A method to reduce the amount of numerical simulation calculations for ultrasonic propagation in GIS breakdown discharge

Abstract

The present invention relates to a method for reducing the amount of numerical simulation calculation of ultrasonic propagation of GIS breakdown discharge, the method comprising: S101, establishing a corresponding numerical physical model according to an existing GIS physical model, solving the model by electromagnetic heat multi-physical field coupling, and obtaining the temperature field and velocity field under the solution model; S102, respectively performing acoustic field calculation of coupled electromagnetic heat temperature distribution and acoustic field calculation of background flow temperature being average temperature; S103, determining whether it is necessary to directly couple the electromagnetic heat temperature distribution result when calculating the acoustic field according to the result of S102; S104, respectively performing acoustic field calculation of coupled electromagnetic heat velocity distribution and acoustic field calculation of background flow being stationary when the background flow temperature is the same; S105, comparing two groups of sound pressure results in S104, and determining whether it is necessary to directly couple the electromagnetic heat velocity distribution result when calculating the acoustic field; S106, determining the final simplified scheme according to the comparison results of S103 and S105. Compared with the prior art, the present invention has the advantages of saving computing resources and the like.

Description

Technical Field

[0001] The invention relates to the field of numerical simulation of ultrasonic propagation of GIS breakdown discharge, and in particular to a method for reducing the amount of calculation in numerical simulation of ultrasonic propagation of GIS breakdown discharge. Background Art

[0002] Gas-insulated metal-enclosed switchgear (GIS) is an important equipment in the power system. It is widely used in the field of power transmission and transformation engineering because of its high safety and small footprint. However, GIS adopts a fully enclosed structure. Even if insulation defects such as SF6 breakdown discharge occur inside the equipment, it is difficult for inspection workers to determine the defect location, or even fail to detect the occurrence of defects, so it is impossible to carry out timely maintenance. The current discharge detection method mainly uses the light, electricity, sound and chemical substances generated during the discharge process to make judgments. The ultrasonic detection method is to locate the defect by detecting the ultrasonic signal generated during the breakdown discharge by the sensor. However, because the ultrasonic signal attenuates greatly in the GIS, especially at the gas-solid interface, reflection and refraction will occur. The sensor arranged on the shell can usually only detect weak signals. If the sensor is far away from the breakdown discharge point, it may not even detect the discharge signal. Therefore, in recent years, scholars at home and abroad have used numerical methods to simulate the propagation process of ultrasonic waves in GIS and study the attenuation characteristics of acoustic wave signals during propagation, so as to optimize the layout of ultrasonic sensors and improve the accuracy of defect detection.

[0003] At present, the use of numerical methods to simulate the ultrasonic propagation process in GIS has the problems of large amount of calculation and long solution time, especially for the solution of three-dimensional numerical models. The main reason is that the frequency of the ultrasonic signal generated by breakdown discharge is relatively high, generally 20 to 100kHz, and the minimum wavelength of the signal is relatively short, generally less than 2mm. In order to ensure the accuracy of the numerical simulation results, the maximum grid size of the sound field needs to be kept at a smaller size related to the minimum wavelength size, which results in a large number of grids in the model. With this large number of grids, each additional physical field added to the model will cause a significant increase in the amount of calculation. For example, when solving the internal sound field of GIS, we improve the accuracy of the simulation by considering the flow of SF6 gas and its uneven distribution in space. However, at this time, the solution of the numerical model requires coupling the sound field with the flow field, temperature field, etc., which greatly increases the amount of numerical calculation. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method to reduce the amount of numerical simulation calculations for ultrasonic propagation of GIS breakdown discharge, aiming to reduce the field quantities that need to be calculated under the sound field grid without affecting the calculation accuracy, simplify the background flow temperature field and velocity field, and provide a new method for reducing the amount of numerical simulation calculations for ultrasonic propagation of GIS breakdown discharge.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] According to one aspect of the present invention, a method for reducing the amount of numerical simulation calculations for ultrasonic propagation in GIS breakdown discharge is provided, characterized in that the method comprises the following steps:

[0007] Step S101, establishing a corresponding numerical physical model according to the existing GIS physical model, solving the model by electromagnetic thermal multi-physical field coupling, and obtaining the temperature field and velocity field under the solution model;

[0008] Step S102, ignoring the background fluid flow, respectively performing acoustic field calculation of coupled electromagnetic thermal temperature distribution and acoustic field calculation of background flow temperature being average temperature;

[0009] Step S103, determining whether it is necessary to directly couple the electromagnetic thermal temperature distribution result when calculating the sound field according to the result of step S102;

[0010] Step S104, when the background flow temperature is the same, respectively performing acoustic field calculation of coupled electromagnetic thermal velocity distribution and acoustic field calculation of static background flow;

[0011] Step S105, comparing the two groups of sound pressure results in step S104 to determine whether direct coupling of electromagnetic heat velocity distribution results is required when calculating the sound field;

[0012] Step S106, determining a final simplification scheme according to the comparison results of step S103 and step S105.

[0013] As a preferred technical solution, in step S101, when the physical model is a large-sized object, the amount of calculation using the coupling calculation is quite large. At this time, the model is simplified first, that is, the three-dimensional model is simplified into a partial two-dimensional model, and a sound field solution method that reduces the amount of calculation is obtained while ensuring accuracy. This method is then applied to the three-dimensional actual model to reduce the total amount of calculation.

[0014] As a preferred technical solution, the sound field calculation in step S102 specifically includes:

[0015] S1021) coupling the temperature field obtained by solving the electromagnetic heat model to the acoustic field model, solving the temperature-acoustic coupling model, and obtaining the instantaneous acoustic pressure signal of each sensor;

[0016] S1022) After setting the background fluid temperature to the average temperature of the SF6 gas obtained by solving the electromagnetic thermal model, the sound field model is directly solved to obtain the instantaneous sound pressure signal of each sensor at this time.

[0017] As a preferred technical solution, the step S103 is specifically as follows:

[0018] The two groups of calculation results in S102 are compared. If the maximum deviation of the sensor sound pressure signal exceeds the acceptable range, the temperature field needs to be coupled to solve the sound field; if the maximum deviation of the sensor sound pressure signal is within the acceptable range, the average temperature of SF6 is used as the background flow temperature to solve the sound field, and the amount of calculation is reduced.

[0019] As a preferred technical solution, the sound field calculation in step S104 is specifically as follows:

[0020] S1041) coupling the flow field obtained by solving the electromagnetic heat model to the acoustic field model, solving the flow-acoustic coupling model, and obtaining the instantaneous acoustic pressure signal of each sensor;

[0021] S1042) SF6 gas is set as a static fluid, that is, u=v=w=0, and then the sound field model is directly solved to obtain the instantaneous sound pressure signal of each sensor.

[0022] As a preferred technical solution, the step S105 is specifically as follows:

[0023] The two sets of results in step S104 are compared; if the maximum deviation of the sensor sound pressure signal exceeds the acceptable range, the flow field needs to be coupled to solve the sound field;

[0024] If the maximum deviation of the sensor sound pressure signal is within an acceptable range, the coupling between the flow field and the sound field is not considered, the SF6 flow rate is set to 0, and the sound field is solved directly, at which time the amount of calculation is reduced.

[0025] As a preferred technical solution, in the steps S103 and S105, according to the characteristics of the sound pressure signal detected by the sensor, two groups of calculated sound pressure signals at the peak are selected for comparison.

[0026] As a preferred technical solution, if the sound pressure signal at the peak is taken for comparison, the maximum sound pressure signal when the sensor signal reaches the peak for the nth time in step S1021 is recorded as P 1,n ; The maximum sound pressure signal when the sensor signal reaches the peak for the nth time in step S1022 is P 2,n; If for each sensor,

[0027] This means that step S1022 can be used to reduce the amount of simulation calculation, where M is the maximum allowable deviation set manually.

[0028] As a preferred technical solution, if the sound pressure signal at the peak is taken for comparison, the sound pressures of the three points near the peak value when the sensor signal reaches the peak value for the nth time in step S1041 are P and 1,n - , P 1,n , P 1,n + ; In step S1042, the sound pressures of the three points near the peak value when the sensor signal reaches the peak value for the nth time are P 2,n - , P 2,n , P 2,n + ; If each sensor satisfies

[0029]

[0030] Then, step (S1042) is used to reduce the amount of simulation calculation, where M is the maximum allowable deviation set manually.

[0031] As a preferred technical solution, step S106 is specifically as follows:

[0032] If step S102 adopts S1022, and step S104 adopts S1042 to simplify the calculation, it is equivalent to using the SF6 average temperature instead of the temperature field coupling and the background fluid static setting instead of the velocity field coupling in the original solution model. At this time, the amount of numerical calculation is reduced to the greatest extent.

[0033] Compared with the prior art, the present invention has the following advantages:

[0034] (1) The present invention simplifies the temperature field and velocity field of the background flow without substantially affecting the calculation accuracy, thereby reducing the field quantity that needs to be calculated under the acoustic field grid, reducing the amount of calculation for numerical simulation of ultrasonic propagation of GIS breakdown discharge, and saving computing resources.

[0035] (2) The present invention reduces the amount of numerical calculation by simplifying some physical fields, and provides ideas for solving some larger three-dimensional acoustic models.

[0036] (3) The present invention can not only be used to reduce the amount of numerical simulation calculations for ultrasonic propagation of GIS breakdown discharge, but can also be used to reduce the amount of calculations for ultrasonic simulation of partial discharge of other power equipment such as transformers. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a step diagram of a method for reducing the amount of numerical simulation calculations for ultrasonic propagation during GIS breakdown discharge provided by an embodiment of the present invention.

[0038] Figure 2 It is a two-dimensional numerical physical model of a 252 kV three-phase GIS busbar provided in an embodiment of the present invention, wherein 1 is a busbar conductor of phase A, 2 is a busbar conductor of phase B, 3 is a busbar conductor of phase C, 4 is a GIS casing, and 5 is SF6 insulating gas.

[0039] Figure 3 This is a diagram of sensor distribution and sound source location in a 252kV three-phase GIS bus room provided by an embodiment of the present invention, wherein 6 is sensor S1, 7 is sensor S2, 8 is sensor S3, 9 is sensor S4, 10 is sensor S5, 11 is sensor S6, and 12 is the sound source location.

[0040] Figure 4 It is a comparison of the sound pressure results of the S2 sensor when the two groups of calculations in step 2 reach the peak for the first time.

[0041] Figure 5 It is a comparison of the sound pressure results of the S2 sensor when the two groups of calculations in step 4 reach the peak for the first time. DETAILED DESCRIPTION

[0042] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0043] The method of reducing the amount of numerical simulation calculations for ultrasonic propagation of GIS breakdown discharge in the present invention comprises the following steps:

[0044] Step 1: Establish the corresponding numerical physical model based on the existing GIS physical model, and arrange an appropriate number of domain point probes in the SF6 gas area to simulate the ultrasonic sensor that detects the sound pressure signal. Perform electromagnetic thermal multi-physical field coupling solution on the model to obtain the temperature field and velocity field under this solution model.

[0045] Step 2: Without considering the background fluid flow, that is, assuming that the SF6 gas is stationary, two sets of calculations are performed separately. (1) The temperature field obtained by solving the electromagnetic thermal model is coupled to the acoustic field model, and the temperature-acoustic coupling model is solved to obtain the instantaneous sound pressure signal of each sensor; (2) After setting the background fluid temperature to the average temperature of the SF6 gas solved by the electromagnetic thermal model, the acoustic field model is directly solved to obtain the instantaneous sound pressure signal of each sensor at this time.

[0046] Step 3: Compare the two sets of calculation results in step 2. If the maximum deviation of the sensor sound pressure signal exceeds the acceptable range, the temperature field needs to be coupled to solve the sound field, and the amount of calculation does not change; if the maximum deviation of the sensor sound pressure signal is within the acceptable range, the average temperature of SF6 can be used as the background flow temperature to solve the sound field, and the amount of calculation is reduced.

[0047] Step 4: Under the condition of the same background flow temperature, two sets of calculations are performed separately. (1) The flow field obtained by solving the electromagnetic thermal model is coupled to the acoustic field model, and the flow-acoustic coupling model is solved to obtain the instantaneous acoustic pressure signal of each sensor; (2) SF6 gas is set as a static fluid, that is, u=v=w=0, and then the acoustic field model is directly solved to obtain the instantaneous acoustic pressure signal of each sensor.

[0048] Step 5: Compare the two sets of results in step 4. If the maximum deviation of the sensor sound pressure signal exceeds the acceptable range, the flow field needs to be coupled to solve the sound field, and the amount of calculation does not change; if the maximum deviation of the sensor sound pressure signal is within the acceptable range, the coupling of the flow field and the sound field can be ignored, the SF6 flow rate is set to 0, and the sound field is solved directly, and the amount of calculation is reduced.

[0049] Step 6: Determine the final simplified solution based on the comparison results of step 3 and step 5. If both step 2 and step 4 can adopt solution (2) to simplify the calculation, it is equivalent to using the SF6 average temperature instead of the temperature field coupling and the background fluid static setting instead of the velocity field coupling in the original solution model. At this time, the amount of numerical calculation is reduced to the greatest extent.

[0050] Further: When the physical model is a large-sized object, the amount of calculation using the coupled calculation is quite large, so the model can be simplified first. For example, the three-dimensional model can be reasonably simplified into a partial two-dimensional model, and the calculations of steps one to five above can be performed on the two-dimensional model first. Under the premise of ensuring accuracy, a sound field solution method with reduced calculation amount can be obtained, and then this method can be applied to the actual three-dimensional model to reduce the total amount of calculation.

[0051] Further: In step 3, the results of the two groups of calculated sound pressure signals at the peak can be compared. The maximum sound pressure signal when the sensor signal reaches the peak for the nth time in step 2 (1) is denoted as P 1,n ; The maximum sound pressure signal when the sensor signal reaches the peak for the nth time in step 2 (2) is P 2,n The maximum allowable deviation range is set to M. If each sensor satisfies

[0052]

[0053] Then, step 2 (2) can be used to reduce the amount of simulation calculations.

[0054] Further: In step three, if a background fluid temperature value defined by oneself is used to make the two sets of calculation results in step two more consistent and with smaller deviation, the defined value can be used instead of the average temperature value to improve the calculation accuracy.

[0055] Further: In step 5, in order to avoid the error of the result caused by time delay, the average value of the three points near the peak of the two groups of results in step 4 can be taken for deviation comparison. The sound pressure of the three points near the peak when the sensor signal reaches the peak for the nth time in step 4 (1) is P 1,n - , P 1,n , P 1,n + ; The sound pressures of the three points near the peak value when the sensor signal reaches the peak value for the nth time in step 4 (2) are P 2,n - , P 2,n , P 2,n + The maximum allowable deviation range is set to M. If each sensor satisfies

[0056]

[0057] Then, step 4 (2) can be used to reduce the amount of simulation calculations.

[0058] Further: In the steps 2 and 4, placing the sensor in a position where the SF6 gas temperature in the GIS bus room is higher, the flow rate is larger, and the sensor is farther away from the discharge sound source can more effectively compare the instantaneous sound pressure signals under the two sets of calculation results.

[0059] The method proposed in the present invention for reducing the amount of numerical simulation calculations for ultrasonic propagation in GIS breakdown discharge aims to simplify the background flow temperature field and velocity field without affecting the accuracy of numerical calculations, reduce the amount of fields that need to be solved under the acoustic field grid, thereby reducing the amount of numerical calculations and saving computing resources. Specific embodiments

[0061] like Figure 1 As shown, the method for reducing the amount of numerical simulation calculations for ultrasonic propagation of GIS breakdown discharge in an embodiment of the present invention mainly includes the following steps:

[0062] S101: Establish the corresponding numerical physical model based on the existing GIS physical model. This implementation case takes the 252kV three-phase common box GIS busbar as the prototype and conducts research on its two-dimensional cross section. Its numerical physical model is as follows: Figure 2As shown. With the center point O as the coordinate origin, six sensors are arranged to detect ultrasonic signals, and their positions are S1 (0, 20cm), S2 (0, 24cm), S3 (0, 28cm), S4 (-15, 5cm), S5 (0, 0cm), and S6 (0, -20cm). The model is solved by electromagnetic thermal multi-physics field coupling to obtain the temperature field and velocity field under this solution model.

[0063] S102: Figure 2 The sound source position in the simulation is set to simulate the Gaussian pulse signal of the breakdown discharge. Then, without considering the background fluid flow, that is, assuming that the SF6 gas is stationary, two sets of acoustic calculations are performed. (1) The temperature field obtained by solving the electromagnetic thermal model is coupled to the acoustic field model, and the temperature-acoustic coupling model is solved to obtain the instantaneous sound pressure signal of each sensor; (2) After setting the background fluid temperature to the average temperature of the SF6 gas solved by the electromagnetic thermal model, the acoustic field model is directly solved to obtain the instantaneous sound pressure signal of each sensor at this time.

[0064] S103: Compare the results of the two groups of sound pressure signals calculated in step 2 when they reach the peak for the first time, assuming that the maximum allowable deviation M is 5%. Figure 4 As shown, at this time, for this sensor

[0065]

[0066] Similarly, the comparison results of the remaining sensors can be obtained. The final results show that step 2 (2) can be used to simplify the temperature field, reduce the coupling process between the temperature field and the acoustic field, and reduce the amount of numerical calculations.

[0067] S104: After the background flow temperature is set to the average temperature of SF6, two groups of calculations are performed. (1) The flow field obtained by solving the electromagnetic thermal model is coupled to the acoustic field model, and the flow-acoustic coupling model is solved to obtain the instantaneous acoustic pressure signal of each sensor; (2) SF6 gas is set to a static fluid, that is, u=v=0, and then the acoustic field model is directly solved to obtain the instantaneous acoustic pressure signal of each sensor.

[0068] S105: Compare the results of the two groups of sound pressure signals calculated in step 4 when they reach the peak for the first time, assuming that the maximum allowable deviation M is 5%. Figure 5 As shown, at this time, for this sensor

[0069]

[0070] Similarly, the comparison results of the remaining sensors can be obtained. The final results show that step 4 (2) can be used to simplify the flow field, reduce the coupling process between the flow field and the acoustic field, and reduce the amount of numerical calculations.

[0071] S106: Determine the final acoustic field solution. That is, the average temperature of SF6 under the electromagnetic thermal model is used as the background fluid temperature, and the background fluid flow rate is set to 0. Under this setting, the model under the acoustic field grid is directly solved to obtain the final acoustic calculation results. The results show that after adopting this method, the total calculation time is shortened by more than half.

[0072] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for reducing the amount of numerical simulation calculations for ultrasonic propagation in GIS breakdown discharge, characterized in that: The method comprises the following steps: Step S101, establishing a corresponding numerical physical model according to the existing GIS physical model, solving the model by electromagnetic thermal multi-physical field coupling, and obtaining the temperature field and velocity field under the solution model; Step S102, ignoring the background fluid flow, respectively performing acoustic field calculation of coupled electromagnetic thermal temperature distribution and acoustic field calculation of background flow temperature being average temperature; Step S103, determining whether it is necessary to directly couple the electromagnetic thermal temperature distribution result when calculating the sound field according to the result of step S102; Step S104, when the background flow temperature is the same, respectively performing acoustic field calculation of coupled electromagnetic thermal velocity distribution and acoustic field calculation of static background flow; Step S105, comparing the two groups of sound pressure results in step S104 to determine whether direct coupling of electromagnetic heat velocity distribution results is required when calculating the sound field; Step S106, determining a final simplification scheme according to the comparison results of step S103 and step S105.

2. The method for reducing the amount of numerical simulation calculations for ultrasonic propagation in GIS breakdown discharge according to claim 1 is characterized in that: In the step S101, when the physical model is a large-sized object, the amount of calculation using the coupling calculation is quite large. At this time, the model is simplified first, that is, the three-dimensional model is simplified into a partial two-dimensional model, and a sound field solution method that reduces the amount of calculation is obtained while ensuring accuracy. This method is then applied to the three-dimensional actual model to reduce the total amount of calculation.

3. The method for reducing the amount of numerical simulation calculations for ultrasonic propagation in GIS breakdown discharge according to claim 1 is characterized in that: The sound field calculation in step S102 specifically includes: S1021) coupling the temperature field obtained by solving the electromagnetic heat model to the acoustic field model, solving the temperature-acoustic coupling model, and obtaining the instantaneous acoustic pressure signal of each sensor; S1022) After setting the background fluid temperature to the average temperature of the SF6 gas obtained by solving the electromagnetic thermal model, the sound field model is directly solved to obtain the instantaneous sound pressure signal of each sensor at this time.

4. The method for reducing the amount of numerical simulation calculations for ultrasonic propagation in GIS breakdown discharge according to claim 1 is characterized in that: The step S103 is specifically as follows: The two groups of calculation results in S102 are compared. If the maximum deviation of the sensor sound pressure signal exceeds the acceptable range, the temperature field needs to be coupled to solve the sound field; if the maximum deviation of the sensor sound pressure signal is within the acceptable range, the average temperature of SF6 is used as the background flow temperature to solve the sound field, and the amount of calculation is reduced.

5. The method for reducing the amount of numerical simulation calculations for ultrasonic propagation in GIS breakdown discharge according to claim 3 is characterized in that: The sound field calculation in step S104 is specifically as follows: S1041) coupling the flow field obtained by solving the electromagnetic heat model to the acoustic field model, solving the flow-acoustic coupling model, and obtaining the instantaneous acoustic pressure signal of each sensor; S1042) SF6 gas is set as a static fluid, that is, u=v=w=0, and then the sound field model is directly solved to obtain the instantaneous sound pressure signal of each sensor.

6. The method for reducing the amount of numerical simulation calculations for ultrasonic propagation in GIS breakdown discharge according to claim 1 is characterized in that: The step S105 is specifically as follows: The two sets of results in step S104 are compared; if the maximum deviation of the sensor sound pressure signal exceeds the acceptable range, the flow field needs to be coupled to solve the sound field; If the maximum deviation of the sensor sound pressure signal is within an acceptable range, the coupling between the flow field and the sound field is not considered, the SF6 flow rate is set to 0, and the sound field is solved directly, at which time the amount of calculation is reduced.

7. The method for reducing the amount of numerical simulation calculations for ultrasonic propagation in GIS breakdown discharge according to claim 1 is characterized in that: In the step S103 and step S105, according to the characteristics of the sound pressure signal detected by the sensor, the results of two groups of calculated sound pressure signals at the peak are selected for comparison.

8. The method for reducing the amount of numerical simulation calculations for ultrasonic propagation in GIS breakdown discharge according to claim 3 is characterized in that: If the sound pressure signal at the peak is taken for comparison, the maximum sound pressure signal when the sensor signal reaches the peak for the nth time in step S1021 is recorded as P 1,n ; The maximum sound pressure signal when the sensor signal reaches the peak for the nth time in step S1022 is P 2,n ; If for each sensor, This means that step S1022 can be used to reduce the amount of simulation calculation, where M is the maximum allowable deviation set manually.

9. The method for reducing the amount of numerical simulation calculations for ultrasonic propagation in GIS breakdown discharge according to claim 5 is characterized in that: If the sound pressure signal at the peak is taken for comparison, the sound pressures of the three points near the peak value when the sensor signal reaches the peak value for the nth time in step S1041 are P 1,n - , P 1,n , P 1,n + ; In step S1042, the sound pressures of the three points near the peak value when the sensor signal reaches the peak value for the nth time are P 2,n - , P 2,n , P 2,n + ; If each sensor satisfies Then, step (S1042) is used to reduce the amount of simulation calculation, where M is the maximum allowable deviation set manually.

10. The method for reducing the amount of numerical simulation calculations for ultrasonic propagation in GIS breakdown discharge according to claim 5, characterized in that: The step S106 is specifically as follows: If step S102 adopts S1022, and step S104 adopts S1042 to simplify the calculation, it is equivalent to using the SF6 average temperature instead of the temperature field coupling and the background fluid static setting instead of the velocity field coupling in the original solution model. At this time, the amount of numerical calculation is reduced to the greatest extent.

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