Real-time online superconducting accelerator cryogenic system construction method, virtual numerical model and system

Abstract

The application discloses a real-time online superconducting accelerator cryogenic system construction method and system. The method comprises the following steps: simplifying the physical property calculation in the cryogenic system to obtain a simplified physical property function of a working medium in the cryogenic system; adopting an agent model technology to simulate the temperature of a key point according to a combination of a one-dimensional pipe model and a zero-dimensional tank model, wherein the one-dimensional pipe model is used to simulate the delay of heat transfer, and the zero-dimensional tank model is used to simulate the heat capacity; and in response to the simplified physical property function and the temperature of the key point, a large-scale nonlinear sparse matrix equation is used to solve the node parameters in the cryogenic system. Through the application, a fast simulator which can independently operate can be provided, and the fast simulator can also be combined with a real cryogenic system to provide analysis and prediction functions for the real cryogenic system.

Description

Technical Field

[0001] This application relates to the field of large-scale cryogenic systems for superconducting accelerators, and in particular to a method for constructing a real-time online cryogenic system for a superconducting accelerator, a virtual numerical model, and a system. Background Technology

[0002] Large-scale cryogenic systems are crucial subsystems of large-scale scientific facilities. In the field of superconducting accelerators, their primary function is to provide cooling for superconducting cavities and superconducting magnets. Typically, based on the working medium, they can be categorized into helium cryogenic systems, nitrogen cryogenic systems, etc. The construction and operation costs of large-scale cryogenic systems are extremely high, often requiring tens or even billions of dollars in construction costs. Furthermore, once completed, the time available for experiments within the cryogenic system itself is very limited, making it difficult to conduct experiments with inherent risks. Therefore, it is necessary to construct a virtual numerical model for cryogenic systems to facilitate various types of research.

[0003] Among related technologies, a steady-state process design method and its numerical model based on operating conditions are adopted. This method assumes that the cryogenic system operates under stable conditions, that is, the time term is not considered in the simulation process. This type of method has a small amount of computation and high calculation accuracy for specific operating conditions, but it is difficult to fully reflect the overall performance of the cryogenic system.

[0004] Furthermore, with the significant increase in computing power, non-steady-state (dynamic) simulation tools have been widely adopted in recent years for research. For example, a real-time dynamic simulation platform for a large-scale hydrogen liquefaction or cryostat uses the commercial simulation tool EcosimPro to build a dynamic simulation model for a large-scale hydrogen cryostat, enabling data interaction between the model and control signals acquired by a PLC. Another example is a real-time simulation platform for a large-scale helium cryogenic system, which also uses EcosimPro to build a dynamic simulation model, then uses another server to run the EPICS control system, and uses the OPC communication protocol to enable real-time communication between the two servers. Summary of the Invention

[0005] This application provides a method, virtual numerical model, and system for constructing a real-time online cryogenic system for a superconducting accelerator to meet the requirements for real-time data generation.

[0006] The embodiments of this application adopt the following technical solutions:

[0007] In a first aspect, embodiments of this application provide a method for constructing a real-time online cryogenic system for a superconducting accelerator, wherein the method includes:

[0008] The property calculations in the cryogenic system are simplified to obtain the simplified property functions of the working fluid in the cryogenic system;

[0009] A surrogate model-based technique is employed to simulate key point temperatures using a combination of a 1D pipe model and a 0D tank model. The 1D pipe model is used to simulate the delay in heat transfer, and the 0D tank model is used to simulate heat capacity.

[0010] In response to the simplified property function and the critical point temperature, the nodal parameters of the cryogenic system are solved using large-scale nonlinear sparse matrix equations.

[0011] In some embodiments, the superconducting accelerator cryogenic system includes various fluids and solid working media.

[0012] Based on the 1D pipe model and the 0D tank model, the high-temperature points on the surface of the superconducting cavity are simulated, and the low-temperature points on the surface of the superconducting cavity are simulated based on the 0D tank model. The temperature values ​​change with boundary conditions and time are obtained through offline 3D simulation.

[0013] The parameters in the 1D pipeline model and the 0D jar model are optimized using a multi-objective genetic algorithm;

[0014] The temperature at the key point is simulated by combining the optimized 1D pipe model and the 0D tank model.

[0015] In some embodiments, Diffeqpy is used as the solver for the large-scale nonlinear sparse matrix equations, while physical constraint equations, physical interpolation initial value guesses, and parallel initial value guesses are added as physical constraints.

[0016] In some embodiments, it also includes:

[0017] The range of initial values ​​for each node in the cryogenic system is obtained using physical empirical values, and parallel computation is performed using the Diffeqpy solver based on the range of initial values ​​for each node.

[0018] In some embodiments, the method further includes: uniformly sampling the range of initial values ​​for each node, performing high-dimensional sampling using the Latin hypercube sampling method, distributing these initial guesses to multiple computation threads in parallel for simultaneous iteration, and selecting the set of computation results with the smallest residual within a specified iteration duration as the final result.

[0019] In some embodiments, the real-time data generation requirements in the cryogenic system of the superconducting accelerator are met while satisfying the preset loss accuracy of the large-scale nonlinear sparse matrix equations.

[0020] In some embodiments, the method further includes: combining the measurement and control system of the real cryogenic system to modify the physical constraints into observations read directly from the sensors.

[0021] In some embodiments, simplifying the property calculations in the cryogenic system to obtain simplified property functions of the working fluid in the cryogenic system includes:

[0022] Based on the working fluid in the cryogenic system and its corresponding operating conditions, the calculation results of the ideal gas law, van der Waals equation, virial equation, and MBWR equation are compared and corrected with commercial property databases. At the same time, data accuracy outside the operating range of this cryogenic system is discarded, and finally, the simplified property function of the working fluid in the cryogenic system is obtained.

[0023] Secondly, embodiments of this application also provide a virtual numerical model, wherein the real-time online superconducting accelerator cryogenic system construction method described in the first aspect is adopted.

[0024] Thirdly, embodiments of this application also provide a real-time online superconducting accelerator cryogenic system construction system, wherein the real-time online superconducting accelerator cryogenic system construction method described in the first aspect is employed.

[0025] The above-described technical solutions adopted in the embodiments of this application can achieve the following beneficial effects:

[0026] The real-time online superconducting accelerator cryogenic system construction method and the resulting system in this application embodiment can serve as the infrastructure for the superconducting accelerator cryogenic system in the digital field, and can provide a foundation for more functions such as subsequent advanced control strategy design, operator training, system performance analysis, fault prediction and diagnosis. Attached Figure Description

[0027] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments of this application and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0028] Figure 1 This is a flowchart illustrating the method for constructing a real-time online superconducting accelerator cryogenic system in an embodiment of this application.

[0029] Figure 2 This is a schematic diagram illustrating the real-time online superconducting accelerator cryogenic system construction method used in this application embodiment for large-scale cryogenic systems. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0031] Research shows that the so-called real-time performance in related technologies actually only refers to the real-time interaction between the dynamic simulation model and the data in the measurement and control system; that is, the data exchange is real-time, but it does not mean that the data generation is also real-time. In essence, it uses the dynamic simulation model to verify the rationality of the control program. In fact, the essence of dynamic simulation models for large-scale cryogenic systems is solving a large system of differential-algebraic equations (DAEs) with time terms, which typically requires a significant amount of computational power to balance computational accuracy and speed.

[0032] Furthermore, existing research generally relies heavily on commercial software provided by foreign companies, such as EcosimPro and Aspen. Their simulation algorithms cannot be freely modified, making it difficult to conduct high-precision simulations of specific components within a given system. Moreover, these commercial software programs inevitably sacrifice computational efficiency in pursuit of versatility, and their simulation speeds for large cryogenic systems fall far short of true real-time levels.

[0033] In view of the above problems, this application provides a real-time online method for constructing a cryogenic system for a superconducting accelerator, which can balance computational accuracy and speed in dynamic simulation modeling of the cryogenic system. Ultimately, a real-time dynamic simulation of a cryogenic superconducting accelerator is achieved, ensuring that the maximum iteration time for a cryogenic system with up to 100 nodes does not exceed 5 seconds per time step. When running offline, it is virtually indistinguishable from a real cryogenic system to operators. This virtual cryogenic system will continue to play an important role in the future development of more functions.

[0034] In this embodiment, "real-time performance" refers to the real-time generation of data, meaning the iterative progression on the time term must be faster than the actual passage of time. For example, to calculate the state of each node in a cryogenic system at least 5 seconds later, the calculation must be completed and displayed on the human-computer interface within at least 5 seconds of computation time. Although more computation time can be gained by extending the time step, many physical phenomena, such as boiling and condensation, occur on a second-scale time scale. Longer time steps may fail to capture these phenomena, leading to a significant decrease in the accuracy of dynamic simulation. Moreover, longer time steps result in slower refresh rates for the human-computer interface, which is not in line with the usage habits of ordinary user interfaces. In this embodiment, the solver is linked with the human-computer interface made using QT6. Every 5 seconds, the calculation results are fed back to the interface, updating the data of each node on the screen. At the same time, adjustable parameters such as valve opening and heater power on the screen are input into the solver to drive the solver to perform the calculation for the next time step. The solver needs to complete the iterative calculation and generate the data of each node within 5 seconds. This process is repeated continuously, enabling the virtual system to run continuously offline, and the 5-second refresh time can basically meet the real-time requirements. For cases with fewer than 50 nodes and a relatively simple model, the method in this application embodiment can further compress the computation time to less than 2 seconds, thus improving its real-time performance.

[0035] like Figure 2 As shown, a large-scale cryogenic system is actually a process industry equipment, mainly composed of a series of components connected in series or parallel, such as compressors, pipes, valves, tanks, heat exchangers, etc. Figure 2 As shown, the flow and heat transfer phenomena of these components can typically be described by their respective 0-dimensional or 1-dimensional differential-algebraic equations (DAEs), including: 1. Compressor (1.1, 1.2); 2. Filter (2.1, 2.2); 3. Heat exchanger (3.1, 3.2, 3.3); 4. Valve (4.1, 4.2, 4.3); 5. Cryogenic Dewar; 6. Turbine; 7. Superconducting equipment; 8. Gas tank. The flow of matter and energy between these components follows the laws of conservation of mass, energy, and momentum. Therefore, these partial differential equations can be connected into a system of equations, and then solved iteratively using numerical methods to obtain the temperature, pressure, and flow rate data at each node. This is the essence of dynamic simulation. Depending on the iterative solution method, it can be divided into sequential modular method, simultaneous equation method, and simultaneous modular method.

[0036] The computation speed of dynamic simulation models is related to the following factors:

[0037] 1. Number of nodes. This refers to the number of nodes in the DAE and the number of unknowns it contains. The more nodes there are, the greater the computational cost of solving the system of equations.

[0038] 2. Equation complexity. Generally, the more detailed the simulation, the greater the computational load required. For example, equations that consider the actual physical properties of gases are far more complex to calculate than those based on the ideal gas law.

[0039] 3. Solution methods. Even for the same set of DAEs, different numerical solution methods can result in significant differences in convergence speed and computational cost.

[0040] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0041] This application provides a method for constructing a real-time online cryogenic system for a superconducting accelerator, such as... Figure 1 The diagram illustrates a real-time online superconducting accelerator cryogenic system construction method in this application embodiment, which includes at least the following steps S110 to S130:

[0042] Step S110: Simplify the property calculations in the cryogenic system to obtain simplified property functions of the working fluid in the cryogenic system.

[0043] The thermal properties of commonly used working fluids in cryogenic systems are simplified. The superconducting accelerator cryogenic system contains various fluids and solid working fluids, operating within a wide temperature range of 2K to 300K and pressure range of 2500Pa to 12MPa. Therefore, their physical properties, such as density, heat capacity, thermal conductivity, and viscosity, vary considerably. Typical dynamic simulation models utilize commercial property libraries such as NIST RefProp and HePak to improve computational accuracy. However, because the property functions are repeatedly called to calculate the specific property values ​​at each node during the iterative calculation of the numerical model, this process accounts for more than 60% of the total computational cost.

[0044] Preferably, in order to minimize this computational overhead, the embodiments of this application compare the calculation results of the ideal gas law, van der Waals equation, virial equation, MBWR (Modified Benedict-Webb-Rubin) equation, etc., for several working fluids and specific operating conditions unique to the cryogenic system of the superconducting accelerator, and then compare and correct them with commercial property databases. At the same time, data accuracy outside the working range of this system is discarded, and finally a simplified property function with low computational load and sufficient accuracy within a specific range is obtained.

[0045] The material property function is obtained through a piecewise / simplification method, which requires less computation and has sufficient accuracy. The specific processing ideas include:

[0046] (1) Compare the calculation results of the virial equation, MBWR (Modified Benedict-Webb-Rubin) equation, etc., and correct them with commercial property databases, discarding the accuracy of data outside the system's working area. (2) Process the property parameters into piecewise linearized functions (rather than computationally intensive polynomial fitting).

[0047] For example, fluids (using helium as an example) involve parameters such as density, heat capacity, thermal conductivity, viscosity, enthalpy / entropy, critical pressure, and phase transition / critical temperature.

[0048] Segmented equations of state (taking helium as an example): Above 250K: Virial equations are used below 1.1-1.5 bara; 200K-100K: RK equations are used below 1.5 bara; 100K-5K: MBWR equations are used; Below 5K and during phase transitions: specific empirical formulas are used.

[0049] Solids (working fluids involved in cryogenic systems), materials involved include: 316 stainless steel, 304 stainless steel, high-purity copper, high-purity niobium, niobium-titanium alloy, G10 glass fiber, high-purity aluminum, etc. Processing parameters: thermal conductivity, heat capacity (both expressed as single-valued functions of temperature). For example, taking helium as an example, its thermal properties include, but are not limited to, density, heat capacity, thermal conductivity, viscosity, enthalpy / entropy (enthalpy and entropy are key state parameters in thermodynamics describing the energy state and disorder of a material system), critical pressure, and phase transition / critical temperature.

[0050] Step S120: Using surrogate model technology, the temperature of key points is simulated by combining a 1D pipe model and a 0D tank model. The 1D pipe model is used to simulate the delay in heat transfer, and the 0D tank model is used to simulate the heat capacity.

[0051] Superconducting accelerator cryogenic systems contain several structurally complex flow and heat transfer components, and users are particularly interested in their detailed temperature distributions. For example, users typically need to closely monitor the maximum surface temperature difference during the cooling process of the superconducting cavity and its helium tank. Traditionally, this complex three-dimensional flow and heat transfer phenomenon requires sophisticated three-dimensional simulation techniques for mesh discretization and solution, which is time-consuming and cannot be calculated using simple 0D or 1D models. However, in practical applications, users are not concerned with every physical quantity within the entire complex flow field, but rather with data from a few key points, such as the maximum / minimum surface temperature of the superconducting cavity.

[0052] To address this, a high-performance surrogate model technique is employed. Specifically, this application proposes a simplified method based on surrogate model technology, combining a 1D pipe model and a 0D tank model to simulate key temperature points in complex structures. The 1D pipe model primarily simulates the delay in heat transfer, while the 0D tank model simulates heat capacity, thereby controlling the slope of temperature changes. The specific parameters of the 1D pipe and 0D tank models are obtained through optimization using several sets of 3D simulation results combined with a genetic algorithm. Once optimization is complete, the temperature changes at key points in complex flow fields can be calculated using a simple combination of 0D and 1D models.

[0053] Step S130: In response to the simplified property function and the critical point temperature, the nodal parameters in the cryogenic system are solved using large-scale nonlinear sparse matrix equations.

[0054] Specifically, this method enables efficient solutions to large-scale nonlinear sparse matrix equations. It employs explicit time-stepping, using a simultaneous equations method as the overall computational framework within each time step. The advantage of this method is its fast computation speed, but its disadvantages include sensitivity to initial conditions and a tendency to fail to converge.

[0055] Preferably, in this embodiment of the application, the open-source Diffeqpy is used as the main differential equation solver, and physical constraint equations, physical interpolation initial value guessing, and parallel initial value guessing are added to improve the convergence speed.

[0056] Preferably, an improved simultaneous equation method is used to quickly solve for the node parameters of the cryogenic system. The physical constraint equations ensure that no non-physical solutions occur during numerical iteration, such as negative flow rates or pressure values ​​exceeding boundary conditions. Physical interpolation initial value guessing refers to guessing key parameters directly from empirical data, rather than using conventional initial value guessing methods, such as the traditional method of solving steady-state equations using local linearization. For example, the range of parameters (pressure, flow rate) at each node can be calculated directly using a set of empirical interpolation formulas based on the valve opening values ​​along the path. This greatly improves the speed of initial value guessing. Parallel initial value guessing refers to uniform sampling within the initial value guess range of each node. Specifically, high-dimensional sampling can be performed using the Latin hypercube sampling method, and these initial guess values ​​are distributed in parallel to multiple computation threads for simultaneous iteration. Within a specified iteration time, the set of calculation results with the smallest residual is selected as the final result.

[0057] The method in this application embodiment significantly improves the solution speed with minimal loss of accuracy, thus meeting the real-time requirements for data generation in large-scale cryogenic virtual systems of superconducting accelerators, and also enabling the acquisition of key temperature point data in complex flow fields.

[0058] By using the method in the embodiments of this application, when the number of nodes is less than 50 and the model is relatively simple, the computation time can be further compressed to less than 2 seconds, thus improving its real-time performance.

[0059] Unlike related technologies, where the number of unknowns in a DAE (Distributed Algorithm) increases with the number of unknowns, the computational burden of solving the equations also increases. Furthermore, more detailed simulations typically require greater computation; for example, equations considering the actual properties of gases are far more complex than those calculated using the ideal gas law. Finally, even with the same set of DAEs, different numerical solution methods often result in significant differences in convergence speed and computational cost. The dynamic simulation model provided by the method in this application's embodiments can meet the real-time data generation requirement.

[0060] In one embodiment of this application, the superconducting accelerator cryogenic system includes various fluids and solid working media. High-temperature points on the surface of the superconducting cavity are simulated using the 1D pipe model and the 0D tank model; low-temperature points on the surface of the superconducting cavity are simulated using the 0D tank model; and offline 3D simulation is used to obtain temperature variation data with boundary conditions and time. A multi-objective genetic algorithm is used to optimize the parameters in the 1D pipe model and the 0D tank model. The optimized combination of the 1D pipe model and the 0D tank model is then used to simulate the temperature at key points.

[0061] Considering that in practical applications, users are not concerned with every physical quantity within the entire complex flow field, but only with data from a few key points, such as the maximum / minimum temperature on the surface of a superconducting cavity, this invention proposes a simplified method based on surrogate modeling. This method combines a 1D pipe model and a 0D tank model to simulate key temperature points in complex structures. The 1D pipe model primarily simulates the delay in heat transfer, while the 0D tank model simulates heat capacity, thereby controlling the slope of temperature changes. The specific parameters of the 1D pipe and 0D tank models are obtained through optimization using several sets of 3D simulation results combined with a genetic algorithm. Once optimization is complete, the temperature changes at key points in the complex flow field can be calculated using a simple combination of 0D and 1D models.

[0062] Construct 0D / 1D models for simulating the surface temperature of a superconducting cavity.

[0063] 1. The input section specifically includes:

[0064] Model with undetermined parameters

[0065] High-temperature points on the surface of a superconducting cavity: one-dimensional pipe model + zero-dimensional tank model

[0066] Low-temperature points on the surface of a superconducting cavity: a zero-dimensional pot model

[0067] Offline data: Temperature values ​​as a function of boundary conditions and time (obtained from offline 3D simulation).

[0068] 2. Optimization steps: Use a multi-objective genetic algorithm to optimize the specific parameters of the pipes / jars.

[0069] 3. Output results: 0D / 1D models of high-temperature and low-temperature points on the surface of a superconducting cavity can be simulated online.

[0070] In one embodiment of this application, Diffeqpy is used as the solver for the large-scale nonlinear sparse matrix equation, while physical constraint equations, physical interpolation initial value guesses, and parallel initial value guesses are added as physical constraints.

[0071] Explicit time-stepping is employed, with simultaneous equations used as the overall computational framework within each time step. The advantage of simultaneous equations is their fast computation speed, but their disadvantage is sensitivity to initial values ​​and a tendency to fail to converge. Therefore, this invention uses the open-source Diffeqpy as the primary differential equation solver, while also incorporating physical constraint equations, physical interpolation initial value guessing, and parallel initial value guessing methods to improve convergence speed.

[0072] An improved method for quickly solving nodal parameters in cryogenic systems.

[0073] 1. Improvement of the initial value guessing method

[0074] Step 1: Obtain the range of initial values ​​for each node using empirical physical formulas.

[0075] Step 2: Use the Latin hypercube sampling method to obtain multiple sets of initial values ​​(one-dimensional arrays) simultaneously.

[0076] 2. Improved methods for solving nonlinear equation systems

[0077] Step 1: Deploy the Diffeqpy solver in multiple threads for parallel computation.

[0078] Step 2: Introduce physical constraints (avoid non-physical constraints such as negative flow rate and pressure values ​​exceeding the boundary).

[0079] 3. Supplementary explanation: The physical interpolation initial value guess does not adopt the traditional local linearization method, but directly calculates the temperature changes of key points in the complex flow field by combining 0-dimensional and 1-dimensional models.

[0080] In one embodiment of this application, the method further includes: obtaining the range of initial values ​​for each node in the cryogenic system using physical empirical values, and performing parallel calculations using a Diffeqpy solver based on the range of initial values ​​for each node.

[0081] In one embodiment of this application, the method further includes: uniformly sampling the range of initial values ​​for each node, performing high-dimensional sampling using the Latin hypercube sampling method, distributing these initial guesses to multiple computation threads in parallel for simultaneous iteration, and selecting the set of computation results with the smallest residual within a specified iteration duration as the final result.

[0082] Physical constraint equations ensure that no non-physical solutions occur during numerical iteration, such as negative flow rates or pressure values ​​exceeding boundary conditions. Physical interpolation initial value guessing refers to guessing key parameters directly from empirical data, rather than using conventional initial value guessing methods, such as traditional local linearization methods for solving steady-state equations. For example, it directly calculates the parameter (pressure, flow rate) range at each node using a set of empirical interpolation formulas based on valve opening values ​​along the path. This significantly improves the speed of initial value guessing. Parallel initial value guessing involves uniform sampling within the initial value guess range at each node, using the Latin hypercube sampling method for high-dimensional sampling, and distributing these initial guesses in parallel across multiple computation threads for simultaneous iteration. Within a specified iteration time, the set of calculation results with the smallest residual is selected as the final result.

[0083] In one embodiment of this application, the real-time data generation requirement in the cryogenic system of the superconducting accelerator is met while satisfying the preset loss accuracy of the large-scale nonlinear sparse matrix equation.

[0084] A method for efficiently solving large-scale nonlinear sparse matrix equations is employed. Explicit time-stepping is used, with a simultaneous equations method serving as the overall computational framework within each time step. The advantage of the simultaneous equations method is its fast computation speed, but its disadvantages include sensitivity to initial conditions and a tendency to fail to converge.

[0085] In one embodiment of this application, it further includes: combining with the measurement and control system of the real cryogenic system to modify the physical constraints into observations directly read from the sensors.

[0086] It can not only operate independently offline, but also be combined with the measurement and control system of a real cryogenic system to modify manually set boundary conditions into values ​​directly read from the sensors, thus enabling more functions such as system performance analysis, fault prediction and diagnosis.

[0087] In one embodiment of this application, the simplified property calculation in the cryogenic system to obtain the simplified property function of the working fluid in the cryogenic system includes: comparing the calculation results of the ideal gas law, van der Waals equation, virial equation, and MBWR equation with the working fluid in the cryogenic system and the corresponding operating conditions, then comparing and correcting with a commercial property database, while discarding data accuracy outside the working range of this cryogenic system, and finally obtaining the simplified property function of the working fluid in the cryogenic system.

[0088] Simplified thermal properties of working fluids are commonly used in cryogenic systems. Superconducting accelerator cryogenic systems contain various fluids and solid working fluids, operating within a wide temperature range of 2K to 300K and pressure range of 2500Pa to 12MPa. Therefore, their physical properties, such as density, heat capacity, thermal conductivity, and viscosity, vary considerably. Typical dynamic simulation models utilize commercial property libraries such as NIST RefProp and HePak to improve computational accuracy. However, because the iterative calculations of the numerical model repeatedly call property functions to calculate specific property values ​​at each node, this process accounts for over 60% of the total computational cost. To minimize this computational overhead, this invention compares the calculation results of the ideal gas law, van der Waals equation, virial equation, and MBWR (Modified Benedict-Webb-Rubin) equation with those of several working fluids and specific operating conditions unique to the cryogenic system of superconducting accelerators. The results are then compared and corrected with commercial property databases. At the same time, data accuracy outside the operating range of this system is discarded, ultimately obtaining simplified property functions with low computational cost and sufficient accuracy within a specific range.

[0089] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for constructing a real-time online cryogenic system for a superconducting accelerator, wherein, The method includes: The property calculations in the cryogenic system are simplified to obtain the simplified property functions of the working fluid in the cryogenic system; A surrogate model-based technique is employed to simulate key point temperatures using a combination of a 1D pipe model and a 0D tank model. The 1D pipe model is used to simulate the delay in heat transfer, and the 0D tank model is used to simulate heat capacity. In response to the simplified property function and the critical point temperature, the nodal parameters of the cryogenic system are solved using large-scale nonlinear sparse matrix equations. Diffeqpy is used as the solver for the large-scale nonlinear sparse matrix equations, and physical constraint equations, physical interpolation initial value guesses, and parallel initial value guesses are added as physical constraints. The range of initial values ​​for each node in the cryogenic system is obtained using physical empirical values, and parallel computation is performed using the Diffeqpy solver based on the range of initial values ​​for each node. Uniform sampling is performed on the range of initial values ​​for each node. High-dimensional sampling is performed using the Latin hypercube sampling method. These initial guesses are then distributed in parallel to multiple computation threads for simultaneous iteration. Within a specified iteration duration, the set of computation results with the smallest residual is selected as the final result.

2. The method as described in claim 1, wherein, The superconducting accelerator cryogenic system includes various fluid and solid working media. Based on the 1D pipe model and the 0D tank model, the high-temperature points on the surface of the superconducting cavity are simulated, and the low-temperature points on the surface of the superconducting cavity are simulated based on the 0D tank model. The temperature values ​​change with boundary conditions and time are obtained through offline 3D simulation. The parameters in the 1D pipeline model and the 0D jar model are optimized using a multi-objective genetic algorithm; The temperature at the key point is simulated by combining the optimized 1D pipe model and the 0D tank model.

3. The method as described in claim 1, wherein, While satisfying the preset loss accuracy of the large-scale nonlinear sparse matrix equations, the real-time data generation requirements in the cryogenic system of the superconducting accelerator are met.

4. The method of claim 1, wherein, Also includes: By combining the measurement and control system with the actual cryogenic system, the physical constraints are modified into observations directly read from the sensors.

5. The method of claim 1, wherein, The simplified property calculations in the cryogenic system, yielding simplified property functions of the working fluid in the cryogenic system, include: Based on the working fluid in the cryogenic system and its corresponding operating conditions, the calculation results of the ideal gas law, van der Waals equation, virial equation, and MBWR equation are compared and corrected with commercial property databases. At the same time, data accuracy outside the operating range of this cryogenic system is discarded, and finally, the simplified property function of the working fluid in the cryogenic system is obtained.

6. A real-time online cryogenic system for a superconducting accelerator, wherein, The method for constructing a real-time online cryogenic superconducting accelerator system as described in any one of claims 1 to 5 is adopted.

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