# Fault Detection of Electric Impact Drills and Coffee Grinders Using Acoustic Signals

## Abstract

**:**

_{D}= 96%, TE

_{CG-A}= 97%, TE

_{CG-B}= 100%).

## 1. Introduction

## 2. Developed Acoustic Based Approach

#### 2.1. MSAF-17-MULTIEXPANDED-FILTER-14

- (1)
- Compute Fast Fourier Transform (FFT) spectra for all states of the EID (for all training vectors). In the presented acoustic based approach the FFT provided a vector of 16384-elements. For 16,384 frequency components, the frequency spectrum is 22,050 Hz. Therefore, each frequency component is every 1.345 Hz. The computed vectors were defined as follows: healthy EID—
**h**= [h_{1}, h_{2}, ..., h_{16,384}], EID with 15 broken rotor blades (faulty fan)—**f**= [f_{1}, f_{2}, ..., f_{16,384}], EID with a bent spring—**s**= [s_{1}, s_{2}, ..., s_{16,384}], EID with a rear ball bearing fault—**b**= [b_{1}, b_{2}, ..., b_{16,384}]. - (2)
- For each training vector compute:
**h**−**f**,**h**−**s**,**f**−**s**,**b**−**h**,**b**−**f**,**b**−**s**. - (3)
- Compute: |
**h**−**f**|, |**h**−**s**|, |**f**−**s**|, |**b**−**h**|, |**b**−**f**|, |**b**−**s**|. - (4)
- Find 1–17 Common Frequency Components (CFCs) or set a parameter Threshold of CFCs (ToCFCs). If there are no CFCs, then set a parameter ToCFCs. The parameter is defined as Equation (1):$$ToCFCs=\frac{\begin{array}{cccc}Number& of& required& CFCs\end{array}}{\begin{array}{cccc}Number& of& all& differences\end{array}}$$

**h**−

**f|.**Let’s suppose that frequency components 110, 160 Hz are found two times for |

**h**−

**s|**. Let’s suppose that frequency components 110, 140 Hz are found two times for |

**f**−

**s**|. Let’s suppose that frequency component 500 Hz is found three times for |

**b**−

**h**|. Let’s suppose that frequency components 600, 610 Hz are found two times for |

**b**−

**f**|. Let’s suppose that frequency components 600, 710 Hz are found two times for |

**b**−

**s**|. There are no CFCs. Only frequency components 110 Hz and 600 Hz are found four times. The MSAF-17-MULTIEXPANDED finds frequency components 110, 130, 140, 160, 500, 600, 610, 710 Hz, if ToCFCs is equal to 0.1111 (2/18). The MSAF-17-MULTIEXPANDED method finds 0 frequency components, if ToCFCs is equal to 0.2777 (5/18).

- (5)
- Form groups of frequency components for a proper recognition. Considering the presented example, it can be noticed that the frequency component 110 Hz is good for |
**h**−**s**| and |**f**−**s**|. The frequency component 130 Hz is good for |**h**−**f**|. The frequency component 500 Hz is good for |**b**−**h**|. The frequency component 600 Hz is good for |**b**−**f**| and |**b**−**s**|. The MSAF-17- MULTIEXPANDED-FILTER-14 finds 1 group consisted of 110, 130, 500, 600 Hz. - (6)
- Form bandwidths of frequency. Considering the presented example, 14 Hz bandwidths are selected. The MSAF-17-MULTIEXPANDED-FILTER-14 uses a value of 14 Hz. The value of 14 Hz is set experimentally. The middle of the first bandwidth is located at 110 Hz. The middle of the second bandwidth is located at 130 Hz. The middle of the third bandwidth is located at 500 Hz. The middle of the fourth bandwidth is located at 600 Hz. Following bandwidths are selected <103–117 Hz>, <123–137 Hz >, <493–507 Hz>, <593–607 Hz>.
- (7)
- Using computed bandwidths, form a feature vector.

**h**−

**f**|, 14—means that, we set 14 Hz frequency bandwidth, for example for frequency 50 Hz it will be <50 − 7 Hz, 50 + 7Hz>.

**h**−

**f**|, |

**h**−

**s**|, |

**f**−

**s**|, |

**b**−

**h**|, |

**b**−

**f**|, |

**b**−

**s**| were computed and are presented in Figure 17, Figure 18, Figure 19, Figure 20, Figure 21 and Figure 22.

#### 2.2. RMS

_{RM}

_{S}—RMS for 1-s sample (44,100 values), n—number of all samples, n = 44,100, x

_{1}, ..., x

_{n}—values of samples 1, ..., n (sampling rate 44,100 Hz).

_{RM}

_{S1}, ..., x

_{RM}

_{S50}—RMS values of the healthy EID, x

_{RM}

_{S51}, ..., x

_{RM}

_{S100}—RMS values of the EID with 15 broken rotor blades (faulty fan), x

_{RM}

_{S101}, ..., x

_{RM}

_{S150}—RMS values of the EID with a bent spring, x

_{RM}

_{S151}, ..., x

_{RM}

_{S200}− RMS values of the EID with a shifted brush (motor off), x

_{RM}

_{S201}, ..., x

_{RM}

_{S250}—RMS values of the EID with a rear ball bearing fault. The computed RMS values of the EID are presented in Table 1, Table 2, Table 3, Table 4 and Table 5.

_{RM}

_{S251}, ..., x

_{RM}

_{S300}—RMS values of the healthy CG-A, x

_{RM}

_{S301}, ..., x

_{RM}

_{S350}—RMS values of the CG-A with a heavily damaged rear sliding bearing, x

_{RM}

_{S351}, ..., x

_{RM}

_{S400}− RMS values of the CG-A with a damaged shaft and heavily damaged rear sliding bearing, x

_{RM}

_{S401}, ..., x

_{RM}

_{S450}—RMS values of the motor off (CG-A off). The values x

_{RM}

_{S401}, ..., x

_{RM}

_{S450}were the same as RMS values of the EID with a shifted brush (EID off). The computed RMS values of the CG-A are presented in Table 6, Table 7 and Table 8.

_{RM}

_{S451}, ..., x

_{RM}

_{S500}—RMS values of the healthy CG-B, x

_{RM}

_{S501}, ..., x

_{RM}

_{S550}—RMS values of the CG-B with a light damaged rear sliding bearing, x

_{RM}

_{S551}, ..., x

_{RM}

_{S600}—RMS values of the motor off (CG-B off). The values x

_{RM}

_{S551}, ..., x

_{RM}

_{S600}were the same as RMS values of the EID with a shifted brush (EID off). The computed RMS values of the CG-B are presented in Table 9 and Table 10.

#### 2.3. NN Classifier

**x**—test feature vector,

**y**—training feature vector, ED(

**x**−

**y**)—Euclidean distance, n—number of features (it is 1 feature for the RMS).

## 3. Recognition Results of the EID, CG-A, CG-B

_{D}= 500 W, rotation speed R

_{D}= 3000 rpm and weight M

_{D}= 1.84 kg.

_{D}):

_{D1}—the efficiency of recognition for D1 class (in the analysis it is one of five classes, for example healthy EID), N

_{D1}—the number of test samples classified as D1 class, N

_{ALL-D1}—the number of all test samples in D1 class. The values of E

_{CG-A}and E

_{CG-B}were computed similarly to E

_{D1}.

_{D}) was also introduced. It was defined as follows Equation (5):

_{D}—the total efficiency of recognition of all classes (five states of the EID), E

_{D}

_{1}—the efficiency of recognition for D1 class (in the presented analysis D1 class—healthy EID), E

_{D}

_{2}—the efficiency of recognition for D2 class (in the presented analysis D2 class—EID with a bent spring), E

_{D}

_{3}—the efficiency of recognition for D3 class (in the presented analysis D3 class—EID with 15 broken rotor blades), E

_{D}

_{4}—the efficiency of recognition for D4 class (in the presented analysis D4 class—EID with a shifted brush), E

_{D}

_{5}—the efficiency of recognition for D5 class (in the presented analysis D5 class—EID with a rear ball bearing fault). The values of TE

_{CG-A}and TE

_{CG-B}were computed similarly to TE

_{D}. Four acoustic signals were used for TE

_{CG-A}. Three acoustic signals were used for TE

_{CG-B}. The computed values of E

_{D}and TE

_{D}were presented in Table 11 and Table 12. Acoustic signals of the EID were processed by the MSAF-17-MULTIEXPANDED-FILTER-14 method and the NN classifier (Table 11).

_{D}and TE

_{D}of the proposed approach were following: E

_{D}= 88–100%, TE

_{D}= 96% for the MSAF-17-MULTIEXPANDED-FILTER-14 method and E

_{D}= 56–100%, TE

_{D}= 83.2% for the RMS. The computed values of E

_{CG-A}and TE

_{CG-A}were presented in Table 13 and Table 14. Acoustic signals of the CG-A were processed by the MSAF-17-MULTIEXPANDED-FILTER-14 method and the NN classifier (Table 13).

_{CG-A}and TE

_{CG-A}of the proposed approach were following: E

_{CG-A}= 88–100%, TE

_{CG-A}= 97% for the MSAF-17-MULTIEXPANDED-FILTER-14 method and E

_{CG-A}= 92–100%, TE

_{CG-A}= 96% for the RMS. The computed values of E

_{CG-B}and TE

_{CG-B}were presented in Table 15 and Table 16. Acoustic signals of the CG-B were processed by the MSAF-17-MULTIEXPANDED-FILTER-14 method and the NN classifier (Table 15).

_{CG-B}and TE

_{CG-B}of the proposed approach were following: E

_{CG-B}= 100%, TE

_{CG-B}= 100% for the MSAF-17-MULTIEXPANDED-FILTER-14 method and RMS.

## 4. Discussion

_{D}. The classes of acoustic signals “CG-A with a heavily damaged rear sliding bearing” and “CG-A with a damaged shaft and heavily damaged rear sliding bearing” had lower values of TE

_{CG-A}. The MSAF-17-MULTIEXPANDED-FILTER-14 method was good method of feature extraction for all analysed classes of acoustic signals.

## 5. Summary and Conclusions

_{D}and TE

_{D}of the proposed approach were following: E

_{D}= 88–100%, TE

_{D}= 96% for the MSAF-17-MULTIEXPANDED-FILTER-14 and E

_{D}= 56–100%, TE

_{D}= 83.2% for the RMS. The computed values of E

_{CG-A}and TE

_{CG-A}of the proposed approach were following: E

_{CG-A}= 88–100%, TE

_{CG-A}= 97% for the MSAF-17-MULTIEXPANDED-FILTER-14 method and E

_{CG-A}= 92–100%, TE

_{CG-A}= 96% for the RMS. The computed values of E

_{CG-B}and TE

_{CG-B}of the proposed approach were following: E

_{CG-B}= 100%, TE

_{CG-B}= 100%.

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 9.**CG-A with a damaged shaft and heavily damaged rear sliding bearing (indicated by yellow circle).

**Figure 15.**(

**a**) Capacity microphone, computer and electric impact drill. (

**b**) Measurement of acoustic signals.

**Figure 23.**Values of features of healthy EID (145 features, seven frequency bandwidths, <271–287 Hz>, <450–490 Hz>, <550–565 Hz>, <2290–2324 Hz>, <11091–11118 Hz>, <11183–11220 Hz>, <11232–11253 Hz>).

**Figure 24.**Values of features of the EID with 15 broken rotor blades (faulty fan) (145 features, seven frequency bandwidths, <271–287 Hz>, <450–490 Hz>, <550–565 Hz>, <2290–2324 Hz>, <11091–11118 Hz>, <11183–11220 Hz>, <11232–11253 Hz>).

**Figure 25.**Values of features of the EID with a bent spring (145 features, seven frequency bandwidths, <271–287 Hz>, <450–490 Hz>, <550–565 Hz>, <2290–2324 Hz>, <11091–11118 Hz>, <11183–11220 Hz>, <11232–11253 Hz>).

**Figure 26.**Values of features of the EID with a rear ball bearing fault (145 features, seven frequency bandwidths, <271–287 Hz>, <450–490 Hz>, <550–565 Hz>, <2290–2324 Hz>, <11091–11118 Hz>, <11183–11220 Hz>, <11232–11253 Hz>).

**Figure 27.**Values of features of the healthy CG-A (29 features, two frequency bandwidths, <515–537 Hz>, <1560–1575 Hz>).

**Figure 28.**Values of features of the CG-A with a heavily damaged rear sliding bearing (29 features, two frequency bandwidths, <515–537 Hz>, <1560–1575 Hz>).

**Figure 29.**Values of features of the CG-A with a damaged shaft and heavily damaged rear sliding bearing (29 features, two frequency bandwidths, <515–537 Hz>, <1560–1575 Hz>).

**Figure 30.**Values of features of the healthy CG-B (43 features, three frequency bandwidths, <94–109 Hz>, <194–207 Hz>, <463–488 Hz>).

**Figure 31.**Values of features of the CG-B with a light damaged rear sliding bearing (43 features, three frequency bandwidths, <94–109 Hz>, <194–207 Hz>, <463–488 Hz>).

Number of Samples | RMS Value | Number of Samples | RMS Value |
---|---|---|---|

x_{RMS1} | 0.237122 | x_{RMS5} | 0.240819 |

x_{RMS2} | 0.231192 | x_{RMS6} | 0.236356 |

x_{RMS3} | 0.234878 | x_{RMS7} | 0.239650 |

x_{RMS4} | 0.238282 | x_{RMS8} | 0.238406 |

Number of Samples | RMS Value | Number of Samples | RMS Value |
---|---|---|---|

x_{RMS51} | 0.322252 | x_{RMS55} | 0.312347 |

x_{RMS52} | 0.316197 | x_{RMS56} | 0.318529 |

x_{RMS53} | 0.317383 | x_{RMS57} | 0.310883 |

x_{RMS54} | 0.305535 | x_{RMS58} | 0.302719 |

Number of Samples | RMS Value | Number of Samples | RMS Value |
---|---|---|---|

x_{RMS101} | 0.250579 | x_{RMS105} | 0.245578 |

x_{RMS102} | 0.244888 | x_{RMS106} | 0.243813 |

x_{RMS103} | 0.244461 | x_{RMS107} | 0.246395 |

x_{RMS104} | 0.249611 | x_{RMS108} | 0.246297 |

Number of Samples | RMS Value | Number of Samples | RMS Value |
---|---|---|---|

x_{RMS151} | 0.006427 | x_{RMS155} | 0.006478 |

x_{RMS152} | 0.006338 | x_{RMS156} | 0.007226 |

x_{RMS153} | 0.008981 | x_{RMS157} | 0.007020 |

x_{RMS154} | 0.009021 | x_{RMS158} | 0.006644 |

Number of Samples | RMS Value | Number of Samples | RMS Value |
---|---|---|---|

x_{RMS201} | 0.235278 | x_{RMS205} | 0.234696 |

x_{RMS202} | 0.236730 | x_{RMS206} | 0.236078 |

x_{RMS203} | 0.233518 | x_{RMS207} | 0.237600 |

x_{RMS204} | 0.234478 | x_{RMS208} | 0.237778 |

Number of Samples | RMS Value | Number of Samples | RMS Value |
---|---|---|---|

x_{RMS251} | 0.203343 | x_{RMS255} | 0.209252 |

x_{RMS252} | 0.203521 | x_{RMS256} | 0.215012 |

x_{RMS253} | 0.201109 | x_{RMS257} | 0.209241 |

x_{RMS254} | 0.205511 | x_{RMS258} | 0.205984 |

Number of Samples | RMS Value | Number of Samples | RMS Value |
---|---|---|---|

x_{RMS301} | 0.234359 | x_{RMS305} | 0.234927 |

x_{RMS302} | 0.234860 | x_{RMS306} | 0.233882 |

x_{RMS303} | 0.231783 | x_{RMS307} | 0.235229 |

x_{RMS304} | 0.237120 | x_{RMS308} | 0.229835 |

Number of Samples | RMS Value | Number of Samples | RMS Value |
---|---|---|---|

x_{RMS351} | 0.239449 | x_{RMS355} | 0.248779 |

x_{RMS352} | 0.246317 | x_{RMS356} | 0.250027 |

x_{RMS353} | 0.246894 | x_{RMS357} | 0.250791 |

x_{RMS354} | 0.247325 | x_{RMS358} | 0.250203 |

Number of Samples | RMS Value | Number of Samples | RMS Value |
---|---|---|---|

x_{RMS451} | 0.248146 | x_{RMS455} | 0.248331 |

x_{RMS452} | 0.254812 | x_{RMS456} | 0.259062 |

x_{RMS453} | 0.248951 | x_{RMS457} | 0.263240 |

x_{RMS454} | 0.240446 | x_{RMS458} | 0.264600 |

Number of Samples | RMS Value | Number of Samples | RMS Value |
---|---|---|---|

x_{RMS501} | 0.131587 | x_{RMS505} | 0.103367 |

x_{RMS502} | 0.121155 | x_{RMS506} | 0.095910 |

x_{RMS503} | 0.103567 | x_{RMS507} | 0.108105 |

x_{RMS504} | 0.094650 | x_{RMS508} | 0.105756 |

**Table 11.**Computed values of E

_{D}and TE

_{D}of the EID using the MSAF-17-MULTIEXPANDED-FILTER-14 method and the NN classifier.

Type of Acoustic Signal | E_{D} (%) |

Healthy EID | 100 |

EID with a bent spring | 92 |

EID with (15 broken rotor blades) faulty fan | 100 |

EID with shifted brush (motor off) | 100 |

EID with rear ball bearing fault | 88 |

TE_{D} (%) | |

Total efficiency of recognition of the EID | 96 |

Type of Acoustic Signal | E_{D} (%) |

Healthy EID | 56 |

EID with a bent spring | 100 |

EID with (15 broken rotor blades) faulty fan | 100 |

EID with shifted brush (motor off) | 100 |

EID with rear ball bearing fault | 60 |

TE_{D} (%) | |

Total efficiency of recognition of the EID | 83.2 |

**Table 13.**Computed values of E

_{CG-A}and TE

_{CG-A}of the CG-A using the MSAF-17-MULTIEXPANDED-FILTER-14 method and the NN classifier.

Type of Acoustic Signal | E_{CG-A} (%) |

Healthy CG-A | 100 |

CG-A with a heavily damaged rear sliding bearing | 100 |

CG-A with a damaged shaft and heavily damaged rear sliding bearing | 88 |

Motor off | 100 |

TE_{CG-A} (%) | |

Total efficiency of recognition of the CG-A | 97 |

**Table 14.**Computed values of E

_{CG-A}and TE

_{CG-A}of the CG-A using the RMS and the NN classifier.

Type of Acoustic Signal | E_{CG-A} (%) |

Healthy CG-A | 100 |

CG-A with a heavily damaged rear sliding bearing | 92 |

CG-A with a damaged shaft and heavily damaged rear sliding bearing | 92 |

Motor off | 100 |

TE_{CG-A} (%) | |

Total efficiency of recognition of the CG-A | 96 |

**Table 15.**Computed values of E

_{CG-B}and TE

_{CG-B}of the CG-B using the MSAF-17-MULTIEXPANDED-FILTER-14 method and the NN classifier.

Type of Acoustic Signal | E_{CG-B} (%) |

Healthy CG-B | 100 |

CG-B with a light damaged rear sliding bearing | 100 |

Motor off | 100 |

TE_{CG-B} (%) | |

Total efficiency of recognition of the CG-B | 100 |

**Table 16.**Computed values of E

_{CG-B}and TE

_{CG-B}of the CG-B using the RMS and the NN classifier.

Type of Acoustic Signal | E_{CG-B} (%) |

Healthy CG-B | 100 |

CG-B with a light damaged rear sliding bearing | 100 |

Motor off | 100 |

TE_{CG-B} (%) | |

Total efficiency of recognition of the CG-B | 100 |

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## Share and Cite

**MDPI and ACS Style**

Glowacz, A.
Fault Detection of Electric Impact Drills and Coffee Grinders Using Acoustic Signals. *Sensors* **2019**, *19*, 269.
https://doi.org/10.3390/s19020269

**AMA Style**

Glowacz A.
Fault Detection of Electric Impact Drills and Coffee Grinders Using Acoustic Signals. *Sensors*. 2019; 19(2):269.
https://doi.org/10.3390/s19020269

**Chicago/Turabian Style**

Glowacz, Adam.
2019. "Fault Detection of Electric Impact Drills and Coffee Grinders Using Acoustic Signals" *Sensors* 19, no. 2: 269.
https://doi.org/10.3390/s19020269