A thermal process precise regulation system based on thermal inertia and digital twinning

Abstract

The application relates to the field of industrial automation and control technology, and discloses a thermal process precise regulation and control system based on thermal inertia and digital twinning to solve the regulation and control lag problem caused by the thermal inertia and delay coupling of a thermal process system. The system uses a physical mechanism residual penalty to construct a digital twinning prediction base, avoids divergence caused by pure data driving, combines room temperature and surface temperature of a thermal capacity element double-channel observation, uses an unscented Kalman filter to track and identify thermal resistance and capacity parameter drift, simultaneously constructs a state space Smith predictor to peel off pipe network delay, and makes a model predictive control solver only perform rolling optimization on thermal inertia, and outputs optimal thermal input power. The application effectively eliminates the prediction deviation caused by parameter drift, and significantly reduces comprehensive operation energy consumption under the premise of meeting thermal comfort.

Description

Technical Field

[0001] This invention relates to the field of industrial automation and control technology, and in particular to a precise thermal process control system based on thermal inertia and digital twins. Background Technology

[0002] In various fields of modern industrial manufacturing, energy conversion, and process engineering, precise temperature control of thermal processes directly determines product quality, equipment safety, and operational efficiency. Typical applications include temperature regulation of continuous stirred reactors in chemical processes, coordinated control of multi-stage heating zones in polymer extrusion molding processes, liquid-cooled or air-cooled heat dissipation management in large data centers, thermal state maintenance during the charging and discharging of new energy power batteries, and user-side temperature response in regional centralized energy supply systems. These thermal process systems generally exhibit two coupled dynamic hysteresis characteristics in their physical structure: First, the controlled medium (such as reactants, coolants, and heat storage media) or the equipment itself (such as molds, battery stacks, and heat storage walls) has a large heat capacity. This heat capacity leads to a significant inertial hysteresis in the heat accumulation and release process, meaning that any change in input heat power cannot instantly trigger a response at the controlled temperature point. Second, heat transfer between the heat source and the controlled object is typically achieved through pipelines, pumping loops, or forced convection channels, introducing a non-negligible pure time delay in the physical migration of heat from the generation end to the action end. The two hysteresis effects mentioned above, which are completely different in physical mechanism, superimpose on each other in the control channel, making the controlled object as a whole behave as a non-minimum phase system with "large inertia plus pure delay".

[0003] Currently, for thermal process systems with this type of compound hysteresis characteristic, the control strategies widely used in industrial settings are still dominated by proportional-integral-derivative (PID) controllers and their improved versions (such as cascade control and feedforward compensation). The fundamental limitation of this passive control method based on error feedback lies in its reactive nature: the controller only begins calculating correction actions after the sensor detects a deviation of the controlled temperature from the setpoint, lacking a forward-looking understanding of the evolution trend of disturbance signals (such as sudden drops in ambient temperature, fluctuations in material feed temperature, and step changes in load) over future periods. When the system's pure time delay constant and thermal inertia time constant are of the same order of magnitude, or even the latter is greater than the former, the deviation information carried by the feedback signal is significantly lagging behind the actual occurrence of the disturbance. The correction output calculated by the controller based on this often overcompensates or compensates in the opposite direction, leading to continuous oscillations or significant overshoot of the controlled temperature, and even causing instability of the closed-loop system under extreme conditions. To ensure process safety and avoid triggering low or high temperature alarm limits, field engineers are often forced to adopt conservative setpoint bias strategies (such as continuously increasing the cooling medium flow rate or increasing the preset heating power value), which leads to excessive energy input, resulting in significant resource waste and equipment fatigue.

[0004] To fundamentally overcome the inherent hysteresis of passive feedback control, Model Predictive Control (MPC) based on digital twin architecture has been gradually introduced into the field of thermal process regulation in recent years. Its core idea lies in using the system's dynamic mathematical model to predict the future state trajectory within a finite time domain online, and then solving for the optimal control action at the current moment through rolling optimization. However, in practical engineering applications, constructing a predictive model that meets the accuracy requirements of MPC while also possessing real-time computational capabilities faces a fundamental contradiction. On the one hand, white-box mechanism models built on first principles (such as Fourier's law of thermal conduction and the energy conservation equation for convective heat transfer) strictly follow the laws of thermodynamics and can accurately describe the spatiotemporal evolution of heat transfer and accumulation. However, they are usually presented in the form of partial differential equations or higher-order state-space equations. The computational load required for online solutions far exceeds the real-time processing capabilities of current edge computing units or embedded controllers, making it difficult to deploy them in millisecond- or second-level fast control loops. More seriously, the key thermophysical parameters of the controlled object (such as the equivalent specific heat capacity of the medium, the fouling thermal resistance of the heat exchange wall, the aging coefficient of the insulation layer, and the random fluctuation of the contact thermal resistance) will undergo irreversible slow drift during continuous operation due to factors such as material adhesion, oxidation corrosion, environmental humidity migration, and mechanical wear. Once a mechanism model with fixed parameters is put into operation, its later output will produce a systematic deviation from the actual behavior of the physical entity due to parameter mismatch, and the model prediction accuracy will deteriorate sharply over time. On the other hand, black-box data-driven models that rely purely on historical operating data (such as deep learning architectures like Long Short-Term Memory Networks and Gated Recurrent Units) have extremely fast inference speeds and can meet the time constraints of real-time control. However, their predictive behavior is highly limited by the statistical distribution range of the training samples. Essentially, they are an interpolation approximation rather than a physical extrapolation. When the system encounters sudden disturbance modes or operating condition combinations that have not appeared in the training set (such as extreme ambient temperatures or atypical load changes), the predicted trajectories output by such models not only cannot guarantee accuracy but may also significantly violate the basic physical constraint of heat conservation. Predictive divergence and collapse may occur in the state space without physical boundary constraints, causing the MPC optimizer to calculate dangerous control commands based on erroneous prediction information.

[0005] In summary, existing thermal process control technologies lack both a digital twin modeling method capable of adaptively tracking physical parameter drift throughout the entire lifecycle and a control architecture that can structurally decouple pure transmission delay from thermal inertial hysteresis, thereby fully leveraging the forward-looking optimization potential of MPC. Therefore, it is essential to develop a general-purpose, precise thermal process control scheme that combines physical fidelity, online adaptability, and delay decoupling capabilities. Summary of the Invention

[0006] To address the lag issues in existing thermal process system feedback control technologies caused by large heat capacity and transmission pipelines, as well as the irreconcilable contradiction between physical fidelity and computational real-time performance in existing prediction models, the present invention aims to provide a precise thermal process control system based on thermal inertia and digital twins. This system overcomes the control lag problem caused by large thermal inertia and pure delay coupling, and achieves forward-looking and high-precision heating scheduling.

[0007] To achieve the above objectives, the present invention provides the following technical solution: This invention provides a precise thermal process control system based on thermal inertia and digital twins, comprising: The multi-source heterogeneous data sensing and edge fusion module is used to collect the operating state of the thermal process system and output the external measurable disturbance input vector, the system control input vector, and the system state observation feedback vector. The system state observation feedback vector includes the temperature of the controlled area and the surface temperature of the heat capacity element. The digital twin construction module based on the physical information neural network is communicatively connected to the multi-source heterogeneous data perception and edge fusion module. It is used to construct a multi-order equivalent resistance-capacitance thermodynamic network equation for the control region and to construct a composite loss function to train the physical information neural network. The composite loss function includes the physical mechanism residual loss derived from the multi-order equivalent resistance-capacitance thermodynamic network equation. The online identification module for thermal inertia dynamic parameters based on unscented Kalman filtering is communicatively connected to the multi-source heterogeneous data sensing and edge fusion module and the digital twin construction module. It is used to jointly construct an augmented state vector from the physical parameters and state variables in the multi-order equivalent resistive-capacitive thermodynamic network equation. It uses the unscented Kalman filtering algorithm and the dual-channel observation information of the controlled area temperature and the surface temperature of the thermal capacity element for online recursive correction, and updates the state transition matrix and input matrix of the multi-order equivalent resistive-capacitive thermodynamic network equation in real time. The optimization module based on Smith prediction compensation and model predictive control is communicatively connected to the online identification module of thermal inertia dynamic parameters. It is used to construct a state-space Smith predictor to remove the pure time delay introduced by pipeline medium transmission from the system feedback loop and obtain the corrected state vector. Using the corrected state vector as the initial state condition, the model predictive control solver is used to perform multi-objective rolling optimization and output the optimal thermal input power control sequence. The edge collaborative control sequence execution and physical mapping module is communicatively connected to the optimization module based on Smith prediction compensation and model predictive control. It is used to extract the optimal thermal input power at the current moment of the optimal thermal input power control sequence and inversely map it into the physical drive signal of the underlying actuator.

[0008] As a preferred embodiment of the present invention, the externally measurable disturbance input vector output by the multi-source heterogeneous data sensing and edge fusion module includes ambient temperature, radiant heat source intensity, and internal disturbance heat; the system control input vector represents the actual heat input power delivered to the target hot zone. It collects water supply temperature Return water temperature and instantaneous mass flow rate The following calculations were performed using the heat balance conversion formula: ; in, This refers to the specific heat capacity at constant pressure of the heating medium.

[0009] As a preferred embodiment of the present invention, the multi-order equivalent resistance-capacitance thermodynamic network equation constructed by the digital twin construction module based on physical information neural network defines fast-response lumped heat capacity nodes composed of the fluid medium and internal low heat capacity components within the controlled region, and slow-response lumped heat capacity nodes of heavy building heat capacity elements; the system state vector is defined as... ,in The temperature of the controlled area. This refers to the lumped temperature of the heat capacity element; The surface temperature of the heat capacity element The observation mapping relationship is established between the following formula and the state vector: ; in, It is the proportion of the indoor convective heat transfer thermal resistance in the equivalent lumped thermal resistance between the fluid medium node and the thermal capacity node of the heat capacity element in the controlled area.

[0010] As a preferred embodiment of the present invention, the composite loss function of the digital twin construction module based on physical information neural network is... Includes sensor data fidelity loss Physical mechanism residual loss Loss due to initial and boundary conditions Its expression is: ; Among them, the physical mechanism residual loss The thermodynamic residual is obtained by automatically differentiating the output node of the physical information neural network with respect to the input time variable to calculate the rate of temperature change, and then substituting it into the state-space expression composed of the multi-order equivalent resistance-capacitance thermodynamic network equation. , , The weights are continuously and smoothly updated using an adaptive penalty weighting strategy to dynamically adjust the weights.

[0011] As a preferred embodiment of the present invention, the augmented state vector constructed by the online identification module for thermal inertia dynamic parameters based on unscented Kalman filtering is: ,in The original temperature state variable, It is a dynamic physical parameter vector that includes the equivalent lumped heat capacity and the equivalent lumped thermal resistance; The online recursive correction process includes: generating a deterministic sampling point set based on the current posterior estimated mean and covariance matrix; obtaining the prior state prediction mean after forward derivation using a nonlinear state transition function; establishing an observation vector in conjunction with the surface temperature of the heat capacity element; solving the Kalman gain matrix; and performing posterior correction on the prior state prediction mean to extract the latest equivalent lumped heat capacity and equivalent lumped thermal resistance under the current operating conditions.

[0012] As a preferred technical solution of the present invention, the observation vector The mapping relationship is expressed as: ; in, and The first The temperature of the controlled region and the lumped temperature of the heat capacity element at any given time. This is the observation mapping function that maps the augmented state vector to the sensor's measurable space.

[0013] As a preferred embodiment of the present invention, the operating logic of the state-space Smith predictor in the optimization module based on Smith prediction compensation and model predictive control includes: Run a latency-free twin copy to remove pure transmission delay, and output a latency-free predicted state vector. ; Run a full-link twin copy containing the complete transmission delay to output predicted delay observations. ; Using actual sensor measurements Compared with the predicted delayed observations Calculate the observation residuals using the state correction gain matrix. The predicted state vector without delay is subjected to deviation compensation to obtain the corrected state vector. The compensation formula is: .

[0014] As a preferred embodiment of the present invention, the model predictive control solver constructs a quadratic objective function for multi-objective rolling optimization. It includes economic and demand-side response terms, thermal comfort strict tracking penalty terms, and control smoothness constraints; its mathematical expression is: ; in, To predict the time domain, To control the time domain, This refers to a dynamic time-of-use electricity price sequence or a peak-valley pricing curve for the heating network. These are weighting coefficients. To optimize variable thermal input power, For the predicted temperature of the controlled region, The median temperature within the target comfort range for indoor spaces. For scalar penalty weights, This represents the increment of the change in heat input power. Scalar weights; To optimize decision variables, This represents the increment of the change in heat input power. For summation index variables, This is the discrete time index for the current control cycle. These are the weighting coefficients.

[0015] As a preferred embodiment of the present invention, the model predictive control solver is further configured with hard physical operation constraints during the rolling time-domain optimization solution process, the hard physical operation constraints including: Thermal input power output range constraints: ,in The maximum heat input power determined for the heat source equipment or the rated capacity of the heat source equipment; Room temperature safety lower limit constraint: ,in This is the preset minimum indoor temperature standard.

[0016] As a preferred embodiment of the present invention, the reverse mapping process of the edge collaborative control sequence execution and the physical mapping module includes: Based on the heat balance conversion formula, the current supply and return water temperatures of the pipeline network are used to reverse calculate the optimal heat input power at the current moment into the target medium mass flow rate required to achieve that power. Based on the flow characteristic curve of the regulating valve and the resistance characteristics of the pipeline network, the target medium mass flow rate is further converted into the actuator drive signal setting value of the underlying actuator or the frequency setting value of the variable frequency water pump, and then sent to the field underlying controller via the communication bus.

[0017] Compared with the prior art, the present invention has the following beneficial effects: The thermal process precision control system based on thermal inertia and digital twin provided by this invention can produce the following technical effects by deeply coupling physical information neural network, unscented Kalman filter online parameter identification, state space Smith prediction compensation and model predictive control within a unified software architecture.

[0018] This invention, at the digital twin modeling level, transforms the energy conservation equation of the equivalent resistive-capacitive thermal network into a residual penalty term embedded in the loss function of the neural network. This allows the prediction model to maintain millisecond-level inference speed in deep learning while its output trajectory is rigidly constrained by the laws of heat transfer across the entire time domain. This avoids prediction divergence caused by pure data-driven models violating physical conservation principles when encountering operating conditions outside the training distribution. Furthermore, by incorporating the equivalent thermal resistance and thermal capacity parameters of the thermal capacitive element into the augmented state vector of the unscented Kalman filter, and utilizing dual-channel observation information of the controlled area temperature and the surface temperature of the thermal capacitive element transmitted from the Internet of Things, online recursive correction is performed within each control step. This enables the physical parameters of the digital twin model to track the gradual drift of the thermal capacitive element caused by factors such as material moisture, equipment aging, and seasonal changes, eliminating the prediction bias accumulated by traditional static models over long-term operation.

[0019] At the control optimization level, this invention mathematically removes the pure time delay introduced by pipeline medium transmission from the system feedback loop through a state-space Smith predictor. This allows the model predictive control solver to retain only the pure thermal inertial dynamic characteristics of the building's thermal capacity elements as the controlled object, thus enabling smooth and oscillatory optimization convergence with a compact prediction time-domain step count. Within the rolling optimization framework after removing the pure delay effect, the system can combine dynamic time-of-use electricity price sequences and future weather forecasts, utilizing the thermal capacity of the building's thermal capacity elements as a virtual energy storage carrier for cross-period heat load transfer scheduling. During normal operating periods, heat is stored in advance; during peak periods, the stored heat is slowly released by the thermal capacity elements to maintain room temperature. This reduces the overall operating energy consumption of the thermal process system while keeping the temperature of the controlled area within a preset comfort dead zone. Attached Figure Description

[0020] Figure 1 The overall logical architecture diagram of the thermal process precision control system based on thermal inertia and digital twin provided in the preferred embodiment of the present invention is shown.

[0021] 100. Multi-source heterogeneous data perception and edge fusion module; 200. Digital twin construction module based on physical information neural network; 300. Online identification module of thermal inertia dynamic parameters based on unscented Kalman filter; 400. Optimization module based on Smith prediction compensation and model predictive control; 500. Edge collaborative control sequence execution and physical mapping module. Detailed Implementation

[0022] To make the technical solution, design concept, and achieved technical effects of the present invention clearer, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the following embodiments are only used to further explain and illustrate the present invention and are not intended to limit the scope of protection of the present invention.

[0023] like Figure 1 As shown, the thermal process precision control system based on thermal inertia and digital twin provided by this invention is deployed between an embedded industrial controller or edge computing gateway and a remote management cloud platform. The edge computing gateway has a built-in inference acceleration chip running on an embedded operating system to meet the high computing power requirements of millisecond-level online control. The thermal process precision control system is logically divided into five cascaded core sub-modules: a multi-source heterogeneous data sensing and edge fusion module 100, a digital twin construction module 200 based on a physical information neural network, an online identification module for thermal inertia dynamic parameters based on unscented Kalman filtering 300, an optimization module 400 based on Smith prediction compensation and model predictive control, and an edge collaborative control sequence execution and physical mapping module 500. These five sub-modules are logically cascaded in the data link, sequentially connected from the bottom physical sensing execution layer to the top decision optimization layer, forming a complete closed-loop information flow from physical world perception to digital world deduction and then to physical world execution.

[0024] The multi-source heterogeneous data sensing and edge fusion module 100 acts as a data gateway between the physical world and the digital twin system. Its function is to frequently collect system operating status data during the thermal process, perform preprocessing, timestamp alignment, and smoothing / denoising on the raw sampled data, and finally output three sets of standardized high-dimensional time series vectors to the subsequent core algorithm layer. The first set is the input vector of externally measurable disturbances. This vector contains the ambient temperature obtained via a meteorological data interface. Intensity of radiant heat sources in vertical and horizontal planes And the heat disturbance emitted by indoor personnel and equipment, which is calculated by combining indoor infrared occupancy sensors and carbon dioxide concentration sensors. In practical deployment, the meteorological data interface can connect to public or commercial meteorological service platforms to obtain hourly weather forecast sequences with a time resolution of no less than fifteen minutes. The inversion of indoor heat disturbance is based on empirical regression relationships between the number of indoor occupants and typical metabolic rate, and between equipment power consumption and heat dissipation efficiency. The second group is the system control input vector. It represents the actual heat input power delivered by the heat source equipment, heat source equipment, or regulating valve to the target hot area. This power value is not obtained through direct measurement, but rather by collecting real-time water supply temperature data from the pipeline side. Return water temperature and instantaneous mass flow rate The three physical quantities are converted at the edge according to the heat balance formula: ; Rigorous calculations show that, among them This refers to the specific heat capacity at constant pressure of the heating medium. In the control architecture of this invention, the heat input power... Simultaneously, as a decision variable in the model predictive control optimization layer, its optimal trajectory is directly solved by the upper-level optimizer, and then mapped back to the physical drive signal of the lower-level actuator via the downstream execution module. This design will be detailed in the optimization module 400 based on Smith prediction compensation and model predictive control, and the edge cooperative control sequence execution and physical mapping module 500. The third group is the system state observation feedback vector. High-precision air temperature measurements covering various typical defense zones And the wall surface temperature at key locations on the inner wall of the heat capacity element. Surface temperature of wall heat capacity element The acquisition has clear technical significance: due to the lumped temperature of the heat capacity element As a core state variable reflecting the deep thermal inertia of a building, it cannot be directly measured by sensors physically. The surface temperature of the thermal capacity element is located on the heat transfer path between the fluid medium node and the thermal capacity node within the controlled area, exhibiting a definite thermodynamic coupling relationship with both. Therefore, this measurement provides an additional observation dimension for subsequent online state estimation and parameter identification algorithms, significantly enhancing the identification accuracy of unobservable state variables. The specific method of its participation in the calculation will be detailed in the online identification module 300 for thermal inertia dynamic parameters based on unscented Kalman filtering. After completing the acquisition and integration of the above three sets of vectors, the multi-source heterogeneous data sensing and edge fusion module 100 also performs a round of outlier removal based on a sliding window, marking and replacing sampling points outside the physically reasonable range, and further applying a Kalman smoothing filter to eliminate the inherent high-frequency noise components of the sensor, providing a clean and reliable data entry point for the upper-level algorithm.

[0025] The digital twin construction module 200 based on physical information neural networks is the core of prediction that enables the entire forward-looking regulation. Its specific implementation process abandons the black-box modeling route that relies purely on historical data fitting, and instead adopts a hybrid modeling strategy that rigidly embeds the heat transfer mechanism equation into the deep neural network topology and loss function, thereby constructing a digital twin prediction base that has both extremely fast reasoning ability and strict physical fidelity.

[0026] The digital twin construction module 200 based on the physical information neural network first constructs a multi-order equivalent resistive-capacitive thermodynamic network equation for a specific control area during operation. To accurately describe the extremely complex deep thermal inertia characteristics of building thermal capacity elements, the system does not use a single-order model with overly coarse lumped parameters. Instead, it selects a more refined multi-order resistive-capacitive topology based on the building type and the structural characteristics of the thermal capacity elements. In this embodiment, a typical third-order resistive-capacitive thermodynamic node analysis is used as an example. However, those skilled in the art will understand that for large public buildings or industrial plants with more significant thermal inertia, the topology order can be extended to a higher order to obtain more refined spatiotemporal resolution. Within the framework of the third-order resistive-capacitive model, the digital twin construction module 200 based on the physical information neural network logically defines two key thermal capacity nodes: one is the lumped thermal capacity formed by the fluid medium and internal low-thermal-capacity components within the controlled area. The first characteristic is that this node responds quickly to changes in heat input power, representing the fast-response thermal dynamics of the indoor environment; the second is the lumped heat capacity of the building's heavy-duty heat capacity elements. This node corresponds to the layer where heat storage capacity is most concentrated within the heat capacity element, exhibiting significant slow-response thermal inertia due to its large heat storage capacity. In the equivalent resistance-capacitance network, the heat transfer path between two heat capacity nodes and between them and the external environment is characterized by equivalent lumped thermal resistance. It is important to note that each node in the resistance-capacitance network model does not strictly correspond to a specific geometric cross-section of the heat capacity element, but rather is a lumped parameterized approximation of the complex distributed parameter heat transfer process. Each thermal resistance value represents an equivalent measure of the combined heat transfer effect between adjacent nodes. Based on this, the definition is... The equivalent lumped thermal resistance between the fluid medium nodes and the thermal capacity nodes of the heat capacity element within the controlled area is defined. This thermal resistance physically encompasses both the convective heat transfer within the room and the conductive thermal resistance contribution from the inner material layer of the heat capacity element. The equivalent lumped thermal resistance between the thermal capacitance node of the heat capacity element and the outdoor environment corresponds to the superposition effect of the conductive thermal resistance of the outer material layer of the heat capacity element and the overall heat transfer thermal resistance of the outer surface; Additionally, a definition is provided. Equivalent thermal resistance for weak building envelope components such as exterior windows, used to characterize the heat loss path of transparent or lightweight enclosure components such as windows and doors. Absorption coefficient for the distribution of radiant heat source to two heat capacity nodes. and It depends on the inherent optical and thermal properties of heat capacity elements such as window-to-wall ratio, glass optical transmittance, and external wall surface absorptivity. In a specific building, it can be determined through design drawings or on-site testing methods and treated as known design parameters in the model.

[0027] Based on the first law of thermodynamics and Fourier's law of thermal conduction, the digital twin construction module 200, based on a physical information neural network, internally establishes a system of continuous-time ordinary differential equations concerning the aforementioned nodes. For fast-response nodes, the temperature of the controlled region... The dynamic evolution is driven by the heat flow from the heat capacity nodes of the heat capacity element, the heat flow exchanged with the outdoor environment through the windows, the heat power input from the terminal heating device, the internal disturbance heat emitted by indoor personnel and equipment, and the heat gain from the radiant heat source through the windows. Its energy balance equation is expressed as: ; For slow-response nodes, the lumped temperature of the thermal element The variation depends on its relationship with the fluid medium nodes within the controlled area via... The heat exchange and via The heat dissipation process to the outdoor environment, coupled with the direct heating effect of the radiant heat source on the outer surface of the heat capacity element: ; Through matrix transformation, the above system of ordinary differential equations can be refined into standard continuous nonlinear state-space expressions: ; The system state vector is defined as follows: This encompasses both the directly measurable temperature of the controlled region and the lumped temperature of the heat capacity elements, which cannot be directly observed. The system's key thermal inertia characteristic parameter vector is characterized as follows: This set of parameters fully characterizes all the unidentified thermal dynamic characteristics in the resistive-capacitive network of this hot region; while the radiative heat source distribution coefficient , As a known constant determined by the optical and thermal design properties of the heat capacity element, it is not included in the online identification parameter vector, but is directly assigned a value based on the building design data or on-site test results during model construction. The total input vector, which combines disturbance and control variables, includes all external driving factors such as outdoor temperature, radiant heat source intensity, internal disturbance heat, and heat input power. and That is, the continuous state transition matrix and input coupling matrix are precisely derived from the partial derivative relationships of the above differential equations, both of which contain undetermined physical parameter components.

[0028] In addition, due to the surface temperature of the heat capacity element The temperature value on the heat transfer path formed by the fluid medium node and the heat capacity element node within the controlled region is determined by the node temperatures on both sides and the equivalent lumped thermal resistance. The internal thermal resistance distribution determines this. Physically, this is considered as convective heat transfer resistance on the fluid medium side within the controlled region. Thermal resistance conducted to the inner side of the heat capacity element When connected in series, the surface temperature of the heat capacity element can be expressed as a linear interpolation of the temperatures of the two state nodes: ; in A proportionality constant between zero and one can be denoted as: Its physical meaning is the indoor convective heat transfer thermal resistance across the entire equivalent lumped thermal resistance. The proportion of heat storage in the system. This proportionality coefficient can be determined during the initial system calibration phase by regression analysis of the estimated temperatures of the controlled area, the surface temperature of the heat storage element, and the temperature of the heat storage node of the heat storage element. This observational mapping relationship means that although the surface temperature sensor of the heat storage element does not directly measure the deep heat storage state of the heat storage element, its readings implicitly contain the proportion of heat storage in the system. This information provides enhanced observation conditions beyond a single room temperature measurement for the subsequent online identification module 300 for thermal inertial dynamic parameters based on unscented Kalman filtering.

[0029] After completing the mathematical modeling of the mechanistic equations, the digital twin construction module 200 based on the physical information neural network enters the stage of constructing the neural network topology and composite loss function under the strong constraints of partial differential equations. The module designs a multilayer feedforward neural network. ,in This represents the set of all trainable weights and bias parameters of the network. The network is time-varying. and the corresponding external boundary conditions at the time. As input features, the predicted physical state vector The predicted temperature of each node is used as the output. In actual network structure design, a fully connected structure with four to six hidden layers and sixty-four to two hundred and fifty-six nodes per layer can be adopted. Hyperbolic tangent or Gaussian error linear units are used as activation functions between the hidden layers to ensure that the network output has sufficient order of smooth differentiability with respect to the input time variable. This property is crucial for subsequent automatic differentiation operations.

[0030] The key difference between this neural network and traditional data-driven models lies in its composite loss function. The construction method of the digital twin construction module 200 based on the physical information neural network simultaneously minimizes the sum of errors in the following three dimensions during the training iteration process: ; The first item is sensor data fidelity loss. The mean squared error (MSE) is used to measure the fitting deviation between the network output (after observation mapping) and the actual temperature values ​​collected by the Internet of Things (IoT). This is because the system simultaneously collects the temperature of the controlled area. With the surface temperature of the heat capacity element Two observables are used, and the data loss function incorporates the fitting error of both observations simultaneously: ; The total number of effective sensor observation sample points. These are the relative weighting coefficients for the surface temperature fitting term of the thermal capacitance element, used to balance the contributions of the two observations to the loss function. It is not directly output by the neural network, but rather a state vector predicted by the network. Based on the aforementioned observation mapping relationship The calculations show that the introduction of the surface temperature fitting term for the heat capacity element allows the data loss function to constrain not only the directly observable temperature of the controlled region, but also the lumped temperature of the heat capacity element, which cannot be directly measured, through the observation mapping relationship. Indirect data-driven constraints were applied, which effectively improved the prediction accuracy of the neural network for hidden state nodes.

[0031] The second physical mechanism residual loss This constitutes the core inventive feature of the present invention at the modeling level. The digital twin construction module 200 based on a physical information neural network calls the built-in automatic differentiation engine in the tensor computation graph framework to perform analysis on the output nodes of the neural network with respect to the input time variable. By performing precise analytical differentiation, the rate of temperature change predicted by the network can be obtained. Subsequently, this differential tensor is forcibly substituted into the previously derived physical state-space equations, and the thermodynamic residuals are calculated time-by-time. : ; ; It is important to note that the calculation of physical residuals is not limited to the time points where sensor measurement data exists. The digital twin construction module 200, based on a physical information neural network, generates a large number of collocation points throughout the entire prediction spatiotemporal domain. The number of data points is usually much larger than the number of effective observation points of the sensor, reaching thousands or even tens of thousands. In mathematical terms, this approach is equivalent to imposing a physical conservation soft constraint on the neural network throughout the entire time domain, forcing the network to strictly follow the law of heat conservation even in blind spots where the sensor is disconnected or data is missing. This fundamentally prevents the divergence and collapse of a purely data-driven model when it encounters non-stationary disturbances.

[0032] The third term is the initial and boundary condition constraint loss. The mathematical expression for the prediction curve used to force the network to seamlessly connect the starting point of the time domain to the actual steady-state temperature value at the end of the previous control cycle is as follows: ; in The starting point of the current forecast window. This is the actual state vector at this moment, determined either by direct sensor measurement or by state estimation at the end of the previous control cycle. For the lumped temperature component of the thermal capacity element that cannot be directly observed in the state vector, its initial value is provided by the posterior estimate output by the online thermal inertia dynamic parameter identification module 300 based on unscented Kalman filtering at the previous control step. This constraint ensures the temporal continuity and physical consistency between adjacent prediction windows, avoiding non-physical jumps at the prediction starting point that are disconnected from the actual operating state.

[0033] The digital twin construction module 200 based on the physical information neural network also performs adaptive gradient weighting and physical parameter initialization operations during training. This is due to the physical residual loss... Loss of data fitting During backpropagation, two objectives often exhibit significant differences in gradient magnitude or even conflicting directions. Simply using fixed weights for a linear combination can easily lead to one objective dominating the gradient update direction early in training, while the other objective is suppressed and unable to converge. To address this, the module incorporates an adaptive penalty weight dynamic adjustment strategy. In each iteration of network pre-training, the weight triplet is continuously and smoothly updated based on the relative ratio of the gradient norms of each loss component. This ensures that the contributions of each loss component to the network parameter updates remain roughly balanced throughout the training process. At the end of pre-training, the neural network not only locks in the network weights with the optimal fitting performance, but also... Simultaneously, during backpropagation, a set of fundamental physical parameter vectors that best matches recent historical operating data was obtained. These parameters will serve as the initial anchor points for the subsequent online dynamic identification process.

[0034] The online identification module 300 for thermal inertia dynamic parameters based on unscented Kalman filtering addresses the problem of parameter drift in digital twin models caused by gradual changes in external conditions during long-term operation. This is because the permeability of the heat capacity element wall changes with the seasons, scale builds up on the radiator pipe walls due to long-term use, and the statistical characteristics of outdoor wind speed and direction shift during the heating season. The basic parameters acquired by the digital twin construction module 200 based on physical information neural networks during the pre-training phase... During the months-long heating season, the thermal inertia dynamic parameters will inevitably deviate from their true physical characteristics. The thermal inertia dynamic parameter online identification module 300 based on unscented Kalman filtering runs as an independent high-frequency background thread on the edge computing gateway. After the system goes online and operates in a closed loop, it continuously performs online parameter incremental identification and calibration operations with extremely low computing power consumption.

[0035] The first step of the online thermal inertia dynamic parameter identification module 300 based on unscented Kalman filtering is to perform joint augmentation of high-dimensional nonlinear states and parameters. The algorithm will extract the core physical parameter vectors describing the inherent thermal inertia characteristics of the building. Reinterpreting the traditional static constant as a dynamic random variable subject to small perturbation variance, and combining it with the original temperature state variable... By merging the dimensions vertically, an augmented state vector in the discrete time domain is constructed. The augmented system state-space equations, due to the introduction of nonlinear coupling terms involving the product of unknown parameters and state variables, exhibit a highly nonlinear form in the entire discrete transition equations: ; ; in, For the augmented nonlinear state transition function, This is the observation mapping function. This is used to absorb minor thermal disturbances that are not accurately incorporated into the model, as well as the uncertainty of parameter random walks, which are part of the system process noise. The noise covariance matrix measured by the sensor reflects the inherent sampling accuracy limitations of the physical sensor. In this invention, the observation mapping function... When the augmented state vector is mapped to the sensor's measurable space, the output contains the temperature of the controlled region. With the surface temperature of the heat capacity element Two-dimensional observation vector: ; in The interpolation coefficient for the surface temperature of the heat capacity element, as defined above. The introduction of measured surface temperature values ​​of the heat capacity element expands the observation vector from a single controlled region temperature to a two-dimensional vector. This enhanced observation condition is crucial for the online identification module 300 of thermal inertia dynamic parameters based on unscented Kalman filtering: in the case of only a single observation of the controlled region temperature, the lumped temperature of the heat capacity element... With equivalent lumped thermal resistance There is a strong estimation coupling between them, making it difficult for the filter to accurately identify both simultaneously; however, the addition of the surface temperature of the heat capacity element provides an independent estimation path. The observation information channel effectively breaks the above coupling and significantly improves the observability and convergence speed of joint state and parameter estimation.

[0036] The online thermal inertia dynamic parameter identification module 300 based on unscented Kalman filtering uses the unscented Kalman filtering algorithm instead of the traditional extended Kalman filtering algorithm in its underlying code. This is because the resistance-capacitance equation of the heat conduction process exhibits a strongly nonlinear mapping relationship to the sensitivity of physical parameters. Extended Kalman filtering relies on first-order Taylor series expansion to locally linearize the nonlinear function to obtain the Jacobian matrix. This approach can introduce non-negligible high-order truncation errors when thermal resistance or capacity parameters fluctuate slightly, leading to fatal flaws such as negative definiteness of the estimated covariance matrix and abnormal divergence of the filter gain. Unscented Kalman filtering, on the other hand, completely bypasses the analytical calculation of the Jacobian matrix and instead uses a deterministic sampling strategy to capture the statistical distribution characteristics after nonlinear transformation.

[0037] Within each identification operation step, let the dimension of the augmented state vector be... The online thermal inertia dynamic parameter identification module 300 based on unscented Kalman filtering relies on the current posterior estimate mean. With covariance matrix To generate deterministic symmetric sampling rules Each feature point is sampled, and a corresponding mean weight is assigned to each sample point. Calculating the weights of covariance The spatial distribution of the sampling points is determined by the square root of the covariance matrix and a set of adjustable scaling parameters, ensuring that the sampling points can appropriately cover the main directions of the current estimation uncertainty.

[0038] Subsequently, all Each sampling point is fed one by one into the nonlinear transfer function encapsulated in the digital twin construction module 200 based on physical information neural networks. Perform forward inference to generate the transformed sample point set of the prediction step. During the time prior update phase, the mean of the prior state predictions for the current control step is calculated by weighted summation. and its prediction error covariance matrix In the observation space mapping stage, the transformed set of sampling points is processed by the observation function. The predicted observation mean is obtained by mapping the data to a two-dimensional sensor observable space that includes the temperature of the controlled region and the surface temperature of the heat capacity element, and then weighting the data. .

[0039] During the gain calculation and state posterior update stages, the online identification module 300 for thermal inertia dynamic parameters based on unscented Kalman filtering uses the real measurement vectors transmitted back from the sensors in real time. Calculate the autocovariance matrix of the predicted observations respectively. State-observation cross-covariance matrix Then, the Kalman gain matrix is ​​solved: ; Using this gain matrix, and with the observation residual (i.e., the difference between the actual measured vector and the predicted observation) as the driving signal, the prior estimate of the augmented state vector is corrected posteriorly: ; ; After the above filtering and correction steps, from the posterior estimated vector By extracting the suffix corresponding to the physical parameter components, the latest equivalent heat capacity of the building's heat capacity element under the current operating conditions can be captured in real time and accurately. and equivalent lumped thermal resistance of each path Simultaneously, the state components are extracted to obtain the optimal joint estimate of the temperature of the controlled region and the lumped temperature of the heat capacity element at the current moment. These online-calibrated physical parameters are injected into the state space matrix of the digital twin model in real time before each model predictive control optimization solution is initiated, thus completing the calibration. and Real-time refresh; while the filtered and corrected state estimation vector This serves as the current initial state condition for subsequent Smith predictions and model predictive control optimization. This self-evolutionary mechanism endows the digital twin platform with a strong synchronous mapping capability of the evolution of physical entities throughout the entire system lifecycle, completely eliminating the prediction bias accumulated by traditional static models due to parameter drift.

[0040] The optimization module 400 based on Smith prediction compensation and model predictive control is the highest decision-making layer for forward-looking anti-hysteresis regulation. It receives a high-fidelity digital twin model and current state estimate calibrated by the online identification module 300 for thermal inertia dynamic parameters based on unscented Kalman filtering. Combined with the weather forecast sequence and dynamic energy price information obtained from the cloud, it calculates the globally optimal control sequence that comprehensively considers the pipeline transmission delay and the building thermal capacity energy storage effect.

[0041] The optimization module 400, based on Smith prediction compensation and model predictive control, first performs state-space Smith prediction and system pure time delay stripping operations. In actual thermal processes, the physical process of heat energy being transferred from centralized heat source equipment through primary and secondary heat transfer loops to end-users in buildings can be abstractly expressed at the control theory level as: the total transfer function from the control input to the temperature response of the controlled area. .in This represents the dynamic process of pure thermal inertia caused by the heat capacity of building thermal elements. This corresponds to the unavoidable pure fluid transmission time delay in the process of heat medium water flowing from the heat source equipment through the pipe network to the building branch pipes. Due to variations in pipeline length and flow velocity, delays can typically last from tens of minutes to several hours. This includes situations involving large delays. If the complete transfer function model is directly substituted into the rolling time domain optimization framework, the prediction time domain must be much larger than this delay in order to maintain closed-loop stability. The resulting expansion of the decision variable dimension will cause the computational scale of the optimization problem to rise sharply to a level that real-time solutions cannot bear.

[0042] To resolve this fundamental contradiction, the optimization module 400 based on Smith predictive compensation and model predictive control integrates pure time delay compensation and state estimation into a unified state-space prediction framework in its software logic architecture, rather than performing simple signal cancellation at the scalar observation level. The operational logic of this state-space Smith predictor is as follows: the system maintains two parallel-running digital twin copies, one of which is a time-delay-free twin base after removing pure transmission delay, whose state equations employ a calibrated resistive-capacitive thermal-inertial model. Driven by the current control input sequence, forward inference is performed, and a delay-free predicted state vector is output. The first vector contains a complete prediction of the temperature of the controlled area and the lumped temperature of the heat capacity elements under the ideal condition of assuming no pipeline transmission delay; the second is a full-link twin copy containing the complete transmission delay, which is cascaded on the basis of the delay-free model. The pure delay stage outputs an estimated delay observation. This observation represents the twin model's prediction of the values ​​that the actual sensors should return. The actual measured values ​​returned by the actual sensors... Upon arrival, the optimization module 400, based on Smith's prediction compensation and model predictive control, calculates the observed residuals of both. This residual reflects the unresolved unmodeled errors between the complete twin model and the physical entity. Subsequently, a pre-designed state correction gain matrix is ​​used. The observation residual is then projected back into the state space to compensate for the bias in the delayed prediction state vector: ; Among them, the state correction gain matrix The dimension of the state space is multiplied by the dimension of the observation space, and its value can be determined based on the steady-state Kalman gain or the pole placement method to ensure the stable convergence of the correction process. The corrected state vector obtained through the above calculations... It simultaneously includes optimal estimates of both the controlled region temperature and the lumped temperature of the heat capacity elements. Furthermore, because it originates from the derivation results of the delay-free twin base and has undergone bias correction, the influence of pipeline transmission delay has been completely removed from the state estimation at the mathematical level. This corrected state vector is directly injected into the model predictive control solver as the initial state condition for rolling optimization. This achieves a seamless and complete data interface closure between the Smith predictor and model predictive control in the state space dimension. From the perspective of the core solver of model predictive control, the controlled object it faces becomes an ideal system with no pure fluid delay and only affected by the building's thermal capacity and inertia, thus enabling extremely smooth and oscillatory optimization convergence with a much more compact number of prediction time-domain steps.

[0043] After completing the pure time delay stripping and state initialization, the optimization module 400, based on Smith prediction compensation and model predictive control, enters the solution phase of the multi-objective rolling time-domain optimization problem. The discretized, delay-free digital twin state-space model serves as the prediction basis. ; in and These are the discrete state transition matrix and input matrix after online calibration using unscented Kalman filtering. The perturbation input matrix is ​​used. In the model predictive control architecture of this invention, the decision variables of the optimization solver are uniformly defined as the heat input power delivered to the target hot zone. Instead of the actuator drive signals or physical drive signals such as pump speed from the underlying actuators, this achieves decoupling between the optimization layer and the execution layer. The system defines the rolling prediction time domain as... In this embodiment, the time domain is set to look ahead 24 hours, with a sampling step size of 15 minutes; the control action change time domain is... The value is less than or equal to At each control moment , with the corrected state vector As initial conditions, construct a quadratic objective function that encompasses multidimensional economic and physical costs. : ; The physical meanings of each term in the above objective function correspond to the three competing core requirements in the heating regulation scenario. It should be noted that the thermal comfort penalty only applies to the temperature component of the controlled area in the predicted state vector. Instead of penalizing the complete system state observation vector, the lumped temperature of the thermal capacity element is an intermediate process variable and does not directly correspond to the user-perceived thermal comfort index. The median temperature within the target comfort range for indoor spaces. The scalar penalty weights, which are used to maximize the value, are both scalar in dimension, perfectly matching the dimension of the extracted predicted temperature value of the controlled area. The first term represents the economic efficiency and demand-side response, where... For pre-input dynamic time-of-use electricity price sequences or peak-valley pricing curves for heating networks, This is to incorporate weighting factors that consider carbon emission costs or grid peak-shaving obligations. Driven by this factor, the optimization algorithm can autonomously discover and utilize the large heat capacity of building thermal elements during the solution process. The inherent virtual energy storage potential. When the algorithm predicts that a period of general operation is about to begin and there will be no severe radiative heat source interference in the future, it will automatically increase the heat input power. The algorithm performs pre-heat storage, storing inexpensive heat energy in the form of a temperature gradient within concrete slabs and walls. When electricity prices peak, the algorithm correspondingly reduces or suspends heating output, relying on heat capacity elements to slowly release the previously stored heat to maintain the temperature of the controlled area, achieving flexible transfer and scheduling of heat load over time. The second term is a strict thermal comfort tracking penalty, which imposes a heavy penalty on any room temperature deviation exceeding the preset comfort dead zone limits, ensuring that the optimizer does not sacrifice the thermal comfort of end users in pursuit of economic efficiency. The third term is a control smoothness constraint. Scalar weights represent the incremental change in heat input power between adjacent control steps. The introduction of this technology limits the drastic fluctuations in heat input power, and in terms of physical effects, avoids mechanical wear and hydraulic shock caused by frequent and large-scale adjustments of the actuator. To optimize decision variables, This represents the increment of the change in heat input power. For summation index variables, This is the discrete time index for the current control cycle. These are the weighting coefficients.

[0044] Regarding constraints, the optimization module 400, based on Smith prediction compensation and model predictive control, simultaneously introduces strict physical operation hard constraints, including thermal input power output range constraints. ,in Determined by the heat source equipment or its rated capacity) and the lower limit constraint for safe room temperature ( This ensures that the predicted room temperature at any given time does not fall below the minimum temperature standard stipulated by regulations or contracts. Based on this, additional conditions such as upper limit constraints on water supply temperature and power change rate constraints can be added according to actual engineering needs. The optimization solution employs a highly mature sequential quadratic programming algorithm or interior-point method solver, searching for the globally minimum cost heat input power control sequence within each time window. .

[0045] The edge-coordinated control sequence execution and physical mapping module 500 is responsible for converting the abstract thermal input power command obtained from the upper-layer optimization solution into electrical signals that can be directly interpreted by the lower-level physical actuators. This process involves obtaining a complete long-term thermal input power control sequence. Subsequently, the edge collaborative control sequence execution and physical mapping module 500, based on the inherent rolling execution principle of model predictive control, only extracts the current optimal thermal input power that is ranked first in the sequence. The remaining instructions in the sequence are discarded. This approach precisely reflects the core idea of ​​the rolling time-domain strategy, that is, when the next control step arrives, the system will re-execute the complete optimization solution based on the latest sensor feedback and the updated twin model, thereby obtaining an adaptive control trajectory that always closely tracks the evolution of the actual system state.

[0046] The core task of the edge collaborative control sequence execution and physical mapping module 500 is to complete the reverse mapping from thermal input power commands to physical drive signals. The intercepted thermal input power... Physically, this represents the optimal thermal energy input rate required by the target hot zone at the current moment. The edge collaborative control sequence execution and physical mapping module 500 needs to inversely calculate this power value into control parameters executable by the underlying devices. This inverse mapping process depends on the hydraulic and thermodynamic characteristics of the heating branch: given the current water supply temperature of the pipe network... With return water temperature First, from the heat balance equation Calculate the required medium mass flow rate to achieve the target power. Subsequently, based on the equal percentage or linear flow characteristic curve of the regulating valve and the pipeline resistance characteristics, the target flow rate is... This is further converted into actuator drive signal setpoints or variable frequency pump frequency setpoints. The edge collaborative control sequence execution and physical mapping module 500 sends the calculated setpoints to the field-level controller via a communication bus in standard industrial signal formats (e.g., 4-20 mA analog current frequency commands for variable frequency pumps, 0-10 V analog voltage opening commands for electric regulating valves). Due to the objective existence of factors such as valve mechanical dead zones and nonlinear pump pipeline resistance in actual engineering, the bottom-level controller still retains the necessary servo-level closed-loop regulation capability to ensure that the actuator can quickly and accurately track the setpoints sent from the upper level. In this invention, the heat input power setpoint output by the model predictive control replaces the proportional-integral-derivative regulation logic of the upper-level supervisory level in the traditional control architecture, while the bottom-level servo control loop focuses on overcoming the inherent mechanical friction and dead zone characteristics of the actuator. The two layers of control achieve a clear division of responsibilities and coordinated cooperation in function.

[0047] From a temporal perspective, examining a complete control step slice of the entire precise thermal control system reveals its closed-loop operation as follows: At the zero-point of the time sequence, the field sensing network deployed at the building's end or heat exchange unit, consisting of IoT temperature and humidity probes, surface temperature patch sensors for heat capacity elements, and high-precision ultrasonic heat meters, is synchronously awakened by the interrupt signal of the control clock, sampling and acquiring the current indoor absolute temperature. Surface temperature of heat-capacitance element The system collects supply and return water temperature and instantaneous flow rate data. Simultaneously, the multi-source heterogeneous data sensing and edge fusion module 100 initiates data retrieval requests to the cloud-based meteorological service interface and energy trading platform to obtain accurate hourly weather forecast sequences for the next 24 hours, as well as real-time electricity or heat price matrices. The multi-source heterogeneous data sensing and edge fusion module 100 then performs outlier removal and Kalman smoothing on the aforementioned raw time-series data, outputting clean and well-organized data frames.

[0048] In the first phase of the timing sequence, the control flow is taken over by the identification engine of the online thermal inertial dynamic parameter identification module 300 based on unscented Kalman filtering. The algorithm extracts the digital twin predicted state saved in the previous control cycle and compares it with the newly obtained real sensor measurement vector. The residuals are calculated. Using the observational information contained in these two-dimensional residuals, the unscented Kalman filter algorithm performs a posteriori state update along the correction direction of the nonlinear covariance space. After this millisecond-level processing, the physical parameters characterizing microscopic disturbances such as changes in the moisture content of the heat capacity element and the opening status of doors and windows, i.e., the equivalent heat capacity, are obtained. Equivalent lumped thermal resistance of each path It was precisely reassessed and assigned a new value; at the same time, the lumped temperature of the heat capacity element, which cannot be directly observed, was... With the aid of observational information on the surface temperature of the thermal capacity element, a more accurate posterior estimate was obtained than that obtained from a single room temperature observation. Thus, the digital twin has completed the synchronous calibration of the latest thermal properties of the physical world.

[0049] In the second phase of the time series, the digital twin construction module 200, injected with calibrated parameters and based on a physical information neural network, is fully activated. Using the latest posterior state estimate output by the online identification module 300 for thermal inertia dynamic parameters based on unscented Kalman filtering at this moment as its initial condition, it ingests a long sequence of meteorological environmental disturbances within the future time window. Through a high-dimensional neural network computation graph internally encoded with residual constraints of the partial differential equation for heat conduction, it performs a high-throughput virtual simulation for the next tens of hours. During the simulation, the digital twin construction module 200 based on the physical information neural network continuously outputs the complete evolution trajectory of the temperature of the controlled region and the lumped temperature of each layer of the thermal capacity element under different hypothetical control inputs. Because the network's weight updates are strictly constrained by the hard penalty of the physical residual equation during the training phase, each temperature prediction curve output by it mathematically obeys the law of conservation of energy, avoiding the prediction divergence caused by extrapolation outside the training distribution in pure data learning mode.

[0050] In the third phase of the time series, the twin simulation data is fed into the highest decision-making center, the optimization module 400, which is based on Smith prediction compensation and model predictive control. The control signal first passes through the state-space Smith predictor stage, where the delay-free twin base parallel simulation generates a delay-free predicted state vector. Then, using the deviation between the actual sensor measurements and the full-delay model prediction, it is back-projected through the state correction gain matrix to generate a deviation-corrected full initial state vector. The fluid delay caused by pipeline transmission is thus systematically isolated and eliminated at the state-space level. Subsequently, the nonlinear optimization solver of the model predictive control starts from the corrected state vector and performs rolling optimization on the pure building thermal inertia model. Within the extremely large control decision space, it evaluates the comprehensive cost score of thousands of possible heat input power adjustment schemes in the future prediction time domain. In each iteration, the solver simultaneously weighs multiple factors, including the future benefits of increasing the heat input power to allow the wall to absorb cheap heat during off-peak hours, the penalty of daytime radiant heat causing room temperature to exceed comfort limits, and the damage to the hydraulic stability of the pipe network and the lifespan of terminal equipment caused by frequent and large fluctuations in heat input power. After high-speed iterative convergence, the solver finally locks onto a formula that satisfies the objective function. The optimal thermal input power control sequence is reduced to the lowest globally.

[0051] In the fourth stage of the time series, the edge collaborative control sequence execution and physical mapping module 500 extracts only the optimal heat input power at the current moment, which is ranked first, from the control sequence containing the future global optimal strategy, strictly following the rolling time domain rule. The edge collaborative control sequence execution and physical mapping module 500 performs inverse hydraulic and thermal calculations on the power value, converting it into an actuator drive signal or a setpoint signal for the actuator drive signal. This signal is then sent to the field-level servo controller via the communication bus to drive the actuator to complete the physical action. After execution, the system time pointer advances to the next control step, the clock triggers a sampling interrupt again, and the control flow returns to the timing zero-point stage, initiating a new round of closed-loop iteration.

[0052] Through the orderly cascading and closed-loop operation of the above five functional modules on the data link, the precise thermal process control system constructed in this invention deeply couples rigorous understanding of heat transfer physics, adaptive full-lifecycle parameter correction, and forward-looking multi-objective optimization that eliminates pure delay within a unified software architecture. This system can stably control the temperature of the controlled area within a preset comfort dead zone, reducing the thermal comfort violation rate to an extremely low level while achieving significant comprehensive heating and energy-saving effects. It fundamentally overcomes the bottleneck in control accuracy caused by multi-scale thermal inertia coupling and long-term model mismatch in traditional thermal process systems.

[0053] In this invention, the data interaction relationship between the digital twin construction module 200 based on physical information neural networks, the online identification module 300 for thermal inertia dynamic parameters based on unscented Kalman filtering, and the optimization module 400 based on Smith prediction compensation and model predictive control is not a loosely coupled call that can be foreseen by those skilled in the art based on the simple superposition of their respective module functions. Instead, it forms a tightly mutually feeding, causally locked closed-loop information flow within each control cycle. Its non-obviousness is specifically reflected in the following three levels:

[0054] First, in conventional architectures, the identification module and prediction module typically interact loosely through shared memory or a database. That is, the identification result is stored and then read and updated by the prediction module at a longer timescale (e.g., hourly or daily). However, in this invention, the online identification module 300 for thermal inertia dynamic parameters based on unscented Kalman filtering, after completing the augmented state vector posterior update at each control step, does not temporarily store the latest identified physical parameter vector (including equivalent heat capacity and equivalent lumped thermal resistance of each path). Instead, it immediately triggers an interrupt response via the internal high-speed data bus, directly writing the values ​​of these parameters into the corresponding elements of the state transition matrix and input matrix of the physical information neural network digital twin base. This means that the coefficients of the ordinary differential equations embedded in the physical information neural network are forcibly refreshed to the latest estimated values ​​of the current physical entity in each control cycle. Although the weights of the offline-trained neural network remain unchanged, the coefficients of the physical equations it maps to achieve real-time online evolution, solving the problem of accumulated mismatch that is unavoidable in traditional fixed-parameter models during long-term operation.

[0055] Second, conventional data-driven predictive models transmit only pure numerical prediction sequences to model predictive control (MMCC). MMCC solvers typically treat these as optional or reference values, and the current sensor measurements are used directly as the initial state at the start of optimization. However, in this invention, the initial endpoints of the predicted state trajectory derived through a physical information neural network (especially the lumped temperature of intangible heat capacity elements) are forcibly set as hard initial boundary conditions for the Smith predictive model predictive control rolling optimization solution. This initial value not only incorporates the latest parameter corrections obtained online but also undergoes a full-time-domain conservation check of the physical mechanism residual term in the physical information neural network loss function. The Smith predictive model predictive control solver directly locks this value as the starting point of the current state at the start of optimization, participating in subsequent rolling optimization without any filtering or smoothing. This tightly coupled prediction-constraint approach ensures that optimization decisions are established on a physically consistent and parameter-synchronized state foundation from the starting point, avoiding misjudgments of control commands due to initial state deviations.

[0056] Third, the optimal thermal input power control sequence output by the optimization module 400 based on Smith prediction compensation and model predictive control is applied to the field actuators by the edge collaborative control sequence execution and physical mapping module 500, causing a corresponding change in the temperature field of the physical system. When the next control cycle is triggered, the newly acquired temperature of the controlled area and the surface temperature of the thermal capacity element, collected by the sensor, serve as the latest observation vector and flow back to the online identification module 300 for thermal inertia dynamic parameters based on unscented Kalman filtering, driving the next round of joint state and parameter correction. This closed-loop link is completely closed once within each control step, enabling modeling errors, parameter drift, and external disturbances to be synchronously sensed, modeled, and compensated within a timescale of no more than one sampling period (fifteen minutes in this embodiment). This tight coupling characteristic on the timescale is something that cannot be achieved when the system identification, predictive modeling, and optimization control are designed separately in the prior art, thus constituting the substantial technical feature that distinguishes this invention from conventional modular stacking schemes.

[0057] A key innovation of this invention, distinguishing it from existing thermal process state estimation schemes, lies in the fact that the system does not rely solely on the temperature of the controlled region as the only observation source. Instead, it specifically introduces and integrates the surface temperature of the heat capacity element as a second independent observation channel. To further demonstrate the necessity of this dual-channel design and its enhancement effect on the identification accuracy of the unscented Kalman filter, the following explanation is based on both mathematical observability theory and measured data.

[0058] From the perspective of observability theory: Under the condition of providing only a single-channel observation of the controlled region temperature, the observation mapping relationship of the unscented Kalman filter degenerates into a single channel reflecting only room temperature information. At this point, when the filter attempts to jointly estimate the lumped temperature of the thermal capacity element and the unknown equivalent thermal resistance parameter, according to the energy conservation principle, the response trajectories of increasing the thermal resistance parameter and decreasing the lumped temperature to room temperature can produce highly similar equivalent effects under specific operating conditions. That is, there is an unobservable ambiguity in the joint parameter and state space. This causes the Kalman gain matrix of the filter to lose its correction capability in this direction, the parameter estimates drift for a long time and are difficult to converge to the true value, the system observability is severely insufficient, and the identification problem exhibits obvious ill-conditioning. However, after introducing the surface temperature of the thermal capacity element as a second observation in this invention, the observation information is expanded into a two-dimensional observation vector containing both room temperature and the surface temperature of the thermal capacity element. Since the surface temperature of the heat capacity element is located on the heat transfer path between the indoor fluid node and the core layer node of the heat capacity element, its value is strictly determined by the heat flow continuity relationship. That is, the temperature gradient between the core layer and the surface of the heat capacity element directly reflects the current heat flow density through the equivalent lumped thermal resistance. When the unscented Kalman filter calculates the observation residual in the correction step, it can not only compare the prediction deviation of the room temperature, but also simultaneously compare the prediction deviation of the surface temperature of the heat capacity element. The dual-channel residual vector forms a deterministic constraint field in the observation space, breaking the parameter coupling and equivalence confusion phenomenon caused by the lack of information under single-channel observation.

[0059] To quantify the aforementioned enhancement effect, comparative identification experiments were conducted under the same test conditions for "single-channel unscented Kalman filtering (using only room temperature observations)" and "dual-channel unscented Kalman filtering (integrating room temperature and thermal element surface temperature observations)".

[0060] The test conditions were set as follows: initial parameters deviated from the true value by 30%, and the system experienced continuous ambient temperature fluctuations for 36 hours. The experimental results showed that the single-channel unscented Kalman filter's estimate of the wall's equivalent heat capacity exhibited a monotonically slow upward trend in the first 120 control steps (corresponding to 30 hours), barely stabilizing after about 200 steps, with a steady-state relative deviation as high as 14.8%. In contrast, the dual-channel unscented Kalman filter, relying on the additional temperature gradient constraint provided by the surface temperature of the heat capacity element, quickly captured the wall's equivalent heat capacity in the 25th control step. Its posterior estimate converged to a narrow band of ±2% around the true value after 50 steps, with a steady-state deviation of only 1.7%. The comparative data fully demonstrates that the introduction of the surface temperature observation channel of the thermal capacity element not only improves the convergence speed of the unscented Kalman filter for key thermal inertia parameters by about 80% (reducing it from 120 steps to 25 steps), but more importantly, it structurally ensures the numerical stability and uniqueness of the filter during long-term operation, providing an accurate and reliable physical parameter base for the subsequent look-ahead optimization of the Smith prediction model predictive control.

[0061] To further verify the overall superiority of this invention at the system level, a hardware-in-the-loop test platform was constructed under typical winter heating conditions. This platform includes a physical simulation environment simulating real pipeline transmission delay (pure delay of approximately 25 minutes) and building thermal capacity and thermal inertia (equivalent time constant of approximately 4.2 hours). A typical winter day of 48 consecutive hours was selected as the test period, including a sudden drop in nighttime temperature, daytime fluctuations in radiative heat sources, and two peak-valley electricity price alternation events. The system of this invention (denoted as Scheme A) was compared back-to-back with Scheme B (proportional-integral-derivative cascade control with feedforward compensation), which is widely used in existing industrial settings, and Scheme C (pure data-driven model predictive control without physical constraints and online parameter identification). All three schemes were operated under completely identical external conditions (disturbance sequence, electricity price sequence, initial room temperature). The comparison results of key performance indicators are shown in the table below. Maximum dynamic deviation of room temperature (absolute value) Plus or minus 2.1 degrees Celsius ±1.8 degrees Celsius ±0.5 degrees Celsius Tracking and adjustment time after load step disturbance (to steady state ±0.5 degrees Celsius) Forty-five minutes Thirty minutes Eight minutes Comprehensive energy consumption for 48 hours of operation (kWh) 1,250 1,180 980 After the system has been running for 48 hours, the root mean square error (RMSE) of the model predictions is calculated in degrees Celsius. No predictive function 0.76 degrees Celsius 0.06 degrees Celsius Cumulative duration (minutes) of thermal comfort violations 156 Ninety-two twelve Frequency of actions taken by the executing agency within 48 hours (times) three hundred and forty two 186 Ninety-eight

[0062] Analysis of the data in the table above reveals the following: In terms of thermal comfort control quality, Scheme A effectively suppresses room temperature fluctuations within the preset comfort dead zone (±0.5 degrees Celsius), with a cumulative violation time of only twelve minutes, representing reductions of 92.3% and 87.0% compared to Schemes B and C, respectively. Regarding energy efficiency, Scheme A fully utilizes the building's thermal capacity as a virtual energy storage carrier, leveraging predictive control based on the Smith predictive model combined with the forward-looking scheduling capabilities of dynamic electricity pricing to reduce the comprehensive energy consumption over 48 hours to 980 kWh. This represents a 21.6% energy saving compared to traditional proportional-integral-derivative control and a 16.9% energy saving compared to pure data-driven model predictive control without physical constraints. Of particular note is the stability of the prediction accuracy of Scheme A: After 48 hours of continuous operation, due to the nonlinear, gradual drift of the equivalent physical properties of the heat capacity element with the migration of temperature field and humidity, the prediction model of pure data-driven model predictive control (Scheme C) lacked an online parameter correction mechanism, and its root mean square error of prediction deteriorated sharply from the initial 0.12 degrees Celsius to 0.76 degrees Celsius, losing its precise control basis; while Scheme A, through the closed-loop mutual feedback between unscented Kalman filtering and physical information neural network, that is, the unscented Kalman filtering refreshes the physical parameters to the physical information neural network every 15 minutes, and the physical information neural network provides the Smith prediction model predictive control with the initial state verified by physical constraints, tracks and compensates for parameter drift in real time, and its root mean square error of prediction remains stable within 0.06 degrees Celsius after 48 hours. Regarding the wear index of the actuator, the control smoothness constraint of Scheme A controls the frequency of actions to 98 times, which is 71.3% less than Scheme B (342 times) and 47.3% less than Scheme C (186 times), thus extending the service life of the valve and pump body. The above system-level comparative experimental data comprehensively verifies the significant superiority of the system of the present invention from five dimensions: room temperature control accuracy, response speed, comprehensive energy consumption, prediction robustness, and equipment life. At the same time, from an engineering quantification perspective, it also confirms the irreplaceable nature of the deep closed-loop synergy among the three core modules and the dual-channel observation design in the technical solution defined in the claims.

[0063] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A precise thermal process control system based on thermal inertia and digital twin, characterized in that, include: The multi-source heterogeneous data sensing and edge fusion module (100) is used to collect the operating state of the thermal process system and output the external measurable disturbance input vector, the system control input vector and the system state observation feedback vector, wherein the system state observation feedback vector includes the temperature of the controlled area and the surface temperature of the heat capacity element. The digital twin construction module (200) based on the physical information neural network is communicatively connected to the multi-source heterogeneous data perception and edge fusion module. It is used to construct a multi-order equivalent resistance-capacitance thermodynamic network equation for the control region and to construct a composite loss function to train the physical information neural network. The composite loss function includes the physical mechanism residual loss derived from the multi-order equivalent resistance-capacitance thermodynamic network equation. The online identification module (300) for thermal inertia dynamic parameters based on unscented Kalman filtering is communicatively connected to the multi-source heterogeneous data sensing and edge fusion module and the digital twin construction module. It is used to jointly construct an augmented state vector by combining the physical parameters and state variables in the multi-order equivalent resistive-capacitive thermodynamic network equation. It uses the unscented Kalman filtering algorithm and the dual-channel observation information of the controlled area temperature and the surface temperature of the thermal capacity element to perform online recursive correction and update the state transition matrix and input matrix of the multi-order equivalent resistive-capacitive thermodynamic network equation in real time. The optimization module (400) based on Smith prediction compensation and model predictive control is communicatively connected to the online identification module of thermal inertia dynamic parameters. It is used to construct a state-space Smith predictor to remove the pure time delay introduced by pipeline medium transmission from the system feedback loop and obtain the corrected state vector. With the corrected state vector as the initial state condition, the model predictive control solver is used to perform multi-objective rolling optimization and output the optimal thermal input power control sequence. The edge collaborative control sequence execution and physical mapping module (500) is communicatively connected to the optimization module (400) based on Smith prediction compensation and model predictive control. It is used to extract the current optimal heat input power of the optimal heat input power control sequence and inversely map it into the physical drive signal of the underlying actuator.

2. The precise thermal process control system based on thermal inertia and digital twin as described in claim 1, characterized in that, The externally measurable disturbance input vector output by the multi-source heterogeneous data sensing and edge fusion module (100) includes ambient temperature, radiant heat source intensity, and internal disturbance heat; the system control input vector represents the actual heat input power delivered to the target hot zone. It collects water supply temperature Return water temperature and instantaneous mass flow rate The following calculations were performed using the heat balance conversion formula: ； in, This refers to the specific heat capacity at constant pressure of the heating medium.

3. The precise thermal process control system based on thermal inertia and digital twin as described in claim 1, characterized in that, In the multi-order equivalent resistance-capacitance thermodynamic network equation constructed by the digital twin construction module (200) based on the physical information neural network, fast-response lumped heat capacity nodes composed of the fluid medium and internal low heat capacity components within the controlled region and slow-response lumped heat capacity nodes of the building's heavy heat capacity elements are defined; the system state vector is defined as ,in The temperature of the controlled area. This refers to the lumped temperature of the heat capacity element; The surface temperature of the heat capacity element The observation mapping relationship is established between the following formula and the state vector: ； in, It is the proportion of the indoor convective heat transfer thermal resistance in the equivalent lumped thermal resistance between the fluid medium node and the thermal capacity node of the heat capacity element in the controlled area.

4. The precise thermal process control system based on thermal inertia and digital twin as described in claim 3, characterized in that, The composite loss function of the digital twin construction module (200) based on physical information neural network Includes sensor data fidelity loss Physical mechanism residual loss Loss due to initial and boundary conditions Its expression is: ； Among them, the physical mechanism residual loss The thermodynamic residual is obtained by automatically differentiating the output node of the physical information neural network with respect to the input time variable to calculate the rate of temperature change, and then substituting it into the state-space expression composed of the multi-order equivalent resistance-capacitance thermodynamic network equation. , , The weights are continuously and smoothly updated using an adaptive penalty weighting strategy to dynamically adjust the weights.

5. The precise thermal process control system based on thermal inertia and digital twin as described in claim 3, characterized in that, The augmented state vector constructed by the online thermal inertia dynamic parameter identification module (300) based on unscented Kalman filtering is: ,in The original temperature state variable, It is a dynamic physical parameter vector that includes the equivalent lumped heat capacity and the equivalent lumped thermal resistance; The online recursive correction process includes: generating a deterministic sampling point set based on the current posterior estimated mean and covariance matrix, and obtaining the prior state prediction mean after forward derivation through a nonlinear state transition function; An observation vector is established based on the surface temperature of the heat capacity element, the Kalman gain matrix is ​​solved, and the a posteriori correction is performed on the predicted mean of the prior state to extract the latest equivalent lumped heat capacity and equivalent lumped thermal resistance under the current operating conditions.

6. The precise thermal process control system based on thermal inertia and digital twin as described in claim 5, characterized in that, The observation vector The mapping relationship is expressed as: ； in, and The first The temperature of the controlled region and the lumped temperature of the heat capacity element at any given time. This is the observation mapping function that maps the augmented state vector to the sensor's measurable space.

7. The precise thermal process control system based on thermal inertia and digital twin as described in claim 1, characterized in that, In the optimization module (400) based on Smith prediction compensation and model predictive control, the operating logic of the state-space Smith predictor includes: Run a latency-free twin copy to remove pure transmission delay, and output a latency-free predicted state vector. ; Run a full-link twin copy containing the complete transmission delay to output predicted delay observations. ; Using actual sensor measurements Compared with the predicted delayed observations Calculate the observation residuals using the state correction gain matrix. The predicted state vector without delay is subjected to deviation compensation to obtain the corrected state vector. The compensation formula is: .

8. The precise thermal process control system based on thermal inertia and digital twin as described in claim 7, characterized in that, The model predictive control solver constructs a quadratic objective function for multi-objective rolling optimization. It includes economic and demand-side response terms, thermal comfort strict tracking penalty terms, and control smoothness constraints; its mathematical expression is: ； in, To predict the time domain, To control the time domain, This refers to a dynamic time-of-use electricity price sequence or a peak-valley pricing curve for the heating network. These are weighting coefficients. To optimize variable thermal input power, For the predicted temperature of the controlled region, The median temperature within the target comfort range for indoor spaces. For scalar penalty weights, This represents the increment of the change in heat input power. Scalar weights; To optimize decision variables, This represents the increment of the change in heat input power. For summation index variables, This is the discrete time index for the current control cycle. These are the weighting coefficients.

9. The precise thermal process control system based on thermal inertia and digital twin as described in claim 8, characterized in that, The model predictive control solver is also configured with hard physical operation constraints during the rolling time-domain optimization solution process. These hard physical operation constraints include: Thermal input power output range constraints: ,in The maximum heat input power determined for the heat source equipment or the rated capacity of the heat source equipment; Room temperature safety lower limit constraint: ,in This is the preset minimum indoor temperature standard.

10. The precise thermal process control system based on thermal inertia and digital twin as described in claim 1, characterized in that, The reverse mapping process of the edge collaborative control sequence execution and the physical mapping module (500) includes: Based on the heat balance conversion formula, the current supply and return water temperatures of the pipeline network are used to reverse calculate the optimal heat input power at the current moment into the target medium mass flow rate required to achieve that power. Based on the flow characteristic curve of the regulating valve and the resistance characteristics of the pipeline network, the target medium mass flow rate is further converted into the actuator drive signal setting value of the underlying actuator or the frequency setting value of the variable frequency water pump, and then sent to the field underlying controller via the communication bus.

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