Multi-objective sensor placement optimization of helicopter rotor blade based on Feature Selection
Introduction
Helicopters have gained importance due to their capabilities of aircraft travel speed (200–300 km/h) and maneuverability, which ensures movement along the shortest route and vertical takeoff [1]. Its most important element is the main rotor blade (MRB), which is usually made of composite material. Due to the intense in-service conditions of aerodynamics, temperature variation, and accelerations, damage can be induced in these structures [2], [3].
Efficient systems, as Structural Health Monitoring (SHM), allow early identification of damage through non-destructive inspection and integrated sensors exploring vibration/modal measures in order to avoid catastrophic failures. The method is based on the principle that damage changes natural frequencies, mode shapes, modal strain energy and damping ratios [4], [5], [6]. Then, using inverse modeling and computational intelligence, it is possible to identify damage.
The main techniques used are meta-heuristics, neural networks, non-probabilistic methodologies, and time-series analyses. However, there is no methodology that is very effective for all problems. New technologies have been proposed and there is space for new ones [7]. Still at the beginning of the century, the first works using SHM and inverse methods associated with finite element method (FEM) updating on MRB appeared.
Pawar & Ganguli [8] proposed a genetic fuzzy system to find the location and extent of damage. In the study, a fuzzy system qualifies the changes in natural frequencies in four damage levels and the Genetic Algorithm (GA) [9] optimizes its rule-base and membership functions. Despite being qualitative damage identification and the author used a simplified MRB (beam), the methodology was accurate.
The same authors repeat this in two other studies: i) using displacements measures instead natural frequencies and residual life classes instead damage levels to create a prediction model that provided the helicopter rotor blade life [10], and ii) changing the genetic fuzzy system by the Support Vector Machine (SVM) classifier. The authors were successful even in noisy situations [11]. Reddy & Ganguli [12] also used machine learning algorithms. In this case, artificial neural networks (ANN) with modal data generated by the FEM to accurately identify damage to MRB. The authors also concluded that the first 5 mode shapes were sufficient for this.
After a few years without further studies, Gomes et al. [13] was the first to propose a methodology for identifying damage in MRB that was able to locate and quantify the damage severity. The proposed inverse method used the FEM updating associated with the Bat Optimization Algorithm (BA) [14] and the authors uniformly distributed 10 sensors on the blade structure and got good results.
As seen, few works were dedicated to propose SHM methodologies for identifying damage in MRB and none of them proposed a MRB sensor placement optimization (SPO) method. However, modern and efficient methodologies have been proposed to identify damage in other types of structures, including FEM updating, frequency response function, ground excitation, signal processing, new machine learning algorithms, among others. The most accurate is the FEM updating and has two fronts: i) the direct problem modeling, where a numerical model of the structure is made, and ii) the model is constantly evaluated by an optimization algorithm that minimizes an objective function composed by structural characteristics [15], [16], [17].
The methodology efficiency and the quality of the answers strongly depend on the optimization algorithm used [6], [18]. Consequently, many meta-heuristics have been proposed for damage identification and SPO, most are dealing with only one objective: i) GA [4], [8], [19], ii) Ant Colony Optimization (ACO) [20], [21], [22], iii) Particle Swarm Optimization (PSO) [23], [24], [25], iv) Firefly Algorithm (FA) [26], [27], [28], v) Sunflower Optimization (SFO) [29], vi) BA [13], [30], [31], and vii) Wolf Algorithm [32], among others.
However, recent studies indicate that the use of multi-objective meta-heuristics, given their ability to evaluate several metrics at the same time, has found better results both in SPO and in damage identification [4], [33], [34]. Even so, the number of workers using multi-objective algorithms in SHM is uncommon. According to Pereira et al. [35], the vast majority uses the Non-sorting Genetic Algorithm II (NSGA-II) [34], [36] or the Multi-objective PSO (MOPSO) [37], [38].
Still, being that the fundamental principle of SHM is to select the smallest number possible of measurement locations from a structure and represent the system with the highest possible accuracy [39], which are obviously conflicting objectives, there is no work in the literature considering any kind of structure that proposes a methodology to approach this. In this paper, a new multi-objective meta-heuristic inspired by lightning and Lichtenberg figures, which is the first and only hybrid algorithm in the literature (population and trajectory-based at the same time) will be used to propose a new SHM methodology.
The Multi-objective Lichtenberg Algorithm (MOLA) [40] recently showed superior results not only to MOPSO or NSGA-II, but also against modern algorithms like Multi-objective Grey Wolf Optimizer (MOGWO) [41] and Multi-objective Grasshopper Optimizer (MOGOA) [42] in complex optimization problems (CEC 2009 and Zitzler-Deb-Thiele test functions).
Firstly, a real AS350 MRB will be experimentally tested to obtain its modal parameters. A numerical model will be elaborated in FEM and an inverse method using the constrained Lichtenberg Algorithm will find the mechanical properties that fit the numerical and experimental models. Then, will be proposed a methodology to address the SPO problem using the MOLA and Feature Selection (FS), which is an important and modern area in data mining that seeks to optimize input data series for machine learning algorithms [43].
The multi-objective optimization problem will have as one of the objectives the number of sensors. The others objectives will be defined as one of the 7 well-known metrics of SPO in literature: Kinetic Energy, Effective Independence, Average Driving-Point Residue, Eigenvalue Vector Product, Information Entropy, Fisher Information Matrix, and Modal Assurance Criterion. The new methodology, named Multi-objective Sensor Selection and Placement Optimization based on Lichtenberg Algorithm (MOSSPOLA) will present the sensor configurations (SC) (number and locations) and the results will be compared/analyzed for the MRB case study. Finally, a damage identification test problem will be presented considering triaxial mode shapes displacements and noise.
The major contributions of this paper are: i) to propose a multi-objective sensor placement optimization methodology considering the number of sensors as one of the objectives complementary to others 7 well-known metrics of SPO; ii) develop and apply feature selection techniques for SPO considering discrete MO optimization; iii) to apply the proposed methodology in a real aeronautical SPO case study; and iv) Validate all the found optimal sensor configurations in an inverse damage identification problem. The manuscript is organized as follows: Section 2 presents the theoretical background. Section 3 presents the methodology of this work. Section 4 brings the results and discussions, and Section 5 concludes the research.
Section snippets
Backgrounds
The concepts necessary for the understanding of this research are: i) damages in MRB; ii) modal data and damage identification; iii) the main metrics used to analyze modal data; iv) State of art about multi-objective optimization in SHM; v) Multi-objective Lichtenberg Algorithm; and v) what is feature selection and how does it relate to meta-heuristics.
Numerical-experimental methodology
The methodology of this study is divided into three steps: i) numerically model an AS 350 MRB that is similar to a real one experimentally tested; ii) develop and apply MOSSPOLA in it; and iii) to apply the SC found in damage identification.
Adjusted numerical model of main rotor blade
The first step to properly adjust the numerical model was to define the range and which natural frequencies to use. Tamer et al. [91] studied vibrations in real helicopters and concluded that the excitation frequencies found in the MRB under normal conditions range from 20 to 25 Hz. In adverse and dangerous situations, it can reach 50 Hz. Therefore, in the bench test of Fig. 2, it was aimed to find the natural frequencies in the range from 0 to 50 Hz.
The FRF for different excitation points was
Conclusion
This work proposed an innovative Structural Health Monitoring methodology for optimal positioning of sensors in an AS350 helicopter main rotor blade considering the experimental modal responses, feature selection techniques and the Multi-objective Lichtenberg optimization Algorithm. With the number of sensors as one objective to be minimized, the 7 well-known metrics in the literature composed a bi-objective problem, where non-dominated solutions in different Pareto were obtained, evaluated and
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors would like to acknowledge the financial support from the Brazilian agency CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior), and FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais – APQ-00385-18).
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