Electrical Signal Characterization of Aloe vera Var. Chinensis Using Non-Parametric and Parametric Signal Analysis

Abstract

Recently, there is a renewed interest from the scientific community in the study of the electrical signal generated by plants due to its wide range of applications in agriculture, for example, environmental monitoring, detection of pests, diseases in crops, etc. Therefore, the aim of this work is to characterize the electrical signal of Aloe vera var. chinensis by using non-parametric and parametric signal analysis techniques, in order to extract some fundamental features which could be used in the design of a bio-dosimeter. Non-parametric analysis of the signal was carried out in the time, frequency, and time-frequency domains, using the short-time Fourier transform (STFT) and the wavelet transform in order to determine the different characteristics and frequency changes over time. Parametric analysis was then performed by using auto-regressive (AR) models for signal prediction and modeling, and in this case the coefficients of the model will be considered as fundamental features to be extracted. It has been identified that the majority of the signal energy is found in low frequencies, possibly associated with physiological processes or changes in the environment. Subsequently, some metrics like mean squared error (MSE), mean absolute error (MAE), and coefficient of determination (R²) were used in order to establish the capability of modeling the signal in its totality, considering that it is affected by the abrupt changes present in the signal. In this way, the relevance of combining both analyses is discussed in order to take their advantages for the benefit of the compression and feature extraction of the electrical signal of Aloe vera var. chinensis. This analysis allows the Aloe vera var. chinensis plant to be used for environmental monitoring, pest and disease detection in crops, or in a pattern recognition and signal classifier systems.

1. Introduction

1.1. Electrical Signal in Plants

In 1973, Burdon Sanderson discovered the transmission of action potentials between cells of Dionaea muscipula [1]. Since then, many studies have been carried out on electrical signals generated by plants. Nowadays, it is known that plant electrical signals are generated by an ionic imbalance. The ions movement generates a potential difference commonly known as voltage [2]. This potential difference is very weak, in the order of millivolts, and is easily affected by the noise of electronic-signal acquisition systems. Electrical signals are the most important physiological responses of plants [3]; they can be generated by different stimuli [4], and abiotic and biotic factors [5]. The electrical response spreads throughout the plant to the different tissues [6], specifically through the xylem and phloem [7]. Electrical signals are classified according to the type of stimulus that causes them, as well as the way in which they propagate in the plant [8]. Different types of electrical signals have been reported in the literature, the most studied are the action potential (AP), the variation potential (PV), and the system potential (SP) [9]. Action potentials (AP) are generated when the plant is exposed to stimuli that do not cause severe damage. Some examples of this type of stimulus are changes in temperature, lighting, and humidity, among others. When this type of signal propagates through the plant, the amplitude of the electrical signal does not decrease [10]. Variation potentials (VP) are signals generated by stimuli considered destructive. Variation potentials (VP) are the signals generated by stimuli that can be considered destructive, for example, a burn caused by fire or crushing, among others. One important characteristic of this kind of signal is that the greater the damage caused to the plant, the greater the traveled signal distance [11].

The system potential (SP) is a signal that is generated when the movement of ions has finished; its activation will depend on the location of the stimulus. For example, if heat is applied to the first leaf of a poplar tree, an SP signal is obtained, while if heat is applied to the fourth leaf, a VP signal is obtained [12]. The study of electrical signals in plants is very broad, since it also depends on the type of plant [13,14], and the type of stress to which the plant is exposed, for example, a hydric stimulus [15]. Further studies should be conducted on the behavior of the electrical signal of plants to take into account its strong randomness and background noise [16].

1.2. The Aloe vera Var. Chinensis Plant as a Biodosimeter

Aloe vera var. chinensis (A. vera) is a plant that presents a stable electrical signal [17]. This makes this plant a valuable proposal as a biodosimeter for environmental monitoring, detection of pests, diseases in crops, etc. Also, A. vera could become an important reference point of information for future research in the study of environmental pollution.

Wang et al. [18] reported the action potential of A. vera appears twice in a period of 500 s, and the time difference between one action potential and another is 260 s while the maximum amplitude recorded is approximately 310 µV. A. vera has shown electrical behaviors that suggest the presence of ion channels and complex bioelectrical responses [19]. Additionally, A. vera exhibits memristor-like behaviors, indicative of the existence of potential difference-activated ion channels, such as K+ channels, that contribute to the plant’s electrical response [20]. These types of behaviors could play a crucial role in the way electrical signals are interpreted and processed [21].

The study of the behavior of the electrical signals of A. vera can be carried out using power-spectrum analysis techniques [19]. Furthermore, using wavelet transform techniques it is possible to perform a more precise characterization of the electrical signal of A. vera. Also, it is possible to model the electrical signals and the functional responses induced in plants by internal processes and external factors, facilitating the identification of changes in the photosynthetic and transpiration activities [22]. These techniques offer a powerful tool for the temporal and frequency analysis of complex bioelectrical signals. The wavelet transform can be combined with auto-regressive models to significantly improve time-series prediction and modeling [23]. The proposed hybrid approach integrates the WSARIMA model with the wavelet transform, achieving greater accuracy in the prediction of the time-series.

Shuang [24] used the wavelet transform to eliminate the noise in the electrical signals of A. vera, improving the signal-to-noise ratio and allowing a clearer interpretation of the data obtained.

In addition, Lanio and other authors [25,26] deepened the understanding of the bioelectrical mechanisms of A. Vera, and Liu [27] decomposed the electrical signal into fundamental components, facilitating the identification of patterns and the modeling of its dynamic behavior over time.

Finally, these features allow the development and training of algorithms for the classification of stimuli related to the environment. For example, the identification of electrical signal characteristics to classify external stimuli such as ozone [28], the classification of chemical agents present in plants using four different curve fits, using the coefficients of each fit [29], and the classification of different tobacco plants contaminated by different concentrations of mercury using principal component analysis (PCA) [30]. Based on all the above analysis, it is possible to propose the A. vera plant as a possible natural biodosimeter.

This paper proposes the use of non-parametric and parametric signal analysis techniques for the characterization and modeling of the electrical signal of the A. vera plant under ideal (laboratory) conditions, as a preliminary study in environmental monitoring. The proposed technique is able to deal with the non-linear, non-stationary, and random with low-frequency characteristics [31]. The wavelet transform was used to determine the behavior of the signal in the time-frequency domain. Subsequently, the use of auto-regressive (AR) models was also implemented to perform signal modeling and prediction. Finally, a comparative of the advantages when using these approaches in the characterization and modeling of this type of electrical signal is discussed. In order to evaluate the effectiveness of methods, metrics such as mean square error (MSE), mean absolute error (MAE), and coefficient of determination (R²) were used, for example, a coefficient of determination of 0.98 was calculated when using the inverse wavelet transform for a particular wavelet function.

2. Materials and Methods

Aloe vera var. chinensis (A. vera) was selected as an object of study for the characterization of electrical signals due to several reasons that differentiate it from other plant species. First, its high sensitivity to external stimuli allows the generation of clear and reproducible electrical signals, which facilitates their analysis and extraction. These characteristics are particularly useful in studies focused on early pest detection and environmental monitoring. In addition, A. vera is a resistant and adaptable plant in arid regions where growing conditions are adverse due to limited availability of water resources, extreme temperatures, and poor soils. These factors make it an optimal model for evaluating electrical signals under environmental stress conditions. Compared to other species such as Arabidopsis thaliana or Phaseolus vulgaris, A. vera offers a significant advantage by requiring less control in its cultivation and growth environment, which allows studies to be conducted in both laboratory and field conditions. The availability of A. vera and its low unit cost represent another important advantage. This plant is widely cultivated and accessible, which allows prolonged experimental studies to be carried out with limited economic resources, in contrast to species that require more specialized conditions. Additionally, A. vera possesses biochemical properties that influence its physiological responses, allowing correlating these with the patterns of its electrical signals [17].

In order to carry out the analysis of the electrical signal of the A. vera plant, the signal acquisition tools and the plant characteristics were established. Subsequently, the conditions to measure the signal were established too. Finally, some different numerical analyses for signal characterization and modeling were performed.

2.1. Measurement Method and Test Plant

For signal measurement, a BL-420E bioengineering test system from Chengdu Taimeng Science and Technology Limited, Chengdu, China, was used. Two electrodes were inserted. The first one was placed on the A. vera leaf, near the stem, approximately 1 cm apart. The second one was inserted into the same leaf of the plant, near the leaf tip. The distance between the electrode tips was 10 cm. The penetration of the electrodes was parallel to the blade with a slight inclination of 25 degrees. With a depth of approximately 0.3 cm. The configuration described is based on two relevant aspects for this work: the protocols and recommendations made by previous studies, as well as the benefit of using the electrode insertion technique in comparison with other types of measurement methods mentioned in the literature [9,31].

In preliminary studies, it was observed that electrodes placed closer to points of high physiological activity (e.g., the vascular system or areas of active transport) record higher amplitude signals, suggesting a better electrical signal response [32].

A. vera plants grown in a laboratory in Zacatecas, Mexico, were used. A total of 15 plants with similar characteristics were used. Since the plants came from the same lot and were under homogeneous conditions (temperature, humidity, light, etc.), the expected variability was low. This allowed a smaller sample size to be used without compromising representativeness. According to a rule of thumb in experimental biology, a sample size larger than 10 per group is usually acceptable for preliminary studies [33]. The mean height is approximately 40 cm. The size of the leaves measures were between six centimeters and eight centimeters long and from three centimeters to four centimeters wide. They were uniform green color, without any evident alteration. A plant with ideal characteristics was selected.

2.2. Signal Acquisition Conditions

Once the plant was selected and the system for signal acquisition was installed, measurements were obtained during periods of 1200 s. The signal was then recorded every 1 millisecond. The environmental conditions at the time of measuring the signal indicated a temperature of 26.6 °C, with a relative humidity of 48%, a light intensity of 323 lux inside the laboratory, an atmospheric pressure of 1004.8 hPa, and a wind speed 0.2 m/s.

2.3. Non-Parametric Signal Analysis

2.3.1. Time Domain Analysis

The first step in the study of the electrical signal is to perform a time domain analysis of the signal. Through this analysis, different statistical characteristics of the signal were obtained such as mean, maximum, minimum, peak to peak, variance, and the number of zero crossings. This last one was determined by counting how many times the signal crosses the mean value in its oscillations throughout the measurement time period. The use of these metrics allowed us to obtain a first description of the electrical signal.

2.3.2. Frequency Domain Analysis

In the first instance, to determine the global frequency variability the fast Fourier transform (FFT) was implemented, which highlighted the fundamental frequencies of the signals.

In the second instance, given the limitations of the use of the FFT, the short-time Fourier transform (STFT) was implemented to obtain a better resolution of the power spectrum. Equation (1) defines the discrete short-time Fourier transform.

$$\mathrm{X}\left(\mathrm{m},\mathsf{\omega }\right)={\sum }_{n=-\infty }^{\infty }x\left[n\right]\mathsf{\omega }[\mathrm{n}-\mathrm{m}]e^{-jwn}$$

(1)

where X(m, ω) is the STFT of the signal, x[n] is the input signal in the time domain to be analyzed, w[n − m] is a scrolled window centered on n = m, e^−jωn is the exponential term of the Fourier transform, m represents time, and ω represents the frequency.

This technique allows the observation of the power spectrum and the characteristics of the frequency behavior of the signal. It is important to note that this analysis is limited due to the linear and non-stationary nature of the signal [7]. The reason for implementing the STFT is due to its advantage in its use for analysis of non-stationary signals, where the frequency characteristics are changing over time, compared to other techniques used such as the fast Fourier transform (FFT). Python version 3.12.4 was used to implement the STFT, using libraries such as Numpy and SciPy. The short-time Fourier transform (STFT) implementation with a Hamming window of 25 samples was a carefully justified choice based on the signal characteristics and the purpose of the analysis. The sampling period (${\mathrm{T}}_{\mathrm{s}}$) was defined as ${\mathrm{T}}_{\mathrm{s}}=1/{\mathrm{f}}_{\mathrm{s}}$, where ${\mathrm{f}}_{\mathrm{s}}$ is the sampling frequency of the system. For a typical sampling of ${\mathrm{f}}_{\mathrm{s}}=1000 \mathrm{H}\mathrm{z}$, the sampling period would be as ${\mathrm{T}}_{\mathrm{s}}=1$ ms, which corresponds to a total window width of 25 ms. The Hamming window was selected because of its ability to reduce discontinuities at the edges of the windows, thus minimizing the effect of spectral leakage. Additionally, the 90% overlap between windows ensures continuity in the temporal analysis, improving the fidelity of the resulting spectrogram.

2.3.3. Time-Frequency Domain Analysis

The analysis of the electrical signal of the Aloe vera var. chinensis (A. vera) in the time-frequency domain was carried out using the wavelet transform. This mathematical tool allows decomposing signals in terms of scale and time, providing a more detailed representation than traditional transforms such as the Fourier transform. Equation (2) defines it as:

$$W_{\psi }(a,b)=\sum _{n=-\infty }^{\infty }x\left[n\right]{\psi }_{a,b}[n]$$

(2)

where W_ψ(a,b) is the wavelet coefficient, x[n] is the input signal in the time domain, ${\psi }_{a,b}\left[n\right]={\displaystyle \frac{1}{\sqrt{a}}}\psi \left({\displaystyle \frac{n-b}{a}}\right)$ is the scaled and translated wavelet function, a is the scale parameter, b is the translation parameter, and ψ is the mother wavelet function.

In this work, different configurations of wavelet functions and decomposition levels were tested to identify the optimal combination to represent the signal properties. Four wavelet functions were selected: “db3”, “sym4”, “coif1” and “haar”. These functions have specific frequency-time domain localization properties, which make them suitable for different signal characteristics. “db3” is ideal for capturing smooth transitions and complex patterns, while “sym4” offers a symmetry that makes it suitable for continuous signals. On the other hand, “coif1” specializes in detecting transient events, and “haar” is efficient for representing abrupt changes. These wavelet functions were combined with four levels of decomposition (4, 5, 6, and 8), exploring a wide range of scales, from high frequencies, associated with fast events, to low frequencies, reflecting global characteristics of the signal. The signal was normalized by dividing each value by the absolute maximum. Subsequently, TWD was carried out. Two metrics were calculated to evaluate the quality of each combination of wavelet function and decomposition level: total energy and entropy. Total energy measures the amount of information captured by the coefficients, while entropy reflects how this energy is distributed among the levels, indicating the degree of concentration or dispersion of information. The development was carried out in Python 3.12.4 and the PyWavelets library has been used [13].

2.4. Parametric Signal Analysis

Non-parametric analysis of the electrical signal using the wavelet transform allowed us to understand the different frequency characteristics and how they vary over time. This is useful to determine key transient patterns of the signal that could indicate specific physiological responses of the plant. But just as non-parametric analysis presents advantages in the study of the signal, exploring parametric approaches allows us to obtain compact and mathematical representations of the signal behavior.

2.4.1. Auto-Regressive Models

In order to carry out a parametric analysis, the auto-regressive (AR) models were implemented; these models are mathematically defined by Equation (3) as follows:

$$x_t={\mathsf{\varphi }}_1{x}_{t-1}+{\mathsf{\varphi }}_2{x}_{t-2}+\dots +{\mathsf{\varphi }}_p{x}_{t-p}+{\epsilon }_t$$

(3)

where x_t is the value of the time-series in time t, ϕ₁, ϕ₂,…, ϕ_p are the parameters or coefficients of the AR model, p is the order of the AR model indicating how many past values are used to predict the current value, and ε_t is the error term at time t which is generally assumed to be white noise with zero mean and constant variance. In this context, the electrical signal of Aloe vera (L.) Burm. f. is characterized as non-stationery and time-dependent, with dynamics that include both slow processes and rapid fluctuations. The use of a model of order p allowed for capturing of the temporal relationships without overfitting the model. The model order (p = 9) was determined experimentally, evaluating different orders and selecting the one that minimized evaluation metrics.

The objective is to capture the linear dependencies present in the A. vera electrical signal. The AutoReg function of the statsmodels library in Python version 3.12.4 was used to fit the AR model. The model was evaluated using various delays to identify the optimal number of delays that minimizes the mean squared error (MSE). The parameters of the AR model were estimated using the Yule-Walker method. The AR model equation was constructed from these parameters, obtaining a mathematical model.

In addition, based on MSE, the best model was determined considering a balance between accuracy and computational complexity. This is common in practical applications (as in this study), where a more compact model may be preferred even if it is not optimal in absolute terms of error.

2.4.2. Inverse Wavelet Transform vs. AR Model

The comparison between the signal reconstruction using the inverse wavelet transform (IWT) and the signal prediction using the mathematical model obtained from auto-regressive models is necessary to complement each other and determine a better characterization and modeling of the A. vera plant signal. To evaluate the effectiveness of both methods, metrics such as mean square error (MSE), mean absolute error (MAE), and coefficient of determination were obtained and are shown in Section 3 (see

Table 1. Statistical characteristics of the electrical signal.

Metrics	Result	Interpretation
Average value	202.73 mv	Basal signal level, reflects a stable state.
Maximum	426.53 mv	Highest value recorded, possibly associated with peak stimuli or activity.
Minimum	150.44 mv	Lowest value recorded, indicating a significant reduction in electrical activity.
Peak to Peak	276.09 mv	Amplitude of electrical oscillations.
Variance	127.37 mv2	Moderate spread in values, reflecting variability in electrical activity.
Zero crossings	504	Frequency of oscillations around the basal value, associated with continuous biological processes.

and

Table 2. Total energy and entropy summary with different mother wavelet functions and levels.

Wavelet Function	Levels	Total Energy	Entropy
db3	4	0.56255	1.14681
	5	0.75573	1.42209
	6	0.78814	1.53511
	8	0.82243	1.66137
sym4	4	0.56547	1.12940
	5	0.73798	1.40917
	6	0.79386	1.56462
	8	0.82074	1.67903
coif1	4	0.46344	1.10881
	5	0.76798	1.34070
	6	0.79133	1.43419
	8	0.82455	1.55817
haar	4	0.68952	1.13347
	5	0.72427	1.27161
	6	0.78246	1.44183
	8	0.82589	1.60776

).

3. Results and Discussion

Based on the methodology described in the previous section, different results were obtained, as described below.

3.1. Case of Non-Parametric Analysis

Figure 1 shows the electrical signals collected from 15 plants in the time domain. The signals exhibit similar behavior across all samples, with an average amplitude of approximately 276.09 millivolts, calculated as the mean of the maximum and minimum differences across all signals. The average maximum value observed is 426.53 millivolts, while the average minimum is 150.44 millivolts. The signals generally demonstrate steady fluctuations over time, indicating consistent system responses. Specific time intervals with rapid fluctuations, such as between 300 and 310 s, may reflect biological activity as previously described [13]. Different types of signal acquisition are observed in the literature and most of them coincide with an abrupt change or voltage spike that is characteristic of the electrical signal of aloe vera [16,18].

The statistical parameters obtained, summarized in Table 1, indicate an average signal value of 202.73 mV across all 15 plants, suggesting that the electrical signals oscillated around this level during the measurement period. In contrast to previously reported works, this study increased the number of plants observed; however, they show similar information to that described in the literature [13,16,18]. This consistent behavior across the samples reflects a relatively stable basal state in the electrical activity of the plants, aligning with normal metabolic processes and the controlled environmental conditions under which the experiment was conducted. The extreme values observed were 426.53 mV (maximum) and 150.44 mV (minimum), resulting in an average range of variation of 276.09 mV. These variations reflect the plants’ ability to respond to external stimuli or environmental changes through fluctuations in their electrical signals. The observed amplitude underscores the dynamic nature of the plants’ electrical activity and their biological responsiveness.

This result could be related to bioelectrical phenomena in the cells of the plants, such as ion flows associated with the opening and closing of ion channels in cell membranes. Across the 15 plants, an average variance of 127.37 mV was observed, indicating a moderate dispersion in the values of the electrical signals. This moderate variance, combined with the abrupt fluctuations seen in specific time intervals, supports the hypothesis of active bioelectrical processes occurring during the measurement period. This could be related to the homeostatic regulation of the plant to adapt to small environmental or internal variations. This being one of the main characteristics of the A. vera plant and the reason for selecting it as an object of study in this work. The signals collectively presented an average of 504 crossings by the mean value, indicating a relatively high frequency of oscillations around the basal level. This behavior can be attributed to the continuous electrical activity in the tissues of the plants, likely related to water and nutrient transport processes, as well as electrophysiological responses to external stimuli or the stress induced by the measurement setup. Additionally, the noise introduced by the electronic system is considered a contributing factor. These observations highlighted the need for digital signal processing techniques, such as the wavelet transform and AR Model, to analyze the signals effectively.

To further validate the consistency across the 15 signals, the cosine similarity coefficient was calculated defined by Equation (4).

$$\mathrm{Cosine} \mathrm{Similarity} ={\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{A}}_{\mathrm{i}}·{\mathrm{B}}_{\mathrm{i}}}{\sqrt{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{A}}_{\mathrm{i}}^2}·\sqrt{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{B}}_{\mathrm{i}}^2}}}$$

(4)

where ${\mathrm{A}}_{\mathrm{i}}$ and ${\mathrm{B}}_{\mathrm{i}}$ are the observations of the signals of two plants (vectors A and B). The numerator ${\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{A}}_{\mathrm{i}}·{\mathrm{B}}_{\mathrm{i}}$ is the dot product of the two vectors. The denominator is the product of the norms of vectors A and B.

This metric quantitatively demonstrated that the differences between the electrical signals were minimal, with an average cosine similarity value close to 1 (0.9969 for all 15 plants), reflecting a high degree of similarity among the signals. Based on this result, a single representative signal was selected for subsequent analyses. This approach ensures that the next stages of the study focus on detailed signal characterization without redundant computations, in addition to being a previously proposed approach to validate the similarity between signals [33].

Once the measurements of the electrical signals of the A. vera plant were reproducible, the power spectrum was determined. The power spectrum represented in Figure 2 is characterized by a predominant concentration of energy in the lower frequencies.

As the frequency increases, the power decays rapidly, following a behavior commonly described in the literature. This drop is particularly noticeable up to about 1 Hz. This type of spectrum is similar to that observed in the literature, where due to the very low frequencies, it appears to contain no energy; however, this is a result that indicates that further analysis and other techniques are required [18].

But it can be observed that the power spectrum shown does not adequately reflect the frequency variations in the signal. Then, the implementation of the STFT to obtain a new power spectrum was necessary.

To obtain a better resolution of the power spectrum, the short-time Fourier transform (STFT) was implemented. Figure 3 shows the power spectrum obtained from the signal.

The spectrum shows that most of the signal power is concentrated at low frequencies. However, components at higher frequencies are also observed. This observation led to the analysis and use of the wavelet transform to have a better resolution and compression of the frequency behavior over time.

The main event is observed by sample 200 with an abrupt response of the electrical signal. The concentration of power at low frequencies indicates a low-frequency main component. This may be related to a slow and continuous physiological process in the plant, such as the transport of nutrients through the xylem or the maintenance of cell turgor under controlled conditions. The high frequency components and the abrupt change correspond to the electrical response of the plant to an external stimulus (environmental or physical) or to an internal chemical activity of the plant. An example of these rapid changes might be related to salicylic acid production or phytoalexin synthesis in response to injury or pathogen attack. The above-mentioned is a result that has caused motivation on the research of electrical signals in plants [19,28,29].

These stimuli generate significant electrical changes in the signal, which could explain the peak observed around sample 200. The results obtained are consistent with the biological nature of the signal, where a mixture of slow and fast processes was expected. These abrupt changes have been reported previously. It is on this feature that researchers have focused on determining key aspects of the electrical signal and is the motivation for this work [19].

After that, the time-frequency domain analysis of the A. vera electrical signal was performed using the wavelet transform. Figure 4 shows the 3D graphical representations of the 16 combinations of wavelet functions and decomposition levels. Each sub-graph, organized in a 4 × 4 matrix, represents a specific configuration, where the X-axis corresponds to time, the Y-axis to the decomposition level, and the Z-axis to the magnitude of the wavelet coefficients. This design visually compares the different combinations, highlighting the properties of each wavelet function and its ability to represent the A. vera electrical signal.

The combination of the wavelet function “db3” with five levels, highlighted in red, showed an optimal balance between energy concentration and the representation of relevant signal details. In comparison, the other configurations, although similar in many respects, showed differences in the distribution of coefficients between levels. The previously mentioned is described in a similar way to that mentioned in Junxia’s work, where he used and tested only a single wavelet mother function to analyze the electrical signal from the plant. In this work, different functions and levels were tested to demonstrate and compare results [13].

In order to justify the best level decomposition, total energy and entropy were calculated. The numerical results, summarized in Table 2, support these observations.

For the “db3” configuration with five levels, the total energy reached a value of 0.75573, showing that this combination captures a significant amount of the signal information. In addition, an entropy of 1.4221 shows an acceptable balance in the distribution of energy among the levels. In contrast, configurations with eight levels, such as “db3” (total energy of 0.82243 and entropy of 1.6614), capture more energy, but have a higher dispersion, which may lose key information from the electrical signal.

On the other hand, the wavelet function “sym4” with five levels presented a similar behavior to “db3”, with a slightly lower total energy (0.73798) and a comparable entropy (1.4092). This suggests that “sym4” could be a valid alternative for analysis, although its ability to capture smooth transitions in the signal appears to be inferior to “db3”. In contrast, “coif1” showed lower total energy at low levels (0.46344 with four levels), and improved using five levels (0.76798), but its higher entropy (1.3407) indicates a lower concentration of energy at specific levels.

Finally, “haar” was efficient for capturing transient events, but presented a lower total energy (0.72427 with five levels) and a lower entropy (1.2716), which emphasizes high-frequency events, at the cost of sacrificing low-frequency details. This makes it suitable for analysis focused on fast events, but less effective for characterizing global signal features.

According to the above results, Figure 5 shows the decomposition into five levels using the mother function db3 of the Daubechies series. The black line is the original signal over time. The blue lines represent each of the five levels of decomposition. The first two levels (one and two) indicate low-frequency components. On the other hand, the later levels (from three to five) capture the abrupt changes already observed in the power spectrum obtained from the STFT. These results are consistent with findings previously described in the literature [13,16].

The non-parametric analysis of the electrical signal of A. vera, carried out using the short-time Fourier transform (STFT) and the wavelet transform, provides a detailed and multifaceted view of the dynamic characteristics or features of the signal. This approach is useful for studying the temporal and frequency properties of the signal and how they may change over time due to different physiological, chemical, or environmental aspects present during the study. Highlighting that the A. vera plant can be used as a study tool in different fields, as already reported by some of the works in the literature [28,29].

3.2. Case of Parametric Analysis

On the other hand, the parametric analysis was performed based on signal modeling using auto-regressive models. This method offers an approach from the predictive point of view using a specific mathematical model with a low number of parameters. Figure 6 shows the relationship between the number of delays (p) and the mean squared error (MSE) obtained by fitting auto-regressive (AR) models of different orders. This analysis allowed identifying the optimal model order to capture the dynamics of the A. vera electrical signal.

The evaluation of the AR(9) model shows a mean squared error (MSE) of 17.86, with coefficients reflecting the decreasing influence of previous measurements over time. This model is computationally efficient and sufficiently accurate to represent the dynamics of the A. vera electrical signal, meeting the objectives of the analysis. On the other hand, AR(15) obtained an MSE of 17.10, which is not a significant difference in terms of performance compared to AR(9) but is in terms of coefficients. This makes it more complex and computationally requires more resources.

Based on the above, Equation (5) shows the obtained model from 9 delays (AR(9)),

x(n) = 34.2836 + 1.2137x(n − 1) − 0.0506x(n − 2)
− 0.4592x(n − 3) − 0.0321x(n − 4)
+ 0.2850x(n − 5) − 0.0722x(n − 6)
− 0.0886x(n − 7) − 0.0366x(n − 8)
+ 0.0715x(n − 9),

(5)

where x(n) represents the signal value at time n, and the coefficients represent the weights of the lagged terms. The model parameters were estimated using the Yule-Walker method. The auto-regressive (AR) model implemented in Equation (4) was defined with an order of nine lags, selected as an advantage between prediction accuracy and model simplicity. Although higher orders (e.g., 15 lags) offered slight improvements in terms of mean squared error (MSE), the AR(9) manages to capture the main temporal dependencies with a significant reduction in the number of parameters. This model is similar and compares with the findings found by Lanzhou Wang, where they show an AR(18) [26].

Figure 7 shows the AR model predictions compared to the original signal measurements. It can be seen that the red line (AR) overlaps the blue line (original) almost completely. However, there are parts where the blue line is overlapped as in the abrupt change in the signal with signal reconstruction very similar to that previously reported in the literature [26].

The obtained model can be considered as simple and efficient from a computational resource usage point of view. This allows the generation of prediction tools in real time or for subsequent analysis with a larger volume of data. Although the AR model shows an acceptable prediction behavior, it is evident that non-parametric methods are better at capturing abrupt events. These results underline the relevance of combining the different approaches to obtain a complete overview of the electrical signal characteristics of A. vera. By highlighting this combination of approaches (non-parametric and parametric),

Table 3. Comparison between the inverse wavelet transform and AR model.

Method	MSE	MAE	R2
Wavelet Transform	0.001	0.01	0.98
AR Model	17.86	3.5	0.85

shows the performance metrics in the reconstruction and prediction of the electrical signal of the A. vera plant from a non-parametric and parametric analysis approach.

Both methods contribute to the analysis and modeling of the electrical signal of A. vera, but present differences in their application and results. On the one hand, the wavelet transform allowed the identification of transient events and abrupt changes in the signal. However, it requires an accurate selection of the mother function to achieve consistent results. In terms of computational cost, a higher capacity is required. On the other hand, the mathematical model obtained with the auto-regressive models presents a compact and efficient form for signal prediction. However, it does not fully capture the nature of the signal. If the interest is in the identification of transient and temporal characteristics, the wavelet transform is a suitable and useful tool. If a compact parametric representation is sought for prediction, AR models are the most appropriate. This type of approach and use of the wavelet transform and AR models, allows us to establish the conditions to perform applications or work focused on specific tasks as described in the literature [28,29].

4. Conclusions

The combination of parametric and non-parametric methods in the analysis of the electrical signal of Aloe vera var. chinensis (A. vera) allows a deep understanding of the features and characteristics of this type of signal. AR models, complemented with the wavelet transform and STFT, provide powerful tools for the study and monitoring of physiological responses in plants. By studying these tools, it is possible to develop more complex analysis systems. For example, an automatic pattern recognition system, where the different characteristics of the signal can be obtained and incorporated, and signal recognition and classification algorithms can be created. In contrast to the above, the use of the combined model (wavelet + AR) could be implemented in low-cost systems for continuous crop monitoring in rural areas. This would allow farmers to receive early warnings about water stress conditions or pest infestation, reducing economic losses.

In addition, A. vera has a rapid electrical response to the presence of a stimulus, giving the support to use it as a biosensor or bio-dosimeter for environmental monitoring or detection of pests and diseases in crops.

This study was performed under controlled laboratory conditions, which could reduce the applicability of the results in real scenarios. In addition, noise introduced by the electronic system could influence the accuracy of the models. Validation of the model under field conditions and integration with machine learning techniques to improve signal classification and prediction is proposed. These limitations emphasize the importance of generating different characterization and modeling approaches, such as the use of a non-parametric and parametric approach in this study.

As future work, it is proposed to validate the model in field conditions and to integrate it with machine learning techniques to improve signal classification and prediction.