Data-Driven Health Assessment in Flight Control System

: The aircraft critical system’s health state will a ﬀ ect ﬂight safety dramatically, such as ﬂight control system, and its health state awareness or assessment is very important to avoid ﬂight accident. A data-driven health assessment based on fuzzy comprehensive evaluation and rough set reduction is proposed for ﬂight control system. Through the working principle and failure mode analysis, the system’s characteristic parameters are constructed to represent health state, and then the comprehensive health index construction is proposed to quantify health state. In the end, case calculation based on some aircraft’s ﬂight data is presented to show the e ﬀ ectiveness of the proposed method.


Introduction
For modern advanced aircraft, flight control system is indispensable to complete normal flight mission and ensure flight safety, which means to stabilize attitude and track scheduled path. So such system's health assessment is necessary to assist maintenance decision, operation schedule, and logistical support optimization, in which it is essential to avoid catastrophic accidents or even loss of human life. A great many scholars have paid attention to flight control or other airborne system's health monitoring and assessment, which may use system's theoretical model, system measured information, or system knowledge and so on.
In this paper, a data-driven health assessment method based on fuzzy comprehensive evaluation and rough sets reduction for flight control system is proposed. Compared with other health assessment methods, the algorithm based on fuzzy comprehensive evaluation and rough set reduction proposed in this paper still has better performance when the data sample size is small. In addition, by introducing the rough set reduction algorithm, it is also possible to objectively calculate the weight of each subsystem, which makes the evaluation results more comprehensive and reliable.The fuzzy comprehensive evaluation is introduced to complete each factor's evaluation based on optimal evaluation valueand so as to avoid the less fault samples problem. Moreover, the rough set reduction is used to calculate the importance or weight of each evaluation factor, which eliminates the subjective and noise effects. Finally, the actual flight data is used to analyze the health state of the flight control system, which proves the effectiveness of the proposed method. The corresponding literature review about this problem is completed as follows.

Health Assessment Model
Flight control system is generally composed of main and auxiliary control system. The main control system uses the different control surfaces to complete the pitch, roll, and yaw motion; for the viewpoint of system operation, it can be divided into pitch, roll, and yaw channels. Furthermore, the auxiliary control system is used to carry out lift enhancement and other auxiliary functions.
The failure mode analysis shows thatthe flight safety is mainly impacted by the main control system and the flaps in the auxiliary control system. In this paper, the system health assessment model is constructed by four channels, e.g., the three main channels and flap channel, which can be shown in Figure 1. In this figure, based on system analysis and flight monitoring parameters selection, thecharacteristic parameters can be extracted to reflect each channel's health state. Furthermore, the weight of each channel's characteristic parameters are given by rough sets reduction and the health assessment is completed at the different channels with fuzzy comprehensive evaluation. Finally, the comprehensive integration is carried out at the flight control system level to get the total quantitative assessment of system health state.
Four channels' characteristic parameters are selected according to Failure Mode and Effect Analysis (FMEA) of flight control system, which is shown in Tables 1 and 2. Therefore, the following three transmission coefficients are selected as parameters that characterize the health status of the main control system: (1) Pitch channel: steering column to elevator transmission coefficient.
(2) Rolling channel: transmission coefficient from steering wheel to aileron.
According to the flap system FMEA, the common failures of the flaps including jamming and inability to retract, etc., will cause the main hydraulic pressure to be abnormal and increase the retraction time. Therefore, the main hydraulic pressure and the flap retraction time can reflect the health status of the flap system, but the flap retraction time is only counted once in each sortie. It is impossible to obtain enough initial samples, so the Main Hydraulic Pressure is selected as the characteristic parameter to characterize the health status of the flap system.

Comprehensive Health Index
In Figure 1, Comprehensive Health Index (CHI) is used to quantify the whole system's health state, whose value is set from 0 to 1. If the characteristic parameters are deviated, which means the corresponding channel health state is abnormal, and the CHI will be varied. Therefore, the system's CHI can be calculated as follows: where CHI is thesystem comprehensive health index, Subsystem Comprehensive Health Index (SCHI) is thehealth index of each channel in Figure 1, W i is the weight of each channel, SCHI i is obtained by the characteristic parametersevaluation of each channel.Taking the pitch channel as an example to illustrate SCHI's calculation process, firstly, the pitch channel's characteristic parameters are extracted, and then the membership of each characteristic parameter is obtained to construct the evaluation matrix and determine the characteristic parameters' weight vector.Finally, the weight vector and evaluation matrix are multiplied to get the evaluation vector, and the SCHI is calculated after quantification. The detailed integration process is described in Section 3.1 below.

Fuzzy Comprehensive Evaluation
The failure record in actual system operation data may be less inevitable, which leadsto the commonly used neural network method and the gray clustering method being less accurate. The fuzzy comprehensive evaluation fuzzily divides the characteristic parameters into several intervals, which constructs the characteristic parameters' fuzzy evaluation matrix in a specific channel, and then performs a row-by-row weighted calculation on this matrix to obtain a channel evaluation vector and gets the channel's health index. During this process, each factor's evaluation is completed by the best value, so it is only necessary to obtain the evaluation value through the comparison benchmark for the fault sample, which avoids the classification boundary ambiguity caused by the fewer fault samples [16]. The specific steps are shown as follows: (1) Selecting characteristic parameters: characteristic parameters that reflect each channel's health state are selected as in Figure 2, which are used as evaluation factors. In this figure, n 1 , n 2 , n 3 , and n 4 are the number of characteristic parameters contained in the four channels.
(2) Establishing the health state interval set: The interval set is hierarchical set of health state of each characteristic parameter and channel. Assuming that there are m levels, the health state interval set can be expressed as: Where L means the health state of each characteristic parameter. Then the relative degradation degree analysis is introduced to normalize each characteristic parameter and construct a membership function with this relative deterioration degree.
(3) Calculating the membership row vector of each characteristic parameter: With the above-mentioned health state interval fuzzily calculation, the corresponding factor membership row vector can be obtained as: where, i = 1, 2, 3, 4 represents the four channels, j = 1, 2 · · · n i , n i indicates the number of characteristic parameters in channel X i in Figure 2. m is the interval number of health stateinterval sets.
(4) Constructing the fuzzy evaluation matrix: With the membership row vector calculation of each characteristic parameter, the membership row vectors of all characteristic parameters in thechannel are combined to construct the fuzzy evaluation matrix: where i = 1, 2, 3, 4, m is the health state interval number, n i is the characteristic parameters number of channel X i . (5) Determining the weight vector of the characteristic parameters in the channel: Based on the characteristic parameters selection in Equation (1), the rough sets reduction described in Section 3.2 below is used to identify the importance of factors for the upper level factors, and then the weight vector is constructed as: (6) Calculating evaluation vector: With the weights w i of the characteristic parameters in the same channel and the fuzzy evaluation matrix R i , the evaluation vector of the channel X i is computed as: (7) Calculating the health index of the channel: As the evaluation vector for channel X i is obtained, the evaluation vector b i is weighted summed and normalized to obtain the health index of the channel SCHI i , which can be shown as: where m is the interval number of health state interval sets, k is the sequence number of elements in b i , k = 1, 2 · · · m

Weight Assignment Based on Rough Sets Reduction Algorithm
For the two-level weight calculation in Figure 2, there are three commonly used assignment methods [17]: subjective, objective, and subjective/objective weighting methods. During the weight assignment process, it is necessary to minimize the subjective factors' impact, and an objective weighting method based on rough sets reduction is used in this section, which removes an attribute from the set firstly and evaluates its importance to determine its weight.
The main idea of rough set is to ensure that the classification ability of the information itself does not change. A new classification method is formed by the relative simplicity of information knowledge, under the condition that the simplicity of knowledge does not change the original classification, and then the expression of new knowledge is formed. The brief process of knowledge in each message can be described using specific mathematical formulas, which makes it capable of processing most rough sets of data. As the knowledge structure of the information is preserved, rough sets processing method is widely used in machine learning, pattern recognition, and data mining.
Rough set algorithm does not need priori data, it only needs to mine the hidden rules from the knowledge itself and extract the importance of attribute components. So, we can obtain the importance of component attributes on information classification, which can be integrated with a weighted comprehensive model to establish objective feature parameter weight distribution methods.
Based on this, the idea of rough sets reduction is to continuously remove certain attributes from the original complete attribute set, and then observe whether the postclassification state has changed greatly; if it does, the importance of this attribute is higher, otherwise the importance is lower. When using the rough set reduction algorithm to calculate the weight of each channel, the membership function of the relative degradation degree of each channel is first constructed, and then the weight value is derived from the attribute importance of each channel, which can reduce the inaccurate weight setting caused by the bias of human subjective judgment, thereby improving the robustness of the evaluation results.
The specific assignment steps are shown as follows: (1) Constructing decision table: Constructing a decision table with different attributes and importance, the lower evaluation factor in Figure 2 is used as the condition attribute in decision table C = c 1 c 2 · · · c n , and the upper factor is used as decision attribute D = d 1 d 2 d 3 d 4 , n = n 1 + n 2 + n 3 + n 4 .
(2) Calculating the attribute conditional information entropy: Supposing X is a subset of attributes in the flight control system evaluation factors, and the x is a specific attribute, the conditional information entropy of x for X is: where U is a finite nonempty set of flight control system.
(3) Calculating the importance of a single attribute: Excluding an attribute c, the importance of c in C based on conditional information entropy is computed as: (4) Calculating the weights: Based on the importance calculation of a single attribute, the weight of the attribute can be obtained as:

Relative Deterioration Degree
Each characteristic parameter has its special physical meaning and dimension, the relative deterioration degree method [18] is used for normalization, and then the membership function is constructed in this subsection. The relative deterioration degree refers to the similarity between the current state of the characteristic parameter and fault state; the value range is set as [0,1]. The value 1 indicates the fault state, and the value 0 is the healthy state. For characteristic parameters analysis of the flight control system, the intermediate type calculation method is adopted to calculate the relative deterioration degree, and its degradation degree function parameters include the maximum x max , minimum x min , and optimal range [x a , x b ], which is shown as:

Certain Type Aircraft Flight Control System Health Assessment
In this section, the flight data of certain types of commercial short-range twin-turboprop aircraft is used to verify the above data-driven health assessment method. Due to the small number of aircraft in service, 60 flights' data are obtained for this verification.
The detailed flight data in Excel table is shown in Figure 3 below.

Health Assessment for a Single Flight
The characteristic parameters of four channels need to be determined firstly for comprehensive health index, and then the health state assessment of the single flight can be completed.
Take the flap channel as an example, the pilot inputs the command by position handle and the hydraulic electromagnetic switch will be open according to this command signal; the high-pressure oil will enter the pipeline through the electromagnetic valve to drive motor, which drives the flap drive shaft to rotate. During this process, the main hydraulic pressure's variation will directly change the flap retracting force and affect the flap system's performance. So, the main hydraulic pressure is taken as the characteristic parameter of the flap's health state. Moreover, based on the flap failure mode, the jamming of the transmission mechanism component will slow down the retracting speed or even stop retracting, so the flap retraction and extension time is introduced as the second characteristic parameter.
To get the membership, the main hydraulic pressure needs to be normalized with the relative degradation degree, and Table 3 gives the parameters of relative degradation function in Equation (11), and then the relative deterioration degree of the main hydraulic pressure is obtained as 0. As the evaluation steps shown in Section 3.1, health state interval set with four levels is established as: health, slight degradation, severe degradation, and warning. Since the characteristic parameter has become a normalized value by relative deterioration degree analysis, the distribution functions of the descending, intermediate, and ascending types are selected to construct the membership function to cover the deterioration interval: which are shown in Figure 4. Then the membership of the main hydraulic pressure can be obtained as follows: Since the sampling time interval of the original data is 1 s, the normalized data has a smaller discrimination. Therefore, 20 experts are invited to judge the flap's retraction and extension time, and there are 17 experts who believe that flap system is healthy, three experts think the flap is slightly damaged, and no experts think the flap is failed. The single factor membership value of the retraction and extension time is obtained as follows: The membership vectors of two characteristic parameters are combined as follows: Meanwhile, the rough sets reduction algorithm is used to assign weights of main hydraulic pressure and retracting time as follows: According to the above Equation (6), the evaluation vector is: The evaluation vector is quantified based on Equation (7) above to obtain the health index of the flap channel SCHI = 0.8908.
Similarly, the deterioration degree function parameters of the other three channels are constructed in Table 4. In which, the transfer coefficient is defined as the slope of control surface deflection and joystick displacement curve. The deterioration degree of the characteristic parameters is obtained and the membership value is calculatedand finally the health index of the channel can be obtained. The relative deterioration degrees of the above characteristic parameters are calculated as follows: Based on the membership function above, the membership vectors of three channels are obtained as: The weights of characteristic parameter in each channel are setas: w i = 1, i = 1, 2, 3.Using the above method, the health indices of the pitch channel, the yaw channel, and the roll channel are obtained as 1, 1, and 1. With the rough sets reduction algorithm, the weights of the four channels are obtained again as in Figure 5. Based on Equation (1), the comprehensive health index is obtained as: CHI = 0.6206. The ability of the flight control system to carry out system or channel functions under different health states is different; according to gray health index theory [19], the health state of flight control system is divided into four levels, which establishes a mapping relationship between the comprehensive health index and the flight control system's health state. The definition of the system comprehensive health index interval is shown in Table 5. Compared with Table 5, the flight control system for this flight is in "functional degradation" state.

Health Assessment for 60 Flights
With health assessment calculation for 60 flights of this aircraft, the health index of the four channels and the comprehensive health index of the flight control system are shown in Figures 6  and 7, respectively.  With the health index interval in Table 5, the health state distributions for 60 flights are shown in Figure 8. In these 60 flights, flight control system is healthy in 33 flights, functional degradation in 25 flights, and significant decline in functionality in 2 flights. Moreover, the 34th and the 54th flights show significant decline in functionality as the red dot in Figure 9, and the 26thflight shows significant decline in functionality as the green dot in Figure 9. The four channels' health indexes for the three flights (26, 34, and 54 flights) are listed in Table 6 below.  This shows that, in the 26th flight, the SCHI for yaw channel and roll channel are lower, which causes the health state to decline, and in the 34th and 54th flights, the SCHI for pitch channel and yaw channel are lower, which causes the health state to have a significant decline in functionality. According to the health characteristics of the three flights, the main reason is that the transfer coefficient K 1 of the pitch channel, the transfer coefficient K 2 of the yaw channel, and the transfer coefficient of the roll channel are not in normal range.
In addition, the Analytic Hierarchy Process (AHP) [20] was used to evaluate the health status of the flight control system for 60 sorties, and compared with the evaluation results based on fuzzy comprehensive evaluation and rough set reduction algorithm(comprehensive evaluation) mentioned in the article, the results are as follows: It shows that the results obtained by the two evaluation methods are mostly consistent, but there are some differences in detail. Compared with the proposed method, in the assessment results obtained by AHP, the number of flights approaching and reaching severe functional degradation has increased, as shown by the green and red dots in Figure 9 and Table 7 (green dots indicate that the flight approaching severe functional degradation, and red dots indicate the flight has reached functional degradation). Further study of the channels'health status of these sorties can concludethat their pitch channels have experienced different degrees of functional degradation, which led to the decline in the health status of the flight control systems of these flights.

Discussions
In the comparison of the above two methods, the AHP evaluation result has more flights that are close to or have reached functional degradation. However, even some flights whose channel function has not reached severe degradation are assessed as severely degraded (such as the 51st flight in Table 7); this is obviously inaccurate. The reason for this is that when constructing the judgment matrix of the AHP method, the weight of the pitch channel's SCHI in Table 7 is set too high, which results in the overall health of some flights whose function is close to severe functional degradation being evaluated as severe functional degradation; in other words, human subjective judgment magnifies the degree of actual failure.
In contrast, the evaluation method based on fuzzy comprehensive evaluation and rough set reduction algorithm proposed in this paper is based on the membership function to solve the weight of each channel; it reduces the inaccurate evaluation caused by the bias of subjective judgment, which improves the reliability and robust of evaluation result and reduces the false alarm rate of the evaluation process.
Furthermore, the evaluation method proposed in this article still has some shortcomings. For the selected characteristic parameters that characterize the health status of the flight control system, although these parameters are set in the standard range when the aircraft leaves the factory, they are constantly changing during the actual flight. Therefore, it is necessary to analyze this impact of uncertainty in future studies.

Conclusions
Based on the health monitoring and maintenance requirement of flight control systems, the health assessment model is established firstly in this paper. With this model, some data-driven methods are introduced to evaluate the health state. Finally, the case study is completed to show the effectiveness of the proposed method, and the following conclusions can be obtained: (1) The calculation results are close to the actual operating condition, which proves that the model is suitable for the flight control system's health assessment. (2) For the weight assignment of each level of the assessment model, the rough sets reduction is introduced to eliminate the subjective factors' influence and overcome the defects based on expert experience. (3) The membership classification error can be avoided by membership value determination method based on the relative deterioration degree, which makes the evaluation matrix more accurate.