An order determination method in direct derivative absorption spectroscopy for correction of turbidity effects on COD measurements without baseline required

Summary In many dimension reduction problems in statistics and machine learning, such as in principal component analysis, canonical correlation analysis, independent component analysis and sufficient dimension reduction, it is important to determine the dimension of the reduced predictor, which often amounts to estimating the rank of a matrix. This problem is called order determination. In this article, we propose a novel and highly effective order-determination method based on the idea of predictor augmentation. We show that if the predictor is augmented by an artificially generated random vector, then the parts of the eigenvectors of the matrix induced by the augmentation display a pattern that reveals information about the order to be determined. This information, when combined with the information provided by the eigenvalues of the matrix, greatly enhances the accuracy of order determination.

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Priority Order Determination Method for Extracting Services Stepwise from Monolithic System

2018 7th International Congress on Advanced Applied Informatics (IIAI-AAI) ◽

10.1109/iiai-aai.2018.00165 ◽

2018 ◽

Author(s):

Atsushi Shimoda ◽

Tsubasa Sunada

Keyword(s):

Determination Method ◽

Priority Order ◽

Order Determination

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A simple order-determination method based on a generalized adaptive law

International Journal of Control ◽

10.1080/0020718508961182 ◽

1985 ◽

Vol 41 (4) ◽

pp. 1037-1050 ◽

Cited By ~ 2

Author(s):

SHINJI SHINNAKA ◽

KANYA TANAKA ◽

TAKASHI SUZUKI

Keyword(s):

Determination Method ◽

Adaptive Law ◽

Simple Order ◽

Order Determination

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An unsupervised learning approach by novel damage indices in structural health monitoring for damage localization and quantification

Structural Health Monitoring ◽

10.1177/1475921717693572 ◽

2017 ◽

Vol 17 (2) ◽

pp. 325-345 ◽

Cited By ~ 25

Author(s):

Alireza Entezami ◽

Hashem Shariatmadar

Keyword(s):

Time Series ◽

Unsupervised Learning ◽

Hypothesis Test ◽

Ar Model ◽

Time Series Models ◽

Damage Localization ◽

Determination Method ◽

Reliability Criterion ◽

Damage Indices ◽

Order Determination

The aim of this article is to propose novel damage indices for damage localization and quantification based on time series modeling. In order to extract damage-sensitive features from time series models, it is essential to choose adequate and robust orders in such a way that the models are able to extract uncorrelated residuals. On this basis, a new iterative order determination method is proposed to select robust orders of time series models under residual analysis by Ljung–Box Q-test. The damage-sensitive features are the parameters and residuals of an AutoRegressive (AR) model obtained from current feature extraction approaches. In this study, the AR model is identified as the most compatible time series model with measured vibration time-domain responses using Box–Jenkins methodology and Leybourne–McCabe hypothesis test. The proposed damage indices are the parametric assurance criterion and the residual reliability criterion that exploit the parameters and residuals of AR models, respectively. The main idea behind locating a damage is to define threshold limits for both damage indices using the features of undamaged conditions based on an unsupervised learning way. The major contributions of this article are to propose an iterative order determination method for time series models and two novel damage indices for locating and quantifying damage. The accuracy and performance of the proposed methods are experimentally demonstrated on a three-story laboratory frame and a model-scale steel structure. Results show that the proposed iterative approach leads to uncorrelated residuals, and the proposed parametric assurance criterion and the residual reliability criterion methods are promising and efficient tools in damage detection problems under varying operational and environmental conditions.

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