Dynamical System Modeling and Stability Investigation�DSMSI-2025

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May 08-10, 2025, Kyiv, Ukraine

MATHEMATICAL MODEL OF PLANT DISEASES CLASSIFIER FOR SMART AGRICULTURE IMPLEMENTED ON SMALL-EDGE DEVICES

Iryna Yurchuk, ^{1, †} Kseniia Dukhnovska^1,∗,†, Oksana Kovtun^{1, †} , Anna Pylypenko^{1, †} and Olga Gurnik

Introduction

Plant health monitoring is an essential aspect of modern precision agriculture, enabling farmers to detect diseases, nutrient deficiencies, and environmental stressors early. This early detection facilitates timely interventions, reducing losses and improving overall agricultural productivity. Traditional plant health monitoring relies on manual inspections, which are labor-intensive, time-consuming, and prone to human error. In contrast, automated systems that integrate multimodal data sources—such as stationary sensors, aerial imagery, and machine learning algorithms—provide a more accurate, scalable, and efficient approach to monitoring and maintaining plant health.

The implementation of the classification task is the source, the successful solution of which is a guarantee of high performance not only of complex monitoring systems, but also of inexpensive solutions involving a minimum set of devices with low technical characteristics.

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Dynamical System Modeling and Stability Investigation, DSMSI-2025

The aim and objectives of the study

The proposed study aims to analyze existing solutions for plant health monitoring and present an affordable, multimodal approach that leverages stationary sensors and visual data to optimize agricultural.

The following objectives were set and achieved to reach the goal:

• To analyze existing solutions for smart agriculture.
• To analyze sources of information collection.
• To develop a classifier for diagnosing plant diseases based on the support vector machine method.
• To compare the resource cost of training the developed classifier with the training of neural networks.

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Plant diseases

Main groups of plant diseases:

• Fungal diseases: The most common group of diseases. Manifested as spots, rot, powdery mildew, rust, etc.
• Bacterial diseases: Cause rot, spotting, wilting of plants.
• Viral diseases: Transmitted by insects. Manifested as mosaic, leaf deformation, dwarfing of plants.
• Phytoplasmosis: A disease caused by microorganisms transmitted by insects.
• Nematodes: Nematodes are microscopic roundworms that parasitize plants. This leads to metabolic disorders, growth retardation, reduced yields and even plant death. Caused by microorganisms transmitted by insects.

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Monitoring system components for Smart Agriculture

• Soil temperature sensors play a key role in modern agriculture, enabling the optimization of plant cultivation processes, determine the ideal time for sowing, as soil temperature directly affects seed germination, and different plants have different temperature requirements.
• Soil moisture sensors enable the optimization of irrigation by determining when and how much water plants need, preventing both overwatering and underwatering.
• PH sensors are an important tool for measuring the acidity or alkalinity of substances, which has a wide range of applications in various industries.
• Level sensors are used to determine the level of substances, whether liquids, powders, or granules. In hydroponics, these sensors play a key role in tracking the nutrient solution level, especially in the context of smart irrigation.

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Mathematical model for plant diseases classifier

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Mathematical model for plant diseases classifier

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Mathematical model for plant diseases classifier

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Mathematical model for plant diseases classifier

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Mathematical model for plant diseases classifier

The practical implementation of teaching this method of plant diseases classifying can be described by the following steps:

1. Digitizing the description of the state of the plant using a selected family of features. For example, the following can be taken: color of the leaves ( yellowing, redness, appearance of spots of different colors), deformation of leaves (coagulation, twisting, appearance of holes), leaf fading ( Turgor's shoe, leaves falling), condition of stems and fruits (brown, black, gray spots, rot), existence of plaque on leaves (powdery mildew, soot fungus), deformation of shoots (curvature, growths) and the presence of pests (insects, spider web, traces of damage). In [13], there is statistical method for avoiding anomalies.

2. For the incoming set of descriptions, the coefficients matrix is constructing.

3. Initial approximation: an arbitrary vector representing a description of one class is selected, and the closest vector of another class is searched for it. For this vector, the closest vector from the first class is searched, etc.

4. Solving problem (14) using the gradient descent method.

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Research methodology and experiments

Avoiding a large one and being able to build a classifier on a small dataset is also a big advantage. Because there is no need to spend 60% of the time preparing the dataset in different landscape conditions, with different typical anomalies or biases.

Figure 1 shows the minimum data required to train a classifier for 100 different diseases belonging to six different classes of plant disease causes. We note that considered method is the one that guarantees the result with minimal time spent on dataset preparation.

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Figure 1: Minimum training sample size

Research methodology and experiments

For the type of devices under consideration, the time spent on training is also an important factor. Figure 2 shows that our method guarantees minimal training time, since the number of hyperparameters is optimized. We also note that the considered approach makes it possible to implement classification based on different types of data: digital images, device indicators, and verbal descriptions of diseases.

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Figure 2: Minimum classifier training time (in minutes)

List of post-classification measures

1. Use of fungicides: effective use of fungicides helps control the development of powdery mildew and reduce crop losses.
2. Increase in plant immunity: regular application of growth stimulants and micronutrients.
3. Timeliness of treatments: application of preparations in the early stages of plant development or prophylactically during critical periods of growth.

4. Compliance with the norms of drug consumption: the use of recommended doses of preparations provides effective protection and prevents the development of resistance in pathogens.

5. Application technology: the use of modern sprayers with uniform distribution of the working solution increases the efficiency of treatments.

Conclusion

The authors analyzed existing solutions for plant health monitoring and present an affordable, multimodal approach that leverages stationary sensors and visual data to optimize agricultural. Obtained classifier for diagnosing plant diseases based on binary relevance approach the which consists of SVM's, needs small dataset and short time for training model.

This approach will allow the classifier to be fully adapted to the needs of a particular area or farm. In the future, the authors plan to expand the approach to classifying not only diseases, but also predicting the possibility of their occurrence based on temperature, humidity, and soil parameters.

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Thank you for your attention

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