Reliability calculation with error tree analysis and breakdown effect analysis for a quadcopter power distribution system

1.1. Quadcopter

The quadcopter, also known as a drone or unmanned aerial vehicle (UAV), consists of four motors fixed at the end of the frame structure. The arms of the frame rotate in a clockwise direction while the remaining pair of rotors rotate in a counter-clockwise direction [12].

1.2. DC brushless motors

Drone lifting thrust is provided by the motors that spin the propellers. The majority of drones are powered by brushless DC motors, which provide superior thrust-to-weight ratios in comparison to DC motors that are brushed. Motors are typically given two ratings: Kv ratings and current ratings. The Kv rating indicates how fast the motor will spin (RPM) for 1 V of applied voltage.

1.3. Propellers

A propeller is a type of fan that produce the lift force required to fly the drone. The physical characteristics of Multi-rotor propellers have a significant impact on their performance. Most of the propellers of cheap drones are usually plastic. In cheap drones, the propellers are plastic, soft and flexible and can be easily replaced. On the other hand, in expensive drones, carbon fiber propellers are usually used, which create less noise and more stability.

1.4. Electronic speed controller

In multi-rotors, the propellers are connected to the motors separately. These motors are controlled by an electric speed controller (ESC) to adjust the rotation speed of each motor. By changing the rotation speed of the individual motors, the ESC can help the multirotor to maneuver in different possible directions.

1.5. Battery

One of the most important components of a quadcopter is its battery, which is effective in improving the performance and flight quality of the quadcopter. The flight energy of the quadcopter is provided by lithium polymer batteries. Lithium battery has a long life. On average, these batteries can be charged at least 300 times.

1.6. Video link

To make image processing, we must use a camera and also a video link in our project. We selected a video link.

1.7. Remote control

The main objective of R/C is to control the quadcopter remotely, and there are two conditions for selecting the suitable one. The first is the number of channels you need, and, in our research, we need four channels (X for Roller, Y for Pitch, Z for Yaw, and Throttle (to control the speed of motors)). The second condition is the range of control.

Fig. 1Diagram of quadcopter subsystems

1.8. Block diagrams of quadcopter

Fig. 1 shows the subsystems and components of the quadcopter, and Fig. 2 shows the type of each component.

Fig. 2Identification diagram of quadcopter components

2.1. System life time distribution model

The system life model is expressed as a probability distribution. In order to calculate it, an uncertain and random life with a number n is chosen by overlapping the failure times in this example. The system lifetime model will be obtained as a density function $f\left(t\right)$, as shown in Fig. 3.

In the figure above, the area below is the density function $f\left(t\right)$ between the two times $t_1$ and $t_2$ equal to the value $\left[F\right(t_2)-F(t_1\left)\right]$. This value represents the ratio of the total statistical population that is broken between two $t_1$ and $t_2$ times [13, 14].

Fig. 3Life time distribution model

2.2. Reliability function

Mathematically speaking, assuming a random variable $t$ that the system reaches a certain failure time, then reliability is defined as follows in Eq. (1):

where, $R_t\ge 0$ and $R\left(0\right)=1$, $\mathrm{l}\mathrm{i}{\mathrm{m}}_{t\to \infty }R\left(t\right)=0$ is. This can be expressed as follows in Eq. (2):

where, $F\left(0\right)=0$ and $\mathrm{l}\mathrm{i}{\mathrm{m}}_{t\to \infty }R\left(t\right)=1$. $F\left(1\right)$ as the cumulative distribution function of the probability of failure before the cumulative distribution is the probability of failure before time $t$:

Assuming no defect occurs at the beginning of the system operation, the above relation is rewritten as follows:

If $h\left(t\right)$ has a fixed value, the final reliability relation is rewritten as follows in Eq. (3):

2.3. Failure modes and effects analysis (FMEA, FMECA)

FMEA is generally the analysis of any potential failure in a product, performance or process to determine its effects. FMEA is a method based on pre-occurrence prevention law. FMEA is a tool that is used with the least risk to predict problems and fix defects in the design or development stages of processes and services. By using this method, the search for items that cause a product or process to fail is provided before that product reaches the production stage [19].

FMEA can improve quality, increase reliability, reduce the need for necessary post-construction changes, and reduce manufacturing and assembly costs. This method was formalized in the 1950s as a failure analysis method, and FMEA training programs were developed by Ford in 1972 and used by 3 major US automakers.

Criticality analysis (FMECA) examines and classifies the severity of the impact of each failure on the success of the mission and equipment. In this method, failure modes are investigated and classified according to their probability of occurrence. In FMCEA analysis, the goal is to find critical items in this analysis, critical items are determined based on three parameters: intensity number (Sn), probability number (PN) and critical number ($CN=SN\times PN$). In the following tables, we examine the FMECA indicators based on the ECSS)Q-ST-30-02C( standard:

The severity number (SN) is proportional to the classification of the damage severity, with the difference that the number 4 is used for the catastrophic state and the number 1 for the negligible state.

Based on this, the catastrophic state of the fault mode is assigned, the effect of which is on the final contractual level of the disaster system and it leads to the loss of the system or its death. Critical mode is assigned to a fault mode whose impact leads to serious damage to the mission but it does not lead to the loss of the mission. The critical mode is assigned to the fault mode, the impact of which leads to less serious injuries system and also leads to temporary loss of mission or transient failure in it. And finally, the ignorable mode is assigned to the fault mode, which does not have a serious impact on the damage to the system, but will still need to be repaired [20].

The probability number (PN) is also between 1 and 4, and the number 4 is for the most probable mode of failure. The critical number (CN) is also the product of the intensity number and the probability number [20].

2.4. Fault tree analysis

Fault tree analysis is one of the widely used methods in reliability and risk assessment. Due to its logical nature, this method covers both qualitative and quantitative evaluations and is considered a good supplement for qualitative methods. While the fault tree is a qualitative graphical model, it can be quantified to provide useful information about the probability of occurrence, importance events and their causes. This method uses Boolean logic (zeros and ones) to combine a set of low-level events and is essentially a top-down approach to identify component-level failures that cause system failures [21-24].

Fault tree analysis can be used to perform the system risk assessment process. The purpose of FTA is to identify the effective causes of system failure and reduce risks before they occur. An invaluable tool for complex systems, which visually shows a logical approach to problem identification. In addition, the efficiency of the system can be obtained with this analysis. This method can be implemented alone or as a complement to the Failure Mode and Effects Analysis (FMEA) method [22-27].

3.1. Reliability

For this project, and according to the temperature conditions inside the quadcopter, the average temperature is about 30 degrees Celsius, so the temperature factor coefficient is 1.1. Also, for the environmental factor that the quadcopter is one of the birds with rotating propellers ($A_{RW}$), the value of the environmental factor is equal to 8. For the quality factor, the mission is divided into two parts, military and civilian. In the military part, the quality factor is 1 and in the civilian part, the quality factor is 2, and we choose the value 1 for it [13, 16, 21].

Therefore, the final failure rate of each part according to Eq. (5) is expressed in Table 3.

3.2. FMEA and FMCEA

Table 7 shows the failure effects analysis for a quadcopter, in which we examined some of the most common quadcopter failures and identified and noted the effect of each failure on quadcopter performance. By doing this, if we observe any of these effects, we can quickly find the cause of the failure and fix it [28-31].

Failure modes that have a severity number of 4 or a critical number higher than 6 are critical. Therefore, cases 2, 3, 5, 6, 8, 10, 13, and 14 are critical cases. Based on the plan's risk-taking policy, the parts that have a greater risk are further analyzed in detail.

3.3. FTA

In Fig. 4-6, the fault tree for the battery and electric motor and the electric board of the quadcopter are drawn.

Fig. 4Error tree for batteries

Fig. 5Error tree for electric motor

Fig. 6Error tree for electrical board