An approximate optimization method for water-resistant aircraft based on surrogate model

Abstract

The present invention discloses an approximate optimization method for water-resistant aircraft based on a proxy model, which belongs to the application field of cross-media aircraft and aircraft. The implementation method of the present invention is as follows: constructing a water-resistant aircraft configuration, the top of the configuration is an aircraft rotating body, the bottom adopts a two-stage sliding surface configuration, and the bottom configuration forms a plane-symmetrical configuration with the plane where the keel line is located; the bottom configuration of the sliding surface of the planing boat is used to reduce the impact overload of the aircraft during high-speed water-hitting as much as possible, while reducing the horizontal speed loss and the pitch angle at the time of leaving the water caused by water-hitting, and combining the approximate optimization technology to adjust and optimize the configuration parameters of the water-resistant aircraft, and replacing the fluid-solid coupling analysis model of the high-speed water-hitting of the water-resistant aircraft with the proxy model, under the premise of meeting various flight kinematic parameters, further reducing the impact load. The present invention can be suitable for application in the high-speed sea-skimming flight state of a cross-media aircraft, can reduce the high-speed water-hitting impact load and ensure the stability of the water-hitting and go-around flight trajectory.

Description

Technical Field

[0001] The invention relates to an approximate optimization method for a water-resistant aircraft based on a proxy model, and belongs to the field of cross-medium aircraft and spacecraft. Background Art

[0002] Cross-medium vehicles, due to their combined capabilities of rapid aerial flight and low-speed underwater cruising, have attracted widespread attention from research institutions both domestically and internationally in recent years. They hold promising application prospects in areas such as marine environmental pollution monitoring, aquatic population migration monitoring, and novel maritime warfare. However, due to complex sea conditions and sensor measurement errors, cross-medium vehicles have a high probability of hitting water during low-altitude, sea-skimming flight, exacerbating the risk of structural damage. Therefore, it is necessary to optimize the design of water-resistant vehicles and reduce the impact loads of water-resistant vehicles by designing reasonable water-resistant configurations. Furthermore, since the kinematic parameters of the vehicle's water-strike process must be obtained through fluid-structure interaction analysis, the simulation computational cost is significantly increased. Traditional optimization methods (such as genetic algorithms and particle swarm optimization) often require directly invoking analytical models thousands of times to explore the design space, making them unsuitable for water-resistant vehicle design optimization problems involving time-consuming analytical models. Therefore, in order to overcome the limitations of traditional methods, it is very necessary to develop an approximate optimization method for water-resistant aircraft based on a surrogate model. By approximating the fluid-solid coupling analysis model of the aircraft hitting water through the surrogate model, the optimization efficiency can be improved, the design cycle can be shortened, and the optimization and modification of the water-resistant aircraft design scheme can be quickly realized in the overall design stage.

[0003] In order to better illustrate the technical solution of the present invention, the following briefly introduces the relevant mathematical tools involved:

[0004] (1) Structured arbitrary Lagrangian-Euler method

[0005] Compared to the traditional arbitrary Lagrangian-Euler (ALE) method, the structured arbitrary Lagrangian-Euler (S-ALE) method provides a structured grid for refined modeling of fluid-structure interaction, thereby preventing liquid leakage and improving simulation efficiency. The governing equations of S-ALE are described below.

[0006] The mass conservation equation is shown in formula (1).

[0007]

[0008] Where ρ is the fluid density; v i is the material speed; w i is the relative velocity between the material and the mesh.

[0009] The momentum conservation equation is shown in equation (2).

[0010]

[0011] Where b i is the fluid volume force; σ ij,j is the differential of the stress tensor with respect to j. ij It can be expressed as

[0012] σ ij =-pδ ij +μ(τ i,j ,τ j,i ) (3)

[0013] Where p is the fluid pressure; δ ij is the Kronecker-δ function; μ is the dynamic viscosity coefficient; τ is the viscous shear stress.

[0014] The energy conservation equation is shown in formula (4).

[0015]

[0016] Where E is the specific energy of the fluid. Summary of the Invention

[0017] In order to avoid the problems of structural damage caused by water striking during low-altitude sea-skimming flight and the large amount of computation required by traditional optimization algorithms, the present invention discloses an approximate optimization method for water-resistant aircraft based on a proxy model to solve the following technical problems: constructing a water-resistant aircraft configuration, using the bottom configuration of the planing surface of a planing boat to minimize the impact overload of the aircraft during high-speed water striking, while reducing the horizontal velocity loss and the pitch angle at the time of exiting the water caused by water striking, and combining the approximate optimization technology to adjust and optimize the configuration parameters of the water-resistant aircraft, further reducing the impact load while satisfying various flight kinematic parameters. The present invention can be suitable for application in high-speed sea-skimming flight of cross-medium aircraft, can reduce the impact load of high-speed water striking and ensure the stability of the trajectory of water-strike and go-around flight.

[0018] The purpose of the present invention is achieved through the following technical solutions.

[0019] The present invention discloses an approximate optimization method for a water-resistant aircraft based on a proxy model, comprising the following steps:

[0020] Step A: Determine the operating conditions, shape, and load conditions of the water-resistant aircraft.

[0021] Step A is implemented as follows:

[0022] Step A-1: Determine the shape of the water-resistant aircraft. To ensure that the aircraft has sufficient lift when flying over the sea and reduce resistance when hitting the water, a variable swept wing with a chord length of L is used. ch With Exhibition Director L spDetermined based on the lift requirements at flight speed V and flight altitude h.

[0023] Step A-2: Determine the internal load of the anti-water aircraft. To balance the resistance of the aircraft during sea-skimming flight, solid propulsion is used. The aircraft is equipped with propellant, payload, steering gear, sensor, power supply unit, and seeker from the tail to the nose. By setting the minimum threshold of the bow radius R bow,min , the minimum threshold of tail radius R rear,min and the maximum tail radius threshold R rear,max , to ensure the internal volume requirements of each section of the aircraft.

[0024] Step B: Combining the structural characteristics of conventional aircraft and water planing boats, a water-resistant aircraft configuration is constructed. This configuration consists of a conventional aircraft rotating body at the top and a two-stage planing surface at the bottom, with the bottom configuration being plane-symmetrical about the plane of the keel line. During high-speed water impact, the bow planing surface touches the water to reduce the aircraft's wetted area, thereby minimizing the impact overload of the aircraft's water impact. This also reduces the water impact speed loss and the pitch angle out of the water, thereby improving the stability of the water impact and go-around trajectory. The water-resistant aircraft configuration achieves a unique geometric representation through 13 control points, thereby constructing a geometric parameterized model of the water-resistant aircraft. The spatial positions of the 13 control points are determined by the following parameters: the ratio of bow length to total length, the ratio of front length to total length, the ratio of middle length to total length, the ratio of maximum width to total length, the ratio of bottom depth to total length, bow inclination angle, front inclination angle, the ratio of bow planing surface width to maximum width, the ratio of front planing surface width to maximum width, the ratio of middle planing surface width to maximum width, bow planing surface inclination angle, front planing surface inclination angle, middle planing surface inclination angle, the ratio of bow width to maximum width, and the ratio of front width to maximum width.

[0025] Step B is implemented as follows:

[0026] Step B-1: Construct a water-resistant aircraft configuration, with the top portion being a conventional aircraft rotational body and the bottom portion employing a two-stage gliding surface configuration. The bottom portion is plane-symmetrical about the plane of the keel line. This water-resistant aircraft configuration is uniquely characterized by its geometric shape using 13 control points, thereby constructing a parameterized geometric model of the water-resistant aircraft.

[0027] Step B-2: Take control point P4 as the origin of the geometric shape coordinates, then x P4 =y P4 =z P4 = 0. The coordinate system is defined as follows: the positive direction of the x-axis is pointing toward the aircraft head, the positive direction of the z-axis is vertically upward, and the y-axis is perpendicular to the xP4z plane. The position that satisfies the right-hand rule is the positive direction of the y-axis.

[0028] Step B-3: According to the coordinate system definition, the y-axis coordinates of points P0 to P4 on the keel line P0P1P2P3P4 are all 0, so y P0 =y P1 =y P2 =y P3 =y P4 = 0. The x-axis coordinate x of point P0 P0 , z-axis coordinate z P0 Calculated according to formula (5).

[0029]

[0030] Where, L is the total length of the aircraft; H is the bottom profile depth of the aircraft; α H It is the ratio of bottom profile depth to total length.

[0031] Step B-4: x-axis coordinate x of point P1 P1 , z-axis coordinate z P1 Calculated by formula (6).

[0032]

[0033] Where, L b is the bow length; α Lb is the ratio of bow length to total length; is the bow inclination angle.

[0034] According to formula (7), the x-axis coordinate x of point P2 is obtained P2 , z-axis coordinate z P2 .

[0035]

[0036] Where, L f is the front length; α Lf is the ratio of the front length to the total length; is the front inclination angle.

[0037] The z-axis coordinate of point P3 P3 is 0, and its x-axis coordinate x P3 Calculated by formula (8).

[0038] x P3 =x P2 -L m =(1-α Lb -α Lf -α Lm )×L (8)

[0039] Where, L m is the middle length; α LmPoints P0 to P3 are connected by a quartic spline curve, which is tangent to the straight line P3P4 at point P3. The spline curve P0P1P2P3 and the straight line P3P4 form the keel line P0P1P2P3P4.

[0040] Step B-5: Point P6, Point P8, Point P 10 , click P 12 The z-axis coordinates of P0 , as shown in formula (9), the z-axis coordinates are expressed as z P6 、z P8 、z P10 、z P12 .

[0041] z P6 =z P8 =z P10 =z P12 =z P0 =α H ·L (9)

[0042] Point P6, Point P8, Point P 10 , click P 12 The y-axis coordinates of are calculated according to formula (10) to formula (12), and the y-axis coordinates are expressed as y P6 、y P8 、y P10 、y P12 .

[0043]

[0044] Where, L wb , L wf With L wm are the widths of the bow, front and middle respectively; γ Wb with γ Wf are the ratios of bow width, front width and maximum width respectively; W is the maximum width; α W is the ratio of maximum width to total length.

[0045] Step B-6: y-axis coordinate y of point P5 P5 and the z-axis coordinate z P5 According to formula (13), we can get

[0046]

[0047] Where, L sb is the bow planing surface width; η sb is the ratio of bow planing surface width to maximum width; θ sb is the inclination angle of the bow planing surface.

[0048] According to formula (14) and formula (15), we can get point P7, point P9, point P 11 The y-axis coordinate and z-axis coordinate of P7 、y P9 、y P11 , the z-axis coordinates are represented as z P7 、z P9 、z P11 .

[0049]

[0050] Where, L sf , L sm are the widths of the front and middle sliding surfaces respectively; η sf ,η sm are the ratios of the front sliding surface width, the middle sliding surface width and the maximum width respectively; θ sf ,θ sm They are the front sliding surface inclination angle and the middle sliding surface inclination angle respectively.

[0051] Step B-7: Point set {P0,P6,P8,P 10} connected by a quadratic spline curve and at point P 10 At the line P 10 P 12 Tangent. The point set {P0, P5, P7, P9} is connected by a spline curve of degree 4 or higher and intersects with the line P9P at point P9. 11 Tangent.

[0052] Formulas (5) to (15) are geometric parameterized models of water-resistant aircraft. The geometric parameterized models of water-resistant aircraft are used to reduce the wetted area of the aircraft by the bow gliding surface touching the water when hitting the water at high speed, thereby reducing the impact overload of the aircraft hitting the water, and at the same time reducing the water-hitting speed loss and the pitch angle out of the water, thereby improving the stability of the water-hitting and go-around trajectory.

[0053] In order to balance accuracy and efficiency, as a preferred method, the point set {P0, P5, P7, P9} is connected by a quartic spline curve.

[0054] Step C: A fluid-structure coupling analysis model for the aircraft hitting the water is established based on the structured Lagrangian-Euler method. By constructing an air-water structured grid, a refined grid is divided near the aircraft hitting the water and at the air-water interface to prevent liquid leakage during the fluid-structure coupling analysis and improve the efficiency of the fluid-structure coupling analysis of the aircraft hitting the water.

[0055] Step C is implemented as follows:

[0056] Step C-1: Based on the constructed geometric parameterized model of the water-resistant aircraft, define the high-speed water-strike condition of the water-resistant aircraft, including the height H of point P4 from the horizontal plane. z , aircraft horizontal speed V x 、Aircraft vertical speed V z .

[0057] Step C-2: Define the air and water domain dimensions, including the water depth L zw , air space height L za , computational domain width L y , calculation domain length L x .

[0058] Step C-3: Calculate the air domain properties using the linear polynomial state equation, as shown in Equation (16).

[0059]

[0060] Where, E a is the initial internal energy per unit volume; V is the relative volume; C j (j=0,1,...,6) are linear polynomial coefficients.

[0061] The water area properties are calculated using the Gruneisen equation of state, as shown in Equation (17).

[0062]

[0063] Where, ρ w is the density of water; C w is the local sound velocity; a is the first-order volume correction coefficient; γ0 is the Gruneisen state equation constant; S i (i=1,2,3) are the coefficients of the Gruneisen equation of state.

[0064] Step C-4: Define the aircraft as a Lagrangian object and calculate the motion parameters of the air domain-water domain-aircraft under high-speed water-striking conditions, including: aircraft overload, aircraft speed, aircraft pitch angle, and aircraft displacement.

[0065] Step D: Constructing a watertight aircraft optimization problem model, using aircraft configuration parameters as optimization variables, and minimizing the maximum impact overload of the watertight aircraft when impacting the water while satisfying the watertight aircraft constraints. The watertight aircraft constraints include horizontal velocity loss, pitch angle at water exit, cross-sectional radius of each part, and vertical velocity at water exit.

[0066]

[0067] Where, α Lb is the ratio of bow length to total length; αLf is the ratio of the front length to the total length; α Lm is the ratio of the middle length to the total length; α W is the ratio of maximum width to total length; α H is the ratio of bottom profile depth to total length; is the bow inclination angle; is the front inclination angle; η sb is the ratio of the bow planing surface width to the maximum width; η sf is the ratio of the front sliding surface width to the maximum width; η sm is the ratio of the middle sliding surface width to the maximum width; θ sb is the inclination angle of the bow planing surface; θ sf is the inclination angle of the front sliding surface; θ sm is the inclination angle of the middle sliding surface; γ Wb is the ratio of bow width to maximum width; γ Wf is the ratio of the front width to the maximum width. The above 15 aircraft configuration parameters are the design variables X of the optimization problem. max ΔV is the maximum impact overload of the aircraft during the water impact process. This parameter is the optimization target of the optimization problem. x is the horizontal speed loss of the aircraft; V is the pitch angle of the aircraft out of water; z,end R is the vertical speed of the aircraft out of water; bow is the cross-sectional radius of the aircraft bow; R rear is the radius of the tail section of the aircraft, and the above five kinematic parameters are the constraints of the optimization problem. vx 、 Γ vz They are the horizontal speed loss threshold, the water exit pitch angle threshold, and the terminal vertical speed threshold. LB With X UB are the lower and upper bounds of the design variables, respectively.

[0068] Step E: A surrogate model-assisted differential evolution algorithm is used to optimize the watertight vehicle optimization problem. The constraints and objective functions in the optimization problem are determined by Steps B and C. With the optimization objective of minimizing the maximum water impact overload, the geometric parameters of the watertight vehicle are optimized. The optimized configuration parameters of the watertight vehicle are obtained by optimizing the vehicle's speed loss, water exit pitch angle, cross-sectional radius of each component, and vertical velocity at water exit. The optimization process is divided into two phases: global exploration and local search. In the global exploration phase, the predicted variance of the watertight vehicle's water impact overload, provided by the KRG surrogate model, is used to construct a feasible criterion based on constraint improvement and optimal fitness, thereby guiding convergence to the optimal configuration solution. In the local search phase, to effectively balance the robustness, approximation accuracy, and construction efficiency of the surrogate model, a RBF-based local optimization problem for the watertight vehicle is constructed and solved in conjunction with a sequential quadratic programming method, thereby improving the optimization convergence speed.

[0069] Step E is implemented as follows:

[0070] Step E-1: Determine the design space, objective function, constraint function, and algorithm parameters for the configuration optimization problem of water-resistant aircraft, including the population size N. P , scaling factor F, crossover probability C R and the maximum number of model calls The Latin hypersquare experimental design method based on Maximin is used to generate N in the initial design space. P Initial sample points are obtained, and the corresponding true targets and constraint function values are calculated, and the sample database of the anti-water vehicle configuration is updated.

[0071] Step E-2: Sort the current sample database according to the feasible criteria and select the top N P The configuration samples of water-resistant aircraft are used as the current parent population. A variety of mutation operators and crossover operators are used to generate the test population Q = {Q R1 ∪Q R2 ∪Q CtoR ∪Q CtoB}.

[0072] Step E-3: Use all samples in the sample database to construct the Kriging proxy model of the water hammer process fluid-solid coupling analysis model and calculate the predicted value of the objective function and the predicted values of each constraint function In addition, the prediction variance s of each function of the population individual is calculated according to formula (19): 2 (x).

[0073]

[0074] Where R is the correlation matrix; R(·,·) is the correlation coefficient; x(i), i=1,2,...,N KRG is the i-th sample in the sample database; is the variance of the Gaussian distribution; I is the identity matrix. New exploration samples of water-resistant aircraft configurations are selected from the experimental population based on the improved feasibility criterion. The true objective function and constraint function values of the new exploration samples are calculated and added to the sample database of water-resistant aircraft configurations.

[0075] Step E-4: Randomly select the initial point of the sequential quadratic programming method from the current population. Select N points that are closer to the initial point from the sample database based on the Euclidean distance. RBF The local RBF proxy model corresponding to the objective function and constraint function of the anti-water aircraft configuration optimization problem is constructed for each sample point. The scale of the sample points for constructing RBF is related to the dimension of the optimization problem, and the calculation formula is as follows

[0076]

[0077] Where n v is the dimension of the optimization problem. RBF When the sample size is larger than that of the existing database, all samples in the database are used to construct the RBF proxy model. The sequential quadratic programming method is used to solve the sub-optimization problem of the anti-waterproof aircraft configuration to obtain new search sample points, calculate the corresponding true objective function and constraint function values, and add them to the anti-waterproof aircraft configuration sample database.

[0078] In order to balance accuracy and efficiency, the mutation operator selects Rand / 1, Rand / 2, Current-to-rand / 1, and Current-to-best / 1 strategies as the preferred choice.

[0079] Step E-5: Determine whether the maximum number of model calls has been reached. If not, return to step E-2 to continue optimization; otherwise, output the optimized parameters of the water-resistant aircraft configuration.

[0080] The method further includes step F: manufacturing a water-resistant aircraft according to the optimized configuration parameters of the water-resistant aircraft obtained in step E, minimizing the impact overload of the aircraft during high-speed water-hitting by configuring the bottom of the planing surface of the planing boat, reducing the risk of water-hitting damage due to complex sea conditions or sensor errors, and improving the stability of the water-hitting and go-around trajectory by reducing the horizontal speed loss and the pitch angle at the time of exiting the water caused by water-hitting.

[0081] Beneficial effects:

[0082] 1. To overcome the risk of damage to conventional aircraft during sea-skimming flight due to water impact, the present invention discloses an approximate optimization method for water-resistant aircraft based on a proxy model. This method employs a water-resistant aircraft configuration with a conventional aircraft spindle at the top and a two-stage gliding surface at the bottom, with the bottom configuration being plane-symmetrical about the plane of the keel line. During high-speed water impact, the bow gliding surface touches the water to reduce the aircraft's wetted area, thereby minimizing the impact overload of the aircraft during water impact. This also reduces the speed loss and pitch angle at water exit, improving the stability of the water-impact go-around trajectory, and ultimately reducing the risk of water impact damage due to complex sea conditions or sensor errors.

[0083] 2. The present invention discloses an approximate optimization method for a water-resistant aircraft based on a proxy model. The proxy model replaces the fluid-solid coupling analysis model of the water-resistant aircraft's high-speed water impact, thereby realizing rapid prediction of the aircraft's kinematic parameters during the water impact process. This can reduce the number of optimization calls to the time-consuming fluid-solid coupling analysis model and improve the efficiency of the water-resistant aircraft configuration optimization.

[0084] 3. The present invention discloses an approximate optimization method for water-resistant aircraft based on a proxy model, which improves the global convergence of optimization through global exploration and improves the optimization convergence speed through local search, has good optimization benefits, and the optimization parameters of the water-resistant aircraft can be suitable for application in various sea-skimming flight conditions to reduce the load of aircraft hitting water. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 This is a schematic diagram of the overall layout of the water-resistant aircraft;

[0086] Figure 2 This is a schematic diagram of the geometric modeling of the water-resistant aircraft, where: Figure 2 (a) is an isometric view of the water-resistant aircraft. Figure 2 (b) is the front view of the water-resistant aircraft. Figure 2 (c) is a right side view of the water-resistant aircraft;

[0087] Figure 3 This is a schematic diagram of the water-hitting working condition of the water-resistance aircraft;

[0088] Figure 4 Flowchart of the agent-assisted differential evolution algorithm;

[0089] Figure 5 This is a comparison diagram of the water-resistant configuration before and after optimization, where Figure 5 (a) is the front view of the configuration comparison, Figure 5 (b) is the right view for configuration comparison;

[0090] Figure 6 Comparison of water striking kinematic parameters of aircraft with different layouts, among which: Figure 6 (a) is the overload-time curve, Figure 6 (b) is the speed-time curve, Figure 6 (c) is the pitch angle-time curve, Figure 6 (d) is the height-time curve;

[0091] Figure 7 Comparison of stress cloud diagrams of water-hitting structures of aircraft with different layouts, among which: Figure 7 (a) is the stress cloud diagram of the conventional configuration, Figure 7 (b) is the stress cloud diagram of the initial configuration of water resistance, Figure 7 (c) is the stress cloud diagram of the optimized anti-water configuration. Figure 7 (d) is the stress cloud diagram scale. DETAILED DESCRIPTION

[0092] In order to better illustrate the purpose and advantages of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments.

[0093] like Figure 4 As shown, this embodiment discloses an approximate optimization method for a water-resistant aircraft based on a proxy model, and the specific implementation steps are as follows:

[0094] Step A: Determine the operating conditions, shape, and load conditions of the water-resistant aircraft.

[0095] Step A is implemented as follows:

[0096] Step A-1: Determine the shape of the water-resistant aircraft. To ensure that the aircraft has sufficient lift when flying over the sea and to reduce the drag when hitting the water, a variable swept wing scheme is adopted with a wing chord length L ch =0.40m and extension length L sp =3.40m is determined based on the lift requirement under the conditions of flight speed V = 240m / s and flight altitude h = 2.50m.

[0097] Step A-2: Determine the internal load and equipment parameters of the water-resistant aircraft. To balance the resistance of the aircraft during sea-skimming flight, a solid propulsion solution is adopted. The propellant, payload, servo, sensor, power supply, and seeker are installed inside the aircraft from the tail to the nose. To ensure the internal volume requirements of each section of the aircraft, a minimum threshold value R for the bow radius is set. bow,min =0.15m, minimum threshold of tail radius R rear,min =0.25m, maximum threshold of tail radius R rear,max =0.30m.

[0098] Step B: Combining the structural characteristics of conventional aircraft and water planing boats, a water-resistant aircraft configuration is constructed. This configuration consists of a conventional aircraft rotating body at the top and a two-stage planing surface at the bottom, with the bottom configuration being plane-symmetrical about the plane of the keel line. During high-speed water impact, the bow planing surface touches the water to reduce the aircraft's wetted area, thereby minimizing the impact overload of the aircraft's water impact. This also reduces the water impact speed loss and the pitch angle out of the water, thereby improving the stability of the water impact and go-around trajectory. The water-resistant aircraft configuration achieves a unique geometric representation through 13 control points, thereby constructing a geometric parameterized model of the water-resistant aircraft. The spatial positions of the 13 control points are determined by the following parameters: the ratio of bow length to total length, the ratio of front length to total length, the ratio of middle length to total length, the ratio of maximum width to total length, the ratio of bottom depth to total length, bow inclination angle, front inclination angle, the ratio of bow planing surface width to maximum width, the ratio of front planing surface width to maximum width, the ratio of middle planing surface width to maximum width, bow planing surface inclination angle, front planing surface inclination angle, middle planing surface inclination angle, the ratio of bow width to maximum width, and the ratio of front width to maximum width.

[0099] Step B is implemented as follows:

[0100] Step B-1: Construct a water-resistant aircraft configuration, with the top portion being a conventional aircraft rotational body and the bottom portion employing a two-stage gliding surface configuration. The bottom portion is plane-symmetrical about the plane of the keel line. This water-resistant aircraft configuration is uniquely characterized by its geometric shape using 13 control points, thereby constructing a parameterized geometric model of the water-resistant aircraft.

[0101] Step B-2: Take control point P4 as the origin of the geometric shape coordinates, then x P4 =y P4 =z P4 = 0. The coordinate system is defined as follows: the positive direction of the x-axis is pointing toward the aircraft head, the positive direction of the z-axis is vertically upward, and the y-axis is perpendicular to the xP4z plane. The position that satisfies the right-hand rule is the positive direction of the y-axis.

[0102] Step B-3: According to the definition of the coordinate system, the y-axis coordinates of points P0 to P4 on the keel line P0P1P2P3P4 are all 0, so y P0 =y P1 =y P2 =y P3 =y P4 = 0. The x-axis coordinate x of point P0 P0 , z-axis coordinate z P0 Calculated according to formula (21).

[0103]

[0104] Where, L = 5.33m is the total length of the aircraft; H is the bottom profile depth of the aircraft; α H It is the ratio of bottom profile depth to total length.

[0105] Step B-4: x-axis coordinate x of point P1 P1 , z-axis coordinate z P1 Calculated by formula (22).

[0106]

[0107] Where, L b is the bow length; α Lb is the ratio of bow length to total length; is the bow inclination angle.

[0108] According to formula (23), the x-axis coordinate x of point P2 is obtained P2 , z-axis coordinate z P2 .

[0109]

[0110] Where, L f is the front length; α Lf is the ratio of the front length to the total length; is the front inclination angle.

[0111] The z-axis coordinate of point P3 P3 is 0, and its x-axis coordinate x P3 It can be calculated by formula (24).

[0112] x P3 =x P2 -L m =(1-α Lb -α Lf -α Lm )×L (24)

[0113] Where, L m is the middle length; α Lm Points P0 to P3 are connected by a quartic spline curve, which is tangent to the straight line P3P4 at point P3. The spline curve P0P1P2P3 and the straight line P3P4 form the keel line P0P1P2P3P4.

[0114] Step B-5: Point P6, Point P8, Point P 10 , click P 12 The z-axis coordinates of P0 , as shown in formula (25), the z-axis coordinates are expressed as z P6 、z P8 、z P10 、zP12 .

[0115] z P6 =z P8 =z P10 =z P12 =z P0 =α H ·L (25)

[0116] Point P6, Point P8, Point P 10 , click P 12 The y-axis coordinates of are calculated according to formula (26) to formula (28), and the y-axis coordinates are expressed as y P6 、y P8 、y P10 、y P12 .

[0117]

[0118] Where, L wb , L wf With L wm are the widths of the bow, front and middle respectively; γ Wb with γ Wf are the ratios of bow width, front width and maximum width respectively; W is the maximum width; α W is the ratio of maximum width to total length.

[0119] Step B-6: y-axis coordinate y of point P5 P5 and the z-axis coordinate z P5 It can be calculated according to formula (29)

[0120]

[0121] Where, L sb is the bow planing surface width; η sb is the ratio of bow planing surface width to maximum width; θ sb is the inclination angle of the bow planing surface.

[0122] According to formula (30) and formula (31), points P7, P9, and P 11 The y-axis coordinate and z-axis coordinate of P7 、y P9 、y P11 , the z-axis coordinates are represented as z P7 、z P9 、z P11 .

[0123]

[0124] Where, L sf, L sm are the widths of the front and middle sliding surfaces respectively; η sf ,η sm are the ratios of the front sliding surface width, the middle sliding surface width and the maximum width respectively; θ sf ,θ sm They are the front sliding surface inclination angle and the middle sliding surface inclination angle respectively.

[0125] Step B-7: Point set {P0,P6,P8,P 10} connected by a quadratic spline curve and at point P 10 At the line P 10 P 12 Tangent. The point set {P0, P5, P7, P9} is connected by a spline curve of degree 4 or higher and intersects with the line P9P at point P9. 11 Tangent.

[0126] Formulas (21) to (31) are geometric parameterized models of water-resistant aircraft. The geometric parameterized models of water-resistant aircraft are used to reduce the wetted area of the aircraft by the bow gliding surface touching the water when hitting the water at high speed, thereby reducing the impact overload of the aircraft hitting the water, and at the same time reducing the water-hitting speed loss and the pitch angle out of the water, thereby improving the stability of the water-hitting and go-around trajectory.

[0127] In order to balance accuracy and efficiency, as a preferred method, the point set {P0, P5, P7, P9} is connected by a quartic spline curve.

[0128] Step C: A fluid-structure coupling analysis model for the aircraft hitting the water is established based on the structured Lagrangian-Euler method. By constructing an air-water structured grid, a refined grid is divided near the aircraft hitting the water and at the air-water interface to prevent liquid leakage during the fluid-structure coupling analysis and improve the efficiency of the fluid-structure coupling analysis of the aircraft hitting the water.

[0129] Step C is implemented as follows:

[0130] Step C-1: Based on the constructed geometric parameterized model of the water-resistant aircraft, define the high-speed water-strike condition of the water-resistant aircraft, including the height H of point P4 from the horizontal plane. z =0.10m, aircraft horizontal speed V x =240m / s, aircraft vertical speed V z =9.8m / s.

[0131] Step C-2: Define the air and water domain dimensions, including the water depth L zw =2.0m, air space height L za =1.0m, calculation domain width L y =2.0m, calculation domain length L x =20.0m.

[0132] Step C-3: Calculate the air domain properties using the linear polynomial state equation, as shown in Equation (32).

[0133]

[0134] Where, E a =2.50×10 5 J / m 3 is the initial internal energy per unit volume; V is the relative volume; C j (j=0, 1, ..., 6) are linear polynomial coefficients, where C0=C2=C3=C4=C5=C6=0, and C1=0.142.

[0135] The water area properties are calculated using the Gruneisen equation of state, as shown in Equation (33).

[0136]

[0137] Where, ρ w =1000kg / m 3 is the density of water; C w =1480m / s is the local sound speed; a=3.0 is the first-order volume correction coefficient; γ0=0.5 is the Gruneisen state equation constant; S i (i=1, 2, 3) are the Gruneisen state equation coefficients, where S1=2.56, S2=-1.986, and S3=0.227.

[0138] Step C-4: Define the aircraft as a Lagrangian object and calculate the motion parameters of the air domain-water domain-aircraft under high-speed water-striking conditions, including: aircraft overload, aircraft speed, aircraft pitch angle, and aircraft displacement.

[0139] Step D: Constructing a watertight aircraft optimization problem model, using aircraft configuration parameters as optimization variables, and minimizing the maximum impact overload of the watertight aircraft when impacting the water while satisfying the watertight aircraft constraints. The watertight aircraft constraints include horizontal velocity loss, pitch angle at water exit, cross-sectional radius of each part, and vertical velocity at water exit.

[0140]

[0141] Where, α Lb is the ratio of bow length to total length; α Lf is the ratio of the front length to the total length; α Lm is the ratio of the middle length to the total length; α W is the ratio of maximum width to total length; α His the ratio of bottom profile depth to total length; is the bow inclination angle; is the front inclination angle; η sb is the ratio of the bow planing surface width to the maximum width; η sf is the ratio of the front sliding surface width to the maximum width; η sm is the ratio of the middle sliding surface width to the maximum width; θ sb is the inclination angle of the bow planing surface; θ sf is the inclination angle of the front sliding surface; θ sm is the inclination angle of the middle sliding surface; γ Wb is the ratio of bow width to maximum width; γ Wf is the ratio of the front width to the maximum width. The above 15 aircraft configuration parameters are the design variables X of the optimization problem. max ΔV is the maximum impact overload of the aircraft during the water impact process. This parameter is the optimization target of the optimization problem. x is the horizontal speed loss of the aircraft; V is the pitch angle of the aircraft out of water; z,end R is the vertical speed of the aircraft out of water; bow is the cross-sectional radius of the bow of the aircraft; R rear is the radius of the tail section of the aircraft. The above five kinematic parameters are the constraints of the optimization problem. LB With X UB are the lower and upper bounds of the design variables, respectively.

[0142] Step E: A surrogate model-assisted differential evolution algorithm is used to optimize the watertight vehicle optimization problem. The constraints and objective functions in the optimization problem are determined by steps B and C. With the optimization objective of minimizing the maximum water impact overload, the geometric parameters of the watertight vehicle are optimized. Under the constraints of velocity loss, pitch angle at water exit, cross-sectional radius of each component, and vertical velocity at water exit, the optimal configuration parameters of the watertight vehicle are obtained. This method consists of two main phases: global exploration and local search. In the global exploration phase, the predicted variance of the watertight vehicle's water impact overload, provided by the KRG surrogate model, is used to construct a feasible criterion based on constraint improvement and optimal fitness, thereby guiding convergence to the optimal configuration solution. In the local search phase, to effectively balance the robustness, approximation accuracy, and construction efficiency of the surrogate model, a RBF algorithm is used to construct the local optimization problem for the watertight vehicle and solve it in conjunction with a sequential quadratic programming method, thereby improving the optimization convergence speed.

[0143] Step E is implemented as follows:

[0144] Step E-1: Determine the design space, objective function, constraint function, and algorithm parameters for the configuration optimization problem of water-resistant aircraft, including the population size N. P, scaling factor F, crossover probability C R and the maximum number of model calls The Latin hypersquare experimental design method based on Maximin is used to generate N in the initial design space. P Initial sample points are obtained, and the corresponding true targets and constraint function values are calculated, and the sample database of the anti-water vehicle configuration is updated.

[0145] Step E-2: Sort the current sample database according to the feasible criteria and select the top N P The configuration samples of water-resistant aircraft are used as the current parent population. A variety of mutation operators and crossover operators are used to generate the test population Q = {Q R1 ∪Q R2 ∪Q CtoR ∪Q CtoB}.

[0146] Step E-3: Use all samples in the sample database to construct the Kriging proxy model of the water hammer process fluid-solid coupling analysis model and calculate the predicted value of the objective function and the predicted values of each constraint function In addition, the prediction variance s of each function of the population individual is calculated according to formula (35): 2 (x).

[0147]

[0148] Where R is the correlation matrix; R(·,·) is the correlation coefficient; x(i), i=1,2,...,N KRG is the i-th sample in the sample database; is the variance of the Gaussian distribution; I is the identity matrix. New exploration samples of water-resistant aircraft configurations are selected from the experimental population based on the improved feasibility criterion. The true objective function and constraint function values of the new exploration samples are calculated and added to the sample database of water-resistant aircraft configurations.

[0149] Step E-4: Randomly select the initial point of the sequential quadratic programming method from the current population. Select N points that are closer to the initial point from the sample database based on the Euclidean distance. RBF The local RBF proxy model corresponding to the objective function and constraint function of the anti-water aircraft configuration optimization problem is constructed for each sample point. The scale of the sample points for constructing RBF is related to the dimension of the optimization problem, and the calculation formula is as follows

[0150]

[0151] Where n v is the dimension of the optimization problem. RBFWhen the sample size is larger than that of the existing database, all samples in the database are used to construct the RBF proxy model. The sequential quadratic programming method is used to solve the sub-optimization problem of the anti-waterproof aircraft configuration to obtain new search sample points, calculate the corresponding true objective function and constraint function values, and add them to the anti-waterproof aircraft configuration sample database.

[0152] In order to balance accuracy and efficiency, the mutation operator selects Rand / 1, Rand / 2, Current-to-rand / 1, and Current-to-best / 1 strategies as the preferred choice.

[0153] Step E-5: Determine whether the maximum number of model calls has been reached. If not, return to step E-2 to continue optimization; otherwise, output the optimized parameters of the water-resistant aircraft configuration.

[0154] The method further includes step F: manufacturing a water-resistant aircraft according to the optimized configuration parameters of the water-resistant aircraft obtained in step E, minimizing the impact overload of the aircraft during high-speed water-hitting by configuring the bottom of the planing surface of the planing boat, reducing the risk of water-hitting damage due to complex sea conditions or sensor errors, and improving the stability of the water-hitting and go-around trajectory by reducing the horizontal speed loss and the pitch angle at the time of exiting the water caused by water-hitting.

[0155] In order to better demonstrate the effectiveness and engineering practicality of the present invention, the present invention will be further explained below by taking the optimization problem of a water-resistant aircraft as an example with reference to the accompanying drawings and tables.

[0156] In this case, the range of the design variables of the optimization problem is: Lb ∈[0.08,0.12],α Lf ∈[0.30,0.40],α Lm ∈[0.30,0.40],α W ∈[0.09,0.15],α H ∈[0.04,0.08], η sb ∈[0.08,0.16],η sf ∈[0.24,0.28],η sm ∈[0.30,0.38],θ sb ∈[28.00°,32.00°],θ sf ∈[20.00°,24.00°],θ sm ∈[14.00°,18.00°],γ Wb ∈[0.40,0.60],γ Wf ∈[0.80,1.00]. Comparison of water-resistant configuration before and after optimization is shown in Figure 5 ,in, Figure 5 (a) is the front view of the configuration comparison, Figure 5 (b) is the right view of the configuration comparison. The comparison of the water-striking kinematic parameters of each layout aircraft is shown in Figure 6 ,in, Figure 6 (a) is the overload-time curve, Figure 6 (b) is the speed-time curve, Figure 6 (c) is the pitch angle-time curve, Figure 6 (d) is the height-time curve. Comparison of stress cloud diagrams of water-hitting structures of aircraft of different layouts is shown in Figure 7 ,in, Figure 7 (a) is the stress cloud diagram of the conventional configuration, Figure 7 (b) is the stress cloud diagram of the initial configuration of water resistance, Figure 7 (c) is the stress cloud diagram of the optimized anti-water configuration. Figure 7 (d) is the stress cloud diagram. The comparison of design variables of the anti-water aircraft scheme before and after optimization is shown in Table 1, and the objective function and constraint conditions are shown in Table 2.

[0157] Table 1 Comparison of design variables of water-resistant aircraft before and after optimization

[0158]

[0159] Table 2 Comparison of optimization objectives and constraints of water-resistant aircraft scheme before and after optimization

[0160]

[0161] The above optimization design results show that the present invention can obtain a set of optimized parameters for the configuration of water-resistant aircraft that can meet the material structural strength and effectively reduce the overload of high-speed water impact at a relatively low computing cost, thereby achieving the expected purpose of the invention and verifying the rationality, effectiveness and engineering practicality of the present invention.

[0162] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention, which is used to explain the present invention and is not used to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An approximate optimization method for a water-resistant aircraft based on a proxy model, characterized by: The following steps are included: Step A: Determine the operating conditions, shape, and load conditions of the water-resistant aircraft; Step B: Combining the structural characteristics of conventional aircraft and water planing boats, a water-resistant aircraft configuration is constructed; the top of the configuration is a conventional aircraft rotating body, and the bottom adopts a two-section gliding surface configuration, and the bottom configuration forms a plane-symmetrical configuration with the plane where the keel line is located; when hitting the water at high speed, the bow gliding surface touches the water to reduce the wetted area of the aircraft, thereby reducing the impact overload of the aircraft hitting the water, while reducing the water-hitting speed loss and the pitch angle out of the water, and improving the stability of the water-hitting and go-around trajectory; the water-resistant aircraft configuration achieves a unique geometric shape representation through 13 control points, that is, the water-resistant aircraft is realized. The geometric parameterized model is constructed; the spatial positions of the 13 control points are determined by the following parameters: the ratio of the bow length to the total length, the ratio of the front length to the total length, the ratio of the middle length to the total length, the ratio of the maximum width to the total length, the ratio of the bottom depth to the total length, the bow inclination angle, the front inclination angle, the ratio of the bow planing surface width to the maximum width, the ratio of the front planing surface width to the maximum width, the ratio of the middle planing surface width to the maximum width, the bow planing surface inclination angle, the front planing surface inclination angle, the middle planing surface inclination angle, the ratio of the bow width to the maximum width, and the ratio of the front width to the maximum width; Step C: A fluid-structure interaction analysis model for the aircraft hitting the water is established based on the structured Lagrangian-Euler method. By constructing an air-water structured grid and dividing the grid into finer areas near the aircraft hitting the water and at the air-water interface, this prevents liquid leakage during the fluid-structure interaction analysis and improves the efficiency of the fluid-structure interaction analysis. Step D: Constructing an optimization problem model for a water-resistant aircraft, using aircraft configuration parameters as optimization variables, and minimizing the maximum impact overload of the water-resistant aircraft when striking water while satisfying the constraints of the water-resistant aircraft; the constraints of the water-resistant aircraft include horizontal velocity loss, pitch angle out of water, cross-sectional radius of each part, and vertical velocity out of water; Step E: A surrogate model-assisted differential evolution algorithm is used to optimize the optimization problem of the water-resistant aircraft. The constraint function and objective function in the optimization problem are determined by steps B and C. Taking the minimum maximum impact overload of water impact as the optimization goal, the geometric parameters of the water-resistant aircraft are optimized. Under the constraints of the speed loss, water exit pitch angle, cross-sectional radius of each part, and vertical speed of water exit, the optimized configuration parameters of the water-resistant aircraft are obtained. The optimization process is mainly divided into two stages: global exploration and local search. In the global exploration stage, the water impact overload prediction variance of the water-resistant aircraft provided by the KRG surrogate model is used to construct a feasible criterion based on constraint improvement and optimal fitness, thereby guiding the convergence near the optimal configuration solution. In the local search stage, in order to effectively compromise the robustness, approximation accuracy and construction efficiency of the surrogate model, the RBF method is used to construct the local optimization problem of the anti-water aircraft and the sequential quadratic programming method is used to solve it, thereby improving the optimization convergence speed.

2. The method for approximate optimization of a water-resistant aircraft based on a proxy model according to claim 1, wherein: The method further includes step F, manufacturing a water-resistant aircraft according to the optimized configuration parameters of the water-resistant aircraft obtained in step E, minimizing the impact overload of the aircraft during high-speed water-hitting by configuring the bottom of the planing surface of the planing boat, reducing the risk of water-hitting damage due to complex sea conditions or sensor errors, and improving the stability of the water-hitting and go-around trajectory by reducing the horizontal speed loss and the pitch angle at the time of exiting the water caused by water-hitting.

3. The method for approximate optimization of a water-resistant aircraft based on a proxy model according to claim 1 or 2, characterized in that: Step A is implemented as follows: Step A-1: Determine the shape of the water-resistant aircraft. To ensure that the aircraft has sufficient lift when flying over the sea and reduce resistance when hitting the water, a variable swept wing with a chord length of L is used. ch With Exhibition Director L sp Determined according to the lift requirements under the conditions of flight speed V and flight altitude h; Step A-2: Determine the internal load of the anti-water aircraft; in order to balance the resistance of the aircraft during sea-skimming flight, solid propulsion is used; the propellant, payload, steering gear, sensor, power supply assembly, and seeker are installed inside the aircraft from the tail to the nose, and the minimum threshold value of the bow radius R is set. bow,min , the minimum threshold of tail radius R rear,min and the maximum tail radius threshold R rear,max , to ensure the internal volume requirements of each section of the aircraft.

4. The method for approximate optimization of a water-resistant aircraft based on a proxy model according to claim 3, wherein: Step B is implemented as follows: Step B-1: Construct a water-resistant aircraft configuration, wherein the top portion is a conventional aircraft rotational body, the bottom portion adopts a two-stage gliding surface configuration, and the bottom portion is plane-symmetrical about the plane of the keel line. The water-resistant aircraft configuration is uniquely characterized by its geometric shape through 13 control points, thereby constructing a geometric parameterized model of the water-resistant aircraft. Step B-2: Take control point P4 as the origin of the geometric shape coordinates, then x P4 =y P4 =z P4 = 0; the coordinate system is defined as: the x-axis is pointing towards the aircraft head, the z-axis is vertically upward, and the y-axis is perpendicular to the xP4z plane. The position that satisfies the right-hand rule is the y-axis positive direction; Step B-3: According to the coordinate system definition, the y-axis coordinates of points P0 to P4 on the keel line P0P1P2P3P4 are all 0, so y P0 =y P1 =y P2 =y P3 =y P4 =0; the x-axis coordinate x of point P0 P0 , z-axis coordinate z P0 Calculated according to formula (5); Where, L is the total length of the aircraft; H is the bottom profile depth of the aircraft; α H is the ratio of bottom profile depth to total length; Step B-4: x-axis coordinate x of point P1 P1 , z-axis coordinate z P1 Calculated by formula (6); Where, L b is the bow length; α Lb is the ratio of bow length to total length; is the bow inclination angle; According to formula (7), the x-axis coordinate x of point P2 is obtained P2 , z-axis coordinate z P2 ; Where, L f is the front length; α Lf is the ratio of the front length to the total length; is the front inclination angle; The z-axis coordinate of point P3 P3 is 0, and its x-axis coordinate x P3 Calculated by formula (8); Where, L m is the middle length; α Lm is the ratio of the middle length to the total length; points P0 to P3 are connected by a quartic spline curve, and are tangent to the straight line P3P4 at point P3. The spline curve P0P1P2P3 and the straight line P3P4 form the keel line P0P1P2P3P4; Step B-5: Point P6, Point P8, Point P 10 , click P 12 The z-axis coordinates of P0 , as shown in formula (9), the z-axis coordinates are expressed as z P6 、z P8 、z P10 、z P12 ; With P6 =z P8 =z P10 =z P12 =z P0 =α H L (9) Point P6, Point P8, Point P 10 , click P 12 The y-axis coordinates of are calculated according to formula (10) to formula (12), and the y-axis coordinates are expressed as y P6 、y P8 、y P10 、y P12 ; Where, L wb , L wf With L wm are the widths of the bow, front and middle respectively; γ Wb with γ Wf are the ratios of bow width, front width and maximum width respectively; W is the maximum width; α W is the ratio of maximum width to total length; Step B-6: y-axis coordinate y of point P5 P5 and the z-axis coordinate z P5 According to formula (13), we can get Where, L sb is the bow planing surface width; η sb is the ratio of bow planing surface width to maximum width; θ sb is the bow planing surface inclination angle; According to formula (14) and formula (15), we can get point P7, point P9, point P 11 The y-axis coordinate and z-axis coordinate of P7 、y P9 、y P11 , the z-axis coordinates are represented as z P7 、z P9 、z P11 ; Where, L sf , L sm are the widths of the front and middle sliding surfaces respectively; η sf ,η sm are the ratios of the front sliding surface width, the middle sliding surface width and the maximum width respectively; θ sf ,θ sm They are the front sliding surface inclination angle and the middle sliding surface inclination angle respectively; Step B-7: Point set {P0,P6,P8,P 10 } connected by a quadratic spline curve and at point P 10 At the line P 10 P 12 Tangent; the point set {P0, P5, P7, P9} is connected by a spline curve of degree 4 or higher, and intersects the line P9P at point P9 11 tangent; Formulas (1) to (11) are geometric parameterized models of water-resistant aircraft. The geometric parameterized models of water-resistant aircraft are used to reduce the wetted area of the aircraft by the bow gliding surface touching the water when hitting the water at high speed, thereby reducing the impact overload of the aircraft hitting the water, and at the same time reducing the water-hitting speed loss and the pitch angle out of the water, thereby improving the stability of the water-hitting and go-around trajectory.

5. The method for approximate optimization of a water-resistant aircraft based on a proxy model according to claim 4, characterized in that: Step C is implemented as follows: Step C-1: Based on the constructed geometric parameterized model of the water-resistant aircraft, define the high-speed water-strike condition of the water-resistant aircraft, including the height H of point P4 from the horizontal plane. z , aircraft horizontal speed V x 、Aircraft vertical speed V z ; Step C-2: Define the air and water domain dimensions, including the water depth L zw , air space height L za , computational domain width L y , calculation domain length L x ; Step C-3: Calculate the air domain properties using the linear polynomial state equation, as shown in Equation (16); Where, E a is the initial internal energy per unit volume; V is the relative volume; C j (j=0,1,...,6) are the coefficients of the linear polynomial; The water area properties are calculated using the Gruneisen equation of state, as shown in Equation (17); Where, ρ w is the density of water; C w is the local sound velocity; a is the first-order volume correction coefficient; γ0 is the Gruneisen state equation constant; S i (i=1,2,3) is the coefficient of Gruneisen equation of state; Step C-4: Define the aircraft as a Lagrangian object and calculate the motion parameters of the air domain-water domain-aircraft under high-speed water-striking conditions, including: aircraft overload, aircraft speed, aircraft pitch angle, and aircraft displacement.

6. The method for approximate optimization of a water-resistant aircraft based on a proxy model according to claim 5, characterized in that: Step D constructs the optimization problem model of water-resistant aircraft as follows: Where, α Lb is the ratio of bow length to total length; α Lf is the ratio of the front length to the total length; α Lm is the ratio of the middle length to the total length; α W is the ratio of maximum width to total length; α H is the ratio of bottom profile depth to total length; is the bow inclination angle; is the front inclination angle; η sb is the ratio of the bow planing surface width to the maximum width; η sf is the ratio of the front sliding surface width to the maximum width; η sm is the ratio of the middle sliding surface width to the maximum width; θ sb is the inclination angle of the bow planing surface; θ sf is the inclination angle of the front sliding surface; θ sm is the inclination angle of the middle sliding surface; γ Wb is the ratio of bow width to maximum width; γ Wf is the ratio of the front width to the maximum width. The above 15 aircraft configuration parameters are the design variables X of the optimization problem; n max is the maximum impact overload of the aircraft during water impact, and this parameter is the optimization target of the optimization problem; ΔV x is the horizontal speed loss of the aircraft; θ end V is the pitch angle of the aircraft out of water; z,end R is the vertical speed of the aircraft out of water; bow is the cross-sectional radius of the bow of the aircraft; R rear is the radius of the tail section of the aircraft. The above five kinematic parameters are the constraints of the optimization problem; Γ vx , Γ θ , Γ vz They are the horizontal speed loss threshold, the water exit pitch angle threshold, and the terminal vertical speed threshold; X LB With X UB are the lower and upper bounds of the design variables, respectively.

7. The method for approximate optimization of a water-resistant aircraft based on a proxy model according to claim 6, characterized in that: Step E is implemented as follows: Step E-1: Determine the design space, objective function, constraint function, and algorithm parameters for the configuration optimization problem of water-resistant aircraft, including the population size N. P , scaling factor F, crossover probability C R and the maximum number of model calls The Latin hypersquare experimental design method based on Maximin is used to generate N in the initial design space. P Initial sample points are obtained, and the corresponding true targets and constraint function values are calculated, and the sample database of the anti-water vehicle configuration is updated; Step E-2: Sort the current sample database according to the feasible criteria and select the top N P The configuration samples of water-resistant aircraft are used as the current parent population; a variety of mutation operators and crossover operators are used to generate the test population Q = {Q R1 ∪Q R2 ∪Q CtoR ∪Q CtoB }; Step E-3: Use all samples in the sample database to construct the Kriging proxy model of the water hammer process fluid-solid coupling analysis model and calculate the predicted value of the objective function and the predicted values of each constraint function In addition, the prediction variance s of each function of the population individual is calculated according to formula (19): 2 (x); Where R is the correlation matrix; R(·,·) is the correlation coefficient; x(i), i=1,2,...,N KRG is the i-th sample in the sample database; is the variance of the Gaussian distribution; I is the unit matrix; new exploration samples of the anti-water aircraft configuration are selected from the test population according to the improved feasibility criterion; the true objective function and constraint function values of the new exploration samples are calculated and added to the sample database of the anti-water aircraft configuration; Step E-4: Randomly select the initial point of the sequential quadratic programming method from the current population; select N points that are closer to the initial point from the sample database based on the Euclidean distance. RBF The local RBF proxy model corresponding to the objective function and constraint function of the anti-water aircraft configuration optimization problem is constructed for each sample point; the scale of the sample points for constructing RBF is related to the dimension of the optimization problem, and the calculation formula is as follows Where n v is the dimension of the optimization problem; when N RBF When the sample size is larger than that of the existing database, all samples in the database are used to construct the RBF proxy model. The sequential quadratic programming method is used to solve the sub-optimization problem of the anti-waterproof aircraft configuration to obtain new search sample points, and the corresponding true objective function and constraint function values are calculated and added to the anti-waterproof aircraft configuration sample database. Step E-5: Determine whether the maximum number of model calls has been reached. If not, return to step E-2 to continue optimization; otherwise, output the optimized parameters of the water-resistant aircraft configuration.

8. The proxy model-based approximate optimization method for a water-resistant aircraft according to claim 7, characterized in that: The point set {P0, P5, P7, P9} is connected by a quartic spline curve.

9. The method for approximate optimization of a water-resistant aircraft based on a proxy model according to claim 8, characterized in that: The mutation operator selects Rand / 1, Rand / 2, Current-to-rand / 1, and Current-to-best / 1 strategies.

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