Optimization Method for Marine Secondary Loop System Based on Improved Multi-Objective Particle Swarm Optimization Algorithm

Abstract

The present invention discloses an optimization method for a marine secondary loop system based on an improved multi-objective particle swarm algorithm. By establishing mathematical models of the main and auxiliary equipment of the secondary loop system and a mathematical model for system heat balance calculation, and coupling the mathematical models of each equipment, a complete mathematical model of the secondary loop system is obtained; based on parameter sensitivity analysis, parameters that have a significant impact on the equipment structure and system performance are selected as optimization variables; the optimization objectives are the lightest weight, smallest volume, and highest effective efficiency of the secondary loop system; under the condition of meeting the determined constraints, an adaptive multi-objective particle swarm algorithm based on angular penalty distance is used for multi-objective optimization design of the weight, volume, and effective efficiency of the secondary loop system, and finally a Pareto optimal solution set and a Pareto front are obtained, and the relative optimal solution is selected by the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS method). The present invention better realizes the matching modeling and optimization of the marine nuclear power secondary loop system based on the improved algorithm, and is of great significance for improving the overall performance of the nuclear power system.

Description

Technical Field

[0001] The invention belongs to the technical fields of engineering thermodynamics, heat transfer, and optimization technology, and particularly relates to a multi-objective optimization of the weight, volume, and effective efficiency of a marine secondary loop system for a marine nuclear power system, which can be realized based on an improved multi-objective particle swarm algorithm. Background Art

[0002] A nuclear power plant is a device that transmits, distributes, and converts the energy generated by nuclear fuel fission into the power required to propel a ship. With the development trend of high power and high propulsion speed of marine nuclear power plants, the weight and volume of the secondary loop system, as one of the important components of the nuclear power plant, have further increased, seriously affecting the overall performance of the system and the maneuverability of the ship; at the same time, due to the limitations of ship weight and space, higher requirements are also put forward for the weight and volume of the secondary loop system. Therefore, multi-objective optimization design of key design indicators such as the weight, volume, and effective efficiency of the nuclear power secondary loop system has important scientific research significance and engineering application value for the development of nuclear power plants with light weight, small volume, and high effective efficiency.

[0003] At present, the optimization design research targeting nuclear power plants mostly optimizes the weight and volume of individual equipment in the system, ignoring the mutual restraint relationship between equipment. The optimal weight and volume of individual equipment do not necessarily guarantee the optimal weight and volume of the system; or it optimizes the total weight and total volume of some main equipment in the system, without considering the comprehensive impact of auxiliary equipment such as generator set steam turbines, auxiliary condensers, deaerators, drain water evaporators, low-pressure steam generators, and turbopump units on the system performance. The multi-objective optimization design research on the weight, volume, and effective efficiency of the secondary loop system is still in its initial stage. Summary of the Invention

[0004] Aiming at the deficiencies of the existing technology, the invention proposes a multi-objective optimization of a marine secondary loop system based on an improved multi-objective particle swarm algorithm. This method fully considers the comprehensive impact of the main equipment and auxiliary equipment of the secondary loop system on the system performance, and integrates the system heat balance calculation mathematical model, the mathematical models of each equipment, and the coupling connection between equipment to obtain a complete mathematical model of the secondary loop system, better realizing system matching modeling and optimization.

[0005] To solve the above technical problems, the invention adopts the following technical solutions:

[0006] An optimization method for a marine secondary loop system based on an improved multi-objective particle swarm algorithm includes the following steps:

[0007] The operating parameters and equipment structure parameters of the secondary circuit system are selected as optimization variables; the weight, volume and effective efficiency of the secondary circuit system are optimized based on the improved multi-objective particle swarm algorithm to obtain the Pareto optimal solution set and Pareto frontier that meet the constraints; finally, the best-inferior solution distance method (TOPSIS method) is used to select the relatively optimal solution from the optimized Pareto optimal solution set, which is used as the optimization scheme for the multi-objective optimization of the weight, volume and effective efficiency of the secondary circuit system.

[0008] Pre-establishing a mathematical model of the secondary circuit system includes the following steps:

[0009] Construct mathematical models of each component device based on the secondary circuit system;

[0010] On the basis of the mathematical models of each device in the secondary circuit system, the import and export parameters of each device are connected according to the system principle diagram to obtain the complete mathematical model of the secondary circuit system;

[0011] Based on the actual steam consumption of each device obtained from the complete mathematical model of the secondary circuit system, the total steam consumption of the secondary circuit system is calculated, and the reactor power and the effective efficiency of the nuclear power plant are calculated. The calculated efficiency is compared with the efficiency obtained by the assumed power to see whether they meet the accuracy requirements. If not, the reactor power is reassigned and iterative calculations are performed to finally obtain the effective efficiency of the nuclear power plant and the weight and volume of the secondary circuit system that meet the mass and energy conservation of each device in the system.

[0012] The mathematical models of the various component equipment include a steam generator mathematical model, a main steam turbine mathematical model, a main condenser mathematical model and an auxiliary equipment mathematical model.

[0013] The optimization variables are expressed as:

[0014]

[0015] Parameters that have a significant impact on the system's effective efficiency include: secondary circuit saturated steam pressure P2, main turbine high and low pressure cylinder power ratio ε p , condenser pressure P c and deaerator working pressure P d ;

[0016] Parameters that have a significant impact on the system weight and volume include: primary circuit working pressure P1, primary circuit coolant average temperature t1, steam generator heat transfer tube outer diameter d so , heat transfer tube section diameter ratio x s , coolant flow rate u1 in the heat transfer tube, outer diameter d of the condenser cooling tube co , cooling pipe section diameter ratio x c and cooling water flow rate u in the cooling pipe c .

[0017] The improved multi-objective particle swarm optimization algorithm comprises the following steps:

[0018] (1) Randomly generate an initial particle swarm of size N, calculate the objective function value of each particle, and initialize the individual optimal, external archive, and global optimal;

[0019] (2) Based on the particle velocity update formula adaptively adjusted by the inertia weight and learning factor, the velocity of each particle is updated to obtain the position of the new generation of particles, and the objective function value of each particle after the update is calculated;

[0020] (3) Update individual optimality and external archive based on Pareto dominance relationship;

[0021] (4) Angle penalty distance is introduced to select mutually non-inferior particles in the external archive to balance the convergence and distribution of particles in the archive;

[0022] (5) Determine whether the number of particles in the external archive exceeds the preset archive threshold. If so, calculate the congestion of each particle using the adaptive grid method, and remove particles that exceed the archive threshold based on the particle congestion from high to low;

[0023] (6) Update the global optimum;

[0024] (7) Repeat steps (2) to (6) until the preset maximum number of iterations is reached, and the positions of all particles in the external archive and the corresponding objective function values, i.e., the Pareto optimal solution set and the Pareto frontier, are output; finally, the best-in-competent solution distance method (TOPSIS method) is used to select the relatively optimal solution from the optimized Pareto optimal solution set, which is the optimization scheme for the multi-objective optimization of the weight, volume, and effective efficiency of the secondary circuit system.

[0025] The objective function is the secondary circuit system weight M ehl Lightest, volume V ehl Minimum and effective efficiency η ehl The highest can be expressed as a function of weight, volume and effective efficiency with the optimization variables:

[0026]

[0027] The particle velocity and position update formula based on the adaptive adjustment of the inertia weight and learning factor is as follows:

[0028]

[0029]

[0030] Where, is the velocity of particle i in the tth iteration; is the position of particle i in the t-th iteration; is the historical best position of particle i up to the t-th iteration; gbestx (t) is the global best position of the population up to the t-th iteration; r1 and r2 are random numbers uniformly distributed between 0 and 1; c1 and c2 are adaptive learning factors; w is an adaptive inertia weight:

[0031]

[0032] In the formula, f is the convergence factor.

[0033] The angle penalty distance is introduced in step (4) to select and discard mutually non-dominated particles in the external archive to balance the convergence and distribution of particles in the archive, specifically as follows:

[0034] The calculation formula of the angle penalty distance is as follows:

[0035] APD(x) = (1 + P(θ)) · d(x)

[0036] In the formula, d(x) is the 2-norm distance of individual x; P(θ) is the penalty factor;

[0037]

[0038]

[0039] In the formula, F(x) is the normalized objective vector; f i (x) is the normalized value of the i-th objective of individual x; m is the number of objective functions; M P is the penalty coefficient, M P = m; t is the current iteration number; T max is the maximum iteration number; α P is the variable speed rate factor, used to control the speed of change of the penalty factor P(θ) with the iteration number; θ(x) is the minimum angle between individual x and individual y in population P, and the calculation formula is as shown in the following formula:

[0040]

[0041]

[0042] A marine secondary loop system optimization device based on an improved multi-objective particle swarm algorithm, including a memory and a processor; the memory is used to store a computer program; the processor is used to implement the marine secondary loop system optimization method based on the improved multi-objective particle swarm algorithm when executing the computer program.

[0043] A computer-readable storage medium stores a computer program thereon. When the computer program is executed by a processor, the optimized method for a marine secondary loop system based on an improved multi-objective particle swarm algorithm is implemented.

[0044] Compared with the prior art, the present invention has the following advantages and beneficial technical effects:

[0045] (1) When modeling the secondary loop system, the present invention not only considers main devices such as steam generators, main steam turbines, and main condensers, but also fully considers the comprehensive influence of auxiliary devices such as generator set steam turbines, auxiliary condensers, deaerators, low-pressure steam generators, drain water evaporators, and turbopump units on the system performance;

[0046] (2) The present invention integrates heat balance calculation with the weight and volume calculation of the secondary loop system, fully considers the mass and energy conservation of the secondary loop system and each device and the coupling influence between devices, and ensures the mutual matching between devices of the system;

[0047] (3) The present invention uses an improved multi-objective particle swarm algorithm to perform optimization calculations on the weight, volume, and effective efficiency of the secondary loop system, and uses the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS method) to select a relatively optimal solution from the obtained Pareto optimal solution set. Finally, the weight of the secondary loop system is optimized by 10.312%, the volume is optimized by 13.380%, and the effective efficiency is optimized by 1.682%. Description of the Drawings

[0048] Figure 1 is the specific flowchart of the method of the present invention;

[0049] Figure 2 is the schematic diagram of the marine nuclear power secondary loop system;

[0050] Figure 3 is the flowchart of the improved multi-objective particle swarm algorithm. Detailed Embodiments

[0051] The following further describes the present invention in detail with reference to the drawings and examples.

[0052] An optimized method for a marine secondary loop system based on an improved multi-objective particle swarm algorithm includes:

[0053] (1) Establish a mathematical model of the main devices of the secondary loop system, including steam generators, main steam turbines, and main condensers;

[0054] (2) Establish a mathematical model of the auxiliary devices of the secondary loop system, including generator set steam turbines, auxiliary condensers, deaerators, feedwater pump turbine units, condensate pump turbine units, circulating water pump turbine units, low-pressure steam generators, drain water vapor generators, and air ejectors, etc.;

[0055] (3) Based on the secondary loop system diagram, the coupling method between various devices, and the system modeling flowchart, establish a mathematical model for system heat balance calculation and a complete mathematical model of the secondary loop system;

[0056] (4) Select optimization variables: First, select parameters that have a significant impact on the effective efficiency of the system as optimization variables, including the saturated steam pressure P2 of the secondary loop, the power ratio ε of the high and low pressure cylinders of the main steam turbine p , the condenser pressure P c and the operating pressure P of the deaerator d ; Second, select parameters that have a significant impact on the weight and volume of the system as optimization variables, including the operating pressure P1 of the primary loop, the average temperature t1 of the primary loop coolant, the outer diameter d of the heat transfer tubes of the steam generator so , the pitch diameter ratio x of the heat transfer tubes s , the flow velocity u1 of the coolant inside the heat transfer tubes, the outer diameter d of the condenser cooling tubes co , the pitch diameter ratio x of the cooling tubes c and the flow velocity u of the cooling water inside the cooling tubes c ;

[0057] (5) Determine the objective function: Take the lightest weight M ehl of the secondary loop system, the smallest volume V ehl and the highest effective efficiency η ehl as the optimization objectives;

[0058] (6) Determine the constraint conditions: Determine the constraint conditions from aspects such as optimization variable constraints, safe operation constraints, performance constraints, and structural dimension constraints;

[0059] (7) Based on the improved multi-objective particle swarm optimization algorithm, perform optimization calculations on the weight, volume, and effective efficiency of the secondary loop system to obtain the Pareto optimal solution set and Pareto front that meet the constraint conditions, and use the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS method) to select a compromise optimization scheme from the Pareto optimal solution set.

[0060] As Figure 1 shown, an optimization method for a marine secondary loop system based on an improved multi-objective particle swarm optimization algorithm includes:

[0061] (1) Establish a mathematical model of the main equipment of the secondary loop system:

[0062] Steam generator mathematical model: Thermal hydraulic calculation parameters mainly include steam generator heat load, secondary side steam production, secondary circuit feed water flow, total heat transfer coefficient of preheating section, total heat transfer coefficient of boiling section, primary side resistance, total resistance of secondary side circulation loop, secondary side circulation motion pressure head and circulation ratio; structural design and strength calculation parameters mainly include heat transfer tube wall thickness, heat transfer tube inner diameter, number of heat transfer tubes, total heat transfer area, upper cylinder wall thickness, upper cylinder outer diameter, upper cylinder height, lower cylinder wall thickness, lower cylinder outer diameter, lower cylinder height, tube sheet thickness and total height of steam generator; weight calculation parameters mainly include upper cylinder weight M st , weight of lower cylinder M xt , cone weight M zt , Upper head weight M sf , weight of lower head M xf , Tube sheet weight M gb , Supporting partition weight M zc , Tube bundle weight M tube and steam-water separator weight M qs ; Volume calculation parameters mainly include the upper cylinder volume V st , volume of lower cylinder V xt , volume of conical cylinder V zt , Upper head volume V sf and the lower head volume V xf Therefore, the steam generator weight M sg for:

[0063] M sg =M st +M xt +M zt +M sf +M xf +M gb +M zc +M tube +M qs (1)

[0064] Steam generator volume V sg for:

[0065] V sg =V st +V xt +V zt +V sf +V xf (2)

[0066] Main steam turbine mathematical model: The thermal calculation parameters mainly include the steam consumption of the main steam turbine, the power of the high-pressure cylinder, the power of the low-pressure cylinder, the enthalpy drop of the high-pressure cylinder, the enthalpy drop of the low-pressure cylinder, and the exhaust steam volume of the low-pressure cylinder; the structural calculation parameters mainly include the nozzle height of the governing stage of the high-pressure cylinder, the moving blade height of the governing stage of the high-pressure cylinder, the nozzle height of the first stage of the non-governing stage of the high-pressure cylinder, the moving blade height of the last stage of the non-governing stage of the high-pressure cylinder, the number of stages of the high-pressure cylinder, the maximum diameter of the high-pressure cylinder, the axial length of the high-pressure cylinder, the nozzle height of the first stage of the low-pressure cylinder, the moving blade height of the last stage of the low-pressure cylinder, the number of stages of the low-pressure cylinder, the maximum diameter of the low-pressure cylinder, and the axial length of the low-pressure cylinder. Therefore, the weight M of the main steam turbine mt is the weight M of the high-pressure cylinder hpc and the weight M of the low-pressure cylinder lpc summed up:

[0067] M mt = M hpc + M lpc (3) <s

[0068] The volume V of the main steam turbine mt is the volume V of the high-pressure cylinder hpc and the volume V of the low-pressure cylinder lpc summed up:

[0069] V mt = V hpc + V lpc (4)

[0070] Main condenser mathematical model: The thermal-hydraulic calculation parameters mainly include the condenser heat load, the heat transfer terminal difference, the cooling water flow rate, the cooling ratio, the overall heat transfer coefficient, the logarithmic mean temperature difference, the cooling area, the total flow resistance of the cooling water, the steam resistance, the condensate subcooling degree, and the condensate temperature; the structural design and strength calculation parameters mainly include the number of cooling tubes, the length of the cooling tubes, the inner diameter of the shell, the thickness of the tube sheet, the number of support baffles, and the thickness of the support baffles; the weight calculation parameters mainly include the weight M of the cooling tubes ct , the weight M of the tube sheet D= (1 + 2) × 100% = 300% ts , the weight M of the support baffles sb , the weight M of the shell shell and the weight M of the water chamber chamber ; the volume calculation parameters mainly include the length of the condenser, the width of the condenser, and the height of the condenser. Therefore, the weight M of the main condenser mc is:

[0071] M mc = M ct + M ts + M sb + M shell + M chamber (5)

[0072] The volume V of the main condenser mc is: It should be noted that there seems to be an incorrect formula "D = (1 + 2) × 100% = 300%" in the original text which might be a mistake. I have translated it as it is but this might need to be corrected in the source material.

[0073] V mc = L mc W mc H mc (6)

[0074] In the formula, L mc is the length of the main condenser; W mc is the width of the main condenser; H mc is the height of the main condenser.

[0075] (2) Establish the mathematical models of the auxiliary equipment of the secondary loop system:

[0076] Mathematical model of deaerator: The design parameters mainly include the heating steam quantity required by the deaerator, the actual output of the deaerator, the heat transfer coefficient, the heat transfer area, the liquid-phase volume mass transfer coefficient, the mass transfer area, the number of atomizing nozzles, the inner diameter of the cylinder, the wall thickness of the cylinder, and the wall thickness of the head.

[0077] Mathematical model of pump: The design parameters mainly include the head, efficiency, and power of the pump.

[0078] Mathematical model of low-pressure steam generator: The design parameters mainly include the steam consumption of the low-pressure steam generator, the total heat transfer coefficient, the heat transfer area, the number of heat transfer tubes, the diameter of the tube bundle, the total height of the tube bundle, the wall thickness of the upper and lower cylinders, the outer diameter of the upper and lower cylinders, and the thickness of the tube sheet.

[0079] Mathematical model of drain water evaporator: The design parameters mainly include the secondary steam production and blowdown of the drain water evaporator.

[0080] Mathematical model of air ejector: The design parameters mainly include the cooling water temperature rise and the cooling water outlet temperature.

[0081] (3) Establish the mathematical model of system heat balance calculation and the complete mathematical model of the secondary loop system:

[0082] According to the known main steam turbine power and the steam turbine power of the generator set, assuming the reactor power, calculate the effective efficiency of the nuclear power plant; based on the mathematical models of each equipment in the secondary loop system, according to Figure 2Determine the connection mode between devices, couple the inlet and outlet parameters of each device to obtain a complete mathematical model of the secondary loop system; based on the actual steam consumption of each device obtained from the complete mathematical model of the secondary loop system, further obtain the total steam consumption of the secondary loop system, calculate the reactor power and the effective efficiency of the nuclear power plant, compare whether the calculated efficiency and the efficiency obtained from the assumed power meet the accuracy requirements. If not, reassign the reactor power for iterative calculation until the effective efficiency of the nuclear power plant and the weight and volume of the secondary loop system that satisfy the mass and energy conservation of each device in the system are obtained. The weight of the secondary loop system is the sum of the weights of the steam generator, main steam turbine, main condenser, generator steam turbine, auxiliary condenser, deaerator, low-pressure steam generator, drain water evaporator, feed water pump steam turbine unit and condensate pump steam turbine unit; the volume of the secondary loop system is the sum of the volumes of the steam generator, main steam turbine, main condenser, generator steam turbine, auxiliary condenser, deaerator, low-pressure steam generator, drain water evaporator, feed water pump steam turbine unit and condensate pump steam turbine unit.

[0083] (4) Select optimization variables:

[0084] Combined with the single-parameter sensitivity analysis method, select the thermal parameters and structural parameters that have a significant impact on the weight, volume and effective efficiency of the secondary loop system as optimization variables. The parameters that have a significant impact on the system effective efficiency include: the saturated steam pressure P2 of the secondary loop, the power ratio ε of the high and low pressure cylinders of the main steam turbine p , the condenser pressure P c and the working pressure P of the deaerator d ; the parameters that have a significant impact on the system weight and volume include: the working pressure P1 of the primary loop, the average temperature t1 of the primary loop coolant, the outer diameter d of the heat transfer tubes of the steam generator so , the pitch diameter ratio x of the heat transfer tubes s , the coolant flow velocity u1 inside the heat transfer tubes, the outer diameter d of the condenser cooling tubes co , the pitch diameter ratio x of the cooling tubes c and the cooling water flow velocity u inside the cooling tubes c . Therefore, select the above 12 parameters as optimization variables, and the optimization variables are expressed as:

[0085]

[0086] (5) Determine the objective function:

[0087] Taking the lightest weight M ehl of the secondary loop system, the smallest volume V [[ID=3"4]] ehl and the highest effective efficiency η ehl as the optimization objectives, the objective function can be expressed as the functional relationship between the weight, volume, effective efficiency and the optimization variables:

[0088]

[0089] (6) Determine the constraint conditions:

[0090] The optimization design should be carried out on the premise of ensuring the safe and stable operation of the system and each device, reasonable performance indicators, and reasonable space layout. Therefore, the constraint conditions during optimization should include optimization variable constraints, safe operation constraints, performance constraints, and structural dimension constraints.

[0091] a) Optimization variable constraints: The values of the primary loop working pressure, average temperature of the primary loop coolant, secondary loop saturated steam pressure, outer diameter of the steam generator heat transfer tubes, pitch diameter ratio of the heat transfer tubes, coolant flow velocity inside the heat transfer tubes, power ratio of the high and low pressure cylinders of the main steam turbine, condenser pressure, outer diameter of the condenser cooling tubes, pitch diameter ratio of the cooling tubes, coolant flow velocity inside the cooling tubes, and deaerator working pressure should all be within a certain range.

[0092] b) Safe operation constraints: Parameters such as the steam generator circulation ratio, circulation velocity, and condenser cooling ratio must be within a reasonable range.

[0093] c) Performance constraints: Parameters such as the steam output of the steam generator, total number of heat transfer tubes, total heat transfer area, total resistance on the primary loop side, partial admission degree of the governing stage of the steam turbine, peripheral velocity of the last stage blade of the steam turbine, residual velocity kinetic energy of the last stage, heat transfer terminal difference of the condenser, number of cooling tubes, total flow resistance of the cooling water, condensate subcooling degree, and steam resistance must be within a reasonable range.

[0094] d) Structural dimension constraints: Parameters such as the diameter of the steam generator tube bundle, total height of the steam generator tube bundle, height-diameter ratio of the steam generator, diameter-height ratio of the last stage of the main steam turbine high pressure cylinder, diameter-height ratio of the last stage of the main steam turbine low pressure cylinder, and length-diameter ratio of the condenser shell should meet industrial requirements.

[0095] (7) Based on Figure 3 Multi-objective optimization of the weight, volume, and effective efficiency of the secondary loop system using the improved multi-objective particle swarm algorithm shown:

[0096] a) Randomly generate an initial particle swarm with a population size of N, ensuring that all particles in the initialized population are particles that meet the constraint conditions. Calculate the objective function value of each particle, and initialize the individual optimal position, external archive, and global optimal position;

[0097] b) Update the velocity of each particle based on the particle velocity update formula (9) with adaptive adjustment of the inertia weight and learning factor. Obtain the position of the new generation of particles according to formula (10), calculate the objective function value of each updated particle, and update the individual optimal position;

[0098]

[0099]

[0100] In the formula, is the velocity of particle i in the t-th iteration; is the position of particle i in the t-th iteration; is the historical optimal position of particle i up to the t-th iteration; gbestx (t) is the global optimal position of the population up to the t-th iteration; r1 and r2 are random numbers uniformly distributed between 0 and 1; c1 and c2 are adaptive learning factors. The initial values of c1 and c2 are both set to 2, and c1 + c2 = 4. In the early stage of optimization, the population is in the exploration and development state. Therefore, increasing c1 and decreasing c2 are beneficial for global optimization and avoiding falling into local optima. As the optimization progresses, the population gradually reaches the convergence state until it is stable. Therefore, decreasing c1 and increasing c2 are beneficial for the population to quickly approach the global optimal region and accelerate convergence; w is the adaptive inertia weight:

[0101]

[0102] In the formula, f is the convergence factor.

[0103] c) Compare and screen each particle in the updated population based on the Pareto dominance relationship and then add them to the external archive. Then, perform a secondary screening on the particles in the archive based on the Pareto dominance relationship;

[0104] d) Introduce the angular penalty distance to reasonably select and discard the non-dominated particles in the external archive, so that the particles in the archive can dynamically balance their convergence and distribution with the multi-objective evolution process, and improve the optimization efficiency;

[0105] The calculation formula of the angular penalty distance is as follows:

[0106] APD(x) = (1 + P(θ))·d(x) (12)

[0107] In the formula, d(x) is the 2-norm distance of individual x; P(θ) is the penalty factor.

[0108]

[0109]

[0110] In the formula, F(x) is the normalized objective vector; f i (x) is the normalized value of the i-th objective of individual x; m is the number of objective functions; M P is the penalty coefficient, M P = m; t is the current iteration number; T max is the maximum iteration number; α Pis the variable rate factor used to control the speed at which the penalty factor \(P(\theta)\) changes with the number of iterations; \(\theta(x)\) is the minimum angle between individual \(x\) and individual \(y\) in population \(P\). The larger \(\theta(x)\) is, the better the distribution of individual \(x\) in the population. The specific calculation formula is shown as follows:

[0111]

[0112]

[0113] e) Determine whether the particles in the archive exceed the pre-set archive threshold. If they do, calculate the crowding degree of each particle according to the adaptive grid method, and remove the particles with high crowding degree until the archive threshold is met;

[0114] f) Calculate the probability of each particle being selected according to the crowding degree of the particles in the updated external archive, and update the global optimal position;

[0115] g) Loop steps b - f until the pre-set maximum number of iterations is reached. Output the positions of all particles in the external archive and the corresponding objective function values, that is, the Pareto optimal solution set and the Pareto front. Finally, use the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS method) to select the relatively optimal solution from the optimized Pareto optimal solution set, which is the optimization scheme for the multi-objective optimization of the weight, volume and effective efficiency of the secondary loop system.

[0116] Next, for a certain type of nuclear power system, the actual calculation process of the multi-objective optimization of the weight, volume and effective efficiency of the marine secondary loop system based on the improved multi-objective particle swarm algorithm is described. The optimization method is as follows:

[0117] (1) Establish mathematical models of equipment such as steam generators, main steam turbines, main condensers, generator turbines, auxiliary condensers, deaerators, low-pressure steam generators, drain water evaporators, feed water pump turbines, condensate pump turbines and air ejectors.

[0118] (2) According to Figure 2 Determine the connection methods of the above equipment, establish a complete mathematical model of the secondary loop system including heat balance calculation. Finally, the error of the effective efficiency of the nuclear power plant is less than 10 -3 .

[0119] (3) Select optimization variables: Select the primary loop working pressure, primary loop coolant average temperature, secondary loop saturated steam pressure, outer diameter of the steam generator heat transfer tubes, heat transfer tube pitch ratio, coolant flow velocity inside the heat transfer tubes, power ratio of the high and low pressure cylinders of the main steam turbine, condenser pressure, outer diameter of the condenser cooling tubes, cooling tube pitch ratio, cooling water flow velocity inside the cooling tubes and deaerator working pressure as optimization variables.

[0120] (4) Determine the objective function: The optimization objectives are to minimize the total weight, minimize the overall volume, and maximize the effective efficiency of the secondary loop system.

[0121] (5) Determine the constraint conditions: The determined constraint conditions and their value ranges are shown in Table 1. All parameters in the table have been normalized based on the original values. The lower and upper limit values of the constraint conditions given in Table 1 are only for a certain type of nuclear power system, and the optimization has been carried out within the value ranges of the constraint conditions listed in Table 1.

[0122] Table 1 Value ranges of constraint conditions

[0123]

[0124]

[0125] (6) Parameter settings of the improved multi-objective particle swarm optimization algorithm: population size N, external archive threshold T, grid equal division number M, and maximum iteration number K.

[0126] (7) Combine the secondary loop system evaluation program with the improved multi-objective particle swarm optimization program to obtain the Pareto optimal solution set and Pareto front that meet the constraint conditions. Finally, the compromise optimization solution selected from the Pareto optimal solution set based on the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS method) is shown in Table 2. The weight of the secondary loop system is optimized by 10.312%, the volume is optimized by 13.380%, and the effective efficiency is optimized by 1.682%. (Note: The optimization results listed in the table are only an example of multi-objective optimization for a certain type of nuclear power system. All parameters in the table have been normalized based on the original values.)

[0127] Table 2 Multi-objective optimization results of the secondary loop system of nuclear power

[0128]

Claims

1. A marine secondary circuit system optimization method based on an improved multi-objective particle swarm optimization algorithm is characterized by: The following steps are involved: Select the secondary circuit system operating parameters and equipment structure parameters as optimization variables; An improved multi-objective particle swarm optimization algorithm is used to optimize the weight, volume, and effective efficiency of the secondary circuit system, obtaining a Pareto optimal solution set and a Pareto frontier that meet the constraints. Finally, a superior-inferior solution distance method is used to select the relatively optimal solution from the optimized Pareto optimal solution set, which serves as the optimization scheme for the multi-objective optimization of the weight, volume, and effective efficiency of the secondary circuit system. Establish the mathematical model of the secondary circuit system in advance, The following steps are involved: Construct mathematical models of each component device based on the secondary circuit system; On the basis of the mathematical models of each device in the secondary circuit system, the import and export parameters of each device are connected according to the system principle diagram to obtain the complete mathematical model of the secondary circuit system; Based on the actual steam consumption of each device obtained from the complete mathematical model of the secondary circuit system, the total steam consumption of the secondary circuit system is calculated, and the reactor power and effective efficiency of the nuclear power plant are calculated. The calculated efficiency is compared with the efficiency obtained by assuming the power to see if it meets the accuracy requirements. If not, the reactor power is reassigned and iterative calculations are performed to finally obtain the effective efficiency of the nuclear power plant and the weight and volume of the secondary circuit system that meets the conservation of mass and energy of each device in the system; The improved multi-objective particle swarm optimization algorithm comprises the following steps: S1 randomly generates an initial particle swarm of size N, calculates the objective function value of each particle, and initializes the individual optimum, external archive, and global optimum; S2 updates the velocity of each particle based on the particle velocity update formula adaptively adjusted by the inertia weight and learning factor, obtains the position of the new generation of particles, and calculates the objective function value of each particle after the update; S3 updates individual optima and external archives based on Pareto dominance relationships; S4 introduces an angle penalty distance to select mutually non-inferior particles in the external archive to balance the convergence and distribution of particles in the archive; S5 determines whether the number of particles in the external archive exceeds a preset archive threshold. If so, the congestion of each particle is calculated according to the adaptive grid method, and the number of particles exceeding the archive threshold is eliminated according to the particle congestion from high to low; S6 updates the global optimum; S7 loops through S2 to S6 until the preset maximum number of iterations is reached, and the positions of all particles in the external archive and the corresponding objective function values, i.e., the Pareto optimal solution set and the Pareto frontier, are output; finally, the TOPSIS method is used to select the relatively optimal solution from the optimized Pareto optimal solution set, which is the optimization solution for the multi-objective optimization of the weight, volume, and effective efficiency of the secondary circuit system; The angle penalty distance introduced in step S4 is used to select mutually non-inferior particles in the external archive to balance the convergence and distribution of particles in the archive, as follows: The angle penalty distance calculation formula is as follows: APD(x)=(1+P(θ))·d(x) Where d(x) is the 2-norm distance of individual x; P(θ) is the penalty factor; Where F(x) is the normalized target vector; f i (x) is the normalized value of the i-th target of individual x; m is the number of target functions; M P is the penalty coefficient, M P =m; t is the current iteration number; T max is the maximum number of iterations; α P is the rate factor used to control how quickly the penalty factor P(θ) changes with the number of iterations; θ(x) is the minimum angle between individual x and individual y in population P, and the calculation formula is as follows:

2. The marine secondary circuit system optimization method based on the improved multi-objective particle swarm optimization algorithm according to claim 1 is characterized in that: The mathematical models of the various component equipment include a steam generator mathematical model, a main steam turbine mathematical model, a main condenser mathematical model and an auxiliary equipment mathematical model.

3. The marine secondary circuit system optimization method based on the improved multi-objective particle swarm optimization algorithm according to claim 1 is characterized in that: The optimization variables are expressed as: Parameters that have a significant impact on the system's effective efficiency include: secondary circuit saturated steam pressure P2, main turbine high and low pressure cylinder power ratio ε p , condenser pressure P c and deaerator working pressure P d ; Parameters that have a significant impact on the system weight and volume include: primary circuit working pressure P1, primary circuit coolant average temperature t1, steam generator heat transfer tube outer diameter d so , heat transfer tube section diameter ratio x s , coolant flow rate u1 in the heat transfer tube, outer diameter d of the condenser cooling tube co , cooling pipe section diameter ratio x c and cooling water flow rate u in the cooling pipe c .

4. The marine secondary circuit system optimization method based on the improved multi-objective particle swarm optimization algorithm according to claim 1 is characterized in that: The objective function is the secondary circuit system weight M ehl Lightest, volume V ehl Minimum and effective efficiency η ehl The highest can be expressed as a function of weight, volume and effective efficiency with the optimization variables:

5. The marine secondary circuit system optimization method based on the improved multi-objective particle swarm optimization algorithm according to claim 1 is characterized in that: The particle velocity and position update formula based on the adaptive adjustment of the inertia weight and learning factor is as follows: Where, is the velocity of particle i in the tth iteration; is the position of particle i in the tth iteration; is the historical optimal position of particle i up to the tth iteration; gbestx (t) is the global optimal position of the population up to the tth iteration; r1 and r2 are random numbers uniformly distributed between 0 and 1; c1 and c2 are adaptive learning factors; and w is the adaptive inertia weight: Where f is the convergence factor.

6. A marine secondary circuit system optimization device based on an improved multi-objective particle swarm algorithm, characterized in that: The system comprises a memory and a processor; the memory is used to store a computer program; the processor is used to implement the marine secondary circuit system optimization method based on the improved multi-objective particle swarm algorithm as described in any one of claims 1 to 5 when executing the computer program.

7. A computer-readable storage medium, characterized in that The storage medium stores a computer program, and when the computer program is executed by the processor, the marine secondary circuit system optimization method based on the improved multi-objective particle swarm algorithm as described in any one of claims 1 to 5 is implemented.

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