Development of an Advanced Ship Simulation and ...

Development of an Advanced Ship Simulation & Control System Using Neural Networks David E. Hess, William E. Faller, Thomas C. Fu and Edward S. Ammeen

Abstract – Initial efforts in a three-year program to develop an advanced simulation & control system for surface ships are described. The system employs a recursive neural network to simulate the motion of the vehicle in the presence of wind and waves. The faster-than-real-time response of the trained network will permit the use of advanced control techniques such as modelreference control or predictive control and the implementation of path planning for improved performance in the presence of adverse environmental conditions. Early results showing accurate simulation of a U.S. Navy ship conducting overshoot (zig-zag) maneuvers in the presence of wind are shown. Index Terms – control systems, environmental factors, intelligent control, marine vehicle control, model reference adaptive control, neural networks, nonlinear estimation, recurrent neural networks, simulation software, state estimation.

I. INTRODUCTION

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he paper describes a program to develop and implement a faster-than-real-time software platform for the automatic control of a ship in waves and wind. The primary goal is to develop a ship simulation software environment coupled with an automatic control system for a surface ship maneuvering in wind and waves. A key element of the system is a Recursive Neural Network (RNN) which serves as the rapid response ship simulation engine. Neural Network research and development for naval applications has been conducted in the Maneuvering and Control Division of the Naval Surface Warfare Center (NSWC) since 1995 and also by Applied Simulation Technologies (AST). The first RNN simulation was developed in 1997 [1], and improvements to the technique rapidly followed [2]. The power of the simulation method was evident when RNN techniques were used to make blind predictions of submarine maneuvers as a team participant in the Office of Naval Research (ONR) Body 1 Submarine Maneuvering Challenge [3]. The challenge was an effort to quantify the current stateof-the-art in submarine maneuvering simulation in which several participants from Government and private This work is supported by the U.S. Office of Naval Research through the Independent Applied Research program conducted at the Naval Surface Warfare Center, Carderock Division. The program monitor is Dr. John H. Barkyoumb, Code 0021. D. E. Hess ([email protected]), T. C. Fu ([email protected]) and E. S. Ammeen ([email protected]) are with the Naval Surface Warfare Center, Carderock Division, West Bethesda, MD 20817-5700 USA. W. E. Faller ([email protected]) is with Applied Simulation Technologies, Cocoa Beach, FL 32931 USA.

1-59975-028-7/05/$20.00 © 2005 ISAP.

organizations provided predictions of the maneuvering behavior of a Radio-Controlled Model (RCM) submarine. The RCM conducted a variety of maneuvers in a specially equipped basin at NSWC. The RNN team led among all participants with the highest number of “Good” predictions as graded by an independent arbiter. The existence of an accurate simulation technique provided the impetus to use an RNN simulation as a plant model in an advanced control system design. Specifically, an RNN simulation of the SEAWOLF submarine was developed from SEAWOLF RCM test data. The simulation was then mated with the tactical steering and diving algorithm (PILOT). Additionally, this combined technology was provided with fault detection capabilities using principal component analysis and other techniques. The robust control and fault detection capabilities provided by this amalgamated system constituted the first advanced control and monitoring (ACM) capability [4]-[5]. Efforts are also currently underway to combine two state of the art technologies, Reynolds Averaged Navier-Stokes (RANS) computations and RNNs, to develop a new class of geometry-to-motion simulation and design tools [6]. In addition to this work, initial efforts toward the development of a surface ship simulation have been performed [7]-[8]. Two maneuvers, tactical circles and horizontal overshoots, were simulated for two ships operating in the open ocean. Each ship was equipped with two propellers and two rudders, and one ship was larger than the other (making separate simulations of interest). The model employed seven basic force and moment terms to describe the influence of the control inputs and of time-dependent flow field effects: thrust from two propellers, lift from two deflected rudders, two righting moments resulting from disturbances in pitch and roll, and a Munk moment acting on the hull. Prediction errors for the circle and overshoot maneuvers were within 5%-10%. This early work was conducted to begin a new simulation capability for surface vehicles, and environmental effects were not considered. These influences could be removed from the tactical circles prior to training, and the results were excellent. However, wind and sea state effects could not be removed from the overshoot data, and the absence of the necessary environmental input terms to the model can be seen in this data. The inclusion of environmental effects will be a necessary improvement to the RNN model for the advanced simulation & control system, and results with the addition of wind forcing will be discussed in a later section.

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Control System Development Module

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Fig. 1. Schematic of the advanced simulation & control system.

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Initial Conditions Fig. 2. RNN simulation with component force modules and environmental input modules.

II. SYSTEM DESCRIPTION The components of the advanced simulation & control system are shown schematically in Fig. 1. The commanded response is delivered to both the ship and to the RNN via matching copies of the automatic control system. The RNN, operating in parallel with the ship, is a software simulation, which provides the vehicle dynamics required to implement predictive control and path planning within the ship automatic control system. The response from both the ship and the reference simulation are compared and monitored for performance conditions including changes in the expected sea state and wave field. Although the simulation will build upon previous successful RNN model architecture, implementation will require the development of new techniques for describing and coupling environmental models with RNN simulations. Wind and wave modules describing the environmental conditions in which the ship is operating are a key element of the system. Outputs from these modules provide input to the ship simulation and RNN as well as to a path-planning

module. The surface ship simulation will enable not only development, but also testing and evaluation of candidate automatic control systems, path planning algorithms, and performance monitoring systems developed using this simulation environment. Although not the primary purpose of the system, the ship response and output from the simulation may also be compared for the purpose of fault monitoring. Hence, blocks have been inserted in the diagram to indicate where hardware and sensor failures might be simulated for development. The next section describes details of the operation of the RNN simulation. III. RNN OVERVIEW A recursive neural network is a computational technique for developing time-dependent nonlinear equation systems that relate input control variables to output state variables. A recursive network is one that employs feedback; namely, the information stream issuing from the outputs is redirected to form additional inputs to the network. A schematic representation of the technique is shown in Fig. 2.

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For this application, the RNN is used to predict the time histories of maneuvering variables of full-scale vehicles conducting maneuvers in the open ocean. Full-scale data describing a series of horizontal overshoot (zig-zag) maneuvers with varying rudder deflection angles and approach speeds have been acquired and used to train and validate the neural network. Upon completion of training, data from maneuvers not included in the set of training maneuvers are input into the simulation, and predictions of the motion of the vehicle are obtained. The input data required for the model consists of time histories of the control variables: two propeller rotation speeds and two rudder deflection angles, along with the initial conditions of the vehicle at some prescribed starting location. As the simulation proceeds, these inputs are combined with past predicted values of the outputs to estimate the forces and moments that are acting on the vehicle. The resulting outputs are predictions of the time histories of the state variables: linear and angular velocity components which can then be integrated to obtain trajectory and attitude, and differentiated to recover the accelerations acting on the vehicle. Environmental data in the form of relative wind speed and direction are measured; input forces and moments using these quantities have been implemented. Thus, the neural network uses forces and moments acting on the vehicle (both from the controls and from the environment) and translates it into vehicle motion. The force modules represent a series of equations designed to pose the problem well for the network by trying to capture the key forces and moments that are driving the motion. The equations need not be exceedingly precise; if a pattern exists between the inputs (forces and moments) and the outputs (vehicle motion), the RNN will discover it. Further details of the implementation of this model follow in subsequent sections, beginning with a description of the maneuvering data used for training and validation. IV. TRAINING & VALIDATION DATA Data for training and validating the neural networks was acquired from a naval vessel operating in the open ocean and conducting horizontal overshoot maneuvers, also known as zig-zags. Horizontal overshoot maneuvers are performed to characterize the handling response and rudder effectiveness of the vehicle, and such quantities as the heading overshoot angle, overshoot time, reach and period are used to establish this behavior. A 30 s period of steady initial conditions is followed by a COMEX order with a further 60 s elapsing before the EXECUTE order is given. After EXECUTE the rudders are deflected to a predetermined entrance angle and maintained in this position. The heading of the vehicle changes in response to the rudder deflection; when the heading has changed by a desired amount (typically equal to the entrance angle), the rudder is reversed and set to the rudder checking angle (usually equal to the entrance angle). Because the vessel does not respond instantly, the heading continues in the same direction for a period of time before slowing and then reversing. This overshoot heading angle quantifies the inherent ability of the ship to change direction. The procedure

is typically repeated for 2.5 cycles. Environmental effects cannot readily be removed from this data; however, the maneuvers are conducted such that the approach course is oriented parallel (or anti-parallel) to the true wind direction. In this manner any influence of the wind on the ship’s turning characteristics should be minimized for both left and right turns. Earlier simulation work, described in [7]-[8], showed that wind forcing was an important input consideration for these maneuvers. Because wind forcing had not been previously modeled, simulation errors were often apparent in the transverse trajectory component. The addition of appropriate inputs to account for wind effects has a dramatic impact on the results as will be seen in a later section. A description of the structure of the neural network follows next. V. NEURAL NETWORK ARCHITECTURE The architecture of the neural network is depicted below in Fig. 3. Feed Forward Connections

Hidden Layer(s) Output Layer

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Recursive (Recurrent) Connections 60-120 Inputs 48-80 Hidden Units (x 2) 6 Outputs 5472 to 16480 weighted coefficients (Platform Dependent) Fig. 3. RNN architecture.

The network consists of four layers: an input layer, two hidden (internal) layers and an output layer, where a layer is a term used to describe a grouping of nodes. Within each layer are nodes, which contain a nonlinear transfer function that operates on the inputs to the node and produces a smoothly varying output. The binary sigmoid function was used for this work; for input x ranging from −∞ to ∞ it produces the output y which varies from 0 to 1 and is defined by y ( x) =

1 . 1+ e−x

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Note that the nodes in the input layer simply serve as a means to couple the inputs to the network; no computations are performed within these nodes. The nodes in each layer are fully connected to those in the next layer by weighted links. As data travels along a link to a node in the next layer it is multiplied by the weight associated with that link. The weighted data on all links terminating at a given node is then summed and forms the input to the transfer function within that node. The output of the transfer function then travels along multiple links to all the nodes in the next layer, and so on. So, as shown in Fig. 3, an input vector at a given time step travels from left to right through the network where it is operated on many times before it finally produces an output

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vector on the output side of the network. A recursive neural network has feedback; the output vector is used as additional inputs to the network at the next time step. For the first time step, when no outputs are available, these inputs are filled with initial conditions. The time step at each iteration represents a step in dimensionless time, ∆ t ′ . Time is rendered dimensionless using the ship’s length and its speed computed from the preceding iteration; thus, the dimensionless time step represents a fraction of the time required for the flow to travel the length of the hull. The neural network is stepped at a constant rate in dimensionless time through each maneuver. Thus, an input vector at the dimensionless time, t ′ , produces the output vector at t ′ + ∆ t ′ , where t′ + ∆ t′ = t′ +

∆ t U (t ′) L

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The network has 78 inputs (and 88 inputs when wind forcing is used). Each hidden layer contains 64 nodes, and each of these nodes uses a bias. The output layer consists of 6 nodes, and does not use bias units. The network contains 134 computational nodes and a total of 9600 weights and biases. The input vector consists of a series of forces and moments which act on the vehicle, and the network then predicts at each time step dimensionless forms of the six state variables: three linear velocity components u, v, and w, and three angular velocity components p, q and r. Specifically, the outputs are defined as u(t ′ + ∆ t ′) , v′ and w′ similar U (t ′) . p(t ′ + ∆ t ′) L p′(t ′ + ∆ t ′) = , q′ and r ′ similar U (t ′)

application of the force or moment and the response of the vehicle. For the hull inputs: Y, K and N, 9 past values are retained; whereas, for Z and M, only 2 past values are kept. Two past values from each of the two propeller thrust terms are retained to provide four additional inputs. Nine past values are kept for each of the rudder lift terms, and one past value for each of the restoring moment terms. For the wind input term, 9 past values are retained as additional inputs. The number of past values to keep is chosen empirically and appears to be a function of the frequency response of the vehicle. For example, retaining information for nine past values implies the network is given information about past events for a period of time required for the flow about the vehicle to travel a distance of 1.8L. Recursed outputs from the prior time step are used as six additional contributions to the input vector. Furthermore, the output vector from one previous time step is retained and made available as six additional inputs. Knowledge of the output velocities for two successive time steps permits the network to implicitly learn about the accelerations of the vehicle. A summary of the various contributions that make up the input vector is provided below in Table 1. TABLE I SUMMARY OF NETWORK INPUTS

Input Description

u′(t ′ + ∆ t ′) =

(3)

These velocity predictions are then used to compute at each time step the remaining kinematic variables: trajectory components, Euler angles and accelerations. The 78 (88) contributions that form the input vector are described as follows. Twelve basic force and moment terms describe the influence of the control inputs and of timedependent flow field effects: hull forces and moments, Y, Z, K, M, N, thrust from two propellers, Tstar and Tport , lift from two deflected rudders, Lstar and Lport , two restoring moments resulting from disturbances in roll and pitch, K r and M r , and a term describing wind forcing acting on the hull, W. These input terms are formulated from knowledge of the controls: propeller rotation speeds and rudder deflection angles, geometry of the vehicle, and from output variables which are recursed and made available to the inputs. The code which defines these input terms are referred to as component force modules in Fig. 2. Additional inputs are obtained by retaining past values of the 12 basic inputs. This gives the network memory of the force and moment history acting on the vehicle and permits the network to learn of any delay that can occur between the

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A detailed description of most of the equations that define each of the input quantities may be found in [7]-[8]. The formulation of the wind force, which acts on the hull of the vehicle, is described next. Results, to be discussed below, have been computed with and without these wind force inputs to assess the impact of environmental effects on the quality of the solution; whereas, the other inputs previously discussed are used for all results.

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A first attempt to define a wind force contribution on the hull in a simple empirical form in order to expose the RNN to environmental influences is given in Eq. 4, where the constant cw is determined by the network during training, VR is the relative wind velocity and θ R is the relative wind direction. W = c wVR2θ R

(4)

This was used for the results presented in this paper, and, as will be seen, has a dramatic positive effect. However, a definition more consistent with the previous inputs which decomposes wind effects into force and moment components is found in [9] and can be defined as X w = cxVR2 cos θ R Yw = c yVR2 sin θ R

N w = cnVR2 sin(2θ R ) , (5)

and this will be used in future work. VI. RESULTS Fig. 4 shows a series of plots of trajectories of horizontal overshoot maneuvers with rudder checking angles of 10° and 20° and for approach speeds from 3.4 m s to 8.1 m s (6.6 kn to 15.7 kn). The plots shown are a subset of the available data and are typical. The top four plots are for maneuvers that were used to train the RNN, and the bottom plots are from maneuvers that were separated from the training maneuvers and held back to test the trained neural network. These are called validation maneuvers. The data in Fig 4 was obtained using a trained RNN without wind forcing inputs. The point was to demonstrate the problems that occur when environmental effects are not included in the model. As can be seen, the RNN predictions are very good for two of the four training maneuvers and for both of the validation maneuvers. However, the predictions for two other training maneuvers, especially run 9040, are not nearly as good. The fact that these prediction problems are occurring in training maneuvers is an indication that one or more important physical inputs are missing, and that the neural network is not learning correctly. On the other hand, the fact that the predictions are good for some of the training maneuvers, and that the network can reproduce results for maneuvers not seen during training is demonstrating that the set of physical inputs is sufficient to capture the details of the motion for a subset of the maneuvers. The measured relative wind speed was not constant over the entire set of maneuvers, and in fact, was significant for runs such as 9070 and 9040. Evidently, intermittent wind forcing is playing a significant role for some of the runs resulting in substantial changes in trajectory. This led to the development of the wind force expression in (4) and its inclusion as 10 additional inputs (including memory of past states) to the network. The new RNN formulation with wind inputs was then trained using the same horizontal overshoot data. Fig. 5 shows trajectory plots of run 9040, which previously had substantial prediction error. The plot on the left is the result prior to the inclusion of wind inputs, and the plot on the right

is the prediction with the new formulation. There is dramatic improvement using the simple expression in (4). Furthermore, the inclusion of wind inputs to the model had no detrimental effect on predictions for maneuvers with no significant wind forcing; those inputs terms simply became negligible. The plots in both Figs. 4 and 5 are of trajectory information, and the x(t ) and y (t ) time series are plotted relative to each other to give a birds-eye view of the path traversed by the vehicle. These variables are obtained by integrating the velocity time series predictions, which are the outputs from the RNN, and transforming from a coordinate system moving with the vehicle to one which is fixed on the ocean surface at the starting location of each maneuver. The point is that the direct outputs from the six-degree-of-freedom simulation can be used to derive other state variables predictions. Fig. 6 shows a selection of these other state variables, plotted versus time, for maneuver 9040. The two columns of plots are configured the same as that of Fig. 5; namely, those on the left are predictions prior to the inclusion of wind inputs, and those on the right are predictions with the new formulation. The first plot is of velocity magnitude, U (t ) = u 2 (t ) + v 2 (t ) + w 2 (t ) ,

(6)

and the other quantities are self-explanatory. The largest improvement with the addition of wind forcing comes with the transverse trajectory component, y (t ) . This is reasonable since the axis of the maneuver is conducted directly into or out of the wind. As the vehicle moves laterally, it exposes an increasing amount of surface area, and the course of the vehicle is altered. The other noticeable improvement is for the heading variable. With the inclusion of wind forcing, the RNN simulation is making excellent predictions for all state variables describing the motion. VII. DISCUSSION The inception of a three-year program to develop an advanced ship simulation and control system has been described. The key component of the system will be an accurate, faster-than-real-time, ship simulation which is carried out by a recursive neural network. Prior work with RNN development has shown it to be an excellent means for simulation of submarine and surface ship motion, and that it can be easily coupled to a control system. For use in the current effort, the RNN ship simulation must be upgraded to include inputs due to forcing from wind and waves. Initial efforts in the current program, documented here, have shown that a simple formulation for wind forcing provides substantial

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improvement in state variable predictions for a ship conducting horizontal overshoot maneuvers in the open ocean. The next step is to incorporate wave effects into the simulation. A set of inputs has been developed, and new information will be required, such as: wave amplitude and encounter frequency (or wavenumber) for regular wave systems or spectral information for random seas. Furthermore, a well-defined and controlled experiment in a known wave field to provide the training data is required. A DDG-51 class model experiment, see Fig. 7, conducting maneuvers in regular waves has been identified. Efforts are underway to prepare this data for training and validation of the RNN simulation with wave forcing included. The success of this effort will have implications for the fleet. Sea Power 21 is the Navy’s vision for future readiness, and it consists of three capabilities: Sea Strike – the projection of offensive power, Sea Shield – the projection of defensive power and Sea Basing – the projection of sovereignty around

Fig. 7. DDG 67 USS Cole

the world [10]. All three categories require sea control and mobility using forward deployed forces. With respect to Sea Basing, CNO Admiral Vernon Clark adds: “The independence of naval vessels operating on the high seas allows us to

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conduct combat operations anywhere, anytime … [and] … use the 70% of the earth’s surface that is covered with water as a vast maneuver space to aid in the warfighting effort.” [11] Sea based forces will require warfighting capabilities located on multiple platforms to be pre-positioned in forward areas. Given these needs, a maneuvering simulation tool providing real-time information for the surfaced based platforms will not only be timely, but will be invaluable for design and advanced control purposes and can be used for fault detection. VIII. REFERENCES [1]

W. E. Faller, W. E. Smith, and T. T. Huang, “Applied Dynamic System Modeling: Six Degree-Of-Freedom Simulation Of Forced Unsteady Maneuvers Using Recursive Neural Networks”, AIAA Paper 97-0336, 35th Aerospace Sciences Meeting, January 6-10, 1997. [2] W. E. Faller, “Recursive Neural Networks: Toward Advances in Simulation and Control”, AIAA Paper 2000-2470, Fluids 2000, Denver, CO, June 19-22, 2000. [3] D. E. Hess and W. E. Faller, “Using Recursive Neural Networks for Blind Predictions of Submarine Maneuvers”, 24th Symposium on Naval Hydrodynamics, Fukuoka, Japan, July 8-13, 2002. Also available from the authors. [4] E. S. Ammeen, and W. E. Faller, “Submarine Advanced Control and Monitoring,” in ASNE Intelligent Ship Symposium IV, Philadelphia, PA, April 2001. [5] E. S. Ammeen, and W. E. Faller, “Developments in Advanced Submarine Control and Monitoring,” in Submarine Technology Symposium 2001, Laurel, MD, May 2001. [6] T. C. Fu, D. E. Hess, and W. E. Faller, “R2 Design: Next Generation Geometry-to-Motion Simulation Tools for Submarine Design,” FY03 Continuing Proposal to ONR, Dr. Ronald Joslin, Program Officer, Sept 2002. Available from the authors. [7] D. E. Hess, W. E. Faller, W. E. Smith and T. T. Huang, “Simulation of Ship Tactical Circle Maneuvers Using Recursive Neural Networks,” Workshop on Artificial Intelligence and Optimization for Marine Applications, Hamburg, Germany, September 23-25, 1998. Also available from the authors. [8] D. E. Hess and W. E. Faller, “Simulation of Ship Maneuvers Using Recursive Neural Networks,” 23rd Symposium on Naval Hydrodynamics, Val de Reuil, France, September 17-22, 2000. Also available from the authors. [9] T. I. Fossen, Guidance and Control of Ocean Vehicles, New York: Wiley, 1994, pp. 94-96, 246-248. [10] L. Spaulding, “The Navy’s Sea Power 21 Strategy”, Wavelengths, NSWCCD, (Jan/Feb 2003), pp.16-17. [11] V. Clark, Chief of Naval Operations, Speech at the War College, June 2002.

IX. BIOGRAPHIES David E. Hess received a Ph.D. in Mechanical Engineering from the Johns Hopkins University in 1990. Since 1994, he has been employed in the Maneuvering and Control Division of the Hydromechanics Department at the Naval Surface Warfare Center in Bethesda, Md. He is currently the Group Leader for the Captive Model & Analysis group, which is responsible for experimentally determining the maneuvering characteristics of towed submarines. Dr. Hess has also been focused on developing advanced neural network based simulation tools for submarines and surface ships for over 10 years. Dr. Hess is an expert in the area of submarine dynamics and submarine model testing with over 20 years experience in hydrodynamics. William E. Faller graduated from the University of Colorado with a Ph.D. in Aerospace Engineering Sciences in 1992. He is an internationally recognized expert with over 15 years experience in computational modeling, nonlinear simulation and the analysis of complex nonlinear systems. Dr. Faller pioneered and developed the technology known as recursive neural networks. He is the owner of Applied Simulation Technologies which provides commercial access to state-of-the-art technologies, using both feedforward and recursive neural networks, for nonlinear simulation, computational modeling and control applications. Thomas C. Fu received a Ph.D. in Mechanical Engineering from the Johns Hopkins University in 1994. Since that time he has been employed in the Maneuvering and Control Division of the Hydromechanics Department at the Naval Surface Warfare Center in Bethesda, Md. He is currently the Group Leader for the Specialized Research & Advanced Development Group which is responsible for developing advanced capabilities and performing unique experiments of Naval interest to help evaluate, understand, and improve various ship and submarine designs in regard to their fluid dynamics behavior. He has over 20 years experience in hydrodynamics. He is also involved in the development of advanced maneuvering and seakeeping simulations utilizing neural networks for design evaluation and analysis, as well as experience in the area of non-acoustic signatures. Edward S. Ammeen graduated from George Mason University in Fairfax, Virginia with a Ph.D. in Information Technology and Engineering in 1995. He is currently the Head of the Maneuvering and Control Division in the Hydromechanics Department of the Carderock Division Naval Surface Warfare Center. The Division is responsible for the development of hydrodynamic, maneuvering, and control simulations of marine vehicles, the determination of marine vehicle characteristics via experimentation, and the development of automatic control and estimation algorithms. He has over 15 years of experience in maneuvering and control with particular emphasis on submarine ship control and advanced control concepts.

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