CN116774576A - Underwater vehicle dynamics black box modeling method based on neural network indirect estimation - Google Patents
Underwater vehicle dynamics black box modeling method based on neural network indirect estimation Download PDFInfo
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Abstract
The invention relates to an underwater vehicle dynamics black box modeling method based on neural network indirect estimation, which comprises the following steps: firstly, collecting a reference model or real data, and forming a data set through normalization and nonlinear transformation processing; then, a black box model of a double-neural-network structure is designed, and a state estimated value at the next moment is calculated; then, according to the difference between the data set information and the state estimation value, gradually correcting the black box model parameters of the double-neural-network structure through a designed algorithm; and finally, evaluating the precision and accuracy of the black box model through the designed statistical performance index and trend performance index, and screening black box model parameters meeting the requirements. The method is realized based on data driving, does not depend on accurate model parameters of the underwater vehicle, has good self-adaptation performance and high approximation precision for modeling problems of the underwater vehicle with different specifications, and simultaneously the algorithm accelerates the training speed of the black box model by utilizing the characteristics of the underwater vehicle.
Description
Technical Field
The invention relates to an underwater vehicle, in particular to an underwater vehicle dynamics black box modeling method based on neural network indirect estimation.
Background
The problem of the dynamics modeling of the underwater vehicle is to solve a mathematical function describing dynamics characteristics by utilizing a mechanism analysis or numerical approximation mode, and the input and output characteristics of the function are consistent with those of the underwater vehicle. Specifically, for a time-invariant nonlinear system, the system state at a certain moment is any legal value s (t), the input control quantity is a (t), the state at the next moment is s (t+1), and then the dynamics modeling is to solve an approximation function f (s (t), a (t)) as close as possible to s (t+1). The dynamic model can be applied to state prediction in the actual sailing process of the underwater vehicle, and provides training data for machine learning control algorithms and other purposes.
The dynamics modeling method of an underwater vehicle can be generally classified into a mechanism modeling method and a black box modeling method.
1. Mechanism modeling
Conventional mechanism modeling methods are typically based on dynamic models of AUVs, and thus most research is directed to improving the accuracy of state estimation by building more accurate dynamic models of AUVs.
The main idea of the linear modeling method is to build a mathematical model to describe an underwater vehicle dynamics modeling system, and the difficulty is to select a reasonable expression, and the dynamics model created by using the linear theory or the Newton-Euler equation is based on a parameterized model. However, there is a certain complexity to obtain accurate hydrodynamic parameters. A large number of manipulability model experiments are completed through methods such as experiments or numerical calculation, and relevant parameters of a dynamics model of the underwater vehicle can be determined. This necessitates a significant investment in time and capital costs. The built model is generally only suitable for some specific maneuvering motions, does not have a real-time online correction function, and has certain limitations.
Since the motion model of the AUV is nonlinear, the linear estimation method generally works only in a small range. In order to solve the problem, a nonlinear state estimation method, such as a black box model based on a dynamic model to improve estimation performance, a method of obtaining more accurate fluid dynamic factors through fluid dynamic calculation to construct a black box model with better performance, is adopted. However, the nonlinear estimation method still relies on an accurate AUV dynamic model, which greatly limits its application in practical situations.
2. Black box modeling method
The black box modeling method is mainly based on the data driving thought, a general dynamic model with infinite approximation performance is constructed, and the characteristics of the solved dynamic model and the original model are consistent through parameter training of output and input.
The advent of artificial intelligence methods provides an effective way to overcome the above difficulties. In order to accurately describe the nonlinear dynamics characteristics of the underwater vehicle, an equivalent nonlinear mapping function of the same dynamics model is established through an intelligent algorithm, parameters in the nonlinear function have no physical meaning, but only an equivalent relation in mathematical meaning, and the modeling method is nonlinear dynamics identification modeling, namely a black box modeling method.
The method has the remarkable advantages that the established mathematical model is only related to system input and output, the real dynamics characteristics of the model are not considered, the acquisition of hydrodynamic parameters in mechanism modeling is avoided, and the higher-order small quantity ignored in the mechanism modeling can be considered, so that the accuracy of black box modeling is generally higher than that of the mechanism modeling.
Artificial neural networks have been developed and applied for many years, and are considered to be a more efficient artificial intelligence algorithm, widely applied in nonlinear dynamics recognition modeling, and considered to be a very efficient algorithm, and widely applied to almost all fields. Its general structure includes input layer, hidden layer and output layer 3, and the hidden layer can be set into one or several layers, in which the different structures of hidden layer and the different selected activation functions can form different artificial neural network algorithms, and the common ones include BP (back propagation) neural network, radial basis function (Radial Basis Function, RBF) neural network and Hop-field neural network. The artificial neural network has good fitting capability on the nonlinear function, and provides an effective means for nonlinear dynamics identification of the underwater vehicle.
3. Black box modeling method based on neural network
Because the artificial neural network has good nonlinear mapping capability, self-learning Xi Shi capability and parallel information processing capability, a new thought is provided for solving the identification problem of an unknown uncertain nonlinear system. The artificial neural network has good fitting capability on the nonlinear function, and provides an effective means for nonlinear dynamics identification of the underwater vehicle.
The neural network method is adopted for comparing outstanding characteristics:
(1) Generalization ability
Samples without training have good prediction capability and control capability. In particular, when some noisy samples exist, the prediction capability is very good, namely the generalization capability is provided;
(2) Nonlinear mapping capability
When the system is clear and the related parameters are obtained directly, the mathematical tools such as numerical analysis, partial differential equation and the like are utilized to build an accurate mathematical model, but when the system is complex, the system is unknown or the information quantity of the system is little, the accurate mathematical model is difficult to build, the nonlinear mapping capability of the neural network is advantageous because the system does not need to be thoroughly understood, but the mapping relation between input and output can be achieved, so that the design difficulty is greatly simplified.
The difficulty of modeling dynamics of an underwater vehicle by adopting a neural network method is that:
(1) The underwater vehicle is a strong coupling underactuated system with six degrees of freedom, the state required to learn and train is huge, the cost of an underwater experiment is high, the original data is precious, and the model training is difficult to directly use the original data;
(2) The hydrodynamic characteristics of the underwater vehicle are greatly influenced by the speed, and it is not practical for practical sailing experiments to collect sailing data at all speeds.
Disclosure of Invention
The invention aims to overcome the problem that the experimental data is huge for the training of the underwater vehicle system in order to improve the estimation precision of the underwater vehicle controller because the underwater vehicle system model is a strong coupling nonlinear system, and the invention aims to carry out the regression training of the black box model by adopting a neural network with infinite approximation capability.
In order to train and obtain the neural network black box model with high precision under the minimum data requirement, the invention combines some relatively clear mechanism characteristics of the underwater vehicle with the neural network technology to establish the dynamics model of the underwater vehicle, and can realize real-time on-line fine adjustment of model parameters according to historical experience data of the navigation process, thereby providing accurate state forecast for the navigation process and further providing an underwater vehicle dynamics black box modeling method based on indirect estimation of the neural network.
In order to solve the technical problems, the technical scheme of the invention provides an underwater vehicle dynamics black box modeling method based on neural network indirect estimation, which comprises the following steps:
first, data collection and preprocessing: collecting reference model or real data of an AUV of the underwater vehicle, carrying out normalization and nonlinear transformation processing, and calculating historical state information to form a data set;
secondly, the structural design of the black box model: according to the characteristics of the underwater vehicle, a black box model of a double-neural-network structure is designed, the input of the black box model is the current state s (t) and the control quantity a (t) of the vehicle, the output is the future state change quantity delta s (t), and the state estimated value of the next moment is calculated through delta s (t) and s (t)
Then, black box model regression training: according to the difference between the data set information and the state estimation value, gradually correcting parameters of a black box model of the double-neural-network structure through a designed algorithm;
finally, evaluating and screening performance of the black box model: evaluating the precision and accuracy of the black box model through the designed statistical performance index and trend performance index, and screening black box model parameters meeting the requirements;
the modeling method specifically comprises the following steps when carrying out regression training on the black box model:
(1) Initializing a data set into a training set and a testing set, and initializing a neural network weight;
(2) Randomly sampling a batch of data from a training set, and carrying out normalization and nonlinear transformation processing on the data;
(3) Performing forward calculation of the neural network to obtain a state variable quantity;
(4) Calculating a state estimation value of the black box model;
(5) Calculating the deviation between the state estimation value and the training set data;
(6) Performing back propagation calculation of deviation of the neural network, and correcting parameters of the neural network;
(7) Repeating steps (2) - (6) until the deviation is less than a set threshold;
(8) According to the designed statistical performance index and trend performance index, evaluating the performance of the trained black box model in the test set, and returning to the step (1) when the evaluation result does not meet the requirement; and outputting the model when the evaluation result meets the requirement.
As an improvement of the above technical solution, the reference model or the actual model of the AUV is expressed in the form of the following equation:
s(t+1)＝f(s(t)，a(t))
when the state s (t) and the control quantity a (t) at a certain moment are input, the state s (t+1) at the next moment is output, and s (t+1) is a calculation result of a mechanism model for a reference model of the AUV; for the actual model of AUV, s (t+1) is the result of the sensor measurement;
the state of the AUV mainly includes the following:
wherein ,[x0 ，y 0 ，z 0 ]Representing the position of the floating center of the AUV relative to an inertial coordinate system; its attitude angle, i.e. roll angleThe pitch angle theta and the yaw angle psi represent the rotation relation between the carrier coordinate system and the inertial coordinate system; [ v x ，v y ，v z] and [ωx ，ω y ，ω z ]The three-axis speed and the angular speed of the AUV in a carrier coordinate system are respectively; the inertial coordinate system is fixed at the designated position in space, north, sky and east are positive directions, and the carrier coordinate system is fixed at the floating center O of AUV b Taking the axial direction, the upward direction and the right side direction of the AUV as positive directions; controlled amount a (t) = [ delta ] e (t)，δ r (t)，δ d (t)，T]Wherein delta e ，δ r ，δ d The rudder angle is a horizontal rudder angle, the rudder angle is a vertical rudder angle and the rudder angle is a differential rudder angle, and T is the rated thrust exerted by the AUV.
As another improvement of the technical scheme, the state estimation value of the black box model established by the modeling method at the next moment is calculatedIn this case, the state increment Δs (t) estimated by the neural network is estimated indirectly +.>At this time, the estimated value of the state at the next time is expressed as +.>
As a further improvement of the above technical solution, the modeling method performs nonlinear transformation on the control quantity a (t) in the input feature during training to obtain a nonlinear control quantity a ', i.e., a' =a (t) v 2, wherein ,v2 ＝||[v x ，v y ，v z ]| 2 。
As a further improvement of the above technical solution, the modeling method performs normalization processing on the input and output data of the neural network simultaneously during the training process.
As a further improvement of the above technical solution, the modeling method constructs an estimator with a dual-network structure of a gesture network and a velocity network, and the calculation formulas of the gesture network and the velocity network are as follows:
z 1 ＝f tanh ((W (0) ) T [s，a])
z 2 ＝f Relu ((W (1) ) T z 1 )
z 3 ＝f Relu ((W (2) ) T z 2 )
z＝f tanh ((W (3) ) T z 3 )
wherein z is the output value of the output layer of the neural network, z 1 Is the input layer output value, z 2 Is the first layer hidden layer output value, z 3 Is the output value of the second hidden layer, W (0) Is the weight of the neural network of the input layer, W (1) Is the weight of the first layer neural network, W (2) Is the weight of the second layer neural network, W (3) Is the third layer neural network weight; [ s, a ]]Is an input value, and comprises a state quantity s and a control quantity a;
neural network activation function f tanh The expression of (X) is:
neural network activation function f Relu The expression of (X) is:
for gesture networks, its output wherein ,Δy0 Is AUV depth y 0 Tracking error of the actual value and the estimated value, < +.>Δθ, Δψ are the roll angle +.>Tracking errors of the actual and estimated values of the pitch angle θ and the yaw angle ψ, [ Δω ] x ，Δω y ，Δω z ]Is the angular velocity [ omega ] x ，ω y ，ω z ]Tracking error of the actual value and the estimated value; whereas for a velocity network its output z= [ Δv ] x ，Δv y ，Δv z ]Wherein [ Deltav x ，Δv y ，Δv z ]Is the linear velocity [ v ] in the x, y, z direction x ，v y ，v z ]Tracking error of the actual value and the estimated value;
meanwhile, the back propagation formula of the gradient is as follows:
δ 4 ＝Δz⊙f′ tanh ((W (3) ) T z 3 )
δ 3 ＝((W (4) ) T δ 4 )⊙f′ Relu ((W (2) ) T z 2 )
δ 2 ＝((W (3) ) T δ 3 )⊙f′ Relu ((W (1) ) T z 1 )
δ 1 ＝((W (2) ) T δ 2 )⊙f′ tanh ((W (0) ) T [s，a])
(i＝2，3，4，z 0 ＝[s，a])
wherein ,δ1 、δ 2 、δ 3 、δ 4 Is an intermediate variable for error propagation in the layer-by-layer direction,is an intermediate variable of error propagation of corresponding neurons of the corresponding layer, z L For the label value, Δz=z-z L J is a loss function, and As a result, the term "-, hadamard product, ->Is the weight of the neural network, < >>Is the intermediate value of the forward computation of the neural network of the corresponding neurons of the corresponding layer;
f′ tanh (X) is f tanh The back propagation gradient formula of (X) is as follows:
f′ Relu (X) is f Relu The back propagation gradient formula of (X) is as follows:
as a further improvement of the above technical solution, the statistical performance index SPI proposed by the modeling method is a statistical result obtained according to a relative error between an estimated value of each estimated state item and a tag value, the tag value is a set actual value corresponding to the estimated value, the statistical object is an output value of an estimator whose relative error with the tag value is greater than a set threshold, and the output value is referred to as an outlier; the calculation formula of SPI is:
wherein ,m is the number of state terms (m=1 when calculated for only a certain state), N is the amount of data extracted from the dataset for testing, s iE To estimate the estimated value of the equation output for the next time state, s iL The label value is corresponding to the estimated state item, and th is a relative error threshold; the single SPI of a certain state is obtained when the state is counted only, the overall SPI is obtained when all the estimated states are counted, and the comparison of the single SPI and the overall SPI can reflect the balance of estimation accuracy.
As a further improvement of the above technical solution, the trend performance index TPI proposed by the modeling method is a time average error of a control curve for calculating each state in a certain time, and the calculation formula is as follows:
wherein Ti is control time, M is state item number, s Fi S is a control curve based on a state estimation equation Mi Is a model-based control curve; meanwhile, in order to avoid the influence of the order of magnitude difference between the states, the control error of each state is subjected to corresponding normalization processing.
At present, the state estimation method for the high-speed AUV is less, and the performance loss in practical application can be caused by directly applying the common black box model to the high-speed AUV due to the difference of kinematic characteristics. In order to solve the problem, the indirect state estimation black box modeling method based on the neural network provided by the invention has the following characteristics:
1. the improvement points for the neural network black box model include:
(1) Indirect estimation;
(2) Nonlinear transformation of control quantity;
(3) Normalizing training data;
(4) Dual network architecture.
2. Two training effect evaluation indexes are provided
In order to judge whether training of the black box model is completed, two evaluation indexes are designed:
(1) A statistical performance index (Statistics Performance Index, SPI) for characterizing the error between the state estimate and the true value output by the estimator;
(2) Trend performance indicators (Tendency Performance Index, TPI) are used to characterize the overall error condition of the estimator with respect to the state estimate and the true value during a voyage of the AUV.
3. Performing simulation verification
Finally, the feasibility and effectiveness of constructing and training the neural network black box model are demonstrated through design simulation verification.
In addition, constraint conditions required by the underwater vehicle dynamics black box modeling method based on the neural network indirect estimation provided by the invention are as follows:
(1) is suitable for an underwater vehicle with an elongated body and a slenderness ratio of about 10;
(2) and (3) sailing at a high speed, wherein the sailing speed is greater than 15m/s.
The underwater vehicle dynamics black box modeling method based on the neural network indirect estimation has the following advantages:
(1) The accurate system mechanism model is not relied on, and the cost of solving the accurate kinetic parameters is reduced;
(2) The search space in the neural network approximation process is reduced by indirectly estimating the variation instead of directly estimating the next state, so that the requirement on the training data quantity is reduced;
(3) By combining with the mechanism information of the AUV of a specific type, nonlinear preprocessing is carried out on the input state of the neural network according to the navigational speed, so that the self-adaptive capacity of the black box model obtained by training on the navigational speed-variable navigational state is effectively improved;
(4) In the actual navigation process, the model can be trained and finely tuned on line by utilizing navigation data, and the self-adaptive capacity of the black box model to different environments is improved;
(5) According to the basic dynamics characteristics of the AUV of a specific type, the complete state prediction is decomposed into a gesture ring and a position ring, and the success rate of model fitting is effectively improved.
The invention relates to the technical field of underwater vehicles, mainly relates to an identification modeling method of nonlinear dynamics of an underwater vehicle, and in particular relates to a black box modeling method for indirect state estimation of an elongated underwater vehicle (Automatic Underwater Vehicle, AUV). The black box dynamics model (black-box dynamic model) constructed by the method can effectively estimate the state of the AUV at the next moment under the condition of knowing the state of the AUV at the current moment and the controlled quantity aiming at the uncertain nonlinear system of underactuated strong coupling of the AUV. The black-box model (black-box model) generated by the indirect state estimation algorithm has low error in statistical characteristics and strong consistency with the original model (original model) in dynamics trend characteristics. The calculation result of the method can provide a large amount of training data support for the machine learning control method, and can ensure the rapid and stable control with strong anti-interference capability in unfamiliar environments even though the modeling is not accurate.
Drawings
FIG. 1 is a block diagram of an underwater vehicle dynamics black box modeling method based on neural network indirect estimation;
FIG. 2 is a training flow chart of the black box model established by the invention;
FIG. 3 is a schematic diagram of a motion coordinate system established for an underwater vehicle by the modeling method of the present invention;
FIG. 4 is a schematic diagram of a pose network of an estimator constructed in accordance with the present invention;
FIG. 5 is a block diagram of a velocity network of an estimator constructed in accordance with the present invention;
FIG. 6 is a graph comparing time-angular velocity curves for five simulated verification cases including the output model of the present invention;
FIG. 7 is a graph comparing time-attitude angle curves for five simulation verification cases including the output model of the present invention;
FIG. 8 is a graph comparing time-line velocity curves for five simulation verification cases including the output model of the present invention.
Detailed Description
The technical scheme provided by the invention is further described below by combining with the embodiment.
1. Motion model of high-speed underwater vehicle
High-speed underwater vehicles are generally referred to as autonomous underwater vehicles in the form of long strips that operate at speeds in excess of 30 knots. This complicates the AUV model that originally had multiple-input multiple-output, strong coupling, underactuation, and nonlinearity characteristics due to the harsh underwater environment coupled with the high speed motion of the AUV. To describe the movement of the AUV, a geodetic coordinate system and a carrier coordinate system are introduced, respectively, as shown in fig. 3.
Wherein the geodetic coordinate system is fixed somewhere in the earth, the carrier coordinate system is usually fixed at the floating center O of the AUV b Its coordinates [ x 0 ，y 0 ，z 0 ]Floating center O representing AUV b Relative to the ground coordinate system, and its attitude angle, i.e. roll angle (roll)The pitch angle (pitch) θ and yaw angle (yaw) ψ are characterized by the angle of rotation between the two coordinate systems. The AUV motion model established based on the coordinate system comprises the following steps:
under a carrier coordinate system, the dynamic equation of the axial translation is as follows:
the dynamic equation of the vertical translation under the carrier coordinate system is as follows:
under a carrier coordinate system, the dynamic equation of the transverse translation is as follows:
under the carrier coordinate system, the kinetic equation of rotation around the axial direction is:
in the carrier coordinate system, the kinetic equation of vertical rotation is as follows:
in the carrier coordinate system, the kinetic equation of rotation around the transverse direction is as follows:
the attack angle and sideslip angle calculation formula:
α＝-arctan(v y /v x ) (7)
the conversion matrix of the triaxial angular velocity to the Euler angular velocity in the carrier coordinate system:
the depth kinetic equation is:
wherein v= [ v ] x ，v y ，v z] and ω＝[ωx ，ω y ，ω z ]The components of the AUV's velocity and angular velocity in the carrier coordinate system, v x ，v y ，v z Respectively the components of the velocity, omega x ，ω y ，ω z Respectively the components of angular velocity;
is the dimensionless angular velocity, +.>Components of dimensionless angular velocity, respectively; x is x c ，y c ，z c The components of the centroid of the AUV on the carrier coordinate system are respectively, and alpha and beta are respectively the attack angle and the sideslip angle; delta e ，δ r ，δ d Respectively a horizontal rudder angle, a vertical rudder angle and a differential rudder angle; t is the rated thrust exerted by the AUV; m and G are mass and gravity, respectively; Δg is negative buoyancy; ρ is the density of water; s and L are the AUV maximum cross-sectional area and length, respectively; j (J) xx ，J yy ，J zz The rotational inertia of the AUV in three axial directions of a carrier coordinate system is respectively; ΔM xp Is an unbalanced moment. The hydrodynamic parameters are furthermore as follows:
C xS is the resistance factor of an area characterized by a maximum cross-sectional area S;
position derivative of roll moment factor to sideslip angle;
position derivative of the roll moment factor to the vertical rudder angle;
position derivative of the roll moment factor to the differential rudder angle;
a rotational derivative of roll torque factor to roll angular velocity;
a rotational derivative of roll torque factor with respect to yaw rate;
position derivative of lift factor with respect to angle of attack;
position derivative of lift factor to rudder angle;
a rotational derivative of lift factor with respect to pitch angle rate;
position derivative of yaw moment factor with respect to sideslip angle;
position derivative of yaw moment factor to vertical rudder angle;
a rotational derivative of yaw moment factor with respect to roll angular velocity;
a rotational derivative of yaw moment factor with respect to yaw rate;
position derivative for the sideslip angle of the sideslip force factor;
position derivative of the side force factor to the vertical rudder angle;
a rotational derivative of the yaw rate for the side force factor;
position derivative of pitch moment factor with respect to angle of attack;
position derivative of pitching moment factor to rudder angle;
a rotational derivative of the pitch moment factor with respect to the pitch angle speed;
λ 11 adding a quality factor for the longitudinal direction;
λ 22 、λ 33 to add quality factor lambda transversely 22 ＝λ 33 ；
λ 44 Adding a moment of inertia factor for the longitudinal direction;
λ 55 、λ 66 to laterally add mass rotate crown Liang Yinshu, lambda 55 ＝λ 66 ；
λ 26 、λ 35 To add a dead moment factor lambda 26 ＝-λ 35 。
2. Evaluation index design of black box dynamics model training process
From the above equations of motion, there are a large number of hydrodynamic parameters in the motion model of the underwater vehicle, which results in a large amount of resource consumption in accurately modeling the AUV. Therefore, the modeling method of the invention is to build an equation of a black box model under the condition of not modeling based on a mechanism, as shown in a formula (11):
the equation can estimate the state of the next moment when the state s (t) and the control quantity a (t) of a certain moment are inputThe modeling method is called a black box model. The state of the AUV mainly includes the following:
the controlled quantity is mainly a (t) = [ delta ] e (t)，δ r (t)，δ d (t)，T]。
In order to evaluate the estimation accuracy of the black box model in the training process, the modeling method provided by the invention provides two indexes: statistical Performance Index (SPI) and Trend Performance Index (TPI).
(1) Statistical Performance Index (SPI)
In order to reduce the influence of the huge difference of the different states of the AUV in order of magnitude, the SPI index provided by the modeling method is a statistical result obtained according to the relative error between the estimated value of each estimated state item and the label value, the statistical object is an output value of an estimator with the relative error between the statistical object and the label value being larger than a set threshold, and the output value is called an outlier. The calculation of the SPI is shown in equation (12), and is a single SPI of a certain state when the state is counted only, and is a total SPI when all the estimated states are counted. The comparison of the two can reflect the equalization of the estimation accuracy.
wherein ,m is the number of state terms (m=1 when calculated for only a certain state), N is the amount of data extracted from the test set for testing, s iE To estimate the estimated value of the equation output for the next time state, s iL And th is a relative error threshold for the tag value corresponding to the estimated state item. The error condition between the estimated value and the true value output by the current estimation equation can be obtained according to the SPI.
(2) Trend Performance Index (TPI)
In order to reflect the learning condition of the black box model on the kinematic characteristics of the original AUV motion model, the black box model and the original model are respectively used for controlling the AUV in the same initial state, and the time average error of the control curve of each state in a certain time is calculated, so that TPI is obtained, and the TPI is shown as a formula (13).
Wherein Ti is control time, M is state item number, s Ei S is a control curve based on a state estimation equation Mi For model-based control curves, corresponding normalization processing is performed on control errors of the states in order to avoid the influence of magnitude differences among the states.
3. AUV black box model based on neural network
Due to the complexity of the AUV motion model itself, the conventional method is often difficult to be adequate in establishing a high-precision black box model, and development of Machine Learning (ML) technology provides a new solution to this problem. Because of the strong coupling and nonlinear nature of the AUV model, regression training of this black box model is to be performed using neural networks with infinite approximation capability. In order to train and obtain a high-precision neural network black box model under the condition of minimum data requirements, the modeling method provided by the invention provides the following improvement scheme.
(1) Indirect estimation by Δs (t)
The indirect estimation is to input the state s (t) and the control quantity a (t) at a certain moment, and output the state at the next moment by the neural networkHowever, this estimation method has a problem that the search space is too large, i.e., in two different states +.>Under the same control quantity a (t), possibly similar in motion characteristics, but with their respective outputs +.>However, there may be a large gap, which increases the learning load of the neural network to some extent, so that the present invention adopts an indirect estimation method, i.e. the estimation result of the neural network is the increment Δs (t) of the state, and at this time, the estimation of the state at the next moment may be expressed as +.>Simulation experiments prove that the improvement reduces the burden of neural network learning and remarkably improves the estimation precision.
(2) Nonlinear conversion of control quantity
In high-speed AUV operation, the body is subjected to fluid dynamics and fluid dynamics moment and the quadratic v of the model of the speed vector 2 In a linear relationship, furthermore, the parameter v is known from the motion model of the AUV 2 The nonlinear conversion factor as the control amount has a large influence on the change in the AUV state. Therefore, in order to improve the training efficiency of the neural network, the training method comprises the following steps ofIs subjected to a similar nonlinear transformation, i.e., a' =a (t) v 2, wherein v2 ＝||[v x ，v y ，v z ]|| 2 . Simulation experiments show that the nonlinear transformation improves the estimation accuracy of the neural network estimator to a certain extent.
(3) Normalization of training data
Because the data used for training the neural network estimator has a large difference in magnitude, for example, the position and the speed of the AUV are far greater than those of other states such as attitude angles and angular speeds in magnitude, the states with small magnitude in the training process can be ignored if the data are not normalized, and the estimation accuracy of the estimator is further affected. In order to improve training efficiency, the invention normalizes the input and output data of the neural network at the same time.
(4) Dual network architecture
To enable the use of a simple fully-connected network while training a neural network black box model with high efficiency. The invention proposes a dual network structure to construct an estimator, i.e. depth y of AUV with gesture network 0 Attitude angleAngular velocity omega x ，ω y ，ω z The regression training is performed, as shown in FIG. 4, in which the inputs are the state quantity s (t) and the control quantity a (t), and the outputs are ∈10 after the calculation of the nerve activation function (tanh, relu, relu, tanh, respectively) of each layer> wherein ,Δy0 ，Δθ，Δψ，Δω x ，Δω y ，Δω z Tracking errors, including position, angle and angle, of the actual and estimated values, respectively, of the relevant parameterA speed; with speed network versus speed v x ，v y ，v z The regression training was performed, as shown in FIG. 5, in which the inputs were the state quantity s (t) and the control quantity a (t), and the output z= [ Deltav ] was calculated by successively passing through the nerve activation functions (tanh, relu, relu, tanh, respectively) of the respective layers x ，Δv y ，Δv z ]The method comprises the steps of carrying out a first treatment on the surface of the Wherein Deltav x ，Δv y ，Δv z Tracking errors of the actual and estimated values of the linear velocity in the x, y, z directions, respectively.
Since the two networks are substantially identical in structure and activation function used, the training complexity does not increase significantly, and the calculation formula is shown as formula (14) below, for a gesture network, the output isWhereas for a velocity network its output z= [ v ] x ，v y ，v z ]。/>
Meanwhile, the back propagation formula of the gradient is shown as formula (15).
wherein ,zL For the label value, Δz=z-z L J is a loss function, and As a Hadamard product.
4. Simulation results
As shown in fig. 1, the structural block diagram of the underwater vehicle dynamics black box modeling method based on the neural network indirect estimation is mainly divided into three processes of training data collection, underwater vehicle black box modeling based on the neural network and application scenes; collecting and storing historical data and real-time data of the underwater vehicle, and using the historical data and the real-time data for offline initial training and online fine tuning training; then, a black box model is established, and when the state and the control quantity at a certain moment are input, the state at the next moment can be indirectly estimated through estimating the state increment; performing regression training on the black box model by adopting a neural network with infinite approximation capability, constructing a controller by adopting a double-network structure, namely performing regression training on the depth, the gesture and the angular speed of the underwater vehicle by adopting a gesture network, and performing regression training on the speed by adopting a speed network; in the training process, nonlinear transformation is carried out on the input characteristics, and normalization processing is uniformly carried out on the input data and the output data; the estimation accuracy of the black box model in the training process is evaluated by using the Statistical Performance Index (SPI) and the Trend Performance Index (TPI) to guide the training process, and the neural network parameters are continuously guided and adjusted to improve the self-adaptive capacity of the black box model, improve the estimation accuracy, and the method is used for the estimator training under various environments to realize the state forecast in the navigation process of the underwater vehicle.
As shown in fig. 2, a training flow chart of the black box model established by the invention is shown. Starting an underwater vehicle to start training, initializing a neural network weight and random seeds, and carrying out batch sampling collection on historical data of the underwater vehicle, wherein the historical data are divided into a training set and a testing set, the data in the training set are used for training, and the data in the testing set are used for testing; data in the training set are selected for training in sequence, and regularization is carried out on the established model; performing nonlinear transformation on the control quantity in the input characteristics; performing forward calculation, and simultaneously performing normalization processing on input and output data of the neural network; indirectly estimating the state of the next moment through the state increment of the underwater vehicle; training the data in the training set to ensure that the deviation < epsilon of the training set 1 ，ε 1 Estimating error parameters for the set training set, updating the weight of the neural network, collecting the weight as real-time data of the underwater vehicle, and performing online fine tuning training; selecting data in the test set for testing and calculating SPI index deviation and TPI index deviation, guiding and adjusting initialized neural network weight, and performing cyclic test until the SPI index deviation<ε 2 Deviation from TPI index<ε 3 ，ε 2 and ε3 Estimating error parameters for the set test set, indicating that training is completeAnd outputting the model after training.
The embodiment combines the related parameters of a 533 caliber high-speed AUV as an original model to verify the black box method for constructing and training the neural network black box model by the algorithm.
The relevant parameters of the original model are shown in the following table:
TABLE 1 parameters of high speed AUV raw model
The simulation verification steps are as follows:
1. establishing an AUV original model by using overall parameters shown in Table 1;
2. based on the original model, a data set [ s (t), a (t), s (t+1) ] is created, which is generated by the original model operation in a randomly initialized state, to generate a training data set for the black box estimator.
3. Building a neural network designed by the modeling method and training a simulation system based on a Tensorflow platform;
4. and (3) based on the data set created in the step (2), training and performance evaluation work are completed by adopting a neural network indirect estimation method.
TABLE 2 simulation conditions and statistical results
Simulation verification comparison was performed using five cases of items 1, 3, 5, 6 (item 1, 3, 5, 6) and the original controller in the above table. It can be seen that:
1. from the description of SPI and TPI, it is clear that the estimated performance differs in these five different cases. The method (item 1) of the invention has good effect in estimating the state of the high-speed AUV. The indirect estimation method is significantly better than the direct estimation method.
2. In the aspect of controlling the estimation precision or dynamic performance, only less training data is used, and the estimator based on the double neural network has better performance than the single-neural network single-NN. In addition, the control input that introduces a nonlinear mapping process may characterize more accurate dynamics than a reference model (real world data).
3. In order to verify the effectiveness of the black box modeling method and whether the dynamic characteristics of the reference model can be captured, a PID controller is adopted, control quantity is added, the dynamic characteristics of the original model are learned, simulation results are shown in fig. 6-8, wherein an Origin curve in the drawing is an effect curve corresponding to the underwater vehicle when the original PID controller is adopted for simulation training.
As shown in FIG. 6, the angular velocities (. Omega.) of item1, 3, 5, 6 and the original PID controller x ,ω y ,ω Z ) -a time (t) curve; as shown in FIG. 7, the attitude angles for item1, 3, 5, 6 and the original PID controller-a time (t) curve; as shown in fig. 8, the linear velocities (v x ,v y ,v Z ) -a time (t) curve; from the graph, the performance estimation effect of item1 meets the design requirement, and the dynamic accuracy of the model is ensured.
Therefore, the indirect estimation black box modeling method based on the neural network has low error in statistical characteristics, small data amount, and strong consistency with the original model in dynamics trend characteristics.
As can be seen from the specific description of the invention, the neural network indirect estimation-based underwater vehicle dynamics black box modeling method reduces the requirement on the training data amount, effectively improves the self-adaptive capacity of the black box model obtained by training in the variable-speed navigation state, and effectively improves the estimation precision of the model.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and are not limiting. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the appended claims.
Claims (8)
1. An underwater vehicle dynamics black box modeling method based on neural network indirect estimation, the modeling method comprising the following steps:
first, data collection and preprocessing: collecting reference model or real data of an AUV of the underwater vehicle, carrying out normalization and nonlinear transformation processing, and calculating historical state information to form a data set;
secondly, the structural design of the black box model: according to the characteristics of the underwater vehicle, a black box model of a double-neural-network structure is designed, the input of the black box model is the current state s (t) and the control quantity a (t) of the vehicle, the output is the future state change quantity delta s (t), and the state estimated value of the next moment is calculated through delta s (t) and s (t)
Then, black box model regression training: according to the difference between the data set information and the state estimation value, gradually correcting parameters of a black box model of the double-neural-network structure through a designed algorithm;
finally, evaluating and screening performance of the black box model: evaluating the precision and accuracy of the black box model through the designed statistical performance index and trend performance index, and screening black box model parameters meeting the requirements;
the modeling method specifically comprises the following steps when carrying out regression training on the black box model:
(1) Initializing a data set into a training set and a testing set, and initializing a neural network weight;
(2) Randomly sampling a batch of data from a training set, and carrying out normalization and nonlinear transformation processing on the data;
(3) Performing forward calculation of the neural network to obtain a state variable quantity;
(4) Calculating a state estimation value of the black box model;
(5) Calculating the deviation between the state estimation value and the training set data;
(6) Performing back propagation calculation of deviation of the neural network, and correcting parameters of the neural network;
(7) Repeating steps (2) - (6) until the deviation is less than a set threshold;
(8) According to the designed statistical performance index and trend performance index, evaluating the performance of the trained black box model in the test set, and returning to the step (1) when the evaluation result does not meet the requirement; and outputting the model when the evaluation result meets the requirement.
2. The method of modeling an underwater vehicle dynamics black box based on neural network indirect estimation according to claim 1, wherein the reference model or actual model of the AUV is expressed in the form of the following equation:
s(t+1)＝f(s(t)，a(t))
when the state s (t) at a certain moment t and the control quantity a (t) are input, the equation outputs the state s (t+1) at the next moment, wherein the state of the AUV mainly comprises the following steps:
wherein ,[x0 ，y 0 ，z 0 ]Representing the position of the floating center of the AUV relative to an inertial coordinate system; its attitude angle, i.e. roll angleThe pitch angle theta and the yaw angle psi represent the rotation relation between the carrier coordinate system and the inertial coordinate system; [ v x ，v y ，v z] and [ωx ，ω y ，ω z ]The three-axis speed and the angular speed of the AUV in a carrier coordinate system are respectively; inertial coordinatesIs fixed at a specified position in space, the north direction, the sky direction and the east direction are taken as positive directions, and a carrier coordinate system is fixed at a floating center O of an AUV b Taking the axial direction, the upward direction and the right side direction of the AUV as positive directions; controlled amount a (t) = [ delta ] e (t)，δ r (t)，δ d (t)，T]Wherein delta e ，δ r ，δ d The horizontal rudder angle, the vertical rudder angle and the differential rudder angle are respectively, and T is the rated thrust exerted by the AUV.
3. The modeling method of the black box of the dynamics of the underwater vehicle based on the indirect estimation of the neural network according to claim 1, wherein the black box model established by the modeling method calculates the state estimation value of the next momentIn this case, the state increment Δs (t) estimated by the neural network is estimated indirectly +.>At this time, the estimated value of the state at the next time is expressed as +.>
4. The modeling method of the underwater vehicle dynamics black box based on the neural network indirect estimation according to claim 1, wherein in the training process of the modeling method, the control quantity a (t) in the input characteristic is subjected to nonlinear transformation to obtain a nonlinear control quantity a ', namely a' =a (t) v 2, wherein v2 ＝||[v x ，v y ，v z ]|| 2 。
5. The modeling method of the underwater vehicle dynamics black box based on the neural network indirect estimation according to claim 1, wherein the modeling method performs normalization processing on input and output data of the neural network simultaneously in a training process.
6. The modeling method of an underwater vehicle dynamics black box based on neural network indirect estimation according to claim 1, wherein the modeling method constructs an estimator with a dual-network structure of a gesture network and a speed network, and the calculation formulas of the gesture network and the speed network are as follows:
z 1 ＝f tanh ((W (0) ) T [s，a])
z 2 ＝f Relu ((W (1) ) T z 1 )
z 3 ＝f Relu ((W (2) ) T z 2 )
z＝f tanh ((W (3) ) T z 3 )
wherein z is the output value of the output layer of the neural network, z 1 Is the input layer output value, z 2 Is the first layer hidden layer output value, z 3 Is the output value of the second hidden layer, W (0) Is the weight of the neural network of the input layer, W (1) Is the weight of the first layer neural network, W (2) Is the weight of the second layer neural network, W (3) Is the third layer neural network weight; [ s, a ]]Is an input value, and comprises a state quantity s and a control quantity a;
neural network activation function f tanh The expression of (X) is:
neural network activation function f Relu The expression of (X) is:
for gesture networks, its output wherein ,Δy0 Is AUV depth y 0 Tracking error of the actual value and the estimated value, < +.>Roll angle +.>Tracking errors of the actual and estimated values of the pitch angle θ and the yaw angle ψ, [ Δω ] x ，Δω y ，Δω z ]Is the angular velocity [ omega ] x ，ω y ，ω z ]Tracking error of the actual value and the estimated value; whereas for a velocity network its output z= [ Δv ] x ，Δv y ，Δv z ]Wherein [ Deltav x ，Δv y ，Δv z ]Is the linear velocity [ v ] in the x, y, z direction x ，v y ，v z ]Tracking error of the actual value and the estimated value;
meanwhile, the back propagation formula of the gradient is as follows:
δ 4 ＝Δz⊙f′ tanh ((W (3) ) T z 3 )
δ 3 ＝((W (4) ) T δ 4 )⊙f′ Relu ((W (2) ) T z 2 )
δ 2 ＝((W (3) ) T δ 3 )⊙f′ Relu ((W (1) ) T z 1 )
δ 1 ＝((W (2) ) T δ 2 )⊙f′ tanh ((W (0) ) T [s，a])
wherein ,δ1 、δ 2 、δ 3 、δ 4 Is an intermediate variable for error propagation in the layer-by-layer direction,is an intermediate variable of error propagation of corresponding neurons of the corresponding layer, z L For the label value, Δz=z-z L J is a loss function, and As a result, the term "-, hadamard product, ->Is the weight value of the neural network,is the intermediate value of the forward computation of the neural network of the corresponding neurons of the corresponding layer;
f′ tanh (X) is f tanh The back propagation gradient formula of (X) is as follows:
f′ Relu (X) is f Relu The back propagation gradient formula of (X) is as follows:
7. the modeling method of the underwater vehicle dynamics black box based on the neural network indirect estimation according to claim 1, wherein the statistical performance index SPI proposed by the modeling method is a statistical result obtained according to the relative error between the estimated value of each estimated state item and a label value, the label value is a set actual value corresponding to the estimated value, and the statistical object is an output value of an estimator with the relative error between the label value and the actual value being greater than a set threshold; the calculation formula of SPI is:
wherein ,m is the number of state terms (m=1 when calculated for only a certain state), N is the amount of data extracted from the dataset for testing, s iE To estimate the estimated value of the equation output for the next time state, s iL The label value is corresponding to the estimated state item, and th is a relative error threshold; the single SPI of a state is the single SPI of that state when it is only counted for that state, and the total SPI is the total when all estimated states are counted.
8. The modeling method of the underwater vehicle dynamics black box based on the neural network indirect estimation according to claim 1, wherein the trend performance index TPI proposed by the modeling method is a time average error of a control curve of each state in a certain time, and the calculation formula is as follows:
wherein Ti is control time, M is state item number, s Ei S is a control curve based on a state estimation equation Mi Is a model-based control curve; and carrying out corresponding normalization processing on the control errors of all the states.
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