Maximum likelihood estimator of operational modal analysis for linear time-varying structures in time–frequency domain

From the viewpoint of vibration control, if the amplitude of the main frequencies of the vibration response can be reduced, the vibration energy of the structure is greatly reduced. Modal parameters, including modal shapes, natural frequencies, and damping ratios, can reflect the dynamics of the structure and can be used to control the vibration. This paper integrates the idea of “forgetting factor weighting” into eigenvector recursive principal component analysis, and then proposes an operational modal analysis (OMA) method that uses eigenvector recursive PCA with a forgetting factor (ERPCAWF). The proposed method can identify the transient natural frequencies and transient modal shapes online and realtime using only nonstationary vibration response signals. The identified modal parameters are also suitable for online, real-time health monitoring and fault diagnosis. Finally, the modal identification results from a three-degree-of-freedom weakly damped linear time-varying structure shows that the ERPCAWF-based OMA method can effectively identify transient modal parameters online using only nonstationary response signals. The results also show that the ERPCAWF-based approach is faster, requires less memory space, and achieves higher identification accuracy and greater stability than autocorrelation matrix recursive PCA with a forgetting factor-based OMA.

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The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

Ibn AL- Haitham Journal For Pure and Applied Science ◽

10.30526/2017.ihsciconf.1815 ◽

2018 ◽

pp. 439

Author(s):

Hazim Mansour Gorgees ◽

Bushra Abdualrasool Ali ◽

Raghad Ibrahim Kathum

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimator ◽

Exponential Distribution ◽

Reliability Function ◽

Bayes Estimator ◽

Likelihood Estimator ◽

Monte Carlo Simulation Technique ◽

Negative Exponential Distribution ◽

Negative Exponential ◽

Better Than

In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

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Transforming variables to central normality

Machine Learning ◽

10.1007/s10994-021-05960-5 ◽

2021 ◽

Author(s):

Jakob Raymaekers ◽

Peter J. Rousseeuw

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimator ◽

Simulation Study ◽

Real Data ◽

Data Sets ◽

Transformation Parameter ◽

Likelihood Estimator ◽

Extensive Simulation ◽

Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

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