Non-Invasive Method for In-Service Induction Motor E ﬃ ciency Estimation Based on Sound Acquisition

Featured Application: The Method has wide application in the industry to estimate the e ﬃ ciency of induction motors in a totally non-invasive way. Abstract: Induction motors (IMs) are present in practically all production processes and account for two-thirds of the energy consumption in industrial settings. Therefore, monitoring them is essential to prevent accidents, optimize production, and increase energy e ﬃ ciency. Monitoring methods found in the literature require a certain level of invasiveness, causing some applications to be unfeasible. In the present study, a new completely non-invasive method implemented in an embedded system performs the embedded processing of the sound signal emitted by an in-service IM to estimate speed, torque, and e ﬃ ciency. Motor speed is estimated from the analysis in the frequency domain using the Fourier Transform. Torque and e ﬃ ciency are estimated from the speed and motor nameplate information. To perform the tests and validate the proposed method / system, a workbench with a controllable torque was used. The workbench was also equipped to allow the results to be compared with the airgap torque method. The results indicate a high accuracy for the nominal load (error of approximately 1%) in the measurement of the e ﬃ ciency and torque, and a mean relative error of 0.2% for the speed.


Introduction
Induction motors (IMs) are used extensively in the industry and are considered the backbone of the industrial sector [1]. Induction motors are responsible for around 68% of energy consumption in the industrial sector worldwide [2]. On average, the IMs of industrial units operate at 60% of their nominal load due to oversized facilities or underload conditions. As a result, their efficiencies are reasonably low [3]. Hence, the implementation of energy efficiency programs and studies focused on their performance should be a priority in the industrial sector [4]. However, few motors are properly monitored, largely due to the high cost of the available monitoring devices [5].
The invasiveness of the efficiency estimation technique also presents a limiting factor, considering that the shutdown of motors to perform tests is nearly inevitable, and the accessibility to these motors

Air Gap Torque Method
Among the low-invasiveness efficiency estimation techniques for induction motors, the air gap torque method (AGT) can be considered the most accurate [10].
The air gap is the gap between the stator and the rotor. The electromechanical energy conversion process occurs when a time-varying magnetic flux produced in the stator crosses the air gap and induces an electromotive force in the rotor winding in short circuit, the magnetic moment (air gap torque) is produced by the tendency of existing fields in the stator and rotor to align its magnetic axes (Answer 3). The air gap torque can be calculated according to where v ca and v ab are the voltages between phases, i a and i b are the two-line currents, r is the resistance of the stator winding and p is the number of poles of the motor. This equation is valid for a three-phase IM connected in a Y configuration and not connected to the neutral, or in a delta configuration using three wires. During the conversion of electrical power into mechanical power, losses occur. Some losses can have tabulated values, for instance, the additional losses (stray load losses) L ar , which are losses associated with the construction flaws of the machine, and the mechanical losses L mec , which are caused by mechanical contact opposed to the movement of the rotor, as shown in Table 1 [5,7]. Table 1. Additional and mechanical losses in the induction motors (IM) [4,6]. Therefore, it is possible to obtain the torque in the motor shaft given as

Nominal Power (kW) Additional Losses (% of Nominal) Mechanical Losses (% of Nominal)
where ω is the angular speed (in rad/s). The value of ω can be estimated by processing the current signal in the frequency domain [11] or in the time domain [12]. The output power can be obtained from the speed and torque in the motor shaft. In turn, the input power is obtained from the real-time values of two current sensors and two voltage sensors. With the input and output power, it is possible to obtain the motor efficiency using

Efficiency Estimation from IM Sound Analysis
The method proposed in this study consists of performing the digital processing of the sound signal emitted by an in-service motor. The firmware is fed with the IM nameplate data. First, the shaft rotational speed of the motor is estimated, then the torque, and lastly, the efficiency can be obtained.
The noise of the rotating motor tends to repeat when the engine is kept at a constant speed during a certain time period, originating multiple harmonics in the frequency domain of the shaft rotational speed fr. Therefore, the peaks found by a Fourier Fast Transform (FFT), due to the shaft rotation, are located in multiple frequency components of the rotational frequency, according to where k = 1, 2, 3, .... Figure 1 presents the FFT of a sound signal (highlighted f p frequency peaks) for a motor with a shaft rotational speed close to 30 Hz. As observed, at 30 Hz, the rotation harmonics are not very clear because the frequency is outside the passband of the microphone used.
harmonics of speed in the signal spectrum, as it is illustrated in Figure 1. Thus, it can be affirmed that the harmonic peaks in the spectrum of the speed signal Equation (4) must be in evidence in relation to other noises that were presented, therefore, independent of the motor class or type, the speed is detectable by the proposed method.
The torque can also be estimated by a sound analysis of the three-phase IM, which follows the estimation of the motor shaft rotational speed. The curve of the torque vs. speed relationship illustrated in Figure 2 is linearized to consider two aspects: the first aspect regards the synchronous speed and zero torque, and the second aspect regards the nominal speed and the nominal torque. The information on the synchronous and nominal speeds is obtained from the motor nameplate. Thus, the torque can be estimated using (6) where is the nominal motor power,  is the nominal speed, and  the is the synchronous speed of the three-phase IM.  The shaft rotational speed can be accurately estimated using the weighted average of the frequencies of the 2 nd and 3 rd harmonics, according tô Determining the motor speed from the sound does not depend on the motor type/class. The analysis is carried out in the frequency domain and it is based on the repeatability of the sound emitted by the motor under stationary or quasi-stationary conditions, reflecting on multiple harmonics of speed in the signal spectrum, as it is illustrated in Figure 1. Thus, it can be affirmed that the harmonic peaks in the spectrum of the speed signal Equation (4) must be in evidence in relation to other noises that were presented, therefore, independent of the motor class or type, the speed is detectable by the proposed method.
The torque can also be estimated by a sound analysis of the three-phase IM, which follows the estimation of the motor shaft rotational speed. The curve of the torque vs. speed relationship illustrated in Figure 2 is linearized to consider two aspects: the first aspect regards the synchronous speed and zero torque, and the second aspect regards the nominal speed and the nominal torque. The information on the synchronous and nominal speeds is obtained from the motor nameplate. Thus, the torque can be estimated usingT where P nom is the nominal motor power, nom is the nominal speed, and syn the is the synchronous speed of the three-phase IM. The power obtained in the shaft is the estimated output power P , which can be expressed by P = T  . (7) Based on the estimated output power in the shaft, curves provided by the manufacturer can be used for the in-service motor efficiency estimation. In the absence of data from the motor manufacturer, an alternative method is to use typical efficiency values for motors of the same efficiency category. Studies conducted by [9] with three EFF1 induction motors of 200kW made by different manufacturers show that the discrepancy of the maximum efficiency of the medium curve using the pattern IEEE 112 B is only 0.7% (answer 1). The load (% of output power in relation to nominal power) versus efficiency curve should be previously recorded in the embedded system firmware. Therefore, the value of the online efficiency can be obtained by interpolation from the P value.
Analysis of the temperature behavior of the induction motor under the efficiency estimation was already carried out by previous works. The major part of the effect of the temperature change in three-phase induction motors is due to the Joule effect in the armature resistance of the motor. According to Lee et al. [27], the stator resistance can vary up to 70% of its nominal value, which would impact in about 4.5% of the final efficiency value for the case of the motor used in the experiments calculated using Equations (1)-(3). The proposed method does not perform temperature compensation since it would increase the invasiveness level and the loss of the portability of the technique, as there is a need to install at least one remote sensor.

Sound Acquisition System
The sound signal emitted by the motor was acquired with an embedded system substantially composed of an Arduino DUE development platform and a CMA-4544PF-W analog microphone electret condenser, as shown in Figure 3. The Arduino DUE platform is formed by a 32-bit ARM microcontroller with an adjustable acquisition frequency, where a sampling frequency of 44.1 kHz was established for this experiment. The CMA-4544PF-W microphone is an omnidirectional microphone with a 44 dB sensitivity and an operational frequency range from 20 Hz to 20 kHz. This dispositive is highly sensitive to noises close to the source and avoids the ones that are far from it. In the tests that were carried out, positioning the dispositive close to the place where the motor is set up, the surrounding noises did not interfere in the system's accuracy, since spurious emissions of high intensity were not found in the signal spectrum.  The power obtained in the shaft is the estimated output powerP out , which can be expressed bŷ P out =Tω.
Based on the estimated output power in the shaft, curves provided by the manufacturer can be used for the in-service motor efficiency estimation. In the absence of data from the motor manufacturer, an alternative method is to use typical efficiency values for motors of the same efficiency category. Studies conducted by [9] with three EFF1 induction motors of 200kW made by different manufacturers show that the discrepancy of the maximum efficiency of the medium curve using the pattern IEEE 112 B is only 0.7% (answer 1). The load (% of output power in relation to nominal power) versus efficiency curve should be previously recorded in the embedded system firmware. Therefore, the value of the online efficiency can be obtained by interpolation from theP out value.
Analysis of the temperature behavior of the induction motor under the efficiency estimation was already carried out by previous works. The major part of the effect of the temperature change in three-phase induction motors is due to the Joule effect in the armature resistance of the motor. According to Lee et al. [27], the stator resistance can vary up to 70% of its nominal value, which would impact in about 4.5% of the final efficiency value for the case of the motor used in the experiments calculated using Equations (1)-(3). The proposed method does not perform temperature compensation since it would increase the invasiveness level and the loss of the portability of the technique, as there is a need to install at least one remote sensor.

Sound Acquisition System
The sound signal emitted by the motor was acquired with an embedded system substantially composed of an Arduino DUE development platform and a CMA-4544PF-W analog microphone electret condenser, as shown in Figure 3. The Arduino DUE platform is formed by a 32-bit ARM microcontroller with an adjustable acquisition frequency, where a sampling frequency of 44.1 kHz was established for this experiment. The CMA-4544PF-W microphone is an omnidirectional microphone with a 44 dB sensitivity and an operational frequency range from 20 Hz to 20 kHz. This dispositive is highly sensitive to noises close to the source and avoids the ones that are far from it. In the tests that were carried out, positioning the dispositive close to the place where the motor is set up, the surrounding noises did not interfere in the system's accuracy, since spurious emissions of high intensity were not found in the signal spectrum. It should be emphasized that the acquisition system was developed because the commercially available smartphones do not have the sensitivity for low-frequency sounds that is required for this type of application.

Method Description
The proposed method works according to the flowchart in Figure 4. The acquired sound signal is subjected to the FFT. Next, the frequencies of harmonics 2 and 3 of the sound signal are detected, and the shaft speed is estimated through Equation (5). Then, the torque is calculated with Equation (6), using the motor nameplate data uploaded to the embedded system firmware. The output power in Equation (7) is estimated from the estimated torque. With the data from the load versus efficiency curve present in the firmware, it is possible to obtain the efficiency by numeric interpolation. For the performed experiments, the peaks related to the harmonics of rotation of the motor for the sound signal were in evidence in relation to the others in the range (see Figure 1). Using Equation (5), it was possible to estimate the speed with accuracy for 100% of the cases. The peaks that will be detected are the ones close to the multiples of the nominal speed of the rotor within the slip range. Interferences with the harmonics of the same amplitude in the frequency range of the motor can It should be emphasized that the acquisition system was developed because the commercially available smartphones do not have the sensitivity for low-frequency sounds that is required for this type of application.

Method Description
The proposed method works according to the flowchart in Figure 4. The acquired sound signal is subjected to the FFT. Next, the frequencies of harmonics 2 and 3 of the sound signal are detected, and the shaft speed is estimated through Equation (5). Then, the torque is calculated with Equation (6), using the motor nameplate data uploaded to the embedded system firmware. The output power in Equation (7) is estimated from the estimated torque. With the data from the load versus efficiency curve present in the firmware, it is possible to obtain the efficiency by numeric interpolation.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 12 It should be emphasized that the acquisition system was developed because the commercially available smartphones do not have the sensitivity for low-frequency sounds that is required for this type of application.

Method Description
The proposed method works according to the flowchart in Figure 4. The acquired sound signal is subjected to the FFT. Next, the frequencies of harmonics 2 and 3 of the sound signal are detected, and the shaft speed is estimated through Equation (5). Then, the torque is calculated with Equation (6), using the motor nameplate data uploaded to the embedded system firmware. The output power in Equation (7) is estimated from the estimated torque. With the data from the load versus efficiency curve present in the firmware, it is possible to obtain the efficiency by numeric interpolation. For the performed experiments, the peaks related to the harmonics of rotation of the motor for the sound signal were in evidence in relation to the others in the range (see Figure 1). Using Equation (5), it was possible to estimate the speed with accuracy for 100% of the cases. The peaks that will be detected are the ones close to the multiples of the nominal speed of the rotor within the slip range. Interferences with the harmonics of the same amplitude in the frequency range of the motor can For the performed experiments, the peaks related to the harmonics of rotation of the motor for the sound signal were in evidence in relation to the others in the range (see Figure 1). Using Equation (5), it was possible to estimate the speed with accuracy for 100% of the cases. The peaks that will be detected are the ones close to the multiples of the nominal speed of the rotor within the slip range. Interferences with the harmonics of the same amplitude in the frequency range of the motor can occur, as in the other methods based on the FFT, but these phenomena were not observed in the tests.
The proposed system would need adaptation in the case of IM powered by speed drives; however widely used machines, including centrifugal pumps, compressors, and fans, are powered directly from the mains, because they do not require a wide adjustment range, high starting torque, or high speed [2], allowing the proposed system to reach a wide range of industrial applications. Figure 5 shows the experimental laboratory workbench used for the measurement and estimation of the speed, torque, and efficiency. It is essentially composed of one three-phase IM (manufacturer WEG, model W22 Plus, nominal power 5 HP, nominal rotation of 1725 rpm) (1), the function of which is to provide torque to the set; one support with two bearings (2), one torque transducer (3), and one continuous current motor (manufacturer Varimot, model 132S, nominal power 1.48 HP, nominal rotation 1800 rpm) (4), which generates a braking torque in the shaft through a continuous voltage applied via a voltage regulator.

Test Workbench
Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 12 occur, as in the other methods based on the FFT, but these phenomena were not observed in the tests.
The proposed system would need adaptation in the case of IM powered by speed drives; however widely used machines, including centrifugal pumps, compressors, and fans, are powered directly from the mains, because they do not require a wide adjustment range, high starting torque, or high speed [2], allowing the proposed system to reach a wide range of industrial applications. Figure 5 shows the experimental laboratory workbench used for the measurement and estimation of the speed, torque, and efficiency. It is essentially composed of one three-phase IM (manufacturer WEG, model W22 Plus, nominal power 5 HP, nominal rotation of 1725 rpm) (1), the function of which is to provide torque to the set; one support with two bearings (2), one torque transducer (3), and one continuous current motor (manufacturer Varimot, model 132S, nominal power 1.48 HP, nominal rotation 1800 rpm) (4), which generates a braking torque in the shaft through a continuous voltage applied via a voltage regulator. The reference values for the speed and torque were collected by direct measurement using a digital tachometer and a torque transducer, respectively. These values were compared to the estimated speed and torque values to validate the proposed method.

Test Workbench
To measure the torque, an HBM T40B-200 torque transducer with flange coupling, nominal torque capacity of 200 Nm, 0.05% full-scale accuracy, and torque measurement capability at rotations up to 20,000 rpm was used. The speed measured directly at the motor shaft was obtained using a Minipa optical tachometer model MDT-2238B, which can operate in two ways: by contact and by photodetection. Due to the unfeasibility of using the contact mode, the optical reading mode was selected. In the photo mode, the measurement can be performed in the range of 2.5 to 100,000 rpm at a detection distance between 50 and 500 mm. Figure 6 presents the scheme of the workbench with controllable torque with all the components involved in the process, from the activation of the IM to the control of the load applied in the shaft by the DC motor, with data collection performed by a personal computer (PC) via a Universal Serial Bus (USB) connection plugged into the DAQ. The bench components are: (1) variable transformer, (2) rectifier, (3) tachometer, (4) direct current generator, (5) torque transducer, (6) IM, (7) current transformers (CTs), (8) power transformers (PTs), (9) AC speed driver, (10) signal conditioning, (11) acquisition system, (12) notebook, (13) DAQ USB-6215, and (14) resistor bank. The reference values for the speed and torque were collected by direct measurement using a digital tachometer and a torque transducer, respectively. These values were compared to the estimated speed and torque values to validate the proposed method.
To measure the torque, an HBM T40B-200 torque transducer with flange coupling, nominal torque capacity of 200 Nm, 0.05% full-scale accuracy, and torque measurement capability at rotations up to 20,000 rpm was used. The speed measured directly at the motor shaft was obtained using a Minipa optical tachometer model MDT-2238B, which can operate in two ways: by contact and by photodetection. Due to the unfeasibility of using the contact mode, the optical reading mode was selected. In the photo mode, the measurement can be performed in the range of 2.5 to 100,000 rpm at a detection distance between 50 and 500 mm. Figure 6 presents the scheme of the workbench with controllable torque with all the components involved in the process, from the activation of the IM to the control of the load applied in the shaft by the DC motor, with data collection performed by a personal computer (PC) via a Universal Serial Bus (USB) connection plugged into the DAQ. The bench components are: (1) variable transformer, (2) rectifier, (3) tachometer, (4) direct current generator, (5) torque transducer, (6) IM, (7) current transformers (CTs), (8) power transformers (PTs), (9) AC speed driver, (10) signal conditioning, (11) acquisition system, (12) notebook, (13) DAQ USB-6215, and (14) resistor bank.
For the shaft torque estimation using the air gap method, the voltages V ab and V ca were measured using a grain-oriented transformer, and the currents I a and I b were obtained using ACS712ELCTR-20A Hall effect sensors manufactured by Alegro. The signal from these sensors go through signal conditioners connected to an NI DAQ 6215 acquisition system manufactured by National Instruments, and the data are stored in a PC for analysis. In the experiments, the acquisitions in the workbench are performed simultaneously with the sound acquisition system developed in this study. Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 12 For the shaft torque estimation using the air gap method, the voltages and were measured using a grain-oriented transformer, and the currents and were obtained using ACS712ELCTR-20A Hall effect sensors manufactured by Alegro. The signal from these sensors go through signal conditioners connected to an NI DAQ 6215 acquisition system manufactured by National Instruments, and the data are stored in a PC for analysis. In the experiments, the acquisitions in the workbench are performed simultaneously with the sound acquisition system developed in this study.

Results
For the experiments, the tests were performed in the IM through direct start-up activation; a torque scale was used with values ranging from 0 to 24 Nm. For each performed test, a constant load was applied to the system. The load is applied to the shaft through the variation of the field circuit voltage of the DC generator. For each load value, the shaft rotational speed of the motor was measured, and the line current values ( , ), the voltages between phases ( and ), the transducer torque signal and the sound signal emitted by the workbench set were acquired. Figure 7 displays a graph of the estimated speed from the sound, the measured speed, and the relative error between the two. In this case, the mean relative error between the two curves was 0.02%.

Results
For the experiments, the tests were performed in the IM through direct start-up activation; a torque scale was used with values ranging from 0 to 24 Nm. For each performed test, a constant load was applied to the system. The load is applied to the shaft through the variation of the field circuit voltage of the DC generator. For each load value, the shaft rotational speed of the motor was measured, and the line current values (I a ,I b ), the voltages between phases (V ab and V ca ), the transducer torque signal and the sound signal emitted by the workbench set were acquired. Figure 7 displays a graph of the estimated speed from the sound, the measured speed, and the relative error between the two. In this case, the mean relative error between the two curves was 0.02%. The graph in Figure 8 presents the measured torques, the torques estimated from the sound, and the torques estimated by the AGT for different loads applied to the shaft. A deviation of the reference torque is observed in the low-slip region. For a load approaching zero, the absolute error for the estimation through the sound (proposed method) was 1.88 Nm, which is 9% of the nominal torque of the motor. The load approaching the nominal torque presented an absolute error of 0.30 The graph in Figure 8 presents the measured torques, the torques estimated from the sound, and the torques estimated by the AGT for different loads applied to the shaft. A deviation of the reference torque is observed in the low-slip region. For a load approaching zero, the absolute error for the estimation through the sound (proposed method) was 1.88 Nm, which is 9% of the nominal torque of the motor. The load approaching the nominal torque presented an absolute error of 0.30 Nm, which corresponds to 1.5% of the nominal torque. The air gap torque method presented an approximately uniform error in relation to the applied loads, with a mean absolute value of 0.26 Nm (1.25% of the nominal torque). The graph in Figure 8 presents the measured torques, the torques estimated from the sound, and the torques estimated by the AGT for different loads applied to the shaft. A deviation of the reference torque is observed in the low-slip region. For a load approaching zero, the absolute error for the estimation through the sound (proposed method) was 1.88 Nm, which is 9% of the nominal torque of the motor. The load approaching the nominal torque presented an absolute error of 0.30 Nm, which corresponds to 1.5% of the nominal torque. The air gap torque method presented an approximately uniform error in relation to the applied loads, with a mean absolute value of 0.26 Nm (1.25% of the nominal torque).  Figure 9 displays the curves obtained for the measured and estimated (sound and AGT) efficiencies. As observed, the sound method (proposed method) fits the measured efficiency curve better than the air gap torque method for loads close to nominal, with a 0.1% error for the nominal load, while the air gap torque method exhibited a deviation of approximately 26% for the load approaching zero and 1% for the nominal load.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 12 Figure 9 displays the curves obtained for the measured and estimated (sound and AGT) efficiencies. As observed, the sound method (proposed method) fits the measured efficiency curve better than the air gap torque method for loads close to nominal, with a 0.1% error for the nominal load, while the air gap torque method exhibited a deviation of approximately 26% for the load approaching zero and 1% for the nominal load. It is noticed in Figure 9 the low accuracy for loads close to 0%, due to the fact that estimating efficiency for very low loads (up to 10% of the nominal power) is a reoccurring problem for noninvasive techniques. From the references utilized in the text, it is noted that [8-10,15,16] do not present results in this power range, from the references in the literature that surveyed curves for this power range [11,13], they show an accuracy similar to the one proposed in this paper.
The proposed method is based on the detection of peaks in the frequency domain of rotational speed harmonics of the motor that differ from the failure peaks in rolling bearings, broken bars, and It is noticed in Figure 9 the low accuracy for loads close to 0%, due to the fact that estimating efficiency for very low loads (up to 10% of the nominal power) is a reoccurring problem for non-invasive techniques. From the references utilized in the text, it is noted that [8][9][10]15,16] do not present results in this power range, from the references in the literature that surveyed curves for this power range [11,13], they show an accuracy similar to the one proposed in this paper.
The proposed method is based on the detection of peaks in the frequency domain of rotational speed harmonics of the motor that differ from the failure peaks in rolling bearings, broken bars, and eccentricity, for example. Then, it is expected that the system works even under the aging process.

Conclusion
The present study conducted analyses to develop and validate a completely non-invasive method to estimate the shaft rotational speed, torque, and efficiency for an in-service IM. The developed sound acquisition system is able to calculate the magnitudes of these values for an in-service motor, performing embedded processing. Several measurements were carried out to validate the proposal through experimental tests on a laboratory workbench, which allowed the comparison of the reference values obtained by instruments with the estimated values for different loads. The proposed method presented a mean relative error of approximately 0.02% for the speed, 1.5% for the torque (nominal load), and 1% for the efficiency (nominal load). Its performance was superior to the AGT regarding efficiency estimation.
Special attention should be drawn to the fact that the results in this study were obtained through tests with direct start-up under static and ideal operational conditions, with the availability of the motor nameplate data and manufacturer information. Field applications require some caution, such as the use of a directional microphone and the confirmation that the target motor in the acquisitions was not rewound.
The proposed system is low-cost, the developed method is completely non-invasive, and high accuracy was obtained for tests performed in the laboratory.
For future works, it is intended to incorporate directional microphones to the portable acquisition system and to use an infrared temperature sensor. Artificial intelligence can be implemented using these new measures to increase efficiency accuracy. It is also intended to test the system in an industrial environment.