Nickel sulfate crystallization refining measurement and control method and system based on digital twinning

Abstract

The present application relates to the technical field of industrial process control, in particular to a nickel sulfate crystallization refining measurement and control method and system based on digital twinning; the method comprises the following steps: realizing data alignment through time lag compensation and disturbance correction, mapping process parameters to structural characteristic quantities based on the crystal growth mechanism, and constructing a crystal state tensor with physical consistency; identifying the crystallization phase according to different stages such as nucleation, competitive growth and stable growth, establishing a differential twinning model, introducing a continuous weight function to realize smooth transition, and combining state error for adaptive correction; constructing a multi-dimensional reliability evaluation system to quantize and grade the prediction results, and introducing safety constraint correction under low reliability state; taking the target crystal structure as the guide, solving the optimal control path through model inversion, and realizing accurate control by using reliability grading scheduling and closed-loop feedback adjustment. The present application effectively improves the stability and product quality consistency of the nickel sulfate crystallization process.

Description

Technical Field

[0001] This invention relates to the field of industrial process control technology, specifically to a method and system for measuring and controlling the crystallization and refining of nickel sulfate based on digital twins. Background Technology

[0002] In the hydrometallurgical refining of nickel sulfate, the crystallization stage has a decisive impact on the particle size, purity, and uniformity of the product, making it one of the key processes for ensuring the quality of new energy battery materials. During actual crystallization, multiple variables, such as temperature, supersaturation, pH value, stirring intensity, and particle size distribution, are collected by different sensors. These variables exhibit objective differences in sampling frequency, response speed, and dynamic behavior, requiring specialized handling to ensure the synchronization and dynamic consistency of process data over time. Furthermore, the crystallization process typically undergoes different evolutionary stages, including nucleation, competitive growth, and stable growth, each with different dominant mechanisms and variable sensitivities, making it difficult for a single model to accurately describe the system behavior throughout the entire process. Digital twin technology, by constructing virtual models to achieve real-time mapping and dynamic simulation of physical processes, provides a new technical path for the precise control of complex industrial processes.

[0003] Chinese invention patent application CN121745501A discloses a method and system for process decision-making and optimization of discrete manufacturing production lines based on digital twins. The main components include: constructing a high-fidelity digital twin model corresponding to the physical production line by combining mechanistic modeling and data-driven modeling; establishing a virtual-physical consistency evaluation index system to achieve deviation identification and dynamic consistency maintenance of the digital twin model; real-time sensing of production disturbances, equipment status changes, and process deviation information; constructing a multi-dimensional correlation model of "parts-process-equipment-quality"; and introducing an improved stochastic gradient descent algorithm to dynamically update and converge the parameters of the agent's policy network, thus constructing a self-evolving update mechanism for the knowledge base.

[0004] In the field of nickel sulfate crystallization and refining, how to transform multi-source process data into structural state expressions with physical semantics, how to adaptively adjust the model structure according to the crystallization stage, and how to introduce a reliability assessment mechanism into the model output are all key issues of current technological development. Therefore, building measurement and control methods and systems for nickel sulfate crystallization and refining based on digital twin technology has clear technical requirements and practical application value. Summary of the Invention

[0005] The purpose of this invention is to address the problems existing in the background technology by proposing a method and system for measuring and controlling the crystallization and refining of nickel sulfate based on digital twins.

[0006] The technical solution of this invention: a method for measuring and controlling the crystallization and refining of nickel sulfate based on digital twins, comprising the following specific implementation steps: S1. By performing dynamic consistency alignment of multi-source data, feature reconstruction driven by crystal growth mechanism, construction of state tensors under structural consistency constraints, and control-oriented evolvable expression, the transformation from raw process data to a crystal structure state space with physical meaning that can participate in control decision-making is completed. S2. Determine the current crystallization stage through multi-feature coupling, construct differentiated sub-models for different stages, introduce continuous weight functions to achieve smooth model transition, and construct an adaptive correction mechanism in combination with structural state error. S3. Perform quantitative analysis on the model output, identify the reliability of the current prediction by combining the hierarchical judgment mechanism, introduce a safety constraint correction strategy in the medium and low confidence state, and use the feedback relationship between confidence and prediction error to adaptively optimize the twin model. S4. The target crystal structure is transformed into a state-space constraint. The optimal control path is obtained by constructing the target deviation function and combining it with the digital twin model for inversion solution. A credibility-level scheduling mechanism is introduced for dynamic weighted correction, and the structural deviation gradient is used for closed-loop feedback adjustment.

[0007] Preferably, in step S1, the dynamic consistency alignment of multi-source data specifically includes: A dynamic perturbation consistency alignment method based on time lag compensation and rate of change is constructed. By performing time shift correction on the original data and introducing a perturbation compensation term, the dynamic behavior consistency of data from different sources at the same time is achieved.

[0008] Preferably, in step S1, the feature reconstruction driven by the crystal growth mechanism specifically includes: transforming the variables of temperature, supersaturation, and stirring intensity into nucleation activity index, crystal growth rate index, and particle size distribution discrete index through nonlinear mapping and multivariate coupling mechanism; The construction of the state tensor under structural consistency constraints specifically includes: constructing a crystal state tensor containing each structural feature quantity and its rate of change, introducing historical reference states and crystallization kinetic constraints, and performing consistency optimization on the state tensor so that each feature satisfies the physical coupling relationship during the crystal growth process.

[0009] Preferably, in step S2, determining the current crystallization stage through multi-feature coupling specifically includes: Based on the standardized crystal state tensor, multidimensional structural features reflecting nucleation activity, particle size growth trend and distribution changes are extracted. A multi-feature coupling decision function is constructed through a weighted competition mechanism to dynamically identify different growth stages, and the state variables are smoothed by combining a sliding time window.

[0010] Preferably, in step S2, constructing differentiated sub-models for different stages and achieving a smooth transition specifically includes: A nucleation-driven model is constructed for the nucleation stage, a competitive growth coupled model is constructed for the competitive growth stage, and a stable growth model is constructed for the stable growth stage. The crystal state tensor and control variables are used as inputs to each sub-model. By constructing a continuous coupling mechanism based on phase weights, the sub-models are combined according to dynamic weights, so that the model output remains smooth during the phase transition.

[0011] Preferably, in step S2, the adaptive correction mechanism constructed in conjunction with structural state errors specifically includes: An adaptive correction mechanism based on crystal structure state error is introduced. By comparing the deviation between the model-predicted state and the actual observed state in real time, an error feedback term is constructed to dynamically correct each phase sub-model. Differentiated correction gains are set according to different stages to suppress model drift.

[0012] Preferably, in step S3, constructing a multi-dimensional credibility assessment system specifically includes: A multi-dimensional credibility index system covering data consistency credibility, model matching credibility, and dynamic evolution rationality is constructed. The indicators of each dimension are calibrated and weighted and integrated to form a unified credibility index. A sliding window smoothing process is used to suppress short-term fluctuations and obtain prediction reliability evaluation results with physical meaning.

[0013] Preferably, in step S3, the classification determination and safety constraint correction specifically include: A hierarchical judgment mechanism is constructed based on the comprehensive credibility index, which maps continuous credibility to high credibility, medium credibility and low credibility states. Introduce constraint corrections in the medium-trust state and trigger protection mechanisms in the low-trust state; For medium-to-low confidence states, the twin prediction results are weighted and fused with the process safety boundary, and the predicted values ​​are converged to the safety range through dynamic weight adjustment.

[0014] Preferably, in step S4, the inversion solution and closed-loop feedback adjustment specifically include: Based on the target deviation function, the phase-driven digital twin model is used for inversion and solution. Control smoothness constraints and state change constraints are introduced, and constraint optimization is carried out in combination with the equipment operation boundary conditions. The rolling optimization strategy is used to gradually approach the optimal control path. After control is executed, the control variables are progressively updated and adjusted by acquiring the system state in real time and calculating the gradient information of the target deviation function, so that the system state continues to converge toward the target crystal structure.

[0015] The technical solution of this invention is a nickel sulfate crystallization refining measurement and control system based on digital twins, which is used to execute the aforementioned nickel sulfate crystallization refining measurement and control method based on digital twins, comprising: The structural state reconstruction and unified expression module is used to collect multi-source heterogeneous data to complete temporal alignment and perturbation compensation, further construct a crystal state tensor with physical consistency, and perform standardization and evolutionary expression processing on the state. The phase-driven digital twin modeling module is used to identify the growth phase of the current crystallization process based on the crystal state tensor, and to build differentiated twin models for different phases. By introducing a phase weight continuous coupling mechanism, a smooth transition between multiple models is achieved. At the same time, the model is adaptively corrected by combining the deviation between the real-time observation state and the model prediction results. The multidimensional credibility assessment and constraint module is used to quantify the prediction results of the digital twin model in multiple dimensions. It comprehensively considers the consistency of input data, the degree of model matching and the rationality of dynamic evolution, and makes a graded judgment based on the credibility level. On this basis, a dynamic fusion mechanism between the prediction results and the process safety boundary is constructed to constrain and correct the prediction state. The inversion control and adaptive execution module is used to construct a state deviation metric based on the target crystal structure parameters, and to solve the optimal control path in reverse based on the digital twin model, generating control commands for cooling rate, stirring intensity and feeding rhythm. At the same time, a credibility-driven control scheduling mechanism is introduced to adjust the control strategy with weights, and the control input is dynamically corrected in combination with the trend of structural deviation changes during execution.

[0016] Compared with the prior art, the above-mentioned technical solution of the present invention has the following beneficial technical effects: This invention designs a method and system for measuring and controlling nickel sulfate crystallization refining based on digital twins. First, by constructing a state reconstruction method centered on crystal structure, it effectively solves the inconsistencies in sampling frequency, response lag, and dynamic characteristics of multi-source sensor data. This transforms the original process data into a crystal state tensor with unified physical semantics and satisfying mechanistic constraints, providing a highly reliable and consistent input foundation for subsequent digital twin modeling, significantly improving data utilization efficiency and the accuracy of state representation. Second, the dynamic modeling method based on crystal growth phase can automatically match differentiated sub-models according to different stages such as nucleation, competitive growth, and stable growth. A continuous weighting function achieves smooth model transitions, avoiding prediction jumps and control oscillations caused by traditional hard switching methods. Combined with an adaptive correction mechanism... This allows the twin model to continuously approximate the real process, significantly enhancing its adaptability to changes in operating conditions and its long-term operational stability. Furthermore, the introduction of a multi-dimensional reliability assessment and hierarchical judgment mechanism enables the model output to have quantifiable reliability evaluation. Under low to medium reliability conditions, constraint correction is performed through safety boundary fusion, ensuring process safety without sacrificing control flexibility. Simultaneously, reliability feedback enables adaptive optimization of model parameters, forming a continuous learning capability. Finally, the inversion optimization control system guided by the target crystal structure transforms quality indicators into state-space constraints. Optimal control paths are generated through rolling optimization and reliability-level scheduling, and closed-loop feedback adjustment ensures that the crystallization process always converges around the target, thereby comprehensively improving the control accuracy, product quality consistency, and production safety of the nickel sulfate crystallization process. Attached Figure Description

[0017] Figure 1 This is a flowchart of a method for measuring and controlling the crystallization and refining of nickel sulfate based on digital twins, as proposed in this invention. Figure 2 This is a system architecture diagram of a nickel sulfate crystallization refining measurement and control system based on digital twin proposed in this invention. Detailed Implementation

[0018] Example 1, as Figure 1 As shown, the present invention proposes a method for measuring and controlling the crystallization and refining of nickel sulfate based on digital twins, which includes the following specific implementation steps: S1. Addressing the issues of "unstructured semantics, dynamic inconsistency, and difficulty in controllability of data" during nickel sulfate crystallization, a state reconstruction method centered on crystal structure is proposed. This method involves dynamic consistency alignment of multi-source data, feature reconstruction driven by crystal growth mechanisms, construction of state tensors under structural consistency constraints, and evolutionary representation oriented towards control. This transforms the original process data into a "crystal structure state space with physical meaning that can participate in control decisions," providing a unified, reliable, and mechanistically constrained input foundation for subsequent digital twin modeling. The specific implementation process is as follows: S11. To address the issues of sampling frequency differences and response lag in multi-source sensor data, a dynamic perturbation consistency alignment method based on time lag compensation and rate of change is constructed. By performing time shift correction on the original data and introducing a perturbation compensation term, data from different sources not only achieve time synchronization at the same moment but also possess dynamic behavioral consistency, thereby ensuring that the acquired data can truly reflect the same physical state. Specifically: In the actual nickel sulfate crystallization process, data such as temperature, concentration, pH value, and particle size are obtained from different types of sensors, which have significant differences in sampling frequency, response delay, and dynamic characteristics. For example, temperature sensors respond quickly, while particle size measurements usually have a significant lag. Therefore, a perturbation consistency correction mechanism is introduced to ensure that the variables are not only time-consistent at a unified time point, but also have consistent dynamic responses. The alignment and correction model is constructed as follows: ; in, This indicates that the i-th type of raw measurement data comes from field sensors (temperature probe, online pH meter, particle size analyzer, etc.). This represents the time lag parameter, obtained through equipment calibration experiments, such as determining it through a step response test. This represents the disturbance compensation function, derived from the statistical response characteristics of the variable to system fluctuations in historical operating data (such as the trend of the influence of temperature changes on supersaturation). This represents the state variables after unified time alignment and dynamic compensation; S12. Based on the completed data alignment, a structural feature mapping method oriented towards crystal growth mechanism is constructed. Process variables such as temperature, supersaturation, and stirring intensity are transformed into structural feature quantities such as nucleation activity and crystal growth trend through nonlinear mapping and multivariate coupling mechanism. This transforms the data from simple process parameters into state expressions with crystal growth semantics, thereby realizing the transformation from process space to structure space and improving the data's specificity in describing crystallization behavior. Specifically: Variables such as temperature, supersaturation, and stirring intensity are transformed into three core structural quantities through a nonlinear mapping function: nucleation activity index (reflecting the trend of new crystal formation), crystal growth rate index (reflecting the trend of crystal size expansion), and particle size distribution dispersion index (reflecting the system homogeneity). The mapping relationship is as follows: ; in, This represents the k-th crystal structure characteristic quantity; The weighting coefficient represents the degree of influence of the i-th variable on the k-th structural feature. It is obtained through regression of historical batch data or experimental calibration and reflects the degree of influence of different variables on crystal behavior. represents a nonlinear mapping function, such as an exponential or piecewise function, used to describe the nonlinear effect of variables on crystallization behavior (e.g., the exponential effect of supersaturation on nucleation rate); n represents the number of variables involved in the modeling. S13. Based on the obtained structural features, a crystal state tensor containing eigenvalues ​​and their rates of change is constructed. Historical reference states and crystallization kinetic constraints are introduced to optimize the consistency of the state tensor, ensuring that the physical coupling relationships between features satisfy the real crystal growth process. This avoids logical conflicts or physical distortions between features, thus forming a unified state representation structure that conforms to both data observation and mechanistic laws. Specifically: After obtaining multiple structural features, to avoid the isolated existence of features, a unified crystal state tensor is further constructed to describe the state of the crystallization system as a whole: ; To ensure that the variables in the tensor conform to the actual crystal growth mechanism, structural consistency constraints are introduced: ; in, The crystal state tensor represents the crystal structure state and its changing trends; m represents the number of structural features and the dimension characterizing the crystal behavior. The rate of change of the k-th structural feature represents the speed of crystal structure evolution. Perform numerical differentiation or filtering estimation; The reference state tensor represents the crystal state under ideal or stable operating conditions and is obtained from statistical data of historical high-quality production batches. Denotes the Frobenius norm; The structural consistency constraint function restricts the relationship between features to satisfy the crystal growth mechanism and is constructed based on physical laws or empirical rules. This represents the constraint weight coefficient, which controls the degree of influence of structural consistency constraints and is determined through experimental optimization. S14. After constructing the state tensor, by scaling it and introducing a dynamic evolution model involving control variables, the static state representation is transformed into a dynamic state space that evolves over time. This allows the crystal structure state to not only describe the current process but also reflect future evolution trends, and can be directly used as input to the digital twin model and control strategy, achieving effective integration between the state representation and the control system. Specifically: After constructing the state tensor, to facilitate subsequent digital twin modeling, it needs to be transformed into an expression with a uniform scale and dynamic evolution capability. The first step is standardization: ; Then, the state evolution relationship is constructed: ; in, Represents the standardized state tensor; denoted as the mean vector, i.e., the average level of historical states; D represents the scale matrix, which characterizes the fluctuation range of each variable (usually a standard deviation matrix), calculated from the variance of historical data; It represents the state evolution function, describing the dynamic law of crystal state change with control variables, and is used for data-driven modeling or mechanism modeling. This represents the control input vector, which is the operational variable that actually regulates the crystallization process.

[0019] S2. Based on the crystal state tensor constructed in step S1, a digital twin dynamic modeling method driven by the crystal growth phase is proposed. This method determines the current crystallization stage through multi-feature coupling and constructs differentiated sub-models for different stages. A continuous weighting function is introduced to achieve smooth model transitions, avoiding the instability issues caused by traditional model switching. Furthermore, an adaptive correction mechanism is constructed by combining structural state errors, enabling the model to continuously approximate the real process as the operating conditions change. This forms a closed-loop modeling system of "state recognition - model matching - continuous coupling - dynamic correction," achieving high-precision dynamic characterization of the nickel sulfate crystallization process. The specific implementation process is as follows: S21. Based on the standardized crystal state tensor output in step S1, extract multi-dimensional structural features reflecting nucleation activity, grain size growth trend, and distribution changes. Construct a multi-feature coupled judgment function through a weighted competition mechanism to dynamically identify different growth stages. Combine this with a sliding time window to smooth the state variables, avoiding misjudgments caused by short-term disturbances. Specifically: In the actual nickel sulfate crystallization process, the formation and growth of crystals is not a uniform process, but rather follows an evolutionary path from nucleation-dominated growth to competitive growth to stable growth. The weights of variables such as temperature, supersaturation, and particle size distribution differ significantly at different stages. Based on the structural state tensor output in step S1, a phase recognition mechanism with multi-feature coupling is constructed, and the phase determination is expressed as follows: ; in, This indicates the growth phase category of the current crystallization process; j represents the phase number (1 for nucleation stage, 2 for competitive growth stage, and 3 for stable growth stage). This represents the phase sensitivity coefficient, which indicates the importance of the k-th feature in the j-th stage. It should be noted that, Segmented statistical analysis derived from historical batch data, for example: in the nucleation stage, the weight of supersaturation-related features is relatively high; in the growth stage, the weight of features related to particle size growth rate is even greater. S22. After completing the growth phase identification, differentiated twin models are established for different crystallization stages. The crystal state tensor and control variables are used as inputs to construct nucleation-driven models, competitive growth coupling models, and stable growth models, respectively, so that the dominant mechanisms of each stage are fully reflected. The model structure and parameters are determined by combining historical data with mechanism analysis, ensuring that the model conforms to actual process laws and has good generalization ability. Specifically: After obtaining the current phase, differentiated sub-models are established for different phases to fully express the dominant mechanism of each stage. The phase-driven model (sub-model) is constructed as follows: ; in, It represents the state evolution function corresponding to the current phase, and the differentiated mechanism model designed for different growth stages describes the law of crystal state evolution over time, which may include factors such as dynamics, thermodynamics, and fluid disturbance; This indicates the control input variables, including cooling rate, stirring intensity, and feed rate; It should be noted that, in the specific implementation, the structural differences between the different sub-models are reflected in: Nucleation stage model: Emphasizes oversaturation driving term and perturbation amplification effect; Competitive growth stage model: Introducing a particle size distribution coupling term to consider inter-crystal resource competition; Stable growth phase model: focuses on the balance between diffusion and heat transfer, and the model response tends to be stable; S23. To address the potential discontinuity issues during phase model switching, a continuous coupling mechanism based on phase weights is constructed. By weighting and combining each sub-model according to dynamic weights, the model output maintains a smooth change during phase transitions. Simultaneously, a weight function is constructed using state features, allowing the weights to continuously evolve with the crystallization process. This ensures the model maintains good stability and continuity under complex conditions. Specifically: Since the stage transitions in actual crystallization are not abrupt but gradual, directly switching sub-models may lead to prediction jumps or control oscillations. Therefore, a phase-weighted continuous coupling mechanism is introduced to output the models of different stages according to their weights, achieving a smooth transition. The smooth coupling expression is as follows: ; in, This represents the model weight coefficient for the j-th stage, calculated based on the phase determination and smoothing function in step S21. This represents the sub-model corresponding to the j-th stage, which corresponds to the differentiated mechanism models of nucleation, competitive growth, and stable growth. It is used to predict the crystal state by weighted combination in the continuous coupling mechanism. S24. During model operation, an adaptive correction mechanism based on crystal structure state error is introduced. By comparing the deviation between the model's predicted state and the actual observed state in real time, an error feedback term is constructed to dynamically correct each phase sub-model. Differentiated correction gains are set according to different stages, enabling the model to make targeted adjustments for different operating conditions. This effectively suppresses model drift and improves the long-term stability and accuracy of the twin model in actual production environments. Specifically: An adaptive correction based on crystal structure state error is introduced to enable the model to be corrected in real time and maintain prediction accuracy. The correction formula is as follows: ; in, This indicates the corrected sub-model, obtained through error feedback correction, which corrects for deviations in actual observation data, thereby improving prediction accuracy and system stability; It represents the actual observed crystal state, and the data is collected in real time by the process site or sensors; This represents the crystal state predicted by the model, output by the current twin model; The phase-correlation correction gain matrix can be determined by fitting historical data or online identification. It should be noted that the correction mechanism can automatically adjust the gain range according to the magnitude of the deviation, avoiding over-correction that could cause system instability. It keeps the model aligned with the actual process, ensuring the reliability of prediction and control, while also being able to cope with process disturbances and raw material differences.

[0020] S3. Based on the phase-driven digital twin prediction results obtained in step S2, a multi-dimensional credibility assessment system is constructed to quantitatively analyze the model output. A hierarchical judgment mechanism is then used to identify the reliability of the current prediction. Furthermore, a safety constraint correction strategy is introduced under low to medium credibility conditions, dynamically fusing the prediction results with the process safety boundary. Simultaneously, the feedback relationship between credibility and prediction error is used to adaptively optimize the twin model, thus forming a closed-loop mechanism of "evaluation-judgment-correction-optimization." The specific implementation process is as follows: S31. By constructing a multi-dimensional credibility index system covering data consistency, model matching degree, and dynamic evolution rationality, the output of the twin model is comprehensively and quantitatively evaluated. Historical operating data is used to calibrate and weight the indicators of each dimension, forming a unified credibility index. Simultaneously, a sliding window smoothing process is employed to suppress short-term fluctuations, thereby obtaining stable and physically meaningful prediction reliability evaluation results. Specifically: In real-world applications, a single error index is insufficient to fully reflect model reliability. Therefore, a multi-dimensional reliability system is constructed from three dimensions: data layer, model layer, and evolution layer. This ensures that reliability evaluation has both comprehensiveness and physical interpretability. The comprehensive reliability definition is as follows: ; in, This represents the overall credibility index, also known as the unified credibility index, which is used to comprehensively evaluate the reliability of the model's current output. It indicates the reliability of data consistency and reflects whether the current input state is within the historical experience space; This indicates the model matching confidence level, reflecting the degree to which the twin model's predictions match actual observations; It indicates the reliability of dynamic evolution and reflects whether the predicted trend of change conforms to the crystal growth law; , and This represents the weighting coefficient, which can be adjusted according to the importance of the process. It should be noted that in the engineering implementation: It can be obtained by comparing the current state tensor with the historical sample library (such as distance metric or cluster center deviation), and is used to determine whether it is in a "known working condition"; It can be calculated from the deviation statistics between the predicted value and the real-time observed value in step S2 (such as the normalized form of the mean square error); This is indicated by comparing the current predicted trend with the evolution trajectory of historical stable operating conditions; S32. A graded judgment mechanism is constructed based on a comprehensive credibility index, mapping continuous credibility to different risk levels and establishing a correspondence between credibility levels and control strategies. In a high-credibility state, the model is allowed to directly participate in control; in a medium-credibility state, constraint correction is introduced; and in a low-credibility state, a protection mechanism is triggered, thereby achieving effective connection between prediction results and industrial control decisions. Specifically: After obtaining the continuous credibility index, in order to make it directly serve control decisions, it needs to be discretized into different risk levels, and a mapping relationship of "credibility-risk-control strategy" needs to be established. The hierarchical function is constructed as follows: ; in, represents a credibility level, level 3 represents a high credibility state, level 2 represents a medium credibility state, and level 1 represents a low credibility state; In the high credibility state, the system allows the twin model prediction to directly participate in control decision-making; In the medium credibility state, a constraint correction mechanism needs to be introduced to avoid amplification of prediction deviation; In the low credibility state, the system triggers a protection mechanism, such as limiting the control amplitude or maintaining stable operation of the current working condition; In addition, the threshold can be adaptively optimized in combination with historical production data, so that the classification mechanism is more suitable for the actual production environment; S33, for medium and low credibility states, a credibility-driven constraint correction mechanism is introduced, which performs weighted fusion on the twin prediction result and the process safety boundary, realizes the convergence of the predicted value to the safe range through dynamic weight adjustment, and sets differentiated constraint strategies according to different state variables, so as to effectively reduce process risk without sacrificing control flexibility and achieve the balance between safety and performance, specifically: Under medium and low credibility conditions, in order to prevent process abnormality caused by model error, it is necessary to perform constraint correction on the prediction result to keep it always within a safe and controllable range, and construct a constraint correction model as follows: ; wherein, represents the corrected safety state; represents the prediction state of the twin model; represents the process safety boundary state, which is determined by experimental data or process specifications; represents the weight function mapped from credibility; It should be noted that in practical engineering: may include key indicators such as the upper limit of crystal particle size and the safe range of supersaturation; can adopt a smooth function (such as Sigmoid) to achieve continuous change and avoid mutation; when the credibility decreases, the system gradually increases the dependence on the safety boundary, thereby reducing the risk; In addition, differentiated constraint weights can be set for different state variables, for example, the constraint on supersaturation is stricter, while a certain fluctuation is allowed for particle size distribution; S34, using the relationship between credibility and prediction error in historical operation data to perform adaptive optimization on the parameters of the twin model, and by constructing a model update mechanism based on credibility feedback, the model increases the adjustment intensity in low credibility areas and remains stable in high credibility areas, thereby gradually improving the adaptability of the model to complex working conditions and realizing continuous learning and performance optimization of the digital twin system, specifically: To achieve long-term stable operation, the relationship between reliability and prediction error is used to continuously optimize the twin model, enabling it to gradually adapt to different operating conditions, and a model update mechanism is constructed: ; in, This represents the updated sub-model; Indicates the target credibility threshold; This represents the learning rate parameter, used to control the update magnitude; It should be noted that in actual implementation: when the confidence level is low and the error is large, the model adjustment range is increased; when the confidence level is high, only fine-tuning is performed to avoid overfitting; a database of "historical operating conditions-confidence level-model parameters" can be established to achieve cross-batch optimization.

[0021] S4. Based on the safety status and reliability level output in step S3, the target crystal structure is transformed into a state-space constraint. By constructing a target deviation function and combining it with a digital twin model for inversion solution, the optimal control path is obtained. A reliability-based hierarchical scheduling mechanism is introduced during control execution to dynamically weight and correct the control strategy. Simultaneously, the structural deviation gradient is used for closed-loop feedback adjustment, ensuring that the control process always converges around the target crystal structure. This achieves an integrated closed-loop control system of "target-driven - model inversion - risk constraint - dynamic execution," significantly improving the stability, controllability, and product quality consistency of the nickel sulfate crystallization process. The specific implementation process is as follows: S41. By mapping multi-dimensional quality indicators such as crystal grain size, distribution uniformity, and impurity control to a target crystal structure tensor, and comparing it with the safety status output in step S3, an overall deviation function is constructed. Simultaneously, the target status is calibrated using historical high-quality batch data or product standards, and the importance of key quality indicators is highlighted through a weighted approach. Specifically: In actual nickel sulfate crystallization production, product quality is usually not determined by a single indicator, but rather by multiple structural indicators, such as average crystal size, particle size distribution width, particle uniformity, and the degree of impurity entrainment. First, these quality indicators are mapped uniformly into a target expression in state space, constructing a target deviation function: ; in, The target crystal structure tensor is represented by its components, which correspond to indicators such as target particle size, distribution dispersion, and nucleation density. In engineering practice, these can be extracted through statistical analysis of historical high-quality batch data or deduced from product specifications. This represents the overall deviation between the current state and the target structure; S42. Based on the target deviation function, the phase-driven digital twin model constructed in step S2 is used for inversion solution, transforming the target crystal structure into the optimal combination of control variables. By introducing control smoothing constraints and state change constraints, abrupt changes in control variables and system oscillations are avoided. Constraint optimization is performed in conjunction with equipment operating boundary conditions. At the same time, a rolling optimization strategy is adopted to gradually approach the optimal control path, making the control decision both forward-looking and stable. This realizes an optimized control mechanism that inversely derives process parameters from the target structure. Specifically: After obtaining the target deviation, the digital twin model constructed in step S2 is used for inverse solving, that is, the optimal control variable change path is derived based on the target deviation, and an inverse optimization model is constructed: ; in, This represents the optimal control input, including but not limited to: cooling rate, stirring frequency, and feed rate; This represents the control smoothing weight, used to limit abrupt changes in the control variable; This represents the constraint weight for state changes, used to avoid drastic state fluctuations; Indicates the change in state; It should be noted that this optimization problem can be solved step by step in the rolling time domain to approximate the optimal path; the control variables must satisfy the physical constraints of the equipment (such as maximum cooling rate and maximum stirring power); if the reliability of the output of step S3 is low, it can be dynamically increased. This makes control more conservative; S43. Introduce the confidence level output from step S3 into the control execution stage. By constructing a confidence-based weight function, dynamically fuse the optimal control quantity obtained from the inversion with the safety reference control. When the confidence level is high, the optimal control is executed first; when the confidence level decreases, the safety control weight is gradually increased. Differentiated weights and buffer mechanisms can be set for different control variables, thereby enabling the control strategy to adaptively adjust with the model reliability, ensuring the stability and safety of the system under complex operating conditions. Specifically: Based on the confidence level provided in step S3, confidence is further incorporated into the control execution process to enable the control strategy to have risk adaptive capabilities; the control fusion model is constructed as follows: ; in, This indicates the final execution control signal; Indicates the reference control value (empirical or safety control curve); This represents the weighting coefficient obtained by mapping from the credibility level; It should be noted that in practical applications: when the system is in a high confidence state, the optimization control is executed first; when the confidence decreases, the weight of the reference control is gradually increased to reduce the risk; different weights can be set for different control variables, for example, more conservative for temperature control and more flexible for stirring control. S44. After control execution, by acquiring the system state in real time and calculating the gradient information of the target deviation function, the control variables are progressively updated and adjusted to ensure that the system state continuously converges towards the target crystal structure. Simultaneously, combining the predictive capability of step S2 and the reliability constraint of step S3, the adjustment range is limited to avoid over-adjustment leading to system oscillation. Furthermore, by accumulating historical control trajectories to optimize control parameters, a closed-loop control process of "execution-feedback-correction-re-optimization" is achieved, thereby ensuring the long-term stable operation of the crystallization process. Specifically: After control is executed, the system status needs to be continuously monitored and dynamically adjusted according to the target deviation to form a closed-loop control system; the closed-loop update mechanism is constructed as follows: ; in, This indicates that the gain is adjusted to control the update speed; The gradient of the deviation function represents the direction of state deviation. It should be noted that if the particle size is too large, the cooling rate should be gradually reduced or the stirring intensity should be increased; if the distribution is uneven, the feeding rhythm or disturbance conditions should be adjusted; the control adjustment should be updated gradually to avoid system oscillation.

[0022] Example 2, as Figure 2 As shown, the present invention proposes a nickel sulfate crystallization refining measurement and control system based on digital twin, which is used to execute a nickel sulfate crystallization refining measurement and control method based on digital twin proposed in Example 1. It includes: a structural state reconstruction and unified expression module, a phase-driven digital twin modeling module, a multi-dimensional credibility assessment and constraint module, and an inversion control and adaptive execution module.

[0023] The structural state reconstruction and unified expression module is used to uniformly collect, time-series align, and dynamically compensate for multi-source heterogeneous data during the crystallization process. It transforms the original process variables such as temperature, supersaturation, pH value, particle size distribution, and stirring intensity into structural feature quantities with crystal growth semantics. Furthermore, it constructs a crystal state tensor with physical consistency to achieve a unified mapping from the process variable space to the crystal structure space. At the same time, it performs standardization and evolutionary expression processing on the state to provide a stable and physically meaningful input basis for subsequent modeling. The phase-driven digital twin modeling module is used to identify the growth phase of the current crystallization process based on the crystal state tensor, and to build differentiated twin models for different phases. By introducing a phase weight continuous coupling mechanism, a smooth transition between multiple models is achieved. At the same time, the model is adaptively corrected by combining the deviation between the real-time observation state and the model prediction results, so that the digital twin model can dynamically evolve with the crystallization process and maintain a high degree of consistency with the real working conditions. The multidimensional credibility assessment and constraint module is used to quantify the prediction results of the digital twin model in multiple dimensions. It comprehensively considers the consistency of input data, the degree of model matching and the rationality of dynamic evolution, and classifies the results according to the level of credibility. On this basis, a dynamic fusion mechanism between the prediction results and the process safety boundary is constructed to constrain and correct the prediction state, ensuring that the model output is within a safe and controllable range under different operating conditions. At the same time, the feedback relationship between credibility and prediction error is used to continuously optimize the twin model parameters, thereby improving the long-term stability of the system under complex operating conditions. The inversion control and adaptive execution module is used to construct a state deviation metric based on the target crystal structure parameters, and to solve the optimal control path in reverse based on the digital twin model, generating control commands such as cooling rate, stirring intensity, and feeding rhythm. At the same time, a reliability-driven control scheduling mechanism is introduced to adjust the control strategy with weights. During the execution process, the control input is dynamically corrected based on the trend of structural deviation changes, forming a closed-loop control process guided by the crystal structure, thereby achieving stable regulation of the nickel sulfate crystallization refining process and precise control of product quality.

[0024] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited thereto. Various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of the present invention.

Claims

1. A method for measuring and controlling the crystallization and refining of nickel sulfate based on digital twins, characterized in that, The specific implementation steps include the following: S1. By performing dynamic consistency alignment of multi-source data, feature reconstruction driven by crystal growth mechanism, construction of state tensors under structural consistency constraints, and control-oriented evolvable expression, the transformation from raw process data to a crystal structure state space with physical meaning that can participate in control decision-making is completed. S2. Determine the current crystallization stage through multi-feature coupling, construct differentiated sub-models for different stages, introduce continuous weight functions to achieve smooth model transition, and construct an adaptive correction mechanism in combination with structural state error. S3. Perform quantitative analysis on the model output, identify the reliability of the current prediction by combining the hierarchical judgment mechanism, introduce a safety constraint correction strategy in the medium and low confidence state, and use the feedback relationship between confidence and prediction error to adaptively optimize the twin model. S4. The target crystal structure is transformed into a state-space constraint. The optimal control path is obtained by constructing the target deviation function and combining it with the digital twin model for inversion solution. A credibility-level scheduling mechanism is introduced for dynamic weighted correction, and the structural deviation gradient is used for closed-loop feedback adjustment.

2. The method for measuring and controlling the crystallization and refining of nickel sulfate based on digital twins according to claim 1, characterized in that, Step S1, which involves dynamic consistency alignment of multi-source data, specifically includes: A dynamic perturbation consistency alignment method based on time lag compensation and rate of change is constructed. By performing time shift correction on the original data and introducing a perturbation compensation term, the dynamic behavior consistency of data from different sources at the same time is achieved.

3. The method for measuring and controlling the crystallization and refining of nickel sulfate based on digital twins according to claim 2, characterized in that, In step S1, the feature reconstruction driven by the crystal growth mechanism specifically includes: transforming the variables of temperature, supersaturation, and stirring intensity into nucleation activity index, crystal growth rate index, and particle size distribution discrete index through nonlinear mapping and multivariate coupling mechanism; The construction of the state tensor under structural consistency constraints specifically includes: constructing a crystal state tensor containing each structural feature quantity and its rate of change, introducing historical reference states and crystallization kinetic constraints, and performing consistency optimization on the state tensor so that each feature satisfies the physical coupling relationship during the crystal growth process.

4. The method for measuring and controlling the crystallization and refining of nickel sulfate based on digital twins according to claim 3, characterized in that, In step S2, determining the current crystallization stage through multi-feature coupling specifically includes: Based on the standardized crystal state tensor, multidimensional structural features reflecting nucleation activity, particle size growth trend and distribution changes are extracted. A multi-feature coupling decision function is constructed through a weighted competition mechanism to dynamically identify different growth stages, and the state variables are smoothed by combining a sliding time window.

5. The method for measuring and controlling the crystallization and refining of nickel sulfate based on digital twins according to claim 4, characterized in that, Step S2, which involves constructing differentiated sub-models for different stages and achieving a smooth transition, specifically includes: A nucleation-driven model is constructed for the nucleation stage, a competitive growth coupled model is constructed for the competitive growth stage, and a stable growth model is constructed for the stable growth stage. The crystal state tensor and control variables are used as inputs to each sub-model. By constructing a continuous coupling mechanism based on phase weights, the sub-models are combined according to dynamic weights, so that the model output remains smooth during the phase transition.

6. The method for measuring and controlling the crystallization and refining of nickel sulfate based on digital twins according to claim 5, characterized in that, In step S2, the adaptive correction mechanism constructed in conjunction with structural state errors specifically includes: An adaptive correction mechanism based on crystal structure state error is introduced. By comparing the deviation between the model-predicted state and the actual observed state in real time, an error feedback term is constructed to dynamically correct each phase sub-model. Differentiated correction gains are set according to different stages to suppress model drift.

7. The method for measuring and controlling the crystallization and refining of nickel sulfate based on digital twins according to claim 6, characterized in that, Step S3, constructing a multi-dimensional credibility assessment system specifically includes: A multi-dimensional credibility index system covering data consistency credibility, model matching credibility, and dynamic evolution rationality is constructed. The indicators of each dimension are calibrated and weighted and integrated to form a unified credibility index. A sliding window smoothing process is used to suppress short-term fluctuations and obtain prediction reliability evaluation results with physical meaning.

8. The method for measuring and controlling the crystallization and refining of nickel sulfate based on digital twins according to claim 7, characterized in that, In step S3, the classification determination and safety constraint correction specifically include: A hierarchical judgment mechanism is constructed based on the comprehensive credibility index, which maps continuous credibility to high credibility, medium credibility and low credibility states. Introduce constraint corrections in the medium-trust state and trigger protection mechanisms in the low-trust state; For medium-to-low confidence states, the twin prediction results are weighted and fused with the process safety boundary, and the predicted values ​​are converged to the safety range through dynamic weight adjustment.

9. The method for measuring and controlling the crystallization and refining of nickel sulfate based on digital twins according to claim 8, characterized in that, In step S4, the inversion solution and closed-loop feedback adjustment specifically include: Based on the target deviation function, the phase-driven digital twin model is used for inversion and solution. Control smoothness constraints and state change constraints are introduced, and constraint optimization is carried out in combination with the equipment operation boundary conditions. The rolling optimization strategy is used to gradually approach the optimal control path. After control is executed, the control variables are progressively updated and adjusted by acquiring the system state in real time and calculating the gradient information of the target deviation function, so that the system state continues to converge toward the target crystal structure.

10. A digital twin-based nickel sulfate crystallization refining measurement and control system, used to execute the digital twin-based nickel sulfate crystallization refining measurement and control method according to any one of claims 1 to 9, characterized in that, include: The structural state reconstruction and unified expression module is used to collect multi-source heterogeneous data to complete temporal alignment and perturbation compensation, further construct a crystal state tensor with physical consistency, and perform standardization and evolutionary expression processing on the state. The phase-driven digital twin modeling module is used to identify the growth phase of the current crystallization process based on the crystal state tensor, and to build differentiated twin models for different phases. By introducing a phase weight continuous coupling mechanism, a smooth transition between multiple models is achieved. At the same time, the model is adaptively corrected by combining the deviation between the real-time observation state and the model prediction results. The multidimensional credibility assessment and constraint module is used to quantify the prediction results of the digital twin model in multiple dimensions. It comprehensively considers the consistency of input data, the degree of model matching and the rationality of dynamic evolution, and makes a graded judgment based on the credibility level. On this basis, a dynamic fusion mechanism between the prediction results and the process safety boundary is constructed to constrain and correct the prediction state. The inversion control and adaptive execution module is used to construct a state deviation metric based on the target crystal structure parameters, and to solve the optimal control path in reverse based on the digital twin model, generating control commands for cooling rate, stirring intensity and feeding rhythm. At the same time, a credibility-driven control scheduling mechanism is introduced to adjust the control strategy with weights, and the control input is dynamically corrected in combination with the trend of structural deviation changes during execution.

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