A multi-objective MGGP grey-box identification approach to design soft sensors

Abstract

Offshore oil extraction is a complex process, requiring several instruments to control the pro- duction in the wells. Among several, the Permanent Downhole Gauge (PDG) sensor, located

inside the production column, is used to measure the pressure and temperature of the oil well. This sensor is subjected to extreme operating conditions, resulting in short service life. The

replacement or maintenance of this sensor is rarely done as it is difficult to access and requi- res production to be stopped. Thus, aiming to overcome the production problem without PDG

sensor data, the use of Soft Sensors (SSs) appears as an alternative. SS are mathematical mo- dels capable of estimating a process variable through other variables as input. In this project,

it is proposed the use of the methodology of systems identification (i.e., i. Dynamic tests, data

collection; ii. Choice of the mathematical representation of the model; iii. Selection of struc- tures for the model; iv. Estimation of parameters; and v. Model validation.) to model an SS

in order to estimate the output of a PDG sensor but not limited to this application, which is

used as motivation. In methodology step ii., the Nonlinear Autoregressive with Exogenous In- puts (NARX) polynomial representation was chosen. For step iii. a multi-objective approach

is proposed, using the evolutionary algorithm Multi-Gene Genetic Programming (MGGP) to perform the task of structure selection from NARX models. Three objectives are minimized,

namely: i. one-step-ahead prediction error (dynamic regime), ii. steady-state error (an appro- ach that reduces computational cost is used), and iii. the number of regressors in the model. In

step iv. it is proposed to estimate the parameters through weighted least squares, which uses information from the dynamic and static regime (auxiliary information). Finally, the models found in the Pareto-optimal sets are validated (step v.) in free-run simulation (in both regimes), and a decision criterion to select the most adequate model is applied. In order to validate the proposed methodology, three experiments are carried out. The first uses a dataset of a stochastic system, in which several comparisons of approaches are made (e.g., number of objectives in the cost function). As a result, it is seen that the methodology can find the regressors and estimate the model parameters correctly, with a lower computational cost than other approaches. The second experiment applies the methodology in a hydraulic pumping system. The model found is competitive in the static and dynamic regime, in addition to being parsimonious. Finally, the same methodology is applied to the petrochemical process dataset, whose output is the PDG pressure. The proposed algorithm selects a model that has a satisfactory behavior in dynamic

regime compared to other works, with twelve regressors and twelve parameters. This demons- trates that the multi-objective MGGP, using auxiliary information, is a good tool for selecting

structures and estimating parameters for NARX models.