## 2 Related Works
### A Design of an Optimized Deep Learning Module (ODLM)
#### 3.3.1 A Design of the VPDS  
The VPDS uses the sensor data received from the vehicle as the input value of the VPDS. The data collected from the in-vehicle sensors are digital numerical data and represents the condition of each part. The VPDS input is represented as \(\mathrm{X}=\{x_{1},\ x_{2},\ x_{3},\ x_{4},\ \ldots,\ x_{n}\}\). Here, \(\mathrm{X}\) means the set of sensors, \(x_{n}\) means the sensor data from each sensor, and n means the number of sensors. For example, a tire temperature sensor and a tire air pressure sensor measure the condition of a tire and an oil pressure sensor measures the condition of engine oil. The output value of the VPDS represents the condition of each part. Each part has three output nodes to diagnose its condition. The VPDS output is represented as \(\mathrm{Y}=\{y_{1},\ y_{2},\ y_{3},\ y_{4},\ \ldots,\ y_{k}\}\). Here, \(\mathrm{Y}\) means the set of all output nodes, \(y_{k}\) means the output value of each node, and the number of output nodes, \(k\) is 3 times the number of parts. Each node of each part represents \"normal\", \"check\", and \"danger\". Let us take 8 outputs of a tire for example. (1) If the normal node for the tire is 1 and the check node and the danger node are 0, then this means the tire is in a normal state. (2) If the check node for the tire is 1 and the normal node and the danger node are 0, then this means the tire is in a checking state. (3) If the danger node for the tire is 1 and the normal node and the check node are 0, then this means the tire is in a dangerous state. (4) If the normal node and the check node for the tire are 1 and the danger node are 0, then this means the tire is in a checking state. (5) If the danger node and the check node for the tire are 1 and the normal node are 0, then this means the tire is in a dangerous state. (6) If the normal node and the danger node for the tire are 1 and the check node are 0, then this means the condition of the tire cannot be judged. (7) If all three nodes of a tire are 0 or 1, then this means the condition of the tire cannot be judged. Figure 7 shows the 8 outputs of a tire. Though an existing Back-propagation algorithm does not decide the number of Hidden Layers and the number of its Nodes, the proposed Back-propagation algorithm that is used by The VPDS  
Figure 7: The structure of the Vehicle Part Diagnosis Sub-module (VPDS). decides the number of them dynamically according to the input sensor data and the number and types of output parts. If there are a number of input and output nodes and a number of Hidden Layers and their nodes, an over-fitting problem can occur. The VPDS in this paper limits the number of Hidden Layers to five to reduce the over-fitting. The number of Nodes in each Hidden Layer is equal to that of input nodes. The Nodes in each Hidden Layer are used to compute the risk of vehicle parts and consumables and the risk of the other parts influenced by a defective part. The VPDS Mathematical Modeling  
The VPDS uses a Back Propagation algorithm with high accuracy and speed for the safety of a vehicle. The Training Data made out of the sensor data are used for the learning of the VPDS. The Training Data are collected from the real time sensor data of a vehicle or the batch sensor data of a Car Service Center. The collected data are integrated numeric data about the normality and abnormality of each part. The Training Dataset is made out of the Training Data based on parts. Figure 7 shows the structure of the VPDS. The h of the Hidden Layer means a node value. The vector of a Hidden Layer is H. The \(y\) of the Output Layer means the condition of the parts. The condition of the parts is classified into 'danger', 'inspection', and 'normality' by the result value of the Output Layer. W-Z represent the weight connecting to each Output Layer and are modified during learning. Formula (1) is the loss function of the VPDS.