On Uncertainty Propagation in Mass, Damping and Stiffness Matrices Identification of Mechanical Systems

2012 ◽  
Author(s):  
Luis U. Medina ◽  
Sergio E. Díaz ◽  
Ningsheng Feng ◽  
Eric J. Hahn
Keyword(s):  
Error Propagation ◽  
Uncertainty Propagation ◽  
Mechanical Systems ◽  
Robust Algorithms ◽  
Error Sources ◽  
Suggested Approach ◽  
Stiffness Matrices ◽  
Accepted Practice ◽  
Noisy Measurements ◽  
Stiffness And Damping

The accuracy in estimating the mass, damping and stiffness matrices for mechanical systems depends on the error propagation through the stages involved in the parameter identification, i.e. excitation and response measurements, signal processing and modeling stages. Robust algorithms are available to estimate the system’s parameters in the presence of “noisy” measurements. However, uncertainties in the identified parameters of mechanical systems have not been usually reported or have simply been overlooked in the identification strategy. An overall uncertainty occurs for each identified parameter, and it may be defined in terms of error propagation. The recognition of relevant error contributions is the key to accomplishing parameter error estimation in the identification process, a task that may imply subtle aspects. An approach is proposed for uncertainty estimation in mass, stiffness and damping matrices for linearized mechanical systems. This approach is formulated as an extension of the accepted practice for evaluating experimental uncertainty for a scalar measurand. Typical error sources throughout the identification stages are also discussed. The suggested approach may be applied to identify mechanical systems in the frequency domain, and is independent of the algorithm used to estimate the system parameters. Practical limitations of the suggested approach are also discussed.

Some Remarks on the Identification of Damping Parameters at the Boundary of Vibrating Systems

1995 ◽  
Vol 48 (11S) ◽  
pp. S107-S110
Author(s):  
Peter Hagedorn ◽  
Ulrich Pabst
Keyword(s):  
Mathematical Modeling ◽  
Modal Analysis ◽  
Mechanical Systems ◽  
Experimental Modal Analysis ◽  
Steel Beam ◽  
Modal Data ◽  
Stiffness And Damping ◽  
Parameter Values ◽  
Vibrating Systems

In many cases, vibrating mechanical systems permit a reliable mathematical modeling with parameter values which are reasonably well known beforehand, except for the joints between different subsystems and at the boundaries. The boundary stiffness, which is often assumed as infinite, and the damping at the boundary, which is frequently ignored, are typically not well known. In this note, we discuss the identification of the boundary stiffness and damping parameters from modal data. As an example, we treat an elastic steel beam, for which an experimental modal analysis had been carried out in our laboratory.

scholarly journals A Study on the Uncertainty of a Laser Triangulator Considering System Covariances

Sensors ◽  
2020 ◽  
Vol 20 (6) ◽  
pp. 1630
Author(s):  
Pablo Puerto ◽  
Beñat Estala ◽  
Alberto Mendikute
Keyword(s):  
Error Propagation ◽  
Measurement Accuracy ◽  
Maximum Error ◽  
Experimental Methodology ◽  
Joint Measurement ◽  
Error Sources ◽  
Processing Times ◽  
Main Error ◽  
Laser Plane ◽  
System Variables

A laser triangulation system, which is composed of a camera and a laser, calculates distances between objects intersected by the laser plane. Even though there are commercial triangulation systems, developing a new system allows the design to be adapted to the needs, in addition to allowing dimensions or processing times to be optimized; however the disadvantage is that the real accuracy is not known. The aim of the research is to identify and discuss the relevance of the most significant error sources in laser triangulator systems, predicting their error contribution to the final joint measurement accuracy. Two main phases are considered in this study, namely the calibration and measurement processes. The main error sources are identified and characterized throughout both phases, and a synthetic error propagation methodology is proposed to study the measurement accuracy. As a novelty in uncertainty analysis, the present approach encompasses the covariances of correlated system variables, characterizing both phases for a laser triangulator. An experimental methodology is adopted to evaluate the measurement accuracy in a laser triangulator, comparing it with the values obtained with the synthetic error propagation methodology. The relevance of each error source is discussed, as well as the accuracy of the error propagation. A linearity value of 40 µm and maximum error of 0.6 mm are observed for a 100 mm measuring range, with the camera calibration phase being the main error contributor.

Reliable Robust Control Design for Uncertain Mechanical Systems

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
R. Sakthivel ◽  
Srimanta Santra ◽  
K. Mathiyalagan ◽  
A. Arunkumar
Keyword(s):  
Mechanical Systems ◽  
Sufficient Conditions ◽  
Schur Complement ◽  
Linear Matrix ◽  
Actuator Failure ◽  
Time Varying Delay ◽  
Stiffness Matrices ◽  
Control Scheme ◽  
Robust Control Design ◽  
Varying Delay

In this article, we consider the problem of reliable H∞ control for a class of uncertain mechanical systems with input time-varying delay and possible occurrence of actuator faults. In particular, we assume that linear fractional transformation (LFT) uncertainty formulations appear in the mass, damping, and stiffness matrices. The main objective is to design a state feedback reliable H∞ controller such that, for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly asymptotically stable while satisfying a prescribed H∞ performance constraint. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and using linear matrix inequality (LMI) approach, a new set of sufficient conditions are derived in terms of LMIs for the existence of robust reliable H∞ controller. Further, Schur complement and Jenson's integral inequality are used to substantially simplify the derivation in the main results. The obtained results are formulated in terms of LMIs which can be easily verified by the standard numerical softwares. Finally, numerical examples with simulation result are provided to illustrate the applicability and effectiveness of the proposed reliable H∞ control scheme. The numerical results reveal that the proposed theory significantly improves the upper bound of time delays and minimum feasible H∞ performance index over some existing works.

Nonparametric Identification of Nonlinear Piezoelectric Mechanical Systems

2018 ◽  
Vol 85 (11) ◽  
Author(s):  
Tian-Chen Yuan ◽  
Jian Yang ◽  
Li-Qun Chen
Keyword(s):  
Hilbert Transform ◽  
Electromechanical Coupling ◽  
Mechanical Systems ◽  
Nonparametric Identification ◽  
Mapping Approach ◽  
Stiffness Characteristic ◽  
The Hilbert Transform ◽  
Stiffness And Damping ◽  
Electric Signals ◽  
Hardening Nonlinearity

Two novel nonparametric identification approaches are proposed for piezoelectric mechanical systems. The novelty of the approaches is using not only mechanical signals but also electric signals. The expressions for unknown mechanical and electric terms are given based on the Hilbert transform. The signals are decomposed and re-assembled to obtain smooth stiffness and damping curves. The current mapping approach is developed to identify accurately a piezoelectric mechanical system with strongly nonlinear electric terms. The developed identification approaches are successfully implemented to simulate signals obtained from different nonlinear piezoelectric mechanical systems, including Duffing nonlinearity, softening and hardening nonlinearity, and Duffing nonlinearity with strong nonlinear electric terms. The proposed approaches are successfully applied to experimental signals of a circular laminated plate device in order to identify the nonlinear stiffness functions, damping functions, electromechanical coupling functions, and equivalent capacitance functions. The results show both softening and hardening nonlinearity in the stiffness characteristic and weak nonlinearity in electric characteristics. The results of the Hilbert transform based approach and the current mapping approach are compared, and the outcomes show good agreements.

A Novel Approach to Kinematic Reliability Analysis for Planar Parallel Manipulators

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Qiangqiang Zhao ◽  
Junkang Guo ◽  
Dingtang Zhao ◽  
Dewen Yu ◽  
Jun Hong
Keyword(s):  
Reliability Analysis ◽  
Error Propagation ◽  
Simulation Method ◽  
Parallel Manipulators ◽  
Plane Motion ◽  
Error Sources ◽  
Novel Approach ◽  
Safe Region ◽  
Motion Groups ◽  
Planar Parallel Manipulators

Abstract Kinematic reliability is an essential index that assesses the performance of the mechanism associating with uncertainties. This study proposes a novel approach to kinematic reliability analysis for planar parallel manipulators based on error propagation on plane motion groups and clipped Gaussian in terms of joint clearance, input uncertainty, and manufacturing imperfection. First, the linear relationship between the local pose distortion coming from the passive joint and that caused by other error sources, which are all represented by the exponential coordinate, are established by means of the Baker–Campbell–Hausdorff formula. Then, the second-order nonparametric formulas of error propagation on independent and dependent plane motion groups are derived in closed form for analytically determining the mean and covariance of the pose error distribution of the end-effector. On this basis, the kinematic reliability, i.e., the probability of the pose error within the specified safe region, is evaluated by a fast algorithm. Compared to the previous methods, the proposed approach has a significantly high precision for both cases with small and large errors under small and large safe bounds, which is also very efficient. Additionally, it is available for arbitrarily distributed errors and can analyze the kinematic reliability only regarding either position or orientation as well. Finally, the effectiveness and advantages of the proposed approach are verified by comparing with the Monte Carlo simulation method.

Perpetual points in natural mechanical systems with viscous damping: A theorem and a remark

2020 ◽  
pp. 095440622093483
Author(s):  
Fotios Georgiades
Keyword(s):  
Rigid Body ◽  
Mechanical Systems ◽  
Dissipative Systems ◽  
Viscous Damping ◽  
Ongoing Research ◽  
Rigid Body Motions ◽  
Gyroscopic Effects ◽  
Nonlinear Mechanical Systems ◽  
Stiffness And Damping ◽  
Perpetual Points

Perpetual points have been defined recently and their role in the dynamics of mechanical systems is ongoing research. In this article, the nature of perpetual points in natural dissipative mechanical systems with viscous damping, but excepting any externally applied load, is examined. In linear dissipative systems, a theorem and its inverse are proven stating that the perpetual points exist if the stiffness and damping matrices are positive semi-definite and they coincide with the rigid body motions. In nonlinear dissipative natural mechanical systems with viscous damping excepting any external load, the existence of perpetual points that are associated with rigid body motions is shown. Also, an additional type of perpetual points due to the added dissipation is shown that exists, and this type of perpetual points, at least in principle can be used for identification of dissipation in nonlinear mechanical systems. Further work is needed to understand the nature of this additional type of perpetual points. In all the examined examples the perpetual points when they exist, they are not just a few points, but they are forming manifolds in state space, the Perpetual Manifolds, and their geometric characteristics worth further investigation. The findings of this article are applied in all mechanical systems with no gyroscopic effects on their motion, e.g. cars, airplanes, trucks, rockets, robots, etc. and can be used as part of the elementary studies for basic design of all mechanical systems. This work paves the way for new design processes targeting stable rigid body motions eliminating any vibrations in mechanical systems.

Analysis of uncertainty propagation through model parameters and structure

2010 ◽  
Vol 62 (6) ◽  
pp. 1230-1239 ◽  
Author(s):  
Abhijit Patil ◽  
Zhi-Qiang Deng
Keyword(s):  
Sensitivity Analysis ◽  
Standard Deviation ◽  
Dissolved Oxygen ◽  
Error Propagation ◽  
Uncertainty Propagation ◽  
Sensitivity Coefficient ◽  
Model Parameters ◽  
Hydrologic Simulation ◽  
Hspf Model ◽  
Forcing Function

Estimation of uncertainty propagation in watershed models is challenging but useful to total maximum daily load (TMDL) calculations. This paper presents an effective approach, involving the combined application of Rosenblueth method and sensitivity analysis, to the determination of uncertainty propagation through the parameters and structure of the HSPF (Hydrologic Simulation Program-FORTRAN) model. The sensitivity analysis indicates that the temperature is a major forcing function in the DO-BOD balance and controls the overall dissolved oxygen concentration. The mean and standard deviation from the descriptive statistics of dissolved oxygen data obtained using the HSPF model are compared to those estimated using Rosenblueth's method. The difference is defined as the error propagated from water temperature through dissolved oxygen. The error propagation, while considering the second order sensitivity coefficient in Rosenblueth's method, is observed to have a mean of 0.281 mg/l and a standard deviation of 0.099 mg/l. A relative low error propagation value is attributed to low skewness of dependent and independent variables. The results provide new insights into the uncertainty propagation in the HSPF model commonly used for TMDL development.

Error sources and error propagation in the Levinson-Durbin algorithm

1993 ◽  
Vol 41 (4) ◽  
pp. 1635-1651 ◽  
Author(s):  
C.N. Papaodysseus ◽  
E.B. Koukoutsis ◽  
C.N. Triantafyllou
Keyword(s):  
Error Propagation ◽  
Error Sources

Dämpfungsmaße in Lagerpassungen*/Identification of damping values for spindle bearing interfaces

2019 ◽  
Vol 109 (05) ◽  
pp. 342-346
Author(s):  
C. Brecher ◽  
T. Motschke ◽  
M. Fey
Keyword(s):  
Dynamic Simulation ◽  
State Of The Art ◽  
Mechanical Systems ◽  
Journal Bearings ◽  
Hertzian Contact ◽  
Analytical Models ◽  
Ball Bearings ◽  
The Past ◽  
Spindle Bearing ◽  
Stiffness And Damping

Die präzise Simulation mechanischer Systeme erfordert neben Steifigkeitswerten für Koppelelemente, die Kenntnis von Dämpfungswerten. Im Gegenteil zu Gleitlagern sind die physikalischen Effekte in Wälzlagern, die zur Energiedissipation führen, nur mit sehr großem rechnerischen Aufwand numerisch beschreibbar und experimentell validierte Modelle besitzen nur in engen Betriebsgrenzen Gültigkeit. Als Hauptdämpfungsquellen wurden bisher Kugel-Laufbahn-Kontakte sowie die Passungen der Lagerringe identifiziert. Letztere werden in diesem Beitrag untersucht. Ziel ist eine Aussage über Grenzen, innerhalb derer sich der Einfluss von Fugendämpfung bewegt   The dynamic simulation of mechanical systems requires reliable stiffness and damping values to enable meaningful results. Especially the inclusion of coupling elements into the simulation always leads to challenges regarding the interpretation of predicted results. Unlike journal bearings, there are no analytical models for roller and ball bearings that allow the prediction of damping values, whereas the prediction of stiffness values is already state of the art. In the past, the Hertzian contact as well as the bearing interfaces were identified as the main damping sources, but till today, no reliable models have been derived. This article deals therefore with a method to quantify the influence of bearing interface damping parameters.

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