Underwater pipeline track prediction method based on extended Kalman filtering and LSTM

Abstract

The invention discloses an underwater pipeline trajectory prediction method based on extended Kalman filtering and LSTM, and the method comprises the steps: building an underwater state space model of a pipeline based on a target tracking theory, and generating the simulation data of an underwater pipeline trajectory; then, an LSTM-EKF is built, and three features are built for LSTM network training input based on an extended Kalman filtering structure; selecting a training algorithm based on a principle of realizing a maximum training effect, including selection of a loss function and selection of a model training algorithm, and training the extended Kalman neural network; and finally, considering the mismatching condition of the pipeline model, testing a basic algorithm, expanding Kalman filtering, and expanding the underwater pipeline prediction result of the Kalman neural network. According to the method, the LSTM network is integrated based on the Kalman filtering process, the interpretability which a traditional deep learning network does not have is increased, compared with a traditional algorithm, the precision is higher, and the difference is little compared with a perfect ideal condition.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater pipeline tracking, and specifically relates to an underwater pipeline trajectory prediction method based on extended Kalman filtering and LSTM. Background Art

[0002] The state estimation of the real-time dynamic system of underwater pipelines is a basic requirement for pipeline tracking tasks. However, in pipeline tracking practice, the linearity and accuracy of the underlying system model are often lacking. The underwater interference environment is complex. The pipeline information obtained by a simple sonar or camera may be distorted due to the shaking of the underwater platform and the interference of water flow. The obtained pipeline position information is very different from the actual situation. In addition, the external environmental interference cannot be simply summarized by Gaussian distribution. The traditional Kalman prediction method is limited. Therefore, whether the underwater pipeline trajectory can be accurately predicted to ensure that the AUV can complete the submarine pipeline inspection task is the main factor restricting the application of AUV in the field of pipeline inspection. At present, deep learning methods have been applied to various aspects of prediction. A new underwater pipeline prediction method based on traditional algorithms and deep learning is proposed. While retaining the advantages of traditional algorithms, it also increases the interpretability of deep learning methods. Summary of the invention

[0003] The purpose of the present invention is to provide an underwater pipeline trajectory prediction method based on extended Kalman filtering and LSTM, referred to as LSTM-EKF. The method based on extended Kalman filtering and LSTM not only solves the problem of poor interpretability of traditional deep learning, but also achieves higher accuracy compared with other algorithms.

[0004] The purpose of the present invention is achieved through the following technical solutions:

[0005] A method for predicting underwater pipeline trajectory based on extended Kalman filtering and LSTM, the steps are as follows:

[0006] Step 1: Based on the target tracking theory, the underwater state space model of the pipeline is established, and the Taylor expansion used to expand the Kalman filter is discretized to generate simulation data of the underwater pipeline trajectory;

[0007] Step 2: Build the extended Kalman neural network LSTM-EKF. Based on the extended Kalman filter structure, construct three features for LSTM network training input;

[0008] Step 3: Select a training algorithm based on the principle of achieving the maximum training effect, including the selection of loss function and model training algorithm, and train the extended Kalman neural network;

[0009] Step 4: Consider the mismatch of pipeline models, test the basic algorithm, expand the Kalman filter, and expand the underwater pipeline prediction results of the Kalman neural network.

[0010] Furthermore, the underwater state space model of the pipeline established in step 1 is:

[0011] Based on the target tracking theory, the underwater environment, and the simplified pipeline state estimation problem, the following two assumptions are made: First, the cable laid on the seabed is continuous and its state is measurable; second, the pipeline trajectory is regarded as the trajectory of the virtual particle movement. The sonar and camera installed on the underwater vehicle measure and estimate the pipeline state information in real time, which is considered to be the state of the virtual particle, and the pipeline is also regarded as the mass point movement; when modeling the underwater pipeline, without considering the depth parameter, the three-dimensional motion model is simplified to a two-dimensional motion model, and the pipeline is converted into the kinematic equation of the horizontal plane, with v as -20dB, r as 0.01, and Pipeline data were generated with Taylor order and T = 0.02 sampling interval.

[0012] Furthermore, the extended Kalman neural network LSTM-EKF constructed in step 2 is:

[0013] A separate LSTM unit is used for each tracked second-order statistical moment; the architecture is divided into separate LSTM units and FC layers and the interconnections between them. The network consists of three LSTM layers, cascaded with dedicated FC input and output layers; the first LSTM layer tracks the unknown state noise covariance Q, thereby tracking m 2 variables; similarly, the second and third LSTMs track Σ and S, and thus have m 2 and n 2 hidden state variables; the LSTM layers are interconnected so that the learned Q is used to calculate Σ, which is then used to obtain S, and finally to generate the Kalman filter gain; based on the structure of the extended Kalman filter, three features are selected as the input of the network, which are the difference between the observed statistical information and the state estimation, as well as the difference between the predicted observation and the actual observation.

[0014] Furthermore, the training algorithm selected in step 3 is:

[0015] LSTM-EKF is a system that uses labeled data sets for supervised training. It uses neural networks to calculate rather than directly generate posterior state estimates. It trains the entire system end-to-end and calculates the loss function based on the posterior estimate of the state. The estimated value belongs to the continuous space and uses the squared error loss function for training. The loss is passed from the output back to the K t In the calculation process, based on the output of LSTM-EKF, we get the K t The loss gradient of

[0016]

[0017] Among them, K t is the Kalman gain, which is used to update the state estimate at time t; Δy t is the increment of the observed value, that is, the difference between the observed value and the predicted value at time t. This value represents the deviation of the observed data relative to the predicted data; Δx t is the increment of the state estimate, that is, the difference between the actual state value and the predicted state value at time t. This value represents the deviation of the actual state from the predicted state; is the loss function L for the Kalman gain K t The partial derivative of ||K represents the impact of the change of Kalman gain on the loss function during the optimization process. The partial derivative is used to guide the adjustment of Kalman gain to minimize the loss function; t Δy t -Δx t || 2 It is the specific form of the squared error loss function, which represents the sum of squared differences between the observation increment and the state increment after Kalman gain adjustment; is the gradient of the loss function to the Kalman gain, indicating how to adjust the Kalman gain to minimize the loss function in the current state;

[0018] The data used for training includes trajectories of different lengths, each of which contains a pair of corresponding observation sequence and state sequence data. During the training process, the mapping relationship from observation to state is learned so that the corresponding state sequence can be accurately predicted when a new observation is given. The regularized mean square error is used as the training loss metric, and the gradient of the loss function with respect to the model parameters is calculated through the time backpropagation algorithm. The network parameters of the time span LSTM-EKF are shared, and forward and backward gradient transfers are performed on the entire trajectory. The calculated gradients will be passed to Adam optimization, and the Adam optimizer will update the model parameters.

[0019] Furthermore, three types of model mismatching situations are considered in step 4, including:

[0020] (1) Mismatch in state evolution caused by using an insufficient-order Taylor series approximation;

[0021] (2) State-observation mismatch: The presence of a mismatch in the observation model is simulated by using data generated by rotating the identity matrix by only one degree; this rotation is equivalent to a sensor bias of ≈0.55%;

[0022] (3) The state observation mismatch caused by the transition from continuous time sampling to discrete time sampling;

[0023] Based on the above conditions, the test is carried out. First, various basic algorithms are considered and the results are compared. The best performance is selected as the reference upper limit of the effect. Second, the prediction results of the extended Kalman filter algorithm when the model structure is completely known, as well as the prediction results of incompletely known and LSTM-EKF are met.

[0024] The beneficial effects of the present invention are:

[0025] (1) The present invention improves and innovates on the basis of the traditional extended Kalman filter method combined with deep learning neural network, and proposes a method for underwater pipeline trajectory prediction based on extended Kalman filter and LSTM, wherein the extended Kalman neural network can solve the limited or approximate state transfer function and observation mapping function, and at the same time, it is not clear that the Kalman prediction under the conditions of noise statistical distribution Q and R is not suitable, and can learn from the labeled data to obtain the second-order statistics without the need for the noise distribution of the ocean environment. The present invention integrates the LSTM network into the Kalman filter process based on the Kalman filter process, which increases the interpretability that the traditional deep learning network does not have.

[0026] (2) The extended Kalman neural network proposed in the present invention is simple and clear in structure and simple and feasible in specific deployment and implementation. The present invention is applied to underwater pipeline prediction to improve the tracking accuracy of the predicted trajectory. The underwater pipeline trajectory prediction method based on extended Kalman filtering and LSTM proposed in the present invention has higher accuracy than traditional algorithms and is not much different from the perfect ideal situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a neural network flow chart of the underwater pipeline trajectory prediction method based on extended Kalman filtering and LSTM in an embodiment of the present invention;

[0028] Figure 2 This is a comparison diagram of the underwater pipeline trajectory prediction method based on extended Kalman filtering and LSTM in an embodiment of the present invention with the traditional algorithm;

[0029] Figure 3 This is a comparison chart of the results of the underwater pipeline trajectory prediction method based on the extended Kalman filter and LSTM in the embodiment of the present invention and the extended Kalman filter algorithm. DETAILED DESCRIPTION

[0030] The present invention is further described below in conjunction with the accompanying drawings.

[0031] Example 1

[0032] This embodiment provides an underwater pipeline trajectory prediction method based on extended Kalman filtering and LSTM, which can estimate the trajectory of underwater pipeline cables, and can also realize state estimation of drones, unmanned vehicle underwater equipment, etc. by changing the state space model. Overall, this embodiment includes two major steps: step S1: establish the state space equation of the underwater pipeline and generate underwater pipeline data; step S2: build an LSTM-EKF neural network, train and compare the prediction effect;

[0033] Step S1: According to the target tracking theory, the underwater pipeline prediction problem is simplified, the underwater pipeline state space equation is established, the state function is provided for the subsequent Kalman filter prediction, and the underwater pipeline data for training is generated;

[0034] The step S1 further comprises the following steps:

[0035] Step S11: Introduce target tracking theory, establish pipeline state equation, and make the following two assumptions to simplify the cable state estimation problem: (1) the cable laid on the seabed is continuous and its state is measurable; (2) the cable trajectory can be regarded as the trajectory of the motion of a virtual particle. The sonar and camera installed on the underwater vehicle can measure and estimate the pipeline state information in real time, which is considered to be the state of the virtual particle, and the pipeline is also regarded as the motion of the mass point.

[0036] Step S12: To further simplify the problem, when modeling underwater pipelines, since the pipeline is laid at a relatively certain depth on the seabed and the measurement accuracy is high, there is no need to perform the model solving process. Without considering the depth parameter, the three-dimensional motion model is simplified to a two-dimensional motion model, and the pipeline is converted into the kinematic equation of the horizontal plane:

[0037]

[0038] Step S13: Discretize the horizontal plane kinematic equations. The discretization form is as follows:

[0039] x k =Fx k-1 +Gu k +w k

[0040] The discretization result is:

[0041]

[0042] Among them, x k-1 is the state vector of the system at time step k-1, and F is the one-step state transfer matrix, which describes the evolution of the system state from time step k-1 to k. is the control input, which is ak 、v k and r k The vector of G is the control input matrix. k is the system noise, including speed measurement noise and heading measurement noise. The speed measurement is given by camera or sonar measurement conversion. The discrete time state evolution model in is adopted, and the process noise is added to generate simulated underwater pipeline state data. The observation function is set to the identity transformation so that the observed value is a noisy version of the real state.

[0043] Step S14: Use the discrete time state evolution model (additional process noise) to generate simulated underwater pipeline data for training the model, and use diagonal noise to generate a covariance matrix:

[0044]

[0045] Step S141: With v = -20dB, r = 0.01, Pipeline data were generated with Taylor order and T = 0.02 sampling interval.

[0046] Step S2: Build an LSTM-EKF neural network and test the network effect.

[0047] The step S2 further comprises the following steps:

[0048] Step S21: Extend the Kalman filter to apply to nonlinear systems:

[0049]

[0050] Among them, x t represents the hidden state vector of the system at time t, which is derived from the hidden state vector x at time t-1 t-1 The process noise e follows a linear white Gaussian noise (AWGN) distribution and a possibly nonlinear state transfer function f(·). t The evolution shows that the process noise has a covariance matrix Q. In equation (5), y t represents the observation vector at time t, which is derived from the current hidden state vector x of the system t Via a possibly nonlinear observation mapping function h(·) and a measurement noise v following an AWGN distribution t The measurement noise v t With the covariance matrix R, EKF linearizes the above nonlinear model and estimates X t-1|t-1 and estimate x t|t-1 Taylor expansion is performed at, where:

[0051] F t =J f (xt-1|t-1 )

[0052] H t =J h (x t|t-1 )

[0053] Step S211: The trajectory prediction process according to the extended Kalman filter algorithm is as follows:

[0054] The state prediction algorithm is as follows. The state prediction equation of the underwater pipeline is defined as:

[0055] x t|t-1 =F·x t-1|t-1

[0056] Among them, x t|t-1 is the predicted value in the target state space at time t, based on the information at time t-1. t-1|t-1 is the estimated value of the target state space at time t-1, that is, the state estimate after combining the observation data at time t-1. F is the state transition matrix of the system, which describes the change of the target state from time t-1 to time t.

[0057] The predicted state covariance equation is defined as follows:

[0058] ∑ t|t-1 =F·∑ t-1|t-1 ·F T +Q

[0059] Among them, ∑ t|t-1 is the state covariance prediction value at time t, describing the error covariance of the state prediction. t-1|t-1 is the estimated value of the state covariance at time t-1, which is the state covariance after combining the observed data at time t-1. Q is the process noise covariance matrix, which represents the additional uncertainty introduced by process noise in the state transfer process.

[0060] y t|t-1 =H·x t|t-1

[0061] The equation for predicting observed values ​​is defined as follows:

[0062] y t|t-1 =H·x t|t-1

[0063] Among them, y t|t-1 The observation value prediction at time t, the observation value obtained based on the state prediction at time t, x t|t-1 is the predicted value of the state at time t.

[0064] The equation for the covariance of the predicted observations is defined as follows:

[0065] St|t-1 =H·Σ t|t-1 ·H T +R

[0066] Among them, S t|t-1 is the covariance of the observed value at time t and the predicted value, Σ t|t-1 is the predicted value of the state covariance at time t. R is the observation noise covariance matrix, which represents the additional uncertainty introduced by the observation noise during the observation process.

[0067] Step S212 extends the trajectory update flow of the Kalman filter algorithm as follows:

[0068] The updated state estimation equation is as follows:

[0069] x t|t =x t|t-1 +K t ·Δy t

[0070] where x t|t is the updated estimate of the target state space at time t. t|t-1 The predicted value of the state at time t. K t is the Kalman gain, which describes the influence of the measurement value on the state estimate: Δy t The difference between the actual observed value and the predicted observed value will be used for neural network training.

[0071] The updated state covariance equation is as follows:

[0072]

[0073] Among them, Σ t|t The state covariance update value at time t. Σ t|t-1 The state covariance prediction value at time t. S t|t-1 The covariance of the observed value at time t with the predicted value.

[0074] Step S22: Design an LSTM neural network and integrate it into the Kalman filter process;

[0075] See also Figure 3 This is a specific LSTM-EKF neural network structure diagram. The entire neural network has three inputs. Δy in step S212 t , and the observed difference And the difference between before and after update

[0076] Step S22: Integrate the LSTM neural network into the prediction process of the extended Kalman filter. The LSTM-EKF only calculates the first-order statistical moment. Specifically, the prior estimate x of the current state t|t-1From the previous posterior estimate x t-1 Then, the prior estimate y of the current observation is t|t-1 is the prior estimate of the current state x t|t-1 It is calculated that LSTM-EKF does not rely on any prior knowledge of noise distribution.

[0077] Step S222: Integrate the LSTM neural network into the extended Kalman update process LSTM-EKF uses the current observation value y t and the prior estimate x of the previous state t|t-1 Calculate the posterior estimate x of the current state t|t Unlike the classic EKF, LSTM-EKF only needs to define Δy t ,y t|t-1 and x t|t The Kalman gain can be learned by feeding it into a recurrent neural network. The inherent memory of the recurrent neural network allows the covariance Σ of the estimation error to be tracked implicitly without the need to know the underlying noise statistics.

[0078] Step S223: Build the entire neural network framework, which includes a fully connected input layer, an LSTM unit layer, and an output fully connected layer. The hidden state size of the LSTM unit is an integer multiplied by m 2 +n 2 ,This design enables the LSTM unit to efficiently track and update Σ through its gating mechanism t |t-1 and S t |t-1 complex statistical moment. First, a fully connected network is used to process the input data. The output of this layer is directly fed into the LSTM unit. Then, the LSTM processes this data and converts its state vector h t Output, state vector h t It will be converted into the required Kalman gain K by a fully connected network with m·n neurons t The estimated value of LSTM-EKF is a supervised neural network trained with labeled data sets to calculate K ι , instead of directly generating the posterior state estimate x v , but this does not affect the end-to-end training of the entire LSTM-EKF system.

[0079] Step S224 designs a neural network loss function, where the loss function is as follows:

[0080]

[0081] Where, the loss is transferred from the output back to K t In the calculation process of LSTM-EKF, we can get the output of Kt The loss gradient.

[0082]

[0083] Step S225: Design a training algorithm for the neural network, use the regularized mean square error as the training loss, and use the time back propagation algorithm to calculate the gradient of the loss function with respect to the model parameters. Specifically, the LSTM-EKF of the time span shares the network parameters, and forward and backward gradients are passed on the entire trajectory. Then, these calculated gradients are passed to the Adam optimizer, which updates the parameters of the model.

[0084] Next, the effectiveness of this embodiment is verified with the help of experimental results. The experiment generates underwater pipeline data through the underwater pipeline state-space equation, demonstrates the filtering effect of traditional filtering methods such as EKF, PF, and UKF under measurement, and selects the EKF with the best effect in the traditional algorithm for comparison with the LSTM-EKF proposed in the present invention.

[0085] See also Figure 2 The results of the traditional filtering algorithm show that EKF has the best prediction effect, while PF and UKF have poor prediction effects. Therefore, EKF is selected as the comparison algorithm of the algorithm of the present invention. The experimental results are shown in Table 1:

[0086] Table 1

[0087] EKF-true EKF UKF PF LSTM-EKF MSE\dB -29.1045 -23.7328 -21.583 -20.722 -9.5824

[0088] After 4000 rounds of training, the implementation results of LSTM-EKF are shown in Table 2:

[0089] Table 2

[0090] EKF-true EKF LSTM-EKF MSE\dB -29.3274 -23.6375 -29.1244

[0091] See also Figure 3 The results of the LSTM-EKF, EKF with complete information, and EKF tests are shown in Figure 2. From the results, we can see that the proposed algorithm is better than the traditional EEKF. LSTM-EKF overcomes the model mismatch problem caused by the discretization of the continuous-time state space model. Thanks to the strong generalization of the neural network, the ability to learn from discrete data has a significant gain over the model-based alternative method. After 4,000 rounds of training, LSTM-EKF has surpassed the EKF algorithm and is almost the same as the actual prediction upper limit.

[0092] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for underwater pipeline trajectory prediction based on extended Kalman filtering and LSTM, characterized by: Here are the steps: Step 1: Based on the target tracking theory, the underwater state space model of the pipeline is established, and the Taylor expansion used to expand the Kalman filter is discretized to generate simulation data of the underwater pipeline trajectory; Step 2: Build the extended Kalman neural network LSTM-EKF. Based on the extended Kalman filter structure, construct three features for LSTM network training input; Step 3: Select a training algorithm based on the principle of achieving the maximum training effect, including the selection of loss function and model training algorithm, and train the extended Kalman neural network; Step 4: Consider the mismatch of pipeline models, test the basic algorithm, expand the Kalman filter, and expand the underwater pipeline prediction results of the Kalman neural network.

2. The underwater pipeline trajectory prediction method based on extended Kalman filtering and LSTM according to claim 1 is characterized in that: The underwater state space model of the pipeline established in step 1 is: Based on the target tracking theory, the underwater environment, and the simplified pipeline state estimation problem, the following two assumptions are made: First, the cable laid on the seabed is continuous and its state is measurable; second, the pipeline trajectory is regarded as the trajectory of the virtual particle movement. The sonar and camera installed on the underwater vehicle measure and estimate the pipeline state information in real time, which is considered to be the state of the virtual particle, and the pipeline is also regarded as the mass point movement; when modeling the underwater pipeline, without considering the depth parameter, the three-dimensional motion model is simplified to a two-dimensional motion model, and the pipeline is converted into the kinematic equation of the horizontal plane, with v as -20dB, r as 0.01, and Pipeline data were generated with Taylor order and T = 0.02 sampling interval.

3. The underwater pipeline trajectory prediction method based on extended Kalman filtering and LSTM according to claim 2 is characterized in that: The extended Kalman neural network LSTM-EKF constructed in step 2 is: A separate LSTM unit is used for each tracked second-order statistical moment; the architecture is divided into separate LSTM units and FC layers and the interconnections between them. The network consists of three LSTM layers, cascaded with dedicated FC input and output layers; the first LSTM layer tracks the unknown state noise covariance Q, thereby tracking m 2 variables; similarly, the second and third LSTMs track Σ and S, and thus have m 2 and n 2 hidden state variables; the LSTM layers are interconnected so that the learned Q is used to calculate Σ, which is then used to obtain S, and finally to generate the Kalman filter gain; based on the structure of the extended Kalman filter, three features are selected as the input of the network, which are the difference between the observed statistical information and the state estimation, as well as the difference between the predicted observation and the actual observation.

4. The underwater pipeline trajectory prediction method based on extended Kalman filtering and LSTM according to claim 3 is characterized in that: The training algorithm selected in step 3 is: LSTM-EKF is a system that uses labeled data sets for supervised training. It uses neural networks to calculate rather than directly generate posterior state estimates. It trains the entire system end-to-end and calculates the loss function based on the posterior estimate of the state. The estimated value belongs to the continuous space and uses the squared error loss function for training. The loss is passed from the output back to the K t In the calculation process, based on the output of LSTM-EKF, we get the K t The loss gradient of Among them, K t is the Kalman gain, which is used to update the state estimate at time t; Δy t is the increment of the observed value, that is, the difference between the observed value and the predicted value at time t. This value represents the deviation of the observed data relative to the predicted data; Δx t is the increment of the state estimate, that is, the difference between the actual state value and the predicted state value at time t. This value represents the deviation of the actual state from the predicted state; is the loss function L for the Kalman gain K t The partial derivative of Kalman gain indicates the influence of the change of Kalman gain on the loss function during the optimization process. The partial derivative is used to guide the adjustment of Kalman gain to minimize the loss function; ∥K t Δy t -Δx t ∥ 2 It is the specific form of the squared error loss function, which represents the sum of squared differences between the observation increment and the state increment after Kalman gain adjustment; is the gradient of the loss function to the Kalman gain, indicating how to adjust the Kalman gain to minimize the loss function in the current state; The data used for training includes trajectories of different lengths, each of which contains a pair of corresponding observation sequence and state sequence data. During the training process, the mapping relationship from observation to state is learned so that the corresponding state sequence can be accurately predicted when a new observation is given. The regularized mean square error is used as the training loss metric, and the gradient of the loss function with respect to the model parameters is calculated through the time backpropagation algorithm. The network parameters of the time span LSTM-EKF are shared, and forward and backward gradient transfers are performed on the entire trajectory. The calculated gradients will be passed to Adam optimization, and the Adam optimizer will update the model parameters.

5. The underwater pipeline trajectory prediction method based on extended Kalman filtering and LSTM according to claim 4 is characterized in that: Three types of model mismatching situations are considered in step 4, including: (1) Mismatch in state evolution caused by using an insufficient-order Taylor series approximation; (2) State-observation mismatch: The presence of a mismatch in the observation model is simulated by using data generated by rotating the identity matrix by only one degree; this rotation is equivalent to a sensor bias of ≈0.55%; (3) The state observation mismatch caused by the transition from continuous time sampling to discrete time sampling; Based on the above conditions, the test is carried out. First, various basic algorithms are considered and the results are compared. The best performance is selected as the reference upper limit of the effect. Second, the prediction results of the extended Kalman filter algorithm when the model structure is completely known, as well as the prediction results of incompletely known and LSTM-EKF are met.

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