Design of a Waste Classification System Using a Low Experimental Cost Capacitive Sensor and Machine Learning Algorithms

Abstract

The management and classification of solid waste is one of the most important challenges worldwide. The objective is to design a basic waste classification system at the source using a low-cost experimental capacitive sensor and machine learning algorithms. For this, two types of sensor models were established (Traditional Model (MT) and Non-Traditional Model (MNT)), which were built with recyclable material and tested with different types of materials, in order to evaluate their behavior and sensitivity level. The results obtained demonstrated that the two sensors responded with acceptable sensitivity levels for each of the materials used as a test; however, the MNT was the one that generated the values with the greatest variability, an aspect that is deemed highly significant, because, thanks to this type of response to various types of materials, it facilitates the classification processes through the use of machine learning algorithms. Finally, the two prototypes of sensors manufactured can be considered of significant relevance for the development of more complex solutions, related to the classification and possible characterization of materials, when compared to the capacitive sensors found on the market, which only then allow us to identify if there is a presence or not of some object through adjustment by potentiometer, generating as a result a digital output. This aspect largely limits the use of commercial capacitive sensors to applications exclusively related to presence or level detection.

1. Introduction

Solid waste management stands among the most pressing global challenges today. The generation of waste has steadily increased, driven by factors such as rapid population growth, accelerated industrialization, and economic development [1]. This trend has given rise to a series of environmental and social problems, particularly regarding public health and the conservation of the natural environment [2]. Proper waste management is essential to mitigate these negative effects, requiring the implementation of efficient processes that encompass waste collection at the source, transportation, treatment, segregation, and final disposal [3]. Developing countries, in particular, face the challenge of optimizing these processes, whose effectiveness largely depends on the knowledge and resources available to the institutions responsible for their implementation [4].

Within the framework of environmental policies, solid waste management holds a fundamental position. Its proper implementation aims not only to reduce environmental impact but also to improve living conditions, prevent public health issues, and promote sustainability [5]. Solid waste classification has gained prominence as a key measure to achieve sustainable economic development goals, reduce poverty, and preserve ecosystems. The adoption of efficient solid waste classification systems is crucial to creating jobs, stimulating the recycling sector, and fostering social well-being [6]. Therefore, efforts must focus on improving waste separation practices at the source, benefiting both the environment and the communities that rely on these economic activities.

Given this scenario, there is a need to develop innovative technologies that optimize waste classification at its origin, enabling a more effective resolution of this issue. With the advancement of emerging technologies such as the Internet of Things (IoT) and Artificial Intelligence, governments worldwide are working toward the creation of “smart cities,” where efficient waste management plays a fundamental role [7]. These technologies have great potential to automate and optimize waste classification processes. However, most solutions developed for waste classification focus on image recognition using techniques such as convolutional neural networks, optical methods, and spectrophotometry, among others. Below are some of the works related to this field:

Machine learning-based systems for specific materials:

• In [8], researchers designed recycling machines equipped with ML to classify glass and plastic bottles. Although effective, these solutions are limited to transparent materials due to the optical properties required for their detection.

Hybrid solutions with spectrophotometry and ML:

• In [9], a study integrated spectrophotometry with ML, achieving high accuracy in waste classification. However, the high cost of implementation makes it difficult to adopt in resource-limited environments.

Classification using convolutional neural networks (CNN):

• In [10], researchers proposed YOLO-Green, a model optimized for real-time detection that classifies waste from images. Although efficient, its performance decreases considerably when processing contaminated waste, a common problem in recycling centers. In [11], researchers developed a system to classify recyclable materials using CNN, achieving an accuracy of 94.5%. However, its implementation depends on expensive machine vision equipment and controlled conditions, which limits its applicability in contaminated environments.

Deep Learning Techniques:

• In [12], researchers propose ConvoWaste, which uses deep neural networks to classify waste into categories such as plastics and metals, achieving an accuracy of 98%.
• In [13], the research proposes an intelligent model to categorize waste using deep learning techniques. AlexNet, DenseNet121, and SqueezeNet have been implemented to perform the classification tasks. The obtained results showed great success in the classification process. DenseNet121 achieved the best performance with a value of 0.9415 in terms of accuracy. However, its reliance on specific databases restricts its generalization to other contexts.

While these methods offer high levels of effectiveness, they often require expensive equipment and are, in many cases, sensitive to the presence of impurities. This makes them unsuitable for environments with high levels of contamination, such as waste collection points, significantly increasing implementation costs and limiting their large-scale adoption.

In this context, the present article proposes an innovative solution through the development of a low-cost capacitive sensor with the capability and sensitivity to facilitate the classification of various types of solid waste at the source, including glass, plastic, metal, and organic waste. This solution utilizes machine learning algorithms, offering an efficient and sustainable alternative to this pressing issue.

2. Materials and Methods

2.1. Solid Waste Classification

The classification or segregation of solid waste is considered by numerous studies as one of the fundamental pillars of the Solid Waste Management System [14]. These wastes are composed of materials, many of which are recyclable, such as paper, cardboard, glass, plastic, rubber, and ferrous and non-ferrous metals, which can be reused in various industrial processes. On the other hand, organic waste has the potential to be transformed for the production of biogas and biofertilizers. However, due to inadequate waste management and incorrect collection practices, common in many cities, serious social, health, and environmental problems have been generated, in addition to economic, resource, and energy losses [15]. As a consequence of this poor management, recycling rates are extremely low and the amount of waste deposited in landfills exceeds their capacity, which negatively impacts society and the natural environment.

When talking about the correct way to separate waste, the method best known and implemented by institutions and at the domestic level is the manual classification method, which consists of depositing waste in different containers. Taking into account their material, this method is supported by pedagogy programs that instruct people on the subject [16]. However, the technology of garbage sorting and environmental monitoring has developed rapidly in recent years, where the combination of the Internet of Things, artificial intelligence and environmental technology has become a trend for solving environmental and social problems. [17].

2.2. Sensors

A sensor is a device that is used to measure or detect a change in the environment or in a physical variable under study, which will deliver an output value under a specific format [18]. An analog sensor produces a voltage or continuous output signal, which is generally proportional to the quantity being measured. Digital sensors, on the other hand, produce discrete digital output signals or voltages that are a digital representation of the quantity being measured. Digital sensors produce a binary output signal in the form of a logic “1” or a logic “0”, (“ON” or “OFF”) or can be represented as a “byte” (8 bits).

2.3. Capacitive Sensor

Capacitive proximity sensors are devices that, without the need for contact, allow the detection of the presence or absence of practically any object regardless of the material (glass, paper, metal, plastic, biological, etc.). They use the electrical property called “capacitance”, where by means of a change in the electric field produced by the object under observation (“dielectric”), it generates a change in the value of the resulting capacitance, thereby facilitating the detection of an object and the possibility of identifying the type of material that composes it [8]. Figure 1 shows the appearance of the capacitive sensor.

When an object is located within the sensitive zone, an alteration of the electric field is produced, varying the resulting capacitance and therefore the frequency of the oscillator. There are two categories of targets that capacitive sensors can detect: the first is conductive and the second is non-conductive. Conductive targets include metal, water, blood, acids, bases, and salt water, among other similar materials. These targets have a higher capacitance and the dielectric strength of the targets is irrelevant [19]. When it comes to metallic elements, the electric field decreases since a phenomenon equivalent to series capacitances occurs.

On the other hand, when dealing with a non-conductive target, it acts as an insulator for the electrode of the sensors. A target dielectric constant, also sometimes called a dielectric constant, is the measure of insulation properties used to determine the sensing distance reduction factor. For non-metallic objects, there is an increase in the electric field due to the increase in the dielectric constant. Capacitive sensors are normally used for the detection of non-metallic materials such as glass, oil, water, cardboard, ceramics, plastic, wood, and paper, among others [20].

Although there are several very high-precision methods for measuring parameters related to magnetic permeability, electrical permittivity, and conductivity of a material, among which microwave measurement methods stand out, these are usually very expensive to implement in materials and equipment, which is why they are not considered suitable for the solution required for the problems associated with the identification of materials for the classification of waste at the source. Given this situation, it is considered feasible to carry out the classification process alternately, using a low-cost sensor, articulated with classification techniques-based machine learning algorithms.

2.4. Design of the Proposed Capacitive Sensors

For the fabrication of the two proposed sensors, recycled aluminum sheets from beer cans were utilized. This material was selected due to its accessibility, reusability, and alignment with the overarching objectives of the project. It is important to note that beer or soft drink cans can be made of either steel or aluminum, depending on the application and the production region, where the availability of these materials may vary. However, in most cases, cans are made of aluminum, as in this study, due to its effectiveness in preserving beverages by protecting them from air, light, and potential contamination risks, including bacteria, viruses, hazardous chemicals, and physical agents.

Moreover, aluminum is an economical and sustainable material, thanks to its high recyclability [21]. Cans are typically coated with a thin layer of paint and plastic. The plastic serves to separate the beverage from the aluminum, preventing chemical reactions between the liquid and the metal or contamination from direct contact. The most common plastics used for this type of coating include polyethylene (PE), polypropylene (PP), polystyrene (PS), polyethylene terephthalate (PET), and polyvinyl chloride (PVC). As an insulating material, plastic possesses a relative electrical permittivity, which directly influences the capacitance value of each sensor.

Table 1. Electrical permittivity values for some types of plastic.

Plastic Type	$\mathbf{Electrical} \mathbf{Permittivity} \mathbf{\left(}{\mathit{\epsilon }}_{\mathit{r}}\mathbf{\right)}$
Polyethylene	2.3
Polystyrene	2.6
Polypropylene	2.2 to 2.6
PVC	2.9
Polyethylene Terephthalate PET	2.8

provides the relative electrical permittivity values for the aforementioned types of plastic [22].

During the construction process of the MT and MNT sensors, a plastic layer (polypropylene) was used as protection against the environment in which they will be used, establishing a value of ${\epsilon }_r=2.6$. In addition, this layer allowed maintaining a constant distance between the plates, avoiding direct contact between them.

2.4.1. Sensor Design MT

This sensor is made up of two concentric plates, where one of the plates is circular with radius a and the other plate has the shape of a circular crown with inner and outer radius b and c, respectively. Figure 2 shows the proposed diagram for the MT sensor, accompanied by the distribution of electrical charges on each of the plates and electric field lines, in order to establish the conditions and key elements for estimating the capacitance value.

For the process to estimate the capacitance value for the MT sensor model, it begins with Equation (1), which corresponds to Gauss’ Law [23], which defines the mathematical expression that allows calculating the electric field (E), by defining a Gaussian surface radius (r) containing the total charge of the capacitor (q) uniformly distributed over the surface area (A) and electrical permittivity $\epsilon (\epsilon ={\epsilon }_o{\epsilon }_r)$.

$$EA={\displaystyle \frac{q}{\epsilon }}={\displaystyle \frac{q}{{\epsilon }_o{\epsilon }_r}}$$

(1)

where

• ${\epsilon }_o:$ Electrical permittivity in a vacuum ($8.85\times {10}^{-12}\left[{\mathrm{C}}^2/\mathrm{N}{\mathrm{m}}^2\right]$)
• ${\epsilon }_r:$ Relative permittivity of the dielectric between the plates of the capacitor.

Solving for the electric field $\left(E\right)$ and replacing the area of the circumference ($A=\pi r^2)$ in expression (1) results in Equation (2):

$$E={\displaystyle \frac{q}{\epsilon A}}={\displaystyle \frac{q}{\epsilon \left(\pi r^2\right)}}$$

(2)

Subsequently, we proceed to define the mathematical expression that allows us to calculate the value of the voltage (V) existing between points a and b. The result of this process is described in Equation (3):

$$\begin{gathered} V=-{\int }_b^{a}E{d}_r=-{\int }_b^a{\displaystyle \frac{q{d}_r}{\epsilon \left(\pi r^2\right)}}=-{\displaystyle \frac{q}{\pi \epsilon }}{\int }_b^a{\displaystyle \frac{d_r}{r^2}} \\ V={\displaystyle \frac{q}{\pi \epsilon }}\left[{\displaystyle \frac{1}{a}}-{\displaystyle \frac{1}{b}}\right]={\displaystyle \frac{q}{\pi \epsilon }}\left[{\displaystyle \frac{b-a}{ab}}\right] \end{gathered}$$

(3)

Finally, the value of the capacitance for the MT sensor ($C_{MT}$) is given by the relationship between the total charge ($q$) and the voltage (V), as presented in Equation (4):

$$C_{MT}={\displaystyle \frac{q}{V}}=\pi \epsilon \left[{\displaystyle \frac{ab}{b-a}}\right]=\pi {\epsilon }_o{\epsilon }_r\left[{\displaystyle \frac{ab}{b-a}}\right]$$

(4)

2.4.2. MNT Sensor Design

This sensor consists of two “E” shaped plates, a design inspired by that of a resistive humidity sensor. In this case, both the area of the plates (${A=A}_1=A_2$) and the number of slots interspersed between them are equal, and are separated by a distance (d). Figure 3 presents the proposed diagram for the MNT sensor, whose parameters are defined by the dimensions a, b, c, and d. Furthermore, illustrates how the positive and negative electric charges are distributed on the plates of the capacitive sensor, showing the electric field lines and their similarity to the model of a parallel plate capacitor, characterized by an area (A) and separation (d).

Therefore, the capacitance value for the MNT capacitive sensor $\left(C_{MNT}\right)$ can be calculated from Equation (5):

$$C_{MNT}={\displaystyle \frac{\epsilon A}{d}}={\displaystyle \frac{{\epsilon }_o{\epsilon }_{r}A}{d}}={\displaystyle \frac{{\epsilon }_o{\epsilon }_r\left[3\left(a-c\right)b+ac\right]}{d}}$$

(5)

3. Results

3.1. Comparative Analysis of Theoretical and Experimental Capacitance for MT and MNT Sensors

In the experiment, a UNI-T UT603 LCR digital capacitance and inductance meter (UNI-T, Shenzhen, China) with a tolerance of 1% was used to determine the capacitance in pF of each of the proposed sensors, considering the conditions and type of waste material.

Figure 4 shows a capacitance value $C_{MT}^{\prime }=21 pF$ delivered by the LCR for the implemented prototype of the MT sensor, when it is free of residues, accompanied by the proposed diagram. From Equation (4), we proceed to calculate the capacitance value $\left(C_{MT}\right)$ according to the sensor dimensions that were considered at the discretion of the researchers for its construction (a = 2.1 cm, b = 2.3 cm, c = 3 cm, and d = 0.2 cm).

$$C_{MT}=\pi {\epsilon }_o{\epsilon }_r\left[{\displaystyle \frac{ab}{b-a}}\right]=17.458 pF$$

(6)

$$e_{abs}=C_{MT}^{\prime }-C_{MT}=3.542\times {10}^{-12}$$

(7)

$$e_r={\displaystyle \frac{C_{MT}^{\prime }-C_{MT}}{C_{MT}}}=0.203$$

(8)

Equations (6)–(8) present the result of this process accompanied by the absolute error ($e_{abs})$ and the relative error ($e_r$) [24] in contrast to the result obtained experimentally, where it can be seen that the theoretical value and the one obtained experimentally are very similar to each other, with reduced error levels taking into account that the capacitance values are of the order of ${10}^{-12}\left(pF\right)$, an aspect that is very common in commercial capacitors, which establish a tolerance value given by the manufacturer and considering that the relative permittivity values of the materials used for the construction of the sensors may vary a little compared to those that were theoretically adopted.

The proposed diagram and the capacitance value of $C_{MNT}^{\prime }=28 pF$ for the implemented MNT sensor prototype, when free of residues, are presented in Figure 5. Using Equation (5), the capacitance value $\left(C_{MNT}\right)$ is determined based on the sensor’s dimensions, which were selected by the researchers during its construction (a = 5 cm, b = 0.9 cm, c = 1.5 cm and d = 0.1 cm).

$$C_{MNT}={\displaystyle \frac{{\epsilon }_o{\epsilon }_{r}A}{d}}=24.5 pF$$

(9)

$$e_{abs}=C_{MNT}^{\prime }-C_{MNT}=3.49\times {10}^{-12}$$

(10)

$$e_r={\displaystyle \frac{C_{MNT}^{\prime }-C_{MNT}}{C_{MNT}}}=0.143$$

(11)

The results of this process are presented in Equations (9)–(11), together with the absolute error ($e_{abs})$ and the relative error ($e_r$) when compared to the results obtained experimentally. It can be observed that the theoretical and experimental values are very similar, as in the previous case, showing low levels of absolute and relative error. From this, it can be concluded that the mathematical expressions proposed for each type of sensor are consistent with the experimental results, which allows establishing a valuable reference point for future research in which it is planned to use any of the proposed models or make modifications regarding their design or dimensions.

3.2. Estimation of the Number of Samples and Analysis of the Information

To carry out the sampling campaigns, the estimation of the sample size required for two independent samples was made, since they are two different sensors (MT and MNT), establishing a power of the test ($\beta =0.9)$, a confidence level of 95% ($\alpha =0.05)$ and an effect size of 0.5 [25]. By using the XLSTAT tool, a minimum size of 85 was obtained as a result for each sample. However, in order to improve accuracy and ensure statistical representativeness, a final size of 100 samples per sensor (MT and MNT) was established.

Additionally, the distribution of the samples was considered uniform for the four types of waste (plastic, glass, metal, and organic), with 25 records per category, establishing an adequate balance in the classification, avoiding biases during the training and testing phase of the machine learning model.

Table 2. Statistical results of capacitance measurements with sensor MT.

Material	Capacitance [pF]
	Mean	Standard Deviation	Confidence Interval (95%)
Plastic	24.680	1.519	(24.084, 25.275)
Glass	25.080	1.394	(24.538, 25.622)
Metal	25.120	1.394	(24.573, 25.666)
Organic	251.120	120.823	(203.757, 298.482)

and

Table 3. Statistical results of capacitance measurements with sensor MNT.

Material	Capacitance [pF]
	Mean	Standard Deviation	Confidence Interval (95%)
Plastic	34.680	1.574	(34.063, 35.297)
Glass	34.880	1.666	(34.227, 35.533)
Metal	31.960	0.934	(31.593, 32.326)
Organic	680.960	324.396	(553.799, 808.120)

show the mean, standard deviation, and confidence intervals for each characteristic, according to the type of material or waste used during the sampling campaign depending on the type of sensor.

Figure 4, Figure 5, Figure 6 and Figure 7 present some of the results obtained during the measurement campaigns, both in the absence of material or waste (Figure 4 and Figure 5), and in the presence of reusable waste such as plastic, glass, and metal, as well as in various types of organic waste. Figure 4 and Figure 6 show some of the results recorded in terms of capacitance using the MT capacitive sensor, registering a value of 21 pF in the absence of material or residue. In turn, values between 22 and 27 pF for reusable materials and values between 80 and 450 pF when dealing with organic waste. On the other hand, Figure 5 and Figure 7 present some of the results in terms of capacitance for the MNT capacitive sensor, registering a value of 28 pF in the absence of material or residue. In turn, values between 31 and 37 pF for reusable materials and values between 150 and 1200 pF when dealing with organic waste.

To visually represent the distribution of data recorded during the sampling campaigns and estimate the variability levels for each type of residue considered as a reference, box plots were generated for each case. These diagrams also aided in evaluating the behavior of the proposed sensors and identifying outliers in the dataset. The results are presented in Figure 8 and Figure 9.

Additionally, the possibility was considered that the size of the sample that was established for the development of the project could have affected in some way the appearance of each of the resulting figures. However, from a practical point of view, according to [26], it is possible to consider that a box plot can be reliable as long as the sample size established for each item is equal to or greater than 20. Taking into account that 25 samples were established for each type of residue, it can be considered that this recommendation is fulfilled and with this the result of each figure can be considered reliable.

Figure 9 and Figure 10 show the box diagrams related to the capacitance [pF] recorded by the MT and MNT sensors. In them it can be seen that the behavior of the capacitance for the readings recorded by the MNT sensor describes a normal distribution for the case of the three types of reusable waste (plastic, glass, and metal), a situation that occurs in a similar way with waste corresponding to glass and metal in the case of the MT sensor. However, for the particular case of plastic in the MT sensor, it describes a positive asymmetry, describing a higher concentration of the values recorded between 50 and 75%.

This is not the case for the organic residues for the two sensors, where a negative asymmetry is observed, thus establishing an indication of a higher concentration of readings for this type of residue between the Q1 and Q2 quartiles, a phenomenon that describes a higher incidence in the MT sensor. In turn, the readings related to plastic for the MT sensor slightly show a higher level of dispersion compared to the readings of the other reusable waste for both types of sensors. Additionally, it can be seen that the values corresponding to the median for the readings recorded by the MT sensor for reusable waste present a common value of approximately 25 [pF] in the three cases, an aspect that occurs similarly for the MNT sensor, where the waste related to plastic and glass describe a median value or Q2 of 35 and for metal, a value of approximately 32. For the particular case of organic waste, approximate values are obtained for the MT and MNT sensors of 200 and 660, respectively, with a higher level of dispersion for the case of the MNT sensors.

The comparative statistical analysis of the MT and MNT sensors reveals significant differences in capacitance measurement for different materials, with the MNT sensor’s performance standing out due to its greater dynamic range. For reusable materials (plastic, glass, and metal), both sensors show relatively homogeneous capacitance values, with similar means and low standard deviations. However, the 95% confidence intervals (CI) of the MNT sensors are slightly wider, which could be attributed to greater sensitivity in the measurement. For example, for glass, the MT sensor presents a CI of (24.538, 25.622), while the MNT sensor widens it to (34.227, 35.533), indicating a shift towards higher capacitance values and a more differentiated measurement between materials.

For organic waste, the superiority of the MNT sensor is evident due to its ability to capture higher capacitance values and greater relative variability, thereby reducing the overlap with reusable materials. The MT sensor records a mean of 251.120 pF with a standard deviation of 120.823 and a wide CI of (203.757, 298.482), while the MNT sensor reaches a mean of 680,960 pF with a standard deviation of 324.396 and a CI of (553.799, 808.120). Not only does this demonstrate that the MNT sensor can more effectively differentiate organic waste from the rest, but its greater dynamic range, as quantified by the ratio of means to standard deviations (coefficient of variation), strengthens its classification capability. In organic waste, the coefficient of variation for the MT sensor is 48.1%, while for the MNT sensor it rises to 47.6%, indicating that, although both present high dispersions, the MNT sensor is more effective in separation thanks to its greater width in the distribution of values.

Capacitance was selected as the sole characteristic for the sorting process due to its high sensitivity to the dielectric properties of materials. This sensitivity allows us to differentiate waste according to its composition in a quantitative way, since organic waste presents significantly higher capacitance values, attributed to its higher dielectric constant and inherent moisture content. In contrast, reusable materials such as plastic, glass, and metal show lower and more homogeneous capacitance values, given their reduced dielectric character. These behavior patterns are clearly evident in the results presented in Figure 8 and Figure 9.

3.3. Comparison of MT Vs. MNT Treatments

In this study, a paired-sample t-test was used due to the characteristics of the experimental design where the capacitance measurements for the MT and MNT sensors were obtained using the same waste samples, which establishes a direct dependency relationship between the observations. This implies that the observations in both groups are not independent, but are directly related, since each pair of data corresponds to the same waste sample evaluated by both sensors.

The paired-sample t-test is appropriate in this case because it evaluates whether the mean of the differences between the measurements of the MT and MNT sensors is significantly different from zero. This approach allows controlling the variability between the samples, focusing only on the differences attributable to the performance of the sensors.

Additionally, although the t-test requires that the differences between pairs follow an approximately normal distribution, this criterion was met after verifying the normality of the data using graphical and statistical methods, ensuring that the results obtained are valid and reliable to establish significant differences between the sensors evaluated.

Since the differences between measurements presented a verifiable normal distribution, the use of the paired t-test was the most appropriate choice, allowing reliable results to be obtained with greater sensitivity to detect significant differences between the sensors evaluated.

Let $X_i$ and $Y_i$ represent the recorded capacitance values (the most relevant characteristic) for MT and MNT sensors, respectively, with $d_i{=X}_i-Y_i$ denoting the difference between the samples. To assess whether the MNT sensor shows superior performance compared to the MT sensor, the following hypotheses are posed:

$$H_o: {\mu }_x\le {\mu }_y$$

$$H_a: {\mu }_x>{\mu }_y$$

where ${\mu }_x$ and ${\mu }_y$ are the means corresponding to the capacitance values obtained during the sampling campaigns for the two types of MT and MNT sensors, respectively. The $H_o$ hypothesis states that MNT is better than the MT and the $H_a$ establishes the opposite condition. To accept or reject the proposed hypotheses, it is necessary to perform a hypothesis contrast on the difference in means with paired sampling, using the so-called paired t-test. For this, the following steps are established [27]:

• Step 1: A new random variable $Z=X-Y$ is defined and the mean value and standard deviation for the variable $Z$ are calculated. The result of this process yielded the values of $-111.28$ and $217.816$ for $\overline{Z}$ and $S_z$, respectively. On the other hand, when defining a new variable Z, it is necessary to make an adjustment in the hypotheses as follows:

  $$H_o: {\mu }_x\le {\mu }_y\to {\mu }_x-{\mu }_y\le 0\to {\mu }_z\le 0$$

  $$H_a: {\mu }_x>{\mu }_y\to {\mu }_x-{\mu }_y>0\to {\mu }_z>0$$
• Step 2: We proceed to calculate the value of the statistic established for the test by using the following expression:

  $$d={\displaystyle \frac{\overline{Z}}{S_z}}\sqrt{n}={\displaystyle \frac{-111.28}{214.816}}\sqrt{100}=-5.180$$

  where d is the value of the statistic and n obeys the number of samples for the two proposed scenarios.
• Step 3: Establish the acceptance range of the $H_o$ for $\left\{t:t<T_{(\alpha ;n-1)}\right\}$ at 5% significance ($\alpha =0.05)$ and $n-1$ degrees of freedom. For the particular case, the value of $T\left(0.05;99\right)=1.6603$, defining the range of acceptance of the $H_o$ between $\left(-\infty ,1.6603\right)$. When evaluating the value of the d statistic, it is observed that it is within the acceptance interval, which is why $H_o$ is not rejected. In view of the above, it is concluded that the sensor supported in the MNT is better than the MT sensor for the proposed scenario, with 95% confidence. Additionally, the MNT sensor describes a higher variance (greater response sensitivity, in the presence of different types of materials and even of the same type) compared to the MT sensor, which is very favorable for the identification and classification of waste or materials.

3.4. Classification of Solid Waste with MNT Sensor Using Machine Learning Algorithms

Among the various machine learning algorithms available, Random Forest was selected for the classification process using the MNT sensor due to its robustness and ability to handle highly variable data. Its ensemble learning approach, combining multiple decision trees, minimizes the risk of overfitting, ensuring stable and accurate predictions even in noisy environments. Furthermore, Random Forest allows the interpretation of feature importance, such as capacitance, facilitating the identification of patterns relevant to waste classification.

While notable differences in capacitance exist between organic and recyclable waste, Random Forest ensures robust and automated classification in cases with smaller dielectric variations or in complex environments with significant data noise. Compared to more advanced algorithms like Support Vector Machines (SVM) or neural networks, Random Forest achieves an optimal balance between accuracy and computational efficiency, making it particularly suitable for resource-constrained deployments.

The training, testing, and validation phases were carried out using the dataset collected during sampling campaigns with the MNT sensor, consisting of 100 records with capacitance (pF) as a feature distributed into two classes: reusable waste (Class 0) and organic waste (Class 1). The data analysis processes were implemented using Python 3.6.3 libraries such as sklearn, matplotlib, pandas, numpy, and scipy, through the Google Colab platform.

For the Random Forest algorithm configuration process, the following parameters were established:

• Number of trees (n_estimators): 100 trees. This value is commonly used as a standard in practical scenarios, and as a recommendation in default configurations of the Scikit-learn library, establishing a balance point between performance and computing time.
• Split criterion: Gini. Used to evaluate the purity of the partitions in each node of the tree.
• Maximum depth (max_depth): No limit. Allowing full growth of the trees and ensuring the capture of complex patterns in the data.
• Minimum leaf sample size (min_samples_leaf): In order to avoid overfitting by reducing variability in the final predictions.

To ensure transparency and minimize experimental errors, the following additional techniques were applied:

• Data normalization: The RobustScaler technique from the sklearn library was used to adjust the capacitance values and mitigate the influence of outliers on the model.
• Data splitting: The dataset was split into 80% for training and 20% for testing using the train_test_split function, using a random seed to ensure reproducibility.

Figure 10 presents the confusion matrix obtained for the Random Forests model, in which there were no false positive or false negative records, correctly classifying the 75 records belonging to Class 0 (reusable waste) and the 25 records of Class 1 (organic waste), demonstrating adequate levels of precision and reliability during the classification process according to the reading made by the sensor. In turn, performance metrics such as accuracy, precision, recall, and F1-score were calculated for the Random Forests model, obtaining a perfect value of 1.0 in all cases. This result reflects optimal performance. Additionally, the absence of overfitting was validated by the consistency of all metrics, thus avoiding relying solely on the accuracy metric, which can be misleading under bias conditions.

Figure 11 presents the graphic validation of the proposed classification model, in which the decision limits used to separate the waste classes can be clearly seen. In turn, the reference line observed horizontally reflects consistent thresholds for the capacitance values corresponding to each type of waste. Finally, for both reusable and organic waste, the capacitance thresholds are in an intermediate tolerance zone, which significantly reduces the risk of incorrect classification when the new data deviate slightly from the values established during the training process.

The MT and MNT sensors, made from recycled materials such as aluminum, represent an economical and sustainable solution compared to commercial sensors. This approach not only significantly reduces production costs but also promotes sustainable practices by incorporating recycled components into their design.

Unlike commercial capacitive sensors, which only provide binary detection (presence or absence), the MT and MNT sensors offer continuous capacitance values, enabling more precise and effective material differentiation. This outstanding capability makes them suitable for applications requiring high classification accuracy, such as the separation of organic and recyclable waste. Additionally, they surpass commercial alternatives based on optical or spectrometry technologies in terms of simplicity and cost.

Another distinguishing feature of the MT and MNT sensors is their sensitivity to dielectric materials, which offers a significant advantage in environments where environmental conditions vary considerably. Unlike commercial optical solutions, which can be affected by external factors such as lighting or dust, the MT and MNT sensors maintain consistent and reliable performance.

These sensors are an innovative and efficient alternative that combine precision, low cost, and sustainability, making them ideal for real-world applications. Their accessible design enhances their feasibility in communities with limited resources compared to advanced technologies that, although precise, require expensive equipment and specialized maintenance. This accessibility also makes them a valuable tool for waste classification at the source, particularly in residential settings, marking a significant difference in waste management and contributing to environmental protection.

Among the limitations identified in the present study is the possibility that the sensitivity of the sensors may be influenced by environmental factors, such as humidity and temperature, which could alter the recorded capacitance values. However, it is reasonable to assume that reusable waste, such as plastics, metals and glass, present significantly lower humidity levels than organic waste, where the humidity concentration could have a more representative impact on the measurements.

Additionally, the long-term durability and scalability of sensors made from recycled materials constitute challenges inherent to any emerging technology. Although these aspects and hypotheses were not analyzed in detail in this manuscript, they do not compromise the validity of the results obtained. This is because the main objective of the study was to demonstrate the technical feasibility of low-cost capacitive sensors and their integration with machine learning algorithms for waste classification.

Although the capacitance values recorded by the sensors are sufficiently differentiable to classify organic and reusable waste without the need to use machine learning algorithms, the inclusion of a classification algorithm such as Random Forest provides significant benefits to the design of the proposed system.

Firstly, it offers robustness against possible fluctuations in capacitance values derived from external factors, such as humidity, variations in temperature, interference from electromagnetic fields generated by nearby devices and other environmental elements. This allows for more accurate classification in real scenarios where operating conditions are often less controlled and data may be affected by noise.

In addition, the implementation of machine learning not only increases the scalability of the system, but also allows integration with more complex datasets, incorporating additional features such as temperature and chemical composition of the waste or historical values. This capability increases the accuracy and adaptability of the model, providing a basis for optimizing both sensor design and classification methodologies in future developments.

From a practical perspective, the use of Random Forest simplifies system automation by reducing the need for human intervention. The model can dynamically adapt to new operating conditions without requiring manual reconfiguration, which is especially valuable in decentralized applications. For example, in communities with limited resources, having a robust and autonomous system is crucial to ensure reliable and continuous performance. In turn, the inclusion of the algorithm contributes significantly to the quantitative and qualitative analysis of the data, improving the reproducibility and validation of the results both in experimental scenarios and in real applications, reinforcing the reliability of the system in line with current trends in the design of smart, sustainable, and scalable technologies.

Finally, these challenges represent clear opportunities for future research, in which controlled tests can be carried out to evaluate the stability of the sensors under variable environmental conditions and to carry out lifespan studies in real application scenarios. In this context, the results presented in this article constitute a fundamental starting point for the advancement of knowledge in this area, providing a solid foundation for future developments that address these limitations with greater depth and rigor.

4. Conclusions

Within the broad spectrum of problems related to environmental protection, solid waste management occupies one of the most important places within environmental management policies, where the main objective is to establish mechanisms that allow this process to be carried out efficiently and in compatibility with the environment and public health. For this reason, the use of technologies such as capacitive sensors and Artificial Intelligence could help to implement economic and efficient solutions that allow the classification of solid waste at the source, minimizing the time necessary for its classification compared to separation process manuals, reduce the health risks that may arise when working with contaminated waste and increase the percentage of waste that can be reused and reprocessed later thanks to the proper separation process. According to the results obtained, the results demonstrated that the two models of capacitive sensors proposed describe an adequate behavior in terms of sensitivity and coherence with the readings registered for each type of material or test residue that was used for its evaluation. However, the MNT sensor model was the one that showed optimal performance in relation to sensitivity and variability for each type of waste, with 95% confidence, allowing waste classification processes through the use of machine learning algorithms. Establishing an economic and reliable alternative for the implementation of this type of solutions at the source and in turn promoting the development of future projects related to the classification of materials in a more selective way, could be oriented to the separation of reusable waste such as glass, paper, plastic, and metal, among others independently or for the specific characterization of materials, with possible industrial applications.