The embedded system performs permanent monitoring of the current to count the amps consumed until the voltage drops to a certain value where the electronic load cannot supply the programmed current or the active battery voltage reaches approximately 10.5 V as a deep discharge. And the charging process starts again to complete a complete cycle. The implemented scheme is shown in Figure 1 (previously developed and published in [19]). In this the electronic load control measures the voltage in a 100 W and 1-ohm resistor connected to the emitter output of the IGBT, the battery current is in proportion to the measured voltage, and when the battery is discharging the voltage between collector and emitter is reduced to keep the voltage in the resistor RL constant and therefore the current through it, also constant, the comparator AO serves as a control element on the voltage of the IGBT gate which at the same time increases or decreases, in the case of discharge, the voltage VCE. The embedded system captures the current and adjusts the op-amp voltages according to the desired current.

Figure 1.

General scheme of the experimental setup [19]

The electronic maintains an almost constant current of around 6 Ah (previously developed and published in [19]) and drops a little at the end of the charge when the measured voltage is approximately 10.5 V. The data is obtained from a data acquisition that consists of an embedded system based on Arduino Nano, with a micro SD storage system and by serial communication on the PC using Matlab®, in addition to a system of voltage divider isolated by operational amplifiers that allow measuring voltages higher than 5 volts and lower than 22 V.

The work that was developed, finally considered the analysis for 6 batteries and 1 additional destroyed new to analyze the initial structure of the electrodes using scanning electron microscopy (SEM), whose maximum initial capacity, when they were new, was 42 Ah, the data acquired through an embedded system and the electronic load designed from an IGBT as a power control element.

100% depth of discharge (DOD) cycles were performed based on 100% discharge when the battery drops to a voltage of 10.5 volts, discharge current was performed at rates of 14.2% of maximum rated capacity, and intercalated discharges of 5% of the nominal capacity to adjust the C20 standard, which is indicated as the maximum charge divided by 20 and which allows the value of the charge to be recorded in the previous charge and discharge cycle at a higher current.

As mentioned before, discharge tests are performed at C3 or 14.2% of the maximum battery capacity. In the case of 42 Ah batteries, the discharge was carried out at 6 A, it should be noted that this relationship is maintained regardless of the state of health (SOH) due to the discharges made in each cycle, the amp count is performed by ensuring of the current in the electronic load through the data acquisition system and using eqs. (1), (2) and (3), the SOC during the load, SOC during the discharge and the SOH are obtained, respectively:

$\begin{array}{cc}\text{SOC}\text{=}{\text{SOC}}_0+\frac{1}{Q_{\max }(k)}{\displaystyle {\int }_0^t\left|I\right|dt}& (1)\\ \text{SOC}\text{=}{\text{SOC}}_0-\frac{1}{Q_{\max }(k)}{\displaystyle {\int }_0^t\left|I\right|dt}& (2)\\ \text{SOH=}\frac{Q_{\max }}{Q_{\max }(k)}& (3)\end{array}$

Where SOC₀ corresponds to the charge that the battery initially had whether it was in the process of charging or discharging, Q_max is the maximum charge of the new battery, and Q_max(k) is the maximum charge after the kth charge-discharge cycle.

Figure 2 (previously developed and published in [19]) shows the internal system of the camera implemented for measuring the transmittance that allows the electrolyte to pass through. This consists of an SHT10 sensor, which is a two-wire interface digital sensor that allows measuring temperature values in the range of 10 °C to 80 °C with a precision of ±0.5 °C, a UVC lamp with a narrow spectral range maximized at 254 nm, a quartz cuvette containing the electrolyte to be measured and a 254 nm UVC sensor. The chamber is closed during measurements. The distance between the lamp and the electrolyte is 0.5 cm and between the electrolyte and the sensor is 1 cm. The transmittance ratio is made by taking as reference the UVC reception of the sensor when it passes through the electrolyte, about the incident signal of the cuvette without the electrolyte.

Figure 2.

Camera for the measurement of UVC 254 nm transmittance [19]

The values of % transmittance and %SOH for all the samples acquired for each of the four cells of the analysed battery (cells 2 to 5) can be seen in Figure 3a and the average of all the measurements of each cell for a SOH, in particular, can be seen in Figure 3b.

Figure 3.

Transmittance % data for each SOH value: Acquired data (a); Averaged data of each cell (b)

The independent variable during data acquisition is %SOH and the dependent variable is % transmittance. Since what is sought is to determine the %SOH from the % of transmittance acquired, a classification method must be sought for the forecast of the SOH that has been given transmittance data. So, grouping the points, without considering that they come from different cells, they are marked on the plane with the independent variable on the x-axis for the % transmittance as shown in Figure 4.

Figure 4.

Experimental data with the change of axes for classification

One of the pattern recognition methods is statistical classification in which the posterior probability (eq. (4) of a sample belonging to a certain class is estimated by evaluating the prior probability of this sample in the process of class segmentation and evaluated according to Bayes's theorem [22] which determines that:

$P({\omega }_i|x)=\frac{P(x|{\omega }_i)P({\omega }_i)}{p(x)}$

The probability of each class defined by P(ω_i|x where x (feature vector), P(x|ω_i) is the prior probability for the data used in training. For example, if there are 2 classes, the total probability is obtained, which depends on the contribution of each class (eq. (5)).

$p(x)={\displaystyle {\sum }_{i=1}^{2}P(x|{\omega }_i)P({\omega }_i)}$

The Bayesian classifier can be set for the two classes as:

The method used for pattern recognition performs better if the appropriate features are chosen, so it is important to represent the data to be analyzed on a feature plane [23]. It implements a univariate and symmetric Gaussian distribution around zero (eq. (6)):

$p(x,x_i)=\frac{e^{\frac{|x-x_i|}{2{\sigma }^2}}}{2\mu {\sigma }_0{}^2}$

Where p(x,x_i) is the probability density and compares it with a Laplacian distribution Figure 5, in which the dotted line is the Gaussian and the upper continuous is the Laplacian signal and between both, the real signal for different levels of the signal analyzed in this case the superficial EMG signals.

The approximation of the signals to a Gaussian distribution rather than a Laplacian one is observed, this phenomenon is repeated for many real phenomena.

Figure 5.

Gaussian and Laplacian distribution

Using a Gaussian distribution for two characteristic axes, the mean, variance, and covariance must be found to determine the line or trend of the data.

Generalization of Gaussian distributions [23] can be rewritten as follows:

$p(x)=\frac{e^{1/2{(x-\mu )}^T{\sum }^{-1}(x-\mu )}}{{(2\pi )}^2{\sum }^{1/2}}$

where μ = E[x] is the mean expected value:

∑ = E[(x - μ)(x - μ)^T] is the covariance matrix

$-=\left[\begin{array}{cc}{\sigma }_1^2& {\sigma }_{21}\\ {\sigma }_{12}& {\sigma }_2^2\end{array}\right]$

Case 1: If σ₁₂ = 0 and σ${\sigma }_1^2={\sigma }_2^2$ grouped data forming a circumference centered on µ;

Case 2: If σ₁₂ = 0 and ${\sigma }_1^2>{\sigma }_2^2$ the data form an ellipse with major axis x₁;

Case 3: If σ₁₂ = 0 and ${\sigma }_1^2<{\sigma }_2^2$ the data form an ellipse with major axis x₂;

Case 4: If σ₁₂≠0 and ${\sigma }_1^2>{\sigma }_2^2$ the data form an ellipse with major axis forming an angle between x₁ y x₂.

The process of charging and discharging in the battery causes its electrodes to undergo structural changes due to the accumulation of lead sulfate that cannot be released, exhausting the effective area of the plates that act as anode and cathode. Especially an accumulation of lead sulfate is observed in the spongy lead plates that serve as the anode and that when they are not in use, they present a micrometric structure (scale of 10 μm) like the one seen in Figure 6a and the structural change with use when the battery has depleted 70% of its initial capacity Figure 6b, recorded by an Scanning electron microscopy (SEM).

Figure 6.

Battery electrode structural changes recorded by SEM: New battery (a); Battery with 70% of use (b)

Although the electrolyte presents a visual change due to the detachment of the electrode particles, these remain at the bottom of the battery due to their density, leaving the electrolyte on the surface in a translucent manner. Figure 7a shows a surface electrolyte sample taken from a new battery. Contrasting with Figure 7b in which the surface sample is taken but from a used battery, in a visual approximation no differences between both electrolytes are appreciated, including the battery electrolyte. The new battery Figure 7c, also becomes translucent like the previous ones, the opposite happens with electrolyte taken from the bottom (Figure 7d) of the used battery which is quite cloudy just after it is extracted and it becomes more transparent as solid particles of higher density are precipitated (Figure 7e). For this reason, a non-visual sample analysis method was used and manage a spectral range in which you could appreciate the differences in the surface electrolyte that you have access to without destroying the battery.

Using a UVC sensor outlined in the previous section, it is possible to experiment with samples subjected to a wavelength of 254 nm, passing the light beam through quartz cuvettes such as those in Figure 7, but taking the surface electrolyte and with different levels of SOH.

Figure 7.

Electrolyte tone at the bottom and surface of the battery: New battery surface electrolyte (a); Used battery surface electrolyte (b); New battery bottom electrolyte (c); Used battery bottom electrolyte (d); Same electrolyte of image d, after 5 minutes (e)

Each battery cell delivers a transmittance value that represents a characteristic from the % transmittance to predict the %SOH. This is achieved by segmenting the transmittance for each of the cells analyzed (cells 2 to 5) and being able to generate four transmittance characteristics, which allow the separation between the classes of each interval of the SOH as shown in Figure 8, where for dimensional reasons only cells 2, 3 and 4 are graphed.

Figure 8.

Transmittance in three battery cells grouping different health state ranges

In the end, the Bayesian classifier presents a good classification handling four intervals of transmittance % with only 2, which indicates a correct classification of 98.5%, erroneous samples in the classifier test, as indicated by the confusion matrix in Figure 9, the training time it was 135 seconds. The indices of the confusion matrix (see Table 2) indicate the selected intervals for the %SOH.

Figure 9.

Bayesian classifier confusion matrix