Wavelet-Based Damage Detection of Multi-Degree-of-Freedom Structures

2004 ◽  
Author(s):  
Yuito Hashimoto ◽  
Arata Masuda ◽  
Akira Sone
Keyword(s):  
Wavelet Transform ◽  
Damage Detection ◽  
Structural Model ◽  
Structural Parameters ◽  
Degree Of Freedom ◽  
Space Representation ◽  
State Space Representation ◽  
Damage Location ◽  
Propagation Of Singularities ◽  
Structural Responses

In this paper, a method is proposed to identify the occurrence and the location of damage from the responses of multi-degree-of-freedom (MDOF) structures based on the wavelet transform, which has the capacity to detect discontinuities and singularities. First, the propagation of singularities in responses is investigated qualitatively in order to explain how the structural responses are influenced by sudden changes of structural parameters (stiffness) resulting from damages. Next, in order to confirm the proposed method for complicated models, we evaluate the influence of sudden changes of structural parameters on responses quantitatively, and the relations between the wavelet transform and the damage location by the aid of the state space representation of the MDOF structures. Finally, laboratory-scale experiments are carried out to verify the performance and detectability of the proposed methods in a fourth story structural model installed by additional stiffness members.

Identification of Structural Parameters by Wavelet Transform of Acceleration Response

1999 ◽  
Author(s):  
Akira Sone ◽  
Ryutaro Segawa ◽  
Shizuo Yamamoto ◽  
Arata Masuda ◽  
Hiroaki Hata
Keyword(s):  
Wavelet Transform ◽  
Numerical Simulations ◽  
Structural Model ◽  
Structural Parameters ◽  
Degree Of Freedom ◽  
Acceleration Response ◽  
Single Degree Of Freedom ◽  
Displacement Response ◽  
Single Degree ◽  
Stiffness And Damping

Abstract The method to identify structural parameters of multi-degree of freedom structures by the wavelet transform of displacement response is previously proposed However, the vibration of structure is measured by the accelerometers. Therefore, if it is possible to identify structural parameters by the wavelet transform of only acceleration responses, it is very useful. In this paper, the method to identify structural parameters such as stiffness and damping by wavelet transform of acceleration responses is presented. To verify the applicability of the proposed method, numerical simulations using the single degree of freedom structure and the four-degree-of-freedom structure and the experiments using simple structural model are conducted. From both results, it has been clear that the proposed method can give the good estimation for the structural parameters.

Study on Damage Detection of Bridge Based on Wavelet Multi-Scale Analysis

2013 ◽  
Vol 639-640 ◽  
pp. 1010-1014 ◽  
Author(s):  
Ke Ding ◽  
Ting Peng Chen
Keyword(s):  
Wavelet Transform ◽  
Damage Detection ◽  
Detection Method ◽  
Mode Shapes ◽  
Scale Analysis ◽  
Multi Scale ◽  
Damage Location ◽  
Transform Coefficients ◽  
Beam Bridge ◽  
Multi Scale Analysis

The damage detection method based on wavelet multi-scale analysis is presented in the paper. The damage location can be identified by analyzing the multi-scale wavelet transform coefficients of curvatures of mode shapes. The extreme value of wavelet transform coefficients indicates the damage location. But it is difficult to detect the location of defect if the defect is near to the equilibrium position of vibration. In order to solve this problem, we put forward a method which is to add the wavelet transform coefficients of multi modals together. The method can effectively overcome the above problem. Three damage situations of simply supported beam bridge are discussed in the paper. The results show that the peaks of wavelet transform coefficients indicate the damage location of structural. It is possible to pinpoint the damage location based on wavelet multi-scale analysis on curvatures of mode shapes.

SOFTENING BRANCHES OF A TWO-DEGREE-OF-FREEDOM SYSTEM INDUCED BY SPATIAL BUCKLING

2006 ◽  
Vol 06 (04) ◽  
pp. 493-512 ◽  
Author(s):  
NOËL CHALLAMEL
Keyword(s):  
Structural Model ◽  
Structural Parameters ◽  
Degree Of Freedom ◽  
Lateral Loading ◽  
Load Parameter ◽  
Imperfection Sensitivity ◽  
Softening Effect ◽  
Out Of Plane ◽  
Secondary Bifurcation ◽  
Two Degree Of Freedom

The aim of this paper is to show how geometrical non-linearity may induce equivalent softening in a simple two-degree-of-freedom spatial elastic system. The generic structural model studied is a generalization of Augusti's spatial model, incorporating lateral loading. This model could be used as a teaching model to understand the softening effect induced by out-of-plane buckling. The lateral loading in the plane of maximal stiffness is considered as the varying load parameter, whereas the vertical load is perceived as a constant parameter. It is shown that a bifurcation occurs at the critical horizontal load. The fundamental path becomes unstable, beyond this critical value. However, two symmetrical bifurcate solutions appear, whose stability depend on the structural parameters value. No secondary bifurcation is observed for this system. The presented system possesses imperfection sensitivity, and imperfection insensitivity, depending on the values of the structural parameters. In any case, for sufficiently large rotations, collapse occurs with unstable softening branches induced by spatial buckling.

Consideration of Complex Support Structure Dynamics in Rotordynamic Assessments

2013 ◽  
Author(s):  
Thomas D. Krüger ◽  
Sauro Liberatore ◽  
Eric Knopf ◽  
Alastair Clark
Keyword(s):  
Dynamic Behaviour ◽  
Computation Time ◽  
Degree Of Freedom ◽  
Space Representation ◽  
Lumped Mass ◽  
Support Structure ◽  
State Space Representation ◽  
Prediction Quality ◽  
Theoretical Approaches

In rotordynamic analyses, support structures are commonly represented by lumped mass systems (single-degree-of-freedom, SDOF). This representation is easy to implement using standard rotordynamic tools. However, in reality the dynamic behaviour of the support structure (e.g. pedestals, casings, foundations) are in general much more complex. Only a multi-degree-of-freedom (MDOF) representation provides modelling close to reality. For many applications the dynamic behaviour of the support structure significantly influences the rotordynamic characteristics of the shaft train and therefore needs to be included in the assessment. Due to this impact, a good quality of the dynamic model used for the support structure is imperative. Regarding the rotor itself, the modelling is well understood and the prediction quality is excellent, not least due to the jointless welded rotor design. Numerous theoretical approaches exist for considering the complex dynamic behaviour of the support structure, all coming along with both drawbacks and opportunities. By discussing the characteristics of established approaches for modelling the support structure, the paper particularly presents an advanced theoretical approach based on a state-space representation using modal parameters. A case study of a real shaft train is shown, including a comparison of achieved results using the SDOF and the presented MDOF approach. By validating with experimental results, the excellent prediction quality of the MDOF approach is confirmed. The implementation of this approach enabled to further improve the reliability and the efficiency, which means high accuracy combined with low computation time, in performing rotordynamic assessments.

Regenerative Chatter in High-Speed Tandem Rolling Mills

2006 ◽  
Author(s):  
Huyue Zhao ◽  
Kornel F. Ehmann
Keyword(s):  
Mode Coupling ◽  
High Speed ◽  
Process Model ◽  
Structural Model ◽  
Rolling Process ◽  
Space Representation ◽  
Regenerative Chatter ◽  
State Space Representation ◽  
Negative Damping ◽  
Delay Differential

Third-octave-mode chatter, the most detrimental form of rolling chatter, is generated by means of negative damping, mode coupling, and regeneration. While mechanisms that include negative damping, and mode coupling have been thoroughly investigated, those associated with the regenerative effect remain elusive. In this paper, the mechanisms that may lead to regenerative chatter are studied through a state-space representation of a multi-stand mill that is constructed by coupling a homogenous dynamic rolling process model with a structural model for the mill stands in a high-speed tandem mill configuration. Stability analysis, by using the integral criterion for the stability of systems described by delay differential equations, is carried out for the regenerative mechanism in order to better understand the effects of rolling parameters on a single stand as well as the overall system. Preliminary simulation results, based on the proposed chatter model, are presented to demonstrate the feasibility and the accuracy of the chatter model, as well as to investigate chatter phenomena too complex to be studied analytically.

The Estimation of Higher-Order Continuous Time Autoregressive Models

1985 ◽  
Vol 1 (1) ◽  
pp. 97-117 ◽  
Author(s):  
A. C. Harvey ◽  
James H. Stock
Keyword(s):  
Continuous Time ◽  
Structural Parameters ◽  
Space Representation ◽  
Computationally Efficient ◽  
Standard Case ◽  
State Space Representation ◽  
Unequally Spaced ◽  
Endogenous Variables ◽  
Order Continuous ◽  
Continuous Time System

A method is presented for computing maximum likelihood, or Gaussian, estimators of the structural parameters in a continuous time system of higherorder stochastic differential equations. It is argued that it is computationally efficient in the standard case of exact observations made at equally spaced intervals. Furthermore it can be applied in situations where the observations are at unequally spaced intervals, some observations are missing and/or the endogenous variables are subject to measurement error. The method is based on a state space representation and the use of the Kalman–Bucy filter. It is shown how the Kalman-Bucy filter can be modified to deal with flows as well as stocks.

Stability Analysis of Chatter in Tandem Rolling Mills—Part 1: Single- and Multi-Stand Negative Damping Effect

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Huyue Zhao ◽  
Kornel F. Ehmann
Keyword(s):  
State Space ◽  
Process Model ◽  
Structural Model ◽  
Rolling Process ◽  
Space Representation ◽  
Mathematical Form ◽  
Stability Criteria ◽  
Model Stability ◽  
State Space Representation ◽  
Negative Damping

Many different modes of chatter in rolling and their possible causes have been identified after years of research, yet no clear and definite theory of their mechanics has been fully established and accepted. In this two-part paper, stability of tandem mills is investigated. In Part 1, state-space models of single- and multi-stand chatter are formulated in a rigorous and comprehensive mathematical form. Then, the stability of the rolling system is investigated in the sense of the single- and multi-stand negative damping effects. First, a single-stand chatter model in state-space representation is proposed by coupling a dynamic rolling process model with a structural model for the mill stand. Subsequently, a multi-stand chatter model is developed by incorporating the inter-stand tension variations and the time delay effect of the strip transportation based on the single-stand chatter model. Stability criteria are proposed and stability analyses are performed to create corresponding stability charts in terms of the single- and multi-stand negative damping mechanism through numerical simulations. Particularly, the effect of friction conditions on chatter is examined and an explanation is given for the existence of an optimum friction condition. In Part 2, the regenerative effect and resulting instabilities are examined. Suitable stability criteria for each mechanism are established and stability charts are demonstrated in terms of relevant rolling process parameters.

Single- and Multi-Stand Chatter Models in Tandem Rolling Mills

2008 ◽  
Author(s):  
Huyue Zhao ◽  
F. Ehmann Kornel
Keyword(s):  
Stability Analysis ◽  
State Space ◽  
Process Model ◽  
Structural Model ◽  
Work Roll ◽  
Rolling Process ◽  
Complete Analysis ◽  
Space Representation ◽  
Mathematical Form ◽  
State Space Representation

Many different modes of chatter and their possible causes have been identified after years of research, yet no clear and definite theory of their mechanics has been established. One of the most important reasons for this can be attributed to the fact that only oversimplified models with a single input and a single output were historically used to formulate chatter in rolling. Such a situation has hindered a complete analysis of the underlying mechanisms. In this paper, a state-space representation of single- and multi-stand chatter models will be proposed in a rigorous and comprehensive mathematical form for stability analysis of the various chatter mechanisms. First, a dynamic model of the rolling process that utilizes homogeneous deformation theory will be established that includes the material strain-hardening and work roll flattening effects. By coupling this dynamic rolling process model with a structural model for mill stands, a single-stand chatter model in a state-space representation will be proposed. Based on the single-stand chatter model, a multi-stand chatter model will be formulated by incorporating the inter-stand tension variations and the time delay effect of the strip transportation. A simulation program will also be presented for the study of the dynamic rolling process in the time domain and for verifying the results from stability analysis.

Numerical Studies on Wavelet-Based Crack Detection Based on Velocity Response of a Beam Subjecting to Moving Load

2013 ◽  
Vol 569-570 ◽  
pp. 854-859 ◽  
Author(s):  
Wei Wei Zhang ◽  
Jia Geng ◽  
Zi Long Zhao ◽  
Zhi Hua Wang
Keyword(s):  
Wavelet Transform ◽  
Damage Detection ◽  
Crack Detection ◽  
Moving Load ◽  
Noise Tolerance ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Damage Location ◽  
Numerical Studies ◽  
Velocity Response

In this paper, the possibility and validity of damage detection based on velocity response of a simply supported beam under the moving load are examined theoretically and numerically. It includes the following parts: First, the theoretic background of the beam vibration subjecting to moving load is briefly described. And then, the velocity responses of a simple supported beam are calculated by software Ansys. Using wavelet transform, the damage location can be identified successfully. At last, the effects of noise and load speed are discussed in detail. Numerical studies show the validity of the proposed method and a good noise tolerance using the velocity response.

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