A method for underwater glider parameter identification based on support vector machine

Abstract

The present invention relates to a method for identifying underwater glider parameters based on a support vector machine. A linear kernel function is used to obtain a model with low complexity. The system parameters can be easily derived from the trained model, and the solved parameters are global optimal solutions. The method has strong generalization capabilities, avoids local extreme value phenomena, and is more suitable for engineering practice. Furthermore, compared with neural networks, the method achieves better identification results with relatively small amounts of data and computational complexity, with an identification relative error of less than 0.023. Compared with other intelligent identification methods, such as neural networks, the linear kernel-based support vector machine parameter identification method has a relatively simple model structure, is easy to derive system parameters from the trained model, and the solved parameters are global optimal solutions. The method has strong generalization capabilities, avoids local extreme value phenomena, and is more suitable for engineering practice.

Description

Technical Field

[0001] The invention belongs to a parameter identification method for an underwater glider, and relates to a parameter identification method for an underwater glider based on a support vector machine. Background Art

[0002] Underwater gliders are effective tools for replacing human operators in underwater resource exploration, environmental monitoring, safety monitoring, and search and rescue operations. To effectively accomplish these tasks, precise control of underwater gliders is essential. Currently, most underwater glider controller designs employ a six-degree-of-freedom equation based on Newton's laws and Lagrange's equations. Because the interaction between the underwater glider and the fluid is difficult to measure directly with sensors, the model incorporates numerous hydrodynamic force / torque terms expressed as hydrodynamic coefficients. These coefficients depend on the glider's shape, motion, and environmental factors, increasing model uncertainty. Therefore, determining the hydrodynamic coefficients is a primary and crucial issue in developing underwater glider control models.

[0003] In engineering applications, the main methods for obtaining hydrodynamic coefficients include numerical calculation, pool plane mechanism testing, and parameter identification. Numerical calculation, typically performed using computational fluid dynamics (CFD) software, is computationally intensive, and the meshing method and boundary conditions affect the results. In pool plane mechanism experiments, sensor and operational errors can lead to unreliable results and lengthy calculation cycles. Parameter identification, a method that has been widely used in recent years for determining hydrodynamic coefficients, offers low cost, better reflection of fluid interactions in actual motion, and, when combined with intelligent algorithms, enhances the adaptability of the results to the environment.

[0004] Support Vector Regression (SVR) is an emerging method for parameter identification. Compared to neural networks, SVRs have more rigorous mathematical theoretical support, are highly interpretable, and do not rely on statistical methods. They simplify common classification and regression problems and are primarily used for small sample sizes, demonstrating excellent performance in solving these problems. SVRs are designed for finite samples, do not require initial parameter estimates, and have good generalization performance. Their solution is a convex function with global optimality. For identifying the hydrodynamic coefficients of underwater gliders, the ε-SVR method is often used, with a linear kernel function as the kernel. Summary of the Invention

[0005] Technical problems to be solved

[0006] In order to avoid the shortcomings of the prior art, the present invention proposes a method for identifying underwater glider parameters based on support vector machines.

[0007] Technical Solution

[0008] A method for identifying underwater glider parameters based on support vector machine is characterized by the following steps:

[0009] Step 1: Given a 10° / 10° differential rudder signal input to the underwater glider system, causing the underwater glider to perform a zigzag motion in the transverse plane, obtain the output data of the underwater glider under the 10° / 10° differential rudder signal, including the input underwater glider state data x and the underwater glider force or torque y;

[0010] Step 2: According to the underwater glider's Z-shaped motion, the underwater glider's dynamic equation is y=w T x+b, where the bias constant b is zero, is changed to y=w T x, w are the hydrodynamic parameters that need to be identified;

[0011] Step 3: Determine the kernel function and hyperparameter values of support vector machine regression;

[0012] Determine the support vector machine regression algorithm as ε-SVR, and select the linear kernel function k(x i ,x j )= <x i ,x j >, hyperparameter ε = 0.1, loss function weight C = 1.414;

[0013] The hydrodynamic parameters are obtained by the support vector machine regression algorithm:

[0014] α i and α i * is the model constant;

[0015] Step 4: Collect n data output from step 1 and calculate α using the sequence minimum optimization method i 、 Given x i calculate Get the hydrodynamic parameters w of the underwater glider.

[0016] The lateral velocity v of the underwater glider dynamic equation is z The kinetic equation is:

[0017]

[0018] in:

[0019]

[0020] C z (v)=m[v y wx -v x w y +x c w z w x +y c w y w z -z c (w x 2 +w y 2 )]

[0021]

[0022] Where m is the mass of the underwater glider, G is the gravity of the underwater glider, S is the cross-sectional area of the underwater glider, L is the length of the underwater glider, and ρ is the density of water. x , v y , v z is the linear velocity of the underwater glider in three directions, w x , w y , w z is the angular velocity of the underwater glider in three directions; ψ is the heading angle, θ is the pitch angle, is the roll angle, α is the attack angle, β is the sideslip angle, are the linear acceleration and angular acceleration of the glider, and v is the resultant velocity of the three linear velocities.

[0023] The dynamic equation of the underwater glider is the rolling angular velocity w x The kinetic equation is:

[0024]

[0025] in:

[0026]

[0027] C K (v)=[my c (v y w x -v x w y )+mz c (v z w x -v x w z )+(J zz -J yy )w y w z ]

[0028]

[0029] Where m is the mass of the underwater glider, G is the gravity of the underwater glider, S is the cross-sectional area of the underwater glider, L is the length of the underwater glider, and ρ is the density of water. x , v y , v z is the linear velocity of the underwater glider in three directions, w x , w y , w z is the angular velocity of the underwater glider in three directions; ψ is the heading angle, θ is the pitch angle, is the roll angle, α is the attack angle, β is the sideslip angle, are the linear acceleration and angular acceleration of the glider, and v is the resultant velocity of the three linear velocities.

[0030] The underwater glider dynamic equation is the heading angular velocity w y The kinetic equation is:

[0031]

[0032] in:

[0033]

[0034] C M (v)=[mz c (v z w y -v y w z )+mx c (v x w y -v y w z )+(J xx -J zz )w z w x ]

[0035]

[0036] Where m is the mass of the underwater glider, G is the gravity of the underwater glider, S is the cross-sectional area of the underwater glider, L is the length of the underwater glider, and ρ is the density of water. x , v y , v z is the linear velocity of the underwater glider in three directions, w x , w y , w z is the angular velocity of the underwater glider in three directions; ψ is the heading angle, θ is the pitch angle, is the roll angle, α is the attack angle, β is the sideslip angle, are the linear acceleration and angular acceleration of the glider, and v is the resultant velocity of the three linear velocities.

[0037] The combined velocity v of the three linear velocities is expressed as follows:

[0038]

[0039]

[0040]

[0041] λ 33 ,λ 35 ,λ 44 ,λ 55 is the inertial hydrodynamic coefficient of the glider; the buoyancy center of the glider is selected as the coordinate origin, x c ,y c , z c is the distance from the center of mass to the center of buoyancy of the glider; J xx , J yy , J zz is the moment of inertia; C z β , m x β , m y β , is the hydrodynamic coefficient, which is the parameter to be identified.

[0042] The number n in step 4 is 200.

[0043] Beneficial effects

[0044] The present invention proposes a method for underwater glider parameter identification based on a support vector machine. The method adopts a linear kernel function to obtain a model with low complexity. The system parameters can be easily derived from the trained model, and the solved parameters are the global optimal solution. The method has strong generalization ability, avoids local extreme value phenomena, and is more suitable for engineering practice. Secondly, compared with neural networks, better identification effects are obtained with relatively small amounts of data and computation, and the relative identification error is less than 0.023.

[0045] Compared with the prior art, the above technical solution conceived by the present invention has the following technical advantages:

[0046] 1. This invention proposes for the first time the use of support vector machine method to solve the problem of underwater glider parameter identification;

[0047] 2. Compared with other intelligent identification methods, such as neural networks, the linear kernel-based support vector machine parameter identification method has a relatively simple model structure. It is easy to derive system parameters from the trained model, and the solved parameters are global optimal solutions. It has strong generalization ability, avoids local extreme value phenomena, and is more suitable for engineering practice.

[0048] 3. Compared with neural networks, better recognition results are achieved with relatively less data and computational complexity, and the relative error is less than 0.023. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 :SVR identification parameter horizontal plane trajectory DETAILED DESCRIPTION

[0050] The present invention will now be further described with reference to the embodiments and accompanying drawings:

[0051] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with tables and simulation results. It should be understood that the specific examples described herein are only used to explain the present invention and are not intended to limit the present invention.

[0052] In step 1, data showing good maneuverability of the underwater glider is obtained, and the system inputs a 10° / 10° differential rudder angle signal to make the underwater glider perform a zigzag motion in the horizontal plane.

[0053] In step 2, the parameter identification method based on support vector machine regression requires that the input and output data satisfy the following relationship:

[0054] y=w T x+b (1)

[0055] Among them, w is the parameter, x is the input data, is the unknown function, b is the bias constant, and y is the output data.

[0056] Considering that the horizontal plane motion mode is fully excited when the glider makes a Z-shaped motion, only the horizontal plane v is identified. z , w x , w y In order to simplify the identification process, the inertial hydrodynamic coefficient is not involved in the parameter identification, and the dynamic equation is rewritten as y = w T x form.

[0057] 1) Underwater glider lateral speed v z The kinetic equation is:

[0058]

[0059] in:

[0060]

[0061] C z (v)=m[v y w x -v x w y +x c w z w x +y c w y w z -z c (w x 2 +w y 2 )]

[0062]

[0063] 2) Underwater glider rolling angular velocity w x The kinetic equation is:

[0064]

[0065] in:

[0066]

[0067] C K (v)=[my c (v y w x -v x w y )+mz c (v z w x -v x w z )+(J zz -J yy )w y w z ]

[0068]

[0069] 3) Underwater glider heading angular velocity w y The kinetic equation is:

[0070]

[0071] in:

[0072]

[0073] C M (v)=[mz c (v z w y -v y w z )+mx c (v x w y -v y w z )+(J xx -J zz )w z w x ]

[0074]

[0075] Where m is the mass of the underwater glider, G is the gravity of the underwater glider, S is the cross-sectional area of the underwater glider, L is the length of the underwater glider, and ρ is the density of water. x , v y , v z is the linear velocity of the underwater glider in three directions, w x , w y , w z is the angular velocity of the underwater glider in three directions; ψ is the heading angle, θ is the pitch angle, is the roll angle, α is the attack angle, β is the sideslip angle, are the linear acceleration and angular acceleration of the glider, and v is the resultant velocity of the three linear velocities. The expression is as follows:

[0076]

[0077]

[0078]

[0079] λ 33 ,λ 35 ,λ 44 ,λ 55 is the inertial hydrodynamic coefficient of the glider; the buoyancy center of the glider is selected as the coordinate origin, x c ,y c , z c is the distance from the center of mass to the center of buoyancy of the glider; J xx , J yy , J zz is the moment of inertia; C z β , m x β , my β , is the hydrodynamic coefficient, which is the parameter to be identified.

[0080] In step 3, the support vector machine regression algorithm is determined to be ε-SVR, and the kernel function is the linear kernel function k(x i ,x j )= <x i ,x j >, hyperparameter ε = 0.1, loss function weight C = 1.414, enter step 4, the support vector machine regression objective function is:

[0081]

[0082] Constraints

[0083] Where w is the parameter to be solved, C is the weight of the loss function, f is the unknown function, x i is the input sample data, y i is the test sample data, ξ i and ξ i * is a slack variable and ε is a hyperparameter.

[0084] Introducing the equation into Lagrange multipliers and transforming it into an unconstrained problem yields the following equation:

[0085] Among them, α i , μ i , is the introduced Lagrange multiplier. The original problem is transformed into:

[0086]

[0087] Minimize L(w,b,ξ,ξ * ), for w,b,ξ,ξ * Taking the partial derivative and setting it to 0 gives:

[0088]

[0089]

[0090] C=α i +u i

[0091] C=α i * +u i *

[0092] α iand α i * The Sequential Minimal Optimization (SMO) method is used to solve the problem, and the linear kernel function is selected to obtain the parameter w:

[0093]

[0094] Combined with the underwater glider model, (8) where w is the hydrodynamic coefficient to be identified, m is the total number of samples in the system, n = 200 in the present invention, α i and α i * is the model constant, is an unknown function, x i Enter sample data for the system.

[0095] In the present invention, a linear kernel function is selected, namely Then we have:

[0096]

[0097] 1) In the present invention, identifying v z Related parameters,

[0098] 2) In the present invention, identification w x Related parameters,

[0099] 3) In the present invention, identification w y Related parameters,

[0100] Identify three times to get the identified hydrodynamic coefficient C z β , m x β , m y β and

[0101] Table 1 SVR identification parameter results

[0102]

Claims

1. A method for underwater glider parameter identification based on support vector machine, characterized in that Here are the steps: Step 1: Given a 10° / 10° differential rudder signal input to the underwater glider system, causing the underwater glider to perform a zigzag motion in the transverse plane, obtain the output data of the underwater glider under the 10° / 10° differential rudder signal, including the input underwater glider state data x and the underwater glider force or torque y; Step 2: According to the underwater glider's Z-shaped motion, the underwater glider's dynamic equation y = w Τ x+b, where the bias constant b is zero, is changed to y=w Τ x, w are the hydrodynamic parameters that need to be identified; Step 3: Determine the kernel function and hyperparameter values of support vector machine regression; Determine the support vector machine regression algorithm as ε-SVR, and select the linear kernel function k(x i ,x j )= <x i ,x j >, hyperparameter ε = 0.1, loss function weight C = 1.414; The hydrodynamic parameters are obtained by the support vector machine regression algorithm: α i and α i * is the model constant; Step 4: Collect n data output from step 1 and calculate α using the sequence minimum optimization method i 、 Given x i calculate Get the hydrodynamic parameters w of the underwater glider; The lateral velocity v of the underwater glider dynamic equation z The kinetic equation is: in: C z (v)=m[v y w x -v x w y +x c w z w x +y c w y w z -z c (w x 2 +w y 2 )] Where m is the mass of the underwater glider, G is the gravity of the underwater glider, S is the cross-sectional area of the underwater glider, L is the length of the underwater glider, and ρ is the density of water; λ 33 ,λ 35 is the inertial hydrodynamic coefficient of the glider, x c 、y c 、z c is the distance from the center of mass to the center of buoyancy of the glider, v x , v y , v z is the linear velocity of the underwater glider in three directions, w x , w y , w z is the angular velocity of the underwater glider in three directions; ψ is the heading angle, θ is the pitch angle, is the roll angle, α is the attack angle, β is the sideslip angle, are the linear acceleration and angular acceleration of the glider, and v is the resultant velocity of the three linear velocities; The rolling angular velocity w of the underwater glider dynamic equation x The kinetic equation is: in: C K (v)=[my c (v y w x -v x w y )+mz c (v z w x -v x w z )+(J zz -J yy )w y w z ] Where m is the mass of the underwater glider, G is the gravity of the underwater glider, S is the cross-sectional area of the underwater glider, L is the length of the underwater glider, and ρ is the density of water; λ 44 is the inertial hydrodynamic coefficient of the glider, x c 、y c 、z c is the distance from the center of mass to the center of buoyancy of the glider, J xx , J yy , J zz is the moment of inertia, v x , v y , v z is the linear velocity of the underwater glider in three directions, w x , w y , w z is the angular velocity of the underwater glider in three directions; ψ is the heading angle, θ is the pitch angle, is the roll angle, α is the attack angle, β is the sideslip angle, is the linear acceleration and angular acceleration of the glider, v is the resultant velocity of the three linear velocities; J xx , J yy , J zz is the moment of inertia; C z β , is the hydrodynamic coefficient, i.e. the parameter to be identified; The heading angular velocity w of the underwater glider dynamic equation y The kinetic equation is: in: C M (v)=[mz c (v z w y -v y w z )+mx c (v x w y -v y w z )+(J xx -J zz )w z w x ] Where m is the mass of the underwater glider, G is the gravity of the underwater glider, S is the cross-sectional area of the underwater glider, L is the length of the underwater glider, and ρ is the density of water; λ 55 ,λ 35 is the inertial hydrodynamic coefficient of the glider, x c 、y c 、z c is the distance from the center of mass to the center of buoyancy of the glider, J xx , J yy , J zz is the moment of inertia, v x , v y , v z is the linear velocity of the underwater glider in three directions, w x , w y , w z is the angular velocity of the underwater glider in three directions; ψ is the heading angle, θ is the pitch angle, is the roll angle, α is the attack angle, β is the sideslip angle, are the linear acceleration and angular acceleration of the glider, and v is the resultant velocity of the three linear velocities.

2. The method for underwater glider parameter identification based on support vector machine according to claim 1, characterized in that: The combined velocity v of the three linear velocities is expressed as follows: λ 33 ,λ 35 ,λ 44 ,λ 55 is the inertial hydrodynamic coefficient of the glider; the buoyancy center of the glider is selected as the coordinate origin, x c ,y c , z c is the distance from the center of mass to the center of buoyancy of the glider.

3. The method for underwater glider parameter identification based on support vector machine according to claim 1, characterized in that: The number n in step 4 is 200.

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