Nonlinear Analysis of an Oscillating Wave Surge Converter in Frequency Domain via Statistical Linearization

2021 ◽  
Author(s):  
Leandro Souza Pinheiro da Silva ◽  
Nataliia Sergiienko ◽  
Boyin Ding ◽  
Benjamin Cazzolato ◽  
Celso Pesce ◽  
...  
Keyword(s):  
Nonlinear Analysis ◽  
Frequency Domain ◽  
Statistical Linearization

Nonlinear Analysis of an Oscillating Wave Surge Converter in Frequency Domain via Statistical Linearization

2020 ◽  
Author(s):  
Leandro S. P. da Silva ◽  
Nataliia Y. Sergiienko ◽  
Benjamin S. Cazzolato ◽  
Boyin Ding ◽  
Celso P. Pesce ◽  
...  
Keyword(s):  
Nonlinear Analysis ◽  
Frequency Domain ◽  
Wave Energy ◽  
Numerical Models ◽  
Computational Cost ◽  
Viscous Drag ◽  
Design Parameters ◽  
Statistical Linearization ◽  
Mean Power ◽  
Energy Devices

Abstract Wave energy devices operate in resonant conditions to optimize power absorption, which leads to large displacements. As a result, nonlinearities play an important role in the system dynamics and must be accounted for in the numerical models for realistic prediction of the power generated. In general, time domain (TD) simulations are employed to capture the effects of the nonlinearities. However, the computational cost associated with these simulations is considerably higher compared to linear frequency domain (FD) methods. In this regard, the following work deals with the nonlinear analysis of an oscillating wave surge converter (OWSC) in the FD via the statistical linearization (SL) technique. Four nonlinearities for the proposed device are addressed: Coulomb-like torque regulated by the direction of motion, viscous drag torque, nonlinear buoyant net torque, and parametric excitation torque modulated by the flap angle. The reliability of the SL technique is compared with nonlinear TD simulations in terms of response probability distribution and power spectrum density (PSD) of the response and torque; and mean power produced. The results have demonstrated a good agreement between TD simulations and SL, while the computation time of the SL model is approximately 3 orders of magnitude faster. As a result, SL is a valuable tool to assess the OWSC performance under various wave scenarios over a range of design parameters, and can assist the development of such wave energy converters (WECs).

Nonlinear Analysis of Rail Vehicle Forced Lateral Response and Stability

1979 ◽  
Vol 101 (3) ◽  
pp. 230-237 ◽  
Author(s):  
J. Karl Hedrick ◽  
A. V. Arslan
Keyword(s):  
Nonlinear Analysis ◽  
Frequency Domain ◽  
Numerical Algorithm ◽  
Design Tool ◽  
Statistical Linearization ◽  
Rail Vehicle ◽  
Rail Vehicles ◽  
Lateral Response ◽  
Wheel Profile ◽  
Track Irregularities

The method of statistical linearization is presented as a design tool for rail vehicles that is capable of including fundamental nonlinearities such as wheel profile geometry and suspension nonlinearities. The method is capable of predicting the response of the vehicle to statistical track irregularities as well as the onset of hunting. The fundamentals of the method, an efficient frequency domain numerical algorithm for stationary response, and a design example are presented. The design example illustrates the influence of wheel profile, gage, track roughness, and suspension variations on vehicle response and stability.

Analysis and Control of Nonlinear Systems

1993 ◽  
Vol 115 (2B) ◽  
pp. 351-361 ◽  
Author(s):  
J. Karl Hedrick
Keyword(s):  
Nonlinear Analysis ◽  
Flight Control ◽  
Model Error ◽  
Forced Response ◽  
Equivalent Linearization ◽  
Statistical Linearization ◽  
Linearization Methods ◽  
Analysis Tools ◽  
Highly Nonlinear ◽  
And Control

This paper describes my work on nonlinear analysis and control over the last twenty years. The first part of the paper concerns the development of nonlinear analysis tools for predicting stability and forced response characteristics of high speed ground vehicles. The principal motivation was to develop an alternative to “brute force” time domain simulation. The developed tools were extensions of “describing function” or “equivalent linearization” methods for both periodic and stochastic excitation. The “statistical linearization” analysis tools were then extended and applied to design control laws for nonlinear stochastic regulators. The second part of the paper was motivated by control system design for highly nonlinear, multivariable systems, such as automotive powertrain control and aircraft flight control. For these classes of systems, statistical linearization procedures are computationally cumbersome and also provide no stability or robustness guarantees. A method which has proven extremely powerful, both theoretically and experimentally, is “sliding control.” This technique is a form of input/output linearization that directly incorporates model error information with stability and performance measures. My students and I found several difficulties in the direct application of this method to automotive and aircraft control. This paper describes our solutions to the problems of repeated model differentiation, differentiation of model error, undesirable “internal dynamics” and systems with saturating control inputs.

Nonlinear Analysis of an Oscillating Water Column Wave Energy Device in Frequency Domain via Statistical Linearization

2019 ◽  
Author(s):  
Leandro S. P. da Silva ◽  
Celso P. Pesce ◽  
Helio M. Morishita ◽  
Rodolfo T. Gonçalves
Keyword(s):  
System Dynamics ◽  
Frequency Domain ◽  
Water Column ◽  
Wave Energy ◽  
Time Domain ◽  
Computational Cost ◽  
Operating Conditions ◽  
Statistical Linearization ◽  
Large Displacements ◽  
Oscillating Water Column

Abstract Wave energy converters (WECs) are often subject to large displacements during operating conditions. Hence, nonlinearities present in numerical methods to estimate the performance of WECs must be considered for realistic predictions. These large displacements occur when the device operates on resonant conditions, which results in maximum energy conversion. The system dynamics are usually simulated via time domain models in order to being able to capture nonlinearities. However, a high computational cost is associated with those simulations. Alternatively, the present work treats the nonlinearities in the frequency domain via Statistical Linearization (SL). The SL results are compared to the Power Spectrum Density (PSD) of time domain simulations to verify the reliability of the proposed method. In this regard, the work initiates with the derivation of the governing equations of the air-chamber and the Oscillating Water Column (OWC). Then, the SL technique is presented and applied. The SL results show a satisfactory agreement for the system dynamics, mean surface elevation, mean pressure, and mean power compared to time domain simulations. Also, the SL technique produces a rapid estimation of the response, which is an effective approach for the evaluation of numerous environmental conditions and design, and further optimization procedures.

Nonlinear Analysis of a Heaving Point Absorber in Frequency Domain via Statistical Linearization

2019 ◽  
Author(s):  
Leandro S. P. da Silva ◽  
Helio M. Morishita ◽  
Celso P. Pesce ◽  
Rodolfo T. Gonçalves
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Statistical Linearization ◽  
Mean Power ◽  
Energy Devices ◽  
Drag Forces ◽  
System A ◽  
Spectrum Density ◽  
The Time Domain ◽  
Heave Motion

Abstract The majority of wave energy devices operate close to resonant conditions to enhance energy conversion resulting in large displacements. As a result, nonlinearities significantly contribute to the dynamics of the system. A typical approach to predict the behavior of the system and power output relies on the derivation of a mathematical model in the time domain to simulate the dynamics through some numerical codes. However, a relatively high computational demand is required for those simulations. In this regard, the present work deals with the nonlinearities in the frequency domain via Statistical Linearization. Two different power-take-off systems are investigated, a linear and a hydraulic one, and their mean power calculations are derived based on the Statistical Linearization. The reliability of the method is verified against the Power Spectrum Density (PSD) of nonlinear time domain simulations. Only the heave motion is analyzed, and several nonlinearities commonly reported for Point Absorbers (PA) were considered, such as cubic stiffness, geometric nonlinearities, drag forces, and Coulomb forces. The approach employed in this work offers a reliable estimation of body dynamics for all nonlinearities considered. In addition, the present method produced a fast estimation, which can be valuable for the assessment of several designs and sea load conditions.

scholarly journals A method of nonlinear analysis in the frequency domain

1980 ◽  
Vol 29 (3) ◽  
pp. 459-483 ◽  
Author(s):  
J. Victor ◽  
R. Shapley
Keyword(s):  
Nonlinear Analysis ◽  
Frequency Domain

scholarly journals The Choice of Evaluation Vibration Car Security

2019 ◽  
pp. 1-14
Author(s):  
L. F. Zheglov ◽  
A. B. Fominykh
Keyword(s):  
Dynamic System ◽  
Frequency Domain ◽  
Time Domain ◽  
Vibration Isolation ◽  
Frequency Characteristics ◽  
Road Surface ◽  
Statistical Linearization ◽  
Support Surface ◽  
Dirt Road ◽  
The Time Domain

In the presented material of the article the debatable question - a question of a choice of the field of mathematical modeling of system of vibration isolation of the car is considered. It is known that such a problem can be solved in the frequency and time domain. Since the primary vibration isolation system of the car has non-linear elements, the question arises: how does the solution of the linearized dynamic system in the frequency domain correspond to the data of calculations of the accepted indicators in the time domain? The problem is solved with a random kinematic perturbation from the road surface. Therefore, when working in the time domain, it is necessary to pre-select the method of statistical linearization from the known in practice design of automatic control systems.Four methods of statistical linearization, using which calculations were carried out in the frequency domain, are considered. For a similar dynamic system with its initial and statistically linearized nonlinear elements, calculations were carried out in the time domain. It is shown that the first method of statistical linearization is the most adaptive, according to the amplitude-frequency characteristics of the system. Such calculations were carried out for two surfaces corresponding to the cobblestone and dirt road at different speeds of the car.The analysis of the calculated amplitude-frequency characteristics was carried out for the "resonant" speed of motion, at which the greatest manifestation of the system nonlinearity takes place. When driving in this mode, the system significantly increases the probability of losing contact with the tire support surface. This violates the safety of the vehicle and the system is out of the vibration safety analysis area. Especially this phenomenon is observed when driving on a dirt road at a "resonant" speed. The final results of the calculations are separate-frequency and integral parameters. The latter do not give priority in the selection of the area of calculation, provided the safety of the vehicle.Thus, it can be concluded that the adequacy of the calculations in the frequency and time domain under really specified conditions of the vehicle on the corresponding road surface. However, testing of the problem to be solved, for example, by the eigenfrequency vector of a conservative system, is advisable to be carried out in the frequency domain.

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