Principal Components in Multivariate Control Charts Applied to Data Instrumentation of Dams

Abstract

A high number of instruments that assess various quality characteristics of interest that have an inherent variability monitors hydroelectric plants. The readings of these instruments generate time series of data on many occasions have correlation. Each project of a dam plant has characteristics that make it unique. Faced with the need to establish statistical control limits for the instrumentation data, this article makes an approach to multivariate statistical analysis and proposes a model that uses principal components control charts and statistical T 2 and to explain variability and establish a method of monitoring to control future observations. An application for section E of the Itaipu hydroelectric plant is performed to validate the model. The results show that the method used is appropriate and can help identify the type of outliers, reducing false alarms and reveal instruments that have higher contribution to the variability.

Bearing assessment tool for longitudinal bridge performance

“…We can justify this decision on the cumulative percentage of variance CPV [68], which measures the amount of variance captured by the first k components, such that where j represents the j th eigenvalue. An acceptable level of variance for the first subspace is typically around 90-95% [64,71].…”

“…An acceptable level of variance for the first subspace is typically around 90-95% of the total variance [64,71]. In this case, we only need two components to reach almost 91% of the total variance, so we define the first subspace with half of the total components and leave the other two components for the second subspace.…”

Diseño de una carta de control basada en Análisis de Componentes Principales. Un caso de estudio

“…Incontestablemente, resultaría inapropiado detener la adición de componentes principales tan pronto como , se localice por debajo de la unidad en la primera ocasión porque es una función de no monotónica decreciente (Bógalo, 2012). Esto deja entrever que no existen cánones o criterios unificados para determinar qué proporción de variabilidad deba ser explicada por las componentes principales (Lazzarotto, Madalena, Chaves, & Texeira, 2016). Sin embargo, para propósitos de monitoreo, se seguirá esta pauta empírica.…”

Principal component analysis applied to the statistical control of multivariate processes

“…Unquestionably, it would be inappropriate to cease adding major components as soon as posible , on the first occasion, is located below the unit, because it is a function of decreasing non-monotonic [20]. This suggests that there are no clear canons and formal criteria to determine what proportion of variability should be explained by successor variables [21]. However, for monitoring purposes, this empirical pattern will be followed.…”