Analysis of motor fan radiated sound and vibration waveform by automatic pattern recognition technique using “Mahalanobis distance”

Analysis of motor fan radiated sound and vibration waveform by automatic pattern recognition... In recent years, as the weight of IT equipment has been reduced, the demand for motor fans for cooling the interior of electronic equipment is on the rise. Sensory test technique by inspectors is the mainstream for quality inspection of motor fans in the field. This sensory test requires a lot of experience to accurately diagnose differences in subtle sounds (sound pressures) of the fans, and the judgment varies depending on the condition of the inspector and the environment. In order to solve these quality problems, development of an analysis method capable of quantitatively and automatically diagnosing the sound/vibration level of a fan is required. In this study, it was clarified that the analysis method applying the MT system based on the waveform information of noise and vibration is more effective than the conventional frequency analysis method for the discrimination diagnosis technology of normal and abnormal items. Furthermore, it was found that due to the automation of the vibration waveform analysis system, there was a factor influencing the discrimination accuracy in relation between the fan installation posture and the vibration waveform. Keywords MT system  Mahalanobis distance (MD)  Feature value  Effectiveness analysis Introduction In a previous study, it has been reported on frequency analysis of the acoustic waveform of a compact motor fan Demand for compact motor fan for cooling the inside of and investigating characteristics appearing in normal and electronic devices is increasing now due to weight reduc- abnormal fans. However, it is currently difficult to dis- tion and space saving of IT equipment. In the quality criminate and diagnose appropriate normal items/abnormal inspection process at the site, quality inspection of compact items from measured values and analysis results obtained motor fan is carried out by sensory test of inspector. This by sound and vibration. sensory test requires a lot of experience in order to accu- In this research, in order to improve the discrimination rately diagnose the subtle difference in sound of fan and analysis accuracy of normality/abnormality concerning difference in vibration, and variation in pass/fail judgment noise and vibration of motor fan, we worked on analysis occurs due to changes in physical condition and environ- research applying waveform information pattern recogni- ment of inspector. tion technology. In order to solve these quality problems, development of an analysis method capable of quantitatively and auto- matically diagnosing the sound/vibration level of a fan is Research purpose required. In many cases, because noise level of fan depends on the noise level of the whole motor, it is important to reduce the noise. Also, if the fan approaches and interferes with the & Eiji Toma toma-e@tomakomai-ct.ac.jp fan cover on the stationary side, remarkable resonance sound may be generated. The fan noise includes a rota- National Institute of Technology, Tomakomai College, tional sound component (fz) which is the product of the Tomakomai, Japan 123 Journal of Industrial Engineering International number of rotations (f) and the number of blades (z) and a reference pattern as a unit space and can judge whether turbulent sound component generated by turbulence of the target data belongs to a unit space or not (Teshima et al. wind flow. Recently, a method of changing the rotation 2017). speed by an inverter is used. In this case, with respect to ventilation noise, the rotational sound component (fz) may MT method generate superior noise at a certain rotational frequency. This outstanding noise is called pure tone and is eval- In the MT system, MT method is a method of determining uated as a noisy sound. From studies of conventional fan outlier degree from unit space by evaluation index of noise, numerous studies on noise reduction have been made Mahalanobis distance (MD) and judging whether it is on rotational sound and turbulent sound from flow analysis normal or abnormal. The MT method is a method for on the number of blades and optimization of blade shape gaining cognizance of whether the target data (otherwise (Noda 2014). referred to as unknown data) belongs to the same standard, In precedent research, there was a case of verifying the homogeneous, group. It is an analysis method that defines a usefulness by introducing Mahalanobis Taguchi (MT) homogeneous population as a unit space for purpose and system which is one of the pattern recognition methods, calculates the distance from the unit space center of and understands a thing effective to some extent. In the unknown (target) data as Mahalanobis distance (MD). case of using pattern recognition method, processing for The MT method stands on a simple concept and is very extracting feature value from measurement data is per- easy to use; among the components of the MT system, the formed. If an invalid feature amount is included in the MT method has the greatest number of practical applica- abnormality detection, sensitivity and reliability of recog- tions (Teshima 2012). nition decrease. As shown in Fig. 1, it is recognized that, if the MD turns Therefore, it is important to set feature values consid- out to be short, the pattern is close to the unit space and ered valid for discrimination without excess or deficiency. that, if the MD turns out to be long, the pattern is distant. Statistical values such as average value and peak value of When the unit space is a normal population, if the MD is the waveform were used as feature value in precedent short, there is a strong possibility that the target data is research. However, in order to improve the accuracy of normal. MD itself was proposed by Indian mathematician discrimination, many feature values and number of samples P.C. Mahalanobis and is the result of converting multi- were required. If it is possible to extract feature values variate information in which multiple variables are inter- effective for abnormality detection from number of few twined complicatedly into distance information (Taguchi samples, discrimination can be performed with high 1992; Yano 2011). efficiency. In this study, we applied a method to extract the feature Formulation of MD quantity from the shape information of the waveform proposed in the MT system as the measurement result of Mahalanobis’ distance is called MD. It is a kind of distance the sound and vibration of the motor fan. By evaluating the for multivariable space. Correlation effect is included in effectiveness of the obtained feature quantity, we worked this distance (Teshima 2012; Suzuki 2012). on analysis research aimed at improving discrimination 1. Normalize data accuracy (Teshima et al. 2017). MD calculation is possible without normalization. But after normalization, covariance in the next step is Analysis principle Pattern recognition Target Unit Space Pattern recognition is a technology to replace information Short distance Normal processing such as human judgment and prediction with computer. In other words, it is a process of evaluating how Center much an unknown input pattern resembles a pre-input Target Long distance Abnormal standard pattern by numerical values and determining which category it belongs to. In this research, MT system was adopted as a pattern Cause diagnostics recognition technology. MT system is an information processing system which constitutes a data group of a Fig. 1 Conceptual drawing of the MT method 123 Journal of Industrial Engineering International 2 3 2 3 correlation coefficient. So evaluation of correlation 1  r u 1k 1 effect is easy. 6 . . . 7 6 . 7 . . . . MD ¼ D ¼ðÞ u  u 4 5 4 5 ð4Þ 1 k . . . . 2. Make covariance matrix r  1 u k1 k x  m k k 1 B u ¼ ð5Þ Covariance matrix ¼ B 1 m : Average of data group 3. Make inverse matrix of covariance matrix r : Standard deviation of data group 2 3 1  r 1k ab 1 B 10 ¼ or 6 . . . 7 . . . ba B 1 01 4 5 . . . ab 1 B r  1 k1 ba B 1 It means the inverse matrix of the correlation matrix. 4. Calculate the square of MD When Eq. (4) is verified in the case of k = 2, 1 r u 2 1 MD ¼ D ¼ðÞ u u 1 2 ab x 1i r 1 u MD ¼ðÞ x ; x 1i 2i ba x 2i The inverse matrix equation of the 2 9 2 matrix is, ab d b MD ¼ XAXðÞ If A is inverse matrix and X is data cd ca a  d  b  c 1 r 1 r r 1 r 1 1  r MD derivation and certification Therefore, the following expression is obtained, The concept of MD is a value obtained by consolidating the 1 r u deviation from the relationship between the distance and ) D ¼ðÞ u u 1 2 1  r r 1 u the correlation from the average of the object of interest in consideration of the correlation of the plurality of variables ¼ ðÞ u  ru  ru þ u 1 2 1 2 (Suzuki 2012). 1  r MD in the relation of the target data of two items is 2 2 u  2ru u þ u 1 2 1 2 given by following expression. 1  r rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 u  2ru u þ u 1 2 It proved to satisfy the expression in H Eq. (1). 1 2 MD ¼ ð1Þ 1  r In the MT method, in order to normalize the average of x  m the squared values of MD to 1, an operation of dividing the 1 1 u ¼ ð2Þ 1 2 value of MD = D by the number of items k is added. Therefore, the calculation formula of MD used in the MT x  m 2 2 u ¼ ð3Þ method is as follows. vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3 2 3 > x ; x : Target data u 1 2 1  r u > 1k 1 < u pffiffiffiffiffiffiffiffi 6 . . . 7 6 . 7 m : Average u . . . . ) D ¼ MD ¼ ðÞ u  u t 4 5 4 5 1 k . . . . > r : Standard deviation r  1 u k1 k r : Correlation coefficient ð6Þ Equations (1)–(3) mean to investigate how many times the distance from the average corresponds to the standard deviation which is an index of the variation of all data. Discrimination method The MD calculation formula obtained by expanding H in Expression (1) to a plurality of items is as follows: With the MT method, normality/abnormality is determined by comparing MD of target data with the threshold value. ðÞ u ...u on the right side is a value normalized by 1 k using the average and standard deviation of subscript When the MD is small close to 1, it is judged that it belongs item data. to the unit space, and if MD is larger than the set threshold 123 Journal of Industrial Engineering International value, it is judged not to belong to the unit space. The changes that may be occurring within short time spans. judgment threshold with the MT method is generally said Furthermore, both frequency analysis and wavelets pre- to boil down to 4 or thereabouts. This is because, for all suppose the human operator’s evaluation and judgment of practical statistical mathematics purposes, if the MD the results they produce. exceeds 4, the probability of unknown (target) data being a The variation and abundance information extraction member of the unit space shrinks to a small possibility method was proposed as a means of expressing the char- (Wakui 2014). acteristics of waveform patterns in more accurately quan- However, it is currently reported that the method of tified terms. setting a threshold using the v distribution is highly In this research, variation and abundance information is effective. For this reason, we set the threshold using the v extracted from the radiated sound waveform from compact distribution in this research. fan motor, and the waveform characterized. First, a parallel In Fig. 2, the abscissa is the Mahalanobis distance, the line (reference line) is drawn on the time axis at a constant ordinate is the probability, and the graph curve (v distri- interval in the waveform in the time domain, and a section bution theoretical curve) means the probability that the on the time axis (extraction width) for calculating the square value of the Mahalanobis distance takes (Yano characteristic amount is set. Next, the number of times of 2004). intersection with the reference line within interval of extraction width is taken as the variation, and sum of the Feature extraction values in the range above the reference line is obtained as the abundance information. Performing calculation of this The features of waveforms include frequency and ampli- variation and abundance information in all sections of the tude, and categories such as average frequency, magnitude waveform data is called ‘‘waveform analysis.’’ of oscillation, and maximum magnitude of oscillation have Figure 3 shows the concept of variation and abundance been commonly used. Frequency analysis (FFT: Fast information (differential and integral characteristics) in Fourier Transform) and wavelet have also been used. feature extraction (Yano 2004; Teshima 2012). Frequency analysis is a technique of expressing the char- acteristics of waveforms in terms of a frequency axis and an energy axis. A wavelet is a technique of expressing the Experimental system of radiated sound characteristics of waveforms in terms of a time axis, in addition to the frequency axis and the energy axis. Noise level of the test fan Frequency analysis and wavelets are excellent methods of explaining the characteristics of waveforms. Nonethe- As shown in Fig. 4, fan motors generally rotate in both less, it cannot quite be said that both convey sufficient directions, so that the blades of the fan use radial blade information on the characteristics of the given waveform (same type as the test fan). Radial blades have low cooling pattern. efficiency and high noise. The noise level is obtained from For instance, frequency analysis is a processing method Eq. (7). However, the evaluation position of the noise is the dealing with waveforms over a relatively long period of axial center height of the motor, and the distance is 1 m. time and is therefore not adept at capturing waveform (Noda 2014). Noise level;Ad½b ¼ 70 log D þ 50 log N þ k D : Outer diameter of the blades½ m ð7Þ N : number of rotations½ rps k : constan tðÞ ¼ 32  36 From Eq. (7), it is important to reduce the outer diam- eter D of the fan in order to lower the noise level. However, since the wind volume and the wind pressure also decrease, the balance between these and the noise becomes important at the time of designing. That is, the relation of Expression (8) is obtained. Wind volume ¼ puUDB ð8Þ Here, u: flow coefficient (0.15–0.25), U: outer periph- eral speed of the blades, and B: width of the outer Fig. 2 Distribution of squared values of MD 123 Journal of Industrial Engineering International Fig. 3 Variation and abundance information Fig. 4 Fan shape peripheral portion of the blades. Attention is required since Table 1 Specification of fan the air volume decreases with the square of D. Fan flame size 92.5 9 92.5 9 25.4 (mm) Blade number 5 Test fan Rated voltage DC12 V Rotational speed 3400 (rpm) In this research, we used two kinds of compact fan motors. Sample items shown in Fig. 5 (and Table 1) are five normal products (#9701–#9705), and sample items shown in Fig. 6 (and Table 2) including 10 normal products (fan 1 to fan 10) are five abnormal products (fan #1–fan #5). The abnormal product has surface buckle, and each displace- ment is 14 lm for fan #1, 25 lm for fan #2, 50 lm for fan #3, 70 lm for fan #4, and 90 lm for fan #5. Surface buckle refers to the size when the end face rotating around a certain axis deviates from a plane perpendicular to this axis during rotation. Fig. 5 Test fan 123 Journal of Industrial Engineering International reason is based on the distance between ear and fan when inspector performs sensory test. Fan recording time was 10 s, sampling frequency was 51.2 [kHz], and signal from microphone was saved in PC via A/D converter. Figure 8 shows the waveform data obtained by measuring the radiated sound of fan. Measurement sample number and time of fan’s radiated sound is ‘‘512,000 samples = 10 s’’ at sampling frequency 51.2 [kHz]. However, it was judged that a more accurate analysis could be performed by cap- turing a behavior change for a short time, and waveform data of ‘‘5120 samples = 0.1 s’’ were analyzed. Analysis procedure The analysis procedure of radiated sound and vibration Fig. 6 Test fan waveform is as follows. Table 2 Specification of fan 1. Feature extraction In order to characterize the waveform, extraction width Fan flame size 42 9 42 9 10 (mm) and reference line set, and variation and abundance Blade number 5 values are extracted as the feature value. Rated voltage DC24 V 2. Creating unit space Rotational speed 10,000 (rpm) Although the unit space consists of a plurality of samples and their variables (feature items), MT method has a condition that the number of samples Measurement of radiated sound in unit space must be larger than the number of variables, and more than 3 times the variable is Measurement of the sound of compact fan motor was taken considered ideal. in a quiet room. A schematic diagram of recording is 3. Setting a threshold shown in Fig. 7. The threshold was determined with a probability of 5% The sound collection was set to 30 mm above the according to the v distribution. This value is consid- rotation axis center from the rotation surface on the fan ered to be the boundary value when judging things in suction side by a  inch condenser microphone. The statistics, and it is called the significance level. 4. MD calculation of target data The waveform analysis of the abnormal fan and feature value of unit space are extracted, and the MD value is calculated by Eq. (6). Fig. 7 Recording system Fig. 8 Waveform data 123 Journal of Industrial Engineering International 5. Effectiveness analysis 20 pieces. Next, taking these into consideration, three Effectiveness analysis is a process of evaluating which waveforms were arbitrarily selected from five normal item is effective for abnormality detection by SN ratio. products (#9701–#9705) so as to be three times the number 6. Evaluation of effectiveness by SN ratio of variables, and a unit space was created. Finally, wave- The MT system includes a success/failure quantifica- form analysis was also performed on normal products not tion proposal for the recognition system. belonging to the unit space, and the MD value was cal- culated. Figure 9 shows the calculation result of the MD Use is made here of the concept of SN ratio (signal-to- value of the normal product. On the graph, it is judged to noise ratio), which provides a functionality evaluation be abnormal because the MD value exceeding the threshold yardstick in quality engineering or MT method. In pattern can be confirmed. However, it is understood that because recognition, generally speaking, the recognition result is the normal product is the target, it is not an appropriate influenced by various factors, ranging from measuring tool analysis result. It is estimated that variables invalid in selection to recognition software parameter settings. Use of discrimination are included in feature values. Therefore, it the SN ratio makes it possible to evaluate the appropri- is necessary to analyze and evaluate which items are highly ateness of the entire recognition system. effective. Figure 10 shows the results of the effectiveness In quality engineering there are concepts of various SN analysis on the target data. The horizontal axis represents ratios, but there are the following two methods for calcu- the variable, and vertical axis represents the SN ratio, lating the SN ratio used in the MT system. which means that the item with the highest value is valid (a) If it is difficult to give a numerical value to the for the judgment. Therefore, Fig. 11 shows the result of degree of abnormality, apply the SN ratio of the calculating the MD value using the variable with the pos- preferably large characteristics. itive SN ratio as the feature value. On the graph, it is (b) When the degree of abnormality can be quantified, judged that the MD value is equal to or less than the apply the SN ratio of the dynamic characteristic. threshold value and it is judged to be normal, and it is judged that the effective feature value can be extracted. It is desirable that the MD value of data known not to belong to the unit space be as large as possible. In this Analysis result of abnormal products research, ‘‘SN ratio of the preferably large characteristics’’ was applied. Next, we analyzed a waveform in a fan of Fig. 6 and In quality engineering, ‘‘larger preferable characteris- extracted feature value. The fixed value is extraction width tics’’ are called preferably large characteristics. Since there 20 and reference line 30. The number of variables is 60. In are generally variations when there are many data, the SN the unit space, nine waveforms were arbitrarily selected ratio is to quantify desirability collectively including from 10 normal products (fan 1 to fan 10) so that the variations. number of samples was three times as large as the variable. The calculation formula of SN ratio (g) of preferably Waveform analysis was performed on abnormal products large characteristic is as shown in Eq. (9). At this time, it is (#fan 1–#fan 5). Figure 12 shows MD values of normal and better that the SN ratio is large. abnormal items not belonging to the unit space. Here, D is the Mahalanobis distance (the value of the From the results, MD values above the threshold were square), and k is the number of signal data not belonging to shown for all abnormal items, and it was determined as the unit space. abnormal. However, among the normal products, items 2 2 2 g ¼10 log 1=D þ 1=D þ  þ 1=D =k ð9Þ 1 2 k Analysis result of radiated sound Analysis result of normal products First, we analyzed a waveform in the fan of Fig. 5 and extracted feature value. The fixed value is extraction width 20, reference line 10. Therefore, 20 samples can be obtained from one waveform. In addition, since the refer- ence line calculates the variation and abundance informa- tion for each extraction width, the number of variables is Fig. 9 MD calculation result of normal products 123 Journal of Industrial Engineering International Fig. 10 Effectiveness analysis result Fig. 13 Effectiveness analysis result negative value is variation and abundance information of reference line. By using variation and abundance infor- mation of reference line at the central portion of the waveform as the feature value, it is shown that accurate abnormality determination is possible. Figure 14 shows the result of calculating the MD value using the variable whose SN ratio is a positive value as the feature quantity from the result of effectiveness analysis of all abnormal items. From the results in the figure, it is found that the normal value is equal to or less than the threshold value and the abnormal item is the MD value that is equal to or more than the threshold value, so it is an appropriate discrimination. Fig. 11 MD calculation result after analysis Experiment system of vibration Vibration measurement When the motor fan is sensory-tested, the inspector holds two positions on the side of the fan frame and diagnoses by hearing and tactile sense near the ear while turning the wrist. Fig. 12 MD calculation result of each sample fan which are judged to be abnormal items beyond the threshold were confirmed. Figure 13 shows the effective- ness analysis result of the waveform of the abnormal pro- duct (#fan 1). From the figure, the SN ratio shows a positive value in the central part, and all values are nega- tive at both ends. The same tendency was shown also in the effectiveness analysis of other abnormal items. A variable taking a Fig. 14 MD calculation result of each sample fan 123 Journal of Industrial Engineering International In this study, we developed an automatic rotary oscil- lating device simulating the handling performed by the inspector and analyzed the vibration waveform pattern by automatic detection of vibration of the motor fan by applying the MT method. Figures 15 and 16 show the automatic rotary oscillating device. As the vibration mea- surement condition, the rotation speed of the servo motor was set to 3 rpm, the fan rotation speed was 3400 rpm, and the measurement time was 40 s. In addition, angle of oscillation h of the fan was measured in the axial direction and the radial direction under three conditions of 15,30, and 45. Waveform data of vibration Fig. 16 Schematic of automatic rotary oscillating device The waveform data of vibration were measured using a level recorder, but the test fan of Fig. 6 had a low vibration level and could not obtain sufficient waveform data. Therefore, in this research, the test fan of Fig. 5 was adopted. #9701, #9702, #9703, #9704, and #9705 of sam- ples with different magnitudes of vibrations were set in order of increasing vibration acceleration level. Figures 17, 18 show the vibration waveform data in the axial direction and the radial direction with the rotary oscillating device with the angle of oscillation of the fan set to h =15. In the vibration waveform in the axial direction of Fig. 17, it can be confirmed that the vibration acceleration level increases in order of the nominal number. On the other hand, since the waveform behavior in the radial Fig. 17 Acceleration level of axial direction with angle of oscillation direction other than #9705 is very small, it is difficult to judge the magnitude of the vibration level from the waveform. Furthermore, the same tendency was observed under different angle of oscillation conditions. Fig. 18 Acceleration level of radial direction with angle of oscillation Therefore, in this study, waveform analysis was per- formed on the axial vibration waveforms of three condi- tions of the fan’s swinging angles of 15,30, and 45 in the same way as the analysis procedure of radiated sound. Fig. 15 Overview of automatic rotary oscillating device 123 Journal of Industrial Engineering International Analysis result of vibration Conclusion The setting value of the waveform analysis in the vibration Method of pattern recognition waveform of the test fan shown in Fig. 5 was set to extraction width 20 and reference line 10. Since the num- Processing to recognize, understand, and predict based on ber of variables is 20, three waveforms are arbitrarily various information obtained from objects is called pattern selected from five normal products (#9701–#9705) so as to recognition. Technology replaces information processing make the number of samples three times as large, and a unit such as human judgment and prediction with computer. space was created. Waveform analysis was also performed Although there are familiar practical examples such as on normal goods not belonging to the unit space to cal- character recognition and fingerprint authentication, it is culate the MD value. still a big technical subject for computers. The MT system In this study, we analyzed vibration waveforms in the adopted in this research is a system of new pattern recog- axial direction of three conditions of fan’s angle of nition and prediction technology proposed by Dr. Taguchi oscillation of 15,30 and 45, and Fig. 19 shows the Genichi (Taguchi 2008; Tamura 2009). result of MD value calculated for each angle of oscillation Although the application field of pattern recognition is of the fan. From Fig. 19, it is determined that the MD diverse, we are expected to apply it in the whole human value is over the threshold value when angles of oscil- activity field of human beings. In particular, it is thought lation are 15 and 30, so it is determined to be abnormal. that it plays an important role in terms of accumulation and Even at angle of oscillation of 45, although there are reproduction of expertise, mainly in manufacturing and places where the MD value is larger than the threshold medical care. The procedure for carrying out pattern value, the best result among the three conditions was recognition can be roughly divided into three stages. The obtained. first step is preparatory preparation, the second step is from Figure 20 shows the results of effectiveness analysis for measurement to feature extraction, and the third step is each angle of oscillation. In the analysis results of angles of recognition processing (Tamura 2009). oscillation of 15 and 30, it is considered that the fact that the number of variables in which the SN ratio becomes Reasons selected negative is large is a factor that increases the MD value. On the other hand, since the number of variables in which the In the MT system, variation information (differential SN ratio becomes negative at angle of oscillation of 45 is characteristic) and abundance information (integration small, it can be judged that feature quantities effective for characteristic) are proposed as a feature extraction tech- discrimination can be extracted. nique. These feature quantities are highly versatile and can Figure 21 shows the result of calculating the MD value be applied to many technical problems. Also, various with the variable whose SN ratio at angle of oscillation of measurement values often draw waveform patterns. Of 45 is positive as the feature quantity. From the results in course, not only the vibration but also the measured values Fig. 21, it can be judged that an appropriate discrimination that change in time series are all waveform patterns. The result was obtained because the MD value is below the technique of extracting the features of the waveform as threshold value. numerical values can be said to be an important technique for problems such as inspection and monitoring (Hasegawa 2007; Taguchi 2002). Research results In this study, we applied the method of extracting the feature quantity from the shape information of the wave- form proposed in the MT system for the measurement result of the sound and vibration of the motor fan. Then, we evaluated the effectiveness of the feature value of the acquired waveform information from the MD value and carried out analytical research aimed at improving the detection accuracy of the discrimination. Ultimately, in waveform analysis of radiated sound and vibration of the Fig. 19 MD calculation result of each angle of oscillation motor fan, appropriate judgment results of normal and 123 Journal of Industrial Engineering International Fig. 20 Effectiveness analysis result merely looking at the information by a person. However, since it is information that can be directly given to a computer, it can be used as it is for pattern recognition. 3. Since frequency analysis shows the average property of a sufficiently long waveform, it is difficult to capture the change occurring in a short time. On the other hand, feature extraction by variation and abundance information extracts feature values every fixed time width, so it is possible to detect a pattern difference in units of time width (Teshima 2012). In addition, from the analysis result of the vibration waveform of the present study in the MD value, it was Fig. 21 MD calculation result of angle of oscillation found that the fluctuation of the vibration width of the waveform tends to become small as the angle of oscillation abnormal items were obtained by extracting feature values increases. effective for detection by effectiveness analysis. Regarding future research activities, we will focus on A general pattern recognition method is said to be able the correlation between angle of oscillation and width by to accurately classify abnormal patterns if many data of application of MT method in discriminant analysis of assumed abnormal patterns can be collected. However, in normality/abnormality from motor fan vibration waveform reality, normal data can be collected, but abnormal data and plan to analyze more specific factors is there. collection becomes more difficult as the scale of the facility becomes more complicated. Since the MT method evalu- Open Access This article is distributed under the terms of the Creative ates the measurement data with the difference from the Commons Attribution 4.0 International License (http://creative normal data group as the reference, data collection for commons.org/licenses/by/4.0/), which permits unrestricted use, dis- tribution, and reproduction in any medium, provided you give learning only needs to be normal data, and this method can appropriate credit to the original author(s) and the source, provide a cope with an unknown abnormal pattern. link to the Creative Commons license, and indicate if changes were In general, frequency analysis (spectral analysis, fast made. Fourier transform analysis, etc.) and wavelet are adopted as a characterization analysis method from waveform infor- mation (Yano 2002; Mori 2005). References The differences between these analysis methods and Hasegawa Y (2007) Story of MT System, Japan Science and variation and abundance information, which are feature Technology Unit, pp 6–11 values in the MT method, are summarized below. Mori T (2005) Application and mathematics of the Taguchi methods. In: Optimization engineering using the Taguchi methods, trendy 1. Because of the frequency analysis and wavelet, the book, Mori Engineer Office, Shizuoka, pp 323–338, 511–583 nature and homogeneity of the waveform are displayed Noda S (2014) Noise and vibration of motor and countermeasure by graphs and figures, so it is an expression understood design method, Scientific Information Publication, pp 19–32, by humans. 103–123 Suzuki M (2012) Introduction to MT system analysis method, Nikkan 2. Since variation and abundance information is numer- Kogyo Shimbun, pp 7–101 ical information expressing the waveform feature, it is difficult to grasp the properties of the waveform by 123 Journal of Industrial Engineering International Taguchi G (1992) Quality engineering lecture no. 5, Quality Teshima S, Tamura K, Hasegawa Y (2017) Standardization and engineering casebook—Japan public, Japan Standards Associa- Quality Control 2017. J Jpn Stand Assoc 70(7):2–31 tion, pp 1–12 Wakui Y (2014) Multivariate analysis understanding, Technical Taguchi G (2002) Evaluation technology for optimization design, commentary, pp 190–200 Japan Standards Association, pp 189–200 Yano H (2002) Introduction to quality engineering numeration, Japan Taguchi G (2008) Technology development in MT system, Japan Standards Association, pp 271–286 Standards Association, pp 27–37 Yano H (2004) Technology development of the information design Tamura K (2009) New technology of pattern recognition by quality with the computer-Simulation and MT system, Japan Standards engineering, Japan Standards Association, pp 26–85 Association, pp 310–368 Teshima S (2012) Introductory MT system. Japan Science and Yano H (2011) Quality engineering guide to raise an engineer power, Technology Publishing, Tokyo, pp 33–57 Japan Standards Association, pp 219–235 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Industrial Engineering International Springer Journals

Analysis of motor fan radiated sound and vibration waveform by automatic pattern recognition technique using “Mahalanobis distance”

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Engineering; Industrial and Production Engineering; Quality Control, Reliability, Safety and Risk; Facility Management; Engineering Economics, Organization, Logistics, Marketing; Mathematical and Computational Engineering
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Abstract

In recent years, as the weight of IT equipment has been reduced, the demand for motor fans for cooling the interior of electronic equipment is on the rise. Sensory test technique by inspectors is the mainstream for quality inspection of motor fans in the field. This sensory test requires a lot of experience to accurately diagnose differences in subtle sounds (sound pressures) of the fans, and the judgment varies depending on the condition of the inspector and the environment. In order to solve these quality problems, development of an analysis method capable of quantitatively and automatically diagnosing the sound/vibration level of a fan is required. In this study, it was clarified that the analysis method applying the MT system based on the waveform information of noise and vibration is more effective than the conventional frequency analysis method for the discrimination diagnosis technology of normal and abnormal items. Furthermore, it was found that due to the automation of the vibration waveform analysis system, there was a factor influencing the discrimination accuracy in relation between the fan installation posture and the vibration waveform. Keywords MT system  Mahalanobis distance (MD)  Feature value  Effectiveness analysis Introduction In a previous study, it has been reported on frequency analysis of the acoustic waveform of a compact motor fan Demand for compact motor fan for cooling the inside of and investigating characteristics appearing in normal and electronic devices is increasing now due to weight reduc- abnormal fans. However, it is currently difficult to dis- tion and space saving of IT equipment. In the quality criminate and diagnose appropriate normal items/abnormal inspection process at the site, quality inspection of compact items from measured values and analysis results obtained motor fan is carried out by sensory test of inspector. This by sound and vibration. sensory test requires a lot of experience in order to accu- In this research, in order to improve the discrimination rately diagnose the subtle difference in sound of fan and analysis accuracy of normality/abnormality concerning difference in vibration, and variation in pass/fail judgment noise and vibration of motor fan, we worked on analysis occurs due to changes in physical condition and environ- research applying waveform information pattern recogni- ment of inspector. tion technology. In order to solve these quality problems, development of an analysis method capable of quantitatively and auto- matically diagnosing the sound/vibration level of a fan is Research purpose required. In many cases, because noise level of fan depends on the noise level of the whole motor, it is important to reduce the noise. Also, if the fan approaches and interferes with the & Eiji Toma toma-e@tomakomai-ct.ac.jp fan cover on the stationary side, remarkable resonance sound may be generated. The fan noise includes a rota- National Institute of Technology, Tomakomai College, tional sound component (fz) which is the product of the Tomakomai, Japan 123 Journal of Industrial Engineering International number of rotations (f) and the number of blades (z) and a reference pattern as a unit space and can judge whether turbulent sound component generated by turbulence of the target data belongs to a unit space or not (Teshima et al. wind flow. Recently, a method of changing the rotation 2017). speed by an inverter is used. In this case, with respect to ventilation noise, the rotational sound component (fz) may MT method generate superior noise at a certain rotational frequency. This outstanding noise is called pure tone and is eval- In the MT system, MT method is a method of determining uated as a noisy sound. From studies of conventional fan outlier degree from unit space by evaluation index of noise, numerous studies on noise reduction have been made Mahalanobis distance (MD) and judging whether it is on rotational sound and turbulent sound from flow analysis normal or abnormal. The MT method is a method for on the number of blades and optimization of blade shape gaining cognizance of whether the target data (otherwise (Noda 2014). referred to as unknown data) belongs to the same standard, In precedent research, there was a case of verifying the homogeneous, group. It is an analysis method that defines a usefulness by introducing Mahalanobis Taguchi (MT) homogeneous population as a unit space for purpose and system which is one of the pattern recognition methods, calculates the distance from the unit space center of and understands a thing effective to some extent. In the unknown (target) data as Mahalanobis distance (MD). case of using pattern recognition method, processing for The MT method stands on a simple concept and is very extracting feature value from measurement data is per- easy to use; among the components of the MT system, the formed. If an invalid feature amount is included in the MT method has the greatest number of practical applica- abnormality detection, sensitivity and reliability of recog- tions (Teshima 2012). nition decrease. As shown in Fig. 1, it is recognized that, if the MD turns Therefore, it is important to set feature values consid- out to be short, the pattern is close to the unit space and ered valid for discrimination without excess or deficiency. that, if the MD turns out to be long, the pattern is distant. Statistical values such as average value and peak value of When the unit space is a normal population, if the MD is the waveform were used as feature value in precedent short, there is a strong possibility that the target data is research. However, in order to improve the accuracy of normal. MD itself was proposed by Indian mathematician discrimination, many feature values and number of samples P.C. Mahalanobis and is the result of converting multi- were required. If it is possible to extract feature values variate information in which multiple variables are inter- effective for abnormality detection from number of few twined complicatedly into distance information (Taguchi samples, discrimination can be performed with high 1992; Yano 2011). efficiency. In this study, we applied a method to extract the feature Formulation of MD quantity from the shape information of the waveform proposed in the MT system as the measurement result of Mahalanobis’ distance is called MD. It is a kind of distance the sound and vibration of the motor fan. By evaluating the for multivariable space. Correlation effect is included in effectiveness of the obtained feature quantity, we worked this distance (Teshima 2012; Suzuki 2012). on analysis research aimed at improving discrimination 1. Normalize data accuracy (Teshima et al. 2017). MD calculation is possible without normalization. But after normalization, covariance in the next step is Analysis principle Pattern recognition Target Unit Space Pattern recognition is a technology to replace information Short distance Normal processing such as human judgment and prediction with computer. In other words, it is a process of evaluating how Center much an unknown input pattern resembles a pre-input Target Long distance Abnormal standard pattern by numerical values and determining which category it belongs to. In this research, MT system was adopted as a pattern Cause diagnostics recognition technology. MT system is an information processing system which constitutes a data group of a Fig. 1 Conceptual drawing of the MT method 123 Journal of Industrial Engineering International 2 3 2 3 correlation coefficient. So evaluation of correlation 1  r u 1k 1 effect is easy. 6 . . . 7 6 . 7 . . . . MD ¼ D ¼ðÞ u  u 4 5 4 5 ð4Þ 1 k . . . . 2. Make covariance matrix r  1 u k1 k x  m k k 1 B u ¼ ð5Þ Covariance matrix ¼ B 1 m : Average of data group 3. Make inverse matrix of covariance matrix r : Standard deviation of data group 2 3 1  r 1k ab 1 B 10 ¼ or 6 . . . 7 . . . ba B 1 01 4 5 . . . ab 1 B r  1 k1 ba B 1 It means the inverse matrix of the correlation matrix. 4. Calculate the square of MD When Eq. (4) is verified in the case of k = 2, 1 r u 2 1 MD ¼ D ¼ðÞ u u 1 2 ab x 1i r 1 u MD ¼ðÞ x ; x 1i 2i ba x 2i The inverse matrix equation of the 2 9 2 matrix is, ab d b MD ¼ XAXðÞ If A is inverse matrix and X is data cd ca a  d  b  c 1 r 1 r r 1 r 1 1  r MD derivation and certification Therefore, the following expression is obtained, The concept of MD is a value obtained by consolidating the 1 r u deviation from the relationship between the distance and ) D ¼ðÞ u u 1 2 1  r r 1 u the correlation from the average of the object of interest in consideration of the correlation of the plurality of variables ¼ ðÞ u  ru  ru þ u 1 2 1 2 (Suzuki 2012). 1  r MD in the relation of the target data of two items is 2 2 u  2ru u þ u 1 2 1 2 given by following expression. 1  r rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 u  2ru u þ u 1 2 It proved to satisfy the expression in H Eq. (1). 1 2 MD ¼ ð1Þ 1  r In the MT method, in order to normalize the average of x  m the squared values of MD to 1, an operation of dividing the 1 1 u ¼ ð2Þ 1 2 value of MD = D by the number of items k is added. Therefore, the calculation formula of MD used in the MT x  m 2 2 u ¼ ð3Þ method is as follows. vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3 2 3 > x ; x : Target data u 1 2 1  r u > 1k 1 < u pffiffiffiffiffiffiffiffi 6 . . . 7 6 . 7 m : Average u . . . . ) D ¼ MD ¼ ðÞ u  u t 4 5 4 5 1 k . . . . > r : Standard deviation r  1 u k1 k r : Correlation coefficient ð6Þ Equations (1)–(3) mean to investigate how many times the distance from the average corresponds to the standard deviation which is an index of the variation of all data. Discrimination method The MD calculation formula obtained by expanding H in Expression (1) to a plurality of items is as follows: With the MT method, normality/abnormality is determined by comparing MD of target data with the threshold value. ðÞ u ...u on the right side is a value normalized by 1 k using the average and standard deviation of subscript When the MD is small close to 1, it is judged that it belongs item data. to the unit space, and if MD is larger than the set threshold 123 Journal of Industrial Engineering International value, it is judged not to belong to the unit space. The changes that may be occurring within short time spans. judgment threshold with the MT method is generally said Furthermore, both frequency analysis and wavelets pre- to boil down to 4 or thereabouts. This is because, for all suppose the human operator’s evaluation and judgment of practical statistical mathematics purposes, if the MD the results they produce. exceeds 4, the probability of unknown (target) data being a The variation and abundance information extraction member of the unit space shrinks to a small possibility method was proposed as a means of expressing the char- (Wakui 2014). acteristics of waveform patterns in more accurately quan- However, it is currently reported that the method of tified terms. setting a threshold using the v distribution is highly In this research, variation and abundance information is effective. For this reason, we set the threshold using the v extracted from the radiated sound waveform from compact distribution in this research. fan motor, and the waveform characterized. First, a parallel In Fig. 2, the abscissa is the Mahalanobis distance, the line (reference line) is drawn on the time axis at a constant ordinate is the probability, and the graph curve (v distri- interval in the waveform in the time domain, and a section bution theoretical curve) means the probability that the on the time axis (extraction width) for calculating the square value of the Mahalanobis distance takes (Yano characteristic amount is set. Next, the number of times of 2004). intersection with the reference line within interval of extraction width is taken as the variation, and sum of the Feature extraction values in the range above the reference line is obtained as the abundance information. Performing calculation of this The features of waveforms include frequency and ampli- variation and abundance information in all sections of the tude, and categories such as average frequency, magnitude waveform data is called ‘‘waveform analysis.’’ of oscillation, and maximum magnitude of oscillation have Figure 3 shows the concept of variation and abundance been commonly used. Frequency analysis (FFT: Fast information (differential and integral characteristics) in Fourier Transform) and wavelet have also been used. feature extraction (Yano 2004; Teshima 2012). Frequency analysis is a technique of expressing the char- acteristics of waveforms in terms of a frequency axis and an energy axis. A wavelet is a technique of expressing the Experimental system of radiated sound characteristics of waveforms in terms of a time axis, in addition to the frequency axis and the energy axis. Noise level of the test fan Frequency analysis and wavelets are excellent methods of explaining the characteristics of waveforms. Nonethe- As shown in Fig. 4, fan motors generally rotate in both less, it cannot quite be said that both convey sufficient directions, so that the blades of the fan use radial blade information on the characteristics of the given waveform (same type as the test fan). Radial blades have low cooling pattern. efficiency and high noise. The noise level is obtained from For instance, frequency analysis is a processing method Eq. (7). However, the evaluation position of the noise is the dealing with waveforms over a relatively long period of axial center height of the motor, and the distance is 1 m. time and is therefore not adept at capturing waveform (Noda 2014). Noise level;Ad½b ¼ 70 log D þ 50 log N þ k D : Outer diameter of the blades½ m ð7Þ N : number of rotations½ rps k : constan tðÞ ¼ 32  36 From Eq. (7), it is important to reduce the outer diam- eter D of the fan in order to lower the noise level. However, since the wind volume and the wind pressure also decrease, the balance between these and the noise becomes important at the time of designing. That is, the relation of Expression (8) is obtained. Wind volume ¼ puUDB ð8Þ Here, u: flow coefficient (0.15–0.25), U: outer periph- eral speed of the blades, and B: width of the outer Fig. 2 Distribution of squared values of MD 123 Journal of Industrial Engineering International Fig. 3 Variation and abundance information Fig. 4 Fan shape peripheral portion of the blades. Attention is required since Table 1 Specification of fan the air volume decreases with the square of D. Fan flame size 92.5 9 92.5 9 25.4 (mm) Blade number 5 Test fan Rated voltage DC12 V Rotational speed 3400 (rpm) In this research, we used two kinds of compact fan motors. Sample items shown in Fig. 5 (and Table 1) are five normal products (#9701–#9705), and sample items shown in Fig. 6 (and Table 2) including 10 normal products (fan 1 to fan 10) are five abnormal products (fan #1–fan #5). The abnormal product has surface buckle, and each displace- ment is 14 lm for fan #1, 25 lm for fan #2, 50 lm for fan #3, 70 lm for fan #4, and 90 lm for fan #5. Surface buckle refers to the size when the end face rotating around a certain axis deviates from a plane perpendicular to this axis during rotation. Fig. 5 Test fan 123 Journal of Industrial Engineering International reason is based on the distance between ear and fan when inspector performs sensory test. Fan recording time was 10 s, sampling frequency was 51.2 [kHz], and signal from microphone was saved in PC via A/D converter. Figure 8 shows the waveform data obtained by measuring the radiated sound of fan. Measurement sample number and time of fan’s radiated sound is ‘‘512,000 samples = 10 s’’ at sampling frequency 51.2 [kHz]. However, it was judged that a more accurate analysis could be performed by cap- turing a behavior change for a short time, and waveform data of ‘‘5120 samples = 0.1 s’’ were analyzed. Analysis procedure The analysis procedure of radiated sound and vibration Fig. 6 Test fan waveform is as follows. Table 2 Specification of fan 1. Feature extraction In order to characterize the waveform, extraction width Fan flame size 42 9 42 9 10 (mm) and reference line set, and variation and abundance Blade number 5 values are extracted as the feature value. Rated voltage DC24 V 2. Creating unit space Rotational speed 10,000 (rpm) Although the unit space consists of a plurality of samples and their variables (feature items), MT method has a condition that the number of samples Measurement of radiated sound in unit space must be larger than the number of variables, and more than 3 times the variable is Measurement of the sound of compact fan motor was taken considered ideal. in a quiet room. A schematic diagram of recording is 3. Setting a threshold shown in Fig. 7. The threshold was determined with a probability of 5% The sound collection was set to 30 mm above the according to the v distribution. This value is consid- rotation axis center from the rotation surface on the fan ered to be the boundary value when judging things in suction side by a  inch condenser microphone. The statistics, and it is called the significance level. 4. MD calculation of target data The waveform analysis of the abnormal fan and feature value of unit space are extracted, and the MD value is calculated by Eq. (6). Fig. 7 Recording system Fig. 8 Waveform data 123 Journal of Industrial Engineering International 5. Effectiveness analysis 20 pieces. Next, taking these into consideration, three Effectiveness analysis is a process of evaluating which waveforms were arbitrarily selected from five normal item is effective for abnormality detection by SN ratio. products (#9701–#9705) so as to be three times the number 6. Evaluation of effectiveness by SN ratio of variables, and a unit space was created. Finally, wave- The MT system includes a success/failure quantifica- form analysis was also performed on normal products not tion proposal for the recognition system. belonging to the unit space, and the MD value was cal- culated. Figure 9 shows the calculation result of the MD Use is made here of the concept of SN ratio (signal-to- value of the normal product. On the graph, it is judged to noise ratio), which provides a functionality evaluation be abnormal because the MD value exceeding the threshold yardstick in quality engineering or MT method. In pattern can be confirmed. However, it is understood that because recognition, generally speaking, the recognition result is the normal product is the target, it is not an appropriate influenced by various factors, ranging from measuring tool analysis result. It is estimated that variables invalid in selection to recognition software parameter settings. Use of discrimination are included in feature values. Therefore, it the SN ratio makes it possible to evaluate the appropri- is necessary to analyze and evaluate which items are highly ateness of the entire recognition system. effective. Figure 10 shows the results of the effectiveness In quality engineering there are concepts of various SN analysis on the target data. The horizontal axis represents ratios, but there are the following two methods for calcu- the variable, and vertical axis represents the SN ratio, lating the SN ratio used in the MT system. which means that the item with the highest value is valid (a) If it is difficult to give a numerical value to the for the judgment. Therefore, Fig. 11 shows the result of degree of abnormality, apply the SN ratio of the calculating the MD value using the variable with the pos- preferably large characteristics. itive SN ratio as the feature value. On the graph, it is (b) When the degree of abnormality can be quantified, judged that the MD value is equal to or less than the apply the SN ratio of the dynamic characteristic. threshold value and it is judged to be normal, and it is judged that the effective feature value can be extracted. It is desirable that the MD value of data known not to belong to the unit space be as large as possible. In this Analysis result of abnormal products research, ‘‘SN ratio of the preferably large characteristics’’ was applied. Next, we analyzed a waveform in a fan of Fig. 6 and In quality engineering, ‘‘larger preferable characteris- extracted feature value. The fixed value is extraction width tics’’ are called preferably large characteristics. Since there 20 and reference line 30. The number of variables is 60. In are generally variations when there are many data, the SN the unit space, nine waveforms were arbitrarily selected ratio is to quantify desirability collectively including from 10 normal products (fan 1 to fan 10) so that the variations. number of samples was three times as large as the variable. The calculation formula of SN ratio (g) of preferably Waveform analysis was performed on abnormal products large characteristic is as shown in Eq. (9). At this time, it is (#fan 1–#fan 5). Figure 12 shows MD values of normal and better that the SN ratio is large. abnormal items not belonging to the unit space. Here, D is the Mahalanobis distance (the value of the From the results, MD values above the threshold were square), and k is the number of signal data not belonging to shown for all abnormal items, and it was determined as the unit space. abnormal. However, among the normal products, items 2 2 2 g ¼10 log 1=D þ 1=D þ  þ 1=D =k ð9Þ 1 2 k Analysis result of radiated sound Analysis result of normal products First, we analyzed a waveform in the fan of Fig. 5 and extracted feature value. The fixed value is extraction width 20, reference line 10. Therefore, 20 samples can be obtained from one waveform. In addition, since the refer- ence line calculates the variation and abundance informa- tion for each extraction width, the number of variables is Fig. 9 MD calculation result of normal products 123 Journal of Industrial Engineering International Fig. 10 Effectiveness analysis result Fig. 13 Effectiveness analysis result negative value is variation and abundance information of reference line. By using variation and abundance infor- mation of reference line at the central portion of the waveform as the feature value, it is shown that accurate abnormality determination is possible. Figure 14 shows the result of calculating the MD value using the variable whose SN ratio is a positive value as the feature quantity from the result of effectiveness analysis of all abnormal items. From the results in the figure, it is found that the normal value is equal to or less than the threshold value and the abnormal item is the MD value that is equal to or more than the threshold value, so it is an appropriate discrimination. Fig. 11 MD calculation result after analysis Experiment system of vibration Vibration measurement When the motor fan is sensory-tested, the inspector holds two positions on the side of the fan frame and diagnoses by hearing and tactile sense near the ear while turning the wrist. Fig. 12 MD calculation result of each sample fan which are judged to be abnormal items beyond the threshold were confirmed. Figure 13 shows the effective- ness analysis result of the waveform of the abnormal pro- duct (#fan 1). From the figure, the SN ratio shows a positive value in the central part, and all values are nega- tive at both ends. The same tendency was shown also in the effectiveness analysis of other abnormal items. A variable taking a Fig. 14 MD calculation result of each sample fan 123 Journal of Industrial Engineering International In this study, we developed an automatic rotary oscil- lating device simulating the handling performed by the inspector and analyzed the vibration waveform pattern by automatic detection of vibration of the motor fan by applying the MT method. Figures 15 and 16 show the automatic rotary oscillating device. As the vibration mea- surement condition, the rotation speed of the servo motor was set to 3 rpm, the fan rotation speed was 3400 rpm, and the measurement time was 40 s. In addition, angle of oscillation h of the fan was measured in the axial direction and the radial direction under three conditions of 15,30, and 45. Waveform data of vibration Fig. 16 Schematic of automatic rotary oscillating device The waveform data of vibration were measured using a level recorder, but the test fan of Fig. 6 had a low vibration level and could not obtain sufficient waveform data. Therefore, in this research, the test fan of Fig. 5 was adopted. #9701, #9702, #9703, #9704, and #9705 of sam- ples with different magnitudes of vibrations were set in order of increasing vibration acceleration level. Figures 17, 18 show the vibration waveform data in the axial direction and the radial direction with the rotary oscillating device with the angle of oscillation of the fan set to h =15. In the vibration waveform in the axial direction of Fig. 17, it can be confirmed that the vibration acceleration level increases in order of the nominal number. On the other hand, since the waveform behavior in the radial Fig. 17 Acceleration level of axial direction with angle of oscillation direction other than #9705 is very small, it is difficult to judge the magnitude of the vibration level from the waveform. Furthermore, the same tendency was observed under different angle of oscillation conditions. Fig. 18 Acceleration level of radial direction with angle of oscillation Therefore, in this study, waveform analysis was per- formed on the axial vibration waveforms of three condi- tions of the fan’s swinging angles of 15,30, and 45 in the same way as the analysis procedure of radiated sound. Fig. 15 Overview of automatic rotary oscillating device 123 Journal of Industrial Engineering International Analysis result of vibration Conclusion The setting value of the waveform analysis in the vibration Method of pattern recognition waveform of the test fan shown in Fig. 5 was set to extraction width 20 and reference line 10. Since the num- Processing to recognize, understand, and predict based on ber of variables is 20, three waveforms are arbitrarily various information obtained from objects is called pattern selected from five normal products (#9701–#9705) so as to recognition. Technology replaces information processing make the number of samples three times as large, and a unit such as human judgment and prediction with computer. space was created. Waveform analysis was also performed Although there are familiar practical examples such as on normal goods not belonging to the unit space to cal- character recognition and fingerprint authentication, it is culate the MD value. still a big technical subject for computers. The MT system In this study, we analyzed vibration waveforms in the adopted in this research is a system of new pattern recog- axial direction of three conditions of fan’s angle of nition and prediction technology proposed by Dr. Taguchi oscillation of 15,30 and 45, and Fig. 19 shows the Genichi (Taguchi 2008; Tamura 2009). result of MD value calculated for each angle of oscillation Although the application field of pattern recognition is of the fan. From Fig. 19, it is determined that the MD diverse, we are expected to apply it in the whole human value is over the threshold value when angles of oscil- activity field of human beings. In particular, it is thought lation are 15 and 30, so it is determined to be abnormal. that it plays an important role in terms of accumulation and Even at angle of oscillation of 45, although there are reproduction of expertise, mainly in manufacturing and places where the MD value is larger than the threshold medical care. The procedure for carrying out pattern value, the best result among the three conditions was recognition can be roughly divided into three stages. The obtained. first step is preparatory preparation, the second step is from Figure 20 shows the results of effectiveness analysis for measurement to feature extraction, and the third step is each angle of oscillation. In the analysis results of angles of recognition processing (Tamura 2009). oscillation of 15 and 30, it is considered that the fact that the number of variables in which the SN ratio becomes Reasons selected negative is large is a factor that increases the MD value. On the other hand, since the number of variables in which the In the MT system, variation information (differential SN ratio becomes negative at angle of oscillation of 45 is characteristic) and abundance information (integration small, it can be judged that feature quantities effective for characteristic) are proposed as a feature extraction tech- discrimination can be extracted. nique. These feature quantities are highly versatile and can Figure 21 shows the result of calculating the MD value be applied to many technical problems. Also, various with the variable whose SN ratio at angle of oscillation of measurement values often draw waveform patterns. Of 45 is positive as the feature quantity. From the results in course, not only the vibration but also the measured values Fig. 21, it can be judged that an appropriate discrimination that change in time series are all waveform patterns. The result was obtained because the MD value is below the technique of extracting the features of the waveform as threshold value. numerical values can be said to be an important technique for problems such as inspection and monitoring (Hasegawa 2007; Taguchi 2002). Research results In this study, we applied the method of extracting the feature quantity from the shape information of the wave- form proposed in the MT system for the measurement result of the sound and vibration of the motor fan. Then, we evaluated the effectiveness of the feature value of the acquired waveform information from the MD value and carried out analytical research aimed at improving the detection accuracy of the discrimination. Ultimately, in waveform analysis of radiated sound and vibration of the Fig. 19 MD calculation result of each angle of oscillation motor fan, appropriate judgment results of normal and 123 Journal of Industrial Engineering International Fig. 20 Effectiveness analysis result merely looking at the information by a person. However, since it is information that can be directly given to a computer, it can be used as it is for pattern recognition. 3. Since frequency analysis shows the average property of a sufficiently long waveform, it is difficult to capture the change occurring in a short time. On the other hand, feature extraction by variation and abundance information extracts feature values every fixed time width, so it is possible to detect a pattern difference in units of time width (Teshima 2012). In addition, from the analysis result of the vibration waveform of the present study in the MD value, it was Fig. 21 MD calculation result of angle of oscillation found that the fluctuation of the vibration width of the waveform tends to become small as the angle of oscillation abnormal items were obtained by extracting feature values increases. effective for detection by effectiveness analysis. Regarding future research activities, we will focus on A general pattern recognition method is said to be able the correlation between angle of oscillation and width by to accurately classify abnormal patterns if many data of application of MT method in discriminant analysis of assumed abnormal patterns can be collected. However, in normality/abnormality from motor fan vibration waveform reality, normal data can be collected, but abnormal data and plan to analyze more specific factors is there. collection becomes more difficult as the scale of the facility becomes more complicated. Since the MT method evalu- Open Access This article is distributed under the terms of the Creative ates the measurement data with the difference from the Commons Attribution 4.0 International License (http://creative normal data group as the reference, data collection for commons.org/licenses/by/4.0/), which permits unrestricted use, dis- tribution, and reproduction in any medium, provided you give learning only needs to be normal data, and this method can appropriate credit to the original author(s) and the source, provide a cope with an unknown abnormal pattern. link to the Creative Commons license, and indicate if changes were In general, frequency analysis (spectral analysis, fast made. Fourier transform analysis, etc.) and wavelet are adopted as a characterization analysis method from waveform infor- mation (Yano 2002; Mori 2005). References The differences between these analysis methods and Hasegawa Y (2007) Story of MT System, Japan Science and variation and abundance information, which are feature Technology Unit, pp 6–11 values in the MT method, are summarized below. Mori T (2005) Application and mathematics of the Taguchi methods. In: Optimization engineering using the Taguchi methods, trendy 1. Because of the frequency analysis and wavelet, the book, Mori Engineer Office, Shizuoka, pp 323–338, 511–583 nature and homogeneity of the waveform are displayed Noda S (2014) Noise and vibration of motor and countermeasure by graphs and figures, so it is an expression understood design method, Scientific Information Publication, pp 19–32, by humans. 103–123 Suzuki M (2012) Introduction to MT system analysis method, Nikkan 2. Since variation and abundance information is numer- Kogyo Shimbun, pp 7–101 ical information expressing the waveform feature, it is difficult to grasp the properties of the waveform by 123 Journal of Industrial Engineering International Taguchi G (1992) Quality engineering lecture no. 5, Quality Teshima S, Tamura K, Hasegawa Y (2017) Standardization and engineering casebook—Japan public, Japan Standards Associa- Quality Control 2017. J Jpn Stand Assoc 70(7):2–31 tion, pp 1–12 Wakui Y (2014) Multivariate analysis understanding, Technical Taguchi G (2002) Evaluation technology for optimization design, commentary, pp 190–200 Japan Standards Association, pp 189–200 Yano H (2002) Introduction to quality engineering numeration, Japan Taguchi G (2008) Technology development in MT system, Japan Standards Association, pp 271–286 Standards Association, pp 27–37 Yano H (2004) Technology development of the information design Tamura K (2009) New technology of pattern recognition by quality with the computer-Simulation and MT system, Japan Standards engineering, Japan Standards Association, pp 26–85 Association, pp 310–368 Teshima S (2012) Introductory MT system. Japan Science and Yano H (2011) Quality engineering guide to raise an engineer power, Technology Publishing, Tokyo, pp 33–57 Japan Standards Association, pp 219–235

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Journal of Industrial Engineering InternationalSpringer Journals

Published: Jun 4, 2018

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