Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states.

Predicting motions of vessels in extreme sea states represents one of the most challenging problems in naval hydrodynamics. It involves computing complex nonlinear wave-body interactions, hence taxing heavily computational resources. Here, we put forward a new simulation paradigm by training recurrent type neural networks (RNNs) that take as input the stochastic wave elevation at a certain sea state and output the main vessel motions, e.g. pitch, heave and roll. We first compare the performance of standard RNNs versus GRU and LSTM neural networks (NNs) and show that LSTM NNs lead to the best performance. We then examine the testing error of two representative vessels, a catamaran in sea state 1 and a battleship in sea state 8. We demonstrate that good accuracy is achieved for both cases in predicting the vessel motions for unseen wave elevations. We train the NNs with expensive CFD simulations offline, but upon training, the prediction of the vessel dynamics online can be obtained at a fraction of a second. This work is motivated by the universal approximation theorem for functionals (Chen & Chen, 1993. IEEE Trans. Neural Netw. 4, 910-918 (doi:10.1109/72.286886)), and it is the first implementation of such theory to realistic engineering problems.

A robotic Intelligent Towing Tank for learning complex fluid-structure dynamics.

We describe the development of the Intelligent Towing Tank, an automated experimental facility guided by active learning to conduct a sequence of vortex-induced vibration (VIV) experiments, wherein the parameters of each next experiment are selected by minimizing suitable acquisition functions of quantified uncertainties. This constitutes a potential paradigm shift in conducting experimental research, where robots, computers, and humans collaborate to accelerate discovery and to search expeditiously and effectively large parametric spaces that are impracticable with the traditional approach of sequential hypothesis testing and subsequent train-and-error execution. We describe how our research parallels efforts in other fields, providing an orders-of-magnitude reduction in the number of experiments required to explore and map the complex hydrodynamic mechanisms governing the fluid-elastic instabilities and resulting nonlinear VIV responses. We show the effectiveness of the methodology of "explore-and-exploit" in parametric spaces of high dimensions, which are intractable with traditional approaches of systematic parametric variation in experimentation. We envision that this active learning approach to experimental research can be used across disciplines and potentially lead to physical insights and a new generation of models in multi-input/multi-output nonlinear systems.

Efficiency of fish propulsion.

The system efficiency of a self-propelled flexible body is ill-defined, hence we introduce the concept of quasi-propulsive efficiency, defined as the ratio of the power needed to tow a body in rigid-straight condition over the power it requires for self-propulsion, both measured for the same speed. Through examples we show that the quasi-propulsive efficiency is a rational non-dimensional metric of the propulsive fitness of fish and fish-like mechanisms, consistent with the goal to minimize fuel consumption under size and velocity constraints. We perform two-dimensional viscous simulations and apply the concept of quasi-propulsive efficiency to illustrate and discuss the efficiency of two-dimensional undulating foils employing first carangiform and then anguilliform kinematics. We show that low efficiency may be due to adverse body-propulsor hydrodynamic interactions, which cannot be accounted for by an increase in friction drag, as done previously, since at the Reynolds number Re = 5 000 considered in the simulations, pressure is a major contributor to both thrust and drag.

Ultra-fast escape maneuver of an octopus-inspired robot.

We design and test an octopus-inspired flexible hull robot that demonstrates outstanding fast-starting performance. The robot is hyper-inflated with water, and then rapidly deflates to expel the fluid so as to power the escape maneuver. Using this robot we verify for the first time in laboratory testing that rapid size-change can substantially reduce separation in bluff bodies traveling several body lengths, and recover fluid energy which can be employed to improve the propulsive performance. The robot is found to experience speeds over ten body lengths per second, exceeding that of a similarly propelled optimally streamlined rigid rocket. The peak net thrust force on the robot is more than 2.6 times that on an optimal rigid body performing the same maneuver, experimentally demonstrating large energy recovery and enabling acceleration greater than 14 body lengths per second squared. Finally, over 53% of the available energy is converted into payload kinetic energy, a performance that exceeds the estimated energy conversion efficiency of fast-starting fish. The Reynolds number based on final speed and robot length is [Formula: see text]. We use the experimental data to establish a fundamental deflation scaling parameter [Formula: see text] which characterizes the mechanisms of flow control via shape change. Based on this scaling parameter, we find that the fast-starting performance improves with increasing size.

Mechanical characteristics of harbor seal (Phoca vitulina) vibrissae under different circumstances and their implications on its sensing methodology.

In this paper, the mechanical properties of harbor seal vibrissae immersed in various solutions are investigated. As there are no nerves along the length of the vibrissae, all the perturbations have to be transmitted to their bases for sensing. Hence, quantification and understanding of the mechanical properties of the vibrissae are essential in determining the perturbations transmitted to the base of the vibrissae. Two experimental setups are devised for measurements of the different properties of the vibrissae. The first experimental setup is performed with a dynamic mechanical analysis machine. The measured properties in these experiments are the modulus of elasticity and the damping of the vibrissae. Dry, saline water-immersed, water-immersed and Hanks' balanced salt solution (HBSS)-immersed vibrissae are tested to determine the effects of these solutions on the properties of the vibrissae. Tests on the duration of immersion are also performed with saline water-immersed vibrissae. The second experimental setup is performed with a mini-shaker connected to a clamp, which rigidly holds the vibrissae at their bases. The measured properties in these experiments are the natural frequencies of the vibrissae. The results indicate that the moduli of elasticity of the vibrissae are found to decrease along their lengths. However, their damping does not vary along the lengths. HBSS-immersed and saline water-immersed vibrissae show similar characteristics on their properties. An analytical model for predicting the natural frequencies of the vibrissae is also derived. Strong agreement with previous studies on the underwater sensing principle of the harbor seal is also established.

A fast-starting mechanical fish that accelerates at 40 m s(-2).

We have built a simple mechanical system to emulate the fast-start performance of fish. The system consists of a thin metal beam covered by a urethane rubber, the fish body and an appropriately shaped tail. The body form of the mechanical fish was modeled after a pike species and selected because it is a widely-studied fast-start specialist. The mechanical fish was held in curvature and hung in water by two restraining lines, which were simultaneously released by a pneumatic cutting mechanism. The potential energy in the beam was transferred into the fluid, thereby accelerating the fish. We measured the resulting acceleration, and calculated the efficiency of propulsion for the mechanical fish model, defined as the ratio of the final kinetic energy of the fish and the initially stored potential energy in the body beam. We also ran a series of flow visualization tests to observe the resulting flow patterns. The maximum start-up acceleration was measured to be around 40 m s(-2), with the maximum final velocity around 1.2 m s(-1). The form of the measured acceleration signal as function of time is quite similar to that of type I fast-start motions studied by Harper and Blake (1991 J. Exp. Biol. 155 175-92). The hydrodynamic efficiency of the fish was found to be around 10%. Flow visualization of the mechanical fast-start wake was also analyzed, showing that the acceleration peaks are associated with the shedding of two vortex rings in near-lateral directions.

In-line motion causes high thrust and efficiency in flapping foils that use power downstroke.

We show experimentally that flapping foil kinematics consisting of a power downstroke and a feathering upstroke together with a properly timed in-line motion, similar to those employed in forelimb propulsion of sea turtles, can produce high thrust and be hydrodynamically as efficient as symmetrically flapping foils. The crucial parameter for such asymmetrically flapping foils is a properly sized and timed in-line motion, whose effect is quantified by a new parameter, the advance angle, defined as the angle of the foil trajectory with respect to the horizontal, evaluated at the middle of the power downstroke. We show, in particular, that optimal efficiency in high aspect ratio rigid foils, accompanied by significant thrust production, is obtained for Strouhal numbers in the range 0.2-0.6 for Reynolds number equal to 13,000, and for values of the advance angle around 0.55pi (100 deg.). The optimized kinematics consist of the foil moving back axially during the downstroke, in the direction of the oncoming flow, and rotating with a large pitch angle. This causes the force vector to rotate and become nearly parallel to the steady flow, thus providing a large thrust and a smaller transverse force. During the upstroke, the foil is feathering while it moves axially forward, i.e. away from the vorticity shed during the power stroke; as a result, the transverse force remains relatively small and no large drag force is produced. Observations from turtles confirm qualitatively the findings from the foil experiments.

Resonant vibrations of bluff bodies cause multivortex shedding and high frequency forces.

A flexibly mounted circular cylinder in cross-flow, with natural frequencies in the inline and transverse directions having a ratio close to 2:1, exhibits drastic changes in the vortex structures in its wake, the frequency content of the fluid forces, and the orbital shape of its resulting motions. Stable multivortex patterns form in the cylinder wake, associated with large high-frequency force components.

Vorticity Control in Fish-like Propulsion and Maneuvering.

Vorticity control is employed by marine animals to enhance performance in maneuvering and propulsion. Studies on fish-like robots and experimental apparatus modelling rigid and flexible fins provide some of the basic mechanisms employed for controlling vorticity.

The dorsal fin engine of the seahorse (Hippocampus sp.).

The muscles, fin ray joints, and supporting structures underlying the dorsal fin are described for two seahorse species: Hippocampus zosterae and Hippocampus erectus. A fan-shaped array of cartilaginous bones, the pterigiophores, form the internal supporting structure of the dorsal fin. Each pterigiophore is composed of a proximal radial that extends from a vertebra to the dorsal side of the animal, where it fuses to a middle radial. The middle radials fuse with each other to form a dorsal ridge upon which sit the spheroidal distal radials. Each distal radial articulates with a fin ray on its dorsal side and is attached to the dorsal ridge on its ventral side by a material that has been histologically identified as elastic cartilage. Together these connections form a two-axis joint that permits elevation, depression, and inclination of the ray. Each fin ray is actuated by two bilateral pairs of muscles, an anterior pair of inclinators, and a posterior pair of depressors. The anteriormost fin ray is actuated by three bilateral pair of muscles, the inclinators, the depressors, and a pair of elevator muscles that are positioned anterior to the inclinators. Preliminary examinations of the ray joints of the pectoral and anal fins of adult H. zostera and the pectoral fins of newborn H. erectus revealed structures similar to that seen in the dorsal fins. To further explore the structure and function of the dorsal fin gross dissections and simple functional tests were performed on H. erectus and H. barbouri and behavioral observations were made of all three species plus Hippocampus kuda.