Estimation Of Hydrodynamic Coefficients Research Articles

Nonlinear dynamics of novel flight-style autonomous underwater vehicle with bow wings, Part I: ASE and CFD based estimations of hydrodynamic coefficients, Part II: Nonlinear dynamic modeling and experimental validations

Accurate dynamic modeling is essential for precise prediction of six degrees-of-freedom (6-DOF) motion and model-based controller design of an autonomous underwater vehicle (AUV). The accuracy of dynamic model of an AUV largely depends upon the precise estimation of hydrodynamic coefficients. Accordingly, to establish the dynamic model based on ASE-estimated hydrodynamic coefficients of the novel flight-style AUV and experimental validations, the study is presented in two parts (Part I: ASE and CFD based estimations of hydrodynamic coefficients and Part II: Nonlinear dynamic modeling and experimental validations).Part I: In this part complete set of nonlinear hydrodynamic coefficients including, added mass, drag, and lift forces and moment coefficients are estimated using ASE technique, which is specifically developed to accurately comprehend the novel AUV design including, AUV hull, fixed wings, control fins, and appendages. Additionally, an improved ASE approach is also proposed to estimate cross flow drag force coefficients. In proposed improved ASE technique, (Cdc) in mathematical formulation is taken from the experimental results of 3D flow past over circular cylinder instead of 2D, as followed previously to estimate the nonlinear cross-flow drag force and moment coefficients (Yvv,Zww,Mww,Nvv,Yrr,Zqq,Mqq&Nrr). The proposed ASE technique is verified and validated in two stages: first, by comparing the ASE-estimated results with CFD-based estimations, and second, by investigating the 6-DOF motion response of the AUV. When compared ASE-estimations with the CFD results for the cross-flow drag force and moment coefficients, the proposed ASE technique has shown a significant improvement (approximately 20%) over the previously employed ASE method. The ASE-estimated results are validated through 6-DOF motion response of AUV during free-running underwater experiments, provided in ‘Part II’. Overall, the proposed ASE technique is considered more effective, direct, and less costly in terms of time and computational efforts, compared to CFD-based or experimental-based estimations of hydrodynamic coefficients of AUVs, particularly torpedo-shaped AUVs.Part II: This part presents a nonlinear dynamic model for a newly designed torpedo-shaped flight-style AUV having complex bow and stern fixed wings and control fins configuration. The model includes precise mathematical formulations to accurately represent the physics of the AUV and underwater environment in terms of hydrodynamic derivatives such as added mass, drag, and lift forces and moment coefficients. These coefficients have been estimated using an ASE method provided in ‘Part I’. The 6-DOF motion response of the AUV has been simulated in both horizontal and vertical planes which includes, zigzag yaw, circle, zigzag pitch, and spiral maneuvers. The lift generated by the bow and stern control fins has been investigated both separately and collectively, especially during complex spiral ascending maneuvers. Moreover, improved ASE technique for cross flow drag coefficients has also been validated through 6-DOF free-running underwater experiments of AUV and insights on impact of cross flow drag coefficients on 6-DOF motion response of AUV has also been provided. Overall, the comparison between the simulated AUV motion and free-running underwater experiments demonstrated consistency, thereby validating the accuracy of the nonlinear dynamic modeling, ASE-based hydrodynamic coefficient predictions, and effectiveness of the newly designed flight-style AUV for underwater operations.

Estimation of hydrodynamic coefficients and simplification of the depth model of an AUV using CFD and sensitivity analysis

Maneuverability is one of the most important performance characteristics of submarines. Before constructing a designed AUV, the hydrodynamic model can be used to determine its inherent motion behavior. Standard submarine motion equations (SSME) are the most widely used hydrodynamic model in which more than 100 coefficients must be estimated. These coefficients are usually determined through conventional experimental and analytical methods. The most common method today is captive model tests, but the separately determining approach is time-consuming and makes it difficult to assess the reliability of the model. This paper proposes an efficient approach for estimating hydrodynamic coefficients (HCs) using computational fluid dynamics (CFD). Instead of captive model tests, the proposed virtual free-running test can provide all the information required to determine all the HCs in only one simulation. Kalman filter estimation methods are used to determine the HCs. Sensitivity analysis and statistical results show that in a typical AUV maneuvering, SSME can be simplified. The final simplified equations of motion have much fewer components than the original model while fitting accuracy remains. Using the experimental data of the well-known DARPA-SUBOFF underwater vehicle, it is shown the proposed virtual free-running and the simplification approaches are effective and reliable.

The estimation of hydrodynamic coefficients of an autonomous underwater vehicle by comparing a dynamic mesh model with a horizontal planar motion mechanism experiment

This study aims to establish a dynamic mesh model based on the horizontal planar motion mechanism (HPMM) test and provide a comprehensive database of hydrodynamic coefficients for the autonomous underwater vehicle (AUV) numerically and experimentally. A series of HPMM tests in National Cheng Kung University's towing tank validated the simulation results. The dynamic mesh model can be performed on oscillation motions of the yaw mode, the pitch mode, and the roll mode by adding a series of comprehensive user-defined functions (UDFs). The test of straight-line motion with constant drift angles, the pure surge test, the pure yaw test, the pure pitch test, the pure yaw test with a constant drift angle, and the pure pitch test with a constant drift angle are all available for the yaw and pitch modes. In addition, the pivot roll test is included in the roll mode. After measuring forces and moments from an individual HPMM test, the hydrodynamic coefficients can be derived by means of Fourier analysis and the least-square method. Since most numerical results are reasonably in good agreement with the experimental data, applying the proposed dynamic mesh model to the simulation of the HPMM tests in the towing tank can be demonstrated.

Hydrodynamic forces on tubular cylinders fitted with sacrificial anodes – numerical analysis

In offshore engineering, the design of effective marine platforms compatible with the offshore environmental condition is a challenging task, especially accurate estimation of hydrodynamic coefficients that affect the viscous forces. Practically, the well-known Morison’s equation is often adopted by designers to calculate wave loads on slender structures, where the values of drag and inertia coefficients are selected as constant values based on the design code of practice’s recommendations. However, the mass and drag coefficients must be determined empirically based on specific met-ocean data for the operation location. Thus, the objective of this study is to evaluate the Hydrodynamic Forces on Circular Cylinders fitted with sacrificial anodes using empirical methods, and validate the results using Computational Fluid Dynamic (CFD). It is found that the major parameters that affect the drag and inertia coefficients are the water depth, wave heights, wave frequencies, the pipe diameters, and the presence of anode fittings.

An approach for the estimation of hydrodynamic coefficients of an underwater vehicle in off-design velocities

In this paper, an approach is proposed for the estimation of hydrodynamic coefficients variation as functions of Reynolds number. The variation of rotary damping linear hydrodynamic coefficients for off-design velocities is studied by simulating the rotating arm test and using computational fluid dynamics. Numerical results are validated by comparison with experimental ones reported in the literature for geometry of the well-known underwater vehicle of DARPA SUBOFF and a good agreement is observed. The numerical tool is employed to study the effects of Reynolds number on hydrodynamic coefficients. Numerical results are used for deriving proper functions that estimates hydrodynamic coefficients using truncated power series expansion along with least square method. It can be concluded that it is more appropriate to use fitted functions instead of constant values especially at low Reynolds numbers.

Robust estimation of hydrodynamic coefficients of an AUV using Kalman and H∞ filters

In this paper, a robust procedure for estimating of nominal hydrodynamic coefficients of an autonomous underwater vehicle (AUV) in presence of parameter uncertainties is proposed. Some parameters of the model of an AUV, such as its hydrodynamic coefficients, may perturb from their nominal values because of changes in its operating conditions and the surrounding environment. This paper presents two different filters for robust identification of the AUV parameters. The robust extended Kalman filter (REKF) and the extended H-infinity (EH∞) filter are implemented to estimate the nominal hydrodynamic coefficients of the AUV. By using a model of a sample AUV and simulating the motion of the vehicle in the diving mode involving parameter perturbations, the performance of the filters is compared. The results show that the REKF outperforms the EH∞ filter in this application. Also, the performance of these estimation algorithms is compared with the standard extended Kalman filter (EKF), using the data obtained from experimental test of a real AUV. It is observed that the model using the identified values of hydrodynamic coefficients of both filters can predict the actual trajectory of the vehicle and the robust filters are more accurate as compared to the standard EKF.

Estimation of Hydrodynamic Coefficients from Results of Real Ship Sea Trials

Abstract This paper suggests an estimation method for ship’s hydrodynamic coefficients, which is based on the system identification method that calculates an optimum value in a mathematical way. For the purpose of modelling existing ships, this study collects real ship sea trial data as benchmarks. Prior to the optimization, a sensitivity analysis is carried out for easy and effective optimization. The simulation results using optimized coefficients agree well with corresponding benchmarks. Following this, with various trim and draught conditions, this study suggests new estimation formulas that concern all trim and draught conditions. Simulation results applying the estimation formulas are satisfactory in regard to a corresponding benchmark, compared to a result obtained by using an existing regression formula.

Estimation of Hydrodynamic Coefficients of a Nonlinear Manoeuvring Mathematical Model With Free-Running Ship Model Tests

Free-running model tests have been carried out based on a scaled chemical tanker ship model, having a guidance, control and navigation system developed and implemented in LabVIEW. In order to make the modelling more flexible and physically more realistic, a modified version of Abkowitz model was introduced. During the identification process, the model’s structure is fixed and its parameters have been obtained using system identification. A global optimization algorithm has been used to search the optimum values and minimize the loss functions. In order to reduce the effect of noise in the variables, different loss functions considering the empirical errors and generalization performance have been defined and implemented in the system identification program. The hydrodynamic coefficients have been identified based on the manoeuvring test data of free-running ship model. Validations of the system identification algorithm were also carried out and the comparisons with experiments demonstrated the effectiveness of the proposed system identification method.

A time-efficient CFD approach for hydrodynamic coefficient determination and model simplification of submarine

Maneuverability is one of the most important performance characteristics of submarines. Hydrodynamic model is increasingly relied on as a design approach to determine the inherent motion behavior of a proposed submarine before construction. Standard submarine motion equations are the most used hydrodynamic model, in which more than 100 coefficients need to be estimated. These coefficients have to be determined by captive model tests, semi-empirical method and potential flow method on the basis of existing approach. The separately determining approach makes it difficult to assess model reliability. This paper proposes a time-efficient approach for the estimation of hydrodynamic coefficients using computational fluid dynamics (CFD) method. Instead of a repetitive and time-consuming process, the proposed spatial captive motion could provide all necessary information for determination of all required coefficients in only one simulation. Linear regression, based on the least square method, is employed to determine coefficients in hydrodynamic model. Statistical investigation, correlation and significance analysis, indicates that the standard submarine motion equations can be further simplified when submarine moving forward with small perturbations along other directions. The final simplified motion equations have much fewer components than the original model while fitting accuracy remained. Validation results prove that spatial captive motion simulation and the simplification approach employed in this paper are effective and reliable. It should have a large scope in further maneuverability research.

A study on hydrodynamic coefficients estimation of modelling ship using system identification method

Predicting and evaluating ship manoeuvring characteristics are very important not only for the design stage, but also for the existing vessels. There are several ways to predict ship’s manoeuvrability and most of them are highly connected with the estimation of hydrodynamic coefficients. This paper presents a new estimation method using the system identification with mathematical algorithms for estimating hydrodynamic coefficient in the ship’s mathematical model. Specifically a double ended ferry which equips four azimuth propulsion systems were chosen as benchmark ship and a set of benchmark data which is generated in the fast time simulation software was provided to conduct mathematical optimization process. Also the initial values for the optimization were borrowed from the empirical regression formulas of the simulation software of Rheinmetall Defence ship simulator. Therefore the newly suggested mathematical optimization algorithm gave a successful result for estimation hydrodynamic coefficients. Proper optimization conditions of the objective function and constraints were also verified during the study.

Estimation of hydrodynamic coefficients for flow around cylinders in side-by-side arrangement with variation in separation gap

A finite-volume method (FVM) using a multi-block grid technique has been applied to investigate the hydrodynamic coefficients and to categorize the two-dimensional flow pattern around a pair of adjacent cylinders (known here after as double cylinders). Matching grids were used at the interface between blocks (cylinders), and the boundary conditions are imposed around the periphery to exchange physical values across the interface. To validate the developed numerical method, a case with laminar viscous flow around a single cylinder was carried out, the results showed good agreement compared to previously published data. Hydrodynamic coefficients, Strouhal number, and stagnation point change were thoroughly investigated as a function of the separation between the two cylinders. It is found that the changes of hydrodynamic coefficients due to variations in separation are well characterized by the five different vortex flow patterns, which can also be used to explain the flow and vortex pattern around the double cylinders.

Analysis on the controlled nonlinear motion of a test bed AUV–SNUUV I

This paper describes the estimation of hydrodynamic coefficients and the control algorithm based on a nonlinear mathematical modeling for a test bed autonomous underwater vehicle (AUV) named by SNUUV I (Seoul National University Underwater Vehicle I). A six degree of freedom mathematical model for SNUUV I is derived with linear and nonlinear hydrodynamic coefficients, which are estimated with the help of a potential code and also the system identification using multi-variable regression. A navigation algorithm is developed using three ranging sonars, pressure sensor and two inclinometers keeping towing tank applications in mind. Based on the mathematical model, a simulation program using a model-based control algorithm is designed for heading control and wall following control of SNUUV I. It is demonstrated numerically that the navigation system together with controller guides the vehicle to follow the desired heading and path with a sufficient accuracy. Therefore the model-based control algorithm can be designed efficiently using the system identification method based on vehicle motion experiments with the appropriate navigation system.

Estimation of hydrodynamic coefficients for an AUV using nonlinear observers

Hydrodynamic coefficients strongly affect the dynamic performance of an autonomous underwater vehicle. Although these coefficients are generally obtained experimentally such as through the planar-motion-mechanism (PMM) test, the measured values are not completely reliable because of experimental difficulties and errors involved. Another approach by which these coefficients can be obtained is the observer method, in which a model-based estimation algorithm predicts the coefficients. In this paper, the hydrodynamic coefficients are estimated using two nonlinear observers - a sliding mode observer and an extended Kalman filter. Their performances are evaluated by comparing the estimated coefficients obtained from the two observer methods with the values as determined from the PMM test. By using the estimated coefficients, a sliding mode controller is constructed for the diving and steering maneuver. It is demonstrated that the controller with the estimated values maintains the desired depth and path with sufficient accuracy.

Theoretical and Experimental Studies of Iterative Learning control of Underwater robot manipulators

On underwater robot manipulators, high speed and high precision are basic requirements in order to improve efficiency of operations. To satisfy these requirements, feedforward control inputs are crucial. For making feedforward inputs, one of the methods is to estimate all parameters of underwater robot dynamics. However, parameter estimation of hydrodynamic coefficients is very difficult because the dynamics is complicated. To overcome such a difficulty, we apply iterative learning control to underwater robots. In this paper, we theoretically discuss the performance of iterative learning control for underwater robot manipulators. Moreover, the effectiveness of the learning control is experimentally verified through several experimental results.