A method for heat-supply network aggregation modeling and parameter identification under node measurement loss

Abstract

The application discloses a kind of node measurement under the condition of missing heat supply network aggregation modeling and parameter identification method, establishes the regional heat supply network aggregation model based on source load node heat mapping relationship;According to the decomposable characteristics of model, multiple load nodes or source nodes with missing measurement are equivalently aggregated into a virtual node, and a virtual node aggregation model of regional heat supply network containing virtual node equivalent temperature term is constructed;For the parameter identification problem under the condition of limited measurement, the mass flow rate distribution relationship between source node and load node and the mirror characteristics of supply and return water network are used to establish the supply and return water network aggregation parameter mapping constraint, and the virtual node equivalent temperature is decomposed;Two-stage Lasso regression parameter estimation method is used to improve the robustness of parameter identification through global sparse constraint and structural sparse constraint;The method of the application can realize the interpretable modeling and parameter identification of regional heat supply network without relying on complete operation data of missing nodes and detailed parameters of network internal pipes.

Description

Technical Field

[0001] This invention belongs to the technical field of regional heating network operation, and mainly relates to a method for aggregation modeling and parameter identification of heating networks under the condition of missing node measurements. Background Technology

[0002] District heating systems are a crucial component of urban energy infrastructure, and their operational efficiency, heating reliability, and low-carbon level directly impact the economy and security of the urban energy system. Establishing an accurate and concise district heating network model can effectively support applications such as operation regulation, status analysis, optimized control, and fault diagnosis of the heating system.

[0003] Existing modeling methods for district heating networks mainly include detailed models and aggregated models. Detailed models typically rely on complete network topology, pipe parameters, and node operating status. Although the physical meaning is clear, these models have high dimensionality and require a large amount of computation. Furthermore, it is difficult to obtain and maintain complete network data in practical engineering. Aggregated models can directly depict the temperature mapping relationship between source nodes and load nodes, offering advantages in reducing model complexity. However, they usually require complete operational measurement data for both source and load nodes.

[0004] However, in actual district heating projects, some source or load nodes may lack complete operational data such as supply and return water temperatures, mass flow rates, and heat loads due to reasons such as missing metering devices, equipment malfunctions, communication anomalies, limitations imposed by historical construction conditions, or access to independent wholesale heating stations. Such missing node measurements typically manifest as the node being unobservable throughout the entire time period, making it difficult to recover data using conventional interpolation, filtering, or data completion methods. Therefore, establishing an interpretable, identifiable, and engineering-application-suitable district heating network model without relying on detailed internal pipeline parameters, despite missing measurement data for some source and load nodes, has become a critical issue that urgently needs to be addressed in district heating network modeling and operational analysis. Summary of the Invention

[0005] This invention addresses the problem of existing district heating network aggregation modeling methods relying on complete source-load node measurements and failing to identify the model when some nodes are completely unobservable. It proposes a new method for aggregation modeling and parameter identification of heating networks under conditions of missing node measurements. First, an aggregation model of the district heating network based on the thermodynamic mapping relationship between source and load nodes is established. Then, based on the model's decomposability, multiple load nodes or source nodes with missing measurements are equivalently aggregated into a single virtual node, constructing a virtual node aggregation model of the district heating network that includes the equivalent temperature term of the virtual node. For parameter identification under limited measurement conditions, the mass flow rate distribution relationship between source and load nodes and the mirror characteristics of the supply and return water network are further utilized to establish aggregation parameter mapping constraints for the supply and return water network, decomposing the equivalent temperature of the virtual node. For the aggregation parameter identification part, a two-stage Lasso regression parameter estimation method is adopted, improving the robustness of parameter identification through global sparsity constraints and structural sparsity constraints. Finally, a posterior analysis model of the equivalent temperature of the virtual node is constructed based on typical heat load characteristics, providing a model foundation for simulation, state analysis, and optimal control of district heating network operation under conditions of missing measurements. The method of this invention demonstrates that interpretable modeling and parameter identification of district heating networks can be achieved without relying on complete operational data of missing nodes and detailed parameters of internal pipelines. It can be effectively applied to many scenarios such as operation simulation and status analysis of district heating systems.

[0006] To achieve the above objectives, the technical solution adopted by this invention is: a method for aggregation modeling and parameter identification of heating networks under conditions of missing node measurements, comprising the following steps:

[0007] S1. Establish a regional heating network aggregation model: The model is based on the thermal mapping relationship between source and load nodes, and includes a water supply network model and a return water network model, specifically:

[0008]

[0009] in, Represents the Hadamah altar; as well as It is a function that converts a matrix to a scalar; and These are the first and second functions of the function. The and the first One element; , , and These are the parameters of the aggregation model; It is the ambient temperature of the heating network pipeline; Indicates load node At any moment The water supply temperature; Indicates the source node At any moment The return water temperature; and These are the supply water temperature matrix of the source node and the return water temperature matrix of the load node, respectively. , These represent the sets of indices for the load node and the source node, respectively.

[0010] S2. Constructing a district heating network aggregation model based on virtual nodes: For load nodes / source nodes without measurement data, all load nodes / source nodes are divided into a set of nodes with measurement data and a set of nodes without measurement data. The return water network aggregation coefficient matrix, the return water temperature matrix of the return water network load nodes, the supply water network aggregation coefficient matrix, and the supply water temperature matrix of the supply water network source nodes are decomposed into measured and unmeasured cases, respectively. The specific details of the district heating network aggregation model based on virtual nodes are as follows:

[0011]

[0012] in, Represents the virtual node at time. For the source node The equivalent return water temperature; Represents the virtual node at time. For load nodes The equivalent water supply temperature; , These represent the aggregation coefficient matrix for nodes with measured loads and the aggregation coefficient matrix for nodes with measured sources, respectively. , These represent the supply water temperature matrix with measured source nodes and the return water temperature matrix with measured load nodes, respectively.

[0013] S3. Parameter identification of virtual node aggregation model under finite measurement conditions: Based on the regional heating network aggregation model based on virtual nodes constructed in step S2, solve the mass flow rate distribution relationship between source and load nodes, establish aggregation parameter mapping constraints for supply and return water networks, decompose the equivalent temperature of virtual nodes, and realize the structural identification under the condition of missing node measurement; for the aggregation parameter identification part, the two-stage Lasso regression parameter estimation method is adopted, and the aggregation parameter matrix is ​​identified through global sparsity constraints and structural sparsity constraints.

[0014] As an improvement of the present invention, it further includes step S4, constructing an effectiveness evaluation system for a regional heating network aggregation model based on virtual nodes: constructing an accuracy evaluation index for the source-load thermal mapping relationship to verify the effectiveness of the virtual node aggregation model; constructing an accuracy evaluation index for the source-load mass flow distribution coefficient and the parameter identification of the regional heating network aggregation model to verify the effectiveness of the parameter identification model and its identifiability; and using the evaluation system to obtain the evaluation results for the virtual node aggregation model identified in step S3.

[0015] Compared with the prior art, the present invention has the following beneficial effects:

[0016] (1) The method of the present invention establishes a regional heating system aggregation model based on the direct mapping relationship between source and load nodes, ensuring the universality and rationality of the present invention.

[0017] (2) In step S2 of the method of the present invention, multiple load nodes or source nodes that are completely missing in the aggregation model can be equivalently aggregated into a virtual node from the perspective of thermodynamic relationship, which further clarifies the physical meaning of the aggregation model based on the virtual node.

[0018] (3) The present invention constructs virtual nodes from the perspective of hydraulic equivalence and ensures the mappability of aggregate parameters of the supply and return water network through the mass flow rate distribution relationship, thus ensuring the structural identifiability of the model under the condition of missing node measurement. At the same time, the present invention adopts a two-stage Lasso regression parameter estimation method, firstly determining the potential non-zero structure of the aggregate parameter matrix through global sparse constraints, and then performing secondary identification through structural sparse constraints, which can improve the robustness of parameter identification under measurement error conditions.

[0019] (4) The present invention constructs a virtual node equivalent temperature posterior analysis model, which can perform periodicity, amplitude range and function fitting characteristic analysis on the overall heat load impact of missing measurement nodes, and provides a model basis for regional heating system operation simulation, state analysis, optimization control and decision support in the case of missing engineering measurements.

[0020] (5) The method of this invention proves that a load node or source node with missing measurements can be equivalently modeled as a virtual node from both thermal and hydraulic perspectives and a regional heating network aggregation model based on the virtual node can be constructed. Compared with existing approximation methods without measurement data, the method of this invention has clear physical meaning and low model complexity. The proposed parameter identification algorithm based on the virtual aggregation model is the first to propose the use of two-stage Lasso regression to satisfy structural sparsity constraints, which can be effectively applied to many scenarios such as large measurement noise and missing measurement data in regional heating network engineering. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the general structure of the present invention based on a district heating network;

[0022] Figure 2 This is a flowchart of the steps of a method for aggregation modeling and parameter identification of a heating network under missing node measurements according to the present invention.

[0023] Figure 3 This is a schematic diagram of the regional heating network aggregation model structure based on the thermal mapping relationship of source and load nodes according to the present invention;

[0024] Figure 4 This is a schematic diagram of the regional heating network aggregation model structure based on virtual nodes according to the present invention;

[0025] Figure 5 This is a schematic diagram of the return water temperature curves of the virtual node and the measured node obtained by the present invention.

[0026] Figure 6 This is a schematic diagram of the district heating system structure in the test example of this invention;

[0027] Figure 7 This is a schematic diagram of the reconstructed source-load node thermal mapping results in the test example of this invention. Detailed Implementation

[0028] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0029] Example 1

[0030] A method for aggregation modeling and parameter identification of heating networks under conditions of missing node measurements is applied to a district heating system, the structure of which is as follows: Figure 1 As shown. A district heating system includes a heat source, a heat load, and is coupled and energy converted between the heat source and the heat load via supply and return water pipes and network aggregation nodes. The process flow is as follows: Figure 2 As shown, it includes the following steps:

[0031] Step S1: Establish a regional heating network aggregation model based on the thermal mapping relationship between source and load nodes;

[0032] The regional heating network aggregation model based on the thermal mapping relationship between source and load nodes consists of two parts: a water supply network model and a return water network model, such as... Figure 3 As shown, the relationships between the supply water temperature of the source node and the supply water temperature of the load node, as well as the relationship between the return water temperature of the load node and the return water temperature of the source node, are depicted respectively. The mathematical form of the model is as follows:

[0033]

[0034] in, Represents the Hadamah altar; as well as It is a function that converts a matrix to a scalar; and They are the first among them The and the first One element; , , and These are the parameters of the aggregation model; It is the ambient temperature of the heating network pipeline; Indicates load node At any moment The water supply temperature; Indicates the source node At any moment The return water temperature; and These are the supply water temperature matrix of the source node and the return water temperature matrix of the load node, respectively. , These represent the sets of indices for the load node and the source node, respectively.

[0035] Water supply temperature matrix of the source node Return water temperature matrix of load nodes The specific definitions are as follows:

[0036]

[0037] in, Represents the moment Source node The water supply temperature; Represents the moment Load Node The return water temperature; The dimension representing the aggregation model; Indicates the number of source nodes; This indicates the number of load nodes.

[0038] Aggregate model parameters , , and The specific definitions are as follows:

[0039]

[0040]

[0041] in, , as well as As given below:

[0042]

[0043]

[0044]

[0045] Among them, model parameters , , , , and It can be derived from the classic node method of district heating networks.

[0046] Step S2: Based on the decomposability of the linear time-invariant aggregation model, construct a district heating network aggregation model based on virtual nodes. Specifically, multiple load nodes or source nodes with missing measurements are equivalently aggregated into a single virtual node, constructing a district heating network virtual node aggregation model that includes the equivalent temperature term of the virtual node, such as... Figure 4 As shown;

[0047] S21. Decompose the correlation quantities with and without measurement nodes.

[0048] S211. If some load nodes lack measurement data, divide all load nodes into a set of nodes with measurement data. and the set of unmeasured nodes ; The complete aggregation coefficient matrix of the recirculation network Decomposed into a matrix of aggregate coefficients for measurable load nodes and the aggregation coefficient matrix of unmeasured load nodes The complete return water network load node return water temperature matrix Decomposed into a matrix of aggregate coefficients for measurable load nodes and the aggregation coefficient matrix of unmeasured load nodes The specific definitions of the variables are as follows:

[0049]

[0050] in, express The List; express The List.

[0051] S212. If some source nodes lack measurement data, divide all source nodes into a set of nodes with measurement data. and the set of unmeasured nodes ; Aggregate the complete water supply network coefficient matrix Decomposed into a matrix of aggregate coefficients of measurement source nodes and the aggregation coefficient matrix of the source nodes without measurement The complete water supply network source node water supply temperature matrix Decomposed into a matrix of aggregate coefficients of measurement source nodes and the aggregation coefficient matrix of the source nodes without measurement The specific definitions of the variables are as follows:

[0052]

[0053] in, express The List; express The List.

[0054] S22. Derive the aggregation model based on virtual nodes;

[0055] S221. Virtual node aggregation model under partial load node absence:

[0056] Rewrite the original aggregation model of the water return network constructed in step S1.

[0057]

[0058] Define the equivalent temperature of virtual nodes satisfy:

[0059]

[0060] The final virtual node aggregation model is obtained:

[0061]

[0062] In the above virtual node aggregation model of the return water network, the effect of the virtual node on the return water temperature of the source node is thermally equivalent to that of the missing measurement load node.

[0063] S222, Virtual node aggregation model with partial source node missing:

[0064] Rewrite the original aggregated model of the water supply network constructed in step S1.

[0065]

[0066] Define the equivalent temperature of virtual nodes satisfy:

[0067]

[0068] The final virtual node aggregation model is obtained:

[0069]

[0070] In the above-mentioned virtual node aggregation model of the water supply network, the effect of the virtual node on the water supply temperature of the load node is thermally equivalent to that of the missing measurement source node.

[0071] Step S3, Parameter Identification of Virtual Node Aggregation Model under Finite Measurement Conditions: For the virtual node aggregation model constructed in Step S2, by solving the mass flow rate distribution relationship between source and load nodes and utilizing the mirror characteristics of the supply and return water network, the aggregation parameter mapping constraint of the supply and return water network is established, and the equivalent temperature of the virtual nodes is decomposed to achieve structural identification under the condition of missing node measurement; for the aggregation parameter identification part, the two-stage Lasso regression parameter estimation method is adopted, and the aggregation parameter matrix is ​​identified through global sparsity constraints and structural sparsity constraints.

[0072] Taking partial load node missing measurement as an example, the parameter identification of the virtual node aggregation model under limited measurement conditions specifically includes the following steps:

[0073] S31. For load nodes with measurements, the water supply network aggregation coefficient is identified based on the measurement data using a two-stage Lasso regression estimator:

[0074] S311, The parameter estimation model for the first stage is:

[0075]

[0076] in, It is the penalty coefficient of the L1 norm.

[0077] S311, The parameter estimation model for the second stage is:

[0078]

[0079] in, It is the aggregation parameter matrix estimated in the first stage. The index of the position of the largest element in the k-th column; It is the aggregation parameter matrix estimated in the first stage. The index of the upper bound of the non-zero element in the k-th column; It is the aggregation parameter matrix estimated in the first stage. The index of the lower bound of the non-zero element in the k-th column; It is the aggregation coefficient matrix The dimension of non-zero elements.

[0080] S32. Solve for the mass flow distribution coefficient matrix of the supply and return water network:

[0081] Define the mass flow distribution coefficient matrix for the water supply and return network. , To describe the mass flow distribution relationship between source and load nodes:

[0082]

[0083] The missing load nodes are hydraulically equivalently aggregated into a single mass flow rate. The mass flow distribution coefficient is Virtual load nodes, satisfy:

[0084]

[0085]

[0086]

[0087] Together with virtual nodes and other measured nodes, construct a system of equations for mass flow distribution coefficients and solve them.

[0088]

[0089] in, Indicates the source node mass flow rate; Indicates load node The mass flow rate. Solving the above system of equations yields the mass flow rate distribution coefficient matrix for the supply and return water network. , .

[0090] S33. Solve for the aggregation coefficient of the backwater network with measurement nodes:

[0091] Since the supply and return water network pipe structure and topology of the district heating network are mirror images, the supply and return water network parameters satisfy:

[0092]

[0093] Therefore, the aggregation coefficient of the return water network with measured load nodes can be calculated based on the aggregation coefficient of the water supply network with measured load nodes and the mass flow distribution coefficient matrix:

[0094]

[0095] S34. Decompose the equivalent temperature of virtual nodes and perform posterior analysis:

[0096]

[0097] When the missing heat load has periodic variations, the flow rate and temperature returned to the source node in the return water network also exhibit periodicity:

[0098]

[0099] Therefore, the flow temperature returned to the source node by the virtual node that aggregates unmeasured load nodes also exhibits periodicity:

[0100]

[0101] Based on the virtual node equivalent temperature curve decomposed in step S34, feature indicators are extracted, including but not limited to period size, amplitude range, and function fitting characteristics.

[0102] The above describes the identification process for missing measurements at some load nodes. Missing measurements at some source nodes are a mirror image of missing measurements at some load nodes, so the identification process is the same.

[0103] In addition to the identification described above, the method of this invention also includes step S4: constructing an effectiveness evaluation system for a regional heating network aggregation model based on virtual nodes. This involves constructing an accuracy evaluation index for the source-load thermal mapping relationship to verify the effectiveness of the virtual node aggregation model; and constructing an accuracy evaluation index for the source-load mass flow distribution coefficient and the parameter identification of the regional heating network aggregation model to verify the effectiveness of the parameter identification model and its identifiability. The parameter identification algorithm proposed in step S3 is used to identify the virtual node aggregation model obtained in step S2, and then the model performance is analyzed according to the effectiveness evaluation system constructed in step S4 to summarize the final evaluation results.

[0104] The effectiveness of the virtual node aggregation model used to reconstruct the heat map is evaluated using three statistical metrics: root mean square error, mean absolute percentage error, and coefficient of determination. Their definitions are as follows:

[0105]

[0106]

[0107]

[0108] Where, represents the sample size; This represents the temperature calculated by the virtual node aggregation model; This indicates the actual measured value.

[0109] To rigorously evaluate the accuracy of the parameter identification method, three matrix-level error metrics are introduced. Let... and Let the elements represent the true matrix elements and the identified matrix elements, respectively. The deviation between the two is quantified using matrix-level root mean square error, mean absolute percentage error, and relative Frobenius norm. Their definitions are as follows:

[0110]

[0111]

[0112]

[0113] Based on MATLAB, the virtual node aggregation model established in step S3 was identified and calculated using Gurobi; then, based on the effectiveness evaluation system of the virtual node-based regional heating network aggregation model constructed in step S4, the accuracy of thermal network parameter identification was tested.

[0114] Given the load curves of randomly disturbed load nodes and the fixed heat power of source nodes, the supply and return water temperatures of source and load nodes at several moments are generated using the classic nodal method for heating networks. The parameters of the virtual node aggregation model of this system are then optimized and identified using this model. Since the aggregation coefficient can be analytically calculated given the system parameters, the aggregation parameters identified through the source and load node operating data are compared and analyzed with the analytically calculated aggregation parameters.

[0115] Figure 5 The table shows the return water temperature curves of the real nodes and the equivalent return water temperature curves of the virtual nodes in the separated return water network. Table 1 illustrates the results of parameter identification of the virtual node aggregation model based on the proposed identification algorithm in a simulated real-world engineering scenario with varying degrees of measurement noise.

[0116] Table 1

[0117]

[0118] Depend on Figure 5 As can be seen, the virtual node modeling and parameter identification method proposed in this invention can effectively decompose the return water temperature of the source node from the measured load node and the return water temperature of the source node from the virtual node (the node without measured load). Table 1 shows that the parameter identification results of the virtual node modeling and parameter identification method proposed in this invention are completely identical under conditions of no measurement noise and complete measurement, and can ensure that the parameter identification error is within 10% at a normal measurement noise level of 1%. -3 Below, under extreme operating conditions with a 10% noise level, the parameter identification error did not exhibit exponential divergence, and the error growth remained linearly stable. These results demonstrate that the virtual node aggregation model identification method proposed in this invention achieves identification results consistent with theoretical values ​​in the absence of measurement errors, possessing theoretical accuracy. Furthermore, it exhibits robustness in the face of varying degrees of noise.

[0119] Test case

[0120] The system applicable to this test case is a 51-node district heating system, such as... Figure 6As shown, the district heating network has one heat source and 26 heat loads. Of these, 20 heat loads lack measurement facilities, while 6 heat loads are measurable. The sampling period for the supply and return water temperatures at the source and load nodes used for parameter identification is 5 minutes, and the simulation data is generated based on the nodal method.

[0121] According to the steps of this invention, a virtual node-based aggregation model is constructed and its parameters are identified. The theoretical parameters and the identified parameters are shown in Tables 2 and 3, respectively. The results of reconstructing the source-load node thermodynamic mapping using the virtual node aggregation model are shown below. Figure 7 As shown:

[0122] Table 2

[0123]

[0124] Table 3

[0125]

[0126] As can be seen from the theoretical and identified values ​​of the aggregation parameters in Tables 2 and 3, the parameter identification method proposed in this invention is accurate and effective, and can accurately identify the precise values ​​of parameters under some measurement conditions in the absence of noise. Figure 7 The temperature curve reconstructed based on the virtual node aggregation model and the baseline curve generated based on the node method almost completely overlap, further verifying the accuracy and effectiveness of the virtual node aggregation model and the corresponding identification algorithm.

[0127] In summary, this invention establishes a regional heating network aggregation model based on the thermal mapping relationship between source and load nodes. Based on the model's decomposability, a virtual node aggregation model is constructed to represent the thermally equivalent aggregation of missing measurement nodes. Furthermore, utilizing the hydraulic equivalence of virtual nodes, the mass flow rate distribution relationship between source and load nodes is solved, and based on the mirror characteristics of the supply and return water networks, aggregation parameter mapping constraints are established, enabling structural identification of the virtual node aggregation model under conditions of missing node measurements. A two-stage Lasso regression parameter estimation method is then employed to identify aggregation parameters exhibiting global and structural sparsity. Finally, the modeling and evaluation results are obtained by combining the constructed virtual node-based regional heating network aggregation model effectiveness evaluation system. This invention achieves low-complexity, interpretable modeling and parameter identification of regional heating networks without relying on complete operational data of missing nodes and detailed internal pipeline parameters. It improves the model's applicability and robustness under conditions of missing engineering measurements and measurement errors, providing effective technical support for operational simulation, state analysis, optimized control, and fault diagnosis of regional heating systems.

[0128] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0129] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A method for aggregation modeling and parameter identification of heating networks under conditions of missing node measurements, characterized in that, Includes the following steps: S1. Establish a regional heating network aggregation model: The model is based on the thermal mapping relationship between source and load nodes, and includes a water supply network model and a return water network model, specifically: in, Represents the Hadamah altar; as well as It is a function that converts a matrix to a scalar; and These are the first and second functions of the function. The and the first One element; , , and These are the parameters of the aggregation model; It is the ambient temperature of the heating network pipeline; Indicates load node At any moment The water supply temperature; Indicates the source node At any moment The return water temperature; and These are the supply water temperature matrix of the source node and the return water temperature matrix of the load node, respectively. , These represent the sets of indices for the load node and the source node, respectively. S2. Constructing a district heating network aggregation model based on virtual nodes: For load nodes / source nodes without measurement data, all load nodes / source nodes are divided into a set of nodes with measurement data and a set of nodes without measurement data. The return water network aggregation coefficient matrix, the return water temperature matrix of the return water network load nodes, the supply water network aggregation coefficient matrix, and the supply water temperature matrix of the supply water network source nodes are decomposed into measured and unmeasured cases, respectively. The specific details of the district heating network aggregation model based on virtual nodes are as follows: in, Represents the virtual node at time For the source node The equivalent return water temperature; Represents the virtual node at time For load nodes The equivalent water supply temperature; , These represent the aggregation coefficient matrix for nodes with measured loads and the aggregation coefficient matrix for nodes with measured sources, respectively. , These represent the supply water temperature matrix with measured source nodes and the return water temperature matrix with measured load nodes, respectively. S3. Parameter identification of virtual node aggregation model under finite measurement conditions: Based on the regional heating network aggregation model based on virtual nodes constructed in step S2, solve the mass flow rate distribution relationship between source and load nodes, establish aggregation parameter mapping constraints for supply and return water networks, decompose the equivalent temperature of virtual nodes, and realize the structural identification under the condition of missing node measurement; for the aggregation parameter identification part, the two-stage Lasso regression parameter estimation method is adopted, and the aggregation parameter matrix is ​​identified through global sparsity constraints and structural sparsity constraints.

2. The method for aggregation modeling and parameter identification of heating networks under conditions of missing node measurements as described in claim 1, characterized in that: In step S1, based on the regional heating network aggregation model of the source-load node thermal mapping relationship, the water supply temperature matrix of the source node... and the return water temperature matrix of the load node Specifically: in, Represents the moment Source node The water supply temperature; Represents the moment Load Node The return water temperature; The dimension representing the aggregation model; Indicates the number of source nodes; This indicates the number of load nodes.

3. The method for aggregation modeling and parameter identification of heating networks under conditions of missing node measurements as described in claim 2, characterized in that: In step S1, the parameters of the aggregation model , , and They are respectively: Among them, aggregation parameters Source-load node flow distribution coefficient and aggregation model dimensions Specifically: in, It is the source node Flow to load nodes mass flow rate; It is composed of load nodes Flow to source load node mass flow rate; Indicates that by node To the node Transmission delay, Indicates that by node To the node The number of shortest path pipelines, , , and These are the equivalent parameters of the water supply and return network pipelines.

4. The method for aggregation modeling and parameter identification of heating networks under missing node measurements as described in claim 1, characterized in that: In step S2, the virtual node at time... For the source node equivalent temperature and virtual nodes at time For load nodes equivalent temperature They are respectively: in, , , , Specifically: in, , These represent the sets of indices with and without measurement source nodes, respectively. , These represent the sets of indices for nodes with and without measured loads, respectively.

5. The method for aggregation modeling and parameter identification of heating networks under conditions of missing node measurements as described in claim 4, characterized in that: Step S3 specifically includes the following steps: S31: For load nodes with measurements, the aggregation coefficient of the water supply network is identified based on the measurement data. The identification model can be transformed into the following optimization problem: in: S32: Define and obtain the mass flow distribution coefficient matrix for the supply and return water network. , The mass flow distribution coefficient solution equation is constructed by combining virtual nodes and other measured nodes to solve the mass flow distribution coefficient matrix of the water supply and return network; the specific solution equation for the mass flow distribution coefficient is as follows: in, Indicates the source node mass flow rate; Indicates load node mass flow rate; S33: Based on the mirror properties of the supply and return water network pipeline structure and topology of the district heating network, and according to the aggregation coefficient of the supply water network with measured load nodes obtained in step S31 and the mass flow distribution coefficient matrix obtained in step S32, the aggregation coefficient of the return water network with measured load nodes is calculated: S34: Decompose the equivalent temperature of the virtual node and perform a posteriori analysis. When the missing heat load has periodic changes, the flow temperature returned to the source node in the return water network also has periodicity. The flow temperature returned to the source node by the virtual node of the aggregated unmeasured load node also has periodicity.

6. The method for aggregation modeling and parameter identification of heating networks under conditions of missing node measurements as described in claim 5, characterized in that: In step S31, the aggregation coefficient of the water supply network with measured load nodes is identified using a two-stage Lasso regression parameter estimation method. The parameter estimation model for the first stage is as follows: in, It is the penalty coefficient of the L1 norm; The parameter estimation model for the second stage is as follows: in, It is the aggregation parameter matrix estimated in the first stage. The index of the position of the largest element in the k-th column; It is the aggregation parameter matrix estimated in the first stage. The index of the upper bound of the non-zero element in the k-th column; It is the aggregation parameter matrix estimated in the first stage. The index of the lower bound of the non-zero element in the k-th column; It is the aggregation coefficient matrix The dimension of non-zero elements.

7. The method for aggregation modeling and parameter identification of heating networks under missing node measurements as described in claim 6, characterized in that: In step S22, the mass flow rate allocation coefficient matrix of the supply and return water network , Specifically: ； The missing load nodes are hydraulically equivalently aggregated into a single mass flow rate. The mass flow distribution coefficient is Virtual load nodes, satisfy: 。 8. The method for aggregation modeling and parameter identification of heating networks under missing node measurements as described in claim 7, characterized in that: The system also includes step S4, which constructs an effectiveness evaluation system for a regional heating network aggregation model based on virtual nodes to evaluate the effectiveness of the virtual node aggregation model that reconstructs the thermal mapping and the accuracy of parameter identification. The evaluation indicators for the effectiveness of the virtual node aggregation model are root mean square error, mean absolute percentage error, and coefficient of determination. The evaluation indicators for the accuracy of parameter identification are the root mean square error, mean absolute percentage error, and relative Frobenius norm at the matrix level to quantify the deviation between the real matrix elements and the identified matrix elements.

9. The method for aggregation modeling and parameter identification of heating networks under conditions of missing node measurements as described in claim 8, characterized in that: The evaluation metrics for the accuracy of parameter identification are as follows: in, and These represent the actual matrix elements and the identified matrix elements, respectively.

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