Effective method for screening discharged battery using support vector
machine and high-resolution acoustic analysis
Tomoaki MAGOME(1) and Kan OKUBO(2)(1) Tokyo Metropolitan University, Tokyo, magome-tomoaki@ed.tmu.ac.jp(2) Tokyo Metropolitan University, Tokyo, kanne@tmu.ac.jp

Abstract
Alkaline dry batteries and nickel-metal hydride (NiMH) rechargeable batteries are used worldwide for various
portable devices that require continuous current. Nevertheless, visual verifying such a battery as discharged or
not remains as difficult checking a watermelon for ripeness. Although one can detect a dead battery using a battery indicator, such a useful tool is not always available. Therefore, a simple and intuitive means of ascertaining
whether a battery is dead or not must be found to avoid problems such as battery leakage. In our previous work,
we proposed an acoustic analysis based method for estimating the discharge state of an alkaline dry battery: ahammering test method can screen dead batteries by analyzing the tone color of the tapping sound. In this report, we propose a more effective method and apply it to NiMH rechargeable batteries. To improve the decisionaccuracy, we also employ a support vector machine (SVM) and super high-resolution recording system, which
can obtain sound up to 100 kHz. Our experimentally obtained results suggest that the proposed method canprovide effective screening.
Keywords: Battery, Nondestructive inspection, Hammering sound, inaudible sound, Support vector machine

1INTRODUCTION

In recent years, demands for alkaline dry batteries and rechargeable batteries has increased especially in emerging countries. It is generally difficult, however, to check whether they are dead (less than about 1.0V) or not.
Although we can surely infer their residual quantity if we use a battery indicator, it is an unusual device indaily life. If a dead battery is misapplied, it sometimes causes safety problems such as breakdown of equipment. Therefore, it was necessary to find the simple and intuition way to screen whether present battery is deador not to avoid these problems.
To overcome these problems, in our previous study, we proved that the alkaline dry batteries can be screened
just by tapping them and listening to its sound[1]. However, despite the fact that rechargeable batteries arewidely used all over the world, the method we proposed was not enough effective to screen rechargeable batteries. Thanks to the development information and communication technology in recent years, more devices cananalyze high tone which is hard or impossible for human to hear (it is called “inaudible sound” in this research;generally higher than 20kHz) at a high resolution. For example, some smart phones can record and play sounds
on the 192kHz/24bits system.
In our previous studies, it was found that the more improved sampling rates the less noise floor level, therefore
it is worth analyzing acoustic architecture in high-frequency band that is generally small amplitude with highresolution.
Therefore, we research and analyze hammering sound of rechargeable batteries including inaudible sound toscreen them for finding out dead one by a new procedure. To estimate the possibility of classifying remainof rechargeable batteries using hammering sound, in this study, we evaluated the accuracy of SVM trained byhammering sound of them including inaudible sound.

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Figure 1. (a) Remains of alkaline dry battery can be discriminated by listening its tapping sound; (b) Remainsof NiMH rechargeable battery can not be discriminated by only listening its tapping sounds; (c) It can bediscriminated by classifier which can analyze its tapping soundFigure 2. Details of 768kHz/32bit super-high-resolution recording system

2EXPERIMENTAL METHODS

2.1 Support vector machineSVM) is the one of the classifier which has high classification ability [2, 3, 4, 5]. Define (xxi , yi )i∈[n] as ntrain data, where x i ∈ Rd is d-dimensional real vector and yi ∈ {−1, 1} is label for x i , and decision function asf (xx) = w T x + b. The optimization problem to evaluate classification boundary which is given by f (xx) = 0 is
expressed as:
wk2 +C ∑ ξi
min kw

w ,b,ξξi∈[n]wT x + b) ≥ 1 − ξi , i ∈ [n]s.t.yi (w(1)ξi ≥ 0, i ∈ [n]where ξ indicates the slack variables and C shows regularization parameter which is one of the hyper parametersof this model. Larger C means less classification error and less computational complexity. In case the data has acomplex distribution, data need to be mapped to higher dimensions by kernel function to solve the optimization
problem. To generate simpler model, in this research, homogeneous polynomial function was used as kernel
function which is expressed as:k(xxi , x j ) = γ(xxi · x j )(2)where γ indicates kernel parameter and polynomial order [6]. This is another hyper parameters of this model.
The performance of this model is determined by these two hyper parameters. To find the best hyper parameters,
there are two searching methods: grid search and Bayesian optimization. Grid search is the full search while
Bayesian optimization is the searching method by maximization acquisition function [7]. The model which is2855

trained on each combination of hyper parameters are evaluated by k-fold cross validation. The performanceof the model which is trained on best combination ow hyper parameters is evaluated by how test data set isclassified correctly by this model.
2.2 The super-high-resolution recording system
The details of super-high-resolution recording system are as follows: the system is in the radio/acoustic anechoic room and there is equipment such as the microphone, the amplifier, the A/D converter and the computers
as shown in the figure 2 [8]. The wall of the radio/acoustic anechoic room consist of radio wave absorberand sound wave absorber. These architectures contribute for reducing level of reflections on the wall and avoid
multi-path phasing. Hence purer sound is able to be collected there. The noise floor in this room and indicates that there is about -12 dB at the lowest in analyzable band thanks to the noise shaping. The analyzable
frequency band is from about 20 Hz to about 100kHz because of the nominal value of the microphone in thissystem. Therefore, the system is enough to analyze acoustic structure in inaudible range and high dynamicrange.
2.3 Hammering methods
The hammering test method is one of the non-destructive inspections to judge internal condition by the response generated by hitting with something such as a hummer. In Japan, for example, this method is used formaintaining concrete structure. As a similar example in daily life, whether a watermelon is ripe or not [9] andwhether a clam is dead or not [10] are able to be discriminated by this method.
In our previous works, it was proved that also whether an alkaline dry battery is dead or not can be estimatedby this method because of the fact that physical organization of discharged alkaline dry battery is denser than
not discharged one while they are about same appearance and weight. To avoid mixing excessive sounds when
they are hit each other and to consider practical using, in this study, we compared with the sounds generated
by hitting discharged or not batteries each other.
2.4 Learning and evaluation
We analyzed ten rechargeable batteries as samples. Five of them are fully charged rechargeable batteries (groupF: F0 to F4) and the others are completely discharged ones (group E: E0 to E4). “eneloop (Panasonic)” wasused as sample rechargeable batteries in this research. The hammering sounds of F0 vs. F1 to F4 and E0vs. E1 to E4 were collected for each fifteen times for each combination by hand. The reason why the hammering sounds were collected by hand is to package the classifier as an application in the future. They werestandardized to have same energy; then amplitude frequency characteristics were gotten by FFT. Audible band
(0 to 20 kHz) and inaudible-included band (0 to 100kHz) of these frequency characteristics was separated byeach ∆F kHz, x i20 and x i100 i ∈ [n] were defined as attribute vectors, or train data, given by energy of eachband, where ∆F was shown in Table. The objective SVM model was trained by ten of training data-set of eachbattery (F1 to F4, and E1 to E4) as in the previous section, where both of C and γ were from 10−3 to 103 andwere equally divided into 30 × 30 logarithmic mesh grid, and the model of each point were evaluated by 5-foldcross validation; then the accuracy of obtained model was calculated by using the other five test data-set. Meansquare error (MSE) was chosen as loss function in the optimization as n1 ∑ni=1 (xi − x̂i )2 , where xi is true value
and x̂i is observed value.
Table 1. The relationship between ∆F and x i∆F (kHz)
Dimension of x i20
Dimension of x i100

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0.1
200
1000

0.2
100500

0.25
80
400

0.54020012010021050

4525

54201021020
1550*23RESULT AND DISCUSSION

3.1 Analysis of hammering sound in each state
Figure 3 shows features of examples of hammering sound. It is assumed that it is hard to differentiate theirremain by their hammering sound because frequency-amplitude characteristics of discharged one resembled fully
charged one.
3.2 Relationship between attribute and model’s accuracy
The results of grid search, Bayesian optimization search and confusion matrix which shows the performance ofeach optimized model given by classification of test data-set are shown as figure 4, figure 5 and 6. The following about how to train SVM model which has high generalization ability for screening rechargeable batteries
were found from these figures. First, it was shown in comparing each b-5 and b-9 of figure 4 to 6 that higher
frequency resolution benefits higher generalization ability. Second, it was shown in comparing a-6 and b-6 ofeach figure that training with wider frequency analyzing including inaudible sound benefits higher generalization
ability in condition under the same frequency resolution. Third, it was shown in comparing a-5 and b-5 of eachfigure that if the same dimension attribute vectors were used, high accuracy can be obtained only trained in theaudible range.

4CONCLUSION

In this study, we proved that the residual quantity of rechargeable battery is able to be almost correctly determined by SVM model which is trained by their hammering sound. That is, it was concluded that the classifier
which has high accuracy can be obtained by training the sounds in wide frequency band and high frequency
resolution. Thanks to the development of the information and communication technology, studies of machinelearning for any sound have prospered nowadays. Because of the same reason, the frequency band of recording
and playing devices become wider and wider.
Furthermore, in recent years, the demand for rechargeable batteries has increased in developed countries to solve
environmental problems. Therefore, we believe that this research will be the basis of further research for theclassification method employing high resolution sound and machine learning in the future.

REFERENCES[1] Tomoaki, M.; Kan, O. Quick and Easy Method Using Acoustic Characteristic for Detection of EmptyAlkaline Dry Battery, Proc. Autumn Meeting of the Acoustical Society of Japan, 2018. [in Japanese][2] Ichiro, T.; Masayuki, K., Support Vector Machine, Kodansha, Bunkyo (Tokyo), 2st edition, 2015.
[3] Christopher, M. Bishop, Pattern Recognition and Machine Learning, Springer Science+Business Media,LLC, New York (U.S.A), 8th edition, 2009.
[4] Sergios, T.; Konstantinos, K., Pattern Recognition, Elsevier, Burlington (U.S.A.), 4th edition, 2009.
[5] Nello, C.;John, S., An Introduction to Support Vector Machines and other kernel-based learning methods,Cambridge University Press (U.K.), 2003.
[6] Shotaro, A., Iwanami-shoten, Chiyoda (Tokyo), 5th edition, 2013.
[7] David, B.,Bayesian Reasoning and Machine Learning, Cambridge Univercity Press (U.K.), 5th edition,2014.
[8] Tomoaki, M.; Shuya, O.; Yuka, M.; Kan, O. Evaluation of 768kHz/32bit super high resolution recording
system in radio/acoustic anechoic room, Proc. Autumn Meeting of the Acoustical Society of Japan, 2017,
pp 539-540. [in Japanese][9] Sun, T.; Huang, K.; Xu, H.; Ying, Y. Research Advances in Nondestructive Determination of Internal
Quality in Watermelon/Melon: A Review, Journal of Food Engineering, Vol 100, 2010, pp 569-577.
[10] Horiuchi, T.; Beppu, T.; Fujioka, Y.; Hara, M. Comparison of Pattern Classification Methods in Discrimination of Inferior Shijimi Clams Based on Acoustic Signals, Journal of Japan Society for Fuzzy Thoryand Intelligent Informatics , Vol 20 (5), 2008, pp817-822. [in Japanese]2857

Figure 3. Details of examples of hammering sound: sound pressure signal (top), spectrogram (middle), andamplitude frequency characteristic (bottom). (a-1,2,3) and (b-1,2,3) in the figure show that the result of analysisof the hammering sound of discharged one and charged one2858

Figure 4. The result of grid search of each model. ∆F and D means band width for separating frequency
amplitude characteristics and dimension of attribute vector, x i20 and x i100 i ∈ [n]2859

Figure 5. The result of bayesian optimizatio of each model. ∆F and D means band width for separating
frequency amplitude characteristics and dimension of attribute vector, x i20 and x i100 i ∈ [n]2860

Figure 6. The confusion matrix of each model. ∆F and D means band width for separating frequency amplitude
characteristics and dimension of attribute vector, x i20 and x i100 i ∈ [n]2861