HEALTH MANAGEMENT USING FAULT DETECTION AND FAULT TOLERANT CONTROL OF MULTICELLULAR CONVERTER APPLIED IN MORE ELECTRIC AIRCRAFT SYSTEM

The increased cost of fuel and maintenance in aircraft system lead to the concept of more electric aircraft, moreover this concept increase the use of power electronic converters in aircraft power system. Since in this application, the reliability is a crucial feature. Therefore, the use of more efficient, reliable and robust power converter with health management capability will be a big challenge. Multicellular topology of power converters has the required performance in terms of efficiency and robustness. However, the increased complexity of control and more power components (power switches and capacitors) goes along with an increase in possibility of failure in multicellular topology. Therefore, the main contribution of this paper is the use of multicellular topology advantageous with fault diagnosis and fault tolerant control in order to increase the robustness reliability. The health management using a fault detection with Fuzzy Pattern Matching (FPM) algorithm when a failure in power switches or flying capacitors of multicellular converter and a Fault Tolerant Control (FTC) with sliding mode of second parallel three cells multicellular converters. Simulation results with Matlab show the increased efficiency and the continuity of work during failure mode in aircraft power system.


INTRODUCTION
Recently, the aircraft system plays an important role in globe world economics, human culture, space discovering, and technology development [1][2]. However, in order to obtain aircraft with fewer carbon emission, fuel saving, quitter flight and reduced weight and noise, the traditionally actuators powered by mechanical, pneumatic, and hydraulic sources such as environmental control, wing ice protection, and fuel pumping systems) are replaced by controlled electric systems [3][4][5]. To this manner, a considerable change in the design of modern aircraft. The planes Airbus A380 and Boeing 787 have more electrical systems compared with previous planes [6]. This increase of electric systems uses leads to the concept of more electric aircraft. Therefore, high voltage power electronic converters are enabling modern aircraft to adjust and control the electric loads. However, the transfer to new concept of more electric aircraft is challenged by strict requirements of safety and continuity of operation in its electrical power systems [7][8][9]. Therefore, the use of more efficient and robust power converter in more electric power system is necessary. Multicellular power converters or flying capacitor topology has more advantageous compared with other power converter topologies, such as reduced stress on power switches, high switching frequency capability and small dv/dt [10][11][12]. In [13][14] a multicellular converter shows a good robustness against parametric variations and current harmonics for a various control method. A simulation and experimental study shows good balancing of capacitor voltages and no interharmonics has been produced in multicellular converter. In [15], the robustness and stability are confirmed for multicellular converter. However, the multicellular topology present higher redundancy of power switches and flying capacitors, and because the aircraft systems need to guarantee the safety and the availability of operation, health management with fault diagnostics and fault tolerant control are necessary. A multicellular converter with fault diagnosis is used in order to enhance the performance of wind turbine system [16]. While, in [17], an approach based on the use of a machine Learning technique is developed to perform an early fault diagnosis method of power switches faults in wind turbine converters with hybrid dynamic classifier for multicellular converter in wind turbines is proposed. In [18] a fault diagnosis and fault DIAGNOSTYKA, Vol. 23, No. 2 (2022) Mahboub MA, Rouabah B, Kafi MR, Toubakh H: Health management using fault detection and fault tolerant … 2 tolerant control of multicellular converter used in shunt active power filter in order to enhance the efficiency and the reliability of active filter, and advanced fault-tolerant control strategy of wind turbine based on squirrel cage induction generator with rotor bar defects in order to extend the lifetime of wind energy conversion system [19].
In electric system of aircraft, different fault diagnosis methods are used in literature. Diagnosis strategy of nonstationary (transient) states of direct current in electric power systems of aircraft [20]. In [21], a fault diagnosis method using acoustic signature of aircraft auxiliary power unit.
However, a Fuzzy Pattern Matching (FPM) algorithm is used in fault diagnosis as reduced time method of classification (the detection, integration and adaptation online) [22][23][24] Therefore, the contribution of this paper is the use of FPM and multicellular topology advantageous in more electric aircrafts with more reliability and increased robustness. These can improve the efficiency and the safety of studied system. This paper proposes a multicellular topology of two parallel converters with fault tolerant control and fault diagnosis using Fuzzy Pattern Matching (FPM) algorithm.
This paper is organized as follow: in section 2 modelling of proposed system than in section 3 presentation of Fuzzy Pattern Matching (FPM) algorithm, in section 4 simulation results with Matlab and finally conclusion in section 5. Figure 1 shows the proposed system structure.

MODELING OF PROPOSED STRUCTURE
The multicellular topology of power converter is presented in figure 2.
is the current of flying capacitor VCi means VC1 and VC2

= −
(3) LL and RL are the resistor and inductor of electric load, S1, S2 and S3 are the state of power switches. The nonlinear model of multicellular converter topology used in photovoltaic system is given by Equation (6).

Sliding mode control
İn references [11][18], the sliding mode control is used and assure the robustness and stability of multicellular converter. Therfore, in this paper the sliding mode control is applied in order to assure an efficient fault tolerant diagnosis ant fault tolerant control.
According to the Equation (6), the mathematical model of proposed topology power converter can expressed by the Equation (7): The sliding mode surface (Sr) is given by: The stability of proposed control is assured by Lyapunov approach The Lyapunov function is expressed byEquation (9): The deriving of Lyapunov function is given in Equation (10): V̇=Sr(x)Sṙ (x) (10) The deriving of sliding surface in Equation (11): Sṙ = ẋ − ẋr ef (11) Substitute of Equation (7) in Equation (12) give the following equation Sṙ =f(x)+g(x)u-ẋr ef (12) The input control u is given in Equation (13) u=u eq +u n (13) Suppose an ideal sliding motion. This can be expressed as Sr(x)=0 and Sṙ (x)=0.

( ) = (21)
A linear interpolation between bins heights at their centers is used to obtain the probability density function (PDF). superior and inferior bins of height zero are added to each histogram probability. So, the goal is to link the centers of the first and last bins to zero (see Fig. 4). When a large number of data is available, the histogram can be assumed to approximate the PDF x will finally be assigned to the class for which it has the highest membership value. More details about the functioning of this method can be found in [16] and the references therein. This method was used because it is simple and has a low and constant classification time according to the size of the database [24].

RESULTS OF SIMULATION STUDIES
Simulation parameters are summarized in table 1. All power switches have ideal operating and all figures are obtained with Matlab software.   In this test of robustness, the reference current is changed from 5A to 10A at 0.2s ( figure 9). These result proves the robustness of proposed control. When C1 is broken the voltage Vc1 deviates from the desired value ( Figure 10) and the static error of voltage Vc2 is increased.
The load current ( Figure 11) deviates from its reference and the static error of load current equal to 1.5A -Failure of capacitor C2 When C1 and C2 are broken the voltage Vc1 and Vc2 deviate from their desired values ( Figure 14). The load current ( Figure 15) deviates from its reference and the static error of load current equal to 3 A Figure 16 shows the feature space of different operating mode. Using a computer with Intel (R) Core(TM) i5 and 2.50 GHz, The FPM classification time for each pattern (the detection, integration and adaptation online) is equal to 3 * 10-1 second. These results prove the effectiveness and efficiency of proposed algorithm.

CONCLUSION
This work presented a multicellular converter used in aircraft system with robust sliding mode control and fault diagnosis strategy using FPM. and fault tolerant control using second multicellular converter. This structure assured the continuity and safety operating in electric parts of more electric aircraft, as well as increase the robustness. when a failure in capacitors of multicellular converter occurred, load current and capacitor voltage deviated from their references, which increase mechanical vibrations and heat stress. The FPM algorithm detect the failure mode from used feature space than the second multicellular converter is working until the arrival of maintenance team. Simulations with software MATLAB/ Simulink proved the effectiveness of the proposed fault diagnosis method with reduced time to eliminate the failure impact on the aircraft system; this can prevent the propagation of failure to other healthy parts of electric system and increase the lifetime of aircraft.
As further direction, we propose to deal with fault prognosis and remaining useful life (RUL) estimation in more electric aircraft.

Source of funding
This work is funded by:

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.