110] The system presets two key thresholds as control triggers: a dynamic imbalance risk level threshold (referred to as the "first threshold"), reflecting the stability of bubble growth, and a spatial correlation index threshold (referred to as the "second threshold"), characterizing the uniformity of the microscopic pore structure. These two thresholds are set based on material properties, product specifications, and long-term process debugging experience. For example, for EPP products with a density requirement of 30-50 kg / m³, the first threshold can be set to "medium risk" (corresponding to the intermediate level in the dynamic imbalance risk assessment), and the second threshold can be set to 0.6 (the spatial correlation index ranges from 0 to 1, with higher values ​​indicating greater pore heterogeneity).

[0111] The system calculates the dynamic imbalance risk level and spatial correlation index in real time. The dynamic imbalance risk level, output by the multi-physics coupling model, is categorized as low, medium, and high, corresponding to stable, potential imbalance, and significant imbalance states during bubble growth. The spatial correlation index, generated through multi-source sensor data fusion and frequency domain analysis, reflects the uniformity of the pore structure in different regions within the molding cavity. Values ​​closer to 0 indicate greater uniformity, while values ​​closer to 1 indicate more significant heterogeneity.

[0112] When the system determines the real-time data of the dynamic imbalance risk level and spatial correlation index, it executes the following logic:

[0113] Conditions for maintaining current parameters: When the dynamic imbalance risk level is below the first threshold (e.g., "low risk") and the spatial correlation index is below the second threshold (e.g., less than 0.6), the bubble growth process is stable, the microscopic pore structure uniformity meets requirements, and no process parameter adjustment is required. For example, at a certain moment, the system displays a dynamic imbalance risk level of "low risk" and a spatial correlation index of 0.45. At this time, the system continues to operate according to the current parameters, including the temperature setpoints of each temperature control unit, the foaming agent injection rate, and the cavity pressure.

[0114] Conditions for triggering global coordinated control: When the dynamic imbalance risk level reaches or exceeds the first threshold (e.g., rising to "medium risk" or "high risk"), or the spatial correlation index reaches or exceeds the second threshold (e.g., ≥0.6), the system determines that global coordinated control of molding process parameters is necessary. The trigger condition can be a single parameter exceeding the limit or two parameters exceeding the limit simultaneously. The following examples illustrate different trigger scenarios:

[0115] Example 1: A single dynamic imbalance risk level exceeding the limit triggers regulation

[0116] During the foaming process of a certain batch of EPP, the multi-physics coupling model outputted a dynamic imbalance risk level of "medium risk" (reaching the first threshold) for a certain area. Specifically, the average migration rate of the bubble nucleation position was 3 mm / s (between 2 and 5 mm / s, which is a medium risk range), and the coefficient of variation of the bubble size distribution was 0.35 (between 0.3 and 0.6, which is a medium risk range). At this point, although the spatial correlation index was 0.58 (lower than the second threshold of 0.6), the system still triggered a global coordinated control instruction because the dynamic imbalance risk level had reached the threshold. The control goal is to reduce the migration rate of the bubble nucleation position and the discreteness of the size distribution. Specific control strategies may include:

[0117] Lower the temperature setting of the corresponding temperature control unit (e.g., lower the temperature of the area from 150°C to 145°C) to slow down the decomposition rate of the foaming agent and the melt flow rate;

[0118] Fine-tune the amount of foaming agent injected to reduce the foaming agent concentration gradient in local areas;

[0119] Increase the cavity pressure by 0.1 MPa to improve the stability of bubble growth.

[0120] Example 2: Exceeding the limit for a single spatial correlation index triggers regulation

[0121] In another production batch, the dynamic imbalance risk level was "low risk," but the spatial correlation index rose to 0.65 (exceeding the second threshold of 0.6). Through multi-source sensor data fusion analysis, it was found that the density fluctuation spectrum characteristics in the axial middle area of ​​the molding cavity showed a significant increase in the proportion of low-frequency energy (from the normal 50% to 70%). The mapping relationship model predicted that the average pore size standard deviation in this area was 25% higher than the normal value, indicating the risk of non-uniform pore distribution. At this time, although the bubble growth process was stable, the system still triggered the global coordinated control instruction because the spatial correlation index exceeded the standard. The control direction is to improve the density uniformity in this area. Specific measures may include:

[0122] Adjust the heat transfer efficiency of adjacent temperature control units to enhance the thermal radiation coupling between the area and the areas above and below (e.g., increase the power output of the temperature control unit);

[0123] Optimize the foaming agent injection path to make the foaming agent more evenly distributed in the cavity axial direction;

[0124] Prolonging the holding time in this area promotes melt flow to balance the pore structure.

[0125] Example 3: Two parameters exceeding the limit at the same time trigger control

[0126] In extreme cases, the dynamic imbalance risk level in a batch of foaming processes rises to "high risk" (e.g., the average migration rate of bubble nucleation sites reaches 6 mm / s, and the coefficient of variation of size distribution is 0.7), while the spatial correlation index reaches 0.8 (far exceeding the second threshold). At this point, the system determines that there is a serious defect risk in the foaming process and immediately triggers the highest level of control instructions. The control strategy needs to target both bubble growth stability and pore uniformity, for example:

[0127] Coordinated cooling of multiple temperature control units (e.g., lowering the high-temperature area by 10°C and raising the low-temperature area by 5°C) reshapes the temperature field distribution to suppress nucleation site migration.

[0128] Significantly increase the cavity pressure to 1.5MPa (0.3MPa higher than the normal operating pressure) to force the bubble growth interface to stabilize;

[0129] Pause the injection of foaming agent for 2 seconds, wait until the melt flow becomes stable, and then re-inject it at a stepped rate to avoid local oversaturation.

[0130] After the control instruction is triggered, the system enters the global collaborative control process. First, the process control decision module generates a control strategy based on a preset parameter adjustment rule base. The rule base stores the mapping relationship between different risk types and control parameters (such as "high dynamic imbalance risk" corresponds to temperature reduction and pressure increase, "high spatial correlation index" corresponds to enhanced thermal radiation coupling and uniform foaming agent injection, etc.). After multiple verifications (such as whether the parameter adjustment range exceeds the equipment safety limit and whether there is a conflict between the parameters of adjacent temperature control units), the control strategy is sent to the sensitivity quantification module and the priority allocation module to perform parameter adjustment sensitivity analysis and control execution priority sorting of the temperature control nodes to ensure that the control actions are implemented in the optimal order.

[0131] The entire judgment process emphasizes a combination of real-time and logical analysis. Using a high-speed data processing module, the system completes real-time calculation and threshold comparison of the dynamic imbalance risk level and spatial correlation index within 500ms, ensuring an early response to process parameter deviations. Furthermore, the use of "OR" logic (a single parameter exceeding the limit triggers control) rather than "AND" logic demonstrates strict control over potential risks in the foaming process, preventing product quality issues caused by untimely processing of single-dimensional defects.

[0132] In practical applications, a dynamic threshold adjustment mechanism is crucial. Operators can reconfigure the first and second thresholds through the human-machine interface based on EPP raw material characteristics (such as blowing agent type and polymer melt viscosity), product structure requirements (such as higher pore uniformity requirements for thick-walled products), or equipment status (such as reduced temperature control accuracy in older equipment). For example, when producing high-value-added precision EPP components, the second threshold can be lowered from 0.6 to 0.5 to trigger control earlier and ensure high pore structure precision. Conversely, when producing general-purpose EPP packaging products, the threshold can be appropriately relaxed to improve production efficiency.

[0133] The system also features control history logging and traceability. Each time global coordinated control is triggered, it automatically records the risk parameter values, control strategy details, adjustment ranges for each temperature control node, and execution sequence at the time of triggering, creating a complete process log. This traceability allows operators to analyze the actual effects of different control strategies, accumulate experience, optimize the rule base, and gradually enhance the system's intelligent decision-making capabilities.

[0134] Through this judgment mechanism based on dual-parameter thresholds, the method achieves scientific identification of the need for molding process parameter control, avoiding frequent and ineffective adjustments due to oversensitivity and preventing quality defects caused by delayed judgment, providing reliable guarantees for the stability of the EPP foaming process and product consistency.

[0135] Example 5: 5:

[0136] When global coordinated control of molding process parameters is required, the heat transfer efficiency of each temperature control unit and the thermal radiation impact of adjacent units are analyzed and the control execution priority is determined. This is achieved through the following steps and examples:

[0137] 1. Correlation analysis between heat transfer efficiency and thermal radiation effect

[0138] Calculate the heat flux conductivity coefficient of each temperature control unit and the thermal radiation superposition effect value between adjacent units. Take a molding cavity containing 6 temperature control units (numbered U1-U6) as an example. Each temperature control unit corresponds to a different area of ​​the cavity (such as U1-U3 is an axial partition, and U4-U6 is a radial partition). The heat flux conductivity coefficient is estimated by Fourier's heat conduction law, taking into account the thermal conductivity of the unit material (such as the thermal conductivity of stainless steel is 16W / m·K), the contact area between the temperature control unit and the melt, and the temperature difference between the units. For example, the temperature of the U1 unit is set to 160℃, the temperature of the adjacent U2 unit is set to 150℃, the contact boundary area between the two is 0.2m², and the thermal conductivity is 16W / m·K. Then the heat flux conductivity coefficient is: (Note: This is only a schematic diagram of the calculation logic. The actual parameters need to be determined according to the equipment specifications.)

[0139] The thermal radiation superposition effect is calculated using the Stefan-Boltzmann law, taking into account the surface emissivity of the unit (e.g., the surface emissivity of oxidized stainless steel is 0.8) and the fourth power difference in temperature. For example, if the surface temperature of unit U4 is 170°C (443K) and the surface temperature of the adjacent unit U5 is 140°C (413K), the radiation heat flux between the two is:

[0140] The thermal radiation superposition effect value of each unit is the sum of the radiation heat flux density of it and all adjacent units, reflecting the degree to which the unit is affected by the surrounding temperature field.

[0141] Establish a correlation index matrix between temperature fluctuations and heat conduction paths. The rows and columns of the matrix are the numbers of the temperature control units, and the element values ​​are the weighted sums of the heat flux conduction coefficients and the radiation superposition effect values ​​between the units (the weights are set based on process experience, such as 70% for heat conduction and 30% for heat radiation). Taking U1 and U2 as an example, the matrix element values ​​are:

[0142] By traversing all adjacent unit pairs, a complete correlation index matrix is ​​formed, and the diagonal elements of the matrix are the thermal inertia coefficients of each unit itself (related to the unit mass and specific heat capacity).

[0143] 2. Quantification of parameter adjustment sensitivity

[0144] Based on the correlation index matrix, a parameter adjustment sensitivity sequence for each node is generated. Sensitivity reflects the degree to which adjusting the parameters of a temperature control unit affects surrounding units and the overall temperature field. For example, if the values ​​of elements U3 and U4 in the matrix are large, it means that adjusting the temperature of U3 will significantly affect the heat transfer efficiency of U4, and therefore the parameter adjustment sensitivity of U3 is high. Sensitivity values ​​are mapped to a range of 0-100 through normalization, with larger values ​​indicating a more significant impact of adjusting the node on the global temperature field.

[0145] Taking the six temperature control units in the example as an example, the calculated sensitivity sequence may be: U1 (65), U2 (78), U3 (82), U4 (55), U5 (48), U6 (39). Among them, U3 is located in the center of the cavity and has strong thermal coupling with multiple adjacent units (such as being adjacent to U2, U5, and U6 at the same time). Its sensitivity value is the highest, indicating that adjusting the temperature setting value of U3 will have a greater impact on the thermal balance of the surrounding area.

[0146] 3. Determining the Priority of Regulation and Control Execution

[0147] Filter highly sensitive nodes: Set a sensitivity threshold (e.g., 50) to filter out nodes with values ​​higher than the threshold. In this example, U1 (65), U2 (78), U3 (82), and U4 (55) meet the criteria, forming the set to be sorted {U1, U2, U3, U4}.

[0148] Weighted calculation and sorting: For the selected nodes, multiply the sensitivity value by its spatial position weight to obtain the weighted value. The spatial position weight is set according to the degree of influence of the node on the foaming quality. For example, the center area of ​​the cavity (U3) has a greater impact on the uniformity of the bubbles, so the weight is set to 1.2; the edge area (U1, U4) has a weight of 1.0; and the transition area (U2) has a weight of 1.1. Calculation example:

[0149] U1: 65×1.0=65

[0150] U2: 78×1.1=85.8

[0151] U3: 82×1.2=98.4

[0152] U4: 55×1.0=55

[0153] Generate a priority queue: Arrange in descending order of weighted values ​​to obtain the final priority queue: U3 (98.4), U2 (85.8), U1 (65), U4 (55). At the same time, remove nodes with weighted values ​​below the critical threshold (such as 50) (in this example, U4's weighted value of 55 is close to the threshold and can be retained).

[0154] Assigning control priorities: The first N nodes in the queue (e.g., N=2) are assigned the highest control priority. The remaining nodes are assigned secondary priorities based on their sensitivity. In this example, U3 and U2 have the highest priority and require parameter adjustment first. U1 and U4 have secondary priority and are adjusted after the highest-priority nodes are adjusted.

[0155] 4. Specific application examples

[0156] Scenario: The dynamic imbalance risk level reaches medium risk, and coordinated control of the temperature field is required.

[0157] During an EPP foaming process, the multiphysics coupling model showed that the migration rate of bubble nucleation sites in the central region of the cavity (corresponding to temperature control unit U3) reached 3.5 mm / s (medium risk), and the spatial correlation index was 0.62 (near threshold). The system triggered global coordinated control, and the specific implementation steps are as follows:

[0158] Correlation analysis and sensitivity calculation:

[0159] The heat flux conduction coefficient and radiation superposition effect value of U3 and adjacent units (U2, U5, U6) were calculated. It was found that the heat conduction coefficient of U3 and U2 was the highest (because the two are in direct contact and the temperature difference is 15°C), and the radiation superposition effect value with U5 was the largest (because the radial distance is close and the surface temperature difference is large).

[0160] In the correlation index matrix, the element values ​​of U3 and each unit are higher than those of other nodes. Its sensitivity value is calculated to be 82, the spatial position weight is 1.2, and the weighted value is 98.4, ranking first in the priority queue.

[0161] Control strategy execution:

[0162] The highest-priority node (U3) was first lowered from 155°C to 150°C to reduce the foaming agent decomposition rate and inhibit nucleation migration. After this adjustment, real-time monitoring of the heat flux conductivity of U3 revealed a decrease in its heat flux relative to U2 from 640W to 520W, indicating reduced heat transfer efficiency and decreased temperature fluctuations in the surrounding area.

[0163] The next-highest-priority node (U2) was raised from 140°C to 145°C to balance the temperature difference with U3 and reduce local overcooling caused by U3's cooling. This adjustment reduced the temperature difference between U2 and U3 from 15°C to 5°C, reducing the radiation stacking effect by 30% and weakening the thermal coupling between the two nodes.

[0164] Secondary priority nodes (U1, U4): Based on the sensitivity ratio, the adjustment range of U1 (sensitivity 65) is 65 / 82≈80% of the highest priority node, that is, the temperature is lowered by 4°C (from 160°C to 156°C); the adjustment range of U4 (sensitivity 55) is 55 / 82≈67%, that is, the temperature is increased by 3°C (from 135°C to 138°C) to maintain the uniformity of the radial temperature gradient.

[0165] Effect verification and iteration:

[0166] Five minutes after the adjustment, the multiphysics model showed that the bubble nucleation migration rate in the U3 region dropped to 2.8 mm / s (close to the low-risk interval) and the spatial correlation index dropped to 0.58 (below the threshold).

[0167] The system continuously monitors the sensitivity changes of each node and finds that the sensitivity value of U3 drops to 70 due to temperature adjustment, while that of U2 rises to 75. The priority queue is automatically updated to ensure that the control process dynamically adapts to changes in the temperature field.

[0168] V. Key Implementation Points

[0169] Sensor layout and data real-time performance: Each temperature control unit must be equipped with a high-precision temperature sensor (±0.5°C accuracy) to collect real-time surface temperature and internal heat flow data. Data sampling frequency should be no less than 20Hz and transmitted to the control system via industrial Ethernet to ensure timely correlation analysis.

[0170] Process experience in weight setting: Spatial position weights should be set based on the product's structural characteristics. For example, when producing thin-walled products, the weight of the cavity edge temperature control units (such as U1 and U4) can be increased to 1.1, as they directly affect the surface quality. When producing thick-walled products, the weight of the center unit (such as U3) should be set to above 1.3 to prioritize control of the internal cell structure.

[0171] Gradient control of adjustment range: To avoid drastic fluctuations in the temperature field, the parameter adjustment range of a single node should be limited to within ±10% (for example, the temperature setpoint adjustment should not exceed ±15°C). If larger adjustments are required, implement them in stages (for example, 5°C each time, with an interval of 2 minutes), and monitor the melt status in real time.

[0172] Multi-objective collaborative optimization: When multiple risk types (such as dynamic imbalance and uneven porosity) coexist, sensitivity calculations must comprehensively consider the priorities of different control objectives. For example, temperature control nodes associated with high dynamic imbalance risk should be prioritized, followed by nodes associated with uneven porosity. Multi-objective balancing can be achieved through weighted allocation.

[0173] 6. System Expansion and Adaptability

[0174] This method is applicable to molding cavities of varying sizes. By increasing or decreasing the number of temperature control units and adjusting the meshing accuracy, it can be adapted to small laboratory equipment (e.g., ≤ 4 temperature control units) or large industrial production lines (e.g., ≥ 20 temperature control units). For complex cavity structures (e.g., those with irregular flow channels), the spatial resolution of heat transfer analysis can be improved by increasing the number of radial and axial temperature control zones.

[0175] Through this control strategy based on thermal coupling analysis and sensitivity quantification, the system can achieve accurate and orderly adjustment of molding process parameters, avoid temperature field disorder caused by blind control, and ensure that the thermodynamic equilibrium of the foaming process is restored in the shortest time, thereby effectively improving the quality stability and production efficiency of EPP products.

[0176] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "includes," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0177] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for optimizing EPP foaming process parameters, characterized in that: The steps include: Real-time monitoring of temperature field distribution and pressure change data during the foaming process to determine whether the thermodynamic state in the molding cavity deviates from the preset process window; When the thermodynamic state deviates from the preset process window, a multi-physics coupling model is constructed to analyze the interaction between foaming agent diffusion and polymer melt flow, and to assess the risk of dynamic imbalance in the bubble growth process within the molding cavity. By combining multi-source sensor data fusion with frequency domain analysis to process density gradient signals in different areas of the molding cavity, the non-uniform distribution characteristics of the microscopic pore structure during the material expansion process can be identified. Based on the dynamic imbalance risk of the bubble growth process and the non-uniform distribution characteristics of the micropore structure, it is determined whether to conduct global coordinated control of the molding process parameters; When global coordinated control of molding process parameters is required, the heat transfer efficiency of each temperature control unit and the thermal radiation impact of adjacent units are correlated and analyzed to quantify the parameter adjustment sensitivity of each temperature control node; Determine the control execution priority of each temperature control node based on parameter adjustment sensitivity; monitor the temperature field distribution and pressure change data during the foaming process in real time to determine whether the thermodynamic state in the molding cavity deviates from the preset process window. Specifically: Synchronously collect temperature gradient data and pressure fluctuation data of each partition of the molding cavity; Generate a thermodynamic state determination matrix based on the temperature distribution curve and pressure change threshold of the preset process window; The real-time collected temperature gradient data and pressure fluctuation data are input into the judgment matrix for pattern matching to detect the deviation amplitude of thermodynamic parameters; When the deviation of the parameters of any partition exceeds the corresponding threshold, the thermodynamic state of the molding cavity is determined to have deviated from the preset process window. By constructing a multi-physics field coupling model to analyze the interaction between the diffusion of the foaming agent and the flow of the polymer melt, the dynamic imbalance risk of the bubble growth process in the molding cavity is evaluated. Specifically: Obtaining foaming agent concentration distribution data and melt viscosity real-time data as model input parameters; Establish a multi-physics coupling equation to describe the mutual constraints between the diffusion rate of the foaming agent and the melt flow velocity; The iterative calculation method is used to solve the spatial distribution relationship between the foaming agent concentration gradient field and the melt shear stress field; By simulating the migration trend of bubble nucleation positions and the discreteness of size distribution, the dynamic imbalance risk level is output. By combining multi-source sensor data fusion with frequency domain analysis to process density gradient signals in different areas of the molding cavity, the non-uniform distribution characteristics of the microscopic pore structure during the material expansion process are identified. Specifically: Collect density detection signals and ultrasonic attenuation coefficient data in the axial and radial directions of the molding cavity; Perform time-frequency conversion on multi-source sensor data and extract the spectral feature vector of density fluctuation; The spectral feature vectors were processed by principal component analysis to reduce the dimension and build a mapping model between density distribution and pore structure. Based on the spatial correlation index output by the mapping relationship model, high-risk areas of non-uniform pore distribution are marked. Based on the dynamic imbalance risk of the bubble growth process and the non-uniform distribution characteristics of the microscopic pore structure, it is determined whether to perform global coordinated regulation of the molding process parameters. Specifically: When the dynamic imbalance risk level is lower than the first threshold and the spatial correlation index is lower than the second threshold, the current process parameters are maintained; When the dynamic imbalance risk level reaches a first threshold or the spatial correlation index reaches a second threshold, a global coordinated control instruction is triggered.

2. The EPP foaming process parameter optimization method according to claim 1, characterized in that: When global coordinated control of molding process parameters is required, the heat transfer efficiency of each temperature control unit and the thermal radiation influence of adjacent units are correlated and analyzed to quantify the parameter adjustment sensitivity of each temperature control node. Specifically: Calculate the heat flux conductivity coefficient of each temperature control unit and the thermal radiation superposition effect value between adjacent units; Establish a correlation index matrix between temperature fluctuations and heat conduction paths to identify the intensity of thermal radiation coupling; According to the distribution range of the element values ​​in the correlation index matrix, the parameter adjustment sensitivity sequence of each node is generated.

3. The EPP foaming process parameter optimization method according to claim 1, characterized in that: The control execution priority of each temperature control node is determined based on the parameter adjustment sensitivity, specifically: Set a sensitivity threshold and filter out the set of temperature control nodes that are higher than the threshold; In the filtered set of nodes, a priority queue is generated by arranging them in descending order of sensitivity values; The first N nodes in the queue are given the highest control priority, and the remaining nodes are assigned secondary priorities according to their sensitivity ratio.

4. The EPP foaming process parameter optimization method according to claim 3, characterized in that: Generate a priority queue by arranging the sensitivity values ​​in descending order, specifically: The sensitivity value of each node is weighted with its corresponding spatial position weight; The final priority queue is generated by reordering according to the weighted calculation results, and nodes with weight values ​​lower than the critical threshold are eliminated.

5. An EPP foaming process parameter optimization system, used to implement the EPP foaming process parameter optimization method according to any one of claims 1 to 4, characterized in that: It includes thermodynamic monitoring module, dynamic coupling analysis module, pore feature recognition module, process control decision module, sensitivity quantification module and priority allocation module; Thermodynamic monitoring module: real-time monitoring of temperature field distribution and pressure change data during the foaming process to determine whether the thermodynamic state in the molding cavity deviates from the preset process window; Dynamic Coupling Analysis Module: When the thermodynamic state deviates from the preset process window, a multi-physics coupling model is constructed to analyze the interaction between foaming agent diffusion and polymer melt flow, and to assess the risk of dynamic imbalance in the bubble growth process within the molding cavity. Pore ​​Feature Recognition Module: When the thermodynamic state deviates from the preset process window, the module processes the density gradient signals of different regions within the molding cavity through multi-source sensor data fusion and frequency domain analysis to identify the non-uniform distribution characteristics of the microscopic pore structure during the material expansion process. Process control decision module: Based on the dynamic imbalance risk of the bubble growth process and the non-uniform distribution characteristics of the micropore structure, it determines whether to perform global coordinated control of the molding process parameters; Sensitivity Quantification Module: When global coordinated control of molding process parameters is required, the heat transfer efficiency of each temperature control unit and the thermal radiation impact of adjacent units are correlated and analyzed to quantify the parameter adjustment sensitivity of each temperature control node. Priority allocation module: determines the control execution priority of each temperature control node according to the parameter adjustment sensitivity.

6. The EPP foaming process parameter optimization system according to claim 5, characterized in that: The sensitivity quantification module includes a heat conduction calculation unit, a radiation coupling analysis unit and a weighted sorting unit, which are respectively used to perform heat flux conduction coefficient calculation, heat radiation superposition effect analysis and sensitivity weighted value sorting operations.

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