Session: 04-05-02 Subsea Structures & Equipment II

Submission Number: 180227

A Comparison Between Modal Bases and Polynomial Bases for Vibration Prediction in Submersible Centrifugal Pumps 

With oil and gas production having expanded into increasingly remote and deeper offshore environments, extending the operational lifespan of Electrical Submersible Pumps (ESPs) and monitoring their structural behavior have become critical challenges. The harsh operating conditions surrounding ESPs not only hinder physical access to the equipment but also limit the number and placement of sensors available for structural health monitoring (SHM). Under such constraints, virtual sensing emerges as an efficient solution, enabling structural response estimation at uninstrumented locations through computational modeling.

This work presents a data-driven virtual sensing methodology for ESPs based on Ridge Regression, orthogonal functional bases (Chebyshev and Fourier), and a backward selection strategy for the optimal choice of polynomial degree and Fourier terms. The proposed approach allows vibration signal reconstruction at non-instrumented locations using a limited set of accelerometers, without relying on modal bases or finite element models. The methodology was experimentally validated on an ESP during integration tests in a mock well, using harmonic vibration signals from six accelerometers mounted along the pump casing.

The predictive performance was assessed using the Time-Frequency Error Response Assurance Criterion (TFERAC), a composite metric that combines the Root Mean Square Error (RMSE), Frequency Response Assurance Criterion (FRAC), and Modified Time Response Assurance Criterion (MTRAC) to evaluate the amplitude and shape of the predicted signal with respect to the measured one. TFERAC results demonstrated that, when using Chebyshev polynomial bases, the prediction errors for sensors 2, 3, 4, and 6 were 0.075, 0.049, 0.054, and 0.0123, respectively. When using the Fourier basis, the predicted outcomes for sensors 2, 3, 4, 5, and 6 were 0.011, 0.048, 0.041, 0.026, and 0.059, respectively.

Moreover, the Fourier-based model outperformed two reference modal-based methods — the Local Correspondence of Modes and Modal Coordinates (LCMC) and the Multi-Objective Genetic Algorithm (MOGA), across all accelerometers, achieving up to 95% reduction in TFERAC. Signal reconstruction in both time and frequency domains exhibited high fidelity and amplitude preservation, confirming the proposed model’s robustness and strong generalization capability under sparse instrumentation conditions.

Presenting Author: Diogenes Bispo Fontes Federal University of Rio de Janeiro

Presenting Author Biography: Diogenes Bispo Fontes holds a B.Sc. in Production Engineering (2018) and an MBA in Offshore Systems Engineering (2020) from COPPE/UFRJ, where he has completed his M.Sc. in Ocean Engineering (2025). His research focuses on vibration prediction and virtual sensing methods for structural health monitoring of offshore equipment using ridge regression and orthogonal functional bases. Professionally, he has over sixteen years of offshore experience in subsea installation, positioning, and maintenance of subsea equipment on drilling and multi-purpose construction vessels.

Authors:

Diogenes Bispo Fontes Federal University of Rio de Janeiro
Ulisses A. Monteiro Federal University of Rio de Janeiro (UFRJ)
Luiz A. Vaz FEDERAL UNIVERSITY OF RIO DE JANEIRO (UFRJ)
Brenno Moura Castro FEDERAL UNIVERSITY OF RIO DE JANEIRO (UFRJ)
Ricardo H. R. Gutiérrez FEDERAL UNIVERSITY OF RIO DE JANEIRO (UFRJ)