Linalool crystallization control method and system based on multi-stage gradient cooling, and medium

Abstract

This application provides a method, system, and medium for controlling menthol crystallization based on multi-stage gradient cooling, relating to the field of menthol crystallization technology. The method includes: rapidly analyzing the menthol solution raw material of the current batch before the start of crystallization; inputting the raw material characteristic dataset into a menthol crystallization digital twin model to simulate potential quality defect risks and construct a defect risk phase map; optimizing the path to avoid high-risk areas; and during the crystallization process, using a multi-stage gradient cooling baseline path as guidance, monitoring the process status in real time, and performing real-time path replanning when the process status deviates from expectations, controlling the crystallization process to execute along a dynamically updated path. This application solves the technical problem of unstable crystal quality caused by the rigid contradiction between natural fluctuations between raw material batches and a fixed multi-stage cooling process in existing technologies, improving crystal quality stability through multi-stage gradient cooling and internal defect monitoring.

Description

Technical Field

[0001] This application relates to the field of menthol crystallization technology, and in particular to a method, system and medium for controlling menthol crystallization based on multi-level gradient cooling. Background Technology

[0002] In existing industrial menthol crystallization production, a multi-stage cooling crystallization process based on a fixed formula is commonly used. This involves pre-setting a cooling curve with multiple temperature plateaus and temperature change rates based on experience, and applying the same cooling program to different batches of raw materials. However, since menthol raw materials are derived from natural extraction, there are objective fluctuations in key characteristics such as impurity composition, initial supersaturation, and nucleation energy between different batches. The fixed cooling program cannot adapt to these fluctuations, creating an irreconcilable contradiction between the flexibility of the raw materials and the rigidity of the process. Existing online monitoring and control technologies, such as simple temperature-concentration feedback, are essentially a lag compensation mode. They can only compensate for deviations in macroscopic parameters, lacking the ability to predict the formation mechanism of internal crystal defects, and cannot proactively intervene before defects occur. This causes the production process to constantly oscillate between trial and error adjustments and post-production remediation, resulting in poor crystal quality stability between different batches and difficulty in guaranteeing product yield.

[0003] In summary, the existing technology suffers from a rigid contradiction between the natural fluctuations in raw material batches and the fixed multi-stage cooling process, which makes the crystallization process unable to adapt and adjust itself. This can easily lead to high-risk areas that induce microscopic defects, further affecting the stability of crystal quality and product yield. Summary of the Invention

[0004] The purpose of this application is to provide a method, system, and medium for controlling menthol crystallization based on multi-stage gradient cooling, in order to solve the technical problem in the prior art where the rigid contradiction between the natural fluctuations between batches of raw materials and the fixed multi-stage cooling process leads to the crystallization process being unable to adaptively adjust, easily entering a high-risk area and inducing micro-defects, which further affects the stability of crystal quality and product yield.

[0005] In view of the above problems, this application provides a method, system and medium for controlling menthol crystallization based on multi-level gradient cooling.

[0006] Firstly, this application provides a menthol crystallization control method based on multi-level gradient cooling. This method is implemented through a menthol crystallization control system based on multi-level gradient cooling. The method includes: before the start of a crystallization batch, rapidly analyzing the menthol solution raw material of the current batch to obtain a raw material characteristic dataset; inputting the raw material characteristic dataset into a menthol crystallization digital twin model to simulate and calculate the potential quality defect risks under different combinations of process parameters; and constructing a digital twin model for the current batch based on the potential quality defect risks. A dedicated defect risk phase map is used, with process parameters as coordinates and defect risk values ​​as levels. Path optimization is performed to avoid high-risk areas in the defect risk phase map, generating a multi-level gradient cooling baseline path. This multi-level gradient cooling baseline path includes multiple temperature plateau segments and / or temperature change rate segments. During crystallization, guided by the multi-level gradient cooling baseline path, the process status is monitored in real time. When the process status deviates from expectations, real-time path replanning is performed within the constraints of the defect risk phase map based on the current status, controlling the crystallization process to execute along the dynamically updated path.

[0007] Optionally, based on the raw material characteristic dataset, the impurity spectrum composition, initial supersaturation of the solution, and estimated initial nucleation energy of the current batch are analyzed and determined; based on the impurity spectrum composition, initial supersaturation of the solution, and initial nucleation energy, the simulation parameters of the menthol crystallization digital twin model are initialized; the preset temperature parameter range and time parameter range are traversed, and different temperature-time combinations are input as process parameter combinations into the initialized menthol crystallization digital twin model to calculate the quality defect risk value corresponding to each process parameter combination; each process parameter combination is correlated and mapped with the corresponding quality defect risk value, and a defect risk phase map specific to the current batch is drawn in the coordinate space composed of temperature parameters and time parameters.

[0008] Optionally, based on the impurity spectrum composition, the model coefficients regarding impurity adsorption energy and eutectic tendency in the menthol crystallization digital twin model are adjusted; based on the initial supersaturation and initial nucleation energy, the initial conditions for simulating crystal nucleation and growth kinetics in the menthol crystallization digital twin model are set; in the menthol crystallization digital twin model coupled with the model coefficients and the initial conditions, preset combinations of process parameters are traversed to predict the risk evolution trajectory of corresponding crystal quality defects under different process conditions, and the corresponding quality defect risk value is quantified and generated.

[0009] Optionally, the defect risk phase map is dynamically generated, and its coordinate dimensions include at least one feature-derived dimension calculated from the raw material feature dataset using a digital twin model of menthol crystallization. The feature-derived dimension includes the crystal interface energy barrier or the competitive adsorption energy of impurities on a specific crystal face, calculated in real time. The crystal interface energy barrier is used to correct the risk level of lattice distortion defects in the defect risk phase map, so that high-risk areas correspond to process parameter areas where the interface energy barrier exceeds the critical value.

[0010] Optionally, in the defect risk phase diagram, an initial process state point and a final process state point for crystallization are defined; regions in the defect risk phase diagram whose quality defect risk value exceeds a preset risk threshold are marked as high-risk regions to be avoided; an objective function is constructed using the avoidance distance of the path from the high-risk region and the total path length as evaluation factors; based on the objective function, in the process parameter coordinate space of the defect risk phase diagram, with the initial process state point and the final process state point as starting points, the optimal continuous cooling trajectory that does not pass through any high-risk regions is solved; the optimal continuous cooling trajectory is piecewise fitted and decomposed into a cooling sequence composed of a temperature plateau segment where the temperature remains constant and a temperature change rate segment where the temperature changes linearly, which serves as the multi-level gradient cooling reference path.

[0011] Optionally, the multi-level gradient cooling baseline path includes at least one process segment that is inconsistent with conventional cooling logic and is used to traverse a specific low-risk region in the defect risk phase map to repair internal defects in the crystal. The process segment is a brief and controlled heating pulse segment inserted in the macroscopic cooling trend, which is configured to reduce the density of specific defects inside the crystal by utilizing the reversible local dissolution effect.

[0012] Optionally, in the defect risk phase diagram, a dynamic safety corridor with boundaries determined by the defect risk gradient is constructed along the multi-level gradient cooling reference path, wherein the multi-level gradient cooling reference path constitutes the central axis of the dynamic safety corridor; the process status is monitored in real time and mapped onto the defect risk phase diagram to obtain real-time status points; it is determined whether the real-time status points are within the constraint boundaries of the dynamic safety corridor; when the real-time status points exceed the constraint boundaries of the dynamic safety corridor, the real-time status points are used as the starting point of a new path, and the end point of the multi-level gradient cooling reference path is used as the update target point, and path optimization is performed again within the constraint range of the defect risk phase diagram to generate a locally optimized path segment from the starting point of the new path to the update target point; the locally optimized path segment is connected with the unexecuted part of the multi-level gradient cooling reference path to form the dynamic update path; wherein the dynamic update path must be located within the low-risk region in the risk value coordinate space of the defect risk phase diagram and must re-enter the central axis of the dynamic safety corridor.

[0013] Optionally, the constraint boundary of the dynamic safety corridor is a dynamic safety boundary. Constructing the dynamic safety boundary includes: determining the risk sensitivity of each point on the multi-level gradient cooling reference path based on the gradient change of the quality defect risk value in the defect risk phase diagram; dynamically setting different widths of allowable deviation ranges for each point on the multi-level gradient cooling reference path based on the risk sensitivity, wherein points with high risk sensitivity correspond to narrower allowable deviation ranges, and points with low risk sensitivity correspond to wider allowable deviation ranges; the allowable deviation ranges of each point together constitute the dynamic safety boundary.

[0014] Secondly, this application also provides a menthol crystallization control system based on multi-level gradient cooling, used to execute the menthol crystallization control method based on multi-level gradient cooling as described in the first aspect. The menthol crystallization control system based on multi-level gradient cooling includes: a raw material analysis module, used to rapidly analyze the menthol solution raw material of the current batch before the start of the crystallization batch to obtain a raw material characteristic dataset; and a defect risk simulation module, used to input the raw material characteristic dataset into a menthol crystallization digital twin model, simulate and calculate the potential quality defect risks under different combinations of process parameters, and construct a defect risk profile specific to the current batch based on the potential quality defect risks. The bitmap, wherein the defect risk phase map uses process parameters as coordinates and defect risk values ​​as levels; the gradient cooling baseline path generation module is used to optimize the path by avoiding high-risk areas in the defect risk phase map, and generate multi-level gradient cooling baseline paths, wherein the multi-level gradient cooling baseline paths include multiple temperature plateau segments and / or temperature change rate segments; the path replanning module is used to monitor the process status in real time during the crystallization process, guided by the multi-level gradient cooling baseline paths, and when the process status deviates from the expectation, to perform real-time path replanning based on the current status within the constraints of the defect risk phase map, and control the crystallization process to execute along the dynamically updated path.

[0015] Thirdly, a computer-readable storage medium storing a computer program that, when executed, implements the steps of the menthol crystallization control method based on multi-level gradient cooling as described in any of the first aspects above.

[0016] One or more technical solutions provided in this application have at least the following beneficial effects: Before the start of a crystallization batch, a rapid analysis of the menthol solution raw material of the current batch is performed to obtain a raw material characteristic dataset; the raw material characteristic dataset is input into a digital twin model of menthol crystallization to simulate and calculate potential quality defect risks under different combinations of process parameters, and based on the potential quality defect risks, a defect risk phase map specific to the current batch is constructed, wherein the defect risk phase map uses process parameters as coordinates and defect risk values ​​as levels; with the goal of avoiding high-risk areas in the defect risk phase map, path optimization is performed to generate a multi-level gradient cooling benchmark path, wherein the multi-level gradient cooling benchmark path includes multiple temperature plateau segments and / or temperature change rate segments; during the crystallization process, guided by the multi-level gradient cooling benchmark path, the process status is monitored in real time, and when the process status deviates from expectations, real-time path replanning is performed based on the current status within the constraints of the defect risk phase map, controlling the crystallization process to execute along the dynamically updated path. In other words, by rapidly analyzing the characteristics of raw materials before each batch and inputting them into a digital twin model, a defect risk phase map specific to the current batch is constructed. The path optimization is performed with the goal of avoiding high-risk areas to generate a multi-level gradient cooling baseline path. The status is monitored in real time during the crystallization process. When the process status deviates from the expected value, the path is dynamically replanned under the constraints of the phase map, so that the crystallization process always runs in a low-risk area, significantly improving the consistency of crystal quality and product yield.

[0017] The above description is merely an overview of the technical solution of this application. To better understand the technical means of this application and to facilitate its implementation according to the description, and to make the above and other objects, features, and advantages of this application more apparent, specific embodiments of this application are described below. It should be understood that the content described in this section is not intended to identify key or important features of the embodiments of this application, nor is it intended to limit the scope of this application. Other features of this application will become readily apparent through the following description. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely exemplary. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0019] Figure 1 This is a schematic flowchart of the menthol crystallization control method based on multi-level gradient cooling in this application.

[0020] Figure 2 This is a schematic diagram of the menthol crystallization control system based on multi-level gradient cooling in this application.

[0021] Figure labeling: Raw material analysis module 11, defect risk simulation module 12, gradient cooling baseline path generation module 13, path replanning module 14. Detailed Implementation

[0022] This application provides a method, system, and medium for controlling menthol crystallization based on multi-stage gradient cooling. It addresses the technical problem in existing technologies where the rigid contradiction between natural batch-to-batch fluctuations in raw materials and a fixed multi-stage cooling process prevents adaptive adjustment during crystallization, easily leading to high-risk regions and inducing microscopic defects, further impacting crystal quality stability and product yield. By rapidly analyzing raw material characteristics before each batch and inputting them into a digital twin model, a defect risk phase map specific to the current batch is constructed. A multi-stage gradient cooling baseline path is generated through path optimization aimed at avoiding high-risk regions. The status is monitored in real-time during crystallization, and when the process status deviates from expectations, the path is dynamically replanned under the constraints of the phase map, ensuring the crystallization process always operates in a low-risk region, significantly improving crystal quality consistency and product yield.

[0023] The technical solutions of this application will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. It should be understood that this application is not limited to the exemplary embodiments described herein. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application. It should also be noted that, for ease of description, only the parts related to this application are shown in the accompanying drawings, not all of them.

[0024] Example 1, please refer to the appendix. Figure 1 This application provides a method for controlling menthol crystallization based on multi-level gradient cooling. The method is executed by a menthol crystallization control system based on multi-level gradient cooling, and specifically includes the following steps:

[0025] Before the crystallization batch begins, a rapid analysis is performed on the menthol solution raw material of the current batch to obtain a raw material characteristic dataset.

[0026] Specifically, before the start of each new batch of menthol crystallization production, a representative sample is taken from the menthol solution raw material storage tank and evenly divided into three portions for impurity profile analysis, initial supersaturation determination, and physical property parameter determination, respectively. The samples are automatically diverted to different online or rapid offline analysis modules.

[0027] A sample was filtered through a 0.45 μm organic filter membrane to remove any potential particulate matter, and then injected into a gas chromatography-mass spectrometry (GC-MS) instrument. The instrument used a programmed temperature ramp mode: the initial column temperature was set to 60 °C, increased to 200 °C at a rate of 5 °C per minute, and held at 200 °C for 10 min. By comparing the retention times and mass spectra of known standards, the types of major impurities in the sample were identified. Quantitative analysis was performed using the external standard method: a series of impurity standard solutions of known concentrations were prepared in advance, and peak areas were obtained by injecting each solution, and a concentration-peak area calibration curve was plotted. The peak areas of the impurities measured in the sample were substituted into the calibration curve to calculate the precise concentration of each impurity. The names and concentrations of all detected impurities were recorded to form a critical impurity profile. The critical impurity profile contains the types and concentrations of the major impurities in the raw material. Impurities can interfere with the normal nucleation and growth of menthol crystals, and may even enter the crystal lattice to form impurity inclusions or induce lattice distortion. Critical impurities typically include isomenthol, menthone, and limonene.

[0028] A series of menthol standard solutions of known concentrations were prepared, and the refractive index of each solution was measured at 20°C. A refractive index-concentration curve was plotted. The measured refractive index of the sample was substituted into this curve to deduce the actual concentration. The same sample was placed in a temperature-controlled sample cell with a circulating water bath, and slowly stirred while cooling at a rate of 0.5°C per minute. The turbidity of the solution was continuously monitored using a laser turbidimeter. When the turbidity began to rise significantly, it indicated that crystals were beginning to precipitate. This temperature was recorded as the saturation temperature of the raw material solution. Based on this saturation temperature, a pre-determined solubility curve was consulted. The solubility curve describes the saturation concentration of menthol in the solvent system at different temperatures. The saturation concentration corresponding to this saturation temperature was obtained. The initial supersaturation was obtained by subtracting the saturation concentration from the actual concentration. The initial supersaturation is the difference between the actual concentration of menthol in the solution before crystallization begins and the saturation concentration at that temperature. Supersaturation is the direct driving force for crystal nucleation and growth; the level of initial supersaturation determines the ease of spontaneous crystal nucleation and the number of initial crystal nuclei.

[0029] The physical properties are the physicochemical properties of the raw material solution itself, including at least dynamic viscosity, density, water content, and surface tension. Dynamic viscosity was measured using an Ubbelohde viscometer in a 20°C constant-temperature water bath: the flow time of the sample in the viscometer capillary was recorded, multiplied by the viscometer constant to obtain the kinematic viscosity, and then multiplied by the density at that temperature to obtain the dynamic viscosity. Density was measured directly using a precision densitometer. Water content was determined using a Karl Fischer coulometric method moisture analyzer: approximately 1 mL of sample was injected into the instrument, which automatically electrolyzed and displayed the water content as a percentage. Surface tension was measured using the platinum plate method at 20°C using a surface tensiometer. All measured physical property values ​​were recorded.

[0030] The names and concentrations of each impurity in the key impurity spectrum, along with the initial supersaturation value, dynamic viscosity, density, moisture content, and surface tension, are compiled into a structured raw material characteristic dataset. This dataset is a set of quantitative indicators obtained through rapid analysis that characterize the crystallization behavior of this batch of raw materials, and includes at least the key impurity spectrum, initial supersaturation, and physical property parameters.

[0031] The raw material feature dataset is input into the menthol crystallization digital twin model to simulate and calculate the potential quality defect risks under different combinations of process parameters. Based on the potential quality defect risks, a defect risk phase map specific to the current batch is constructed. The defect risk phase map uses process parameters as coordinates and defect risk values ​​as levels.

[0032] Furthermore, this application also includes the following steps: based on the raw material characteristic dataset, analyze and determine the impurity spectrum composition, initial supersaturation of the solution, and estimated initial nucleation energy of the current batch; based on the impurity spectrum composition, initial supersaturation of the solution, and initial nucleation energy, initialize the simulation parameters of the menthol crystallization digital twin model; traverse the preset temperature parameter range and time parameter range, input different temperature-time combinations as process parameter combinations into the initialized menthol crystallization digital twin model, and calculate the quality defect risk value corresponding to each process parameter combination; correlate and map each process parameter combination with the corresponding quality defect risk value, and draw a defect risk phase map specific to the current batch in the coordinate space composed of temperature parameters and time parameters.

[0033] Furthermore, this application also includes the following steps: adjusting the model coefficients regarding impurity adsorption energy and eutectic tendency in the menthol crystallization digital twin model based on the impurity spectrum composition; setting the initial conditions for the simulation of crystal nucleation and growth kinetics in the menthol crystallization digital twin model based on the initial supersaturation and initial nucleation energy; and in the menthol crystallization digital twin model coupled with the model coefficients and the initial conditions, traversing preset combinations of process parameters, predicting the risk evolution trajectory of corresponding crystal quality defects under different process conditions, and quantifying and generating the corresponding quality defect risk value.

[0034] Furthermore, this application also includes the following steps: the defect risk phase map is dynamically generated, and its coordinate dimensions include at least one feature-derived dimension calculated from the raw material feature dataset through a digital twin model of menthol crystallization. The feature-derived dimension includes the crystal interface energy barrier or the competitive adsorption energy of impurities on a specific crystal face, calculated in real time. The crystal interface energy barrier is used to correct the risk level of lattice distortion defects in the defect risk phase map, so that the high-risk region corresponds to the process parameter region where the interface energy barrier exceeds the critical value.

[0035] Specifically, the impurity profile, including the name and concentration of each impurity, is extracted from the raw material characteristic dataset, along with the initial supersaturation value. The initial nucleation energy is estimated based on the impurity profile and supersaturation. The nucleation energy is directly proportional to the cube of the interfacial tension and inversely proportional to the square of the supersaturation. A baseline nucleation energy value for a pure menthol solution is pre-fitted experimentally and then corrected based on the influence coefficient of impurity concentration on interfacial tension. The presence of impurities typically reduces interfacial tension, thereby lowering the nucleation energy, ultimately resulting in the output initial nucleation energy. The initial nucleation energy is the free energy barrier that must be overcome to form a stable crystal nucleus in the solution at the start of crystallization. The magnitude of the initial nucleation energy depends on the purity of the raw material, supersaturation, and the presence of impurities. A lower initial nucleation energy makes spontaneous nucleation more likely, potentially leading to explosive nucleation.

[0036] The impurity profile, initial supersaturation, and initial nucleation energy are used as basic parameters and written into the configuration file of the digital twin model. The solution volume, total solute, impurity types, and initial concentrations are set in the digital twin model. The initial temperature, initial supersaturation are set as the baseline value for the nucleation driving force, and the initial nucleation energy is set as the key input for calculating the nucleation rate. After these settings are completed, the digital twin model has been personalized for the current batch of raw materials.

[0037] Exhaustive simulation calculations are performed within a pre-defined process operating space, defined by temperature and time parameter ranges. This operating space is discretized into tens of thousands of specific temperature-time combinations, such as temperature steps of 1°C and time steps of 1 hour, forming a series of temperature-time combinations, each representing a possible cooling curve. The initialized digital twin model is then sequentially substituted into each hypothetical process path for simulation calculations.

[0038] For each impurity, its adsorption energy on the main growth crystal plane needs to be determined based on its molecular structure, functional groups, and interaction with the menthol crystal plane. A database of adsorption energies for various common impurities on different crystal planes was pre-determined through molecular simulation or single-crystal experiments. Based on the types of impurities detected in the current batch, the corresponding adsorption energy values ​​were retrieved from the database, and the adsorption coefficient of that impurity in the digital twin model was adjusted accordingly. Simultaneously, based on previous eutectic experimental data, a eutectic tendency coefficient was assigned to each impurity, ranging from 0 to 1; a higher value indicates a greater likelihood of eutectic formation with menthol. Impurity adsorption energy is the energy released when impurity molecules adsorb onto the menthol crystal surface. Higher adsorption energy makes it easier for impurities to adhere to the crystal surface, hindering the normal addition of menthol molecules and leading to a decrease in crystal growth rate or lattice distortion. Eutectic tendency is the tendency for impurity molecules to co-crystallize with menthol molecules to form a mixed crystal. Impurities with a high eutectic tendency are more likely to enter the crystal lattice, forming impurity inclusions and reducing product purity.

[0039] The initial supersaturation determines the strength of the initial nucleation driving force, while the initial nucleation energy determines the height of the nucleation barrier. Substituting the initial supersaturation and initial nucleation energy into the menthol crystallization digital twin model automatically calculates the initial homogeneous or heterogeneous nucleation rate. The initial nucleus number distribution is set; without external seed crystals, the initial nucleus number is typically set to 0, and the menthol crystallization digital twin model will automatically generate the first batch of nuclei when the supersaturation reaches a critical value. If seed crystals are required in the process design, the size distribution and quantity concentration of the seed crystals must be set in the initial conditions. After all these settings are configured, the menthol crystallization digital twin model can begin simulation calculations.

[0040] The simulation iterates through preset combinations of process parameters, running a complete crystallization process simulation for each temperature-time combination. It records the dynamic changes of various quality defect indicators during the process and outputs a comprehensive risk value after the simulation. The required temperature range is determined, such as from the initial temperature to the final temperature, and an appropriate temperature step size is selected. The temperature step size should not be too large, otherwise areas with drastic risk changes will be missed; nor should it be too small, otherwise the computational load will be excessive. Temperature and time parameters form a two-dimensional grid, where each grid point represents a specific temperature value and the time point at which that temperature is held. A complete cooling path can be viewed as a function of temperature changing with time, and after discretization, it can be described by a series of temperature-time points. For each discrete temperature-time combination, i.e., for each preset cooling endpoint temperature and corresponding time, it is used as the input condition for the digital twin model. Specifically, the model's temperature control function is set to cool from the initial temperature at a constant rate or in stages to the endpoint temperature and hold it until that time point, and the simulation is run. During simulation, the menthol crystallization digital twin model iteratively calculates changes in key variables at minute-level time steps, including solution supersaturation, homogeneous nucleation rate, crystal growth rate, dynamic adsorption coverage of impurities on the crystal surface, impurity entry rate into the crystal lattice, cumulative lattice strain energy, and crystal size distribution evolution. The menthol crystallization digital twin model embeds sub-models directly related to defect formation. For example, when the impurity adsorption coverage exceeds a certain critical value, a lattice distortion calculation module is triggered; when the crystal growth rate exceeds the diffusion mass transfer limit, an impurity inclusion calculation module is triggered. Based on the current solution conditions and crystal state, the risk increment at the current moment is calculated. By accumulating or integrating the risk increments at all moments, the risk evolution trajectory of the defect during the entire crystallization process is obtained. The trajectory is typically output as a time series curve, with time on the horizontal axis and the instantaneous risk value on the vertical axis.

[0041] After the simulation runs for the set total time, the menthol crystallization digital twin model outputs the various quality indicators of the final crystal product. Based on pre-defined quality defect judgment rules, each indicator is converted into a dimensionless risk index. For example, for impurity inclusion defects, the ratio of the total mass of impurities detected inside the crystal to the total mass of the product is calculated, divided by the maximum allowable residual limit of the impurity, such as 0.5%, to obtain the impurity inclusion risk index. If it exceeds 1, it indicates non-compliance. For lattice distortion, the average strain energy of the crystal is calculated and divided by a safety threshold, such as 0.15 J / g, to obtain the distortion risk index. For crystal form inhomogeneity, the risk index is calculated based on the degree of deviation between the proportion of different crystal forms and the target crystal form proportion. Based on the weight of each defect in the product quality requirements, such as purity weight 0.6, particle size distribution weight 0.3, and crystal form weight 0.1, the various risk indices are weighted and summed to obtain the comprehensive quality defect risk value under this combination of process parameters. This value is also between 0 and 1, where 0 indicates no risk, 1 indicates reaching critical risk, and greater than 1 indicates high risk and unacceptable.

[0042] A two-dimensional coordinate space is established, with temperature as the x-axis and time as the y-axis, covering both temperature and time ranges. Each temperature-time combination and its corresponding quality defect risk value are entered into this coordinate space as data points. For points not directly calculated in the discrete traversal, interpolation is used to estimate their risk values. Smoothness is ensured during interpolation to avoid unreasonable abrupt changes. After filling, a basic risk value distribution cloud map is obtained. For each point in the two-dimensional coordinate space, the crystal interface energy barrier for stable crystallization under that condition, as well as the competitive adsorption energy of each impurity on the main growth crystal plane, are calculated. The crystal interface energy barrier is obtained from molecular dynamics simulations or empirical formulas, with input parameters including temperature, supersaturation, solvent composition, and impurity concentration. The competitive adsorption energy is calculated using the Langmuir adsorption isotherm combined with the impurity adsorption energy database, outputting the coverage and adsorption free energy of different impurities on different crystal planes. These calculation results are stored as feature-derived dimension values.

[0043] Feature-derived dimensions, in addition to the original temperature and time coordinates, are physicochemical quantities directly related to the defect formation mechanism, obtained in real-time through a digital twin model of menthol crystallization. These can be superimposed on the phase diagram as an additional dimension or used to correct the original risk level. Typical feature-derived dimensions include the crystal interface energy barrier and the competitive adsorption energy of impurities on specific crystal faces. The crystal interface energy barrier is the free energy barrier that menthol molecules must overcome when diffusing from the solution and attaching to the crystal surface. The higher the interface energy barrier, the more difficult it is for molecules to join the crystal lattice, the slower the crystal growth, and the more likely it is to lead to incomplete lattice arrangement, thus inducing lattice distortion. The interface energy barrier is affected by factors such as temperature, supersaturation, and impurity adsorption. The competitive adsorption energy of impurities on specific crystal faces is the energy released by impurity molecules when they compete with menthol molecules for adsorption sites on a specific crystal face. The greater the competitive adsorption energy, the easier it is for impurities to occupy growth sites, thus hindering the normal binding of menthol, leading to impaired crystal growth or the formation of defects.

[0044] The feature-derived dimensions are fused and corrected with the quality defect risk value. Correction rules are predefined; for example, when the interface energy barrier exceeds a certain critical value, such as 5 kJ / mol, an additional penalty term is added to the lattice distortion risk, the magnitude of which is proportional to the extent exceeding the critical value. When the competitive adsorption energy of a certain impurity is greater than the adhesion energy of the menthol molecule itself, such as greater than 40 kJ / mol, the impurity inclusion risk increases sharply. In this case, the risk value of the corresponding region should be directly increased by one level, such as from 0.4 to 0.8. In this way, the corrected quality defect risk value is generated. The corrected risk value is then remapped into coordinate space to obtain the updated risk distribution.

[0045] A two-dimensional graph is plotted with temperature as the horizontal axis and time as the vertical axis. Color mapping is used to represent risk levels: green or blue indicates low risk (0-0.3), yellow indicates medium risk (0.3-0.7), red indicates high risk (0.7-1.0), and dark red or purple indicates extremely high risk (>1.0). Contour lines are drawn on the graph to mark the contour lines for risk values ​​of 0.3, 0.7, and 1.0, dividing the coordinate space into low-risk, medium-risk, high-risk, and prohibited zones. Simultaneously, contour lines representing feature-derived dimensions are overlaid on the same graph; for example, dashed lines are used to plot the interface energy barrier critical value contour line, and dotted lines are used to plot the competitive adsorption energy contour line. The final defect risk phase map is stored in electronic image format and associated with the corresponding batch number.

[0046] Because the feature-derived dimensions are calculated in real-time based on the menthol crystallization digital twin model, and the actual crystal quality data detected after each crystallization is fed back to the menthol crystallization model to correct the model parameters, the defect risk phase map for the same batch can be dynamically updated based on new simulation results or actual feedback. For example, when the actual crystal defect rate at a certain process point is higher than the predicted value, the correction coefficient for that region is adjusted in reverse to make the phase map more accurate. The updated phase map is then stored in the batch process database.

[0047] Building upon the basic risk value calculation, the original risk value is weighted, shifted, or thresholded using feature-derived dimensions, so that the high-risk regions in the final phase diagram can more accurately reflect the actual crystal defect generation conditions. For example, when the interface energy barrier exceeds a certain critical value, even if the original risk value is not high, the corresponding region should be marked as high-risk.

[0048] For example, the raw material characteristic dataset includes 88.3% L-menthol, 3.2 mg / mL isomenthol, 1.5 mg / mL menthone, 0.8 mg / mL limonene, 0.4 mg / mL menthol acetate, an initial supersaturation of 7.3 g / 100 mL, and an estimated initial nucleation energy of 4.06 × 10⁻⁶. 4 J / m 3The digital twin model was initialized with a solution volume of 500 L, a total amount of L-menthol of 500 L × 18.6 g / 100 mL = 93 kg, a total amount of isomenthol of 1.6 kg, menthone of 0.75 kg, limonene of 0.4 kg, and menthol acetate of 0.2 kg, at an initial temperature of 22 °C. The process parameter combinations were iterated and risk values ​​were calculated. The temperature range was set from 20 °C to -8 °C with a step size of 2 °C, for a total of 15 temperature points; the time range was set from 0 to 72 h with a step size of 2 h, for a total of 37 time points; a total of 555 process parameter combinations were calculated. The menthol crystallization digital twin model was run to simulate each combination. Examples of some results are as follows: Temperature 20℃, Time 12h, Impurity inclusion rate 0.5%, Lattice strain energy 0.02J / g, Particle size variation coefficient 0.25, Overall risk value 0.08; Temperature 10℃, Time 24h, Impurity inclusion rate 1.2%, Lattice strain energy 0.05J / g, Particle size variation coefficient 0.31, Overall risk value 0.18; Temperature 0℃, Time 36h, Impurity inclusion rate 2.8%, Lattice strain energy 0.12J / g, Particle size variation coefficient 0.38, Overall risk value 0.32; Temperature -2℃, Time 36h, Impurity inclusion rate 1.9%, Lattice strain energy 0.5%, Lattice strain energy 0.02J / g, Particle size variation coefficient 0.25, Overall risk value 0.08; Temperature 10℃, Time 24h, Impurity inclusion rate 1.2%, Lattice strain energy 0.05J / g, Particle size variation coefficient 0.31, Overall risk value 0.32; Temperature -2℃, Time 36h, Impurity inclusion rate 1.9%, Lattice strain energy 0.05J / g, Particle size variation coefficient 0.02J / g, Overall risk value 0.32; Strain energy 0.09 J / g, particle size variation coefficient 0.35, overall risk value 0.21; Temperature -2℃, Time 48h, Impurity inclusion rate 5.1%, Lattice strain energy 0.17 J / g, Particle size variation coefficient 0.46, Overall risk value 0.67; Temperature -5℃, Time 48h, Impurity inclusion rate 8.7%, Lattice strain energy 0.25 J / g, Particle size variation coefficient 0.52, Overall risk value 1.46; Temperature -8℃, Time 72h, Impurity inclusion rate 12.3%, Lattice strain energy 0.36 J / g, Particle size variation coefficient 0.61, Overall risk value 2.20. A defect risk phase diagram was plotted, with temperature from 20℃ to -8℃ on the x-axis and time from 0 to 72h on the y-axis. Interpolation was used to fill all points. A temperature above 2°C for less than 30 hours is green (low risk); a temperature between -2°C and 2°C for 30 to 44 hours is yellow (medium risk); a temperature below -2°C for more than 40 hours is red (high risk); and a temperature below -5°C for more than 50 hours is dark red (extremely high risk).

[0049] Traversing the entire temperature-time parameter space, rather than examining only a few points, comprehensively reveals the risk distribution and avoids unintended high-risk zones. The defect risk phase map clearly marks the safe zone, transition zone, and forbidden zone with colors and contour lines. Using this map as a constraint map, the optimal cooling curve can be quickly planned, significantly reducing the cost of repeated trial and error. When online monitoring detects a deviation in the process state, the risk level of the current location can be immediately found on the phase map, and a local path can be replanned to bypass the red area, ensuring that crystallization always occurs within the safe zone.

[0050] With the goal of avoiding high-risk areas in the defect risk phase map, path optimization is performed to generate a multi-level gradient cooling benchmark path, which includes multiple temperature plateau segments and / or temperature change rate segments.

[0051] Furthermore, this application also includes the following steps: defining the initial process state point and the final process state point of crystallization in the defect risk phase diagram; marking the areas in the defect risk phase diagram where the quality defect risk value exceeds a preset risk threshold as high-risk areas to be avoided; constructing an objective function using the avoidance distance of the path deviating from the high-risk area and the total path length as evaluation factors; based on the objective function, in the process parameter coordinate space of the defect risk phase diagram, with the initial process state point and the final process state point as starting points, solving for the optimal continuous cooling trajectory that does not pass through any high-risk areas; performing piecewise fitting on the optimal continuous cooling trajectory, decomposing it into a cooling sequence composed of a temperature plateau segment where the temperature remains constant and a temperature change rate segment where the temperature changes linearly, as the multi-level gradient cooling reference path.

[0052] Furthermore, this application also includes the following steps: the multi-level gradient cooling reference path includes at least one process segment that is inconsistent with conventional cooling logic and is used to traverse a specific low-risk region in the defect risk phase diagram to repair internal defects of the crystal. The process segment is a brief and controlled heating pulse segment inserted in the macroscopic cooling trend, which is configured to reduce the density of specific defects inside the crystal by utilizing the reversible local dissolution effect.

[0053] Specifically, in the temperature-time coordinate space of the defect risk phase diagram, two key points are identified: the initial process state point and the final process state point. The initial process state point is the point in the defect risk phase diagram corresponding to the start of the crystallization process, and its coordinates are determined by the starting temperature and starting time. The starting temperature is usually the initial temperature of the raw material, and the starting time is 0. The final process state point is the point in the defect risk phase diagram corresponding to the end of the crystallization process, and its coordinates are determined by the ending temperature and the total crystallization time. The ending temperature is usually the temperature at which crystallization is completed, and the total time is the desired crystallization cycle. Both the initial and final process state points must fall within the low-risk region of the phase diagram, or at least not within the high-risk region. If the initial or ending point itself is located in a high-risk region, the starting conditions need to be adjusted or the ending point needs to be reselected.

[0054] The quality defect risk value of each grid point in the defect risk phase map is read. All continuous areas with risk values ​​greater than a preset risk threshold are extracted and marked as high-risk areas to be avoided. These high-risk areas are considered obstacles, and no cooling path may traverse them. The preset risk threshold is a pre-defined limit for quality defect risk values, such as 0.7. Areas with risk values ​​exceeding this threshold are considered unacceptable and must be avoided in path planning.

[0055] Using the avoidance distance from high-risk areas and the total path length as evaluation factors, an objective function is constructed. A larger minimum avoidance distance between the path and the high-risk area indicates greater safety; a shorter total path length signifies a shorter crystallization cycle and lower energy consumption. These two factors are combined into a weighted summation of a comprehensive cost function: Comprehensive Cost = Negative Weighted Avoidance Distance plus Weighted Path Length. The weighting coefficients are adjusted according to actual production requirements: if extremely high purity is required, the weight of avoidance distance is increased; if production capacity is tight, the weight of path length is increased.

[0056] A path planning algorithm is used to find the optimal path from the initial point to the endpoint on the defect risk phase map. During algorithm execution, the cost of each grid point is determined by its risk value and the cumulative path length from the starting point to that point. During the search, the path is allowed to move in any direction, but the final result is a continuous curve that does not cross any high-risk areas and minimizes the objective function. The solution is a smooth curve containing heating segments to bypass obstacles or enter specific low-risk areas. Specifically, the quality defect risk value of each grid point in the defect risk phase map is read, and a cost is assigned to each grid point accordingly. If the risk value of a grid point is greater than a preset threshold, such as 0.7, the cost of that grid point is set to infinity, indicating that passage is prohibited; if the risk value is less than or equal to the threshold, the cost is set to the risk value itself, or a small value proportional to the risk level of that point. The grid cell containing the initial process state point is marked as the starting point. The grid cell containing the final process state point is marked as the endpoint. If the starting point or endpoint happens to fall on a high-risk grid that prohibits passage, the position of the starting point or endpoint needs to be adjusted to a nearby low-risk grid. In the grid graph, movement is allowed from the current grid point in eight adjacent directions: up, down, left, right, and the four diagonals. The time coordinate can only increase forward, not backward, therefore movement in the direction of decreasing time is prohibited. The temperature coordinate can both decrease and increase, allowing movement that increases or decreases temperature. The distance moved in each step is equal to the Euclidean distance of the grid step size. The classic Dijkstra algorithm is used to search for the lowest total cost path from the start point to the end point on the grid graph. An open list is maintained, initially containing the start point. At each step, the grid point with the lowest total cost is selected from the open list, its allowed neighborhood is expanded, the cumulative cost from the start point through the current point to the neighborhood points is calculated, and the open list is updated. The search ends when the end point is removed from the open list. By tracing back the parent node pointer from the end point, a sequence of grid points traversed by the optimal path can be obtained. Since the algorithm prohibits entering high-risk grids, the obtained path automatically avoids all high-risk areas. The grid path is a series of grid center points connected by straight line segments, exhibiting a jagged appearance; the grid path is smoothed. Spline interpolation is used to fit a discrete point sequence into a smooth, continuous curve, which must remain within a low-risk region and not cross high-risk regions. After smoothing, an optimal continuous cooling trajectory that can be described by a mathematical function is obtained, typically expressed as a function of time as the independent variable and temperature as the dependent variable. The smoothed trajectory is then checked to ensure it still satisfies all constraints: it does not enter high-risk regions, does not exceed set temperature and time boundaries, and the rate of temperature change is within the actual equipment's capabilities. If constraints are violated, the smoothing parameters are adjusted appropriately, or the process is corrected by returning to the grid path.

[0057] The optimal continuous cooling trajectory is piecewise linearly fitted. Since actual crystallization equipment typically only operates in either isothermal plateau or linear temperature variation mode, the curve needs to be approximated as a series of straight line segments and horizontal segments. Inflection points and plateau regions on the curve are identified. Significantly horizontal segments are extracted as temperature plateau segments; the sloping lines connecting these plateau segments are extracted as temperature variation rate segments, and their slopes are calculated as the cooling / heating rates. For arc segments with large curvature, multiple straight line segments with small slopes are used for approximation, ultimately resulting in a sequence consisting of alternating plateau and temperature variation segments. This sequence is output as a multi-level gradient cooling baseline path. The multi-level gradient cooling baseline path contains multiple temperature plateaus and multiple temperature variation rate segments, representing the optimal cooling scheme specific to the current batch of raw materials.

[0058] Based on the characteristics of the defect risk phase map, the path planning intentionally guides the trajectory through a specific low-risk region, corresponding to a short-term heating process. The specific parameters of the heating pulse segment, such as the heating start point, heating amplitude, duration, and cooling return, are determined by the shape of the low-risk region in the phase map. For example, the phase map may contain a repair window with a temperature between -2℃ and 2℃ and a time window of 1 hour. Heating within this window will not cause quality defects; instead, the crystal can be repaired using a reversible dissolution effect. A short and controlled heating pulse segment is inserted into the baseline path. When the temperature drops to a certain intermediate value, such as 0℃, the cooling process is paused, and the temperature is increased at a certain rate to a higher temperature, such as 2℃, held for a short time, such as 0.5 hours, and then decreased back to the original temperature at the same rate before continuing the original cooling plan. The goal of this heating pulse segment is to preferentially dissolve the imperfect parts of the crystal surface. Then, during the temperature drop back, the dissolved menthol molecules recrystallize on the more perfect crystal surface, thereby reducing the lattice distortion density and impurity inclusion rate. The reversible local dissolution effect refers to the phenomenon where the most unstable parts of a crystal surface preferentially dissolve when the temperature rises. Since the dissolution is reversible, when the temperature drops again, the dissolved molecules will regrow on a more perfect crystal surface, thus repairing the original defects.

[0059] In the phase diagram, areas with temperatures below -2℃ for more than 40 hours are marked in red (risk > 0.7), while areas with temperatures below -5℃ for more than 50 hours are marked in dark red (risk > 1.0). Red and dark red areas are marked as obstacles. Objective function weights are set: avoidance distance weight = 0.7, path length weight = 0.3. Overall cost = -0.7 × minimum avoidance distance + 0.3 × path length. The actual output temperature drops from (22℃, 0h) to (0℃, 48h) at a rate of approximately 0.45℃ / h. Using the rapid travel method, the trajectory points (time, temperature) are obtained as follows: (0,22), (6,19), (12,16), (18,13), (24,10), (30,7), (36,4), (40,2), (42,1), (44,2), (46,1), (48,-1), (49,-3), (50,-5). The total time is actually 52h, which includes a heating segment from (42,1) to (44,2) and then cooling back to (46,1), which is the heating pulse. The fitted cooling sequence is as follows: A plateau segment is maintained at 22℃ for 0.5 hours to homogenize the solution; a temperature-changing segment cools from 22℃ to 10℃ at a rate of 0.5℃ / h, taking 24 hours; a plateau segment is maintained at 10℃ for 2 hours; a temperature-changing segment cools from 10℃ to 2℃ at a rate of 0.33℃ / h, taking 24 hours. The actual fitted sequence is: Temperature-changing segment 1 cools from 22℃ to 10℃ at a rate of 0.5℃ / h, lasting 24 hours, reaching the target temperature in 24 hours; Plateau segment 1 is maintained at 10℃ for 2 hours, reaching the target temperature in 26 hours; Temperature-changing segment 2 cools from 10℃ to 2℃ at a rate of 0.4℃ / h, lasting 20 hours, reaching the target temperature in 46 hours; The heating pulse segment heats from 2℃ to 3.5℃ at a rate of 0.8℃ / h, taking approximately 1.9 hours, reaching the target temperature in 47.9 hours. h; holding at 3.5℃ for 0.5h, reaching the target temperature in 48.4h; cooling to 2℃ at 0.8℃ / h, taking 1.9h, reaching the target temperature in 50.3h; temperature change segment 3 cools from 2℃ to -2℃ at a cooling rate of 0.25℃ / h, lasting 16h, reaching the target temperature in 66.3h. In practice, a faster cooling rate should be used to cool from 2℃ to -5℃ at a rate of 0.35℃ / h, taking 20h, for a total time of 70.3h. To meet the total time requirement of approximately 48h, a tighter path is planned: the rate is changed to 2℃ / h, then 0 to 2℃ takes 1h, holding for 0.2h, and 2 to 0℃ takes 1h, for a total of 2.2h. This way, the total time can be controlled within 48h. The actual pulse segment should be heating to 2℃ at 2℃ / h, holding for 0.2h, and then cooling back to 0℃ at 2℃ / h.

[0060] By marking high-risk areas in the risk phase map as obstacles, the path planning algorithm can automatically bypass process parameter combinations that can lead to defects such as lattice distortion and impurity inclusion, thus preventing quality problems from occurring at the source rather than remediating them afterward.

[0061] During the crystallization process, guided by the multi-level gradient cooling baseline path, the process status is monitored in real time. When the process status deviates from the expected value, real-time path replanning is performed based on the current status within the constraints of the defect risk phase diagram, controlling the crystallization process to execute along the dynamically updated path.

[0062] Furthermore, this application also includes the following steps: In the defect risk phase diagram, along the multi-level gradient cooling reference path, a dynamic safety corridor with boundaries determined by the defect risk gradient is constructed, wherein the multi-level gradient cooling reference path constitutes the central axis of the dynamic safety corridor; the process status is monitored in real time, and the process status is mapped onto the defect risk phase diagram to obtain real-time status points; it is determined whether the real-time status points are within the constraint boundaries of the dynamic safety corridor; when the real-time status points exceed the constraint boundaries of the dynamic safety corridor, the path is re-optimized within the constraint range of the defect risk phase diagram, taking the real-time status points as the starting point of a new path and the end point of the multi-level gradient cooling reference path as the update target point, to generate a locally optimized path segment from the starting point of the new path to the update target point; the locally optimized path segment is connected to the unexecuted portion of the multi-level gradient cooling reference path to form the dynamic update path; wherein the dynamic update path must be located within a low-risk region in the risk value coordinate space of the defect risk phase diagram and must re-enter the central axis of the dynamic safety corridor.

[0063] Furthermore, this application also includes the following steps: the constraint boundary of the dynamic safety corridor is a dynamic safety boundary; constructing the dynamic safety boundary includes: determining the risk sensitivity of each point on the multi-level gradient cooling reference path based on the gradient change of the quality defect risk value in the defect risk phase diagram; dynamically setting different widths of allowable deviation ranges for each point on the multi-level gradient cooling reference path based on the risk sensitivity, wherein points with high risk sensitivity correspond to narrower allowable deviation ranges, and points with low risk sensitivity correspond to wider allowable deviation ranges; the allowable deviation ranges of each point together constitute the dynamic safety boundary.

[0064] Specifically, a multi-level gradient cooling baseline path is plotted on a defect risk phase map. The multi-level gradient cooling baseline path is a continuous curve from the initial process state point to the final process state point. Each point on the phase map has a corresponding quality defect risk value. Therefore, each point on the baseline path also has a corresponding risk value, as well as the gradient of the risk value near that point with respect to its location.

[0065] For each discrete point on the baseline path, calculate the partial derivative of the quality defect risk value at that point with respect to temperature. At that point, keeping the time coordinate constant, measure the risk value when the temperature increases and decreases by a small amount, and then calculate the rate of change of the risk value. The larger the absolute value of the rate of change, the more sensitive the risk is to temperature deviations; the rate of change is the risk sensitivity. Here, we consider the sensitivity in the time direction, but deviations in the temperature direction are more likely to occur in real-time control, so we mainly focus on temperature sensitivity.

[0066] A baseline allowable deviation width is defined, and this width is scaled according to risk sensitivity. For points with high risk sensitivity, the allowable deviation range should be narrowed, i.e., actual allowable deviation = baseline width / sensitivity amplification factor. For points with low risk sensitivity, the allowable deviation range can be widened, even exceeding the baseline width. To prevent excessively frequent replanning due to an overly narrow deviation range, a minimum allowable deviation is set; simultaneously, to prevent the range from becoming meaningless due to excessive width, a maximum allowable deviation is set, which constitutes the allowable deviation range for that point. The allowable deviation range is the maximum deviation of the actual process state from the baseline value in the temperature direction at a given point on the baseline path. The deviation range extends a certain distance from the baseline path as its central axis, towards both the temperature rise and temperature fall sides. The magnitude of the deviation range is inversely proportional to the risk sensitivity.

[0067] Connecting the upper deviation limits of all path points forms a smooth upper boundary curve, and connecting the lower deviation limits of all path points forms a smooth lower boundary curve. The strip-shaped area between these two curves constitutes the dynamic safety corridor. Because the allowable deviation range varies with the path points, the width of the corridor also changes: the corridor narrows in areas of high risk sensitivity and widens in areas of low risk sensitivity. The central axis of the corridor is the baseline path.

[0068] In real-time control of the crystallization process, the current actual temperature and time are continuously monitored and mapped onto the defect risk phase map to obtain the real-time status point. It is then determined whether this real-time status point is located within the dynamic safety corridor. For the point on the baseline path corresponding to the current time, i.e., the temperature that should be reached at this time according to the baseline path plan, the allowable deviation range for this point, including the upper and lower boundary temperatures, is obtained from the definition of the dynamic safety corridor. The temperature of the real-time status point is compared with these two boundaries. If the real-time temperature is less than or equal to the upper boundary and greater than or equal to the lower boundary, it is determined to be within the corridor; otherwise, it is determined to be outside the boundary. If it is within the corridor, the crystallization process continues according to the original baseline path without intervention.

[0069] When the boundary is exceeded, the current real-time state point is immediately recorded as the starting point of the new path. Note that the time coordinate of this starting point must be greater than the initial time, while the temperature coordinate may be higher or lower than the temperature of the baseline path. The target point for replanning remains unchanged, which is the final process state point of the original baseline path, i.e., the endpoint temperature and total crystallization time. At the same time, the segments in the original baseline path that have not yet been executed after the current time are marked as segments to be replaced.

[0070] Starting from the new path's origin and ending at the original destination, the path planning algorithm is re-executed on the defect risk phase map. The phase map is discretized into a grid, and high-risk areas are set as impassable. The objective function comprehensively considers the path length and the avoidance distance from high-risk areas. Since the new starting point has deviated from the original path, the planned new path will typically bypass the risk areas near the current location and may employ a different cooling rate or heating pulse than the original path, covering the interval from the new starting point to the destination.

[0071] The newly planned locally optimized path segment is then connected to the original baseline path segment that has not yet been executed. During this connection, temporal continuity needs to be addressed. The new path's starting point is the time of the new starting point, and its ending point is the total time of the original ending point. The portion of the original baseline path from the new starting point time to the ending point time is completely replaced. However, in actual splicing, to ensure a smooth control transition, a smooth transition is used in the initial segment of the new path. For example, the temperature gradually changes from the current actual temperature to the planned temperature in the first few minutes to avoid abrupt changes in control variables. After the connection is completed, a complete dynamically updated path is formed, with the first segment being the already executed original baseline path and the second segment being the newly planned locally optimized path.

[0072] Check if the dynamically updated path meets the following requirements: the entire path must not enter high-risk areas in the defect risk phase map; the new planned segment must eventually merge into the central axis of the original dynamic safety corridor, that is, at some point before the endpoint, the temperature-time point of the new path coincides with the baseline path, or at least falls within the allowable deviation range of the original corridor. If the merging conditions are not met, appropriately extend the new path or adjust the endpoint constraint of the planning algorithm to force a return to the central axis near the endpoint. After successful verification, the dynamically updated path is issued to the execution mechanism, and the crystallization process is then executed along the new path.

[0073] During execution along the dynamically updated path, the control system continues to monitor the status in real time and uses the same logic to determine whether it has exceeded the dynamic safety corridor corresponding to the new path again. If it does, replanning is triggered again. This cycle repeats, achieving online adaptive control throughout the entire process and ensuring that the crystallization process always operates within a low-risk area. Replanning is not simply returning to the original path, nor is it blindly and rapidly cooling down; rather, it involves resolving the optimal path from the current state to the endpoint under phase diagram constraints. Since the objective function still considers path length and avoidance distance, the new path can shorten the remaining crystallization time as much as possible while ensuring safety, reducing energy consumption and equipment occupancy.

[0074] In summary, the menthol crystallization control method based on multi-level gradient cooling provided in this application has the following beneficial effects: Before the start of a crystallization batch, the menthol solution raw material of the current batch is rapidly analyzed to obtain a raw material characteristic dataset; the raw material characteristic dataset is input into a menthol crystallization digital twin model to simulate and calculate the potential quality defect risks under different combinations of process parameters; based on the potential quality defect risks, a defect risk phase map specific to the current batch is constructed, with process parameters as coordinates and defect risk values ​​as levels; path optimization is performed with the goal of avoiding high-risk areas in the defect risk phase map, generating a multi-level gradient cooling benchmark path, which includes multiple temperature plateau segments and / or temperature change rate segments; during the crystallization process, guided by the multi-level gradient cooling benchmark path, the process status is monitored in real time, and when the process status deviates from expectations, real-time path replanning is performed within the constraints of the defect risk phase map based on the current status, controlling the crystallization process to execute along the dynamically updated path. In other words, by rapidly analyzing the characteristics of raw materials before each batch and inputting them into a digital twin model, a defect risk phase map specific to the current batch is constructed. The path optimization is performed with the goal of avoiding high-risk areas to generate a multi-level gradient cooling baseline path. The status is monitored in real time during the crystallization process. When the process status deviates from the expected value, the path is dynamically replanned under the constraints of the phase map, so that the crystallization process always runs in a low-risk area, significantly improving the consistency of crystal quality and product yield.

[0075] Example 2: Based on the same inventive concept as the menthol crystallization control method based on multi-stage gradient cooling in Example 1, this application also provides a menthol crystallization control system based on multi-stage gradient cooling. Please refer to the appendix. Figure 2 The menthol crystallization control system based on multi-level gradient cooling includes: The raw material analysis module 11 is used to quickly analyze the menthol solution raw material of the current batch before the start of the crystallization batch to obtain a raw material characteristic dataset; the defect risk simulation module 12 is used to input the raw material characteristic dataset into the menthol crystallization digital twin model to simulate and calculate the potential quality defect risks under different combinations of process parameters, and construct a defect risk phase map specific to the current batch based on the potential quality defect risks. The defect risk phase map uses process parameters as coordinates and defect risk values ​​as levels; the gradient cooling baseline path generation module 13 is used to optimize the path to avoid high-risk areas in the defect risk phase map and generate a multi-level gradient cooling baseline path. The multi-level gradient cooling baseline path includes multiple temperature plateau segments and / or temperature change rate segments; the path replanning module 14 is used to monitor the process status in real time during the crystallization process, guided by the multi-level gradient cooling baseline path, and perform real-time path replanning based on the current status within the constraints of the defect risk phase map when the process status deviates from the expectation, controlling the crystallization process to execute along the dynamically updated path.

[0076] Furthermore, the defect risk simulation module 12 in the menthol crystallization control system based on multi-level gradient cooling is also used for: analyzing and determining the impurity spectrum composition, initial supersaturation of the solution, and estimated initial nucleation energy of the current batch based on the raw material characteristic dataset; initializing the simulation parameters of the menthol crystallization digital twin model based on the impurity spectrum composition, initial supersaturation of the solution, and initial nucleation energy; traversing the preset temperature parameter range and time parameter range, inputting different temperature-time combinations as process parameter combinations into the initialized menthol crystallization digital twin model, calculating the quality defect risk value corresponding to each process parameter combination; associating and mapping each process parameter combination with the corresponding quality defect risk value, and drawing a defect risk phase diagram specific to the current batch in the coordinate space composed of temperature parameters and time parameters.

[0077] Furthermore, the defect risk simulation module 12 in the menthol crystallization control system based on multi-level gradient cooling is also used to: adjust the model coefficients of the menthol crystallization digital twin model regarding impurity adsorption energy and eutectic tendency based on the impurity spectrum composition; set the initial conditions for the crystal nucleation and growth kinetics simulation in the menthol crystallization digital twin model based on the initial supersaturation and initial nucleation energy; and in the menthol crystallization digital twin model coupled with the model coefficients and the initial conditions, traverse the preset process parameter combinations, predict the risk evolution trajectory of corresponding crystal quality defects under different process conditions, and quantify and generate the corresponding quality defect risk value.

[0078] Furthermore, the defect risk simulation module 12 in the menthol crystallization control system based on multi-level gradient cooling is also used for: the defect risk phase map is dynamically generated, and its coordinate dimensions include at least one feature-derived dimension calculated from the raw material feature dataset through the menthol crystallization digital twin model. The feature-derived dimension includes the crystal interface energy barrier or the competitive adsorption energy of impurities on a specific crystal face calculated in real time. The crystal interface energy barrier is used to correct the risk level of lattice distortion defects in the defect risk phase map, so that the high-risk area corresponds to the process parameter area where the interface energy barrier exceeds the critical value.

[0079] Furthermore, the gradient cooling baseline path generation module 13 in the menthol crystallization control system based on multi-level gradient cooling is also used to: define the initial process state point and the final process state point of crystallization in the defect risk phase diagram; mark the areas in the defect risk phase diagram where the quality defect risk value exceeds a preset risk threshold as high-risk areas to be avoided; construct an objective function using the avoidance distance of the path from the high-risk area and the total path length as evaluation factors; based on the objective function, in the process parameter coordinate space of the defect risk phase diagram, with the initial process state point and the final process state point as starting points, solve for the optimal continuous cooling trajectory that does not pass through any high-risk areas; perform piecewise fitting on the optimal continuous cooling trajectory, decompose it into a cooling sequence composed of a temperature plateau segment where the temperature remains constant and a temperature change rate segment where the temperature changes linearly, as the multi-level gradient cooling baseline path.

[0080] Furthermore, the gradient cooling reference path generation module 13 in the menthol crystallization control system based on multi-level gradient cooling is also used to: include at least one process segment in the multi-level gradient cooling reference path that is inconsistent with the conventional cooling logic and is used to traverse a specific low-risk region in the defect risk phase diagram to repair internal defects of the crystal. The process segment is a brief and controlled heating pulse segment inserted in the macroscopic cooling trend, which is configured to reduce the density of specific defects inside the crystal by utilizing the reversible local dissolution effect.

[0081] Furthermore, the path replanning module 14 in the menthol crystallization control system based on multi-level gradient cooling is also used for: constructing a dynamic safety corridor with boundaries determined by the defect risk gradient along the multi-level gradient cooling reference path in the defect risk phase diagram, wherein the multi-level gradient cooling reference path constitutes the central axis of the dynamic safety corridor; monitoring the process status in real time and mapping the process status to the defect risk phase diagram to obtain a real-time status point; determining whether the real-time status point is located within the constraint boundary of the dynamic safety corridor; when the real-time status point exceeds the constraint boundary of the dynamic safety corridor, taking the real-time status point as the starting point of a new path and the end point of the multi-level gradient cooling reference path as the update target point, re-optimizing the path within the constraint range of the defect risk phase diagram to generate a locally optimized path segment from the starting point of the new path to the update target point; connecting the locally optimized path segment with the unexecuted part of the multi-level gradient cooling reference path to form the dynamic update path; wherein the dynamic update path must be located within the low-risk area in the risk value coordinate space of the defect risk phase diagram and must re-enter the central axis of the dynamic safety corridor.

[0082] Furthermore, the path replanning module 14 in the menthol crystallization control system based on multi-level gradient cooling is also used to: determine the risk sensitivity of each point on the multi-level gradient cooling reference path according to the gradient change of the quality defect risk value in the defect risk phase diagram; dynamically set different widths of allowable deviation ranges for each point on the multi-level gradient cooling reference path according to the risk sensitivity, wherein points with high risk sensitivity correspond to narrower allowable deviation ranges, and points with low risk sensitivity correspond to wider allowable deviation ranges; the allowable deviation ranges of each point together constitute the dynamic safety boundary.

[0083] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Figure 1 The menthol crystallization control method and specific examples based on multi-level gradient cooling in Example 1 are also applicable to the menthol crystallization control system based on multi-level gradient cooling in this embodiment. Through the foregoing detailed description of the menthol crystallization control method based on multi-level gradient cooling, those skilled in the art can clearly understand the menthol crystallization control system based on multi-level gradient cooling in this embodiment. Therefore, for the sake of brevity, it will not be described in detail here. For the systems / devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant details can be found in the method section.

[0084] In Example 3, based on the same inventive concept as the menthol crystallization control method based on multi-level gradient cooling in Example 1, this application also provides a computer-readable storage medium storing a computer program that, when executed, implements the steps of the menthol crystallization control method based on multi-level gradient cooling described in any one of Examples 1.

[0085] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0086] Obviously, those skilled in the art can make several improvements and modifications to this application without departing from the principles of this application, and these improvements and modifications also fall within the protection scope of this application.

Claims

1. A method for controlling menthol crystallization based on multi-stage gradient cooling, characterized in that, include: Before the start of a crystallization batch, a rapid analysis of the menthol solution raw material for the current batch is performed to obtain a raw material characteristic dataset; The raw material feature dataset is input into the menthol crystallization digital twin model to simulate and calculate the potential quality defect risks under different combinations of process parameters. Based on the potential quality defect risks, a defect risk phase map specific to the current batch is constructed. The defect risk phase map uses process parameters as coordinates and defect risk values ​​as levels. With the goal of avoiding high-risk areas in the defect risk phase map, path optimization is performed to generate a multi-level gradient cooling benchmark path, which includes multiple temperature plateau segments and / or temperature change rate segments. During the crystallization process, guided by the multi-level gradient cooling baseline path, the process status is monitored in real time. When the process status deviates from the expected value, real-time path replanning is performed based on the current status within the constraints of the defect risk phase diagram, controlling the crystallization process to execute along the dynamically updated path.

2. The method for controlling menthol crystallization based on multi-stage gradient cooling as described in claim 1, characterized in that, The raw material characteristic dataset is input into the menthol crystallization digital twin model to simulate and calculate the potential quality defect risks under different combinations of process parameters. Based on the potential quality defect risks, a defect risk phase map specific to the current batch is constructed, including: Based on the raw material characteristic dataset, the impurity spectrum composition, initial supersaturation of the solution, and estimated initial nucleation energy of the current batch are analyzed and determined. Based on the impurity spectrum composition, initial supersaturation of the solution, and initial nucleation energy, the simulation parameters of the menthol crystallization digital twin model are initialized. Iterate through the preset temperature and time parameter ranges, input different temperature-time combinations as process parameter combinations into the initialized menthol crystallization digital twin model, and calculate the quality defect risk value corresponding to each process parameter combination. By associating and mapping each combination of process parameters with the corresponding quality defect risk value, a defect risk phase diagram specific to the current batch is drawn in a coordinate space composed of temperature and time parameters.

3. The method for controlling menthol crystallization based on multi-stage gradient cooling as described in claim 2, characterized in that, Calculate the quality defect risk value corresponding to each combination of process parameters, including: Based on the impurity spectrum composition, the model coefficients regarding impurity adsorption energy and eutectic tendency in the menthol crystallization digital twin model are adjusted. Based on the initial supersaturation and initial nucleation energy, the initial conditions for simulating crystal nucleation and growth kinetics in the digital twin model of menthol crystals are set. In the menthol crystallization digital twin model that couples the model coefficients with the initial conditions, the preset combination of process parameters is traversed to predict the risk evolution trajectory of the corresponding crystal quality defects under different process conditions, and the corresponding quality defect risk value is quantified and generated.

4. The method for controlling menthol crystallization based on multi-stage gradient cooling as described in claim 3, characterized in that, The defect risk phase map is dynamically generated, and its coordinate dimensions include at least one feature-derived dimension calculated from the raw material feature dataset through a menthol crystallization digital twin model. The feature-derived dimension includes the crystal interface energy barrier or the competitive adsorption energy of impurities on a specific crystal face, which is calculated in real time. The crystal interface energy barrier is used to correct the risk level of lattice distortion defects in the defect risk phase diagram, so that the high-risk region corresponds to the process parameter region where the interface energy barrier exceeds the critical value.

5. The method for controlling menthol crystallization based on multi-stage gradient cooling as described in claim 1, characterized in that, Aiming to avoid high-risk areas in the defect risk phase map, path optimization is performed to generate a multi-level gradient cooling baseline path, including: In the defect risk phase diagram, the initial process state point and the final process state point of crystallization are defined; The areas in the defect risk phase diagram where the quality defect risk value exceeds a preset risk threshold are marked as high-risk areas to be avoided. An objective function is constructed using the avoidance distance from high-risk areas and the total length of the path as evaluation factors. Based on the objective function, in the process parameter coordinate space of the defect risk phase diagram, taking the initial process state point and the final process state point as the starting points, the optimal continuous cooling trajectory that does not pass through any high-risk areas is solved. The optimal continuous cooling trajectory is segmented and fitted to generate a cooling sequence consisting of a temperature plateau segment where the temperature remains constant and a temperature change rate segment where the temperature changes linearly, which serves as the reference path for the multi-level gradient cooling.

6. The method for controlling menthol crystallization based on multi-stage gradient cooling as described in claim 5, characterized in that, The multi-level gradient cooling baseline path includes at least one process segment that is inconsistent with conventional cooling logic and is used to traverse a specific low-risk region in the defect risk phase map to repair internal defects in the crystal. The process segment is a brief and controlled heating pulse segment inserted in the macro-cooling trend, which is configured to reduce the density of specific defects inside the crystal by utilizing the reversible local dissolution effect.

7. The method for controlling menthol crystallization based on multi-stage gradient cooling as described in claim 6, characterized in that, During the crystallization process, guided by the multi-level gradient cooling baseline path, the process status is monitored in real time. When the process status deviates from the expected value, real-time path replanning is performed based on the current status within the constraints of the defect risk phase diagram. This controls the crystallization process to execute along the dynamically updated path, including: In the defect risk phase diagram, a dynamic safety corridor with boundaries determined by the defect risk gradient is constructed along the multi-level gradient cooling reference path, wherein the multi-level gradient cooling reference path constitutes the central axis of the dynamic safety corridor. The process status is monitored in real time, and the process status is mapped onto the defect risk phase diagram to obtain real-time status points; Determine whether the real-time status point is located within the constraint boundary of the dynamic safety corridor; When the real-time state point exceeds the constraint boundary of the dynamic safety corridor, the real-time state point is taken as the starting point of the new path, and the end point of the multi-level gradient cooling reference path is taken as the updated target point. The path optimization is performed again within the constraint range of the defect risk phase map to generate a locally optimized path segment from the starting point of the new path to the updated target point. The locally optimized path segment is connected to the unexecuted portion of the multi-level gradient cooling baseline path to form the dynamically updated path; The dynamic update path must be located within a low-risk region in the risk value coordinate space of the defect risk phase map, and must be re-integrated into the central axis of the dynamic safety corridor.

8. The method for controlling menthol crystallization based on multi-stage gradient cooling as described in claim 7, characterized in that, The constraint boundary of the dynamic safety corridor is the dynamic safety boundary. Constructing the dynamic safety boundary includes: Based on the gradient change of the quality defect risk value in the defect risk phase diagram, the risk sensitivity of each point on the multi-level gradient cooling reference path is determined. Based on the risk sensitivity, different allowable deviation ranges are dynamically set for each point on the multi-level gradient cooling reference path, wherein points with high risk sensitivity correspond to narrower allowable deviation ranges, and points with low risk sensitivity correspond to wider allowable deviation ranges. The dynamic safety boundary is formed by the allowable deviation ranges at each point.

9. A menthol crystallization control system based on multi-stage gradient cooling, characterized in that, The step for implementing the menthol crystallization control method based on multi-stage gradient cooling according to any one of claims 1 to 8, wherein the menthol crystallization control system based on multi-stage gradient cooling comprises: The raw material analysis module is used to quickly analyze the menthol solution raw material of the current batch before the start of the crystallization batch to obtain the raw material characteristic dataset; The defect risk simulation module is used to input the raw material feature dataset into the menthol crystallization digital twin model, simulate and calculate the potential quality defect risks under different combinations of process parameters, and construct a defect risk phase map specific to the current batch based on the potential quality defect risks. The defect risk phase map uses process parameters as coordinates and defect risk values ​​as levels. The gradient cooling baseline path generation module is used to optimize the path by avoiding the high-risk areas in the defect risk phase map and generate a multi-level gradient cooling baseline path, which includes multiple temperature plateau segments and / or temperature change rate segments. The path replanning module is used to monitor the process status in real time during the crystallization process, guided by the multi-level gradient cooling baseline path. When the process status deviates from the expectation, it performs real-time path replanning based on the current status within the constraints of the defect risk phase diagram, and controls the crystallization process to execute along the dynamically updated path.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed, implements the steps of the menthol crystallization control method based on multi-level gradient cooling as described in any one of claims 1 to 8.

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