A virtual-real fusion experiment solving and deduction method based on plane topology

Abstract

The application discloses a kind of based on plane topology virtual-real fusion experiment solving and deduction method, specifically for: S1 constructs topological network: the connecting relationship between utensil and utensil is abstracted as a plane topological network;S2 constructs topological matrix equation: after being abstracted as node and branch from plane topological structure, based on MNA, establish unified equation group, and introduce conservation relationship and branch constitutive relation at node level, after converting all branch constitutive relation into matrix form, diagonal impedance matrix is introduced;S3 solve result drive experiment deduction: construct node analysis model based on plane topology;Obtain solving result by node analysis model;Then the solving result is used for the deduction of experimental process and animation presentation.The method is based on improved MNA to the plane topological structure formed by experimental utensil and its connecting relationship carries out unified modeling and solving, significantly reduces system development and maintenance cost, and improves the deduction accuracy and scoring credibility under the scene of free building.

Description

Technical Field

[0001] This invention belongs to the field of educational informatization and virtual simulation technology, specifically involving a method for solving and deducing virtual-real fusion experiments based on planar topology. Background Technology

[0002] In virtual simulation experimental systems, users can freely combine experimental apparatus to conduct exploratory learning. However, this free combination leads to complex experimental structures and introduces a high degree of uncertainty. In chemical experiments, when various apparatuses such as reaction devices, gas washing devices, drying devices, and collection devices are arbitrarily connected through rubber tubes or glass conduits, the experimental system needs to determine in real time the direction of fluid transport, distribution ratio, and final result within the complex interconnected structure. Such interconnected structures are not predetermined but dynamically change with user operation, making it difficult to predict the experimental process using a pre-set procedure.

[0003] The above problems are usually addressed using a conditional judgment approach, which involves enumerating possible connection scenarios and writing judgment rules for different paths to determine whether a substance can be transported from one device to another. However, when multiple reaction sources, multiple branching paths, or multi-level series structures exist simultaneously in an experiment, the number of connection combinations increases exponentially, and the number of rules increases dramatically, making the fixed-rule approach clearly infeasible.

[0004] However, in the field of electrical engineering, although the improved node analysis method can effectively solve the overall problem of multiple power sources and multiple branches in complex circuits, it assumes by default that the wires can diverge in multiple directions at the nodes, which is significantly different from the physical characteristics of "single terminal - single connection" of rubber tubes or glass conduits in chemical experiments.

[0005] Chinese patent document CN109410343A discloses a method and system for biological experiments based on virtual reality. This invention relates to the field of virtual reality simulation. It generates biological structural model data by acquiring geometric feature data and experimental initialization structural data of organisms; it acquires biological behavioral and growth characteristics to generate biological perception model data; it acquires experimental settings such as light, water, temperature, wind, and soil parameters to generate an environmental model; and it dynamically synthesizes a virtual reality model of the organism using a 3D graphics engine based on the biological category, the biological structural model data, the biological perception model data, and the environmental model. This prior art achieves the generation of virtual reality biological experimental samples and simulates various special effects of real-world samples more realistically, resulting in highly reliable experimental results.

[0006] Chinese patent document CN110473441A discloses a smart learning-based virtual simulation system and method for chemical experiments, including a compound and component trigger event listener module and a chemical reaction simulator module. The compound and component trigger event listener module contains multiple listening points, which listen for the following information: changes in component attributes triggered between components or the generation of new components; combinations of compounds and components, where the compound's attributes are assigned to the new attributes of the components; and combinations of compounds to obtain the generated compounds and reaction phenomena. The chemical reaction simulator module listens for the mixing states of components and compounds, calls upon the periodic table and a vast amount of compound structural information, and intelligently calculates the generated compounds, reaction phenomena, and information on remaining compounds based on the compounds and reaction conditions using reaction equation functions. However, this existing technology can only handle single, deterministic, and known main reactions, does not support side reactions, and relies solely on "event listening and rule matching," lacking true intelligent learning capabilities and inference and scoring mechanisms.

[0007] Therefore, there is an urgent need for a virtual-real fusion experimental solution and deduction method based on planar topology. This method provides a general and scalable technical path for process deduction under complex experimental structures through a simulation experimental solution method based on planar topology. Summary of the Invention

[0008] The technical problem to be solved by this invention is to provide a virtual-real fusion experimental solution and deduction method based on planar topology. The experimental deduction method with Modified Nodal Analysis (MNA) as the core is not reflected in the improvement of a single experimental process or performance form, but in the formation of a systematic innovation that is different from conventional solutions at the basic method level of experimental deduction.

[0009] To address the aforementioned technical problems, this invention provides a method for solving and deducing virtual-real fusion experiments based on planar topology, specifically including the following steps:

[0010] S1 Constructing a Topology Network: Obtain the equipment and the connections between the equipment in the experimental scenario. By matching the interfaces of each equipment with the corresponding nodes, the equipment and the connections between the equipment are abstracted into a planar topology network, and a planar topology structure that satisfies the constraints is constructed.

[0011] S2 constructs the topological matrix equation: After abstracting the planar topology into nodes and branches, a unified set of equations is established based on MNA, and conservation relations and branch constitutive relations are introduced at the node level. After converting all branch constitutive relations into matrix form, a diagonal impedance matrix is ​​introduced to obtain an improved topological matrix.

[0012] S3 solution results drive experimental simulation: Define the experimental source, calculate the node pressure P, and then calculate the branch flow Q. Use the node pressure P and branch flow Q as unified state variables for experimental simulation. The virtual simulation system updates these state variables at each simulation time step. Construct a node analysis model based on planar topology. Obtain the solution results through the node analysis model. Then use the solution results to simulate the experimental process and present them in the animation presentation layer.

[0013] By adopting the above technical solution, the device connection structure freely built by the user in the virtual simulation experiment is uniformly abstracted into a planar topology network, and the topological relationship is used as the only logical input for experimental deduction, which fundamentally avoids the enumeration and condition judgment of specific experimental paths in traditional methods. This paper introduces and modifies the MNA (Multi-Node Networking) concept in circuit analysis, enabling experimental deduction to no longer rely on preset rules. Instead, it automatically obtains the physical state of each device and the material transport results by solving the overall equation system composed of nodes and branches. Addressing the real physical characteristics of rubber tubes in chemical experiments ("single terminal - single connection"), the assumption of multi-path divergence in traditional MNA is structurally modified, ensuring that the topology model maintains its overall solution advantage while strictly conforming to actual experimental constraints. Furthermore, chemical reaction rates are introduced into the topology solution system, directly mapped to source terms in the improved MNA equations. This allows materials generated by multiple reaction devices in the same experimental network to naturally couple and influence each other at the mathematical level, without the need for manually setting priorities or path rules. This significantly breaks through the technical path of traditional virtual experiments that relies on fixed scripts and decentralized judgment logic, providing a scalable, interpretable, and highly universal deduction method for virtual simulation experiments in freely constructed, multi-source collaborative, and complex connected scenarios.

[0014] Preferably, the method further includes step S4, which scores the experimental deduction: The solution results of the node analysis model (improved MNA) serve as the common basis for the experimental animation and scoring mechanism. This involves incorporating topological legality, deduction consistency, and goal achievement into a unified computable framework. The score is defined as a combination mapping of several evaluation functions to P and Q, thereby obtaining the scoring result. Using the solution results of the improved MNA as the common basis for the experimental animation and scoring mechanism achieves a unified foundation for experimental logic, visual presentation, and evaluation judgment, transforming experimental scoring from result-based judgment to a quantitative assessment based on the entire topology deduction process.

[0015] Preferably, the specific steps of step S1, which involves establishing a matching relationship between the interfaces of each device and the nodes, to construct a planar topology that satisfies the constraints, are as follows:

[0016] S11: Define the appliance nodes and the branches connecting the appliances, and define the node pressure vector and the branch flow vector;

[0017] S12: Define the transmission characteristics of chemically treated rubber hoses;

[0018] S13: Define the source of occurrence to construct a planar topology that satisfies the constraints.

[0019] Preferably, the specific steps of step S11 are as follows:

[0020] S111: Let there be N equipment nodes in the experiment, denoted as set N. Each node It corresponds to a specific tool;

[0021] S112: Let there be a total of M connecting devices, denoted as set M. Each branch road Connect two appliance nodes and assign directions to them in the system;

[0022] S113: In chemical experiments, for apparatus involving chemical quantities, if the chemical quantity is equivalent to the node potential variable and replaced with the pressure state inside the apparatus, then the branch current is replaced with the flow rate of the substance in the rubber tube.

[0023] Define the nodal pressure vector: ;

[0024] in, Represents a node That is, the internal pressure of a certain device at the current moment, which is the driving force that determines the gas pushing outward from the device;

[0025] S114: Define the branch flow vector: ;

[0026] in, Indicates a branch The volumetric flow rate or molar flow rate (corresponding to a rubber tube or glass conduit) is determined by the sign of the branch direction: if the actual gas flow direction is the same as the branch direction, then... ,on the contrary .

[0027] Preferably, in step S1, for the case with chemical rubber tubing, the transmission characteristics of the chemical rubber tubing are defined as branch impedance parameters. This is used to comprehensively characterize the obstruction effect of pipes on flow, and the branch impedance parameters... By the head of the pipe , inner diameter The impedance is calculated from parameters such as fluid viscosity. To ensure the universality of the topology analysis method, this invention does not limit the specific physical model of the impedance, but only requires that it can vary with the pipe properties. In the derivation, this impedance corresponds to the resistance / admittance concept of electrical MNA, and is used to determine how the pressure difference is distributed as flow rate.

[0028] Preferably, since there are "source terms" in chemical experiments, such as gas being generated in a reaction flask, which acts like a power source in a circuit, causing the pressure at a certain node to continuously rise or generating an equivalent injection flow rate; therefore, in step S1, the vector of the generation source (such as a reaction device or power source) is defined as: ;

[0029] in, Represents a node The "equivalent injection rate" is used to describe the device's gas contribution to the network per unit time; if modeled in the form of flow conservation, then... "Injected flow" can be used; if modeled as a dynamic form of pressure, then... "Pressure growth driver" is a good option.

[0030] Preferably, an injection flow form is used to directly couple with the conservation equations.

[0031] To reflect the physical constraint of "single terminal - single connection" by adopting the above technical solution, this invention establishes a matching relationship for each appliance interface during the topology construction stage: each interface can only be matched with one endpoint of a branch, thereby avoiding the illegal situation of "one interface connecting two pipes" in the graph structure. This constraint ensures that although the topology can be complexly combined, the connection relationship of each port is unique, thus guaranteeing that the deduction result is physically achievable.

[0032] Preferably, the specific steps of step S2 are as follows:

[0033] S21: First, construct the node-branch association matrix. Its elements are defined as:

[0034] ;

[0035] in, Represents the i-th node n i With branch b of the jth branch j The connection and directional relationships, b j Indicates a branch; n i N represents the number of nodes; M represents the total number of branches. It represents the set of real numbers.

[0036] This matrix is ​​determined solely by the planar topology network generated in step S1 and is independent of the specific type of experiment. When the user plugs or unplugs the connecting pipes to change the connection relationship, the system only needs to update the corresponding column of A to reconstruct the equation system in real time without having to write any conditional judgments about the "path".

[0037] S22: Subsequently, a conservation relationship is introduced at the node level. In the gas production and transmission problem, the net outflow at a node should be equal to the injection source term at that node. Therefore, the node conservation equation is established as follows:

[0038] ;

[0039] Equivalent to: ;

[0040] Among them, let For branch flow vectors, The equivalent flow vector injected into a node, the i-th component of the left-hand AQ can be represented as:

[0041] ;

[0042] in, Represents a node The algebraic sum of the flows of all connected branches, i.e., the "net outflow"; right side This represents the equivalent injected traffic to that node; Let j represent the flow vector of the j-th branch; explain with an example: if It is a reaction flask, and the reaction is producing gas. ;like If it is an external exhaust port or equivalent sink for an absorption device, then... If a node only acts as a relay point and neither produces nor consumes gas, then In this way, the simultaneous gas production of multiple reaction devices naturally manifests as multiple The system does not need additional rules to determine "which source takes priority";

[0043] S23: The nodal pressure and branch flow are correlated through the branch constitutive relation (equivalent to "Ohm's Law"), with the following formula:

[0044] ;

[0045] in, Indicates a branch The starting node, Indicates a branch The endpoint (in the same direction as the branch road). The pressure difference between the devices at both ends of the rubber hose (i.e., the j-th branch) is... Let be the equivalent impedance of the j-th branch; this formula directly expresses a key fact in chemical experiments: gas is pushed from a high-pressure device to a low-pressure device, and the intensity of this push (flow rate) is determined by both the pressure difference and the pipe impedance. If a pipe is longer or narrower, then... Increasing the pressure difference results in a smaller flow rate for the same pressure differential; conversely... Smaller values ​​result in larger flow rates, thus automatically creating a "distribution effect" in complex topologies;

[0046] S24: Write the constitutive relations of all branches in matrix form, and introduce the diagonal impedance matrix. Its admittance form We can obtain: ;

[0047] in, The j-th component is exactly the branch The algebraic expression of the pressure difference between the two nodes is that the node pressure P is transformed into the pressure difference of each branch through the correlation matrix A; That is, Z j (j=1,2,…,M) represents the unified correspondence to the j-th branch b. j impedance;

[0048] G represents the admittance matrix, which maps the pressure difference to the flow rate;

[0049] Substituting this equation into the conservation equation This yields a unified solution equation for nodal pressures only: ,make: Then the equation can be written as: KP=S;

[0050] In this equation, K is entirely determined by topology and impedance parameters, P is the appliance pressure state obtained from the solution, and S is the source term for each node. This equation is the core of this invention, integrating MNA into chemical topology derivation: the system no longer "finds paths," but instead obtains the global pressure distribution by solving a system of linear equations, thereby obtaining the flow rate of each pipe. Therefore, regardless of how freely users connect, the more complex the topology, the more the advantages of this method become apparent.

[0051] Preferably, the specific steps for scoring the experimental deduction in step S4 are as follows:

[0052] Define the target node set (e.g., gas collecting cylinder node) and set of critical branches (e.g., the branch from the gas washing bottle to the gas collecting bottle), construct the target achievement items, specifically:

[0053] ;

[0054] Among them, F T It is the objective function, representing the overall optimization target value of the system, used to measure the combined effect of the target node pressure achievement and the traffic constraints of key branches under the current network conditions; It is the target node set, representing the set of nodes that need to be focused on or optimized; It is the set of critical branches, representing the set of branches that have a significant impact on the operation of the system; It is a node target characterization function, used to describe the degree of achievement or trend of change of the target node pressure; It is a branch constraint characterization function, used to describe the effectiveness constraints of the flow in key branches; It represents the node pressure, indicating the pressure state variable at the node. It represents the branch flow, indicating the flow on the j-th branch.

[0055] Preferably, in the scoring of step S4, if it is necessary to penalize backflow or short-circuit bypass caused by faulty connections, then the following applies: If a penalty term is added to the critical branch, or to situations that cause an abnormal increase in pressure at a node, then the final scoring formula is expressed as:

[0056] ;

[0057] in, This represents the backflow / reverse flow risk term (constructed from the flow sign and amplitude of the key branch). This indicates the connection compliance item (constructed from "one-to-one port matching" and experimental rule constraints). , , The weights are configurable. Since these evaluation functions are directly based on the interpretable physical meaning of P and Q, the scoring can not only provide scores, but also generate interpretable feedback, such as indicating that "there is a continuous backflow in a certain branch" or "abnormal pressure at a certain node prevents delivery to the target device", thus supporting the process guidance in teaching scenarios.

[0058] Using the above technical solution, in terms of the scoring mechanism, this invention does not limit the scoring to "whether the final phenomenon occurs," but rather incorporates topological legality, deduction consistency, and goal achievement into a unified computable framework. To this end, this invention defines the scoring as a combination mapping of several evaluation functions to P and Q. For example, in the evaluation mode, if the goal is "to stably deliver the produced gas to the gas collecting cylinder and avoid backflow," the system can make a judgment by constraining the flow sign and amplitude of key branches and the pressure range of key nodes.

[0059] Preferably, in step S3, after the virtual simulation system updates these state variables at each simulation time step, it can obtain information such as "which devices are in a high-pressure gas production state," "which pipelines have effective flow," and "whether the flow direction is reversed." Simultaneously, the animation layer no longer participates in physical judgment but instead... Mapped to gas particle density or flow rate, the symbols will be... The flow direction is mapped to realize the animation of gas flow in rubber tubes, the filling animation inside the device, and the multi-source confluence animation. This decoupling mechanism makes the animation effects independent of fixed paths: when the user changes the connection topology, causing A to change, and thus P and Q to change, the animation will automatically present a new flow process according to the value change, avoiding the problem of "the animation logic fails when the topology changes" in traditional solutions.

[0060] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0061] (1) This method transfers and improves the node analysis concept in the field of circuit analysis from traditional electrical networks, and uses it to uniformly model and solve the planar topology structure composed of experimental instruments and their connection relationships. Thus, under the condition that the user freely connects instruments to form arbitrarily complex connected structures, the method can realize the overall deduction of the experimental process and the calculation of state evolution.

[0062] (2) This invention realizes a complete closed loop from “users arbitrarily connecting to form a planar topology” to “improving MNA to automatically solve pressure-flow distribution” and then to “numerical-driven animation and scoring”. The key is to use A to describe the topology, G to describe the branch transmission characteristics, and S to describe the injection of multi-source products, thereby transforming the complex deduction problem that traditionally requires path enumeration into a reusable and scalable matrix solution problem, significantly reducing the system development and maintenance costs, and improving the deduction accuracy and scoring credibility in freely constructed scenarios.

[0063] (3) This invention breaks through the technical path of traditional virtual experiments that rely on fixed scripts and decentralized judgment logic, and provides a scalable, interpretable and highly universal deduction and scoring mechanism for virtual simulation experiments in freely constructed, multi-source collaborative and complex connected scenarios. Attached Figure Description

[0064] Figure 1 This is a flowchart of the virtual-real fusion experimental solution and deduction method based on planar topology of the present invention;

[0065] Figure 2 This is an example of the multi-source, multi-path effect obtained using the virtual-real fusion experimental solution and deduction method based on planar topology of the present invention. Figure 1 ;

[0066] Figure 3 The multi-source is obtained by using the virtual-real fusion experimental solution and deduction method based on planar topology of the present invention. Detailed Implementation

[0067] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. The following embodiments are only used to illustrate the technical solutions of the present invention more clearly, and should not be used to limit the scope of protection of the present invention.

[0068] Those skilled in the art will understand that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0069] Example: Figure 1 As shown, the method for solving and deducing the virtual-real fusion experiment based on planar topology specifically includes the following steps:

[0070] The method for solving and deducing the virtual-real fusion experiment based on planar topology includes the following steps:

[0071] S1 Constructing a Topology Network: Obtain the equipment and the connections between the equipment in the experimental scenario. By matching the interfaces of each equipment with the corresponding nodes, the equipment and the connections between the equipment are abstracted into a planar topology network, and a planar topology structure that satisfies the constraints is constructed.

[0072] In step S1, the apparatus and its connections in the experimental scenario are first abstracted into a planar topology network. The specific steps for constructing a planar topology that satisfies the constraints are as follows: (The steps involve establishing a matching relationship between the interfaces of each apparatus and the nodes, and then constructing the planar topology that satisfies the constraints.)

[0073] S11: Define the appliance nodes and the branches connecting the appliances, and define the node pressure vector and the branch flow vector;

[0074] S12: Define the transmission characteristics of chemically treated rubber hoses;

[0075] S13: Define the source of occurrence to construct a planar topology that satisfies the constraints.

[0076] In some specific embodiments, step S11 specifically includes the following steps:

[0077] S111: Let there be N equipment nodes in the experiment, denoted as set N. Each node It corresponds to a specific tool;

[0078] S112: Let there be a total of M connecting devices, denoted as set M. Each branch road Connect two appliance nodes and assign directions to them in the system;

[0079] S113: In chemical experiments, for apparatus involving chemical quantities, if the chemical quantity is equivalent to the node potential variable and replaced with the pressure state inside the apparatus, then the branch current is replaced with the flow rate of the substance in the rubber tube.

[0080] Define the nodal pressure vector: ;

[0081] in, Represents a node That is, the internal pressure of a certain device at the current moment, which is the driving force that determines the gas pushing outward from the device;

[0082] S114: Define the branch flow vector: ;

[0083] in, Indicates a branch The volumetric flow rate or molar flow rate (corresponding to a rubber tube or glass conduit) is determined by the sign of the branch direction: if the actual gas flow direction is the same as the branch direction, then... ,on the contrary .

[0084] In some specific embodiments, in step S1, for the case with chemical rubber tubing, the transmission characteristics of the chemical rubber tubing are defined as branch impedance parameters. This is used to comprehensively characterize the obstruction effect of pipes on flow, and the branch impedance parameters... By the head of the pipe , inner diameter The impedance is calculated from parameters such as fluid viscosity. To ensure the universality of the topology analysis method, this invention does not limit the specific physical model of the impedance, but only requires that it can vary with the pipe properties. In the derivation, this impedance corresponds to the resistance / admittance concept of electrical MNA, and is used to determine how the pressure difference is distributed as flow rate.

[0085] In some specific embodiments, because there are "source terms" in chemical experiments, such as gas being generated in a reaction flask, which acts like a power source in a circuit, causing the pressure at a certain node to continuously rise or generating an equivalent injection flow rate; therefore, in step S1, the vector of the generation source (such as a reaction device or power source) is defined as: ;

[0086] in, Represents a node The "equivalent injection rate" is used to describe the device's gas contribution to the network per unit time; if modeled in the form of flow conservation, then... "Injected flow" can be used; if modeled as a dynamic form of pressure, then... A "pressure growth driving term" can be adopted. In this specific embodiment, the injected flow rate is used to directly couple with the conservation equations.

[0087] S2 constructs the topological matrix equation: After abstracting the planar topology into nodes and branches, a unified set of equations is established based on MNA, and conservation relations and branch constitutive relations are introduced at the node level. After converting all branch constitutive relations into matrix form, a diagonal impedance matrix is ​​introduced to obtain an improved topological matrix.

[0088] The specific steps of step S2 are as follows:

[0089] S21: First, construct the node-branch association matrix. Its elements are defined as:

[0090] ;

[0091] in, Represents the i-th node n i With branch b of the jth branch j The connection and directional relationships, b j Indicates a branch; n i N represents the number of nodes; M represents the total number of branches. It represents the set of real numbers.

[0092] This matrix is ​​determined solely by the planar topology network generated in step S1 and is independent of the specific type of experiment. When the user plugs or unplugs the connecting pipes to change the connection relationship, the system only needs to update the corresponding column of A to reconstruct the equation system in real time without having to write any conditional judgments about the "path".

[0093] S22: Subsequently, a conservation relationship is introduced at the node level. In the gas production and transmission problem, the net outflow at a node should be equal to the injection source term at that node. Therefore, the node conservation equation is established as follows:

[0094] ;

[0095] Equivalent to: ;

[0096] Among them, let For branch flow vectors, Inject the equivalent flow vector into the node. The i-th component of the left-hand AQ can be represented as:

[0097]

[0098] in, Represents a node The algebraic sum of the flows of all connected branches, i.e., the "net outflow"; right side This represents the equivalent injected traffic to that node; Let j represent the flow vector of the j-th branch; explain with an example: if It is a reaction flask, and the reaction is producing gas. ;like If it is an external exhaust port or equivalent sink for an absorption device, then... If a node only acts as a relay point and neither produces nor consumes gas, then In this way, the simultaneous gas production of multiple reaction devices naturally manifests as multiple The system does not need additional rules to determine "which source takes priority";

[0099] S23: The nodal pressure and branch flow are correlated through the branch constitutive relation (equivalent to "Ohm's Law"), with the following formula:

[0100] ;

[0101] in, Indicates a branch The starting node, Indicates a branch The endpoint (in the same direction as the branch road). The pressure difference between the devices at both ends of the rubber hose (i.e., the j-th branch) is... Let be the equivalent impedance of the j-th branch; this formula directly expresses a key fact in chemical experiments: gas is pushed from a high-pressure device to a low-pressure device, and the intensity of this push (flow rate) is determined by both the pressure difference and the pipe impedance. If a pipe is longer or narrower, then... Increasing the pressure difference results in a smaller flow rate for the same pressure differential; conversely... Smaller values ​​result in larger flow rates, thus automatically creating a "distribution effect" in complex topologies;

[0102] S24: Write the constitutive relations of all branches in matrix form, and introduce the diagonal impedance matrix. Its admittance form We can obtain: ;

[0103] in, The j-th component is exactly the branch The algebraic expression of the pressure difference between the two nodes is that the node pressure P is transformed into the pressure difference of each branch through the correlation matrix A; That is, Z j (j=1,2,…,M) represents the unified correspondence to the j-th branch b. j impedance;

[0104] G represents the admittance matrix, which maps the pressure difference to the flow rate;

[0105] Substituting this equation into the conservation equation This yields a unified solution equation for nodal pressures only: ,make: Then the equation can be written as: KP=S;

[0106] In this equation, K is entirely determined by topology and impedance parameters, P is the appliance pressure state obtained from the solution, and S is the source term for each node. This equation is the core of this invention, integrating MNA into chemical topology derivation: the system no longer "finds paths," but instead obtains the global pressure distribution by solving a system of linear equations, thereby obtaining the flow rate of each pipe. Therefore, regardless of how freely users connect, the more complex the topology, the more the advantages of this method become.

[0107] S3 Solution Results Drive Experimental Deduction: Define the experimental source, calculate the node pressure P, and then calculate the branch flow rate Q. Use the node pressure P and branch flow rate Q as unified state variables for experimental deduction. The virtual simulation system updates these state variables at each simulation time step. Construct a node analysis model based on planar topology. Obtain the solution results through the node analysis model. Then, use the solution results to deduce the experimental process and present them in the animation layer. In step S3, after the virtual simulation system updates these state variables at each simulation time step, it can obtain information such as "which devices are in a high-pressure gas-generating state," "which pipes have effective flow," and "whether the flow direction is reversed." Simultaneously, the animation layer no longer participates in physical judgment but instead... Mapped to gas particle density or flow rate, the symbols will be... Mapped to the flow direction, this enables animations of gas flow in rubber tubes, filling of equipment, and multi-source convergence. This decoupling mechanism ensures that animation effects do not depend on fixed paths: when the user changes the connection topology, causing A to change, and thus the node pressure P and branch flow Q to change, the animation will automatically adapt to the changes in values ​​and present a new flow process, avoiding the problem of "animation logic failing when the topology changes" in traditional solutions.

[0108] S4 scores the experimental deduction: It uses the improved MNA solution as the common basis for both the experimental animation and the scoring mechanism. This involves incorporating topological validity, deduction consistency, and goal achievement into a unified computable framework. The score is defined as a combination mapping of several evaluation functions to node stress P and branch flow Q, thus obtaining the scoring result. Using the improved MNA solution as the common basis for both the experimental animation and the scoring mechanism achieves a unified foundation for experimental logic, visual presentation, and evaluation judgment, transforming experimental scoring from result-based judgment to a quantitative assessment based on the entire topology deduction process.

[0109] The specific steps for scoring the experimental deduction in step S4 are as follows:

[0110] Define the target node set (e.g., gas collecting cylinder node) and set of critical branches (e.g., the branch from the gas washing bottle to the gas collecting bottle), construct the target achievement items, specifically:

[0111] ;

[0112] Among them, F T It is the objective function, representing the overall optimization target value of the system, used to measure the combined effect of the target node pressure achievement and the traffic constraints of key branches under the current network conditions; It is the target node set, representing the set of nodes that need to be focused on or optimized; It is the set of critical branches, representing the set of branches that have a significant impact on the operation of the system; It is a node target characterization function, used to describe the degree of achievement or trend of change of the target node pressure; It is a branch constraint characterization function, used to describe the effectiveness constraints of the flow in key branches; It represents the node pressure, indicating the pressure state variable at the node. It represents the branch flow, indicating the flow on the j-th branch.

[0113] If, in the scoring of step S4, it is necessary to penalize backflow or short-circuit bypasses caused by faulty connections, then the following will be penalized: If a penalty term is added to the critical branch, or to situations that cause an abnormal increase in pressure at a node, then the final scoring formula is expressed as:

[0114] ;

[0115] in, This represents the backflow / reverse flow risk term (constructed from the flow sign and amplitude of the key branch). This indicates the connection compliance item (constructed from "one-to-one port matching" and experimental rule constraints). , , All weights are configurable. Since these evaluation functions are directly based on the interpretable physical meaning of node pressure P and branch flow Q, the scoring can not only provide scores, but also generate interpretable feedback, such as indicating that "there is a continuous backflow in a certain branch" or "abnormal pressure in a certain node prevents delivery to the target device", thus supporting the process guidance in teaching scenarios.

[0116] Using the above technical solution, in terms of the scoring mechanism, this invention does not limit the scoring to "whether the final phenomenon occurs," but rather incorporates topological legality, deduction consistency, and goal achievement into a unified computable framework. Therefore, this invention defines the scoring as a combination mapping of several evaluation functions to node pressure P and branch flow rate Q. For example, in the evaluation mode, if the goal is "to stably deliver the generated gas to the gas collecting cylinder and avoid backflow," the system can make a judgment by constraining the sign and amplitude of the key branch flow rate and the pressure range of the key nodes. The final experimental results are shown in […].Figures 2-3 As shown.

[0117] like Figure 2 As shown, the device includes two test tubes as gas sources, each containing potassium permanganate, which is heated by an alcohol lamp to generate gas. Each test tube is connected to a water tank via an outlet conduit, allowing gas to enter the water tank and create bubbles. In this invention, this process is abstracted as a node-branch network structure based on planar topology. Gas is transported from the source node to the water tank node along each branch path, and is uniformly described by node conservation relationships and branch flow directions. When heating continues, the system maintains forward transport; when heating stops and pressure is insufficient, the flow in some branches may weaken or even reverse, manifesting as water in the tank flowing back along the conduit, corresponding to a change in the branch flow sign and abnormal node states in the virtual simulation.

[0118] like Figure 3 As shown, in Figure 2 Based on the existing structure, a sealed test tube is placed in the middle of the gas outlet conduit as a transfer unit. The transfer test tube has an inlet and an outlet. Gas from the source enters the transfer test tube through the conduit, and is then transported to the water tank through another conduit, where it also exhibits bubbling at the water tank end. In the derivation method of this invention, this structure, by introducing a transfer node, divides the original single branch into multiple segments, allowing the gas to be distributed and transferred between multiple nodes and branches, forming a relatively complex connection topology. In this invention, the modeling method based on the improved node analysis method can uniformly solve and deduce this type of multi-branch network, analyze the influence of different paths on gas transmission, and further determine the flow distribution of each branch. Thus, the final gas flow rate entering the water tank can be derived, and in a virtual-real fusion environment, it is represented by the size and change of bubbles at the end of the conduit, thereby achieving a correspondence between the network structure and experimental phenomena.

[0119] For those skilled in the art, the specific embodiments are merely exemplary descriptions of the present invention. Obviously, the specific implementation of the present invention is not limited to the above-described manner. Any non-substantial improvements made using the inventive concept and technical solution of the present invention, or the direct application of the inventive concept and technical solution to other situations without modification, are all within the protection scope of the present invention.

Claims

1. A method for solving and deducing virtual-real fusion experiments based on planar topology, characterized in that, Specifically, the following steps are included: S1 Constructing a Topology Network: Obtain the equipment and the connections between the equipment in the experimental scenario. By matching the interfaces of each equipment with the corresponding nodes, the equipment and the connections between the equipment are abstracted into a planar topology network, and a planar topology structure that satisfies the constraints is constructed. S2 constructs the topological matrix equation: Based on MNA, a unified set of equations is established, and conservation relations and branch constitutive relations are introduced at the node level. After converting all branch constitutive relations into matrix form, a diagonal impedance matrix is ​​introduced to obtain an improved topological matrix. S3 solution results drive experimental simulation: Define the experimental source, calculate the node pressure P, and then calculate the branch flow Q. Use the node pressure P and branch flow Q as unified state variables for experimental simulation. At the same time, the virtual simulation system updates these state variables at each simulation time step, thereby constructing a node analysis model based on planar topology. Obtain the solution results through the node analysis model. Then use the solution results to simulate the experimental process and present them in the animation presentation layer.

2. The method for solving and deducing virtual-real fusion experiments based on planar topology according to claim 1, characterized in that, It also includes step S4, which scores the experimental simulation: the solution results of the node analysis model are used as the basis for the scoring mechanism, that is, topological legality, simulation consistency and goal achievement are incorporated into a unified computable framework, and the score is defined as a combination mapping of several evaluation functions to node pressure P and branch flow Q, thereby obtaining the scoring result.

3. The method for solving and deducing virtual-real fusion experiments based on planar topology according to claim 1, characterized in that, The specific steps of step S1, which involves establishing a matching relationship between the interfaces of each device and the nodes to construct a planar topology that satisfies the constraints, are as follows: S11: Define the appliance nodes and the branches connecting the appliances, and define the node pressure vector and the branch flow vector; S12: Define the transmission characteristics of chemically treated rubber hoses; S13: Define the source of occurrence to construct a planar topology that satisfies the constraints.

4. The method for solving and deducing virtual-real fusion experiments based on planar topology according to claim 3, characterized in that, The specific steps of step S11 are as follows: S111: Let there be N equipment nodes in the experiment, denoted as set N. Each node It corresponds to a specific tool; S112: Let there be a total of M connecting devices, denoted as set M. Each branch road Connect two appliance nodes and assign directions to them in the system; S113: In chemical experiments, for apparatus involving chemical quantities, the chemical quantity is replaced by the pressure state inside the apparatus, which is equivalent to the node potential variable, thereby replacing the branch current with the flow rate of the substance in the rubber tube. Define the nodal pressure vector: ; in, Represents a node That is, the internal pressure of a certain device at the current moment, which is the driving force that determines the gas pushing outward from the device; S114: Define the branch flow vector: ; in, Indicates a branch The volumetric flow rate or molar flow rate, with the sign corresponding to the branch direction: if the actual gas flow direction is consistent with the branch direction, then... ,on the contrary .

5. The method for solving and deducing virtual-real fusion experiments based on planar topology according to claim 4, characterized in that, In step S12, for those with chemical rubber tubing, the transmission characteristics of the chemical rubber tubing are defined as branch impedance parameters. This is used to comprehensively characterize the obstruction effect of pipes on flow, and the branch impedance parameters... By the head of the pipe , inner diameter It is obtained by converting parameters such as fluid viscosity.

6. The method for solving and deducing virtual-real fusion experiments based on planar topology according to claim 4, characterized in that, In step S13, the vector of the source is defined as: ; in, Represents a node The "equivalent injection rate" is used to describe the device's gas contribution to the network per unit time; if modeled in the form of flow conservation, then... "Injected flow" can be used; if modeled as a dynamic form of pressure, then... "Pressure growth driver" is a good option.

7. The method for solving and deducing virtual-real fusion experiments based on planar topology according to claim 4, characterized in that, The specific steps of step S2 are as follows: S21: First, construct the node-branch association matrix. Its elements are defined as: ； in, Represents the i-th node n i With branch b of the jth branch j The connection and directional relationships, b j Indicates a branch; n i N represents the total number of nodes, and M represents the total number of branches. S22: Subsequently, conservation relations are introduced at the node level to establish the node conservation equations, specifically: ； Equivalent to: ; Among them, let For branch flow vectors, Inject equivalent flow vectors into nodes; This represents the flow vector of the j-th branch; the i-th component of the left-hand AQ can be represented as: ； in, Represents a node The algebraic sum of the flows of all connected branches, i.e., the "net outflow"; right side This represents the equivalent injected traffic to that node; S23: Correlate nodal pressure with branch flow through branch constitutive relations, using the following formula: ； in, Indicates a branch The starting node, Indicates a branch The endpoint The pressure difference between the two ends of the rubber hose. Let be the equivalent impedance of the j-th branch; S24: Write the constitutive relations of all branches in matrix form, and introduce the diagonal impedance matrix. Its admittance form ,get: ; in, The j-th component is exactly the branch The algebraic expression of the pressure difference between the two nodes is that the node pressure P is transformed into the pressure difference of each branch through the correlation matrix A; That is, Z j (j=1,2,…,M) represents the unified correspondence to the j-th branch b. j impedance; G represents the admittance matrix, which maps the pressure difference to the flow rate; Substituting this equation into the conservation equation This yields a unified solution equation for nodal pressures only: ,make: Then the equation can be written as: KP=S; where K is completely determined by the topology and impedance parameters, P is the appliance pressure state obtained by solving, and S is the source term of each node.

8. The method for solving and deducing virtual-real fusion experiments based on planar topology according to claim 2, characterized in that, The specific steps for scoring the experimental deduction in step S4 are as follows: Define the target node set and critical branch set Construct the goal achievement items, specifically: ； Among them, F T It is the objective function, representing the overall optimization target value of the system, used to measure the combined effect of the target node pressure achievement and the traffic constraints of key branches under the current network conditions; It is the target node set, representing the set of nodes that need to be focused on or optimized; It is the set of critical branches, representing the set of branches that have a significant impact on the operation of the system; It is a node target characterization function, used to describe the degree of achievement or trend of change of the target node pressure; It is a branch constraint characterization function, used to describe the effectiveness constraints of the flow in key branches; It represents the node pressure, indicating the pressure state variable at the node. It represents the branch flow, indicating the flow on the j-th branch.

9. The method for solving and deducing virtual-real fusion experiments based on planar topology according to claim 8, characterized in that, If, in the scoring of step S4, it is necessary to penalize backflow or short-circuit bypasses caused by faulty connections, then the following will be penalized: If a penalty term is added to the critical branch, or to situations that cause an abnormal increase in pressure at a node, then the final scoring formula is expressed as: ； in, Indicates the risk item of backflow / reverse flow. Indicates the compliance items for connection. , , All are configurable weights.

10. The method for solving and deducing virtual-real fusion experiments based on planar topology according to claim 8, characterized in that, In step S3, after the virtual simulation system updates these state variables at each simulation time step, the animation rendering layer no longer participates in physical judgment, but instead... Mapped to gas particle density or flow rate, the symbols will be... The direction of flow is mapped to realize the animation of gas flow in rubber tubes, the animation of filling the inside of the device, and the animation of multiple sources merging.

Images