Research on case-based reasoning for determining maintenance intervals of civil aircraft systems

The development of a rational and effective maintenance program is an important way to keep the safety and the economy of the aircraft industry. The maintenance program indicates maintenance types and intervals of all components. As development maintenance types of the components are simple, interval is a key to developing the maintenance program. In this paper, Case-Based Reasoning (CBR) is introduced to determine the intervals of components. It focuses on the expression and adjustments of the case. Finally, the reliability data of components in Boeing 737 is taken as an example to certify this method. The results show that this method can determine the maintenance intervals effectively, and so it has important engineering application value.


Introduction
Most new products are the result of improvements to old ones, with certain similarities in various aspects such as functionality, working conditions, functional failures, functional impacts, and structure.Some systems also include standardized products.For newly developed aircraft, when conducting MSG-3 analysis, there is a serious lack of information on the use and maintenance of the aircraft.Analysts will need to refer to the experience of similar or identical aircraft systems/subsystems for analysis and judgment.This is the idea of Case-Based Reasoning (CBR) [1][2][3] .
The method of CBR is to formulate specific rules, apply past problem-solving solutions, and combine them with the actual conditions of the target object, then reuse or modify them, output new decision plans, and retain them in the case library [4][5][6][7] .The basic condition for using CBR to solve the target problem is that historical cases similar to the target problem can be found in the case library, the two solutions have similarities, and the same or similar problems may occur in the future [7][8][9][10] .Therefore, in this article, a multi-stage framework structure is proposed based on CBR to establish a model for determining maintenance intervals of civil aircraft systems.Finally, the example analysis in this article also confirms the effectiveness of the method used in determining maintenance intervals for aircraft systems.

Case-based reasoning for determining maintenance intervals
Due to the similarity between civilian aircraft, there are varying degrees of similarity between aircraft from the same manufacturer and those developed by different manufacturers.Therefore, clues to solving current maintenance task analysis problems can be found from the analysis experience of similar aircraft models.Case-based reasoning refers to borrowing old examples or experiences to solve new problems.This idea is consistent with the idea of case-based reasoning methods [5][6][7][8] .

Case Representation
The efficiency of case-based reasoning is closely related to case representation.The case presentation involves several issues: what information to choose to store in a case; how to choose a suitable case content description structure; and how to organize and index the case library.For cases that reach tens of thousands and are very complex, case organization and indexing issues are important.
Maintenance interval cases include a large amount of MSG-3 analysis information, such as basic data of important maintenance items (MIS), functions, faults, cause analysis, MSG-3 logic decision-making information, etc.If the information above is described in detail, it bring difficulty to the expression and operation of the case.In this article, it is determined that the attributes of the aircraft system MSG-3 analysis case are composed of two parts: MSI basic description attributes, including aircraft type, ATA chapter, and fault impact category; MSI task analysis process attributes, including tie fault interval, maintenance task type, and maintenance task interval.

Case retrieval
The retrieval and selection of cases is a very important step in the CBR method.The selection of similar cases based on "maintenance work and objects" includes two parts: retrieval and selection.In this article, the definition of case similarity is as follows: Among them, a T i and a P i represent the attribute values of the target problem T and case P regarding attribute i. MAX i and MIN i represent the maximum and minimum values of the i-th attribute in all cases (including the target problem), respectively.
The similarity measurement value of quantitative attributes is calculated, and a character-type field described in natural language in the qualitative attribute book is selected.When the target problem and case have the same text about the same attribute, the similarity value of the attribute is 1, otherwise, it is 0.
The comprehensive similarity S(T, C) is obtained by aggregating qualitative and quantitative attributes, which is expressed as:

Case revision and retaining
Through case retrieval, a candidate case set arranged in descending order of similarity was obtained, and MSG-3 analysts can choose one or several cases with high similarity as references.There are often some differences between the selected MSG-3 analysis cases and the structural cases to be analyzed, which cannot be directly applied and require appropriate adjustments.By adjusting, it can be considered that the similarity between the target problem and the case is the similarity between the problem interval and the case interval.For the selected case, the attribute similarity is recalculated using the following formula:

Determination of target case interval
The maintenance interval calculation method for the target case is as follows: Where I j represents the interval value obtained from the j-th case; I p f represents the interval value of the j-th case; S(T, P j ) represents the similarity between case P j and problem T.

Case analysis
The continuous airworthiness document stipulates that when a type certificate for an aircraft, the applicant must develop a maintenance outline.The maintenance outline is a minimum initial scheduled maintenance requirement approved by the management authority for a specific transport aircraft and installed engines, with the core issue of determining maintenance intervals and maintenance work.The determination of maintenance intervals is divided into three stages: case representation, case selection, and case rewriting and saving.For example, the main attributes of the target case in this article are shown in Table 1.

Case selection
According to the method in Section 2.2, the attribute similarity of the target case is calculated, as shown in Table 3.The MTBF is 0.2; Fault type is 0.5; Task is 0.1.The overall similarity of the case is calculated using Formula (2) as shown in Table 4.

Revision and Retaining of the Cases
After selecting similar cases through the above selection methods, it can be considered that the similarity between the target problem and the case is the similarity between the problem interval and the case interval.For the selected cases, the attribute similarity is recalculated using Formula (3) as shown in Table 5.

Determination of target case interval
According to Formula (4), the maintenance intervals corresponding to each similar case of the target case are calculated as shown in Table 7.According to Formula (4), the average interval is I`=1575.

Conclusion
In this section, the representation, selection, and rewriting of cases are discussed in detail, and B737 is used as an example to determine the maintenance interval for the target case.From the results, it can be seen that the standard inspection interval provided by Boeing for this task is 1600 FH, while the error of the CBR method for 1575 FH is 1.56%.The reason for the large error in the CBR method is due to the low similarity of the overall case.So for CBR, this interval is also acceptable.Finally, with the CBR method, the corresponding attributes of the new target are estimated based on experience, so this algorithm provides a good method for practical engineering applications.

Table 2 .
. Main attributes of the target case.Representation of case In this article, relevant attributes of similar cases are extracted, as shown in Table2.Main attributes of similar cases.

Table 3 .
Similarity of attributes in similar cases/

Table 4 .
The overall similarity of cases.reliable similarity threshold is determined based on expert opinions, and similar cases are screened in this article.Cases with a similarity greater than 0.7 are selected as examples.Therefore, Cases 3 and 4 are retained.

Table 5 .
Rewritten case attribute The overall similarity of the case is recalculated using Formula (2) as shown in Table6.

Table 6 .
The overall similarity of the rewritten case.

Table 7 .
Maintenance intervals for similar cases.