Research on Classification Maintenance Strategy for More Electric Aircraft Actuation Systems Based on Importance Measure

Abstract

In this paper, a practical maintenance algorithm is proposed to improve the reliability of actuation systems and their components, specifically addressing the consistency degradation caused by faults in the symmetric actuation system components of more electric aircraft (MEA). By integrating important measures with traditional genetic algorithms, the accuracy of the algorithm is improved. Prior to maintenance, a reasonable classification of components is built to mitigate the adverse effects of extreme fault conditions on the algorithm. This approach improves both the effectiveness and efficiency of the algorithm, rendering the overall maintenance strategy better suited for real-world needs. Finally, comparative simulations confirm the algorithm’s superior performance in reliability improvement, demonstrating its substantial contribution to the field of MEA maintenance and reliability.

1. Introduction

In recent years, to enhance ecological construction and promote greener production and lifestyles to reduce carbon emissions, more electric aircraft (MEA) have rapidly developed. In MEA, hydraulic energy is increasingly being replaced by electrical energy in the actuation system. Modern MEA systems unify onboard secondary power sources into electrical energy, significantly improving economic efficiency and the safety and stability of aircraft operations [1]. Well-known international aircraft, such as Gulfstream G650, Boeing 787, and Airbus A380, are equipped with multi-electric actuation systems, which include hydraulic actuators (HAs), electro-hydrostatic actuators (EHAs), and electromechanical actuators (EMAs). This study focuses on the actuation system of the Gulfstream G650, which features a symmetric system comprising HA and EHA. Here, “symmetry” refers to “very similar or equal properties”. The Gulfstream G650 actuation system includes symmetric structures, such as the left and right elevators, rudder, left and right ailerons, as well as left and right spoilers. These symmetric systems provide redundancy and heterogeneity, reducing fuel costs and enhancing aircraft reliability [2,3,4,5].

With the rapid development of MEA, researchers have increasingly focused on reliability assessment and health maintenance to address related issues and their impact on maintenance effectiveness and costs. Moreover, some scholars have summarized comprehensive methods for the health management and reliability assessment of multi-electric actuation systems and discussed future developments [6,7]. For instance, Berri et al. [8] proposed a novel strategy using fusion methods for real-time fault detection, diagnosis, and component life prediction in multi-electric actuation systems to ensure operational safety. In addition, Liu et al. [9] combined data-driven models with machine learning (ML) to develop a reliability assessment framework for aircraft actuation systems, offering valuable insights for civil aircraft operation reliability analysis, special case handling, maintenance, and design. Furthermore, Wang et al. [10] established a reliability assessment method for non-similar redundant actuation systems and provided a comprehensive definition and calculation method for the actuation systems of the Airbus A380. Added to that, Yu et al. [11] utilized bond graph modeling to study heterogeneous actuation systems in MEA, proposing a new fault isolation method and testing its effectiveness. These studies provide a theoretical foundation for maintenance and repair work, helping to identify weak links in the system. However, most of the current research has focused on fault diagnosis, life prediction, and health management, with limited specific research on maintenance strategies and component repairs for actuation systems.

The concept of the importance measure (IM), also known as the Birnbaum importance measure (BIM), was first proposed by Birnbaum in 1969 [12]. Since then, extensive research has been conducted on the IM, leading to the development of various importance measures to address different reliability improvement problems [13,14]. For example, Liu et al. [15] introduced a reliability analysis process using two importance indicators based on the IM theory, analyzing a dual-source, dual-load, dual-component power grid system and constructing a preventive maintenance strategy through component importance ranking. Furthermore, Vu et al. [16] proposed a steady-state grouping maintenance strategy for multi-component systems applicable to systems with series, parallel, k-out-of-n, and other mixed structures. In addition, Huseby et al. [17] considered the lifecycle of periodic components and semi-Markov processes, proposing four new importance measures for repairable polymorphic systems based on the classical BIM. Moreover, Fu et al. [18] presented a genetic algorithm-based time-correlated importance measure to address the component reassignment problem for degraded components. Added to that, Liu et al. [19] developed a cost-based importance measure tailored for a minimum cost–reliability optimization model (ROM) and integrated it with genetic algorithms to achieve an optimal maintenance plan at minimal cost. Furthermore, Ma et al. [20] proposed a multi-objective Birnbaum importance non-dominated sorting genetic algorithm II to determine the optimal maintenance scheme for reconfigurable systems. As for Qiu et al. [21], they proposed a two-stage method based on Birnbaum’s importance to solve the TCAP problem and provided a practical example demonstrating the feasibility and applicability of the method. Moreover, Zhao et al. [22] proposed a multi-state weak point analysis method based on the integrated importance measure (IIM), validating it by comparing it with classical multi-state importance measures and the BIM. In addition, Wu et al. [23] and Dui et al. [24] summarized the applications of BIM in reliability maintenance, resilience management, and reliability optimization in engineering.

These studies indicate that maintenance algorithms and strategies derived from importance measures are applicable to hydraulic and electromechanical systems in specific work scenarios. For instance, Wang et al. [25] discussed the health management modeling of the Boeing 737’s multi-electric actuation system from a theoretical perspective and referenced the aircraft maintenance manual. Moreover, Zhang et al. [26] utilized Gaussian processes to describe component degradation for reliability assessment and combined it with an importance measure to determine weak links in the system, facilitating resource allocation during maintenance and repair and laying a solid foundation for subsequent research.

Based on the literature reviewed, it is evident that, while there is substantial theoretical research on maintenance algorithms using importance measures, there is a notable lack of targeted research on maintenance strategies specifically for MEA actuation systems. The complex architecture of these systems and the challenges associated with allocating costs are often not adequately addressed. To address these issues, this paper constructs a reliability model using bond graph modeling and employs the physics-of-failure (POF) approach to collect real-time operating data. An improved genetic algorithm-based maintenance and replacement classification standard, grounded in importance measures, is proposed. This approach aims to maximize the reliability of the multi-electric actuation system within a fixed cost, thereby reducing maintenance costs while ensuring the safe and stable operation of MEA.

To summarize, the remaining sections of this paper are organized as follows: Section 2 focuses on the classification criteria of the different components in the proposed maintenance strategy, the importance measure utilized to rank the contribution of component reliability to system reliability, and maintenance and replacement cost consideration. Section 3 proposes the specific content and process of the maintenance algorithm combined with interesting measures and briefly describes the reliability model of the MEA actuation system considered in this paper. Moreover, Section 4 verifies the outputs of the proposed reliability model as well as the proposed maintenance strategy algorithm through relevant simulation experiments. Finally, Section 5 discusses the shortcomings of this research and future directions, and concludes the work presented in this paper.

2. Research on Maintenance Strategies

In this section, we provide a detailed description of the maintenance strategy proposed to improve system reliability. We introduce a classification strategy for individual components based on traditional maintenance algorithms. Moreover, we have standardized the costs associated with maintenance and replacement to enhance the rationality of the decision-making process. This approach not only improves system reliability but also reduces maintenance costs and time.

2.1. Classification of Maintenance for Actuation System Components

In engineering, components degrade continuously during operation, eventually leading to failure. To develop effective maintenance processes, it is crucial to classify components into different states, allowing for more scientific and rational maintenance. Currently, research indicates that in mechanical, electrical, and hydraulic systems, the relationship between maintenance cost and reliability is exponential. As reliability approaches the unit, improving it becomes increasingly difficult and costly. Additionally, when a component’s failure reaches a critical level, its repair feasibility significantly decreases, leading to anomalies in traditional maintenance algorithms when using exponential functions to compute costs.

According to these exponential functions, the cost of improving reliability for severely failed components is very low, which contradicts actual situations. In reality, severe damage usually makes repair more challenging, increasing time, technical difficulties, and economic costs, thereby reducing repair feasibility. Therefore, this article proposes classifying components based on their specific operating conditions during detection. This approach aims to improve the rationality of maintenance strategies, further reduce maintenance costs, and improve the efficiency of subsequent maintenance algorithms, making the maintenance strategy more applicable to real-time engineering situations.

Here, we classify component operating conditions into three categories: no maintenance required, maintenance required, and too severe failure requiring replacement. We introduce indicator $\eta$ to determine these three states, as follows:

$${\eta }_i={\displaystyle \frac{p_i}{p_{iw}}}$$

(1)

where $p_i$ represents the current output power of component i, $p_{iw}$ denotes the rated power of component i, and ${\eta }_i$ indicates the output efficiency of component $i$ at this time. The output efficiency of the component ${\eta }_i$ can be generated by comparing the real-time output with the rated one, enabling the evaluation indicator quantification to determine its operating and output status. Based on the different components’ characteristics, threshold values are set based on scientific rules to classify the work proposed in this article. The specific classification criteria are set as follows:

(a) No maintenance required: when ${\eta }_i$ > $a_1$, it is considered that the output of component i is normal and close to the rated power, indicating that the component has minimal degradation and low impact on system output; therefore, its maintenance is not necessary;

(b) Maintenance required: when $a_1$ > ${\eta }_i$ > $a_2$, it is considered that component i has experienced a certain amount of degradation and requires maintenance to improve its reliability;

(c) Replacement required: when $a_2$ > ${\eta }_i$, it is considered that component i has suffered a severe failure and repair feasibility is low, requiring replacement to restore it to a new state.

Therefore, the classification thresholds for various components in the actuation system carried by MEA are displayed in the

Table 1. Classification thresholds for system components.

	Motor	Hydraulic Pump	Hydraulic Cylinder	Hydraulic Rod
$a_1$	0.98	0.97	0.98	0.97
$a_2$	0.78	0.8	0.8	0.8

.

2.2. Importance-Based Ranking Method

Existing maintenance strategies for MEA actuation systems primarily focus on fault diagnosis and health management. While these methods improve system stability to some extent, they often suffer from inadequate precision and high maintenance costs. This study addresses these issues by introducing a GA enhanced with importance measures, which significantly improves the efficiency and reliability of MEA system maintenance. This innovative approach holds considerable practical significance in the field of MEA system maintenance.

The concept of importance measures, initially proposed by Birnbaum, represents the contribution of changes in component reliability to overall system reliability. For instance, Liu et al. [15] developed a cost-constrained ROM and introduced a cost-constrained reliability importance measure (CRIM) combined with genetic algorithms (GAs). This approach effectively addresses the challenge of maintenance decision-making under cost constraints.

When faced with limited costs, making maintenance decisions to improve system reliability requires defining cost constraints. According to Kuo’s research [27], cost constraints can be expressed as follows:

$$\begin{array}{l}\max R=f\left(\Delta r_1,\Delta r_2,\cdot \cdot \cdot ,\Delta r_n|\overrightarrow{r}\right)\\ s.t.\{\begin{array}{l}C=g\left(\Delta r_1,\Delta r_2,\cdot \cdot \cdot ,\Delta r_n|\overrightarrow{r}\right)\le C_0\\ \Delta r_i\le r_{i,\max }-r_i\\ i=1,2,\cdot \cdot \cdot ,n\end{array}\end{array}$$

(2)

where $\overrightarrow{r}=\left(r_1,r_2,\cdot \cdot \cdot ,r_n\right)$ represents the current reliability of component $n$, $R$ denotes the system reliability, $C$ indicates the total cost of a reliability improvement that should not exceed the cost constraint $C_0$, and $r_i$ and $r_{i,\max }$ are the current reliability and reliability upper limit of component I, respectively. Moreover, $\Delta r_i$ denotes the reliability increment of component $i$, with $r_{i,\max }-r$ representing the upper limit of the reliability increment.

The definition of a reliability importance measure is given by the following equation, which represents the contribution of the improvement in the reliability of component i, per unit cost, to the overall system’s reliability. It is expressed as follows:

$$I_i^{CRIM}=\underset{\Delta r_i\to 0}{\lim }{\displaystyle \frac{R\left(r_i+\Delta r_i,\overrightarrow{r}\right)-R\left(r_i,\overrightarrow{r}\right)}{C\left(r_i+\Delta r_i,\overrightarrow{r}\right)-C\left(r_i,\overrightarrow{r}\right)}}={\displaystyle \frac{\partial R}{\partial c_i}}$$

(3)

where $C\left(r_i+\Delta r_i,\overrightarrow{r}\right)-C\left(r_i,\overrightarrow{r}\right)$ represents the cost of improving the reliability of component i ranging from $r_i$ to $r_i+\Delta r$, and $R\left(r_i+\Delta r_i,\overrightarrow{r}\right)-R\left(r_i,\overrightarrow{r}\right)$ denotes the system reliability increment resulting from enhancing the reliability of component $i$ from $r_i$ to $r_i+\Delta r$.

Moreover, the cost–reliability function for components typically includes exponential, logarithmic, and inverse proportional cost–reliability functions. Current research indicates that mechanical and electrical equipment in electromechanical and hydraulic systems commonly adopt exponential cost–reliability functions [28]. Therefore, in this paper, the cost–reliability function for aircraft actuation system components is modeled using the exponential function, expressed as follows:

$$c_i\left(r_i\right)=c_{i,b}\cdot \exp \left\{\left(1-f_i\right)\cdot {\displaystyle \frac{r_i-r_{i,\min }}{r_{i,\max }-r_i}}\right\}$$

(4)

where $c_{i,b}$ is the baseline cost of component i, $f_i$ denotes the feasibility of improving the reliability of component i, and the feasibility parameter $f_i$ represents a constant value varying between 0 and 1. This expression highlights the difficulty of increasing the reliability of the component with respect to other components in the system, and its value depends on factors such as design complexity, technical limitations, and criticality of the component itself. The challenge of improving the reliability of the different components in the system will vary [29]. According to the exponential cost–reliability function, the more challenging it is to improve the reliability of a component subsystem, the greater the cost will be. Let $r_{i,\min }$ represent the lower limit of the reliability of component i. Assuming ${\alpha }_i=\left(r_i-r_{i,\min }\right)/\left(r_{i,\max }-r_i\right)$ and set the function $F\left(f_i,{\alpha }_i\right)=\left(1-f_i\right)\cdot {\left(1+{\alpha }_i\right)}^2\cdot \exp \left\{\left(1-f_i\right)\cdot {\alpha }_i\right\}$, this represents the expression for measuring the importance of the reliability of components based on the exponential cost–reliability function, expressed as follows: Assuming ${\alpha }_i=\left(r_i-r_{i,\min }\right)/\left(r_{i,\max }-r_i\right)$ and set the function $F\left(f_i,{\alpha }_i\right)=\left(1-f_i\right)\cdot {\left(1+{\alpha }_i\right)}^2\cdot \exp \left\{\left(1-f_i\right)\cdot {\alpha }_i\right\}$, then measure the importance of the reliability of components based on the exponential cost–reliability function defined as follows:

$$I_i^{CRIM}={\displaystyle \frac{R\cdot \left(r_{i,\max }-r_{i,\min }\right)}{r_i\cdot c_{i,b}\cdot F\left(f_i,{\alpha }_i\right)}}$$

(5)

2.3. Maintenance and Replacement Costs

Section 2 highlighted that this paper adopts the exponential cost–reliability function to compute maintenance costs, as shown in the expression defining the exponential cost–reliability function paradigm. The mathematical expression for calculating the cost in the maintenance algorithm is defined as follows:

$$c_i\left(r_i\right)=c_{i,b}\cdot \exp \left\{\left(1-f_i\right)\cdot {\displaystyle \frac{r_i-r_{i,\min }}{\Delta r_i}}\right\}$$

(6)

where $\Delta r_i$ denotes the numerical improvement in the reliability of component i during maintenance. Moreover, Equation (6) represents the cost required to increase the reliability of component i from $r_i$ to $r_i+\Delta r_i$. The cost formula for replacing component i is defined as follows:

$$c_i\left(r_{it}\right)=c_{i,b}\cdot \exp \left\{\left(1-f_i\right)\cdot {\displaystyle \frac{r_{it}-r_{i,\min }}{1-r_{it}}}\right\}$$

(7)

where $r_{it}$ represents the reliability of component i when the output efficiency ${\eta }_i$ of component i equals its replacement threshold $a$. In this paper, the replacement cost of component i is set to the cost to repair it to a reliability level of 1 from $r_{it}$. When it is determined that component i should be replaced instead of repaired, it indicates that, after ${\eta }_i$ < $a_2$, the cost of repairing will exceed the cost of replacement, making repair less feasible. Therefore, we set the reliability $r_{it}$ of component ${\eta }_i$ = $a_2$ as the critical value between the repair cost and replacement cost. This means that, at this reliability level, the cost of repairing component i is approximately equal to the replacement cost. Both costs are calculated using formulas, thereby achieving a scientific unification between repair and replacement decisions for components.

3. Maintenance Algorithm and Reliability Model

In the previous section, the proposed maintenance strategy was analyzed in detail. In this section, the maintenance strategy and the algorithm are combined to develop a targeted maintenance algorithm for actuation systems. A brief introduction of the reliability model of the actuation system in a MEA is proposed, providing reliability data to support the maintenance simulation work.

3.1. Genetic Algorithm with Enhanced Local Search Capability

The maintenance strategy is implemented by combining the importance ranking of degraded components with heuristic algorithms. These, later, are commonly used in conjunction with the importance measure, including traditional GAs, ant colony algorithms (ACAs), and particle swarm optimization (PSO). Among them, GAs are the most widely used due to their efficiency, parallelism, and global search capacities. GAs can automatically acquire and accumulate knowledge about the search space during the search process and adaptively control it to obtain the optimal solution. They are particularly effective for solving NP-hard problems. However, traditional GAs are prone to getting stuck in local optima. To address this issue, this paper integrates an importance measure with a GA to create an optimized GA with enhanced local search capabilities. This optimized algorithm is more effective in addressing the problem of cost constraint reliability improvements in maintenance strategies. The flowchart of this algorithm is illustrated in Figure 1.

To solve the maintenance strategy under cost constraints, this paper employs a floating-point encoding method to represent chromosomes. Since the goal is to enhance the reliability of components, floating-point encoding allows for the precise representation of each component individually, thereby improving the algorithm’s overall accuracy. Additionally, this encoding method is particularly well-suited to handling complex decision problems and incorporating constraints such as cost limits and reliability improvement thresholds. In this approach, each gene represents the amount of reliability improvement for a specific component, and all genes are combined to form a chromosome $\Delta r=\left(\Delta r_1,\Delta r_2,\cdot \cdot \cdot ,\Delta r_n\right)$. The encoding space is determined by the corresponding component’s reliability improvement range, which is the maximum possible increase in reliability for each component. Consequently, the encoding space for gene i is set as $\left[0,r_{i,\max }-r\right]$.

Through the process of generating the initial population, the same restrictions—based on the maximum reliability improvement value for each component—are applied to the chromosome $\Delta r_i$. This ensures that each gene $\Delta r_i$, randomly generated in the population, is within the range of $\left[0,r_{i,\max }-r\right]$. As a result, this will avoid the occurrence of invalid values in the initial population and improve the overall speed and iteration speed of the algorithm.

When individuals in the population do not meet the ROM cost constraint requirement, their fitness function value is penalized, resulting in a smaller score. The fitness function is defined as $F=R/\left(1+\beta \cdot \max \left\{0,1-C_0/C\right\}\right)$, where $\beta$ denotes the penalty coefficient, a very large positive number. Therefore, when $C\le C_0$, $F=R$; otherwise, when $C>C_0$, $F$ tends to zero. In this way, it ensures that individuals exceeding the cost limit have a near-zero probability $P_i$ of being selected in the roulette wheel selection process, leading to their eventual elimination from the population.

There, the algorithm terminates based on two conditions. The first condition is the maximum number of iterations M, which ensures that the algorithm will produce a solution after a finite number of generations. The second condition is based on the stability of the optimal solution over a specific number of consecutive generations, mm. This means that if, for mm consecutive iterations, the solutions of neighboring chromosomes are very close and the difference in system reliability between two consecutive generations is less than a predefined threshold, the algorithm will terminate. The second condition helps reduce the algorithm’s running time by indicating when the results obtained in two consecutive iterations are almost the same, thereby confirming that the optimal solution has been reached and improving the overall algorithm efficiency.

If the termination conditions are not met, the algorithm proceeds with roulette wheel selection. Since the best solution obtained in each iteration may not always be the global optimum, it is important to avoid getting stuck in local optima during computation. To avoid this, the selection probabilities for individuals with better fitness have a higher chance of being selected:

$$F={\displaystyle \sum _{i=1}^n{f}_i}$$

(8)

$$P_i={\displaystyle \frac{f_i}{{\displaystyle \sum _{i=1}^n{f}_i}}}$$

(9)

where $F$ represents the sum of the population fitness values, $n$ is the number of individuals in the population, $f_i$ denotes the fitness value of individual i, and $P_i$ indicates the probability that individual i survives in the roulette wheel selection process.

Roulette wheel selection is used to choose individuals for the next generation based on their fitness value $P_i$ within the population. This approach ensures that individuals closer to the optimal solution have a higher probability of being retained. Meanwhile, it preserves population diversity, which helps to prevent the algorithm from becoming trapped in local optima.

Based on the CRIM local search rule, we first identified the gene k that contributes the most to system reliability, considering both the improvement in component reliability and the associated economic cost. The second step was to enhance the reliability of the component corresponding to the top-ranked CRIM. Let $c_k=f\left(r_k\right)$ denote the cost–reliability function. The maximum reliability improvement for component $k$ is $\Delta r_k^{c_1}=f^{-}\left(C_1+c_k\left(r_k\right)\right)-r_k$, whereas the current available cost is $C_1=C_0-CC$, where CC denotes the used cost and $r_k$ indicates the reliability of component k before improvement. The maximum reliability improvement limit ${\alpha }_k=\min \left\{r_{k,\max }-r_k,\Delta r_k^{C_1}\right\}$ was then calculated by combining cost and gene $k$.

In the subsequent phase involving replication, crossover, and mutation, a local search was conducted. During this phase, the gene value of component k was randomly adjusted within a specified range. The fitness function value was recalculated and compared with the previous value. If the new value was higher, the old chromosome was replaced; otherwise, it remained unchanged. This process helped the GA identify components that most urgently required maintenance under economic constraints, thereby enhancing the algorithm’s local search capability and improving both its iteration speed and reliability enhancement effectiveness. Finally, an elite strategy was applied, preserving the top 5% solutions based on fitness for the next iteration. This approach ensured that the current optimal solution was retained, leading to a comprehensive maintenance strategy algorithm.

3.2. Actuation System Reliability Model

In this section, we present a brief overview of the reliability model for the actuation system of the MEA under consideration in this paper. The full process is depicted in Figure 2.

Currently, the Gulfstream G650 is equipped with a heterogeneous actuation system that includes both HAs and EHAs. The HA comprises components such as the pump source, hydraulic cylinder, and hydraulic rod, whereas the EHA includes the motor, hydraulic pump, hydraulic cylinder, and hydraulic rod. In this configuration, the HA acts as the primary actuator, while the EHA serves as a backup that takes over when the HA falls down. In this study, the reliability assessment of the actuation system was conducted through the following three steps:

Step 1: establishing the failure physical model of the actuation system: Based on the bond graph modeling approach and considering the specific construction of the actuation system, a detailed physical energy transfer model and signal energy transfer model were constructed. Simultaneously, a comprehensive analysis was conducted on three common degradation mechanisms in the actuation system operation: wear, fatigue, and aging. These mechanisms led to the accumulation of dissipated energy and the coupling of local and system failures. By integrating these mechanisms into the bond graph model, a robust actuation system failure coupling model was formed. Figure 3 illustrates the bond graph model of the heterogeneous actuation system from a single control surface. Different colors of arrows in the Figure 3 represent different types of energy transfer: blue for hydraulic energy, orange for electrical energy, and purple for mechanical energy.

Step 2: parameter sampling based on a Monte Carlo simulation: Analyzed the probability distribution of key parameters associated with wear, fatigue, and aging in the model. Performed parameter sampling from these distributions and introduced a 5% variation in the sampled parameters to account for uncertainties in parameter distribution.

Step 3: reliability assessment: Substituted the sampled arrays of the three key parameters into the actuation system failure coupling model. Used statistical methods to compute the probability density distribution of the lifespan of the actuation system and its components. Integrated the probability density distribution function of the lifespan to conduct the reliability assessment. The results and data for the reliability assessment of the actuators and components were generated through this process. For detailed information on the specific model and process in the reliability assessment, refer to the previous study [30].

At the same time, the bond graph model offers the advantage of real-time observation of the operational outputs of the system and its components. The parameters mentioned in Section 2, such as reliability $r_{it}$, component output efficiency $\eta$, and the real-time power output of the components $p_i$, can all be derived from the bond graph model of the actuation system used in this study.

4. Actuation System Maintenance Simulation Analysis

In Section 2, a comprehensive maintenance strategy algorithm for the actuation system was developed. In this section, the reliability data obtained from the actuation system reliability model discussed in Section 3 will be used to simulate the maintenance of both HA and EHA components. Given the significant impact of failure coupling on the left spoiler observed in the reliability assessment study, we focus on extracting and analyzing the reliability and maintenance data related to the left spoiler when it is integrated into the actuation system during a failure. The specific data can be found in

Table 2. HA-related maintenance data.

	Pump Source	HA Hydraulic Cylinder	Hydraulic Rod	HA
$f_i$	0.5	0.4	0.5	—
$R_i$	0.75	0.72	0.89	0.48
${\eta }_i$	0.88	0.84	0.91	—
$r_{i,\max }$	0.98	0.97	0.97	—
$r_{i,\min }$	0.6	0.62	0.6	—
$c_{i,b}$	3	5	3	—

and

Table 3. EHA-related maintenance data.

	Motor	Hydraulic Pump	Hydraulic Cylinder	Hydraulic Rod	EHA
$f_i$	0.45	0.5	0.4	0.5	—
$R_i$	0.85	0.81	0.75	0.89	0.459
${\eta }_i$	0.9	0.82	0.8	0.91	—
$r_{i,\max }$	0.98	0.98	0.97	0.97	—
$r_{i,\min }$	0.65	0.6	0.62	0.6	—
$c_{i,b}$	4	3	5	3	—

.

In this section, mainstream heuristic algorithms currently used in maintenance strategies are introduced for comparison. Traditional GAs and PSO algorithms are also selected [31,32]. PSO is an evolutionary computation technique commonly employed for optimization and strategy problems. Therefore, in this section, a PSO algorithm is proposed and compared to a GA based on the importance measure obtained in the previous section.

The data used in the three algorithms is shown in Table 2 and Table 3, and parameters, such as cost limit, cost baseline, and number of iterations, are set consistently to ensure the comparison rationality. Moreover, Figure 4 and Figure 5 illustrate the comparative analysis of maintenance results for the HA and EHA in the actuation system.

The reliability data of the components after maintenance, using the three algorithms, are shown in

Table 4. Reliability data of HA components after maintenance.

Algorithm	Pump Source	HA Hydraulic Cylinder	Hydraulic Rod	HA
Improved GA	0.9422	0.9417	0.9542	0.846
GA	0.9559	0.9154	0.9562	0.834
PSO	0.9579	0.9124	0.9578	0.837

and

Table 5. Reliability data of EHA components after maintenance.

Algorithm	Motor	Hydraulic Pump	Hydraulic Cylinder	Hydraulic Rod	EHA
Improved GA	0.9521	0.9518	0.9466	0.9542	0.814
GA	0.9584	0.9514	0.9123	0.9562	0.794
PSO	0.9338	0.9589	0.9214	0.9578	0.789

. It is evident that the improved GA proposed in this paper not only achieves superior final reliability improvement results but also benefits from the incorporation of the importance measure. This allows the improved GA to focus on critical aspects of maintenance tasks while seeking the optimal solution. As a result, the convergence speed of the improved GA is significantly better than that of both the traditional GA and the PSO algorithm.

Meanwhile, we conducted a further comparative analysis of the performance of the three algorithms. As shown in Figure 6, a box plot is presented for the EHA repair results of 100 trials using the same data for the three different algorithms. The plot includes the median line, mean value, and 1.5 range in the interquartile range (IQR) of the repair results for each algorithm. This provides a further comparative analysis of the performance of the three algorithms. From Figure 6, it can be observed that the proposed improved GA outperforms the traditional repair algorithms in terms of both the final repair’s effectiveness and stability.

5. Conclusions and Future Works

This paper proposes a practical maintenance strategy to improve the reliability of MEA actuating systems. Initially, by effectively classifying components, the strategy addresses the limitations of traditional reliability cost index functions, which are unreasonable in cost calculations. This approach removes the impact of extreme conditions, such as severe component failures, on maintenance cost calculations, making the maintenance strategy more rational.

By utilizing importance theory under ROM cost constraints, the paper sets up a target function and cost constraints based on the actual problem of classifying the contribution of component reliability improvements within the overall system’s reliability. This ranking helps in identifying the components with the highest maintenance priority within cost constraints.

Finally, the importance ranking method is integrated with a traditional GA to identify components that offer the highest combined cost efficiency and reliability improvement contribution. This integration enhances the local search capability of the traditional GA, resulting in a more effective maintenance algorithm for the actuating system. The performance of the proposed maintenance strategy is evaluated using reliability data from various components and systems and compared with two other traditional heuristic algorithms. The results demonstrate that the proposed method not only converges faster during the maintenance process but also achieves better reliability improvements in the field of actuating system maintenance.

However, there are some limitations in this study. Specifically, the improved GA based on cost constraints involves multiple parameters that need to be manually adjusted based on practical experience, such as population size, number of iterations, crossover and mutation rates, and elite strategy, to retain the number of individuals. These parameter settings can significantly affect the final maintenance results.

Finally, future work could explore the use of reinforcement learning for automatic parameter tuning. This approach would enable the algorithm to iteratively learn and improve parameters, thereby ensuring the efficiency and accuracy of the maintenance algorithm.