ARX (AutoRegressive models with eXogenous variables) are the simplest models within the equation error family but are endowed with many practical advantages concerning both their estimation and their predictive use since their optimal predictors are always stable. Similar considerations can be repeated for ARARX models where the equation error is described by an AR process instead of a white noise. The ARX and ARARX schemes can be enhanced by introducing the assumption of the presence of additive white noise on the input and output observations. These schemes, that will be denoted as “ARX + noise” and “ARARX + noise”, can be seen as errors-in-variables models where both measurement errors and process disturbances are taken into account. This paper analyzes the problem of identifying ARX + noise and ARARX + noise models. The proposed identification algorithms are derived on the basis of the procedures developed for the solution of the dynamic Frisch scheme. The paper reports also Monte Carlo simulations that confirm the effectiveness of the proposed procedures.

This note introduces an extended environment for Kalman filtering that considers also the presence of additive noise on input observations in order to solve the problem of optimal (minimal variance) estimation of noise-corrupted input and output sequences. This environment includes as subcases both errors-in-variables filtering (optimal estimate of inputs and outputs from noisy observations) and traditional Kalman filtering (optimal estimate of state and output in presence of state and output noise). A Monte Carlo simulation shows that the performance of this extended filtering technique leads to the expected minimal variance estimates.

This work aims to provide useful insights into the course of action and the challenges faced by machine manufacturers when dealing with the actual application of Prognostics and Health Management procedures in industrial environments. Taking into account the computing capabilities and connectivity of the hardware available for smart manufacturing, we propose a particular solution that allows meeting one of the essential requirements of intelligent production processes, i.e., autonomous health management. Indeed, efficient and fast algorithms, that does not require a high computational cost and can be appropriately performed on machine controllers, i.e., on edge, are combined with others, which can handle large amounts of data and calculations, executed on remote powerful supervisory platforms, i.e., on the cloud. In detail, new condition monitoring algorithms based on Model-of-Signals techniques are developed and implemented on local controllers to process the raw sensor readings and extract meaningful and compact features, according to System Identification rules and guidelines. These results are then transmitted to remote supervisors, where Particle Filters are exploited to model components degradation and predict their Remaining Useful Life. Practitioners can use this information to optimise production planning and maintenance policies. The proposed architecture allows keeping the communication traffic between edge and cloud in the nowadays affordable “Big data” range, preventing the unmanageable “Huge data” scenario that would follow from the transmission of raw sensor data. Furthermore, the robustness and effectiveness of the proposed method are tested considering a meaningful benchmark, the PRONOSTIA dataset, allowing reproducibility and comparison with other approaches.