## 2 The ProbPlot via IR-AVPCA Technique for Bearing Fault Detection and Diagnosis (BFDD)
### AVPCA-Base Image Recognition
#### 2.2.3 Absolute Value Principal Component Analysis (AVPCA) for Bearing Fault Detection and Diagnosis  
In this paper, to make the proposed vibration-based BFDD via image recognition more suitable for online condition monitoring, we used AVPCA, which is an improved version of the classical PCA but with no mathematical complications simply by taking the absolute value of the weights to generate the bases, and the use of the sum of squared error (SSE) distances [4]. Furthermore, the probability plot parameters (the intercept and slope) will vary with the presence of the different bearing faults, but differently. Since the effect of the presence of the bearing faults causes variations of the faulty parameters that comprise particular information related to the fault itself, the considered AVPCA algorithm will extract a number of characteristic vectors from these features (images) that are mutually orthogonal. To apply the AVPCA method for the online BFDD, the study is divided into two procedures: (1) a data acquisition and features & eigenfaces generation procedure and (2) an online fault detection and diagnosis procedure. Hence, the collected vibration signal data set is divided into two parts: training data (known data) and testing data (unknown data). The training data are regarded as the historic data and are used to build the training database--i.e., the healthy base vector \(H_{b}{}^{I}\) and the faulty base matrix \(F_{b}{}^{m-1}\)--whereas the testing data are used to generate the data-test base vector \(T_{b}{}^{new}\) and then to verify the performance of the proposed ProbPlot via IR-AVPCA technique for bearing fault detection and diagnosis.  
The overall bearing fault detection and diagnosis-based ProbPlot via IR-AVPCA technique flowchart is summarized in Figure 3.  
Experimental Results of the Proposed ProbPlot via IR-AVPCA Vibration-Based Ball Bearing Fault Detection and Diagnosis  
In order to evaluate the performances of the proposed ProbPlot via IR-AVPCA algorithm for bearing fault detection and diagnosis, an experimental setup with a 750W BLDC motor powered by a TMC-7 BLDC motor driver (TM Tech Co., Ltd., Gyeonggi-do, 27-11, South Korea) for vibration-based bearing fault detection and diagnosis was conducted, as shown in Figure 4.  
Figure 3: The overall bearing fault detection-based ProbPlot via IR-AVPCA technique flowchart.  
Two accelerometer sensors (model: 352C33 PCB) (PCB Piezotronics, Inc., International Distributors, Gyeonggi-do, South Korea.) were used to gather the vibration signals; the first was set up on the top of the BLDC motor to be a reference, and the second was installed above the tested bearing (NSK 6204 with eight balls type) (see Figure 5). The different bearing faults, i.e., ORF, IRF, and BBF, were artificially created by drilling axially a 1 mm hole through the outer-race, the inner-race, and the ball, respectively.  
A constant load torque was added to the experimental test-bench by attaching a flywheel just before the tested bearing. NI cDAQ-9178 8-slot USB chassis was used to acquire the required vibration signals with the use of the NI9234 module. A 17.06 kHz sampling frequency was considered for sampling and Matlab R2012a was considered for processing.  
Two different environments were considered: a constant speed environment and a variable speed environment.  
First, a constant motor speed of \(w_{r}\) = 2500 rpm was considered while the vibration-based bearing fault detection and diagnosis algorithm was running, see Figure 6.  
Figure 4: The experimental setup: (**a**) test-bench and (**b**) data-acquisition equipment.  
Figure 5: Schematic diagram of experimental setup.  
Second, a variable motor speed of \(w_{r}\)\(\epsilon\)[1600, 2400] rpm was considered while the vibration-based bearing fault detection and diagnosis algorithm was running, see Figure 7.  
The used dataset description is shown in Table 1.