An intelligent management system for supercritical foamed protective product production

Abstract

The application relates to the technical field of intelligent management, and discloses an intelligent management system for supercritical foaming protection product production, which comprises the following steps: reading three-dimensional model point cloud data of products to be arranged in batches, quantifying thermodynamic relaxation scheduling time lag through spatial micro-element integration; capturing sensing data of a foaming kettle in real time to solve transient mass leakage production capacity; comparing the two indexes to generate a resource mismatch waste cost coefficient; then, an iteration group is constructed to seek optimization with the goal of minimizing the total cost, and a global production arrangement starting time point is obtained; the system generates a dynamic compensation power allocation instruction according to the above and sends the instruction to a foaming device, and meanwhile, cumulative error energy in an execution period is extracted to compare with a bottom line surface energy, so that a micropore morphology collapse risk index is obtained; finally, core effective work and total dissipation energy are summarized, and a system dynamic resource scheduling utilization benefit index is calculated. The application realizes objective energy quantization scheduling of production management, and reduces resource dissipation and the probability of generating defective products.

Description

Technical Field

[0001] This invention relates to the field of intelligent management technology, and more specifically, to an intelligent management system for the production of supercritical foamed protective products. Background Technology

[0002] Supercritical foamed protective products (such as bulletproof liners and ergonomic cushioning modules) exhibit extremely complex three-dimensional geometric gradient distortions with varying thicknesses to conform to stress distribution patterns. During the depressurization, nucleation, and maturation stages of supercritical foaming, the escape of fluid from the polymer matrix and heat conduction are strictly governed by objective laws of diffusion and thermal conduction. Traditional manufacturing execution systems (MES) and related production scheduling schemes commonly employ static scheduling paradigms with fixed processing times for each batch. However, when dealing with foamed objects of varying thicknesses: if equipment scheduling is set for short periods in thin-walled areas, the thick-walled areas will experience extremely high internal pressure due to incomplete thermodynamic relaxation, leading to micropore rupture and morphological collapse; conversely, if scheduling is set for long periods in thick-walled areas, the thin-walled areas will suffer from excessive relaxation, resulting in micropore shrinkage and aging, and significantly wasting the time required for high-pressure foaming reactors and other heavy assets. Summary of the Invention

[0003] This invention provides an intelligent management system for the production of supercritical foamed protective products, which solves the technical problems mentioned in the background art.

[0004] This invention provides an intelligent management system for the production of supercritical foamed protective products, applied to a production platform comprising multiple foaming devices equipped with foaming kettles, including:

[0005] Read the point cloud data of the three-dimensional model of the products to be scheduled for production, and calculate the thermodynamic relaxation scheduling time delay and the corresponding theoretical ideal uniform mass release rate. The sensor data of the foaming kettle is captured in real time, and the transient mass release capacity is calculated. By comparing the theoretical ideal uniform mass release rate with the transient mass release capacity, a resource mismatch and waste cost coefficient is generated. An iterative group is constructed to optimize the process with the goal of minimizing the total cost coefficient of resource mismatch and waste, and the global production scheduling start time is obtained. Based on the global production scheduling start time, a dynamic compensation power allocation instruction is generated and sent to the foaming equipment; The actual power consumption feedback of the foaming equipment during the execution period is obtained, and the cumulative error energy comparison baseline surface energy between the foaming equipment and the dynamic compensation power allocation command is extracted to obtain the micropore morphology collapse risk index. Calculate the total effective work required for the foaming phase transition, and generate effective benefits by combining the micropore morphology collapse risk index; Based on the total dissipated energy obtained from the feedback of the actual power consumption, and combined with the effective benefits, the system dynamic resource scheduling and utilization efficiency index is calculated.

[0006] The beneficial effects of this invention include: by deeply merging the product's 3D model data with the real-time sensing data of the foaming equipment, the fluid diffusion time delay of spatial micro-elements and the dynamic release capacity of the equipment are accurately quantified; thereby constructing a spatiotemporal mismatch cost matrix and performing global sequence arrangement, and then issuing dynamic compensation power allocation instructions to the execution end, directly avoiding the risk of micropore rupture and morphological collapse caused by supply and demand imbalance at the level of objective energy conservation, realizing the optimal dynamic allocation of the occupation time and energy flow dissipation of multiple foaming equipment, and comprehensively improving the efficiency of workshop-level resource scheduling and product yield. Attached Figure Description

[0007] Figure 1 This is a flowchart of an intelligent management system for the production of supercritical foamed protective products according to the present invention. Detailed Implementation

[0008] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0009] like Figure 1 As shown, an intelligent management system for the production of supercritical foamed protective products is applied to a production platform containing multiple foaming devices equipped with foaming kettles, including: Read the point cloud data of the three-dimensional model of the products to be scheduled for production, and calculate the thermodynamic relaxation scheduling time delay and the corresponding theoretical ideal uniform mass release rate. The sensor data of the foaming kettle is captured in real time, and the transient mass release capacity is calculated. By comparing the theoretical ideal uniform mass release rate with the transient mass release capacity, a resource mismatch and waste cost coefficient is generated. An iterative group is constructed to optimize the process with the goal of minimizing the total cost coefficient of resource mismatch and waste, and the global production scheduling start time is obtained. Based on the global production scheduling start time, a dynamic compensation power allocation instruction is generated and sent to the foaming equipment; The actual power consumption feedback of the foaming equipment during the execution period is obtained, and the cumulative error energy comparison baseline surface energy between the foaming equipment and the dynamic compensation power allocation command is extracted to obtain the micropore morphology collapse risk index. Calculate the total effective work required for the foaming phase transition, and generate effective benefits by combining the micropore morphology collapse risk index; Based on the total dissipated energy obtained from the feedback of the actual power consumption, and combined with the effective benefits, the system dynamic resource scheduling and utilization efficiency index is calculated.

[0010] This implementation is applied to a production platform containing multiple foaming equipment with foaming kettles. The core system program is deployed on an industrial control computer, which communicates with the production platform's fieldbus gateway via Ethernet. The fieldbus gateway establishes bidirectional data interaction with the programmable logic controllers, 3D model reading modules, multi-parameter sensor terminals, and power acquisition modules of each foaming equipment via PROFINET bus. All terminal devices achieve clock synchronization through a network time protocol, with a time synchronization error not exceeding 10% of the sampling period. The sampling period is uniformly set to 1 second, which can be adjusted within the range of 0.1 seconds to 60 seconds according to production accuracy requirements.

[0011] The system operates on a continuous state machine, encompassing the initial ready state, scheduling calculation state, instruction issuance state, operation monitoring state, exception handling state, and scheduling termination state. Upon power-up, the system enters the initial ready state. After completing hardware self-tests and data link verification, it jumps to the scheduling calculation state when the scheduling trigger conditions are met. After scheduling calculations are completed, it jumps to the instruction issuance state. Once the instruction is issued and execution confirmation is received, it jumps to the operation monitoring state. If an abnormal condition is detected during operation monitoring, it jumps to the exception handling state. After exception handling is completed, it jumps to the corresponding state based on the operating condition. Finally, after all batch jobs are completed, it jumps to the scheduling termination state.

[0012] The system scheduling trigger mechanism combines event-driven and timed triggering. Event-driven triggering conditions include the completion of 3D model input for the batch of products to be scheduled, completion of foaming equipment operation and release, abnormal fluctuations in equipment operating status data, and completion of batch operation and release of equipment resources. Immediate scheduling is triggered immediately when any event-driven triggering condition is met. Timed triggering involves rolling optimization scheduling every 60 seconds when no event-driven trigger occurs. During rolling optimization scheduling, batches already scheduled are not included in the scheduling queue. The criterion for starting scheduling is that the pressure inside the foaming kettle reaches 90% of the saturation set pressure. Assigned but not yet started batches can be reassigned based on real-time operating conditions. The trigger threshold for reassignment is when the resource mismatch waste cost coefficient increases by more than 20% compared to the initial allocation value. During reassignment, the original allocation instruction is first invalidated, and then the corresponding batch is re-included in the scheduling queue to complete the new allocation calculation. When the time synchronization error exceeds 10% of the sampling period, scheduling calculation is paused and an exception handling is triggered. Scheduling calculation is restarted after the synchronization error returns to the allowable range.

[0013] All sensor-acquired data undergoes a unified preprocessing workflow, including outlier removal and moving average filtering. Outlier removal uses the 3σ criterion, calculating the mean and standard deviation of 20 consecutive sampling periods. Data exceeding the mean plus or minus three times the standard deviation is considered outliers and replaced with linear interpolation from two consecutive valid sampling periods. Moving average filtering uses a 5-point moving average filter, calculated using the following formula:

[0014] In the formula, The filtered output data is at time t; This represents the original data collected at time t; This is the system's standard sampling period. When there are fewer than 5 sampled data points, the arithmetic mean of the existing valid data is used as the filtered output value.

[0015] The system reads the point cloud data of the 3D model of the products to be produced and performs point cloud data preprocessing. The 3D model point cloud data is spatial point cloud data generated after the 3D CAD model of the products to be produced is meshed. The point cloud data format is STL or PLY. Meshing uses a hexahedral structured mesh, and the mesh resolution can be adjusted from 0.1 mm to 5 mm according to the geometric complexity of the product. The mesh resolution of sharp corners, thin walls, and hole areas is automatically densified to 50% of the global resolution. Point cloud preprocessing includes point cloud denoising, simplification, and non-closed point repair. Point cloud denoising uses a statistical outlier removal algorithm to remove outliers whose average distance from their neighbors exceeds the global average distance plus 2 standard deviations. Point cloud simplification uses a voxel downsampling algorithm to ensure that the point cloud density matches the mesh resolution. Non-closed point clouds use a Poisson surface reconstruction algorithm to repair holes and generate a closed product outer surface model. Non-pressure relief surfaces such as product clamping surfaces and sealing surfaces are not included in the external surface pressure relief calculation domain. They are treated as far-field nodes when initializing mesh nodes using the fast travel method and do not participate in the initialization of converged nodes with a distance value of 0.

[0016] Based on the preprocessed point cloud data, the shortest diffusion distance from the coordinate element to the outer surface is calculated. The coordinate element is a spatial unit within the product matrix corresponding to a single mesh after meshing, and each coordinate element corresponds to a unique spatial coordinate (x, y, z). The shortest diffusion distance is the shortest Euclidean distance from the coordinate element to the closed outer surface of the product, solved using the fast travel method. The solution steps are as follows: Initialize the mesh nodes, mark all mesh nodes on the outer surface of the product as converged nodes, and set the corresponding distance value to 0; mark the first-order neighbor nodes of the converged nodes as narrowband nodes, and calculate the distance value from the narrowband nodes to the outer surface; mark the remaining nodes as far-field nodes, and set the corresponding distance value to infinity. Traverse the narrowband nodes and select the node with the smallest distance value as the new converged node; Update the neighboring nodes of the newly converged node. If a neighboring node is a far-field node, mark it as a narrow-band node and recalculate the distance values ​​of all neighboring nodes. Repeat steps 2 to 3 until all grid nodes are marked as converged nodes, and output the shortest diffusion distance corresponding to each coordinate element.

[0017] The unit of the shortest diffusion distance is meters. After the calculation is completed, the shortest diffusion distance of the boundary element is taken as the minimum value of the distance between adjacent internal elements.

[0018] Calculate the fluid diffusion coefficient under the current temperature and pressure. The fluid diffusion coefficient is the molecular diffusion coefficient of the supercritical fluid under the current polymer matrix, temperature, and pressure conditions, expressed in square meters per second. The fluid diffusion coefficient should preferably be determined using measured values ​​from the polymer material handbook under the corresponding temperature and pressure conditions. If no measured values ​​are available, the free volume model should be used for calculation. The formula is as follows:

[0019] In the formula, Let be the fluid diffusion coefficient at temperature θ and pressure P; This is a pre-factor, with a value of 1e-4 square meters per second; This is the free volume overlap correction factor, with a value ranging from 0.5 to 1, and 0.6 for polymer systems; The critical free volume of the polymer is taken from a polymer material handbook. The free volume of the polymer at temperature θ and pressure P is calculated using the following formula:

[0020] In the formula, The free volume at the glass transition temperature is taken as 0.025 cubic centimeters per gram; This is the free volume thermal expansion coefficient, with values ​​taken from polymer material handbooks; The glass transition temperature of the polymer is expressed in Kelvin. The free volume compressibility coefficient is taken from a polymer materials handbook. Atmospheric pressure is measured in Pascals.

[0021] Obtain the initial saturation concentration and environmental equilibrium concentration of the micro-element. The initial saturation concentration of the micro-element is the fluid equilibrium concentration within the polymer matrix coordinate micro-element under saturated conditions in a foaming reactor, expressed in kilograms per cubic meter. It is calculated using Henry's Law, with the following formula:

[0022] In the formula, Let be the initial saturation concentration of the coordinate element (x, y, z). For temperature ,pressure The Henry's coefficient, expressed in kilograms per cubic meter per pascal, is derived from phase equilibrium experimental data of supercritical fluid and polymer systems. When experimental data is unavailable, a fitting formula for the Henry's coefficient as a function of temperature and pressure is used; this fitting formula is a polynomial empirical equation. ,in These are empirical constants extracted from a basic property library of similar polymers; The pressure is set for the saturated operating condition of the foaming vessel, in Pascals. The environmental equilibrium concentration is the fluid equilibrium concentration of the polymer matrix at room temperature and under normal pressure after depressurization, in kilograms per cubic meter. It is taken as the fluid saturation concentration at 298 Kelvin under normal pressure, and is taken as 0.01 kilograms per cubic meter.

[0023] The concentration ratio is obtained by dividing the initial saturation concentration of the infinitesimal element by the equilibrium concentration in the environment, and then the natural logarithm of the concentration ratio is calculated. The formula for calculating the concentration ratio is:

[0024] In the formula, The concentration ratio of the coordinate element (x, y, z); Let be the initial saturation concentration of the coordinate element (x, y, z); This represents the environmental equilibrium concentration. When the concentration ratio is less than 1, a concentration ratio of 1 is used to ensure that the natural logarithm term is non-negative and to avoid distortion of the calculation results.

[0025] The volume integral is calculated by multiplying the square of the shortest diffusion distance by the quotient of the fluid diffusion coefficient, and then by the natural logarithm of the concentration ratio, over the macroscopic volume of the product. This volume integral calculation is performed based on a gridded infinitesimal element model, and the discrete formula is as follows:

[0026] In the formula, Let represent the macroscopic volume of the i-th production batch to be scheduled, in cubic meters. This represents the shortest diffusion distance corresponding to the nth grid element, in meters. The fluid diffusion coefficient at the current temperature and pressure is expressed in square meters per second. This represents the concentration ratio corresponding to the nth grid element. Let n be the volume of the nth grid element, in cubic meters. This represents the total number of mesh elements after the product has been meshed.

[0027] Dividing the volume integral calculation result by the macroscopic volume of the product yields the thermodynamic relaxation scheduling time delay, calculated using the following formula:

[0028] In the formula, The thermodynamic relaxation scheduling time delay for the i-th batch of products to be scheduled is in seconds. Let represent the macroscopic volume of the i-th production batch to be scheduled, in cubic meters. is the shortest diffusion distance from the coordinate element (x, y, z) to the outer surface, in meters; θ represents the fluid diffusion coefficient at the current temperature θ and pressure P, expressed in square meters per second. Let be the initial saturation concentration of the coordinate element (x, y, z), in kilograms per cubic meter. The concentration is the environmental equilibrium concentration, expressed in kilograms per cubic meter; dV is the spatial volume element, expressed in cubic meters. For heterogeneous composite products, the volume fraction is calculated separately for each material layer, and then weighted and summed according to the volume ratio of each layer to obtain the final volume fraction result.

[0029] Obtain the total mass of fluid to be discharged in the batch. The total mass of fluid to be discharged in the batch is the total mass of supercritical fluid that needs to be discharged from the polymer matrix during the depressurization phase of the batch to be discharged, in kilograms. The calculation formula is:

[0030] In the formula, Let be the total mass of fluid to be discharged for the i-th production batch; The saturated adsorption capacity of the polymer matrix for the i-th batch of products is expressed in kilograms per kilogram. It is obtained by gravimetric analysis or by calculating the ratio of the initial saturated concentration to the polymer density. The environmental equilibrium adsorption capacity of the polymer matrix for the i-th batch of products is expressed in kilograms per kilogram and is calculated by the ratio of the environmental equilibrium concentration to the polymer density. The net mass of the polymer matrix of the i-th batch of products to be produced is expressed in kilograms and is obtained from production feed data.

[0031] Divide the total mass of fluid to be discharged in a batch by the thermodynamic relaxation scheduling time lag to obtain the theoretical ideal uniform mass release rate. The calculation formula is as follows:

[0032] In the formula, Let be the theoretical ideal uniform mass release rate of the i-th batch of products to be scheduled for production, in kilograms per second; The total mass of fluid to be discharged for the i-th production batch is expressed in kilograms. The thermodynamic relaxation scheduling delay for the i-th production batch is expressed in seconds. When the thermodynamic relaxation scheduling delay is less than one sampling period, it is taken as the duration of one sampling period to avoid calculation errors caused by dividing by zero.

[0033] The system captures real-time sensor data from the foaming reactor and performs data preprocessing. The sensor data includes the absolute temperature inside the reactor, the absolute pressure inside the reactor, the opening degree of the pressure relief valve, and the inlet and outlet temperatures of the valve. This data is collected by sensors installed on the corresponding parts of the foaming reactor. The temperature sensors are platinum resistance temperature sensors, installed at three locations inside the foaming reactor (top, middle, and bottom), with a sampling accuracy of no less than 0.1 Kelvin. The pressure sensors are piezoresistive pressure sensors, installed on the side wall of the foaming reactor body, with a sampling accuracy of no less than 100 Pascals. The valve opening sensor is installed within the servo drive of the pressure relief valve, with a sampling accuracy of no less than 0.1% of full opening. The preprocessed temperature data is the arithmetic mean of the values ​​collected by the three temperature sensors, and the preprocessed pressure data is the filtered average of three consecutive sampling periods from the pressure sensor.

[0034] The thermodynamic state factor is obtained by dividing the molar mass of the gas by the product of the universal gas constant and the absolute temperature, and then taking the square root of the result. The molar mass of the gas is the molar mass of the fluid used in supercritical foaming, in kilograms per mole; the molar mass of supercritical carbon dioxide is taken as 0.04401 kilograms per mole. The universal gas constant is a fixed physical constant, taken as 8.314 joules per mole per Kelvin. The absolute temperature is the real-time thermodynamic temperature inside the foaming vessel after pretreatment, in Kelvin. The formula for calculating the thermodynamic state factor is:

[0035] In the formula, is the thermodynamic state factor at time t, in the square root of kilograms per joule; R is the molar mass of the gas, expressed in kilograms per mole; R is the universal gas constant, expressed in joules per mole per Kelvin. Let t be the absolute temperature of the j-th foaming vessel at time t, in Kelvin.

[0036] The transient pressure difference is obtained by subtracting the current internal pressure of the foaming reactor from the ambient atmospheric pressure. The current internal pressure is the real-time absolute pressure inside the pre-treated foaming reactor, measured in Pascals. The ambient atmospheric pressure is the real-time absolute pressure of the production workshop, measured in Pascals, and is collected by an ambient pressure sensor installed in the workshop. The formula for calculating the transient pressure difference is:

[0037] In the formula, Let be the transient pressure difference of the j-th foaming vessel at time t, in Pascals; Let be the current internal pressure of the j-th foaming vessel at time t, in Pascals; The pressure is ambient atmospheric pressure, expressed in Pascals. When the transient pressure difference is less than 0, it is taken as 0 to ensure the calculation result is non-negative.

[0038] The transient mass relief capacity is obtained by continuously multiplying the valve flow constant, effective opening area, transient pressure difference, and thermodynamic state factor. The valve flow constant is a dimensionless parameter, taken from the factory calibration parameters of the pressure relief valve; if no calibration parameters are available, it is taken as 0.65. The effective opening area is the effective flow area of ​​the pressure relief valve at the current opening degree, in square meters, and is taken from the calibration curve of valve opening degree versus effective area, which uses the equal percentage flow characteristic equation. Calculation, where For the fully open area, The valve has an inherent adjustable ratio. The effective opening area when the valve is fully open is taken as the flow area corresponding to the valve's nominal diameter, and when the valve is fully closed, the effective opening area is taken as 0. During the pressure relief process, when the ratio of the pressure inside the vessel to the ambient atmospheric pressure exceeds the critical pressure ratio of 1.89, it is determined to be a choking flow condition, and a choking flow correction factor of 1.0 is introduced, requiring no additional correction; when the pressure ratio is less than the critical pressure ratio, a subsonic flow correction factor is introduced, and the formula for calculating the correction factor is:

[0039] In the formula, is the subsonic flow correction factor, dimensionless; k is the gas adiabatic index, with a value of 1.3 for carbon dioxide. The formula for calculating the transient mass release capacity is:

[0040] In the formula, The transient mass discharge capacity of the j-th foaming device at time t is expressed in kilograms per second. The valve flow constant is dimensionless. The effective opening area of ​​the pressure relief valve of the j-th foaming equipment is expressed in square meters. Let be the transient pressure difference of the j-th foaming vessel at time t, in Pascals; is the thermodynamic state factor at time t; This is a correction factor for subsonic flow, dimensionless, and takes a value of 1 under choked flow conditions.

[0041] The difference between the theoretical ideal uniform mass release rate and the transient mass release capacity is squared. This squared difference is then integrated over a time interval from zero to the thermodynamic relaxation scheduling delay to obtain the dynamic variance integral. The time integration is calculated using the trapezoidal integration method, with the integration step size being the system's general sampling period. When data packets are lost in a single sampling period, linear interpolation of the two preceding and following valid sampling periods is used to complete the data. When there are fewer than three consecutive sampling periods of data loss, the data from the most recent valid sampling period is used. When there are more than three consecutive sampling periods of data loss, the square of the difference in this integration interval is taken as the square of the theoretical ideal uniform mass release rate. The formula for calculating the dynamic variance integral is:

[0042] In the formula, The dynamic variance integral of the i-th production batch allocated to the j-th foaming equipment is expressed in square kilograms per square second multiplied by seconds. Let be the theoretical ideal uniform mass release rate of the i-th batch of products to be scheduled for production, in kilograms per second; The transient mass discharge capacity of the j-th foaming device at time t is expressed in kilograms per second. dt is the thermodynamic relaxation scheduling time delay for the i-th production batch, in seconds; dt is the integral time element, in seconds.

[0043] The normalized production scheduling baseline term is obtained by multiplying the square of the theoretical ideal uniform mass release rate by the thermodynamic relaxation scheduling time lag. This normalized baseline term eliminates the influence of different batch production capacity sizes on the cost coefficient, achieving horizontal comparability of cost coefficients between different batches. The formula for calculating the normalized production scheduling baseline term is:

[0044] In the formula, The normalized production scheduling baseline item is used to allocate the i-th production batch to the j-th foaming equipment, and the unit is consistent with the dynamic variance integral. Let be the theoretical ideal uniform mass release rate of the i-th batch of products to be scheduled for production, in kilograms per second; The thermodynamic relaxation scheduling time lag for the i-th production batch is expressed in seconds. When the theoretical ideal uniform mass release rate is 0, the normalized scheduling baseline term is set to 1 to avoid calculation errors caused by dividing by zero.

[0045] Dividing the dynamic variance integral by the normalized production scheduling baseline term yields the resource misallocation and waste cost coefficient, calculated using the following formula:

[0046] In the formula, The resource misallocation and waste cost coefficient for the i-th production batch to be scheduled and assigned to the j-th foaming equipment is dimensionless. This is the integral of the dynamic variance; This serves as the normalized production scheduling baseline. When the batch operation duration does not match the equipment availability window, a timing penalty is added on top of the resource mismatch waste cost coefficient. The timing penalty is the ratio of the mismatch duration to the thermodynamic relaxation scheduling delay, ensuring that the allocation scheme for timing conflicts corresponds to a higher cost coefficient.

[0047] Initialize an iterative population consisting of the current planned production start time and generate a first and second true random number. The number of individuals in the iterative population is set to 20 to 100. When the number of batches to be scheduled does not exceed 10, the number of individuals is 20. For every 5 additional batches, the number of individuals increases by 10, with a maximum of 100. Each iterative individual corresponds to a set of planned production start times for the batches to be scheduled, in seconds. The initial planned production start times are generated according to a first-come, first-served rule, that is, the earliest available time points are sequentially allocated to available devices according to the batch entry order, while a random offset of 0 to 3600 seconds is added to generate the initial population. The initial scheduling time adjustment step size ranges from -600 seconds to 600 seconds, and the initial value is randomly generated in a uniform distribution. The first and second true random numbers are generated by a hardware random number generator, and are uniformly distributed random numbers ranging from 0 to 1, and are regenerated in each iteration. When the number of batches to be scheduled exceeds the total number of foaming equipment, the first M batches are selected in the order of batch entry to participate in this iteration of optimization, where M is the total number of foaming equipment, and the remaining batches are included in the next scheduling cycle.

[0048] The system inertial damping is generated by dividing the total cost variance of the current iterative group by the sum of the total cost variance and the square of the mean. The total cost is the sum of the resource mismatch and waste cost coefficients of all batches to be allocated corresponding to the iterative individual. The total cost variance is the variance of the total cost of all individuals within the iterative group, and the total cost mean is the arithmetic mean of the total costs of all individuals within the iterative group. The system inertial damping is a dimensionless parameter, ranging from 0 to 1, used to balance the global exploration capability and local convergence capability of the iterative process. The formula for calculating the system inertial damping is:

[0049] In the formula, The system inertial damping at the k-th iteration; Let V be the variance of the total cost of the iterative population at the k-th iteration; This represents the mean of the total cost of the iterative population at the k-th iteration. When the variance of the total cost is 0, the system inertial damping is set to 0 to ensure iteration convergence.

[0050] Obtain the individual's historical best cost, current individual cost, and the global best cost for the entire group in each iteration. Also obtain the individual's historical best time point and the global best time point. The individual's historical best cost is the minimum total cost achieved by the corresponding individual in all iterations; the current individual cost is the total cost of the individual in the current iteration step; the global best cost is the minimum total cost achieved by the entire group in all iterations. The individual's historical best time point is the scheduling start time when the corresponding individual achieves its historical best cost; the global best time point is the scheduling start time when the entire group achieves its global best cost. In the first iteration, the individual's historical best cost is taken from the initial individual cost, and the individual's historical best time point is taken from the initial planned scheduling start time; the global best cost is taken from the minimum individual cost in the initial group, and the global best time point is taken from the initial planned scheduling start time for the corresponding individual.

[0051] The updated scheduling time adjustment step size is obtained by multiplying the current scheduling time adjustment step size by the system inertial damping, adding the product of the first true random number, the ratio of the individual's historical best cost to the current individual cost, and the difference between the individual's historical best time node and the current planned production start time, and then adding the product of the second true random number, the ratio of the global best cost to the current individual cost, and the difference between the global best time node and the current planned production start time. The calculation formula is as follows:

[0052] In the formula, This is the scheduling time adjustment step size for the i-th batch corresponding to the p-th iteration individual in the (k+1)-th iteration, in seconds; The system inertial damping at the k-th iteration; The scheduling time adjustment step size for the i-th batch corresponding to the p-th iteration individual in the k-th iteration, in seconds; The historical optimal cost for the p-th iteration individual; This represents the current individual cost of the p-th iteration at the k-th iteration. This is the first truly random number; This represents the historical best time point for the individual in the i-th batch corresponding to the p-th iteration individual, in seconds; This represents the start time of the current planned production schedule for the i-th batch corresponding to the p-th iteration individual in the k-th iteration, in seconds. The globally optimal cost for the iterative population; This is the second truly random number; This represents the globally optimal time point for the i-th batch of the iterative population, expressed in seconds. If the current individual cost is less than 1e-9, the current individual cost is set to 1e-9 to avoid the error of dividing by zero.

[0053] The current planned production start time is added to the updated scheduling time adjustment step size for iterative updates. The iterative update formula is:

[0054] In the formula, This represents the updated planned production start time for the i-th batch corresponding to the p-th iteration individual in the (k+1)-th iteration, in seconds. This represents the start time of the current planned production schedule for the i-th batch corresponding to the p-th iteration individual in the k-th iteration, in seconds. This is the updated scheduling time adjustment step size in seconds for the p-th iterative individual corresponding to the i-th batch in the (k+1)-th iteration. During the iterative update process, if the planned production start time is earlier than the current real time, it is corrected to the current real time. When multiple batches allocated to a single foaming machine have overlapping timelines, a penalty function method is used to penalize the total cost. The penalty term is the dimensionless ratio obtained by dividing the timeline overlap duration by the thermodynamic relaxation scheduling lag of the corresponding batch, multiplied by 10, to ensure that individuals with timeline conflicts correspond to a higher total cost. After the iterative individual goes out of bounds and is corrected, the cost of the corresponding current individual is updated synchronously.

[0055] Iterative convergence determination and output of the global scheduling start time. The iterative convergence condition is that the number of iterations reaches 200, or the change in the global optimal cost of the group is less than 1e-6 over 50 consecutive iterations. The iteration terminates when either condition is met. If the number of iterations reaches the upper limit but convergence is not achieved, the solution corresponding to the global optimal cost during the iteration process is taken as the final solution. After the iteration terminates, the scheduling start time corresponding to the global optimal cost obtained during the iteration process is output as the global scheduling start time. When multiple iterations have the same global optimal cost, the time node corresponding to the individual with the shortest total operation time is selected as the global scheduling start time. Before output, the optimal solution is checked for hard constraints. Hard constraints include that a single foaming equipment can only be assigned one batch to be scheduled at the same time, there is no conflict in the batch operation sequence, and the scheduling start time is not earlier than the current real time. If the constraints are not met, the process reverts to the previous optimal solution that meets the constraints. If there is no solution that meets the constraints, the iterative group is re-initialized to complete the optimization calculation.

[0056] The absolute value of the difference between the transient mass release capacity and the theoretical ideal uniform mass release rate is calculated and multiplied by the enthalpy difference of the isoenthalpic expansion of the supercritical fluid to obtain the basic phase change compensation power. The enthalpy difference of the isoenthalpic expansion of the supercritical fluid is the difference in enthalpy as the supercritical fluid expands isoenthalpically from the working state inside the foaming vessel to the ambient atmospheric pressure state, expressed in joules per kilogram. This value is obtained by querying the enthalpy value under the corresponding working condition from the NIST Chemistry WebBook standard thermodynamic database. The calculation formula is as follows:

[0057] In the formula, The enthalpy difference represents the isenthalpic expansion ratio of a supercritical fluid. The specific enthalpy of the fluid under the working conditions inside the foaming kettle; Here, is the specific enthalpy of the fluid at ambient atmospheric pressure. The formula for calculating the basic phase transition compensation power is:

[0058] In the formula, The basic phase transition compensation power at time t is expressed in watts. The transient mass discharge capacity of the j-th foaming device at time t is expressed in kilograms per second. Let be the theoretical ideal uniform mass release rate of the i-th batch of products to be scheduled for production, in kilograms per second; The enthalpy difference is the isoenthalpic expansion ratio of a supercritical fluid, expressed in joules per kilogram.

[0059] Obtain the real-time temperature change rate of the foaming equipment and take its absolute value. The real-time temperature change rate is the first derivative of the absolute temperature inside the foaming vessel with respect to time, in Kelvin per second. It is calculated using the first-order backward difference method, based on filtered temperature data from three consecutive sampling periods. The calculation formula is as follows:

[0060] In the formula, Let be the real-time temperature change rate of the j-th foaming device at time t; Let be the absolute temperature of the j-th foaming kettle at time t, in Kelvin; The system's standard sampling period is measured in seconds. When there are fewer than three sampling points, the temperature change rate is calculated using the first-order difference between two adjacent sampling periods.

[0061] The matrix temperature control compensation power is obtained by multiplying the absolute value of the real-time temperature change rate by the pre-acquired net mass of the polymer matrix and the polymer specific heat capacity. The polymer specific heat capacity is the isobaric specific heat capacity of the polymer material within the current temperature range, measured in joules per kilogram per Kelvin. This value is derived from the material's manufacturer-specified parameters, and the dynamic value at the corresponding real-time temperature is used when the temperature changes. The formula for calculating the matrix temperature control compensation power is as follows:

[0062] In the formula, The substrate temperature control compensation power at time t is expressed in watts. The net mass of the polymer matrix of the i-th batch of products to be scheduled for production is expressed in kilograms. The specific heat capacity of the polymer is expressed in joules per kilogram per Kelvin. Let be the absolute value of the real-time temperature change rate of the j-th foaming device at time t, expressed in Kelvin per second.

[0063] The basic phase change compensation power is added to the substrate temperature control compensation power to generate a dynamic compensation power allocation command. The calculation formula is as follows:

[0064] In the formula, The dynamic compensation power allocation instruction for the j-th foaming device at time t, in watts; The basic phase transition compensation power at time t is expressed in watts. The power for substrate temperature control compensation at time t is expressed in watts. Dynamic compensation power allocation commands are set with limiting rules, ensuring the maximum allowable power change rate does not exceed 10% per second of the rated power. When the command value exceeds the equipment's rated power range, the upper and lower limits of the equipment's rated power are used as the command output value. The generated dynamic compensation power allocation command is sent to the corresponding foaming equipment's programmable logic controller (PLC) via the fieldbus gateway. The command issuance cycle is consistent with the system's general sampling cycle, and the command is strictly synchronized with the global production scheduling start time. The command's time resolution is consistent with the sampling cycle. When the production scheduling time is adjusted, the command smoothly transitions to the new scheduling time, with a transition time of no less than 10 sampling cycles. If no equipment execution confirmation is received within 10 seconds of the command being issued, the command is reissued. If no confirmation is received after three consecutive issuances, exception handling is triggered.

[0065] Calculate the absolute value of the difference between the dynamic compensation power allocation command and the actual power consumption feedback. The actual power consumption feedback is the real-time input power of the foaming equipment, measured in watts, acquired by a power sensor in the power supply circuit of the foaming equipment. The acquired data undergoes a unified preprocessing procedure. The formula for calculating the difference is:

[0066] In the formula, The absolute value of the power difference at time t, in watts; The dynamic compensation power allocation instruction for the j-th foaming device at time t, in watts; This is the actual power consumption feedback of the j-th foaming device at time t, in watts.

[0067] The cumulative error energy is obtained by integrating over a time interval from the global production scheduling start time to the time when the thermodynamic relaxation scheduling lag is added. The time integration uses the trapezoidal integration method, with the integration step size being the system's general sampling period. When a batch operation terminates early, the endpoint of the integration interval is the operation termination time; when a batch operation completes late, the endpoint of the integration interval is extended to the operation completion time. The formula for calculating the cumulative error energy is:

[0068] In the formula, Let be the cumulative error energy of the i-th batch of products, in joules; This is the global production scheduling start time for the i-th batch of products, in seconds; The thermodynamic relaxation scheduling delay for the i-th batch of products is in seconds. dt represents the absolute value of the power difference at time t, in watts; dt is the integral time element, in seconds.

[0069] The target specific surface area of ​​the foamed micropores and the surface free energy of the polymer melt are obtained, and then multiplied by the pre-obtained net mass of the polymer matrix to obtain the baseline surface energy. The target specific surface area of ​​the foamed micropores is the specific surface area of ​​the foamed micropores required by the product design, expressed in square meters per kilogram, and derived from the product design parameters. The surface free energy of the polymer melt is the surface free energy of the polymer melt at the foaming temperature, expressed in joules per square meter, and is obtained from measured data in the polymer material handbook; when no measured value is available, the pendant drop method is used. The formula for calculating the baseline surface energy is:

[0070] In the formula, Let be the baseline surface energy of the i-th batch of products, in joules; The net mass of the polymer matrix for the i-th batch of products is expressed in kilograms. The target specific surface area of ​​the foamed micropores for the i-th batch of products is expressed in square meters per kilogram. This represents the surface free energy of the polymer melt, expressed in joules per square meter. When the baseline surface energy is less than 1e-9 joules, we take the baseline surface energy as 1e-9 joules to avoid calculation errors caused by dividing by zero.

[0071] Divide the cumulative error energy by the baseline surface energy, calculate the exponent with the natural constant as the base, and then subtract one to obtain the micropore morphology collapse risk index. The calculation formula is as follows:

[0072] In the formula, , is the micropore morphology collapse risk index for the i-th batch of products, dimensionless; Let be the cumulative error energy of the i-th batch of products, in joules; Let be the baseline surface energy of the i-th batch of products, in joules; exp is an exponential function with the natural constant e as its base. After the risk index is calculated, if the value exceeds the preset threshold 1, a closed-loop intervention is immediately triggered to adjust the dynamic compensation power allocation command and correct the power deviation.

[0073] The natural yield survival attenuation coefficient is obtained by exponentially multiplying the negative micropore morphology collapse risk index as the exponent of the natural constant. This coefficient is a dimensionless parameter, ranging from 0 to 1, used to quantify the attenuation effect of micropore collapse risk on effective product yield. A higher risk index corresponds to a smaller attenuation coefficient and a lower product yield. The formula for calculating the natural yield survival attenuation coefficient is as follows:

[0074] In the formula, Let be the natural yield survival decay coefficient for the i-th batch of products, which is dimensionless. Let be the micropore morphology collapse risk index for the i-th batch of products, which is dimensionless.

[0075] Multiplying the total mass of fluid to be discharged in a batch by the enthalpy difference of the isenthalpic expansion ratio of the supercritical fluid yields the total effective work done at the core. Multiplying this by the natural yield survival attenuation coefficient and summing the results over all batches yields the effective benefit. The calculation formula is as follows:

[0076] In the formula, The total effective benefit of all batches is expressed in joules; N is the total number of batches to be scheduled for production. The total mass of fluid to be discharged for the i-th batch of products, in kilograms; The enthalpy difference is the isenthalpic expansion ratio of a supercritical fluid, expressed in joules per kilogram. Let be the natural yield survival decay coefficient for the i-th batch of products, which is dimensionless.

[0077] The actual power consumption of each foaming device is fed back and integrated within the corresponding operating range, and then added to the baseline static energy loss to obtain the total dissipated energy. The operating range is from the start time of production scheduling for the corresponding foaming device to the end time of batch operation. The criteria for determining the end time of batch operation are that the pressure inside the foaming vessel drops to within 1.1 times the ambient atmospheric pressure and the temperature inside the vessel drops below 50 degrees Celsius. The baseline static energy loss is the sum of the fixed energy consumption of all auxiliary equipment within the production platform during the production cycle, in joules, including the fixed energy consumption of the circulating water system, control system, and lighting system. It is calculated based on the operating time and rated power within the production cycle, and for multi-batch production, it is allocated according to the proportion of each batch's operating time to the total production time. The formula for calculating the total dissipated energy is:

[0078] In the formula, The total energy dissipated by the production platform is expressed in joules; K represents the total number of foaming equipment. This is the start time for production scheduling of the batch corresponding to the j-th foaming equipment, in seconds; This refers to the completion time of the batch of work corresponding to the j-th foaming equipment, in seconds; dt represents the actual power consumption feedback of the j-th foaming device at time t, in watts; dt is the integral time element, in seconds. The reference static energy loss is expressed in joules. When the total energy dissipation is less than 1e-9 joules, the total energy dissipation is taken as 1e-9 joules to avoid calculation errors caused by dividing by zero.

[0079] Dividing the effective benefits by the total dissipated energy yields the system's dynamic resource scheduling and utilization efficiency index, calculated using the following formula:

[0080] In the formula, The efficiency index is a dimensionless index for dynamic resource scheduling and utilization in the system. A higher value indicates higher system resource utilization efficiency and better overall production benefits. After the efficiency index is calculated, the index value for the current scheduling cycle is compared with historical data. When the index value decreases by more than 10% compared with the historical average, scheduling strategy optimization is triggered, and the weight parameters of the iterative optimization and the initial population generation rules are adjusted.

[0081] The embodiments of this example have been described above. However, this example is not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of this example, and all of them are within the protection scope of this example.

Claims

1. An intelligent management system for the production of supercritical foamed protective products, applied to a production platform comprising multiple foaming devices equipped with foaming kettles, characterized in that, Configured for execution: Read the point cloud data of the three-dimensional model of the products to be scheduled for production, and calculate the thermodynamic relaxation scheduling time delay and the corresponding theoretical ideal uniform mass release rate. The sensor data of the foaming kettle is captured in real time, and the transient mass release capacity is calculated. By comparing the theoretical ideal uniform mass release rate with the transient mass release capacity, a resource mismatch and waste cost coefficient is generated. An iterative group is constructed to optimize the process with the goal of minimizing the total cost coefficient of resource mismatch and waste, and the global production scheduling start time is obtained. Based on the global production scheduling start time, a dynamic compensation power allocation instruction is generated and sent to the foaming equipment; The actual power consumption feedback of the foaming equipment during the execution period is obtained, and the cumulative error energy comparison baseline surface energy between the foaming equipment and the dynamic compensation power allocation command is extracted to obtain the micropore morphology collapse risk index. Calculate the total effective work required for the foaming phase transition, and generate effective benefits by combining the micropore morphology collapse risk index; Based on the total dissipated energy obtained from the feedback of the actual power consumption, and combined with the effective benefits, the system dynamic resource scheduling and utilization efficiency index is calculated. This includes reading the point cloud data of the 3D model of the products to be produced in the batch, calculating the thermodynamic relaxation scheduling time lag and the corresponding theoretical ideal uniform mass release rate, including: Calculate the shortest diffusion distance from the coordinate element to the outer surface and square it, then divide it by the fluid diffusion coefficient at the current temperature and pressure. Obtain the initial saturation concentration of the micro-element and the environmental equilibrium concentration, divide the initial saturation concentration of the micro-element by the environmental equilibrium concentration to obtain the concentration ratio, and calculate the natural logarithm of the concentration ratio. Multiply the square of the shortest diffusion distance by the quotient of the fluid diffusion coefficient by the natural logarithm of the concentration ratio, and perform a volume fraction calculation within the macroscopic volume range of the product. Divide the volume fraction calculation result by the macroscopic volume of the product to obtain the thermodynamic relaxation scheduling time delay; Obtain the total mass of fluid to be discharged in a batch, divide the total mass of fluid to be discharged in a batch by the thermodynamic relaxation scheduling time delay, and obtain the theoretical ideal uniform mass release rate; The comparison between the theoretical ideal uniform mass release rate and the transient mass release capacity generates a resource misallocation and waste cost coefficient, including: The difference between the theoretical ideal uniform mass release rate and the transient mass release capacity is calculated and squared. The result is then integrated over a time interval from zero to the thermodynamic relaxation scheduling time lag to obtain the dynamic variance integral. The normalized production scheduling baseline term is obtained by multiplying the square of the theoretical ideal uniform mass release rate by the thermodynamic relaxation scheduling time lag. Dividing the dynamic variance integral by the normalized production scheduling benchmark term yields the resource mismatch and waste cost coefficient.

2. The intelligent management system for the production of supercritical foamed protective products according to claim 1, characterized in that, Real-time capture of sensor data from the foaming vessel to calculate transient mass release capacity includes: The thermodynamic state factor is obtained by dividing the molar mass of the gas by the product of the universal gas constant and the absolute temperature, and then taking the square root of the result. The current internal pressure of the foaming vessel and the ambient atmospheric pressure are obtained, and the transient pressure difference is calculated by subtracting them. The transient mass release capacity is obtained by continuously multiplying the valve flow constant, effective opening area, transient pressure difference, and thermodynamic state factor.

3. The intelligent management system for the production of supercritical foamed protective products according to claim 1, characterized in that, An iterative group is constructed with the objective of minimizing the total cost coefficient of resource mismatch and waste to find the global production scheduling start time, including: Initialize an iterative population consisting of the current planned production start time, and generate a first true random number and a second true random number; Divide the total cost variance of the current iteration group by the sum of the total cost variance and the square of the mean to generate the system inertial damping; Obtain the individual's historical best cost, current individual cost, and global best cost for the group; obtain the individual's historical best time point and global best time point; Multiply the current scheduling time adjustment step by the system inertial damping, add the product of the first true random number, the ratio of the individual's historical best cost to the current individual cost, and the difference between the individual's historical best time node and the current planned production start time, and then add the product of the second true random number, the ratio of the global best cost to the current individual cost, and the difference between the global best time node and the current planned production start time to obtain the updated scheduling time adjustment step; The current planned production start time is added to the updated scheduling time adjustment step size and iteratively updated to output the global production start time.

4. The intelligent management system for the production of supercritical foamed protective products according to claim 1, characterized in that, Based on the global production start time, a dynamic compensation power allocation instruction is generated and sent to the foaming equipment, including: Calculate the absolute value of the difference between the transient mass release capacity and the theoretical ideal uniform mass release rate, and multiply it by the enthalpy difference of the isoenthalpic expansion ratio of the supercritical fluid to obtain the basic phase change compensation power; The real-time temperature change rate of the foaming equipment is obtained and its absolute value is taken. This value is then multiplied by the pre-obtained net mass of the polymer matrix and the specific heat capacity of the polymer to obtain the matrix temperature control compensation power. The basic phase change compensation power is added to the substrate temperature control compensation power to generate the dynamic compensation power allocation command.

5. The intelligent management system for the production of supercritical foamed protective products according to claim 1, characterized in that, By extracting the cumulative error energy comparison baseline surface energy between the dynamic compensation power allocation command and the baseline surface energy, a micropore morphology collapse risk index is derived, including: Calculate the absolute value of the difference between the dynamic compensation power allocation command and the actual power consumption feedback, and perform integration within the time interval from the global production scheduling start time to the time when the thermodynamic relaxation scheduling time lag is added, to obtain the cumulative error energy. The target specific surface area of ​​the foamed micropores and the surface free energy of the polymer melt are obtained, and then multiplied by the pre-obtained net mass of the polymer matrix to obtain the baseline surface energy. Divide the cumulative error energy by the baseline surface energy, calculate the exponent with the natural constant as the base, and then subtract one to obtain the micropore morphology collapse risk index.

6. The intelligent management system for the production of supercritical foamed protective products according to claim 1, characterized in that, Based on the total dissipated energy obtained from the feedback of the actual power consumption, and combined with the effective benefits, the system dynamic resource scheduling and utilization efficiency index is calculated, including: The negative micropore morphology collapse risk index is used as the exponent of the natural constant and then exponentially calculated to obtain the natural yield survival decay coefficient. The total mass of fluid to be discharged in a batch is multiplied by the enthalpy difference of the isenthalpic expansion ratio of the supercritical fluid to obtain the total effective work done by the core. This is then multiplied by the natural yield survival attenuation coefficient and summed over all batches to obtain the effective benefit. The actual power consumption feedback of each foaming device is integrated and summarized within the corresponding operating range, and the baseline static energy loss is added to obtain the total dissipated energy. Dividing the effective benefits by the total dissipated energy yields the system's dynamic resource scheduling and utilization efficiency index.

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