Effect of the number of samples on parameter bias in closed-loop system identification with routine-operating data

• Autor: Durand Solis, Jocelyn Alicia
• Formato: tesis de maestría
• Fecha de Publicación: 2025
• Institución: Pontificia Universidad Católica del Perú
• Repositorio: PUCP-Tesis
• Lenguaje: español
• OAI Identifier: oai:tesis.pucp.edu.pe:20.500.12404/33025
• Enlace del recurso: http://hdl.handle.net/20.500.12404/33025
• Nivel de acceso: acceso abierto
• Materia: Región de confianza; Sistemas de control por retroalimentación; Método de Montecarlo; Modelos matemáticos; https://purl.org/pe-repo/ocde/ford#2.00.00

In many industrial applications, system models are identified using routine closed-loop operating data. However, such data are often limited in length and variability due to operational constraints and feedback suppression, which challenge the reliability of parameter estimates. A key question therefore arises: how many data points are needed to obtain trustworthy estimates when working with routine operating data? This thesis addresses this question by evaluating two complementary methods for constructing confidence regions of model parameters under closed-loop conditions with different data length. The first method is an empirical Monte Carlo approach, which estimates the parameters of the autoregres- sive with exogenous inputs (ARX) model through repeated simulations and applies kernel density estimation (KDE) to construct the empirical 95% confidence regions. The second method is the sign-perturbed sums (SPS) approach, which guarantees nonasymptotic confidence regions with exact coverage probability under the assumption of symmetric and independent noise. Using three first-order plus dead-time (FOPDT) process models and different noise levels, the thesis investigates how sample size and noise variance influence the accuracy and robustness of parameter estimates. The results show that classical asymptotic confidence intervals often underestimate uncer- tainty with small datasets, while SPS maintains valid coverage. Three-dimensional plots of the Monte Carlo results and a summary plot of the median versus data size indicate that, for the three plants studied, at least 2,000 samples are required to obtain accurate, approximately unbiased estimates with a 95% confidence region. Overlays of SPS and KDE confidence regions provide additional insight into bias. They suggest that it is possible to obtain 95% confidence regions with a dataset on the order of 2,000 samples too. The effect of noise variance was also examined. It was found that the controller was largely able to suppress its impact on system identification.