## 3 Analysis of the Fault State and Establishment of the Fault Data Sample
### Analysis of Fault Signal
#### 3.1.2 Low Fuel Supply Pressure  
The low fuel supply pressure failure is simulated by changing the value of the oil pressure regulating valve. Under normal conditions, the oil pressure of the 3 W engine is 3.0 Bar, and the oil pressure regulator is limited to 2.5 Bar during fault simulation. When the fuel supply pressure is low, it will not only cause the decrease of the unit time power of the engine but also decrease the amount of injected fuel, which will increase the oxygen concentration in the exhaust gas and increase the air-fuel  
Figure 3: Vibration waveform of nozzle failure and normal condition. (**a**) Nozzle fault vibration waveform, (**b**) Normal vibration waveform. Figure 2: Change chart of speed and air-fuel ratio under normal and nozzle failure conditions. (**a**) Chart of speed variation with throttle opening, (**b**) Chart of transient air-fuel ratio change with different air-fuel ratios. ratio. Since the power is the product of torque and angular velocity, the low fuel supply pressure will also decease the torque when under the same rotation speed. In addition, low fuel supply pressure will make the engine speed difficult to stabilize. For example, assume that the current engine speed is 4000 r/min, the throttle opening is the same as the normal state. According to the engine pulse spectrum map, the fuel injection pulse width is constant. Since the oil pressure is small, the fuel injection amount is reduced, and the engine speed will be reduced. At this time, compared with the normal state, at the same speed, the throttle opening becomes larger than normal. So, the ECU will increase the injection pulse width. If the influencing factor of the increases of the pulse width is greater than the influence of the oil supply, it will increase the engine speed to about 4000 r/min. The existence of this cycle will make the engine speed difficult to stabilize. Figure 4 shows the relationship between engine speed and torque under normal conditions and low fuel supply pressure. The black line in Figure 4a represents the speed in the normal state, and the red line represents the speed in the low fuel supply pressure. It can be gotten from Figure 4a that the engine speed is difficult to stabilize when the fuel pressure is too low. Figure 4b represents the relationship between the engine and the torque, where the black line represents the normal data and the red line represents the torque at low fuel pressure. It can be seen that the engine output torque is lower when the fuel pressure is lower at the same speed. Figure 5 reflects the vibration waveform of the engine at a speed of 3500 r/min. Figure 5a represents the change of the vibration signal with time under normal conditions while Figure 5b represents the change of the vibration signal with time when the fuel pressure is too low. By observing these two figures, it can be seen that under normal conditions, the peak of the vibration signal is greater than 2 V, and when the fuel pressure is too low, the peak of the vibration signal of the cylinder is less than 2 V, which means that when the fuel pressure is too low, the work per unit time is less, and the vibration energy of the engine is smaller. Figure 4: Rotating speed and torque change diagram. (**a**) Curve of rotating speed varying with time, (**b**) Curve of torque varying with time. Figure 6 reflects the changes in engine temperature and speed with normal conditions and low fuel pressure. Figure 6a represents the change of cylinder temperature with the speed under normal conditions. It can be seen from it that when the cylinder is running continuously at a speed of 4500 r/min, the cylinder temperature will exceed 170 degrees, and a fan which uses the PID algorithm to adjust the temperature of the cylinder will be turned on to cool the 3 W engine. With this measure, the temperature of the cylinder will remain around 170 degrees. Figure 6b reflects the situation when the fuel pressure is low.