We compared graphs showing the signal strength values for each FFTed frequency of a normal-state machine noise and that of a fault-state machine noise and discovered differences in the graph area (sum of the signal strengths in the entire frequency spectrum). We define this graph area as the noise area herein. Based on these characteristics, when comparing the noise areas of the collected machines with the normal noise area, the graph can be diagnosed as a fault if a difference occurs beyond the specified error range.

This diagnostic process was categorized into two phases: offline and online. In the offline phase, machine noises that are from normally operating machines are collected in advance, and the noise areas of each noise are calculated. At this time, the noise collection from each machine and the calculation of the noise area are performed repeatedly several times, and their average value is stored into a database as a fingerprint.

Next, in the online phase, the noise from a specific machine is collected in real time and the noise area thereof is calculated. Subsequently, the noise area is compared with the value from the fingerprint map generated in the offline phase (Figure 1).

Figure 1: 
Online phase in noise integration technique

For this, we used a tool that integrated numerically discrete datasets provided by MATLAB. The function code used is trapz(abs(FFT_data)), where FFT_data is the value obtained by the FFT conversion of the input sound source data, and trapz( ) is a function that performs discrete integration by creating a trapezoid using data points [5]. Using this function, the area can be categorized into trapezoidal shapes to calculate the area under the discrete dataset. (Figure 2)

Figure 2: 
Example of using trapz( ) function

The signal similarity measurement technique can diagnose faults by calculating the consistency between the frequency spectrum of a normal and an abnormal state. This technique uses the mscohere( ) function as a signal comparison analysis tool provided in MATLAB.

Using the mscohere( ) function, FFT data are transformed to a strength-squared coherence estimation value at a specific frequency to obtain data with a signal similarity between 0 and 1 in all frequency domains as a y-axis value [6]. It can be used to diagnose machine faults as each fault condition has unique noise characteristics. The data representing the inherent noise characteristics can be diagnosed as a fault by estimating the similarity of the normal state data in the same frequency domain. Therefore, if this technique for estimating the similarity between data is used, then the cause of the fault can be analyzed and the fault diagnosed.

Figure 3 shows an example of similarity estimation between two sets of data at a specific frequency domain. Figure 4 depicts the procedure of this technique.

Figure 3: 
Example of mscohere( ) function

Figure 4: 
Signal similarity measurement technique

Based on the experimental results above, the noise integration technique was applied. In the offline phase of the technique, a fingerprint map (normal noise area) was created. In the online phase, the noise area of each fault state was obtained. Table 3 shows the results of the fault diagnosis technique.

The area value in Table 3 is the value obtained by integrating the average value after recording and averaging 50 times for each condition under the same measurement conditions.

The noise area value was derived as follows:

• 1. The operating sound of the motor for each condition was recorded and saved as sound source data. (data1~50)
• 2. The saved sound source files were loaded as data in MATLAB, FFT was performed, and the average value was calculated. (FFT1~50, FFT_mean)
• 3. By applying the absolute average value of the obtained FFT data to the trapz function, the noise area value for each condition was derived. (Noise area=trapz(abs(FFT_data)))

By performing this process, the reliability of the diagnosis reference fingerprint map can be increased.

The normal noise area differs significantly from other noise areas. If these differences are outside the range of the normal state, then they can be diagnosed an abnormal.

However, the external background noise during diagnosis in the actual field is a non-negligible factor when using this technique; therefore, we performed an additional experiment.

The mixed noise resulting from the diesel engine noise and motor noise without a tightened casing occurring simultaneously was recorded. For comparing, the diesel engine noise and loosed motor noise were recorded separately. The noise areas of the three noises were obtained using our program. The results are shown in Table 4.

The noise area value of the engine noise was extracted from the noise area of the mixed noises, i.e., 1.4738 × 10⁷ (= 6.2768 × 10⁷ - 4.8030 × 10⁷). Comparing this area value with the engine noise recorded separately (1.6707 × 10⁷), it was confirmed that an excellent match was obtained even though the engine noise source from the speaker was used owing to the limitations of the experimental environment.

However, in actual environments, the difference value can be calculated using the average data accumulated from mixed noises, background noise, and device noise. When utilizing these real noise data, faults can be diagnosed even when the noises of the field are mixed.

In the initial study pertaining to the signal similarity measurement technique, data analysis was not well performed because the signal similarity calculation results were inconsistent. Therefore, as a result of careful analysis, it was discovered that the cause was the recording sound.

The mscohere( ) function, which measures the similarity of FFT data of two operating sounds, calculates the y-value of signal similarity between 0 and 1 for each frequency x-value. When viewing the frequency spectrum of the sound recorded in the early study with the naked eye, the spectra under the same conditions almost matched with each other. Therefore, a simple similarity measurement was expected to enable diagnosis; however, this was not achieved.

This problem is explained as follows: When the average value of the normal state FFT data and the data of 50 foreign matter mixing conditions are measured for signal similarity, if the normal state average value and the foreign substance mixing condition are 60% identical, then all 50 similarities should be approximately 0.6; however, in the actual results, the consistency values indicated a large deviation.

In other words, because the operating sound of the electric motor was not constant because it was generated by the rotation of the rotor, the arrangement of the frequency value and amplitude between the two sound sources was not always the same and a certain difference would be indicated even if the same sound was heard.

Therefore, if the amplitude difference for each frequency of each sound source is not resolved, then it will be difficult to diagnose a fault. Therefore, a method to reduce this error and output a consistent similarity value was investigated.

Consequently, a frequency interval mean technique was devised. If the arrangement of amplitude values for each frequency for each sound source is not the same and the signal similarity is difficult to compare accurately owing to the large amount of data, the problem will be solved based on the hypothesis that the error can be reduced by averaging each interval after segmenting the entire frequency section. This method has been demonstrated successful in previous studies.

When the experiment was conducted by applying this improvement method, a consistent similarity was derived for each condition, unlike the previous similarity values with large deviations, and the average value of the similarities indicated a clear difference in distinguishing the cause of failure for each condition. The details of the experiment are as follows.

For the analysis of each condition, first, the average value of the FFT data in the steady state was calculated with the similarity of 50 normal state data to obtain a reference value that can be determined to be a steady state; subsequently, it was compared with the value from the existing similarity measurement to determine the improvement gained.

First, the frequency x-values of 480,000 data from the normal-state FFT average value were segmented into 480 groups by 1000 and averaged for each group.

Subsequently, by measuring the signal similarity with each of the 50 sets of data in the normal state, the performance difference obtained by using and not using the frequency averaging technique can be confirmed.

The MATLAB code used in the process is as follows:

FFT=fft(data);
A=reshape(FFT,1000,480);
FFT_m=mean(A);
mean(mscohere(FFT_avg, FFT_m));
mscohere(FFT_avg, FFT_m);

If the mscohere( ) function is input, then the similarity graph for each frequency can be output; if it is input to the mean function, the average of the similarity for each frequency can be obtained.

Hence, when the interval mean technique was applied and the average of 50 similarity measurements was obtained, a high agreement rate of 0.8248 was indicated; meanwhile, when it was not applied, a low agreement rate of 0.5031 was indicated, and a large deviation was observed for each agreement value. A comparison of the results is shown in tabular form in Figure 12.

Figure 12: 
Results from applying frequency interval mean method

The technique of reducing the deviation of the signal similarity by segmenting the frequency x-value into 1000 units and averaging it improved the signal similarity by approximately 39%.

Therefore, based on the improvement method above, the results of measuring the similarity between the normal state and the signal for each failure condition are as shown in the table in Figure 13.

Figure 13: 
Signal similarity measurement by fault cases

In addition, a graph that measures the degree of similarity is presented based on the state of foreign matter mixing as an example such that it can be confirmed using a visual indicator. (Figure 14).

Figure 14: 
Mean of normal state – No.5 foreign substance mixing data

The table of measurement results shows that the similarity decreased significantly when a failure occurred compared with the signal similarity value in the normal state.

In addition, it was confirmed that the degree of similarity for each failure condition differed significantly. If the signal similarity measurement technique is applied, then the cause of failure can be determined during failure diagnosis.

Hence, it was confirmed that the signal similarity measurement technique yielded a higher diagnostic accuracy and a better fault cause determination function than the numerical data integration technique.