Multi-output Gaussian process regression underwater vehicle system identification algorithm based on depth part auto-encoder

Abstract

A multi-output Gaussian process regression underwater vehicle system identification algorithm based on a depth part auto-encoder comprises the following steps: designing an amplitude-adjustable zigzag vertical rudder input signal, obtaining state data of an underwater vehicle, and dividing the state data into a training set and a verification set; constructing an autoregression model based on underwater vehicle dynamics according to the state data; building a depth part auto-encoder according to the auto-regression model; low-dimensional feature data extracted by the depth part auto-encoder is used as input of a multi-output Gaussian process, output of the auto-regression model is used as output of the multi-output Gaussian process, hyper-parameters of the multi-output Gaussian process are searched through a particle swarm algorithm, and model training is carried out; when a model training error reaches preset precision, completing model training, and verifying the model by adopting verification set data; the problems that high-dimensional input of the multi-output Gaussian process can increase calculation of a kernel function and search time of hyper-parameters, the complexity of a model is increased, and prediction efficiency of the multi-output Gaussian process is reduced are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater vehicle navigation prediction, and in particular relates to a multi-output Gaussian process regression underwater vehicle system identification algorithm based on a deep partial autoencoder. Background Art

[0002] Due to its long range, high precision and reusability, underwater vehicles have become an indispensable tool for human understanding and exploration of the ocean, and have been widely used in recent years. The dynamic system model is the basis for underwater vehicle motion state control, state monitoring, fault diagnosis and fault-tolerant system development, and is one of the core contents of underwater robot research. Non-parametric modeling requires almost no prior information about the structure of the underwater robot model to obtain accurate predictions. The multi-output Gaussian process regression model has a statistical basis, and its essence is a regression model based on the Bayesian framework. The model has good performance in dealing with small samples, nonlinear problems and other problems. On the one hand, the output data comes with a confidence interval, which is a major feature of the Gaussian process; on the other hand, statistical methods are used to find the conditional distribution between the input variable and the output variable, so as to establish the regression equation of the two. The result predicted by the multi-output Gaussian process regression model is not a single precise value, but a predicted value containing the mean and variance, and its prediction result is an interval. Therefore, the multi-output Gaussian process regression model can substitute the uncertainty of the prediction into the next prediction for uncertainty transfer.

[0003] However, multi-output Gaussian process modeling requires a large number of samples to cover the feature space, especially for complex nonlinear systems such as underwater vehicles, which require sufficient input feature information to enhance the generalization ability of the model and improve prediction accuracy. However, the high-dimensional input of the multi-output Gaussian process will increase the calculation time of the kernel function and the search time of hyperparameters, increase the complexity of the model, and reduce the prediction efficiency of the multi-output Gaussian process. Summary of the invention

[0004] In order to overcome the above-mentioned technical problems, the present application provides a multi-output Gaussian process regression underwater vehicle system identification algorithm based on a deep partial autoencoder. In view of the problem that the high-dimensional input of the multi-output Gaussian process will increase the calculation time of the kernel function and the search time of the hyperparameters, increase the complexity of the model, and reduce the prediction efficiency of the multi-output Gaussian process, it is proposed to use a deep partial autoencoder to reduce the input dimension of the multi-output Gaussian process, thereby reducing the loss function of the encoder network. At the same time, the autoencoder extracts features from the high-dimensional state data of the underwater vehicle in the high-dimensional space, and uses the obtained low-dimensional feature data as the input of the multi-output Gaussian process regression algorithm, thereby improving the prediction efficiency of the multi-output Gaussian process regression.

[0005] In order to achieve the above purpose, the technical solution adopted in this application is as follows: A multi-output Gaussian process regression underwater vehicle system identification algorithm based on deep partial autoencoder, comprising the following steps: Step 1, designing an adjustable amplitude sawtooth vertical rudder input signal, applying the adjustable amplitude sawtooth vertical rudder input signal to the underwater vehicle system, obtaining the state data of the underwater vehicle, and dividing the training set and the verification set; Step 2, constructing an autoregressive model based on the underwater vehicle dynamics according to the state data of the underwater vehicle obtained in step 1; Step 3: build a deep partial autoencoder according to the autoregressive model constructed in step 2, and use the training set data to train the deep partial autoencoder network, and use the low-dimensional feature data extracted by the deep partial autoencoder network to construct a loss function to update the gradient of the deep partial autoencoder; Step 4. Use the low-dimensional feature data extracted by the deep partial autoencoder as the input of the multi-output Gaussian process, use the output of the autoregressive model as the output of the multi-output Gaussian process, search for the hyperparameters of the multi-output Gaussian process through the particle swarm algorithm, and perform model training; Step 5: When the model training error reaches the preset accuracy, the model training is completed, and the model is verified using the validation set data.

[0006] Obtain the status data of the underwater vehicle, including: obtaining the linear speed and angular velocity ,in, , , They represent the longitudinal speed, vertical speed and lateral speed of the vehicle respectively; , , They represent the rolling angular velocity, heading angular velocity and pitch angular velocity of the vehicle respectively; , , Respectively represent the lateral, longitudinal and vertical positions of the aircraft; , , They represent the roll angle, pitch angle and heading angle of the aircraft respectively.

[0007] The autoregressive model is expressed as:

[0008] in, is the status data of the underwater vehicle, The input for the underwater vehicle includes the rudder angle and thruster. is the order of the autoregressive model, is Gaussian white noise with a mean of 0 and a variance of , is the predicted state of the underwater vehicle.

[0009] The deep part of the autoencoder built is expressed as:

[0010] In the formula, represents the low-dimensional state extracted by the deep part autoencoder, Represents the mapping from raw input to output features established by a deep partial autoencoder network.

[0011] The encoding process of the encoder of the deep partial autoencoder is expressed as:

[0012]

[0013] Among them, the status data of the underwater vehicle In the first layer network weights After linear weighting, under the mapping of the activation function tanh function, the first layer output is obtained , and the encoder layer output features are obtained in turn , Indicates the bias of each layer of the network; The decoding process of the decoder of the deep partial autoencoder is to extract the encoder layer output features The process of generating raw data is expressed as:

[0014] in, As the input of the decoder, through the network weights Multiply them together, and under the mapping of the activation function tanh function, we finally get the desired output o. The loss function is designed based on the output error of the deep partial autoencoder, the output error of the multi-output Gaussian process, and the LASSO regularization criterion, and is expressed as:

[0015] In the formula, , is the penalty coefficient, is the number of samples in the training set, is the expected output of the deep partial autoencoder, is the actual output of the deep partial autoencoder, is the weight of the deep part autoencoder feature layer, The number of neurons in the feature layer connected to the deep part of the autoencoder, y is the predicted output of the multi-output Gaussian process, is the prediction error, It is expressed as:

[0016] In the formula, is the actual output of the underwater vehicle, is the penalty coefficient.

[0017] The network structure of the deep partial autoencoder is [27-64-32-6-32-64-9], the network input data is 27 dimensions, the output feature data is 6 dimensions, and the encoder output data is 9 dimensions.

[0018] The mapping relationship between the multi-output Gaussian process and the deep partial autoencoder is expressed as:

[0019] In the formula, represents the low-dimensional state extracted by the deep part autoencoder, represents the feature input to output mapping based on the multi-output Gaussian process, is Gaussian white noise.

[0020] The model training error is measured using the root mean square error.

[0021] The outputs of the autoregressive model are: predicted lateral velocity, roll rate, and heading rate.

[0022] Compared with the prior art, the beneficial effects of this application are: 1. This application designs a method based on the combination of a deep partial autoencoder and a multi-output Gaussian process system, which reduces the input space dimension of the multi-output Gaussian process and improves the prediction efficiency of the multi-output Gaussian process.

[0023] 2. The deep partial autoencoder designed in this application has an output dimension that is smaller than the input dimension. Compared with traditional encoders, it not only reduces the training error of the network, but also improves the training speed of the encoder network.

[0024] 3. The loss function designed in this application enables the encoder to effectively extract the state data characteristics of the underwater vehicle according to the prediction target, thereby reducing the input dimension of the multi-output Gaussian process and improving the training efficiency of the multi-output Gaussian process. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a method flow chart of the present application; Figure 2 It is the algorithm framework diagram of this application; Figure 3 It is a schematic diagram of the structure of the deep partial autoencoder; Figure 4 This is the prediction effect diagram of the heading angular velocity of the underwater vehicle; Figure 5 This is the effect diagram of the lateral velocity prediction of the underwater vehicle; Figure 6 This is the prediction effect diagram of the rolling angular velocity of the underwater vehicle; Figure 7 is the training error plot of a standard autoencoder; Figure 8 is the training error graph of the deep partial autoencoder. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solution and advantages of the present application more clear, the present application is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described here are only used to explain the present application and are not used to limit the present application.

[0027] The present application is further described below in conjunction with embodiments, and the present application includes but is not limited to the following embodiments.

[0028] like Figure 1 , 2 As shown, the present application provides a multi-output Gaussian process regression underwater vehicle system identification algorithm based on a deep partial autoencoder, and the specific process is as follows: Step 1, design an adjustable sawtooth vertical rudder input signal, apply the adjustable sawtooth vertical rudder input signal to the underwater vehicle system, and obtain 12 state data of the underwater vehicle: specifically including: obtaining the linear velocity and angular velocity ,in, , , They represent the longitudinal speed, vertical speed and lateral speed of the vehicle respectively; , , They represent the rolling angular velocity, heading angular velocity and pitch angular velocity of the vehicle respectively; , , Respectively represent the lateral, longitudinal and vertical positions of the aircraft; , , Respectively represent the roll angle, pitch angle and heading angle of the aircraft, and divide the data set into 50% for training and 50% for validation; Step 2: construct an autoregressive model based on the underwater vehicle dynamics model. Considering the characteristics of the underwater vehicle model, this application adopts a nonlinear autoregressive model (NARX) with external input, which is expressed as: (1) Formula (1) is the NARX model, is the status data of the underwater vehicle, The input for the underwater vehicle includes the rudder angle and thruster. is the order of the NARX model, is Gaussian white noise with a mean of 0 and a variance of , is the predicted state of the underwater vehicle; In this application, the mapping relationship between the multi-output Gaussian process and the deep partial autoencoder can be expressed as: (2) (3) In the formula, represents the low-dimensional state extracted by the deep part autoencoder, represents the feature input to output mapping based on the multi-output Gaussian process, Represents the mapping from raw input to output features established by the autoencoder network.

[0029] First, the high-dimensional input of the autoregressive model in formula (1) is used as the encoder network Input, the low-dimensional feature data obtained As a multi-output Gaussian process The predicted target state is the output of the autoregressive model in formula (1).

[0030] Step 3: build a deep partial autoencoder according to the autoregressive model constructed in step 2, and use the training set data to train the deep partial autoencoder network, and use the low-dimensional feature data extracted by the deep partial autoencoder network to construct a loss function to update the gradient of the deep partial autoencoder; Design a deep partial autoencoder to extract features from the multi-dimensional data input by the underwater vehicle system, reduce the input dimension of the Gaussian process, and reduce the computational complexity of multi-output Gaussian process prediction. In this application, based on the characteristics of the underwater vehicle system, the network structure of the deep partial autoencoder is [27-64-32-6-32-64-9], the network input is 27 dimensions, the output is 6 dimensions, and the encoder output is 9 dimensions.

[0031] Assuming input , the encoding process of the encoder of the deep part autoencoder is expressed as: (4) (5) Among them, the status data of the underwater vehicle In the first layer network weights After linear weighting, under the mapping of the activation function tanh function, the first layer output is obtained , and the encoder layer output features are obtained in turn , Represents the bias of each layer of the network.

[0032] The decoding process of the decoder of the deep partial autoencoder is through the extracted features The process of generating raw data: (6) in, As the input of the decoder, through the network weights Multiply them together, and under the mapping of the activation function tanh function, we finally get the desired output o. The input of the traditional autoencoder is s, and the output should also be s. However, in order to improve the training speed, the autoencoder designed in this application has a lower dimension of output o than the original input s, that is, , reducing the training time of the deep partial autoencoder network and reducing the training error.

[0033] The loss function designed according to the error of the deep partial autoencoder, the error of the multi-output Gaussian process, and the LASSO regularization criterion is expressed as: (7) In the formula, , is the penalty coefficient, is the number of samples in the training set, is the expected output of the deep partial autoencoder, is the actual output of the deep partial autoencoder, is the weight of the deep part autoencoder feature layer, The number of neurons in the feature layer connected to the deep partial autoencoder; is the predicted output of the multi-output Gaussian process, The prediction error is expressed as: (8) In the formula, is the actual output of the underwater vehicle, is the penalty coefficient.

[0034] The loss function of the deep partial autoencoder designed in this application not only includes the output error of the deep partial autoencoder itself, but also includes the output error of the multi-output Gaussian process, so that the features extracted by the deep partial autoencoder are more accurate and the prediction accuracy of the multi-output Gaussian process is improved. The L1 regularization criterion of LASSO sparses the feature layer, reduces the dimension of the feature layer, and thus reduces the dimension of the multi-output Gaussian process.

[0035] In step 4, the six features of the underwater vehicle extracted by the depth encoder and the input rudder angle and thruster of the underwater vehicle are used as the input of the multi-output Gaussian process, and the output of the autoregressive model is used as the output of the multi-output Gaussian process to predict the state of the underwater vehicle. .

[0036] Due to the longitudinal velocity of the underwater vehicle Generally, it is constant, and its vertical plane is mostly in a stable state during the diving process, that is, the vertical speed is a constant value, and the pitch angle remains basically unchanged, that is, , Therefore, this application only identifies the horizontal plane state of the underwater vehicle, that is, the lateral speed , rolling angular velocity , heading angular velocity .

[0037] For underwater vehicle systems, the deep partial autoencoder network designed in this application can reduce the 27-dimensional feature data to 6 dimensions as the input of the multi-output Gaussian process regression algorithm, such as Figure 3 According to the characteristics of the underwater vehicle system and empirical estimation, the model order n=3 is selected, that is, the input of the encoder is , the output of the decoder is Then the 6 features extracted by the encoder and the 2 input vertical rudders that control the horizontal plane state are used. , differential rudder Together as the input of the multi-output Gaussian process algorithm, the state lateral velocity of the underwater vehicle is predicted , rolling angular velocity , heading angular velocity .

[0038] Adjust the penalty coefficient of the loss function according to the prediction effect, , , The particle swarm population is set to 20, the maximum number of iterations is 100, and the accuracy of iteration termination is After the training is completed, the validation set is used for verification in step 5.

[0039] Simulation Results Analysis like Figures 4 to 6 As shown, the multi-output Gaussian process of the present application can accurately predict the underwater vehicle attitude, where the red solid line represents the predicted state (heading angular velocity, lateral angular velocity and rolling angular velocity), the blue dotted line represents the true value, and the gray area represents 2 Confidence interval; e.g. Figure 4As shown, the horizontal axis represents time, the vertical axis represents the heading angular velocity, and the root mean square error (RMSE) of the heading angle predicted by this application is 0.0027 rad / s; Figure 5 As shown, the horizontal axis represents time, the vertical axis represents lateral velocity, and the root mean square error (RMSE) of the predicted lateral velocity is 0.0030 m / s; Figure 6 As shown, the horizontal axis represents time, the vertical axis represents the rolling angular velocity, and the root mean square error (RMSE) of the rolling angular velocity does not exceed 0.0029 rad / s.

[0040] From the perspective of prediction time, when predicting 200 s of data, without adding the deep partial autoencoder, the prediction time of the multi-output Gaussian process is 8.49 s. After the deep partial autoencoder extracts features, the prediction time is reduced to 5.22 s, which improves the prediction time by 38%.

[0041] like Figure 7 and Figure 8 As shown, the horizontal axis is the number of iterations, and the vertical axis is the root mean square error. Figure 7 and Figure 8 By comparison, it can be seen that the training process error of the deep partial autoencoder is smoother than that of the standard autoencoder, and the error of the deep autoencoder is smaller. In addition, under the same sample, the training time of the partial autoencoder designed in this application is 9s, and the training time of the standard autoencoder is 20s, which improves the training speed of the autoencoder network.

[0042] It can be seen that from the perspective of time and error, the multi-output Gaussian process regression algorithm based on the deep partial horizontal coordinate autoencoder has higher prediction efficiency.

[0043] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the protection scope of the present invention.

Claims

1. A multi-output Gaussian process regression underwater vehicle system identification algorithm based on deep partial autoencoder, characterized in that: The following steps are involved: Step 1, designing an adjustable amplitude sawtooth vertical rudder input signal, applying the adjustable amplitude sawtooth vertical rudder input signal to the underwater vehicle system, obtaining the state data of the underwater vehicle, and dividing the training set and the verification set; Step 2, constructing an autoregressive model based on the underwater vehicle dynamics according to the state data of the underwater vehicle obtained in step 1; Step 3: build a deep partial autoencoder according to the autoregressive model constructed in step 2, and use the training set data to train the deep partial autoencoder network, and use the low-dimensional feature data extracted by the deep partial autoencoder network to construct a loss function to update the gradient of the deep partial autoencoder; Step 4. Use the low-dimensional feature data extracted by the deep partial autoencoder as the input of the multi-output Gaussian process, use the output of the autoregressive model as the output of the multi-output Gaussian process, search for the hyperparameters of the multi-output Gaussian process through the particle swarm algorithm, and perform model training; Step 5: When the model training error reaches the preset accuracy, the model training is completed, and the model is verified using the validation set data.

2. According to claim 1, a multi-output Gaussian process regression underwater vehicle system identification algorithm based on deep partial autoencoder is characterized in that: Obtaining the state data of the underwater vehicle, specifically including: obtaining the linear velocity v = [v x v y v z ω x ω y ω z ] T and angular velocity Among them, v x 、v y 、v z Respectively represent the longitudinal velocity, vertical velocity and lateral velocity of the vehicle; ω x ,ω y ,ω z They represent the rolling angular velocity, heading angular velocity and pitch angular velocity of the aircraft respectively; x, y, z represent the lateral, longitudinal and vertical positions of the aircraft respectively; θ and ψ represent the rolling angle, pitch angle and heading angle of the vehicle respectively.

3. The multi-output Gaussian process regression underwater vehicle system identification algorithm based on deep partial autoencoder according to claim 2 is characterized in that: The autoregressive model is expressed as: y(k)=f[s(k-1),…s(kn),…u(k)]+ε(k) Among them, s is the state data of the underwater vehicle, u is the input of the underwater vehicle, including the rudder angle and the thruster, n is the order of the autoregressive model, ε is Gaussian white noise with a mean of 0 and a variance of y is the predicted state of the underwater vehicle.

4. The multi-output Gaussian process regression underwater vehicle system identification algorithm based on deep partial autoencoder according to claim 3 is characterized in that: The deep part of the autoencoder built is expressed as: z=f DPAE [s(k-1),s(k-2),…s(k-n),u(k)] Where z represents the low-dimensional state extracted by the deep part autoencoder, and f DPAE Represents the mapping from raw input to output features established by a deep partial autoencoder network.

5. The multi-output Gaussian process regression underwater vehicle system identification algorithm based on deep partial autoencoder according to claim 4 is characterized in that: The encoding process of the encoder of the deep partial autoencoder is expressed as: Among them, the state data s of the underwater vehicle is linearly weighted by the first layer network weight W1, and under the mapping of the activation function tanh function, the first layer output h1 is obtained, and the encoder layer output feature z is obtained in turn, and b represents the bias of each layer network; The decoding process of the decoder of the deep partial autoencoder is the process of generating the original data through the extracted encoder layer output feature z, which is expressed as: Among them, z is used as the input of the decoder. By multiplying it with the network weight W, under the mapping of the activation function tanh function, the desired output o is finally obtained.

6. The multi-output Gaussian process regression underwater vehicle system identification algorithm based on deep partial autoencoder according to claim 5 is characterized in that: The loss function is designed based on the output error of the deep partial autoencoder, the output error of the multi-output Gaussian process, and the LASSO regularization criterion, and is expressed as: In the formula, λ and β are penalty coefficients, N is the number of training set samples, and o is the expected output of the deep part autoencoder. is the actual output of the deep partial autoencoder, is the weight of the deep autoencoder feature layer, n z The number of neurons in the feature layer of the deep autoencoder connected, y is the predicted output of the multi-output Gaussian process, L(μ) is the predicted error, and L(μ) is expressed as: Where y' is the actual output of the underwater vehicle, and α is the penalty coefficient.

7. The multi-output Gaussian process regression underwater vehicle system identification algorithm based on deep partial autoencoder according to claim 6 is characterized in that: The network structure of the deep partial autoencoder is [27-64-32-6-32-64-9], the network input data is 27 dimensions, the output feature data is 6 dimensions, and the encoder output data is 9 dimensions.

8. The multi-output Gaussian process regression underwater vehicle system identification algorithm based on deep partial autoencoder according to claim 7 is characterized in that: The mapping relationship between the multi-output Gaussian process and the deep partial autoencoder is expressed as: y(k)=f MOGP (z)+ε(k) Where z represents the low-dimensional state extracted by the deep part autoencoder, and f MOGP It represents the feature input to output mapping based on the multi-output Gaussian process, and ε is Gaussian white noise.

9. The multi-output Gaussian process regression underwater vehicle system identification algorithm based on deep partial autoencoder according to claim 8, characterized in that: The model training error is measured using the root mean square error.

10. The multi-output Gaussian process regression underwater vehicle system identification algorithm based on deep partial autoencoder according to claim 1, characterized in that: The outputs of the autoregressive model are: predicted lateral velocity, roll rate, and heading rate.

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