**1. Introduction**

Aviation subsystem architectures are evolving substantially as a result of the more electric aircraft (MEA) concept, which, among other improvements, calls for the gradual replacement of hydraulic and electro-hydraulic actuators (EHA) with electro-mechanical actuators (EMA). In fact, it is believed that this paradigm shift would result in significant weight reductions, substantial life cycle cost (LCC) savings [1,2], lower repercussion on the environment, and, last but not least, increased reliability of the entire aircraft system [3].

Flight control surfaces in commercial aircrafts are currently actuated using FBW (flyby-wire) technology: the pilot commands are translated into low-power electrical signals that are then managed by a computer and passed to hydraulic servovalves, which finally drive the appropriate aerodynamic surface and close the position control loop. The result is an electrical control, which, however, still leverages hydraulic power [4,5]. The core concept is aiming at an all-in-one electrical solution that can meet the necessary safety criteria [6,7], encompassing the most power-demanding aircraft subsystems. The authors in [8] provided a brief overview of the usage of EMAs and electro-hydraulic actuators (EHA) on the most widespread aircraft platforms. In what is considered the forefather of the electric aircraft par excellence, the Boeing 787, EMAs and EHAs are already taking the place of hydraulic actuators. The latest versions of the Airbus A350 and A380 follow the same principle, but EMAs are still only used for secondary flight controls (e.g., flaps, slats, spoilers), while EHAs are installed for both primary and secondary flight controls. It is clear that some challenges still limit a seamless replacement of EMAs in place of hydraulically driven actuation devices [7,9] for primary flight controls. This article follows the ideas

**Citation:** Baldo, L.; Querques, I.; Dalla Vedova, M.D.L.; Maggiore, P. A Model-Based Prognostic Framework for Electromechanical Actuators Based on Metaheuristic Algorithms. *Aerospace* **2023**, *10*, 293. https://doi.org/10.3390/ aerospace10030293

Academic Editor: Spiros Pantelakis

Received: 26 January 2023 Revised: 8 March 2023 Accepted: 10 March 2023 Published: 16 March 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

presented in [10] and aims to propose a possible step forward by exploiting prognostics. De facto, it is critical to evaluate the implications of the substitution of an hydraulic subsystem with its electrical alternative, in terms of the usage, implementation, monitoring, and the equipment's reliability and safety. In the case of hydraulic systems, a potential failure (for example, a pressure drop caused by a leak) can be detected far before a load is demanded by appropriate pressure sensors.

Electrical system failures give rise to completely different problems from the power electronics point of view [11], as well as from the actuation one: new safety concerns are raised because no preventive mitigation plan can be implemented to reduce the impact of the fault itself if no additional auxiliary system is envisioned. As a consequence, the system must be exceedingly fault-tolerant. On top of that, EMAs show some issues that are less influential for hydraulic actuators, such as EMC, the mechanical jamming of the overall subsystem, and overheating problems, due to the high currents. A possible solution could be represented by hardware redundancy; however, this would result in weight increases, as well as incompatibilities with actuation requirements [12], therefore reducing the benefits of MEA principles.

Prognostics main selling point stands in the capability of detecting and identifying component early failures and track down their progression during the equipment use. This result brings a lot of positive outcomes with it; one of the most important is definitely the possibility of exploring innovative types of maintenance strategies (CBM, opportunistic and predictive maintenance [13–15]). On top of that, prognostics and health management (PHM) strategies could really be useful to back EMAs up, in order for them to reach the required safety standards for safety-critical applications, such as primary flight control actuation. Prognostics can be then seen as an effective mean to assist EMAs, thanks to its ability to identify hidden faults and prevent the related potential hazardous or catastrophic failure conditions. Prognostics sphere of influence stands in the monitoring and tracking of component or system parameters during their operation [16]: in this way, by checking the operational values and physical outputs, incipient failures can be detected resulting in the improvement of mission readiness, upgrade of RAMS capabilities, and a reduction of LCCs [17,18]. There is an ongoing substantial effort in the research community that focuses on the development of PHM systems for EMAs: a very detailed literature review on the matter can be found in [19]. Prognostics can be categorized based on many different criteria. The most general one is linked to the way the data used for the comparison is generated: data-driven [20], model-based [21,22], or hybrid. The method followed by the authors in this work is strictly model-based, due to the lack of enough real-life data to build the prognostic framework upon. The developed prognostic strategy is envisioned within an operational scenario and, as such, a general concept of operation (ConOps) is proposed, along with the high-level failure detection and identification (FDI) methodology. After that, a detailed explanation of the employed metaheuristic search algorithms (MSAs) and a brief overview of the models is reported. Two different models are used in this work: an high fidelity one (RM—-reference model) and a low fidelity counterpart (MM—monitoring model), the latter being in the core of the prognostic framework. This work continues the ongoing effort started in [23], where a similar strategy was applied on brushless BLDC trapezoidal motors: in this case, the employed motor is a sinusoidal PMSM motor. Finally, the results and comparisons between the algorithms are reported.

### **2. Related Work**

Metaheuristic algorithms for prognostics are only partially approached due to the limitations linked to the computational cost. However, there are many studies that already focused on MSAs to solve prognostic challenges. For instance, the authors already applied a similar strategies to a BLDC motor [23]. The literature on MSA is vast and covers almost every field of academic and industrial research. Furthermore, it must be said that the field of mathematical optimization using MSA is an extremely fast paced research area where new algorithms applied on very different application are being published continuously. We focused our literature review on MSA application in the prognostic field. In [24], a PHM framework for lithium-ion batteries has been developed using an improved PSO. PSO has been used also in [25] for power transformers PHM and in [26] for wind turbine gearbox RUL estimation. The same application on lithium-ion batteries has been the focus of [27,28], which proposed the use of teaching–learning-based optimization (TLBO) for multiple degradation factors condition and hunger game search (HGS), respectively. The authors in [29] proposed a fuel cell health estimation strategy using, among other technique, a very popular MSA: the cuckoo search algorithm (CSA), inspired by cuckoo species parasitism. In [30], the authors used PSO to optimize the objective function related to rotating component prognostics. MSAs can also be used to optimize neural network parameters, as performed in [31], with landslide mapping, prediction, and prognostics or in [31], where CSA was employed.

As far as aerospace applications are concerned, a few works have been found and examined. A very interesting approach has been proposed in [32], where a combination of genetic algorithms (GAs) and a bio inspired artificial immune system has been used to schedule predictive maintenance tasks in a PHM framework. The same authors approached GAs and variable neighbourhood search (VNS) to solve the same problem in [33]. Aircraft motion planning issues have been the focus of [34], where a review of different populationbased MSAs has been carried out, showing that PSO is the most used approach. A very relevant study [35] proposed ant colony optimization (ACO), in order to integrate PHM in aircraft maintenance planning, from a CBM perspective.

After a detailed literature review, which focused the fundamental queries "Prognostics", "Metaheuristic Algorithm", "Bio-inspired", and a wide range of secondary keyworkds, no work that focused the prognostic area applied to the EMA/aerospace domain using MSA has been found, to the best of our knowledge.
