Sliding mode predictive control method for heave motion based on time-delay compensation of support vector machine
By combining support vector machines with sliding mode predictive control, the time delay problem of the deep-sea crane heave compensation system was solved, accurate prediction and control accuracy were improved under different sea conditions, and the demand for neural network training sample sets was reduced.
Patent Information
- Application Number
- CN202310095833.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-02-03
- Publication Date
- 2025-09-23
- Estimated Expiration
- 2043-02-03
AI Technical Summary
The time delay problem of the deep-sea crane heave compensation system affects the control accuracy and stability. The existing prediction method has the problems that the prediction accuracy is affected by the sea conditions and the network structure parameters rely on empirical settings.
The support vector regression method is used to predict the heave motion of the hull, and combined with the sliding mode predictive control method of the recursive neural network, the heave motion of the deep-sea crane is predicted through the support vector machine time-delay compensation to solve the delay problem.
It achieves accurate prediction of the heave motion of the deep-sea crane hull under different sea conditions, improves the control accuracy of the heave compensation system, reduces the demand for neural network training sample sets, overcomes the over-learning problem, and enhances the compensation effect of the controller.
Smart Images
Figure CN116047911B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of compensation control, and in particular relates to a heave motion sliding mode predictive control method based on support vector machine time lag compensation. Background Art
[0002] Because deep-sea crane heave compensation systems have complex mechanical actuators and the controller's control relies on sensor detection, the system often experiences time lag. This delay often severely impacts the control accuracy and stability of the deep-sea crane's heave compensation system. To mitigate the negative effects of this system delay, a very short-term forecast of the deep-sea crane's hull heave motion is required, allowing the controller to proactively control the deep-sea crane's load based on this predicted result.
[0003] Currently, prediction methods for deep-sea crane hull heave motion include time series prediction (ARMA), Kalman filter prediction, Smith prediction, neural network prediction, and decomposition prediction. Qin Yang combined fast Fourier transform and Kalman filter methods to establish a deep-sea crane hull heave motion prediction model and conducted simulation analysis of the prediction results. The results showed that the prediction accuracy of this method is affected by sea conditions. Lou Mengyao used the NARX neural network to predict heave motion. The NARX neural network prediction method was compared with the Kalman prediction method, verifying the feasibility of the NARX neural network for predicting hull heave motion. However, the structural parameters of the NARX neural network must be set based on experience, and network training requires a large sample set. Summary of the Invention
[0004] In order to solve the technical problems existing in the existing technology, the present invention adopts the support vector regression method to predict the heave movement of the hull under different sea conditions, and combines it with the sliding mode predictive control method based on recursive neural network to compensate for the heave of deep-sea cranes, thereby solving the control error caused by the system delay problem.
[0005] To achieve the above objectives, the technical solution adopted by the present invention is: a heave motion sliding mode predictive control method based on support vector machine time lag compensation, using support vector regression to predict the heave motion of the hull, the specific steps are as follows:
[0006] Set a set of hull motion data (x s1 ,y s1 ),…,(x sl ,y sl ), construct a linear regression function:
[0007] y s =f(xs ,ω)=ω·x s +b (1)
[0008] Among them, x s 、y s Represents the hull heave motion data, x si 、y si Indicates the i-th heave motion data, there are l hull heave motion data in total, y si ,y si ∈R, ω is the weight vector, b is a constant;
[0009] Assume that the linear insensitive loss function is ε:
[0010]
[0011] Introducing ξ i and With two slack variables, the optimization is transformed into a minimization problem:
[0012]
[0013] Because heave data don't fall completely on the fitted curve, but mostly lie near it, the support vector machine uses two equally spaced curves around the fitted curve to represent the offset range of the heave data points from the fitted curve. To minimize this offset and achieve a good fit, its minimum value is required. Since function fitting inevitably involves some special points that deviate significantly from the fitted curve, the introduction of slack variables relaxes the requirements for these special points; otherwise, a good curve cannot be fitted. c represents the emphasis placed on these special points; a larger c indicates greater emphasis on these special points; m represents the number of slack variables.
[0014] The corresponding constraints are:
[0015]
[0016] Introduce the Lagrangian function:
[0017]
[0018] Among them, α i and is a Lagrange multiplier, and
[0019] Solving for the parameters, the regression function can be simplified to:
[0020]
[0021] Introducing the concept of kernel function, formula (6) can be transformed into:
[0022]
[0023] The kernel function K is generally a linear kernel, a polynomial kernel, a sigmoid kernel, a radial basis kernel, etc. The present invention adopts a radial basis kernel function, and its specific formula can be expressed as follows:
[0024] K(x s ,y s )=exp(-||x s -y s || 2 / σ 2 ) (8)
[0025] Where, σ is the kernel width;
[0026] Although the sliding mode predictive control method achieves good control accuracy, in the actual operation of deep-sea cranes, due to the influence of factors such as the inertia of the mechanical structure and signal transmission, the system often has certain time delay problems, which affects the control performance of the deep-sea crane heave compensation system.
[0027] When the delay is not considered, the displacement of the hull heave motion at time t is y s (t), the expected displacement is y r (t), then the reference displacement y of the input controller can be obtained by calculation a (t) is y r (t)-y s (t), the controller is based on the actual displacement y(t) of the deep-sea crane load and the reference displacement y a (t), and outputs the control signal u(t) to the controlled object (deep-sea crane heave compensation system actuator) through calculation. The controlled object adjusts the load displacement to y according to the control signal r (t)-y s (t). Since the time delay is not considered, the load displacement caused by the heave motion of the hull is y s (t), so by adding the two together, the final load displacement of the deep-sea crane heave compensation system can be obtained as:
[0028] y=[y r (t)-y s (t)]+y s (t) = y r (t) (9)
[0029] y r (t) is the expected displacement, y s (t) is the displacement of the hull heave motion at time t;
[0030] However, due to the existence of factors such as system inertia, the system has a certain degree of delay. In order to simulate the system delay, the present invention adds e -τs module, where τ is the delay time.
[0031] At this time, the displacement of the hull heave motion at time t is y s (t), the expected displacement is y r (t), reference displacement y a (t) is y r (t)-y s (t). The controller is based on the actual displacement y(t) of the deep-sea crane load and the reference displacement y a (t) is calculated and the control signal u(t) is output to the controlled object. Due to the existence of time delay factors, the controlled object adjusts the load displacement to y according to the control signal. r (t)-y s At (t), the time has become t+τ, and the load displacement caused by the heave motion of the hull is y s (t+τ), at this time, the two are added together to obtain the final load displacement of the deep-sea crane heave compensation system:
[0032] y=[y r (t)-y s (t)]+y s (t+τ)=y r (t)+δ (10)
[0033] Where δ = y s (t+τ)-y s (t), it can be seen from the above formula that when the system delay is considered, the controller cannot compensate for the deep-sea crane load well, and there is always a control error δ.
[0034] In order to compensate for the error caused by the time delay problem, the present invention predicts the heave and sink motion of the deep-sea crane hull through a support vector machine.
[0035] The displacement of the hull heave motion at time t is y s (t), the hull heave displacement is input into the support vector machine, and the hull heave displacement at time t+τ is predicted to be At this time, the expected displacement of the hull is y r (t), the reference displacement y of the input controller can be obtained a (t) is The controller is based on the current displacement y(t) of the deep-sea crane load and the reference displacement Through calculation, the control signal u(t) is output to the controlled object, and the controlled object adjusts the load displacement according to the control signal: At this time, the load displacement caused by the heave motion of the hull is ys (t+τ), from which it can be concluded that the final displacement of the deep-sea crane load is:
[0036]
[0037] in, When the prediction is more accurate, y s (t+τ) and Approximately equal, at this time We can get:
[0038]
[0039] It can be seen that adding the support vector machine prediction part can effectively solve the control error caused by the time delay problem.
[0040] Compared with the prior art, the specific beneficial effects of the present invention are embodied in the following: The present invention discloses an extremely short-term prediction method of a support vector machine, and combines it with a sliding mode predictive control method based on an SSA-Elman neural network, which can achieve accurate prediction of the hull heave displacement of a deep-sea crane. After adding the support vector machine prediction model, the controller can effectively solve the control error caused by the time delay problem. Moreover, unlike neural networks, support vector machines can seek the optimal solution to the problem through small samples, overcoming the "over-learning" problem that is common in neural network prediction methods. Compared with the NARX neural network, the sample set required for network training of the SSA-Elman neural network is greatly reduced, and the structural parameters in the network can be optimized and adjusted through SSA. Under different sea conditions, the accuracy of heave compensation is significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS
[0041] Figure 1 This is the schematic diagram of the heave compensation system without considering the delay.
[0042] Figure 2 Schematic diagram of the heave compensation system taking time delay into account.
[0043] Figure 3 This is the schematic diagram of the heave compensation system after adding the prediction model.
[0044] Figure 4 This is the predicted curve of hull heave displacement under level 4 sea conditions.
[0045] Figure 5 This is the prediction error diagram of the hull heave displacement under level 4 sea conditions.
[0046] Figure 6 This is a comparison table of the predicted results of hull heave and sink displacement under level 4 sea conditions.
[0047] Figure 7 This is the predicted curve of hull heave displacement under level 5 sea conditions.
[0048] Figure 8 This is the prediction error diagram of the hull heave displacement under level 5 sea conditions.
[0049] Figure 9 This is a comparison table of the predicted results of hull heave and sink displacement under sea condition level 5.
[0050] Figure 10 This is the predicted curve of hull heave displacement under level 6 sea condition.
[0051] Figure 11 This is the prediction error diagram of the hull heave displacement under sea condition level 6.
[0052] Figure 12 This is the prediction result of the hull heave displacement under level 6 sea conditions.
[0053] Figure 13 This is a comparison chart of heave compensation before and after prediction under level 4 sea conditions.
[0054] Figure 14 This is a local comparison chart of heave compensation before and after prediction under level 4 sea conditions.
[0055] Figure 15 This is a comparison chart of heave compensation before and after prediction under level 5 sea conditions.
[0056] Figure 16 This is a local comparison chart of heave compensation before and after prediction under level 5 sea conditions.
[0057] Figure 17 This is a comparison chart of heave compensation before and after prediction under level 6 sea conditions.
[0058] Figure 18 This is a local comparison chart of heave compensation before and after prediction under level 6 sea conditions.
[0059] Figure 19 A comparison chart of heave compensation in different sea conditions. DETAILED DESCRIPTION
[0060] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.
[0061] The heave motion sliding mode predictive control method based on support vector machine time-delay compensation uses support vector regression to predict the heave motion of the hull. The specific steps are as follows:
[0062] Set a set of hull motion data (x s1 ,y s1 ),…,(xsl ,y sl ), construct a linear regression function:
[0063] y s =f(x s ,ω)=ω·x s +b (1)
[0064] Among them, x s 、y s Represents the hull heave motion data, x si 、y si Indicates the i-th heave motion data, there are l hull heave motion data in total, x si ,y si ∈R, ω is the weight vector, b is a constant;
[0065] Assume that the linear insensitive loss function is ε:
[0066]
[0067] Introducing ξ i and Two slack variables transform the optimization problem into a minimum value:
[0068]
[0069] Because heave data don't fall completely on the fitted curve, but mostly lie near it, the support vector machine uses two equally spaced curves around the fitted curve to represent the offset range of the heave data points from the fitted curve. To minimize this offset and achieve a good fit, its minimum value is required. Since function fitting inevitably involves some special points that deviate significantly from the fitted curve, the introduction of slack variables relaxes the requirements for these special points; otherwise, a good curve cannot be fitted. c represents the emphasis placed on these special points; a larger c indicates greater emphasis on these special points; m represents the number of slack variables.
[0070] The corresponding constraints are:
[0071]
[0072] Introduce the Lagrangian function:
[0073]
[0074] Among them, α i and is a Lagrange multiplier, and
[0075] Solving for the parameters, the regression function can be simplified to:
[0076]
[0077] Introducing the concept of kernel function, formula (6) can be transformed into:
[0078]
[0079] The kernel function K is generally a linear kernel, a polynomial kernel, a sigmoid kernel, a radial basis kernel, etc. The present invention adopts a radial basis kernel function, and its specific formula can be expressed as follows:
[0080] K(x s ,y s )=exp(-||x s -y s || 2 / σ 2 ) (8)
[0081] Where, σ is the kernel width;
[0082] Although the sliding mode predictive control method achieves good control accuracy, in the actual operation of deep-sea cranes, due to the influence of factors such as the inertia of the mechanical structure and signal transmission, the system often has certain time delay problems, which affects the control performance of the deep-sea crane heave compensation system.
[0083] like Figure 1 As shown, when the delay is not considered, the displacement of the hull heave motion at time t is y s (t), the expected displacement is y r (t), then the reference displacement y of the input controller can be obtained by calculation a (t) is y r (t)-y s (t), the controller is based on the actual displacement y(t) of the deep-sea crane load and the reference displacement y a (t), and outputs the control signal u(t) to the controlled object (deep-sea crane heave compensation system actuator) through calculation. The controlled object adjusts the load displacement to y according to the control signal r (t)-y s (t). Since the time delay is not considered, the load displacement caused by the heave motion of the hull is y s (t), so by adding the two together, the final load displacement of the deep-sea crane heave compensation system can be obtained as:
[0084] y=[y r (t)-y s (t)]+y s (t) = y r (t) (9)
[0085] yr (t) is the expected displacement, y s (t) is the displacement of the hull heave motion at time t;
[0086] However, due to the existence of factors such as system inertia, the system has a certain degree of delay. In order to simulate the system delay, the present invention adds e -τs module, where τ is the delay time.
[0087] like Figure 2 As shown, at this time, the displacement of the hull heave motion at time t is y s (t), the expected displacement is y r (t), reference displacement y a (t) is y r (t)-y s (t). The controller is based on the actual displacement y(t) of the deep-sea crane load and the reference displacement y a (t) is calculated and the control signal u(t) is output to the controlled object. Due to the existence of time delay factors, the controlled object adjusts the load displacement to y according to the control signal. r (t)-y s At (t), the time has become t+τ, and the load displacement caused by the heave motion of the hull is y s (t+τ), at this time, the two are added together to obtain the final load displacement of the deep-sea crane heave compensation system:
[0088] y=[y r (t)-y s (t)]+y s (t+τ)=y r (t)+δ (10)
[0089] Where δ = y s (t+τ)-y s (t), it can be seen from the above formula that when the system delay is considered, the controller cannot compensate for the deep-sea crane load well, and there is always a control error δ.
[0090] In order to compensate for the error caused by the time delay problem, the present invention predicts the heave and sink motion of the deep-sea crane hull through a support vector machine.
[0091] like Figure 3 As shown, the displacement of the hull heave motion at time t is y s (t), the hull heave displacement is input into the support vector machine, and the hull heave displacement at time t+τ is predicted to be At this time, the expected displacement of the hull is y r (t), the reference displacement y of the input controller can be obtained a (t) is The controller is based on the current displacement y(t) of the deep-sea crane load and the reference displacement Through calculation, the control signal u(t) is output to the controlled object, and the controlled object adjusts the load displacement according to the control signal: At this time, the load displacement caused by the heave motion of the hull is y s (t+τ), from which it can be concluded that the final displacement of the deep-sea crane load is:
[0092]
[0093] in, When the prediction is more accurate, y s (t+τ) and Approximately equal, at this time We can get:
[0094]
[0095] It can be seen that adding the support vector machine prediction part can effectively solve the control error caused by the time delay problem.
[0096] To verify the accuracy of the support vector machine prediction method, we used a time delay of τ = 0.1s and trained the support vector machine using ship heave data derived from PM spectrum simulation. After training, the support vector machine was used to predict the heave motion of the ship under different sea conditions.
[0097] Among them, under level 4 sea conditions, the real-time prediction results of the support vector machine for the hull heave motion are as follows: Figure 4 、 Figure 5 、 Figure 6 shown.
[0098] Under level 5 sea conditions, the real-time prediction results of the support vector machine for the hull heave motion are as follows: Figure 7 、 Figure 8 、 Figure 9 shown.
[0099] Under sea condition level 6, the support vector machine predicts the ship's heave motion as follows: Figure 10 、 Figure 11 、 Figure 12 shown.
[0100] Under different sea conditions, the support vector machine can predict the heave motion of the deep-sea crane hull τ time in advance, and has high prediction accuracy for the heave motion of the hull under different sea conditions.
[0101] In order to verify the heave compensation effect of the controller on the deep-sea crane after adding the support vector machine, the present invention adopts the sliding mode predictive control method based on SSA-Elman as the system controller to control the deep-sea crane. The support vector machine prediction model is added to predict the heave motion of the hull. The heave compensation results with the support vector machine added are compared with those without the support vector machine. The results are as follows: Figure 13-19 shown.
[0102] After adding the support vector machine prediction model, the heave compensation accuracy of the deep-sea crane heave compensation system was significantly improved. Therefore, the support vector machine very short-term prediction method adopted by the present invention can effectively solve the time delay problem existing in the heave compensation system.
[0103] This paper discloses a very short-term prediction method using a support vector machine (SVM) and combines it with a sliding mode predictive control method based on an SSA-Elman neural network. This method can accurately predict the heave displacement of a deep-sea crane. By adding the SVM prediction model, the controller can effectively address control errors caused by time delays.
[0104] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of the present invention.
Claims
1. A heave motion sliding mode predictive control method based on support vector machine time-delay compensation is characterized by: Support vector regression is used to predict the hull heave motion. The specific steps are as follows: Set a set of hull motion data (x s1 ,y s1 ),…,(x sl ,y sl ), construct a linear regression function: y s =f(x s ,ω)=ω·x s +b (1) Among them, x s 、y s Represents the hull heave motion data, x si 、y si Indicates the i-th heave motion data, there are l hull heave motion data in total, x si ,y si ∈R, ω is the weight vector, b is a constant; Assume that the linear insensitive loss function is ε: Introducing ξ i With ξ i * With two slack variables, the optimization is transformed into a minimization problem: c represents the importance attached to special points. The larger c is, the more attention is paid to these special points. m represents the number of slack variables. The corresponding constraints are: In order to solve the above minimum problem, the Lagrangian function is introduced: Among them, α i and is a Lagrange multiplier, and α i , Solving for the parameters, the regression function can be simplified to: Since it is difficult to distinguish whether a data point is within or outside the region determined by the fitting curve in low-dimensional space, the concept of kernel function is introduced, and the kernel function K(x si ,x s ) instead of (x si ·x s ), formula (6) is transformed into: Among them, the kernel function K adopts the radial basis kernel function, and its specific formula can be expressed as: (8) Where, σ is the kernel width; When the time delay is not considered, the final load displacement of the deep-sea crane heave compensation system is: y=[y r (t)-y s (t)]+y s (t)=y r (t) (9) y r (t) is the expected displacement, y s (t) is the displacement of the hull heave motion at time t; Due to the existence of time delay factors, the controlled object adjusts the load displacement to y according to the control signal r (t)-y s At (t), the time has become t+τ, τ is the delay time, and the load displacement caused by the heave motion of the hull is y s (t+τ), at this time, the two are added together to obtain the final load displacement of the deep-sea crane heave compensation system: and=[and r (t)-y s (t)]+y s (t+τ)=y r (t)+δ (10) Where δ = y s (t+τ)-y s (t), it can be seen from the above formula that when the system delay is considered, the controller cannot compensate for the deep-sea crane load well, and there is always a control error δ; The support vector machine prediction model is introduced, and the displacement of the hull heave motion at time t is y s (t), the hull heave displacement is input into the support vector machine, and the hull heave displacement at time t+τ is predicted to be At this time, the expected displacement of the hull is y r (t), the reference displacement y of the input controller can be obtained a (t) is The controller is based on the current displacement y(t) of the deep-sea crane load and the reference displacement Through calculation, the control signal u(t) is output to the controlled object, and the controlled object adjusts the load displacement according to the control signal: At this time, the load displacement caused by the heave motion of the hull is y s (t+τ), from which it can be concluded that the final displacement of the deep-sea crane load is: in, Due to the short-term forecasting function of support vector machine, y s (t+τ) and Approximately equal, at this time have to: