Regression analysis and parameter identification

SIMULATION ◽  
1967 ◽  
Vol 9 (1) ◽  
pp. 39-47 ◽  
Author(s):  
Arthur I. Rubin ◽  
Stanley Driban ◽  
Wayne W. Miessner
Keyword(s):  
Equations Of Motion ◽  
Real Problem ◽  
Unknown Parameters ◽  
Aerodynamic Stability ◽  
Transient Time ◽  
Regression Problem ◽  
Stability Derivatives ◽  
Straight Line ◽  
Time Histories ◽  
The Stability

The steps necessary to derive the regression differential equations for a set of unknown parameters are presented. A simple straight-line algebraic regression problem is re viewed. A real problem, that of finding the aerodynamic stability derivatives for the lateral equations of motion of an airplane, is presented. Preliminary results, using real airplane transient time histories, are compared with simu lated transients obtained using wind-tunnel values for the stability derivatives.

Stability of the Vertical Autorotation of a Single-Winged Samara

1992 ◽  
Vol 59 (4) ◽  
pp. 1000-1008 ◽  
Author(s):  
D. Seter ◽  
A. Rosen
Keyword(s):  
Equilibrium State ◽  
Equations Of Motion ◽  
Numerical Differentiation ◽  
Aerodynamic Stability ◽  
Small Perturbations ◽  
Stability Derivatives ◽  
Basic Equilibrium ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Derivatives Of

A numerical model to investigate the stability of the vertical autorotation of a singlewinged samara is presented. This model is obtained after the method of small perturbations about an equilibrium state is applied on the nonlinear equations of motion of the samara. The aerodynamic stability derivatives of the wing are obtained by numerical differentiation. The model is used in order to study the influence of different parameters on the stability. Since the stability is highly dependent on the basic equilibrium state, the influence of the different parameters on the basic state is also presented and discussed. The theoretical model is validated by comparing its results with qualitative experimental results.

scholarly journals A Study of the Stability of a Plate-Like Load Towed beneath a Helicopter

1971 ◽  
Vol 13 (5) ◽  
pp. 330-343 ◽  
Author(s):  
D. F. Sheldon
Keyword(s):  
Equations Of Motion ◽  
Physical Parameters ◽  
Recent Experience ◽  
Wind Tunnel Testing ◽  
Stability Derivatives ◽  
Direct Indication ◽  
Metric Dimensions ◽  
Set Up ◽  
The Stability ◽  
Derivative Information

Recent experience has shown that a plate-like load suspended beneath a helicopter moving in horizontal forward flight has unstable characteristics at both low and high forward speeds. These findings have prompted a theoretical analysis to determine the longitudinal and lateral dynamic stability of a suspended pallet. Only the longitudinal stability is considered here. Although it is strictly a non-linear problem, the usual assumptions have been made to obtain linearized equations of motion. The aerodynamic derivative data required for these equations have been obtained, where possible, for the appropriate ranges of Reynolds and Strouhal number by means of static and dynamic wind tunnel testing. The resulting stability equations (with full aerodynamic derivative information) have been set up and solved, on a digital computer, to give direct indication of a stable or unstable system for a combination of physical parameters. These results have indicated a longitudinal unstable mode for all practical forward speeds. Simultaneously the important stability derivatives were found for this instability and modifications were made subsequently in the suspension system to eliminate the instabilities in the longitudinal sense. Throughout this paper, all metric dimensions are given approximately.

Determination of Stability Derivatives by Impulse-Response Techniques

1977 ◽  
Vol 14 (02) ◽  
pp. 265-275
Author(s):  
Carl A. Scragg
Keyword(s):  
Memory Effect ◽  
Impulse Response ◽  
Traditional Method ◽  
Equations Of Motion ◽  
Experimental Results ◽  
Regular Motion ◽  
Stability Derivatives ◽  
The Stability ◽  
Derivatives Of

This paper presents a new method of experimentally determining the stability derivatives of a ship. Using a linearized set of the equations of motion which allows for the presence of a memory effect, the response of the ship to impulsive motions is examined. This new technique is compared with the traditional method of regular-motion tests and experimental results are presented for both methods.

scholarly journals Periodic stability analysis of wind turbines operating in turbulent wind conditions

2016 ◽  
Author(s):  
Riccardo Riva ◽  
Stefano Cacciola ◽  
Carlo Luigi Bottasso
Keyword(s):  
Stability Analysis ◽  
Wind Turbines ◽  
Equations Of Motion ◽  
Reduced Order ◽  
Stochastic Disturbance ◽  
Multibody Model ◽  
Time Histories ◽  
Identification Technique ◽  
Model Independent ◽  
The Stability

Abstract. In this work, a method for the stability analysis of wind turbines is described. A system identification technique, formulated for handling stochastic disturbances, is used to identify a periodic reduced order model from suitable recorded time histories of the system. Afterwards, such reduced model is analyzed according to Floquet theory. The formulation is model-independent, in the sense that it does not require knowledge of the equations of motion of the periodic system being analyzed, and it is applicable to an arbitrary number of blades and to any configuration of the machine. In addition, as wind turbulence can be viewed as a stochastic disturbance, the method is also applicable to real wind turbines operating in the field. The characteristics of the new method are verified first with a simplified analytical model, and then using a high-fidelity multibody model of a multi-MW wind turbine. Results are compared with those obtained by the well known operational modal analysis approach.

Helicopters

1922 ◽  
Vol 26 (142) ◽  
pp. 390-407
Author(s):  
John Case
Keyword(s):  
Experimental Work ◽  
Steady Motion ◽  
Forward Motion ◽  
Stability Equation ◽  
Aerodynamic Efficiency ◽  
Helicopter Flight ◽  
Stability Derivatives ◽  
Straight Line ◽  
The Subject ◽  
The Stability

SummaryThe present article is an account of some calculations on helicopters.Airscrews have been calculated for different conditions according to two theories: (1) the multiplane interference theory; (2) Glauert's vortex theor). According to both there should be no difficulty in designing a screw to give a good lift at a reasonable rate of climb, and the ceiling should also be quite good. When we consider the speed of falling, with the screws free-wheeling, the two theories give widely different results, and the practicability of the helicopter depends largely upon this question being settled. Simple airscrew theory shows that at least moderate speeds should be obtainable by inclining the airscrew axis. For many reasons it seems desirable that the screws should have at least four blades; gyroscopic couples on the whole machine are eliminated; the forces are widely fluctuating during forward motion with only two blades; the stability derivatives and equations are simplified; but the aerodynamic efficiency will be impaired. In general the stability equation is of the tenth degree, and the lateral and longitudinal stabilities are not separable when the machine, in a state of steady motion in a straight line, receives an asymmetrical disturbance.The following notes are the results of an attempt to investigate the theoretical possibilities of the helicopter, and generally to develop some branches of the theory of helicopters. In this country extremely little work on the subject seems to have been published, and the only experiments I have been able to find are those given in the Report of the Advisory Committee for 1917-18 (Vol. II.). Several articles have appeared in “ L'Aérophile ” from time to time, notably by Lamé, Touissaint and Margoulis, and some experimental work has been done by Eiffel. But it is extremely difficult to find adequate experimental results with which to compare any theory ; for instance it is very rare to find results of tests on airscrews working under helicopteral conditions, and also the aerodynamic data of the aerofoil sections used. In the matter of stability I do not know of any experimental work at all.I shall give first the results of my investigations into airscrews for helicopters, and then proceed to the consideration of the dynamics of helicopter flight and the development of the stability equations.

scholarly journals The finite-dipole dynamical system

2012 ◽  
Vol 468 (2146) ◽  
pp. 3006-3026 ◽  
Author(s):  
Andrew A. Tchieu ◽  
Eva Kanso ◽  
Paul K. Newton
Keyword(s):  
Equations Of Motion ◽  
Point Vortices ◽  
Inviscid Fluid ◽  
Straight Line ◽  
Single Dipole ◽  
Gradient Based ◽  
Finite Distance ◽  
The Difference ◽  
The Stability ◽  
Induced Velocity

The notion of a finite dipole is introduced as a pair of equal and opposite strength point vortices (i.e. a vortex dipole) separated by a finite distance. Equations of motion for N finite dipoles interacting in an unbounded inviscid fluid are derived from the modified interaction of 2 N independent vortices subject to the constraint that the inter-vortex spacing of each constrained dipole, ℓ, remains constant. In the absence of all other dipoles and background flow, a single dipole moves in a straight line along the perpendicular bisector of the line segment joining the two point vortices comprising the dipole, with a self-induced velocity inversely proportional to ℓ. When more than one dipole is present, the velocity of the dipole centre is the sum of the self-induced velocity and the average of the induced velocities on each vortex comprising the pair due to all the other dipoles. Each dipole orients in the direction of shear gradient based on the difference in velocities on each of the two vortices in the pair. Several numerical experiments are shown to illustrate the interactions between two and three dipoles in abreast and tandem configurations. We also show that equilibria (multi-poles) can form as a result of the interactions, and we study the stability of polygonal equilibria, showing that the N =3 case is linearly stable, whereas the N >3 case is linearly unstable.

Stable Calibrations of Six-DOF Serial Robots by Using Identification Models with Equalized Singular Values

Robotica ◽  
2021 ◽  
pp. 1-22
Author(s):  
Zhouxiang Jiang ◽  
Min Huang
Keyword(s):  
Industrial Robot ◽  
Singular Values ◽  
Calibration Method ◽  
Identification Accuracy ◽  
Condition Numbers ◽  
Measurement Instruments ◽  
Unknown Parameters ◽  
Calibration Methods ◽  
Six Dof ◽  
The Stability

SUMMARY In typical calibration methods (kinematic or non-kinematic) for serial industrial robot, though measurement instruments with high resolutions are adopted, measurement configurations are optimized, and redundant parameters are eliminated from identification model, calibration accuracy is still limited under measurement noise. This might be because huge gaps still exist among the singular values of typical identification Jacobians, thereby causing the identification models ill conditioned. This paper addresses such problem by using new identification models established in two steps. First, the typical models are divided into the submodels with truncated singular values. In this way, the unknown parameters corresponding to the abnormal singular values are removed, thereby reducing the condition numbers of the new submodels. However, these models might still be ill conditioned. Therefore, the second step is to further centralize the singular values of each submodel by using a matrix balance method. Afterward, all submodels are well conditioned and obtain much higher observability indices compared with those of typical models. Simulation results indicate that significant improvements in the stability of identification results and the identifiability of unknown parameters are acquired by using the new identification submodels. Experimental results indicate that the proposed calibration method increases the identification accuracy without incurring additional hardware setup costs to the typical calibration method.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

Hertz Contact Force Model With Permanent Indentation in Impact Analysis of Solids

1992 ◽  
Author(s):  
Hamid M. Lankarani ◽  
Parviz E. Nikravesh
Keyword(s):  
Contact Force ◽  
Impact Analysis ◽  
Equations Of Motion ◽  
Solid Particles ◽  
Hertzian Contact ◽  
Contact Period ◽  
Force Model ◽  
Unknown Parameters ◽  
Contact Force Model ◽  
Energy And Momentum

Abstract A continuous analysis method for the direct-central impact of two solid particles is presented. Based on the assumption that local plasticity effects are the sole factor accounting for the dissipation of energy in impact, a Hertzian contact force model with permanent indentation is constructed. Utilizing energy and momentum considerations, the unknown parameters in the model are analytically evaluated in terms of a given coefficient of restitution and velocities before impact. The equations of motion of the two solids may then be integrated forward in time knowing the variation of the contact force during the contact period. For Illustration, an impact of two soft metallic particles is studied.

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