A multi-output gaussian process regression underwater vehicle system identification algorithm based on deep partial autoencoder

Abstract

The application discloses a multi-output Gaussian process regression underwater vehicle system identification algorithm based on a deep partial self-encoder, and comprises the following steps: designing an adjustable amplitude sawtooth vertical rudder input signal, acquiring state data of an underwater vehicle and dividing a training set and a verification set; constructing an autoregressive model based on underwater vehicle dynamics according to the state data; building a deep partial self-encoder according to the autoregressive model; taking low-dimensional feature data extracted by the deep partial self-encoder as input of a multi-output Gaussian process, taking output of the autoregressive model as output of the multi-output Gaussian process, searching hyperparameters of the multi-output Gaussian process through a particle swarm algorithm, and training the model; when a model training error reaches preset precision, the model training is completed, and the model is verified by using verification set data; and the problem that high-dimensional input of the multi-output Gaussian process increases calculation of a kernel function and searching time of the hyperparameters, increases complexity of the model and reduces prediction efficiency of the multi-output Gaussian process is solved.

Description

Technical Field

[0001] This invention belongs to the field of underwater vehicle navigation prediction technology, specifically relating to a multi-output Gaussian process regression underwater vehicle system identification algorithm based on a depth partial autoencoder. Background Technology

[0002] Underwater vehicles, due to their long range, high operational precision, and reusability, have become indispensable tools for humankind in understanding and exploring the ocean, and their application has become increasingly widespread in recent years. Dynamic system models are the foundation for underwater vehicle motion control, condition monitoring, fault diagnosis, and fault-tolerant system development, and are one of the core contents of underwater robot research. Nonparametric modeling requires almost no prior information about the underwater robot model structure to obtain accurate predictions. Multi-output Gaussian process regression models have a statistical basis; essentially, they are regression models based on a Bayesian framework. This model performs well in handling small samples and nonlinear problems. On the one hand, the output data inherently contains confidence intervals, a key characteristic of Gaussian processes; on the other hand, statistical methods are used to find the conditional distribution between input and output variables, thereby establishing a regression equation between them. The prediction result of a multi-output Gaussian process regression model is not a single precise value, but a predicted value that includes the mean and variance, and its prediction result is an interval. Therefore, multi-output Gaussian process regression models can carry over the uncertainty of the prediction to the next prediction, thus propagating uncertainty.

[0003] However, multi-output Gaussian process (MIG) modeling requires a large number of samples to cover the feature space, especially for complex nonlinear systems such as underwater vehicles. Sufficient input feature information is needed to enhance the model's generalization ability and improve prediction accuracy. However, the high-dimensional input of MMG increases the computation time of the kernel function and the search time of hyperparameters, increasing the complexity of the model and reducing the prediction efficiency of MMG. Summary of the Invention

[0004] To overcome the aforementioned technical problems, this application provides a multi-output Gaussian process regression underwater vehicle system identification algorithm based on a deep partial autoencoder. Addressing the issue that the high-dimensional input of the multi-output Gaussian process increases the computation time of the kernel function and the search time of hyperparameters, thereby increasing model complexity and reducing the prediction efficiency of the multi-output Gaussian process, this application proposes using a deep partial autoencoder to reduce the input dimension of the multi-output Gaussian process, thus reducing the loss function of the encoder network. Simultaneously, the autoencoder extracts features from the high-dimensional state data of the underwater vehicle in high-dimensional space, using the obtained low-dimensional feature data as input to the multi-output Gaussian process regression algorithm, thereby improving the prediction efficiency of the multi-output Gaussian process regression.

[0005] To achieve the above objectives, the technical solution adopted in this application is as follows: A multi-output Gaussian process regression algorithm for underwater vehicle system identification based on a depth partial autoencoder includes the following steps: Step 1: Design an adjustable amplitude sawtooth vertical rudder input signal, apply the adjustable amplitude sawtooth vertical rudder input signal to the underwater vehicle system, obtain the underwater vehicle's state data, and divide the system into training and validation sets. Step 2: Based on the underwater vehicle state data obtained in Step 1, construct an autoregressive model based on underwater vehicle dynamics. Step 3: Build a deep partial autoencoder based on the autoregressive model constructed in Step 2, train the deep partial autoencoder network using the training set data, 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 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 using the particle swarm optimization algorithm, and train the model. Step 5: Once the model training error reaches the preset accuracy, the model training is complete. Then, the model is validated using the validation set data.

[0006] Acquire the status data of the underwater vehicle, specifically including: acquiring the linear velocity. and angular velocity ,in, , , These represent the longitudinal velocity, vertical velocity, and lateral velocity of the aircraft, respectively. , , These represent the roll rate, yaw rate, and pitch rate of the aircraft, respectively. , , These represent the lateral, longitudinal, and vertical positions of the aircraft, respectively. , , These represent the roll angle, pitch angle, and heading angle of the aircraft, respectively.

[0007] The autoregressive model is expressed as:

[0008] in, This is the status data of the underwater vehicle. Inputs to underwater vehicles include rudder angle and thrusters. The order of the autoregressive model is given by [the model name]. It is Gaussian white noise with a mean of 0 and a variance of 0. , The predicted state of the underwater vehicle.

[0009] The constructed depth-part autoencoder is represented as:

[0010] In the formula, This represents the low-dimensional state extracted by the depth autoencoder. This represents the mapping from the original input to the output features established by the deep partial autoencoder network.

[0011] The encoding process of the depth-part autoencoder is represented as follows:

[0012]

[0013] Among them, the status data of underwater vehicles First layer network weights After linear weighting, the first layer output is obtained under the mapping of the activation function tanh. The encoder layer output features are obtained sequentially. , This represents the bias of each layer of the network. The decoding process of a depth partial autoencoder decoder involves extracting the output features of the encoder layer. The process of generating the original data can be represented as follows:

[0014] in, As input to the decoder, through interaction with network weights Multiplying these components and mapping them using the activation function tanh, we finally obtain the desired output o. The loss function is designed based on the output error of the depth autoencoder, the output error of the multi-output Gaussian process, and the LASSO regularization criterion, and is expressed as:

[0015] In the formula, , The penalty coefficient is... The number of samples in the training set. The desired output of the depth partial autoencoder. This is the actual output of the depth-part autoencoder. The weights of the feature layer of the deep autoencoder are... The number of feature layer neurons in the deep partial autoencoder, where y is the predicted output of the multi-output Gaussian process. For the prediction error, Represented as:

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

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

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

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

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

[0021] The output of the autoregressive model is the 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 a 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 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 features of the underwater vehicle based on 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. Attached Figure Description

[0025] Figure 1 This is a flowchart of the method in this application; Figure 2 This is a diagram of the algorithm framework of this application; Figure 3 This is a schematic diagram of the depth autoencoder structure; Figure 4 This is a diagram illustrating the predicted heading angular velocity of an underwater vehicle. Figure 5 This is a diagram illustrating the predicted lateral velocity of an underwater vehicle. Figure 6 This is a rendering of the predicted roll rate of an underwater vehicle. Figure 7 This is a training error map of a standard autoencoder; Figure 8 This is the training error map of the depth autoencoder. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0027] The present application will be further described below with reference to the embodiments, which include, but are not limited to, the following embodiments.

[0028] like Figure 1 , 2 As shown, this application provides a multi-output Gaussian process regression underwater vehicle system identification algorithm based on a depth partial autoencoder, the specific process of which is as follows: Step 1: Design an adjustable amplitude sawtooth vertical rudder input signal and apply it to the underwater vehicle system to acquire 12 status data points of the underwater vehicle, specifically including: acquiring linear velocity. and angular velocity ,in, , , These represent the longitudinal velocity, vertical velocity, and lateral velocity of the aircraft, respectively. , , These represent the roll rate, yaw rate, and pitch rate of the aircraft, respectively. , , These represent the lateral, longitudinal, and vertical positions of the aircraft, respectively. , , The roll angle, pitch angle, and yaw angle of the aircraft are represented respectively. The dataset is divided into a training set and a validation set, with 50% as the training set and 50% as the validation set. 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, expressed as: (1) Equation (1) is the NARX model. This is the status data of the underwater vehicle. Inputs to underwater vehicles include rudder angle and thrusters. Let be the order of the NARX model. It is Gaussian white noise with a mean of 0 and a variance of 0. , For the predicted state of underwater vehicles; In this application, the mapping relationship between the multi-output Gaussian process and the depth partial autoencoder can be expressed as: (2) (3) In the formula, This represents the low-dimensional state extracted by the depth autoencoder. This represents the feature input-to-output mapping established based on a multi-output Gaussian process. This represents the mapping from the original input to the 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. The input is used to obtain low-dimensional feature data. As a multi-output Gaussian process The input is the target state, and the output of the autoregressive model is the formula (1).

[0030] Step 3: Build a deep partial autoencoder based on the autoregressive model constructed in Step 2, train the deep partial autoencoder network using the training set data, 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. This paper designs a depth-part autoencoder to extract features from the multidimensional input data of an underwater vehicle system, reducing the input dimensionality of the Gaussian process and lowering the computational cost of multi-output Gaussian process prediction. Based on the characteristics of the underwater vehicle system, this application constructs a depth-part autoencoder network structure of [27-64-32-6-32-64-9], with a 27-dimensional input, a 6-dimensional output, and a 9-dimensional encoder output.

[0031] Assuming input The encoding process of the depth-part autoencoder is represented as follows: (4) (5) Among them, the status data of underwater vehicles First layer network weights After linear weighting, the first layer output is obtained under the mapping of the activation function tanh. The encoder layer output features are obtained sequentially. , This represents the bias of each layer of the network.

[0032] The decoding process of a depth partial autoencoder decoder is based on the extracted features. The process of generating raw data: (6) in, As input to the decoder, through interaction with network weights Multiplying these components and mapping them using the activation function tanh, we finally obtain the desired output o. Traditional autoencoders have an input 's' and should output 's' as well. However, the autoencoder designed in this application, in order to improve training speed, has an output 'o' with a lower dimension than the original input 's'. This reduces the training time of deep partial autoencoder networks and lowers training error.

[0033] The loss function designed based on the errors of the depth autoencoder, the multi-output Gaussian process, and the LASSO regularization criterion is expressed as follows: (7) In the formula, , The penalty coefficient is... The number of samples in the training set. The desired output of the depth partial autoencoder. This is the actual output of the depth-part autoencoder. The weights of the feature layer of the deep autoencoder are... The number of feature layer neurons in the deep partial autoencoder; For the predicted output of a multi-output Gaussian process, The error in the prediction is expressed as: (8) In the formula, This represents the actual output of the underwater vehicle. This 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 the output error of the multi-output Gaussian process, making the features extracted by the deep partial autoencoder more accurate and improving the prediction accuracy of the multi-output Gaussian process. The L1 regularization criterion of LASSO sparsifies the feature layer, reducing the dimensionality of the feature layer, thereby reducing the dimensionality of the multi-output Gaussian process.

[0035] In step 4, the six features of the underwater vehicle extracted by the depth encoder, along with the input rudder angle and thruster of the underwater vehicle, are used as inputs to a multi-output Gaussian process. 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 speed of the underwater vehicle Generally, the vertical velocity remains constant, and its vertical plane is mostly in a stable state during the descent, i.e., the vertical velocity is constant. The pitch angle remains essentially constant, i.e., , Therefore, this application only identifies the lateral plane state of the underwater vehicle, i.e., its lateral velocity. Roll rate angular velocity of heading .

[0037] For underwater vehicle systems, this application designs a depth-part autoencoder network to compress 27-dimensional feature data to 6 dimensions, which is then used as input to a multi-output Gaussian process regression algorithm. Figure 3 The structure is shown. Based on the characteristics of the underwater vehicle system and empirical estimation, the model order n=3 is selected, meaning the encoder input is... The decoder output is Then, the six features extracted by the encoder and the two input vertical rudders controlling the transverse plane state are used. Differential rudder Together, they are used as inputs to a multi-output Gaussian process algorithm to predict the lateral velocity of an underwater vehicle. Roll rate angular velocity of heading .

[0038] Adjust the penalty coefficient of the loss function based on the prediction performance. , , The particle swarm optimization population size is set to 20, the maximum number of iterations is 100, and the iteration termination precision is [value missing]. After training is complete, step 5 involves validation using a validation set.

[0039] Simulation Result Analysis like Figures 4 to 6 As shown, the multi-output Gaussian process of this application can accurately predict the attitude of an underwater vehicle. The solid red lines represent the predicted states (heading angular velocity, lateral angular velocity, and roll angular velocity), the dashed blue lines represent the true values, and the gray area represents 2... Confidence interval; such as Figure 4As shown, the horizontal axis represents time, and the vertical axis represents the heading angular velocity. The root mean square error (RMSE) of the heading angle predicted in this application is 0.0027 rad / s; Figure 5 As shown, the horizontal axis represents time, and the vertical axis represents lateral velocity. 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 roll velocity, and the root mean square error (RMSE) of roll velocity does not exceed 0.0029 rad / s.

[0040] Analyzing the prediction time, predicting 200 seconds of data without a deep partial autoencoder and using a multi-output Gaussian process takes 8.49 seconds. After feature extraction using a deep partial autoencoder, the prediction time is reduced to 5.22 seconds, improving the prediction time by 38%.

[0041] like Figure 7 and Figure 8 As shown, the horizontal axis represents the number of iterations, and the vertical axis represents the root mean square error. Figure 7 and Figure 8 The comparison shows that the training error of the deep partial autoencoder is smoother than that of the standard autoencoder, and the error of the deep autoencoder is smaller. Furthermore, under the same sample conditions, the training time of the partial autoencoder designed in this application is 9 seconds, while the training time of the standard autoencoder is 20 seconds, thus improving the training speed of the autoencoder network.

[0042] Therefore, it can be seen from both time and error perspectives that the multi-output Gaussian process regression algorithm based on the depth part of the horizontal axis autoencoder has higher prediction efficiency.

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

Claims

1. A method for identifying underwater vehicle systems based on a multi-output Gaussian process regression using a depth partial autoencoder, characterized in that, Includes the following steps: Step 1: Design an adjustable amplitude sawtooth vertical rudder input signal, apply the adjustable amplitude sawtooth vertical rudder input signal to the underwater vehicle system, obtain the underwater vehicle's state data, and divide the system into training and validation sets. Step 2: Based on the underwater vehicle's state data obtained in Step 1, construct an autoregressive model based on the underwater vehicle's dynamics; the autoregressive model is expressed as: in, This is the status data of the underwater vehicle. Inputs to underwater vehicles include rudder angle and thrusters. Let be the order of the autoregressive model. It is Gaussian white noise with a mean of 0 and a variance of 0. , For the predicted state of underwater vehicles; Step 3: Based on the autoregressive model constructed in Step 2, build a deep partial autoencoder (MMO). Train the MMO network using the training set data. Use the low-dimensional feature data extracted by the MMO network to construct a loss function to update the gradient of the MMO. The constructed MMO is represented as follows: In the formula, This represents the low-dimensional state extracted by the depth autoencoder. This represents the mapping from the original input to the output features established by the deep partial autoencoder network; Step 4: Use the low-dimensional feature data extracted by the deep 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 using the particle swarm optimization algorithm, and train the model. Step 5: Once the model training error reaches the preset accuracy, the model training is complete. Then, the model is validated using the validation set data.

2. The method for identifying underwater vehicle systems based on a multi-output Gaussian process regression using a depth partial autoencoder as described in claim 1, characterized in that, Acquire the status data of the underwater vehicle, specifically including: acquiring the linear velocity. and angular velocity ,in, , , These represent the longitudinal velocity, vertical velocity, and lateral velocity of the aircraft, respectively. , , These represent the roll rate, yaw rate, and pitch rate of the aircraft, respectively. , , These represent the lateral, longitudinal, and vertical positions of the aircraft, respectively. , , These represent the roll angle, pitch angle, and heading angle of the aircraft, respectively.

3. The method for identifying underwater vehicle systems based on a multi-output Gaussian process regression using a depth partial autoencoder according to claim 2, characterized in that, The encoding process of the depth-part autoencoder is represented as follows: Among them, the status data of underwater vehicles First layer network weights After linear weighting, the first layer output is obtained under the mapping of the activation function tanh. The encoder layer output features are obtained sequentially. , This represents the bias of each layer of the network. The decoding process of a depth partial autoencoder decoder involves extracting the output features of the encoder layer. The process of generating the original data can be represented as follows: in, As input to the decoder, through interaction with network weights Multiplying these components and mapping them using the activation function tanh, we finally obtain the desired output o.

4. The method for identifying underwater vehicle systems based on a multi-output Gaussian process regression using a depth partial autoencoder according to claim 3, characterized in that, The loss function is designed based on the output error of the depth autoencoder, the output error of the multi-output Gaussian process, and the LASSO regularization criterion, and is expressed as: In the formula, , The penalty coefficient is... The number of samples in the training set. The desired output of the depth partial autoencoder. This is the actual output of the depth-part autoencoder. The weights of the feature layer of the deep autoencoder are... The number of feature layer neurons in the deep partial autoencoder, where y is the predicted output of the multi-output Gaussian process. For the prediction error, Represented as: In the formula, This represents the actual output of the underwater vehicle. This is the penalty coefficient.

5. The method for identifying underwater vehicle systems based on a multi-output Gaussian process regression using a depth partial autoencoder according to claim 4, characterized in that, The network structure of the depth autoencoder is [27-64-32-6-32-64-9]. The network input data is 27-dimensional, the output feature data is 6-dimensional, and the encoder output data is 9-dimensional.

6. The method for identifying underwater vehicle systems based on a multi-output Gaussian process regression using a depth partial autoencoder according to claim 5, characterized in that, The mapping relationship between the multi-output Gaussian process and the depth partial autoencoder is expressed as: In the formula, This represents the low-dimensional state extracted by the depth autoencoder. This represents the feature input-to-output mapping established based on a multi-output Gaussian process. It is Gaussian white noise.

7. The method for identifying underwater vehicle systems based on a multi-output Gaussian process regression using a depth partial autoencoder according to claim 6, characterized in that, The model training error is measured using the root mean square error.

8. The method for identifying underwater vehicle systems based on a multi-output Gaussian process regression using a depth partial autoencoder according to claim 1, characterized in that, The output of the autoregressive model is the predicted lateral velocity, roll rate, and heading rate.

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