Identification of Structural Parameters in Mistuned Bladed Disks

1997 ◽  
Vol 119 (3) ◽  
pp. 428-438 ◽  
Author(s):  
Marc P. Mignolet ◽  
Chung-Chih Lin
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Structural Model ◽  
Structural Parameters ◽  
Model Parameters ◽  
Disk Model ◽  
Response Data ◽  
State Response ◽  
Bladed Disk ◽  
True Model

The present investigation focused on the estimation of the parameters of a structural model to represent “at best” a set of measurements of the steady state response of a mistuned bladed disk. The applicability of the least squares and maximum likelihood approaches to the identification of the bladed disk model from this data is first investigated. The advantages and drawbacks of these techniques motivate the introduction of a new mixed least squares-maximum likelihood formulation which is shown to recover well the true model parameters from noisy simulated response data.

scholarly journals Two-stage Bayesian system identification using Gaussian discrepancy model

2020 ◽  
pp. 147592172093352
Author(s):  
Feng-Liang Zhang ◽  
Siu-Kui Au ◽  
Yan-Chun Ni
Keyword(s):  
System Identification ◽  
Structural Model ◽  
Structural Parameters ◽  
Stage Ii ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Model Parameters ◽  
Modeling Error ◽  
Two Stage ◽  
Classical Statistics

System identification aims at updating the model parameters (e.g. mass and stiffness) associated with the mathematical model of a structure based on measured structural response. In this process, a two-stage approach is commonly adopted. In Stage I, modal parameters including natural frequencies and mode shapes are identified. In Stage II, the modal parameters are used to update structural parameters such as those related to stiffness, mass, and boundary conditions. A recent Bayesian formulation allows the identification results in the first stage to be incorporated in the second stage directly via Bayes’ rule without using a heuristic model (often based on classical statistics) that transfers the information from Stages I to II. This opens up opportunities for explicitly accounting for modeling error in the structural model (Stage II) through the conditional distribution of modal parameters given structural model parameters. Following this approach, this article investigates a methodology where the modeling error between the two stages is incorporated with Gaussian distributions whose statistical parameters are also updated with available data. Leveraging on special mathematical structure induced by the model, computational issues are resolved and an analytical investigation is performed that yields insights on the role of modeling error and whether its statistics can be distinguished from those of identification uncertainty (defined for given structural model). The proposed methodology is verified using synthetic data and applied to a laboratory-scale structure.

Recursive Least-Squares Time Domain Identification of Structural Parameters

1977 ◽  
Vol 44 (1) ◽  
pp. 135-140 ◽  
Author(s):  
P. Caravani ◽  
M. L. Watson ◽  
W. T. Thomson
Keyword(s):  
Least Squares ◽  
Structural Parameters ◽  
Gaussian White Noise ◽  
Initial Guess ◽  
Recursive Least Squares ◽  
Rapid Convergence ◽  
Domain Identification ◽  
Response Data ◽  
Dynamic Excitation ◽  
Two Degree Of Freedom

A method of identifying structural parameters such as damping and stiffness of a building from its time response under dynamic excitation is presented. A least-squares recursive computer algorithm which requires no matrix inversion is developed and tested with the response of a two-degree-of-freedom structure including Gaussian white noise. The algorithm provides means to account for both the model uncertainty and the investigators’ confidence in the initial guess of the parameters. These statistical quantities can be updated with passage of time. The study indicates that rapid convergence to the correct values of the parameters takes place even under severe noise in the response data.

Meta-Analytical SEM: Equivalence Between Maximum Likelihood and Generalized Least Squares

2018 ◽  
Vol 43 (6) ◽  
pp. 693-720
Author(s):  
Ke-Hai Yuan ◽  
Yutaka Kano
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Correlation Matrix ◽  
Structural Equation ◽  
Structural Model ◽  
Meta Analysis ◽  
Generalized Least Squares ◽  
Equation Modeling ◽  
Correlation Matrices ◽  
Latent Constructs

Meta-analysis plays a key role in combining studies to obtain more reliable results. In social, behavioral, and health sciences, measurement units are typically not well defined. More meaningful results can be obtained by standardizing the variables and via the analysis of the correlation matrix. Structural equation modeling (SEM) with the combined correlations, called meta-analytical SEM (MASEM), is a powerful tool for examining the relationship among latent constructs as well as those between the latent constructs and the manifest variables. Three classes of methods have been proposed for MASEM: (1) generalized least squares (GLS) in combining correlations and in estimating the structural model, (2) normal-distribution-based maximum likelihood (ML) in combining the correlations and then GLS in estimating the structural model (ML-GLS), and (3) ML in combining correlations and in estimating the structural model (ML). The current article shows that these three methods are equivalent. In particular, (a) the GLS method for combining correlation matrices in meta-analysis is asymptotically equivalent to ML, (b) the three methods (GLS, ML-GLS, ML) for MASEM with correlation matrices are asymptotically equivalent, (c) they also perform equally well empirically, and (d) the GLS method for SEM with the sample correlation matrix in a single study is asymptotically equivalent to ML, which has being discussed extensively in the SEM literature regarding whether the analysis of a correlation matrix yields consistent standard errors and asymptotically valid test statistics. The results and analysis suggest that a sample-size weighted GLS method is preferred for combining correlations and for MASEM.

scholarly journals The Odd Exponentiated Half-Logistic Exponential Distribution: Estimation Methods and Application to Engineering Data

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1684 ◽  
Author(s):  
Maha A. D. Aldahlan ◽  
Ahmed Z. Afify
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Exponential Distribution ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Finite Sample ◽  
Anderson Darling ◽  
Von Mises ◽  
Cramer Von Mises

In this paper, we studied the problem of estimating the odd exponentiated half-logistic exponential (OEHLE) parameters using several frequentist estimation methods. Parameter estimation provides a guideline for choosing the best method of estimation for the model parameters, which would be very important for reliability engineers and applied statisticians. We considered eight estimation methods, called maximum likelihood, maximum product of spacing, least squares, Cramér–von Mises, weighted least squares, percentiles, Anderson–Darling, and right-tail Anderson–Darling for estimating its parameters. The finite sample properties of the parameter estimates are discussed using Monte Carlo simulations. In order to obtain the ordering performance of these estimators, we considered the partial and overall ranks of different estimation methods for all parameter combinations. The results illustrate that all classical estimators perform very well and their performance ordering, based on overall ranks, from best to worst, is the maximum product of spacing, maximum likelihood, Anderson–Darling, percentiles, weighted least squares, least squares, right-tail Anderson–Darling, and Cramér–von-Mises estimators for all the studied cases. Finally, the practical importance of the OEHLE model was illustrated by analysing a real data set, proving that the OEHLE distribution can perform better than some well known existing extensions of the exponential distribution.

Mass Spring Interlocked Bladed Disk Model

2020 ◽  
Author(s):  
Oscar Córdoba
Keyword(s):  
Analytical Solution ◽  
Mass Matrix ◽  
Model Parameters ◽  
Disk Model ◽  
Nodal Diameter ◽  
Common Boundary ◽  
Bladed Disk ◽  
Similar Scheme ◽  
Mass Spring ◽  
Frequency Curves

Abstract A simplified bladed disk model with cantilever and interlock conditions is described. Blade is composed of three masses, two for the lower and higher part of the shroud, and one for the main core of the blade. A similar scheme is employed in the disk. The different masses in the model are linked with springs introducing the stiffness between them. Additional disk restrictions reduce the model capabilities but account the effect of common boundary conditions. The model simplicity allows an analytical solution with polynomials to understand the fundamentals of vibration. The extended stiffness and mass matrix with Lagrange multipliers are used. The modal frequencies and modes as function of the nodal diameter are studied. The interlock solution is compared to cantilever and different sorts of frequency curves have been identified and classified. Some basic conclusions related to the model parameters are achieved.

scholarly journals A new generalization of the inverse Lomax distribution with statistical properties and applications

2021 ◽  
Vol 8 (4) ◽  
pp. 89-97
Author(s):  
Hassan et al. ◽  
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Statistical Properties ◽  
Maximum Likelihood Estimates ◽  
Entropy Measure ◽  
Model Parameters ◽  
Lomax Distribution ◽  
Inverse Lomax Distribution ◽  
Mean Square Errors

In this paper, we introduce a new generalization of the inverse Lomax distribution with one extra shape parameter, the so-called power inverse Lomax (PIL) distribution, derived by using the power transformation method. We provide a more flexible density function with right-skewed, uni-modal, and reversed J-shapes. The new three-parameter lifetime distribution capable of modeling decreasing, Reversed-J and upside-down hazard rates shapes. Some statistical properties of the PIL distribution are explored, such as quantile measure, moments, moment generating function, incomplete moments, residual life function, and entropy measure. The estimation of the model parameters is discussed using maximum likelihood, least squares, and weighted least squares methods. A simulation study is carried out to compare the efficiencies of different methods of estimation. This study indicated that the maximum likelihood estimates are more efficient than the corresponding least squares and weighted least squares estimates in approximately most of the situations Also, the mean square errors for all estimates are decreasing as the sample size increases. Further, two real data applications are provided in order to examine the flexibility of the PIL model by comparing it with some known distributions. The PIL model offers a more flexible distribution for modeling lifetime data and provides better fits than other models such as inverse Lomax, inverse Weibull, and generalized inverse Weibull.

scholarly journals Maximum Likelihood Estimation of the VAR(1) Model Parameters with Missing Observations

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Helena Mouriño ◽  
Maria Isabel Barão
Keyword(s):  
Stochastic Process ◽  
Missing Data ◽  
Maximum Likelihood ◽  
Moving Average ◽  
Practical Importance ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Missing Observations ◽  
Data Set ◽  
The Impact

Missing-data problems are extremely common in practice. To achieve reliable inferential results, we need to take into account this feature of the data. Suppose that the univariate data set under analysis has missing observations. This paper examines the impact of selecting an auxiliary complete data set—whose underlying stochastic process is to some extent interdependent with the former—to improve the efficiency of the estimators for the relevant parameters of the model. The Vector AutoRegressive (VAR) Model has revealed to be an extremely useful tool in capturing the dynamics of bivariate time series. We propose maximum likelihood estimators for the parameters of the VAR(1) Model based on monotone missing data pattern. Estimators’ precision is also derived. Afterwards, we compare the bivariate modelling scheme with its univariate counterpart. More precisely, the univariate data set with missing observations will be modelled by an AutoRegressive Moving Average (ARMA(2,1)) Model. We will also analyse the behaviour of the AutoRegressive Model of order one, AR(1), due to its practical importance. We focus on the mean value of the main stochastic process. By simulation studies, we conclude that the estimator based on the VAR(1) Model is preferable to those derived from the univariate context.

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