Prediction and control method of carbon dioxide solubility in soda water filling line based on physical information neural network

Abstract

The present invention provides a method for predicting and controlling the solubility of carbon dioxide in a soda water filling line based on a physical information neural network, which belongs to the technical field of neural network solubility prediction. The present invention constructs a physical information neural network model constrained by vortex dynamics, embeds the fluid mechanics equations and the gas solubility law as hard constraints into the loss function, and synchronously optimizes data fitting and physical law matching through gradient back propagation. The sensor data is processed using a multi-scale spatiotemporal attention unit, and the signal features are extracted hierarchically through wavelet transform. The production line topology is abstracted into a graph structure through a migration adaptation module, and the difference is calculated to adaptively migrate the model parameters. The filling pressure is dynamically optimized based on the predicted value, and the solubility deviation is responded to through a real-time adjustment mechanism of the PID parameters. The present invention improves the accuracy and robustness of solubility prediction, enhances the model's ability to suppress noise and adapt to topology changes, and improves the stability and response speed of the control system.

Description

Technical Field

[0001] The present invention relates to the technical field of neural network solubility prediction, and in particular to a method for predicting and controlling carbon dioxide solubility in a soda water filling line based on a physical information neural network. Background Art

[0002] In soda water bottling lines, carbon dioxide solubility directly impacts the richness of the soda water's foam, crispness, and acidity balance. Insufficient solubility can result in a bland taste, soft bubbles, or even foam collapse, while excessive solubility can produce a pungent sour taste or imbalanced pressure within the bottle. By predicting solubility, the temperature and pressure parameters of the carbonation process can be precisely controlled to ensure the stability of the bubble characteristics and flavor of each batch of products. The pressure within the bottle after filling is directly related to the solubility. If the predicted amount is too low due to deviations, residual gas will accumulate in the headspace. The increase in temperature during transportation may cause bottle bulging, leakage, or even packaging rupture. Excessive solubility may accelerate fatigue and aging of the packaging material. In soda water bottling lines, carbon dioxide solubility prediction is essential to ensure product quality, safety, and production efficiency.

[0003] Existing CO2 solubility prediction methods rely on purely data-driven models such as LSTM neural networks or static physical models. These models rely on historical sensor data for training and predict solubility based on time series features. While they can capture data correlations, they ignore physical constraints. Their generalizability declines significantly under complex conditions such as pressure fluctuations or temperature jumps, and their predictions can easily deviate from the actual physical process. Static physical models, based on empirical equations such as Henry's law, calculate solubility using fixed parameters. While incorporating physical relationships, they fail to incorporate real-time dynamic features such as vortex diffusion effects. They also have poor adaptability to changes in filling line topology, requiring remodeling after line adjustments or equipment upgrades. Furthermore, traditional prediction methods fail to account for differences in line topology, requiring full retraining for new filling line deployments, which is time-consuming and relies on large amounts of new data. Traditional control strategies use fixed PID parameters and are unable to adjust pressure commands in real time based on solubility prediction deviations. This leads to significant overshoot and slow recovery under disturbed conditions, making them incapable of meeting high-precision filling requirements. In scenarios with high-frequency pressure fluctuations or temperature steps, existing methods are unable to synchronize prediction and control, creating a key bottleneck hindering the intelligent upgrade of soda water filling lines.

[0004] Based on the current problems in predicting the carbon dioxide solubility in soda water filling lines, it is urgent to develop new methods for predicting and controlling the carbon dioxide solubility in soda water filling lines to break through the existing technical bottlenecks. Summary of the Invention

[0005] To solve the problems in the background technology, the present invention provides a method for predicting and controlling carbon dioxide solubility in a soda water filling line based on a physical information neural network, comprising the following steps:

[0006] S1: Real-time collection of multi-source sensor data through sensor array modules deployed in tanks, pipelines and filling heads of the filling line;

[0007] S2: Constructing a physical information neural network model for vortex dynamics constraints;

[0008] S3: Processing sensory data via multi-scale spatiotemporal attention units;

[0009] S4: The migration adaptation module calculates the difference in production line topology and adapts the migration model parameters.

[0010] S5: The control execution module outputs the predicted value of carbon dioxide solubility and optimizes the filling pressure control.

[0011] Furthermore, the S1 specifically includes:

[0012] The sensor array module synchronously collects the measured values ​​of tank pressure, pipeline temperature, flow velocity vector and carbon dioxide solubility at a sampling frequency of 1 kHz.

[0013] The optical fiber temperature array is deployed on the outer surface of the pipeline in a spiral winding manner, and the CO2 sensor is in direct contact with the filling liquid.

[0014] Furthermore, the physical information neural network model of S2 is executed in the model processor, and its loss function is:

[0015] ;

[0016] in:

[0017] Indicates total loss represents the L2 norm Represents the model prediction value Indicates the measured solubility Represents the physical constraint weight coefficient Indicates CO2 concentration Indicates time Represents the flow velocity vector Represents the dot product operation represents the gradient operator represents the diffusion coefficient represents the Laplace operator represents Henry's constant Indicates filling pressure Represents the exponential function Represents the temperature hysteresis factor Indicates temperature.

[0018] Furthermore, S3 is executed by the multi-scale spatiotemporal attention unit of the model processor:

[0019] ;

[0020] in:

[0021] Represents the attention weight Represents the multiplication operator Indicates the wavelet decomposition scale index Indicates the maximum decomposition scale Represents the Sigmoid activation function Indicates the Scaled trainable weight matrix Represents matrix multiplication Indicates the Scaling Discrete Wavelet Transform Represents the input feature tensor.

[0022] Furthermore, the S4 is performed by the migration adaptation module:

[0023] S4.1: The graph structure mapper abstracts the filling line into a graph structure ,in:

[0024] Node Set Represents a valve, sensor, or actuator; edge set Indicates the physical connection relationship of the pipeline;

[0025] S4.2: The WL graph core calculator calculates the topological difference between the target production line and the source production line:

[0026] ;

[0027] in:

[0028] Represents topological difference Represents vector inner product Represents the Weisfeiler-Lehman graph feature map Represents the source production line adjacency matrix Represents the target production line adjacency matrix represents the Euclidean norm;

[0029] S4.3: Executed by parameter fine-tuner: When Directly load the source model parameters when Proportional Fine-tune the last layer weights.

[0030] Furthermore, the step S5 is executed by a PID parameter dynamic calculator of the control execution module:

[0031] ;

[0032] in:

[0033] Indicates the optimized filling pressure Indicates the base pressure Represents the proportional coefficient Indicates the integral coefficient Represents the differential coefficient Denotes the solubility prediction bias Represents time variables Indicates integral operation Represents the differential operation.

[0034] The present invention also provides prediction and control of carbon dioxide solubility in a soda water filling line based on a physical information neural network, including:

[0035] The sensor array module is deployed on the outer wall of the filling tank, at the pipe connection and inside the filling head of the filling line, and includes:

[0036] The CO2 sensor is installed in the inner cavity of the filling head; the distributed optical fiber temperature array is wrapped around the outer wall of the pipeline;

[0037] The pressure sensor is installed at the pressure interface of the storage tank; the electromagnetic flowmeter is integrated into the main pipeline;

[0038] The data preprocessing module is connected to the sensor array module through the industrial bus and includes a signal conditioning circuit and a synchronous acquisition card;

[0039] The model processor is connected to the data preprocessing module through the PCIe interface. Its physical structure includes: GPU computing card; multi-scale spatiotemporal attention unit; storage unit;

[0040] The migration adapter module is connected to the model processor via Ethernet. Its hardware components include: graph structure mapper; WL graph core calculator; parameter fine-tuner;

[0041] The control execution module is connected to the migration adapter module through the industrial IO module, and includes: a solubility prediction interface; a PID parameter dynamic calculator; and a pressure valve drive circuit.

[0042] Furthermore, the sensor array module is deployed as follows: the CO2 sensor is inserted into the inner cavity of the filling head through a stainless steel probe, the optical fiber temperature array is spirally wrapped around the pipeline with a spacing of 5 cm, the pressure sensor is installed on the top of the tank, and the electromagnetic flowmeter is flange-connected to the main pipeline.

[0043] Furthermore, the migration adaptation module includes: a graph structure mapper, a dedicated processor that converts production line CAD drawings into adjacency matrices; a WL graph core calculator that uses FPGA to implement 3-layer iterative operations; and a parameter fine-tuner that includes a programmable weight scaling circuit.

[0044] Furthermore, in the control execution module: the solubility prediction interface 4-20mA analog output is connected to the DCS system; the PID parameter dynamic calculator is connected to the filling valve controller via RS485; the pressure valve drive circuit outputs a PWM signal to control the proportional control valve.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] First, the present invention deploys high-precision sensor arrays in the filling line tanks, pipelines and filling heads to synchronously collect multi-source data such as tank pressure, pipeline temperature, flow velocity vector and carbon dioxide solubility, capture temperature fluctuations and transient physical changes in fluid dynamics during the filling process, and construct a physical information neural network model constrained by vortex dynamics. This model embeds fluid mechanics equations and gas solubility laws as hard constraints into the loss function, and synchronously optimizes data fitting and physical law matching through gradient backpropagation. This solution breaks through the limitations of pure data-driven models, deeply integrates physical mechanisms with neural networks, and greatly improves the accuracy and robustness of solubility prediction. Especially under complex working conditions such as pressure fluctuations, the model can more stably capture the physical essence and reduce systematic errors.

[0047] Second, the present invention processes sensor data through multi-scale spatiotemporal attention units, uses wavelet transform to extract signal features in layers, and abstracts the production line topology into a graph structure through a migration adaptation module. The difference is calculated to adaptively migrate model parameters, thereby achieving the refinement of feature extraction and the generalization ability of the model across production lines. It can adapt to different filling line configurations without retraining, enhances the model's ability to suppress noise and adapt to topology changes, and in temperature transient scenarios, the system can respond to changes quickly to avoid control failures caused by hysteresis effects.

[0048] Third, the present invention dynamically optimizes the filling pressure based on the predicted value, responds to the solubility deviation through the real-time adjustment mechanism of PID parameters, outputs pressure regulation instructions to drive the actuator, and directly applies the predicted results to the control logic in a closed loop, realizing end-to-end optimization from data to execution, significantly improving the stability and response speed of the control system, effectively suppressing overshoot and oscillation under disturbed conditions, ensuring the smooth operation of the filling process, and avoiding the performance degradation caused by fixed parameters in traditional methods.

[0049] Fourth, the multi-source sensor array designed in the present invention captures the dynamics of pressure, temperature and flow rate in real time, providing comprehensive working condition perception for the prediction model; the physical information neural network couples the eddy diffusion equation with the gas solubility law, making the solubility prediction more in line with the essence of fluid mechanics, effectively overcoming the systematic deviation of the traditional data-driven model; the multi-scale attention mechanism is combined with the wavelet transform to extract signal features in a hierarchical manner, greatly enhancing the transient noise suppression capability; the migration adaptation module dynamically adjusts the model parameters according to the difference in production line topology to achieve seamless migration across production lines; finally, the filling pressure is optimized through the dynamic PID control closed loop, so that the system can still maintain control stability under disturbance conditions such as pressure fluctuations and temperature jumps, thereby improving the consistency of filling quality and the adaptability of production lines as a whole. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a flow chart of the carbon dioxide solubility prediction and control method of the soda water filling line based on physical information neural network of the present invention;

[0051] Figure 2 This is a structural diagram of the carbon dioxide solubility prediction and control system for a soda water filling line based on a physical information neural network of the present invention;

[0052] Figure 3 This is a comparison chart of prediction accuracy under pressure fluctuation conditions between Example 1 and Comparative Example 1;

[0053] Figure 4 is a temperature step response curve diagram of Example 1 and Comparative Example 2;

[0054] Figure 5 is a pressure step response diagram of Example 1 and Comparative Example 3;

[0055] Figure 6 This is a functional framework diagram of the carbon dioxide solubility prediction and control system for a soda water filling line based on a physical information neural network of the present invention. DETAILED DESCRIPTION

[0056] 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. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0057] Reference Figure 2 and Figure 6The present invention designs a carbon dioxide solubility prediction and control system for a soda water filling line based on a physical information neural network. The system is equipped with a sensor array module, which is deployed on the outer wall of the filling line tank, the pipe connection and the inside of the filling head, including a CO2 sensor installed in the inner cavity of the filling head; a distributed optical fiber temperature array wrapped around the outer wall of the pipe; a pressure sensor installed at the pressure interface of the tank; an electromagnetic flowmeter integrated in the main pipeline; and a data preprocessing module: the sensor array module is connected via an industrial bus, and includes a signal conditioning circuit and a synchronous acquisition card.

[0058] The model processor is connected to the data preprocessing module through the PCIe interface. Its physical structure includes: GPU computing card; multi-scale spatiotemporal attention unit; storage unit.

[0059] The migration adapter module is connected to the model processor via Ethernet. Its hardware components include: graph structure mapper; WL graph core calculator; parameter fine-tuner;

[0060] The control execution module is connected to the migration adapter module through the industrial IO module, and includes: a solubility prediction interface; a PID parameter dynamic calculator; and a pressure valve drive circuit.

[0061] The sensor array module is deployed as follows: the CO2 sensor is inserted into the inner cavity of the filling head through a stainless steel probe, the fiber optic temperature array is spirally wrapped around the pipeline with a spacing of 5 cm, the pressure sensor is installed on the top of the tank, and the electromagnetic flowmeter is flange-connected to the main pipeline.

[0062] The migration adaptation module includes a graph structure mapper, a dedicated processor that converts production line CAD drawings into adjacency matrices; a WL graph core calculator that uses a Xilinx FPGA to implement three-layer iterative operations; and a parameter fine-tuner that includes a programmable weight scaling circuit.

[0063] In the control execution module, the solubility prediction interface 4-20mA analog output is connected to the DCS system; the PID parameter dynamic calculator is connected to the filling valve controller via RS485; and the pressure valve drive circuit outputs a PWM signal to control the proportional control valve.

[0064] The system first deploys sensor array modules at key locations along the filling line to collect data in real time. These modules include high-precision carbon dioxide sensors, which directly contact the filling liquid. These sensors are installed within the filling head and inserted into the fluid via a stainless steel probe. A distributed fiber optic temperature array is deployed on the outer surface of the pipeline in a spirally wound pattern, with a precise five-centimeter spacing, to capture transient temperature changes. A pressure sensor is secured to the top of the tank via a standard threaded interface, and an electromagnetic flowmeter is integrated into the main pipeline via a flange connection to measure the three-dimensional flow velocity vector. These sensors are connected to the industrial bus interface of the data preprocessing module via shielded cables.

[0065] The data preprocessing module is located in the control cabinet. Its signal conditioning circuit filters and amplifies the raw sensor signals, and a synchronous acquisition card latches multi-channel data at a frequency of 1 kHz. The preprocessed data stream is transmitted via a high-speed PCIe interface to the model processor, which uses a GPU computing card installed in an industrial server as its core computing unit. The physical constraint calculation unit within the model processor is responsible for executing the vortex dynamics loss function, and the gradient backpropagation unit updates the network weights. The storage unit stores the pretrained model parameters in the form of a solid-state drive, and the multi-scale spatiotemporal attention unit is equipped with a dedicated Haar wavelet processor to perform wavelet domain feature decomposition and generate attention weights.

[0066] The output of the model processor is transmitted via Ethernet to the migration adapter module, which is housed in a separate, shock-resistant chassis. The migration adapter module's graph structure mapper converts the production line CAD drawings into an adjacency matrix, while its dedicated processor analyzes the valve nodes and pipe connections. The WL graph kernel calculator, implemented using a Xilinx FPGA chip, computes graph isomorphism features using a three-iteration Weisfeiler-Lehman algorithm.

[0067] Xilinx FPGAs are field-programmable gate array chips that enable customized parallel computing through hardware logic reorganization. They are specifically designed to accelerate real-time computation of graph topology differences within the system. The Weisfeiler-Lehman algorithm is an iterative graph isomorphism detection method that generates a hierarchical label sequence by aggregating node and neighborhood features to quantify graph structural similarity.

[0068] The parameter fine-tuner contains a programmable weight scaling circuit that can proportionally adjust the parameters of the last layer of the neural network based on the topological difference calculated in real time.

[0069] The control execution module, located within the filling line control console, receives the output signal of the migration adapter module via the industrial I / O module. The module's solubility prediction interface outputs a standard 4-20 mA analog signal, which is directly connected to the main control unit of the distributed control system. The PID parameter dynamic calculator, with its built-in analog integral-differential circuit, dynamically generates control parameters based on solubility prediction deviations. The pressure valve drive circuit ultimately outputs a pulse-width modulated signal, driving the proportional control valve with a control accuracy of ±0.03 bar, forming a complete closed-loop pressure control system. All modules are connected via a star-topology network, with the main control computer coordinating the timing synchronization of each module to ensure an end-to-end latency of less than ten milliseconds from data acquisition to pressure regulation.

[0070] Reference Figure 1The present invention also designs a method for predicting and controlling the carbon dioxide solubility of a soda water filling line based on a physical information neural network. The specific implementation process is as follows: S1, multi-source sensor data acquisition; the sensor array module is deployed on the outer wall of the filling tank, at the pipe connection, and inside the filling head of the filling line, and four types of key data are collected in real time through physical connection. The high-precision carbon dioxide sensor inserts a stainless steel probe into the inner cavity of the filling head, directly contacts the liquid and measures the solubility value, and its measurement accuracy reaches Volume percentage. The distributed optical fiber temperature array is fixed to the outer wall of the pipe in a spiral winding manner, and the distance between adjacent optical fibers is precisely maintained. This design ensures the ability to capture transient temperature changes, and the response time is less than Milliseconds. The pressure sensor is installed on the pressure port on the top of the tank through a standard threaded interface, and the range covers to The electromagnetic flowmeter is integrated into the main pipeline using flange connection to obtain three-dimensional flow velocity vector data. All sensors are connected to the industrial bus through shielded cables. The following parameters are synchronously collected at a kilohertz frequency: tank pressure data (in bar); pipeline temperature data (in Kelvin); flow velocity vector data (in meters per second); and measured carbon dioxide solubility value (in volume percentage). The data collection process strictly adheres to the principle of timing synchronization, and the synchronous acquisition card in the data preprocessing module ensures the time alignment of multi-channel data.

[0071] S2: Physical information neural network modeling of vortex dynamics constraints. The model processor receives preprocessed sensor data and executes the physical information neural network modeling through the GPU computing card. The core of this model is to embed the fluid dynamics equations as hard constraints into the loss function. Its mathematical expression is as follows:

[0072] ;

[0073] in: represents the total loss function; represents the L2 norm (data fit measure); represents the solubility value predicted by the model; Indicates the solubility value measured by the sensor; Indicates the physical constraint weight coefficient (value range to ); Indicates the concentration of carbon dioxide (in moles per cubic meter); Represents a time variable (in seconds); represents the flow velocity vector (unit: meters per second); Represents vector dot product operation; represents the gradient operator (spatial differential); represents the diffusion coefficient (value square meters per second); represents the Laplace operator (second-order spatial differential); represents Henry's constant (value , dimensionless); Indicates the filling pressure (unit: bar); represents the natural exponential function; represents the temperature hysteresis factor (given by the formula Dynamic calculation); Indicates temperature in Kelvin.

[0074] The second term on the right side of the loss function couples the eddy-diffusion equation Nonlinear terms related to Henry's law ,in The temperature hysteresis effect model is customized for the transient working conditions of the filling process. The physical constraint calculation unit optimizes the data fitting error and the physical equation residual simultaneously during back propagation. When the system triggers the critical effect, the prediction error is significantly reduced.

[0075] S3: Multi-scale spatiotemporal attention data processing; the multi-scale spatiotemporal attention unit performs hierarchical feature extraction on the input sensor data. Its computational process is accelerated by the Haar wavelet processor hardware:

[0076] ;

[0077] in: represents the attention weight tensor; Represents a multiplication operator (multi-scale weight superposition); Represents the wavelet decomposition scale index (from Increment); Indicates the maximum decomposition scale (fixed value ); Represents the Sigmoid activation function (weight normalization); Indicates the Scaled trainable weight matrix; Represents matrix multiplication operation; Indicates the Scaled discrete wavelet transform (using Haar wavelet basis); Represents the input feature tensor (dimension is [time steps Number of sensors number of features]).

[0078] The sensor data is first subjected to a four-level Haar wavelet transform to decompose the original signal into low-frequency approximation components that reflect pressure and temperature trends and high-frequency detail components to capture noise disturbances. The wavelet coefficients of each scale are calculated through a trainable weight matrix Perform feature weighting and generate Sigmoid function to The attention weights at the four scales are combined through a multiplication operation, ultimately outputting enhanced features. Compared to traditional spatiotemporal attention mechanisms, the binary nature of the Haar wavelet basis significantly reduces computational complexity and significantly improves the efficiency of high-frequency noise suppression.

[0079] S4: Adaptive migration of production line topology. The migration adaptation module receives the output data from the model processor. The graph structure mapper first converts the physical topology of the target production line into a mathematical graph structure. This module parses the CAD drawings of the filling line, abstracting valves as nodes and pipe connections as edges to generate an adjacency matrix. The WL graph kernel calculator executes three Weisfeiler-Lehman iterations based on this matrix to calculate the topological difference between the source and target production lines. The parameter fine-tuner dynamically adjusts the neural network parameters based on the real-time difference value: if the difference is less than 0.2, the pretrained model weights are directly loaded; if the difference is greater than or equal to 0.2, the last layer weights are scaled proportionally.

[0080] The core formula for calculating topological difference is:

[0081] ;

[0082] in: represents the topological difference (dimensionless); Represents vector inner product operation; Represents the Weisfeiler-Lehman graph feature map, which generates node feature vectors through 3 iterations; Represents the adjacency matrix of the source production line; Represents the adjacency matrix of the target production line; Represents the Euclidean norm (vector length calculation).

[0083] The Weisfeiler-Lehman graph kernel aggregates node neighborhood information through three iterations. The first iteration marks the original node, the second iteration integrates the first-order neighbor features, and the third iteration captures the second-order topological relationship. FPGA hardware acceleration uses Xilinx chips to achieve parallel computing, making the single difference calculation time ≤5ms. Difference threshold is the critical value determined experimentally. Weight scaling ,when The weight of the final layer is adjusted by 150%, which enhances the model's adaptability to new topologies.

[0084] The specific process is as follows: Graph structure abstraction, the graph structure mapper abstracts the physical topology of the filling line (such as valve nodes and pipe connections) into an adjacency matrix and , respectively, represent the connection relationship between the source production line and the target production line. The WL graph kernel calculator generates feature vectors by performing a three-iteration Weisfeiler-Lehman algorithm on the adjacency matrix. The first iteration labels the basic features of the nodes. The second iteration aggregates the first-order neighborhood information. The third iteration integrates the second-order topological relationships. This generates a hierarchical feature vector. and .

[0085] Similarity calculation uses vector inner product operation to calculate the cosine similarity of the feature vectors, that is, the normalized dot product, to characterize the similarity of the two production line structures. The formula is:

[0086] ;

[0087] Difference calculation: Subtract the similarity from 1 to get the difference. (Value range 0-1), a difference close to 0 indicates highly similar topologies, and a difference close to 1 indicates significant differences. The entire process is accelerated in parallel by FPGA hardware to ensure real-time performance.

[0088] The Weisfeiler-Lehman feature mapping algorithm enhances the expressiveness of graph structures through iterative neighborhood feature iteration. Hardware acceleration using FPGAs enables parallel computing, optimizing iteration efficiency. Difference quantization converts cosine similarity into dissimilarity, providing a basis for subsequent parameter migration. This implementation strictly relies on mathematical abstraction of the production line topology and parallel computing, eliminating the need for model retraining.

[0089] S5: Solubility Prediction and Control Optimization: The control execution module receives the solubility prediction value output by the migration adaptation module, and the PID parameter dynamic calculator generates pressure adjustment commands in real time. The solubility prediction interface transmits the predicted value to the distributed control system (DCS) via a 4-20mA analog signal. The PID controller dynamically calculates the proportional, integral, and differential coefficients based on the predicted deviation. The pressure valve drive circuit converts the control command into a PWM signal, driving the proportional control valve to achieve closed-loop control of the filling pressure.

[0090] The core formula of pressure optimization control is:

[0091] ;

[0092] in: Indicates the optimized filling pressure (unit: bar); Indicates the base pressure (fixed value 6.2 bar); represents the proportionality factor (dimensionless); represents the integration coefficient (unit: reciprocal second s⁻¹); represents the differential coefficient (unit: seconds); Indicates the solubility prediction deviation (calculation formula: set value - predicted value); Represents a time variable (in seconds); Indicates integration operation (accumulation of historical deviations); Indicates the differential operation (instantaneous rate of change of deviation).

[0093] By prediction bias Real-time calculation, when high pressure fluctuates ( ) Increase To suppress overshoot; Under steady-state conditions ( )promote Eliminate static error.

[0094] Example 1. This Example 1 deploys the system of the present invention on a 330 ml aluminum can filling production line. The baseline pressure of the production line is set to 6.2 bar, and the temperature environment is controlled within the range of 4±1 degrees Celsius. The sensor array module is installed as follows: three high-precision carbon dioxide sensors are vertically inserted into the inner cavity of the filling head through a stainless steel probe to ensure direct contact with the liquid; a distributed optical fiber temperature array is spirally wound on the outer wall of the main delivery pipeline at a spacing of five centimeters; two pressure sensors are fixed to the top of the storage tank through a threaded interface; and an electromagnetic flowmeter is integrated at the inlet of the main pipeline using a flange connection. All sensors are connected to the data preprocessing module in the control cabinet through shielded cables. The module synchronously collects the tank pressure, pipeline temperature, flow velocity vector and solubility measured values ​​at a frequency of 1 kHz through the industrial bus.

[0095] There is a sinusoidal fluctuation with a frequency of 2 Hz and an amplitude of ±0.2 bar in the filling pressure line, and a temperature step change of 4°C to 6°C is performed every five minutes. 1.8 million sets of data points are collected for 30 minutes, with a pressure fluctuation range of 5.8 to 6.6 bar and a temperature change gradient of ±0.5 Kelvin per second. The pre-processed data is transmitted to the model processor via the PCIe interface. The processor is equipped with an NVIDIA T4 graphics card and performs physical constraint neural network training under the PyTorch framework. The training process uses physical constraint weight coefficients , temperature hysteresis factor By formula Dynamic calculation, where The temperature value is collected in real time. The multi-scale spatiotemporal attention unit uses the Haar wavelet basis for four-level decomposition, and the time window length is set to 50 ms.

[0096] The implementation process is as follows: Sensor array modules are deployed at the filling line's tanks, pipelines, and filling heads to collect multi-source sensor data in real time. Specifically, a high-precision carbon dioxide sensor is inserted into the filling head cavity via a stainless steel probe, directly contacting the liquid to measure solubility. A distributed fiber optic temperature array is spirally wrapped around the pipeline with a 5 cm pitch to capture transient temperature changes. A pressure sensor is installed at the top interface of the tank to measure tank pressure. An electromagnetic flowmeter is integrated into the main pipeline to obtain three-dimensional flow velocity vectors. These sensors synchronously collect data via an industrial bus at a frequency of 1 kHz, including tank pressure (range: 5.8-6.6 bar), pipeline temperature (Kelvin units), flow velocity vector (meters per second), and measured carbon dioxide solubility (volume percentage). Simultaneously, a sinusoidal pressure fluctuation with a frequency of 2 Hz and an amplitude of ±0.5 bar and a temperature step change every 5 minutes from 4°C to 6°C are simulated, collecting 1.8 million data points over 30 minutes.

[0097] The model processor builds a physical information neural network model of vortex dynamics constraints. The model is trained in the PyTorch framework, and the loss function uses the total loss formula:

[0098] ;

[0099] The physical constraint weight coefficient Set to 1.3, the temperature hysteresis factor By formula Dynamic calculation, is the temperature and diffusion coefficient collected in real time Fixed to square meters per second, Henry's constant The training data accounts for 70%, and the remaining 30% is used for verification. The model optimizes the data fitting error and the physical equation residual.

[0100] The model processor processes the sensor data through a multi-scale spatiotemporal attention unit. This unit uses the Haar wavelet basis to perform a four-level wavelet decomposition with a maximum decomposition scale of , the time window length is set to 50 milliseconds; the attention weight is calculated using the formula:

[0101] ;

[0102] in is the Sigmoid activation function, is the trainable weight matrix, Represents discrete wavelet transform; this process decomposes the original signal into low-frequency and high-frequency components, and fuses multi-scale weights through multiplication operations to enhance feature extraction capabilities. At the same time, the comparison group used Db4 and Coiflet wavelet bases to verify the effect.

[0103] The migration adaptation module calculates the topology difference of the production line and adapts the migration model parameters. Specifically, the graph structure mapper converts the target production line CAD drawing into a graph structure. , where the node set Represents a valve, such as adding a diverter valve node , edge set Indicates a pipe connection, such as The length is shortened by 30%. The WL graph core calculator uses a Xilinx FPGA to perform three Weisfeiler-Lehman iterations to calculate the topological difference:

[0104] ;

[0105] Measured ; Parameter fine-tuner according to the difference value, proportional Scale the weights of the last layer of the neural network to complete the adaptive migration of the model. It will take effect when

[0106] The control execution module outputs the predicted value of carbon dioxide solubility and optimizes the filling pressure control. The solubility prediction value is output to the distributed control system through the 4-20 mA analog interface; the PID parameter dynamic calculator is based on the prediction deviation , dynamic calculation parameters of set value minus predicted value, reference pressure Set to 6.2 bar, the proportionality factor , integral coefficient and differential coefficients According to the formula:

[0107] ;

[0108] When the absolute value of the deviation exceeds 0.1% by volume, the To suppress overshoot; to verify the robustness, a +0.5 bar pressure step disturbance lasting 10 seconds was artificially injected, and the control accuracy and stability were monitored.

[0109] Comparative Example 1. In this comparative example 1, the same implementation conditions as in Example 1 are adopted, except that the traditional LSTM prediction model is implemented. The LSTM prediction model adopts a three-layer stacked structure design, each layer contains 128 hidden units, and the input layer dimension is set to 5, which corresponds to key sensor data such as tank pressure, pipeline temperature, and three spatial components of flow velocity vector. The output layer outputs the solubility prediction value through a fully connected layer with a sigmoid activation function, and a Dropout rate of 0.3 is set to prevent the model from overfitting.

[0110] In the training configuration phase, the model defines a network structure with two LSTM layers and one fully connected layer. The loss function uses the standard mean square error calculation. The optimizer uses the Adam algorithm and sets the learning rate to 0.001. The entire training process is completely data-driven and does not introduce any physical constraints.

[0111] During the data processing stage, the LSTM model used exactly the same 1.8 million data points as those used in the present invention, covering the pressure fluctuation range of 5.8 to 6.6 bars. The time series was processed into a time window of 100 steps, corresponding to a time span of 100 milliseconds. All features were z-score standardized and strictly divided into 70% training set and 30% test set.

[0112] During the training process, the batch size was fixed at 256, the number of training rounds was set to 100, and only the mean squared error loss function was used for optimization. Finally, a mean squared error of 0.0021 was achieved on the validation set, which shows that the model has basic data fitting capabilities but lacks the inherent constraints of physical laws.

[0113] Figure 3 This is a comparison chart of prediction accuracy under pressure fluctuation conditions between Example 1 and Comparative Example 1. Figure 3 The black dotted line shown in the figure represents the theoretical perfect prediction state, and its mathematical expression is y=x, which indicates the ideal situation where the predicted value is completely equal to the measured value. This reference line is drawn according to linear regression theory. When the predicted value is completely consistent with the measured value, all data points should fall on this straight line. The distance between the point and the line intuitively reflects the size of the prediction error. The data points of Example 1 are closely clustered around the line, with an average distance of only 0.008, while the LSTM prediction points of Comparative Example 1 deviate significantly from the line, with an average deviation distance of 0.035.

[0114] exist Figure 3 In the scatter plot, the blue filled dots represent the prediction results of Example 1 of the present invention, the red filled dots represent the prediction results of LSTM in Comparative Example 1, and the black dotted line clearly indicates the ideal fitting line.

[0115] The final comparative analysis shows that the prediction points of the present invention are symmetrically distributed on both sides of the ideal line, with a maximum deviation of only 0.01% and occurring at the pressure peak stage, while the LSTM prediction points show a systematic negative offset, with an average deviation of -0.03%, and a maximum deviation of 0.09% during the temperature transition period. This difference stems from the fact that the present invention incorporates the physical laws of fluid mechanics and captures transient features through a multi-scale attention mechanism, while LSTM relies solely on data-driven and exhibits obvious instability when operating conditions fluctuate.

[0116] Comparative Example 2 was implemented using a conventional physical information neural network (PINN). The same sensor array module was deployed on a 330ml aluminum can filling line, including a high-precision CO2 sensor inserted into the filling head via a stainless steel probe, a fiber optic temperature array spirally wrapped around the pipe with a 5cm pitch, a pressure sensor mounted on the top of the tank, and an electromagnetic flowmeter flanged to the main pipe. All sensors synchronously collected tank pressure, pipe temperature, flow velocity vector, and CO2 solubility measurements at a sampling frequency of 1kHz. Data acquisition lasted 30 minutes, covering a pressure range of 5.8-6.6 bar and a temperature step of 4-6°C.

[0117] The physical information neural network loss function constructed by the model processor is:

[0118] ;

[0119] The key difference is the use of a fixed temperature hysteresis factor , rather than the dynamic calculation formula of Example 1 Physical constraint weight coefficient Set to 1.3, the diffusion coefficient , Henry's constant The training used 70% of the data, a batch size of 256, and was optimized for 100 epochs in the PyTorch framework.

[0120] PyTorch is an open-source Python-based deep learning framework. It utilizes dynamic computational graphs, allowing users to flexibly define and modify neural network structures during model training, just like writing regular Python code. PyTorch is highly research-friendly and easy to debug. It offers a powerful tensor computation library, automatic differentiation for gradient calculation, and a rich library of modules for building various complex neural networks. It provides a complete toolchain covering the entire deep learning development lifecycle, from data loading and preprocessing to model building, training, and deployment, enabling efficient computation on both CPUs and GPUs.

[0121] In the temperature step test, when the pipe temperature jumps from 4℃ to 6℃, the fixed The value was unable to dynamically respond to temperature changes, and the model prediction exhibited significant hysteresis. Within 3 seconds of the temperature change, the deviation between the predicted solubility and the actual value continued to increase, with the maximum hysteresis deviation reaching 0.25%vol, significantly higher than the 0.08%vol in Example 1. This hysteresis effect caused the control system to adjust slowly under temperature transient conditions, with a pressure valve response delay of approximately 1.2 seconds.

[0122] Figure 4 is the temperature step response curve of Example 1 and Comparative Example 2, from Figure 4 It can be seen from the figure that the temperature step signal is The instantaneous transition occurs in seconds; the measured solubility is Seconds to reach the peak value of the rate of change; Example 1 predicts that seconds to start responding, while Example 2 is delayed to Second.

[0123] The green vertical line represents the moment when the temperature changes step by step. The green line is located on the horizontal axis. The green line shows the instantaneous time point when the temperature signal jumps from 4°C to 6°C, which is a key time reference for analyzing the dynamic response of the system. The area to the right of the line is the response stage after the temperature mutation, and the area to the left of the green line is the steady-state condition. Comparative Example 2 deviates significantly from the measured value to the right of the green line, which intuitively shows the response delay caused by the fixed temperature lag factor. Example 1 quickly approaches the measured value after the green line, while Comparative Example 2 continues to deviate after the green line, highlighting the superiority of the dynamic temperature compensation model.

[0124] exist Figure 4 In the temperature step response curve, the yellow semi-transparent area covers The time range of seconds is set, and the solubility deviation interval is framed, which represents the maximum hysteresis deviation range between the predicted value and the measured value of Comparative Example 2; in the yellow area, the vertical distance between the comparative example 2 and the measured value is significantly greater than that of Example 1, indicating that the fixed temperature hysteresis factor causes the predicted curve to "catch up" with the measured value slowly, forming a continuous hysteresis.

[0125] Dynamic temperature compensation ensures that the predicted curves nearly overlap with the measured values, with minimal hysteresis. The text "Maximum hysteresis deviation: 0.25%vol" within the area clearly quantifies the worst-case performance of Comparative Example 2. If the model from Comparative Example 2 were used, the control system would generate erroneous pressure adjustment commands during the period corresponding to the yellow area due to prediction hysteresis. The actual CO2 solubility in the filled bottles could exceed the tolerance range, resulting in product failure.

[0126] The blue line of Example 1 in the yellow area is completely aligned with the measured red line, proving that its dynamic temperature compensation mechanism effectively eliminates the hysteresis effect. Seconds, time constant of comparative example 2 seconds; in Seconds, the deviation of Example 1 is 0.02%vol, and the deviation of Comparative Example 2 is 0.18%vol; the maximum hysteresis deviation occurs at seconds, while Comparative Example 2 reached 0.25% vol.

[0127] The final steady-state value of Example 1 is 4.48%vol; the final steady-state value of Comparative Example 2 is 4.45%vol; this shows that the dynamic temperature hysteresis factor makes the response speed of Example 1 3.3 times faster than that of Comparative Example 2. Example 1 increases the hysteresis compensation rate to 92%, effectively suppressing the overshoot phenomenon during temperature transition; Comparative Example 2 has a fixed temperature hysteresis factor. The hysteresis error band continues to expand within 1 second; the hysteresis effect causes the control system to adjust more than 1 second under temperature transient conditions, verifying the dynamic The necessity of formula; Figure 4 The conclusions that can be drawn include that the temperature hysteresis effect is the main disturbance source of filling line control, the dynamic temperature compensation model can reduce the CO2 solubility fluctuation by 37%, and the filling qualification rate increases by about 2.8% for every 10% increase in the compensation rate.

[0128] Comparative Example 3 uses a traditional PID control scheme. The implementation conditions are based on the same 330 ml aluminum can filling production line hardware environment as Example 1, but a fixed parameter PID controller is used instead of the dynamic calculation mechanism of the present invention. The specific implementation steps are as follows:

[0129] First, the sensor array module was deployed. It included a high-precision CO2 sensor inserted into the filling head via a stainless steel probe, a fiber optic temperature array spirally wrapped around the pipe wall at 5 cm intervals, a pressure sensor mounted on the top of the tank, and an electromagnetic flowmeter flanged to the main pipeline. All sensors synchronously collected tank pressure, pipeline temperature, flow velocity vector, and CO2 solubility measurements at a sampling frequency of 1 kHz. The data was transmitted via an industrial bus to a data preprocessing module for signal conditioning and synchronous acquisition.

[0130] Next, the model processor does not use the physical constraint neural network or multi-scale attention unit of the present invention, but directly uses a traditional PID controller. The parameters of this controller are fixed: the proportional coefficient Set the empirical value to 0.8, the integral coefficient Set to 0.05 s⁻¹, the differential coefficient Set to 0.1 s. The pressure control formula is:

[0131] ;

[0132] The base pressure Fixed at 6.2 bar, deviation The control signal is connected to the filling valve controller through the RS485 interface, and the pressure valve drive circuit outputs a PWM signal to drive the proportional control valve, forming a closed-loop control.

[0133] To verify control performance, a 10-second pressure step with an amplitude of +0.5 bar was artificially injected. During the test, the solubility deviation and pressure response were monitored. The results showed that fixed PID parameters were sluggish in transient conditions, with an overshoot of 23.1%, a settling time of 8.2 seconds, and a steady-state error of ±0.25 bar. This demonstrates that traditional methods have significant limitations in terms of disturbance suppression and rapid convergence.

[0134] Figure 5 is the pressure step response diagram of Example 1 and Comparative Example 3, from Figure 5 As can be seen in the , the amplitude diagram shows the change of system gain with frequency. Comparative Example 3 has a higher gain in the low frequency band, but the gain decays rapidly to below -20 dB after about 1 rad / s, indicating a narrow bandwidth. The gain of Example 1 remains at a high level in a wider frequency band, with a bandwidth of about 2.5 rad / s, indicating that it has a stronger ability to suppress high-frequency disturbances. The phase diagram shows the change of phase lag with frequency. The phase lag of Comparative Example 3 exceeds 150 degrees at the gain crossover frequency, and the phase margin is less than 30 degrees, suggesting poor system stability. The phase lag of Example 1 at the gain crossover frequency is only about 100 degrees, and the phase margin exceeds 60 degrees, indicating that the system is more stable.

[0135] Comparative Example 3 has an obvious resonance peak near 0.5 rad / s, and the gain increases suddenly, corresponding to the overshoot phenomenon; the gain curve of Example 1 is smooth, without obvious resonance, and meets the low overshoot characteristics. The dynamic PID control of Example 1 significantly improves the bandwidth, allowing the system to respond to pressure step disturbances more quickly, which directly leads to the adjustment time being shortened from 8.2 seconds to 1.5 seconds. The high phase margin ensures that Example 1 has no oscillation under transient conditions, and the overshoot is suppressed to within 4.1%, while the low phase margin causes the overshoot of Comparative Example 3 to be as high as 23.1%. The optimization of bandwidth and phase margin verifies the necessity of dynamic PID parameter calculation of the present invention, and through real-time adjustment Based on the solubility deviation, the system can adaptively compensate for the disturbance, and the steady-state error is much lower than that of comparative example 3.

[0136] A comparison between Example 1 and Comparative Example 3 shows that Example 1 achieves higher robustness and better stability in the frequency domain through the dynamic control of the physical constraint neural network and the multi-scale attention unit, breaking through the bottleneck of traditional PID in filling line control.

[0137] For those skilled in the art, the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or scope of the present invention. Therefore, the embodiments of the present invention are exemplary and non-restrictive.

Claims

1. A method for predicting and controlling carbon dioxide solubility in a soda water filling line based on a physical information neural network, characterized in that: The following steps are involved: S1: Real-time collection of multi-source sensor data through sensor array modules deployed in tanks, pipelines and filling heads of the filling line; S2: Constructing a physical information neural network model for vortex dynamics constraints; S3: Processing sensory data via multi-scale spatiotemporal attention units; S4: The migration adaptation module calculates the difference in production line topology and adapts the migration model parameters. S5: The control execution module outputs the predicted value of carbon dioxide solubility and optimizes the filling pressure control; The physical information neural network model of S2 is executed in the model processor, and its loss function is: ； in: Indicates total loss represents the L2 norm Represents the model prediction value Indicates the measured solubility Represents the physical constraint weight coefficient Indicates CO2 concentration Indicates time Represents the flow velocity vector Represents the dot product operation Represents the gradient operator represents the diffusion coefficient represents the Laplace operator represents Henry's constant Indicates filling pressure Represents the exponential function Represents the temperature hysteresis factor Indicates temperature; The S3 is performed by the multi-scale spatiotemporal attention unit of the model processor: ； in: Represents the attention weight Represents the multiplication operator Indicates the wavelet decomposition scale index Indicates the maximum decomposition scale Represents the Sigmoid activation function Indicates the Scaled trainable weight matrix Represents matrix multiplication Indicates the Scaling Discrete Wavelet Transform Represents the input feature tensor.

2. The method according to claim 1, characterized in that Said S1 specifically includes: The sensor array module synchronously collects the measured values ​​of tank pressure, pipeline temperature, flow velocity vector and carbon dioxide solubility at a sampling frequency of 1 kHz.

3. The method according to claim 1, characterized in that The S4 is executed by the migration adaptation module: S4.1: The graph structure mapper abstracts the filling line into a graph structure ,in: Node Set Represents a valve, sensor, or actuator; edge set Indicates the physical connection relationship of the pipeline; S4.2: The WL graph core calculator calculates the topological difference between the target production line and the source production line: ； in: Represents topological difference Represents vector inner product Represents the Weisfeiler-Lehman graph feature map Represents the source production line adjacency matrix Represents the target production line adjacency matrix represents the Euclidean norm; S4.3: Executed by parameter fine-tuner: When Directly load the source model parameters when Proportional Fine-tune the last layer weights.

4. The method according to claim 1, wherein S5 is executed by the PID parameter dynamic calculator of the control execution module: ； in: Indicates the optimized filling pressure Indicates the base pressure Represents the proportional coefficient Indicates the integral coefficient Represents the differential coefficient Denotes the solubility prediction bias Represents time variables Indicates integral operation Represents the differential operation.

5. A carbon dioxide solubility prediction and control system for a soda water filling line based on a physical information neural network for implementing the method described in any one of claims 1 to 4, characterized in that: include: The sensor array module is deployed on the outer wall of the filling tank, at the pipe connection and inside the filling head of the filling line, and includes: The CO2 sensor is installed in the inner cavity of the filling head; the distributed optical fiber temperature array is wrapped around the outer wall of the pipeline; The pressure sensor is installed at the pressure interface of the storage tank; the electromagnetic flowmeter is integrated into the main pipeline; The data preprocessing module is connected to the sensor array module through the industrial bus and includes a signal conditioning circuit and a synchronous acquisition card; The model processor is connected to the data preprocessing module through the PCIe interface. Its physical structure includes: GPU computing card; multi-scale spatiotemporal attention unit; storage unit; The migration adapter module is connected to the model processor via Ethernet. Its hardware components include: graph structure mapper; WL graph core calculator; parameter fine-tuner; The control execution module is connected to the migration adapter module through the industrial IO module, and includes: a solubility prediction interface; a PID parameter dynamic calculator; and a pressure valve drive circuit.

6. The system according to claim 5, characterized in that The sensor array module is deployed as follows: The CO2 sensor is inserted into the inner cavity of the filling head through a stainless steel probe, the optical fiber temperature array is spirally wrapped around the pipe with a spacing of 5 cm, the pressure sensor is installed on the top of the tank, and the electromagnetic flowmeter is flange-connected to the main pipeline.

7. The system according to claim 5, characterized in that The migration adaptation module includes: A graph structure mapper, a dedicated processor that converts production line CAD drawings into adjacency matrices; a WL graph core calculator, which uses FPGA to implement 3-layer iterative operations; and a parameter fine-tuner, which includes a programmable weight scaling circuit.

8. The system according to claim 5, wherein: In the control execution module: The solubility prediction interface is connected to the DCS system; the PID parameter dynamic calculator is connected to the filling valve controller via RS485; the pressure valve drive circuit outputs a PWM signal to control the proportional control valve.

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