Liquid hydrogen storage tank heat insulation structure multi-objective optimization method based on quasi-two-dimensional model and NSGA-2 algorithm

Abstract

The invention relates to a liquid hydrogen storage tank heat insulation structure multi-objective optimization method based on a quasi-two-dimensional model and an NSGA-2 algorithm. The method comprises the steps that digital modeling is conducted on a liquid hydrogen storage tank variable-density multi-layer heat insulation structure and a steam cooling screen based on the quasi-two-dimensional model; taking the position of the steam cooling screen and the layer number of each spacing layer heat insulation layer as optimization objects, and taking the manufacturing cost and the heat insulation performance of the heat insulation structure of the liquid hydrogen storage tank as optimization objectives to construct a multi-objective optimization model; and solving the multi-objective optimization model based on an NSGA-2 algorithm to obtain the optimal values of the position of the steam cooling screen and the number of layers of the heat insulation layers of the spacing layers as optimization results. Compared with the prior art, the method can synchronously improve the heat insulation efficiency and reduce the manufacturing cost, and has the remarkable advantages of high model precision and excellent optimization efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of high vacuum and low temperature thermal insulation, and in particular to a multi-objective optimization method for the thermal insulation structure of a liquid hydrogen storage tank based on a quasi-two-dimensional model and an NSGA-2 algorithm. Background Art

[0002] Against the backdrop of declining reserves of traditional fossil energy, global warming has become a core challenge hindering sustainable human development. To address the climate crisis and reduce carbon emissions, the large-scale application of hydrogen energy has become a key strategic direction for the energy transition of major economies worldwide. As a key link in the hydrogen energy industry chain, liquid hydrogen storage technology has attracted considerable attention due to its high efficiency, economical cost, and safety. Given hydrogen's extremely low boiling point (-20K) and heat of vaporization, liquid hydrogen storage tanks require high-performance insulation systems to minimize evaporation losses.

[0003] Variable-density high-vacuum multi-layer thermal insulation structures have been widely used due to their efficient thermal insulation effects. In order to further improve their performance, technical personnel in this field need to optimize the parameters of their thermal insulation structures. In this regard, some existing technologies provide corresponding optimization methods. For example, Chinese patent CN119578231A discloses a variable-density high-vacuum multi-layer thermal insulation structure and an optimization method thereof. The optimization method includes the following steps: determining the design parameters and performance indicators of the variable-density high-vacuum multi-layer thermal insulation structure, and functionalizing each performance indicator based on the design parameters to obtain a simulation function of each performance indicator; establishing an optimal arrangement problem of the variable-density high-vacuum multi-layer thermal insulation structure based on the simulation function of each performance indicator, and using a genetic algorithm to solve the optimal arrangement problem to achieve the optimization of the variable-density high-vacuum multi-layer thermal insulation structure; when using the genetic algorithm to solve the optimal arrangement problem, a population of individuals is generated based on the number of insulation layers between each reflective screen of the variable-density high-vacuum multi-layer thermal insulation structure, and the heat flux density function of the variable-density high-vacuum multi-layer thermal insulation structure is used as a fitness function. However, in the above optimization method, the optimization goal is limited to improving the insulation performance and ignores the manufacturing cost factor. In addition, the numerical modeling of the liquid hydrogen storage tank adopts a one-dimensional model. This method assumes that the temperature at each point of the steam cooling screen is uniform, resulting in insufficient accuracy of heat flow calculation and reduced reliability of structural design. At the same time, the deviation seriously affects the accuracy of multi-objective optimization, making it difficult for the optimization results to balance multi-objective requirements such as insulation performance and cost, greatly weakening its engineering practical value.

[0004] Therefore, there is an urgent need for an algorithm to optimize the liquid hydrogen storage tank under a quasi-two-dimensional model for multi-objective optimization of its insulation performance and manufacturing cost. Summary of the Invention

[0005] The purpose of the present invention is to provide a multi-objective optimization method for the thermal insulation structure of liquid hydrogen storage tanks based on a quasi-two-dimensional model and the NSGA-2 algorithm in order to address the defects of the above-mentioned existing technologies that cannot balance the multi-objective requirements such as thermal insulation performance and cost. By establishing a quasi-two-dimensional thermodynamic model that integrates the heat transfer mechanism of the steam cooling screen, the accuracy of the tank heat leakage calculation is significantly improved; then, an optimization system is constructed with the thermal insulation structure parameters as the decision variables and the manufacturing cost and heat flux density as the dual objectives. The NSGA-2 algorithm based on the Pareto front is used for multi-objective optimization, and finally the optimal engineering solution is obtained through standardization processing and weight distribution strategy. This method realizes the quantitative trade-off between the thermodynamic performance and economic indicators of the tank insulation structure, and provides a new theoretical framework for the design of cryogenic containers.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A multi-objective optimization method for the insulation structure of liquid hydrogen storage tanks based on a quasi-two-dimensional model and the NSGA-2 algorithm includes:

[0008] Digital modeling of the variable-density multi-layer insulation structure and steam cooling screen of the liquid hydrogen storage tank based on a quasi-two-dimensional model;

[0009] A multi-objective optimization model was constructed with the steam cooling screen position and the number of insulation layers in each spacer layer as optimization objects, and the insulation structure cost and insulation performance of the liquid hydrogen storage tank as optimization targets.

[0010] The multi-objective optimization model was solved based on the NSGA-2 algorithm to obtain the optimal values of the steam cooling screen position and the number of insulation layers in each spacer layer as the optimization results.

[0011] The digital modeling of the variable-density multi-layer insulation structure and steam cooling screen of the liquid hydrogen storage tank based on the quasi-two-dimensional model includes:

[0012] The performance index of variable density high vacuum multi-layer insulation structure is expressed in the form of function:

[0013] q total,i,j =q r,i,j +q s,i,j +q g,i,j

[0014] Where: q total,i,j is the total heat flux density of the j-th layer of the high vacuum multi-layer insulation structure of the liquid hydrogen storage tank with variable density, q r,i,j is the radiation heat transfer heat flux density of the j-th grid of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, q s,i,j is the solid heat conduction heat flux density of the jth grid layer of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, q g,i,jis the residual gas heat flux density of the j-th grid layer of the variable-density high-vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank;

[0015] The performance index and heat transfer process of the steam cooling screen are expressed in the form of functions:

[0016] Q outer,j +Q VCS,j-1 =Q inner,j +Q VCS,j

[0017]

[0018] The above are the performance indicators and heat exchange process of a single steam cooling screen. outer,j is the heat from the outside to the steam cooling screen of the j-th grid, Q VCS,j-1 Q is the heat of the steam cooling screen flowing from the j-1th grid into the jth grid, inner,j Q is the heat from the steam cooling panel flowing into the insulation structure. VCS,j is the heat of the steam cooling screen flowing from the jth grid into the j+1th grid,

[0019]

[0020] The above are the performance indicators and heat exchange process of the series double steam cooling screen. The steam cooling screen near the cold end is called VCS1, and the steam cooling screen near the hot end is called VCS2. VCS2,(M-j) Q is the heat that flows from the Mj-th grid to the M-j+1-th grid in VCS2. middle,j is the heat flowing into the middle of the insulation structure from VCS2, Q VCS2,(M+1-j) Q is the heat flowing from the M+1-jth node to the M+2-jth node in VCS2. VCS1,j-1 Q is the heat that flows from the j-1th grid to the jth grid by VCS1. VCS1,j is the heat flowing from the jth grid to the j+1th grid by VCS1, and M is the total number of longitudinal grids in the quasi-two-dimensional model.

[0021] The heat flux density of the radiation heat exchange is:

[0022] q r,i,j =K r,i,j (T i,j+1 -T i,j )

[0023]

[0024] where K r,i,j is the radiation heat transfer coefficient of the jth grid layer of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, T i,j+1is the reflection screen temperature of the j+1th grid layer of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, T i,j is the reflection screen temperature of the jth grid layer of the variable density high vacuum multilayer insulation structure of the i-th liquid hydrogen storage tank, σ is the Stefan-Boltzmann constant, and its value is 5.67×10 -8 W / (m 2 ·K 4 ), ε C is the reflectivity of the cold end reflection screen, ε H is the reflectivity of the hot end reflection screen, and its value is 0.04.

[0025] The solid thermal conductivity heat flux density is:

[0026] q s,i,j =K s,i,j (T i,j+1 -T i,j )

[0027] K s,i,j =C2fλ / DX i

[0028]

[0029] Among them: K s,i,j is the solid heat transfer coefficient of the jth grid layer of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, C2 is an empirical constant, and its value is 0.008 for the polyester spacer layer, f is the relative density of the spacer layer, and its value is 0.02 for the polyester spacer layer, λ is the thermal conductivity of the spacer layer, DX i is the thickness of the i-th spacer layer.

[0030] The residual gas heat flux density is:

[0031] q g,i,j =K g,i,j (T i,j+1 -T i,j )

[0032] K g,i,j =C1Pα

[0033]

[0034] γ=c p / c v

[0035] Among them: K g,i,jis the heat transfer coefficient of the residual gas in the jth grid of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, C1 is the empirical constant, P is the residual gas pressure, α is the capacity coefficient, R is the ideal gas constant, M is the molecular mass of the residual gas in the insulation layer, T is the vacuum wall room temperature of the residual gas in the insulation layer, γ is the adiabatic index, and c p is the specific heat capacity of the residual gas at constant pressure, c v is the specific heat of the residual gas at constant volume.

[0036] The functional expression of the total thermal resistance and the temperature of each layer in the mathematical modeling of the variable density high vacuum multi-layer insulation structure is:

[0037] K Total,i,j =K r,i,j +K s,i,j +K g,i,j

[0038]

[0039] Among them: K Total,i,j is the total heat transfer coefficient of the j-layer grid of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, R i,j is the total thermal resistance of the jth layer of the grid in the variable density high vacuum multilayer insulation structure of the i-th liquid hydrogen storage tank, A is the heat exchange area of the high vacuum multilayer insulation structure, T n,j is the reflection layer temperature of the jth grid layer of the variable density high vacuum multi-layer insulation structure of the nth liquid hydrogen storage tank, T C is the cold end temperature of the variable density high vacuum multi-layer insulation structure of the liquid hydrogen storage tank, T N,j is the reflection layer temperature of the jth grid layer of the Nth layer liquid hydrogen storage tank variable density high vacuum multi-layer insulation structure.

[0040] The mathematical expression of the optimization objective of the multi-objective optimization model is:

[0041]

[0042]

[0043] Among them: the two objective functions are minf(x) to minimize the heat leakage of the liquid hydrogen storage tank, ming(x) to minimize the manufacturing cost of the liquid hydrogen storage tank insulation structure, and D Spacers is the thickness of a single insulation layer, is the average area of the nth spacer layer, f Spacers is the manufacturing cost of the insulation layer per unit volume, L1 is the length of VCS1, r1 is the radius of the outer diameter of VCS1, L2 is the length of VCS2, r2 is the radius of the outer diameter of VCS2, d is the thickness of the steam cooling screen, f vcsis the manufacturing cost of the steam cooling screen per unit volume, H is the height of the inner tank of the liquid hydrogen storage tank, D is the diameter of the inner tank of the liquid hydrogen storage tank, K1 is the number of bundles of VCS1, K2 is the number of bundles of VCS2, and R is the radius of the inner tank of the liquid hydrogen storage tank;

[0044] The mathematical expression of the constraint conditions of the multi-objective optimization model is:

[0045]

[0046] The above are the constraints. Specifically, the number of insulation layers in each spacer layer is greater than or equal to 1 and less than or equal to 6, the total number of insulation layers is greater than or equal to 3N and less than or equal to 6N, the position of VCS1 and VCS2 is greater than 1 and less than N, and x 1,vcs1 Indicates the VCS1 position of the first individual in the population, x 1,vcs2 Indicates the VCS2 position of the first individual in the population, x 1,N It indicates the number of insulation layers of the first individual in the population counting from the cold end to the nth layer of insulation layer.

[0047] The multi-objective optimization model is solved based on the NSGA-2 algorithm to obtain the optimal values of the steam cooling screen position and the number of insulation layers of each spacer layer as the optimization result, including:

[0048] Initialize the steam cooling screen position and the number of insulation layers in each spacer layer to obtain the initial population;

[0049] Based on the quasi-two-dimensional modeling of liquid hydrogen storage tanks and the objective function, genetic operations are performed to obtain the global optimization solution set;

[0050] Each global optimization solution set is normalized and weighted scored.

[0051] The genetic operation based on the quasi-two-dimensional modeling of the liquid hydrogen storage tank and the objective function and obtaining the global optimization solution set include:

[0052] Genetic operations include: non-dominated sorting, calculation of crowding, crossover, mutation, and elite retention;

[0053] Non-dominated sorting refers to the core method for screening equilibrium solutions in multi-objective optimization. Its core is that if a solution is not inferior to another solution in all optimization objectives and is strictly better in at least one objective dimension, the former is considered to dominate the latter. The solution set hierarchy is constructed by screening layer by layer. First, individuals that are not dominated by any other solution are extracted from the candidate solution set to form the first level. Then, the solutions in this level are excluded and the above screening process is repeated to generate subsequent levels in sequence until all solutions are classified.

[0054]

[0055] If one of the above formulas is satisfied, it means that point x dominates point y;

[0056] The computational crowding index is an indicator for evaluating the distribution density of solutions in the same non-dominated layer in multi-objective optimization. It is achieved by quantifying the distance between adjacent solutions of individuals in the target space. This indicator avoids excessive clustering of solutions by prioritizing individuals in sparse areas, thus ensuring the diversity and wide coverage of the Pareto frontier.

[0057]

[0058] The crowding degree of each individual is d 1,i and d 2,i Initialized to 0, after sorting, the crowding of the border individuals is set to infinite, and the crowding of other individuals is calculated using the above formula. The larger the crowding, the sparser the individuals around it, and the more likely it is to be selected into the next generation;

[0059] Crossover, mutation and elite retention are the core evolutionary strategies in genetic algorithms. Their synergistic effect balances global search and local optimization capabilities. Crossover simulates biological gene recombination, exchanging part of the genetic structure of two parent individuals to generate new individuals, promoting population diversity and integrating high-quality features; mutation randomly perturbs individual genes with low probability, breaking through local optimal limitations and enhancing the algorithm's ability to explore unknown areas; elite retention directly retains the best individuals in each generation to the next generation, avoiding the loss of high-quality solutions during evolution and ensuring the convergence of the algorithm. The three together constitute a closed-loop mechanism of generation, exploration and retention.

[0060] Normalize each global optimization solution set and perform weighted scoring:

[0061]

[0062] Total score(i) =W1Score1(i)+W2Score2(i)

[0063] Where: Score1(i) represents the normalized score of the i-th solution of the objective function f(x), f min is the optimal value of the objective function, f i is the i-th solution of the objective function f(x), Score(i) represents the normalized score of the i-th solution of the objective function g(x), g min is the optimal value of the objective function, g i is the i-th solution of the objective function g(x), Total Score(i) is the weighted total score of the i-th solution, W1 is the weighting coefficient of the normalized score of the objective function f(x), and W2 is the weighting coefficient of the normalized score of the objective function g(x).

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] 1. Compared with traditional insulation structures, the present invention integrates variable-density vacuum multi-layer insulation structure and steam cooling screen technology. It cleverly utilizes the cold energy released by low-temperature evaporation of liquid hydrogen. Through efficient heat recovery and barrier mechanism, it significantly deepens the insulation performance of liquid hydrogen storage tanks, greatly reduces cooling loss, and effectively improves the safety and stability of liquid hydrogen storage.

[0066] 2. Compared to traditional one-dimensional models of liquid hydrogen storage tanks, this invention uses a quasi-two-dimensional model to model the liquid hydrogen storage tank. This model fully considers the dynamic impact of temperature changes within the steam cooling panel, further improving the simulation accuracy of the heat transfer process of the liquid hydrogen storage tank's insulation structure. More importantly, it solves the problem that the one-dimensional model, due to its accuracy in multi-objective optimization, makes it difficult to balance multiple objectives such as insulation performance and cost, thus significantly reducing its engineering value.

[0067] 3. This invention introduces a groundbreaking multi-objective optimization algorithm, NSGA-2, for liquid hydrogen storage tanks. This algorithm simulates natural evolutionary processes, systematically weighing two key metrics: insulation performance and manufacturing cost. It accurately explores the Pareto frontier solution set under complex constraints, achieving the optimal balance between efficient insulation and economic cost for liquid hydrogen storage tanks. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 Schematic diagram of the thermal insulation structure of the liquid hydrogen storage tank under the quasi-two-dimensional model of the present invention;

[0069] Figure 2 Schematic diagram of the main steps of the method of the present invention;

[0070] Figure 3 This is a schematic diagram of experimental verification of an embodiment of the present application;

[0071] Where: 1, inner wall of the liquid hydrogen storage tank, 2, outer wall of the liquid hydrogen storage tank, 3, reflective screen, 4, thermal insulation layer, 5, steam cooling screen inlet pipe, 6, steam cooling screen outlet pipe, 7, the jth grid layer of steam cooling screen 2, and 8, the jth grid layer of steam cooling screen 1. DETAILED DESCRIPTION

[0072] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0073] Example 1

[0074] like Figure 1As shown in the figure, the liquid hydrogen storage insulation system primarily consists of a variable-density vacuum multi-layer insulation structure and a steam cooling screen. The variable-density vacuum multi-layer insulation structure consists of a reflective layer and an insulation layer. The reflective layer reduces heat generated by radiative heat transfer, so a double-layer aluminum film with low emissivity was selected in this model. The insulation layer reduces heat conduction, so a nylon mesh with low thermal conductivity was used as the insulation material. In the liquid hydrogen storage insulation system, heat from the external environment is transferred to the liquid hydrogen storage tank through the insulation structure. The liquid hydrogen absorbs the heat and partially evaporates to produce low-temperature hydrogen. The low-temperature hydrogen flows through the steam cooling screen pipes, absorbing the sensible heat from the adjacent reflective layer. To improve the heat transfer efficiency between the steam cooling screen tubes and the reflective layer, the steam cooling screen tubes are made of copper with high thermal conductivity. Compared to traditional one-dimensional models, the quasi-two-dimensional model incorporates a refined meshing strategy, discretizing the steam cooling channel into multiple small mesh cells along the axial direction. Based on this, the heat and mass transfer parameters within each mesh are calculated through a layer-by-layer iterative process. This modeling method breaks through the simplified assumptions of the one-dimensional model and can more realistically restore the thermal characteristics in complex flow channels, making the calculation results significantly close to the actual engineering conditions, and effectively improving the prediction accuracy and reliability of the insulation performance of liquid hydrogen storage tanks.

[0075] like Figure 2 As shown, the optimization method provided in this embodiment includes the following steps:

[0076] Step S1: digitally modeling the variable-density multi-layer insulation structure and steam cooling screen of the liquid hydrogen storage tank based on a quasi-two-dimensional model;

[0077] The step S1 specifically includes:

[0078] Step S1-1: Express the performance indicators of the variable-density high-vacuum multi-layer thermal insulation structure in a functional form, and then obtain simulation functions of each performance indicator.

[0079] (1) The performance index of the variable density high vacuum multi-layer insulation structure is expressed in the form of a function, and the formula is as follows:

[0080] q total,i,j =q r,i,j +q s,i,j +q g,i,j

[0081] Where: q total,i,j is the total heat flux density of the j-th layer of the high vacuum multi-layer insulation structure of the liquid hydrogen storage tank with variable density, q r,i,j is the radiation heat transfer heat flux density of the j-th grid of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, q s,i,j is the solid heat conduction heat flux density of the jth grid layer of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, q g,i,jis the residual gas heat flux density of the j-th grid layer of the variable-density high-vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank.

[0082] (2) The heat flux density of radiation heat transfer is expressed in functional form as follows:

[0083] q r,i,j =K r,i,j (T i,j+1 -T i,j )

[0084]

[0085] Among them: K r,i,j is the radiation heat transfer coefficient of the jth grid layer of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, T i,j+1 is the reflection screen temperature of the j+1th grid layer of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, T i,j is the reflection screen temperature of the jth grid layer of the variable density high vacuum multilayer insulation structure of the i-th liquid hydrogen storage tank, σ is the Stefan-Boltzmann constant, which is 5.67×10 -8 W / (m 2 ·K 4 ), ε C is the reflectivity of the cold end reflection screen, ε H is the reflectivity of the hot end reflection screen, and its value is 0.04.

[0086] (3) The heat flux density of solid thermal conductivity is expressed in the form of a function, as follows:

[0087] q s,i,j =K s,i,j (T i,j+1 -T i,j )

[0088] K s,i,j =C2fλ / DX i

[0089]

[0090] where K s,i,j is the solid heat transfer coefficient of the jth grid layer of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, C2 is an empirical constant, and its value is 0.008 for the polyester spacer layer, f is the relative density of the spacer layer, and its value is 0.02 for the polyester spacer layer, λ is the thermal conductivity of the spacer layer, DX i is the thickness of the i-th spacer layer.

[0091] (4) The residual gas heat flux density is expressed in functional form as follows:

[0092] q g,i,j =Kg,i,j (T i,j+1 -T i,j )

[0093] K g,i,j =C1Pα

[0094]

[0095] γ=c p / c v

[0096] where K g,i,j is the heat transfer coefficient of the residual gas in the jth grid of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, C1 is the empirical constant, P is the residual gas pressure, α is the capacity coefficient, R is the ideal gas constant, M is the molecular mass of the residual gas in the insulation layer, T is the vacuum wall room temperature of the residual gas in the insulation layer, γ is the adiabatic index, and c p is the specific heat capacity of the residual gas at constant pressure, c v is the specific heat of the residual gas at constant volume.

[0097] (5) The total thermal resistance and temperature of each layer of the variable density high vacuum multi-layer insulation structure are expressed in the form of a function. The formula is as follows:

[0098] K Total,i,j =K r,i,j +K s,i,j +K g,i,j

[0099]

[0100] where K Total,i,j is the total heat transfer coefficient of the j-layer grid of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, R i,j is the total thermal resistance of the jth layer of the grid in the variable density high vacuum multilayer insulation structure of the i-th liquid hydrogen storage tank, A is the heat exchange area of the high vacuum multilayer insulation structure, T n,j is the reflection layer temperature of the jth grid layer of the variable density high vacuum multi-layer insulation structure of the nth liquid hydrogen storage tank, T C is the cold end temperature of the variable density high vacuum multi-layer insulation structure of the liquid hydrogen storage tank, T N,j is the reflection layer temperature of the jth grid layer of the Nth layer liquid hydrogen storage tank variable density high vacuum multi-layer insulation structure.

[0101] Step S1-2: Express the performance index of the steam cooling screen and its heat exchange process in the form of a function.

[0102] Q outer,j +Q VCs,j-1 =Q inner,j +Q VCS,j

[0103]

[0104] The above are the performance indicators and heat exchange process of single steam cooling screen. outer,j is the heat from the outside to the steam cooling screen of the j-th grid, Q VCS,j-1 Q is the heat of the steam cooling screen flowing from the j-1th grid into the jth grid, inner,j Q is the heat from the steam cooling panel flowing into the insulation structure. VCS,j is the heat flowing from the jth grid layer to the j+1th grid layer of the steam cooling screen.

[0105]

[0106] The above is the performance index and heat exchange process of the series double steam cooling screen. In this application, the steam cooling screen near the cold end is called VCS1, and the steam cooling screen near the hot end is called VCS2. VCS2,(M-j) Q is the heat that flows from the Mj-th grid to the M-j+1-th grid in VCS2. middle,j is the heat flowing into the middle of the insulation structure from VCS2, Q VCS2,(M+1-j) Q is the heat flowing from the M+1-jth node to the M+2-jth node in VCS2. VCS1,j-1 Q is the heat that flows from the j-1th grid to the jth grid by VCS1. VCS1,j is the heat flowing from the jth grid to the j+1th grid by VCS1, and M is the total number of longitudinal grids in the quasi-two-dimensional model.

[0107] Step S2: A multi-objective optimization model is constructed with the steam cooling screen position and the number of insulation layers of each spacer layer as optimization objects, and the insulation structure cost and insulation performance of the liquid hydrogen storage tank as optimization targets.

[0108] Take the series-type double steam cooling panel composite density high vacuum multi-layer insulation structure as an example:

[0109]

[0110] In this application, the number of individuals in the population is I, x 1,1 Indicates the number of insulation layers of the first individual in the population starting from the cold end, x 1,N Indicates the number of insulation layers of the first individual in the population counting from the cold end to the Nth layer of insulation layer, x 1,vcs1 Indicates the VCS1 position of the first individual in the population, x 1,vcs2 Indicates the VCS2 position of the first individual in the population, x I,1 The number of insulation layers of the first spacer layer counted from the cold end by the first individual in the population, x I,N It represents the number of insulation layers of the Nth layer of insulation layer from the cold end of the I-th individual in the population, xI,vcs1 represents the VCS1 position of the I-th individual in the population, x I,vcs2 Indicates the VCS2 position of the first individual in the population.

[0111] Step S202: Clarify the multi-objective optimization function and its constraints.

[0112]

[0113] The two objective functions are minf(x) to minimize the heat leakage of the liquid hydrogen storage tank, ming(x) to minimize the manufacturing cost of the liquid hydrogen storage tank insulation structure, and D Spacers is the thickness of a single insulation layer, is the average area of the nth spacer layer, f Spacers is the manufacturing cost of the insulation layer per unit volume, L1 is the length of VCS1, r1 is the radius of the outer diameter of VCS1, L2 is the length of VCS2, r2 is the radius of the outer diameter of VCS2, d is the thickness of the steam cooling screen, f vcs is the manufacturing cost of the steam cooling screen per unit volume, H is the height of the inner tank of the liquid hydrogen storage tank, D is the diameter of the inner tank of the liquid hydrogen storage tank, K1 is the number of bundles of VCS1, K2 is the number of bundles of VCS2, and R is the radius of the inner tank of the liquid hydrogen storage tank.

[0114]

[0115] The above are the constraints, specifically the number of insulation layers in each spacer layer is greater than or equal to 1 and less than or equal to 6, the total number of insulation layers is greater than or equal to 3N and less than or equal to 6N, and the positions of VCS1 and VCS2 are greater than 1 and less than N.

[0116] Step S3: Solve the multi-objective optimization model based on the NSGA-2 algorithm to obtain the optimal value of the steam cooling screen position and the number of layers of each spacer insulation layer as the optimization result.

[0117] The step S3 specifically includes:

[0118] Step S3-1: Initialize the encoding using the position of the steam cooling panel of the variable-density high-vacuum multi-layer insulation structure and the number of insulation layers of each spacer layer as independent variables to obtain an initial population.

[0119] Step S3-2: performing genetic operations based on the quasi-two-dimensional modeling of the liquid hydrogen storage tank and the objective function to obtain a global optimization solution set.

[0120] The genetic operations include: non-dominated sorting, calculation of crowding, crossover, mutation, and elite retention.

[0121] Non-dominated sorting is a core method for screening equilibrium solutions in multi-objective optimization. Its core principle is to determine that a solution dominates another solution if it is non-inferior to the other solution in all optimization objectives and strictly superior in at least one objective dimension. This method constructs a hierarchical structure of solution sets through layer-by-layer screening. First, individuals that are not dominated by any other solution are extracted from the candidate solution set to form the first level (i.e., the Pareto optimal frontier). This level of solutions is then eliminated and the screening process is repeated to generate subsequent levels until all solutions are classified.

[0122]

[0123] If one of the above formulas is satisfied, it means that point x dominates point y.

[0124] Computational crowding is a metric used to assess the density of solutions within a non-dominated layer in multi-objective optimization. It is achieved by quantifying the distance between individuals in the objective space. This metric prioritizes individuals in sparse regions, preventing excessive clustering of solutions and ensuring a diverse and broad Pareto front.

[0125]

[0126] The crowding degree of each individual is d 1,i and d 2,i Initialized to 0, after sorting, the crowding of the boundary individuals is set to infinity, and the crowding of other individuals is calculated using the above formula. The larger the crowding, the sparser the individuals around it, and the more likely it is to be selected into the next generation.

[0127] Crossover, mutation, and elite retention are the core evolutionary strategies in genetic algorithms. Their synergistic effect balances global search and local optimization capabilities. Crossover simulates biological gene recombination, exchanging parts of the genetic structure of two parent individuals to generate new individuals, promoting population diversity and integrating high-quality features. Mutation randomly perturbs individual genes with low probability, breaking through local optimal constraints and enhancing the algorithm's ability to explore unknown areas. Elite retention directly retains the best individuals in each generation to the next, preventing the loss of high-quality solutions during evolution and ensuring algorithm convergence. Together, these three constitute a closed-loop "generate-explore-retention" mechanism, balancing the diversity of solution sets and convergence efficiency in complex optimization problems. This is the theoretical foundation for multi-objective evolutionary algorithms to achieve efficient global optimization.

[0128] Step S3-3: normalize each global optimization solution set and perform weighted scoring:

[0129]

[0130] Total Score(i) =W1Score1(i)+W2Score2(i)

[0131] Where Score1(i) represents the normalized score of the i-th solution of the objective function f(x), f min is the optimal value of the objective function, f i is the i-th solution of the objective function f(x), Scor□(i) represents the normalized score of the i-th solution of the objective function g(x), g min is the optimal value of the objective function, g i is the i-th solution of the objective function g(x), Total Score(i) is the weighted total score of the i-th solution, W1 is the weighting coefficient of the normalized score of the objective function f(x), and W2 is the weighting coefficient of the normalized score of the objective function g(x).

[0132] In addition, this application selected experimental data obtained by NASA on its MLI / VCS20-layer small liquid hydrogen testbed for comparative verification. The experimental data showed that the quasi-two-dimensional model showed good accuracy in simulating the evaporation rate of liquid hydrogen, especially when compared with the experimental results, it was significantly better than the traditional one-dimensional model. Figure 3 As shown, the calculation results of the quasi-2D model are more consistent with the experimental data than the one-dimensional model. Specifically, the maximum deviation between the simulation results of the one-dimensional model and the experimental data is 36.33%, while the maximum deviation of the quasi-2D model is only 3.13%. In addition, the average deviation of the one-dimensional model is 31.73%, while the average deviation of the quasi-2D model is reduced to 2.42%. These results fully demonstrate that the quasi-2D model can more accurately reflect the experimental data when simulating the liquid hydrogen evaporation rate in the VCS system than the 1D model, further verifying the advantages of the quasi-2D model in liquid hydrogen storage and transmission calculations.

[0133] If the above functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

Claims

1. A multi-objective optimization method for the insulation structure of a liquid hydrogen storage tank based on a quasi-two-dimensional model and the NSGA-2 algorithm, characterized in that: include: Digital modeling of the variable-density multi-layer insulation structure and steam cooling screen of the liquid hydrogen storage tank based on a quasi-two-dimensional model; A multi-objective optimization model was constructed with the steam cooling screen position and the number of insulation layers in each spacer layer as optimization objects, and the insulation structure cost and insulation performance of the liquid hydrogen storage tank as optimization targets. The multi-objective optimization model was solved based on the NSGA-2 algorithm to obtain the optimal values of the steam cooling screen position and the number of insulation layers in each spacer layer as the optimization results.

2. The multi-objective optimization method for the insulation structure of a liquid hydrogen storage tank based on a quasi-two-dimensional model and the NSGA-2 algorithm according to claim 1 is characterized in that: The digital modeling of the variable-density multi-layer insulation structure and steam cooling screen of the liquid hydrogen storage tank based on the quasi-two-dimensional model includes: The performance index of variable density high vacuum multi-layer insulation structure is expressed in the form of function: q tota l,i,j=q r,i,j +q s,i,j +q g,i,j Where: q total,i,j is the total heat flux density of the j-th layer of the high vacuum multi-layer insulation structure of the liquid hydrogen storage tank with variable density, q r,i,j is the radiation heat transfer heat flux density of the j-th grid of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, q s,i,j is the solid heat conduction heat flux density of the jth grid layer of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, q g,i,j is the residual gas heat flux density of the j-th grid layer of the variable-density high-vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank; The performance index and heat transfer process of the steam cooling screen are expressed in the form of functions: Q outer,j +Q VCS,j-1 =Q inner,j +Q VCS,j The above are the performance indicators and heat exchange process of a single steam cooling screen. outer,j is the heat from the outside to the steam cooling screen of the j-th grid, Q VCS,j-1 Q is the heat of the steam cooling screen flowing from the j-1th grid into the jth grid, inner,j Q is the heat from the steam cooling panel flowing into the insulation structure. VCS,j is the heat of the steam cooling screen flowing from the jth grid into the j+1th grid, The above are the performance indicators and heat exchange process of the series double steam cooling screen. The steam cooling screen near the cold end is called VCS1, and the steam cooling screen near the hot end is called VCS2. VCS2,(M-j) Q is the heat that flows from the Mj-th grid to the M-j+1-th grid in VCS2. middle,j is the heat flowing into the middle of the insulation structure from VCS2, Q VCS2,(M+1-j) Q is the heat flowing from the M+1-jth node to the M+2-jth node in VCS2. VCS1,j-1 Q is the heat that flows from the j-1th grid to the jth grid by VCS1. VCS1,j is the heat flowing from the jth grid to the j+1th grid by VCS1, and M is the total number of longitudinal grids in the quasi-two-dimensional model.

3. The multi-objective optimization method for the thermal insulation structure of a liquid hydrogen storage tank based on a quasi-two-dimensional model and an NSGA-2 algorithm according to claim 2 is characterized in that: The heat flux density of the radiation heat exchange is: q r,i,j =K r,i,j (T i,j+1 -T i,j ) Among them: K r,i,j is the radiation heat transfer coefficient of the jth grid layer of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, T i,j+1 is the reflection screen temperature of the j+1th grid layer of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, T i,j is the reflection screen temperature of the jth grid layer of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, σ is the Stefan-Boltzmann constant, ε C is the reflectivity of the cold end reflection screen, ε H is the reflectivity of the hot end reflection screen.

4. The multi-objective optimization method for the insulation structure of a liquid hydrogen storage tank based on a quasi-two-dimensional model and the NSGA-2 algorithm according to claim 2 is characterized in that: The solid thermal conductivity heat flux density is: q s,i,j =K s,i,j (T i,j+1 -T i,j ) K s,i,j =C2fλ / DX i Among them: K s,i,j is the solid heat transfer coefficient of the jth grid layer of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, C2 is the empirical constant, f is the relative density of the spacer layer, λ is the thermal conductivity of the spacer layer, DX i is the thickness of the i-th spacer layer.

5. The multi-objective optimization method for the insulation structure of a liquid hydrogen storage tank based on a quasi-two-dimensional model and the NSGA-2 algorithm according to claim 2 is characterized in that: The residual gas heat flux density is: q g,i,j =K g,i,j (T i,j+1 -T i,j ) K g,i,j =C1Pα γ=c p / c v Among them: K g,i,j is the heat transfer coefficient of the residual gas in the jth grid of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, C1 is the empirical constant, P is the residual gas pressure, α is the capacity coefficient, R is the ideal gas constant, M is the molecular mass of the residual gas in the insulation layer, T is the vacuum wall room temperature of the residual gas in the insulation layer, γ is the adiabatic index, and c p is the specific heat capacity of the residual gas at constant pressure, c v is the specific heat of the residual gas at constant volume.

6. The multi-objective optimization method for the insulation structure of a liquid hydrogen storage tank based on a quasi-two-dimensional model and the NSGA-2 algorithm according to claim 2 is characterized in that: The functional expression of the total thermal resistance and the temperature of each layer in the mathematical modeling of the variable density high vacuum multi-layer insulation structure is: K Total,i,j =K r,i,j +K s,i,j +K g,i,j Among them: K Total,i,j is the total heat transfer coefficient of the j-layer grid of the variable density high vacuum multi-layer insulation structure of the i-th liquid hydrogen storage tank, R i,j is the total thermal resistance of the jth layer of the grid in the variable density high vacuum multilayer insulation structure of the i-th liquid hydrogen storage tank, A is the heat exchange area of the high vacuum multilayer insulation structure, T n,j is the reflection layer temperature of the jth grid layer of the variable density high vacuum multi-layer insulation structure of the nth liquid hydrogen storage tank, T C is the cold end temperature of the variable density high vacuum multi-layer insulation structure of the liquid hydrogen storage tank, T N,j is the reflection layer temperature of the jth grid layer of the Nth layer liquid hydrogen storage tank variable density high vacuum multi-layer insulation structure.

7. The multi-objective optimization method for the insulation structure of a liquid hydrogen storage tank based on a quasi-two-dimensional model and the NSGA-2 algorithm according to claim 2 is characterized in that: The mathematical expression of the optimization objective of the multi-objective optimization model is: Among them: the two objective functions are minf(x) to minimize the heat leakage of the liquid hydrogen storage tank, ming(x) to minimize the manufacturing cost of the liquid hydrogen storage tank insulation structure, and D Spacers is the thickness of a single insulation layer, is the average area of the nth spacer layer, f Spacers is the manufacturing cost of the insulation layer per unit volume, L1 is the length of VCS1, r1 is the radius of the outer diameter of VCS1, L2 is the length of VCS2, r2 is the radius of the outer diameter of VCS2, d is the thickness of the steam cooling screen, f vcs is the manufacturing cost of the steam cooling screen per unit volume, H is the height of the inner tank of the liquid hydrogen storage tank, D is the diameter of the inner tank of the liquid hydrogen storage tank, K1 is the number of bundles of VCS1, K2 is the number of bundles of VCS2, and R is the radius of the inner tank of the liquid hydrogen storage tank; The mathematical expression of the constraint conditions of the multi-objective optimization model is: The above are the constraints. Specifically, the number of insulation layers in each spacer layer is greater than or equal to 1 and less than or equal to 6, the total number of insulation layers is greater than or equal to 3N and less than or equal to 6N, the position of VCS1 and VCS2 is greater than 1 and less than N, and x 1,vcs1 Indicates the VCS1 position of the first individual in the population, x 1,vcs2 Indicates the VCS2 position of the first individual in the population, x 1,N It indicates the number of insulation layers of the first individual in the population counting from the cold end to the nth layer of insulation layer.

8. The multi-objective optimization method for the insulation structure of a liquid hydrogen storage tank based on a quasi-two-dimensional model and the NSGA-2 algorithm according to claim 7 is characterized in that: The multi-objective optimization model is solved based on the NSGA-2 algorithm to obtain the optimal values of the steam cooling screen position and the number of insulation layers of each spacer layer as the optimization result, including: Initialize the steam cooling screen position and the number of insulation layers in each spacer layer to obtain the initial population; Based on the quasi-two-dimensional modeling of liquid hydrogen storage tanks and the objective function, genetic operations are performed to obtain the global optimization solution set; Each global optimization solution set is normalized and weighted scored.

9. The multi-objective optimization method for the insulation structure of a liquid hydrogen storage tank based on a quasi-two-dimensional model and the NSGA-2 algorithm according to claim 8, characterized in that: The genetic operation based on the quasi-two-dimensional modeling of the liquid hydrogen storage tank and the objective function and obtaining the global optimization solution set include: Genetic operations include: non-dominated sorting, calculation of crowding, crossover, mutation, and elite retention; Non-dominated sorting refers to the core method for screening equilibrium solutions in multi-objective optimization. Its core is that if a solution is not inferior to another solution in all optimization objectives and is strictly better in at least one objective dimension, the former is considered to dominate the latter. The solution set hierarchy is constructed by screening layer by layer. First, individuals that are not dominated by any other solution are extracted from the candidate solution set to form the first level. Then, the solutions in this level are excluded and the above screening process is repeated to generate subsequent levels in sequence until all solutions are classified. If one of the above formulas is satisfied, it means that point x dominates point y; The computational crowding index is an indicator for evaluating the distribution density of solutions in the same non-dominated layer in multi-objective optimization. It is achieved by quantifying the distance between adjacent solutions of individuals in the target space. This indicator avoids excessive clustering of solutions by prioritizing individuals in sparse areas, thus ensuring the diversity and wide coverage of the Pareto frontier. The crowding degree of each individual is d 1,i and d 2,i Initialized to 0, after sorting, the crowding of the border individuals is set to infinite, and the crowding of other individuals is calculated using the above formula. The larger the crowding, the sparser the individuals around it, and the more likely it is to be selected into the next generation; Crossover, mutation and elite retention are the core evolutionary strategies in genetic algorithms. Their synergistic effect balances global search and local optimization capabilities. Crossover simulates biological gene recombination, exchanging part of the genetic structure of two parent individuals to generate new individuals, promoting population diversity and integrating high-quality features; mutation randomly perturbs individual genes with low probability, breaking through local optimal limitations and enhancing the algorithm's ability to explore unknown areas; elite retention directly retains the best individuals in each generation to the next generation, avoiding the loss of high-quality solutions during evolution and ensuring the convergence of the algorithm. The three together constitute a closed-loop mechanism of generation, exploration and retention.

10. The multi-objective optimization method for the insulation structure of a liquid hydrogen storage tank based on a quasi-two-dimensional model and the NSGA-2 algorithm according to claim 8, characterized in that: Normalize each global optimization solution set and perform weighted scoring: Total Score(i) =W1Score1(i)+W2Score2(i) Where: Score1(i) represents the normalized score of the i-th solution of the objective function f(x), f min is the optimal value of the objective function, f i is the i-th solution of the objective function f(x), Score(i) represents the normalized score of the i-th solution of the objective function g(x), g min is the optimal value of the objective function, g i is the i-th solution of the objective function g(x), Total Score(i) is the weighted total score of the i-th solution, W1 is the weighting coefficient of the normalized score of the objective function f(x), and W2 is the weighting coefficient of the normalized score of the objective function g(x).

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