**1. Introduction**

To ensure the safe and continuous operation of aircraft, maintenance is a key activity [1]. Efficient maintenance can save high maintenance costs and can increase the service life of aircraft structures. Recently, the development of the structural health monitoring approach (condition-based maintenance) has enabled maintenance engineers to more frequently monitor the health condition of aircraft structures [2]. For this purpose, additional sensors are embedded in structures to provide health information, thus making condition-based maintenance more expensive than scheduled maintenance. Therefore, the practice of scheduled maintenance remains more dominant than condition-based maintenance. The main challenge in scheduled maintenance is the determination of efficient inspection intervals to reduce maintenance costs and maintain high safety standards [3].

The proportion of FRCPs in aircraft structures is increasing every year as the technical limitations of composite materials are gradually resolved [4]. FRCPs offer high stiffness, high strength-to-weight ratio, and excellent fatigue performance, making them suitable for the manufacturing of complex aircraft composite structures. Aircraft industries, such as Boeing 787 and Airbus A380, are using composite materials for their primary structures, such as the fuselage skin and wing spars [5]. Unlike metals, these composites suffer from complex damage mechanisms because of their anisotropic properties. Among these, fatigue delamination and debonding damage are the major causes of failure in composites [6–8].

**Citation:** Khalid, S.; Kim, H.-S.; Kim, H.S.; Choi, J.-H. Inspection Interval Optimization for Aircraft Composite Tail Wing Structure Using Numerical-Analysis-Based Approach. *Mathematics* **2022**, *10*, 3836. https:// doi.org/10.3390/math10203836

Academic Editors: Camelia Petrescu and Valeriu David

Received: 20 September 2022 Accepted: 14 October 2022 Published: 17 October 2022

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During aircraft flight, fatigue load continuously occurs, thus making the structures more susceptible to fatigue delamination damage [9]. Therefore, for the accurate prediction of the life span of composite structures, it is important to predict the fatigue delamination damage.

The commonly applied maintenance method in the aviation industry is the maintenance steering group 3 (MSG-3) [10], which aids in determining the inspection interval of aircraft structures. However, MSG-3 has the disadvantage of being heavily dependent on engineering experience, while the functional/structural detail evaluation of various new composite aircraft structures is limited. Therefore, the use of MSG-3 is inadequate for direct application to composite structures. Furthermore, it is difficult to maintain structural uniformity in composites because of the inaccuracies of the manufacturing process and the random variation in properties in composites. Therefore it is challenging to predict the failure of composite materials using the traditional deterministic approaches [11]. The usage of deterministic approaches results in the underutilization of the composite material. To utilize the material to its full capacity without compromising its structural safety, the uncertainties in the composite material should be considered for its realistic design, which is not possible in deterministic analysis. Probabilistic analysis offers a solution of incorporating the uncertainties in the design variables to compute the inherent risk in a structure subjected to service loading conditions. Therefore probabilistic approaches [12–14] have received considerable attention when it comes to addressing the uncertainty in design and maintenance.

Recently, Dinis et al. [15] proposed a probabilistic-design-based approach for aircraft maintenance and repair. The approach employed the usage of a Bayesian network to cope with the uncertainty in both scheduled and unscheduled maintenance. A real dataset based on 372 aircraft industrial maintenance projects was used. Similarly, Chen et al. developed an approach for the optimization of inspection intervals for composite structures for dent and delamination damage. The idea was to quantify the structural residual strength and maintenance cost for the different inspection intervals. The proposed approach was implemented on an aircraft wing. A historical dataset from the Chinese aircraft industry was used to develop the proposed approach. A POD curve created using general visual inspection (GVI) and detailed inspection (DET) data was selected as a method of damage detection. The probability of detecting damage according to dent damage was calculated using a Monte Carlo simulation. From these simulation results, a procedure for calculating the optimal inspection cycle that considered the structural reliability and maintenance cost was presented. However, the main limitation of this approach was that it was based on the actual repair data after the damage was confirmed. The approach did not consider the cause and progression of the delamination and dent damage.

Similarly, Dinggiang et al. [11] developed an optimized inspection interval approach by considering dent and delamination damage. The study used the maintenance records of 12 aircraft over 10 years of operation time. Impact damage was considered the main cause of damage, and the average expected number of impacts per year was calculated by comparing the maintenance history of such impact damage and the service life of the aircraft. The failure probability of the structure was calculated by simulating the residual strength and damage growth of the structure according to the impact damage that occurred during the service life operation. This study also utilized the actual maintenance data. The limitations of this approach were the limited damage data and that it was difficult to obtain the damage maintenance data from the aircraft industry. Further, the obtained data included the information after the damage occurred, and lacked information on the damage progression and the accurate cause of the damage. To overcome the data availability problem and the lack of progressive damage knowledge, an FEA-based approach can be used. Gianella et al. [16] developed a probabilistic framework for fatigue reliability assessment by considering multi-source uncertainties. The sensitivity of each input variable was obtained, and the influence of the variable on the life prediction was derived. The abovepresented literature approaches are all based on real aircraft maintenance and damage data. However, the main limitation of the approaches available in the literature is the availability

of real aircraft maintenance data to develop structural health monitoring approaches for the prediction of the fatigue life of the composite structures. The acquisition of the real damage data requires the embedding of additional sensors on the skin of aircraft structures, thus making the maintenance strategies more expensive. Therefore, to overcome the unavailability of the real-life operating data problem, this study proposed a methodology that uses the FEA-based model for the generation of fatigue damage growth curves and further implements this approach for the risk assessment and optimization of the inspection interval of the KT-100 aircraft tail wing structure. To the authors' best knowledge, no such study can be found in the literature that utilized a finite-element-analysis-based approach for the inspection interval optimization of aircraft composite structures.

In this study, a novel FEA-based approach was proposed for the inspection interval optimization of an aircraft composite tail wing structure. First, the FEA-based fatigue delamination model was constructed for the composite specimen and was verified through comparison with experimental data. The verified FEA model was extended to the composite aircraft tail wing structure of a KT-100 aircraft (Korea Aerospace Industries, Ltd., KAI). In this case, a Monte Carlo simulation was performed by building a response surface model that considered the uncertainty of the mechanical parameters. Through this process, the risk according to each flight time could be quantitatively evaluated, and the inspection interval was optimized by selecting the combination with the lowest number of repeated inspections within the conditions that met the permitted risk criteria.
