# Soft sensors for dust estimation with high accuracy: AI-driven approach for CSP solar mirror soiling classification

Ayoub Oufadel, Masaab El Ydrissi, Ibrahim Taabane, Alae Azouzoute, Alami Hassani Aicha, Hicham Ghennioui

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Ayoub Oufadel, Masaab El Ydrissi, Ibrahim Taabane, Alae Azouzoute, Alami Hassani Aicha, et al.. Soft sensors for dust estimation with high accuracy: AI-driven approach for CSP solar mirror soiling classification. International Journal of Sustainable Energy, 2025, 44 (1), pp.2475305. 10.1080/14786451.2025.2475305. hal-05025632

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# Soft sensors for dust estimation with high accuracy: AI-driven approach for CSP solar mirror soiling classification

Ayoub Oufadel, Masaab El Ydrissi, Ibrahim Taabane, Alae Azouzoute, Alami Hassani Aicha & Hicham Ghennioui

**To cite this article:** Ayoub Oufadel, Masaab El Ydrissi, Ibrahim Taabane, Alae Azouzoute, Alami Hassani Aicha & Hicham Ghennioui (2025) Soft sensors for dust estimation with high accuracy: AI-driven approach for CSP solar mirror soiling classification, *International Journal of Sustainable Energy*, 44:1, 2475305, DOI: 10.1080/14786451.2025.2475305

**To link to this article:** https://doi.org/10.1080/14786451.2025.2475305

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© 2025 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group

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Published online: 17 Mar 2025.

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# Soft sensors for dust estimation with high accuracy: Al-driven approach for CSP solar mirror soiling classification

Ayoub Oufadel<sup>a</sup>, Masaab El Ydrissi<sup>a</sup>, Ibrahim Taabane<sup>b,c</sup>, Alae Azouzoute<sup>d</sup>, Alami Hassani Aicha<sup>a</sup> and Hicham Ghennioui<sup>a</sup>

## ABSTRACT

Concentrating solar power plants convert solar energy into electricity by using mirrors to concentrate sunlight, but dust, particularly in arid and semi-arid regions, reduces their efficiency. This study proposes an innovative Al-based approach for monitoring and predicting soiling. For real-time analysis of CSP mirror images, a ResNet-50 convolutional neural network (CNN) is used, while a recurrent neural network (RNN) with a long, short term memory (LSTM) architecture predicts future soiling rates using the temporary variation in this parameter. By integrating mirror imagery and meteorological data, our hybrid Al model effectively combines CNN for image analysis and RNN temporal predictions, with high accuracy ranging from 89.5% to 95.2%, depending on the application. The application of advanced Al techniques can significantly improve the management of concentrated solar power plants and lead to significant breakthroughs in the solar energy industry.

## ARTICLE HISTORY

Received 31 August 2024
Accepted 28 February 2025

## KEYWORDS

Concentrating solar power (CSP); dust accumulation; artificial intelligence (AI); image processing; meteorological data

## 1. Introduction

The conversion of solar energy into electricity in CSP plants uses mirrors or lenses to concentrate sunlight on a receiver which are towers or tubes with a heat transfer fluid, which is used to heat water in a heat exchanger to produce high-pressure steam to drive a turbine that generates electricity. Solar tower power plants are the most common, with the heat transfer fluid heated to temperatures of up to 500°C. Fresnel mirror power plants, on the other hand, heat the fluid to lower temperatures of around 200°C. By 2022, the total installed capacity of concentrated solar power plants worldwide was 6.2 GW, with Spain, the USA, India and South Africa being the main producers.

The expansion of CSP in arid and semi-arid regions faces a major challenge due to the accumulation of dust and the scarcity of water for cleaning, whether this accumulation is due to natural processes or to the proximity of industrial activities. It negatively affects the optical efficiency of the mirrors, leading to a significant reduction in overall plant efficiency, which can reach 1.07%/ day of plant performance according to (Maftah et al. 2022). To ensure optimum performance,

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<footnote><sup>a</sup>Laboratory of Signals, Systems, and Components, Sidi Mohamed Ben Abdellah University, Fez, Morocco;</footnote>

<footnote><sup>b</sup>Laboratory of Intelligent Systems, Geo-resources and Renewable Energies (SIGER), Sidi Mohamed Ben Abdellah University, Fez, Morocco; <sup>c</sup>Institute of Electronics and Digital Technologies (IETR), University of Rennes, Rennes, France; <sup>d</sup>Fluid Mechanics team, Laboratory of Mechanics and Energetics, Faculty of Sciences, University Mohammed First Oujda, Morocco</footnote>
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regular cleaning is necessary, but this operation consumes a lot of natural resources and manpower, thus increasing the Operating Expense (OPEX) of the maintenance operation. Optimising the cleaning frequency by taking weather forecasts into account is essential to minimise costs, which can be reduced by up to 25% (Azouzoute et al. 2021).

A review of the literature reveals an increasing trend towards the application of artificial intelligence (AI) to solve complex problems in the solar energy sector. AI is replacing traditional models such as linear regression or classic distributions like Gaussian distribution for several reasons: their ability to capture complex relationships, superior performance on complex data, adaptability to unstructured data, self-learning, and generalisation capabilities, as well as the evolution of techniques and computing resources (Vaid et al. 2023). Generally, the modelling of numerical data and image processing, which can be linked through regression and classification techniques (Zhang et al. 2024a, 2024b). Studies such as (Jaybhaye et al. 2023) have proposed a method for detecting and locating damage on solar panels. By analysing thermal patterns, the proposed approach effectively identifies hot spots on the panel surface, indicating potential defects or damage. This method not only reduces inspection time but also the costs associated with manual visual inspection. Similarly, for photovoltaics Li et al. (2023) introduce an innovative approach to defect detection on PV panels. By incorporating Ghost convolution with BottleneckCSP and a tiny target prediction head within the YOLOv5 framework, the study addresses the challenge of identifying multiple small defects with high accuracy.

However, the management of soiling in CSP installations is less studied in the literature compared to photovoltaics. This phenomenon is divided into two types according to the typology of data: either by image processing and classification or by modelling numerical data. El Galassi et al. (2023) used image processing to quantify the dust accumulation rate on CSP mirrors by analysing nighttime images. The images reveal the backscatter of light by dust particles, allowing for the calculation of a Brightness Index (BIX) correlated with mirror cleanliness and dust deposition density. The method is precise, with a correlation factor of 89.9% with mirror cleanliness. However, the drawback of this technique is that it links the soiling rate to the colour density – a theory that can be flawed because this technique does not consider the layering of dust and the typology and distribution of dust, which varies depending on the days of deposition. Other studies have utilised numerical data for modelling and predicting defects in solar installations by directly simulating the physical phenomena impacting solar facilities. These studies employ models such as polynomial distribution, simple linear regression, multiple linear regression, as well as nonlinear models based on nonlinear distributions or neural networks like MLP (Gacto et al. 2019). These methods model soiling based on meteorological data using both linear and nonlinear models (Hussain et al. 2020; Maftah et al. 2022; Oufadel et al. 2023), or by modelling the power output to compare the measured value with the predicted one, where any discrepancy may indicate issues with the installation, as in the case of photovoltaic mirrors (Oufadel et al. 2024).

Many papers in the literature have proposed several different methods for such models using image processing algorithms and numerical data modelling for the sake of estimating, predicting or detecting this problem. Today, for real-time detection or prediction, using tracers as instrumentation is expensive, and these processes can be inexact with regard to long-term processes. In addition, many research projects have ignored early states before forecasting, which may degrade the forecast quality. In this paper, we present a new approach which is a mixture of a deep learning model such as ResNet-50 for the processing of images and an MLP model used for the integration of meteorological data. The first is responsible for classifying the soiling rate in real-time, while the second model forecasts the variation of this parameter over the next days. In contrast to only CNN or MLP models, this combines the advantage of being able to study the intricate visuals and predict the trends in the next few days. The LSTM model predicts the change in dust by incorporating the weather conditions in the coming days. This makes sense because it allows for real-time assessment of system performance while also being able to predict performance over a
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reasonable period of time. Combining these models allows us not only to determine the degree of soiling in real-time, but also to determine the best time for the planned maintenance and improve its efficiency. This hybrid strategy optimises both the functioning and maintenance requirements which would otherwise be hard to achieve with a pure CNN or RNN architecture, in order to quantify - correctly and in real-time the implemented soiling over the mirrors. The challenge is to manage maintenance in order to plan useful cleaning operations, with the objective of minimising operational costs and maximising electricity production. And It's almost the same approach we developed earlier for photovoltaic systems, giving a high accuracy of over 90% (Nnolim 2018).

The present investigation is based on authentic CSP plants since it includes data collected at the GEP Research Center and a methodology that combines image acquisition, advanced data treatment as well as exploitation of the predictive ability of AI. The results will be used for a better preparation for maintenance purposes, thereby enhancing the longevity and functionality of concentrated solar power plants. Furthermore, this approach could have positive implications for the economic and environmental profitability of solar energy, thus supporting the sustainable development of the energy industry.

## 2. Context and methodology

### 2.1. Study area and data

We created the database for our study at the GEP Research Center based on results from our previous study, DustInSMS, and we worked with CSP Fresnel mirrors at a 1 MWe power plant. The Fresnel mirrors have geometric dimensions of 50 × 120 cm. The work was carried out during the dry season, a period of five months, from April 1 to August 31, 2018. The image analysis data collection was performed with the DustInSMS system. Specular reflectivity was measured by a D&S reflectometer with a 25 mrad acceptance angle for the Fresnel mirrors. We then also test a flat mirror sample of 10 × 10 cm with an RGB camera.

In addition, we collected the dust deposited on this segment in a Petri dish and weighed it to obtain the total amount of dust deposited for this period. Milking was repeated after this protocol (REF, M1, M2, M3, M4, M5). The images were captured in a controlled environment using a box with a black background and uniform lighting provided by the camera's flash. It is not possible to capture images under variable lighting conditions without compromising the model's accuracy.

Measurements were taken under different exposure durations as shown in the below:

- Reference (REF): Reference images representing clean mirrors.

- M1: Mirrors exposed for 1 day.

- M2: Mirrors exposed for 3 days.

- M3: Mirrors exposed for 7 days.

- M4: Mirrors exposed for 15 days.

- M5: Mirrors exposed for 1 month or more.

Each dataset is organised into separate folders, with a label specifying the corresponding class. A CSV file accompanies each set, summarising the reflectivity and density for each image, while also providing the date of sampling.

The second dataset includes meteorological information collected at two different sites in Morocco, which we have previously used in studies (Hussain et al. 2020; Maftah et al. 2022; Oufadel et al. 2023). The parameters considered in this category include the minimum, maximum, and average values of irradiation, temperature, humidity, wind speed, and wind direction. These meteorological data are also structured in CSV files, thereby facilitating their integration and joint analysis with the field-acquired data. This holistic approach allows for the exploration of potential
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relationships between weather conditions and mirror characteristics, thus contributing to a
thorough understanding of the factors influencing the measurements made.

## 2.2. Data analysis

### 2.2.1. Data of DUSTinSMS

Reflectivity measurements. Table 1 represents the results of a detailed analysis of the impacts of dust accumulation on the reflectivity of Fresnel mirrors used in Concentrated Solar Power (CSP) plant installations. Drawing upon data collected by the DustinSMS device at the GEP Research Center, we explore the effects of various degrees of dust exposure on the physical characteristics of the mirrors. The study covers a dry period of five months, from April to August 2018, during which the mirrors were subjected to real environmental conditions to assess the impact of accumulated dust on their performance. We begin by presenting the methodology employed for data collection and analysis, including specular reflectivity measurements and quantitative evaluations of dust density on the mirrors. We then detail the results obtained, highlighting variations in mirror reflectivity based on exposure time to dust. This system uses a black background to handle variations in lighting, reducing the effect of sky reflections and thus cutting down on variations in brightness due to direct sunlight. That is how this model manages to provide good consistency in its images, especially for those times of the day when lighting changes-for example, at dawn and dusk. Besides that, through the deep learning methodologies put into the model, the identification of soiling patterns has been robust even under these differences in lighting conditions. Other future works will be to optimise the camera settings along with the model training over a wide range of environmental lighting conditions.

The reference mirrors, not exposed to external conditions, exhibit exceptional reflectivity of 96%. However, the dust density is negligible, measured at 0 mg. These data establish a baseline for assessing subsequent changes in exposed mirrors. The results from exposed mirrors show a significant downward trend in reflectivity with increasing exposure duration. Mirrors exposed for one day (m1) show an average reflectivity of 94.6%, a slight but already observable decrease. This reduction becomes more pronounced over time, reaching 67.9% for mirrors exposed for one month (m5). Dust density on the mirrors gradually increases with the duration of exposure. Reference mirrors show no significant dust density, but after just one day of exposure (m1), a density of 0.6 mg is measured. This density increases as the exposure duration extends, reaching 2.1 mg for mirrors exposed for one month (m5).

<table><caption>**Table 1.** Analysis of dust accumulation on fresnel mirrors.</caption><thead><tr><th>Miroir date</th><th>R1 (%)</th><th>R2 (%)</th><th>R3 (%)</th><th>R4 (%)</th><th>R5 (%)</th><th>V_MOY (%)</th><th>Number of days of exposure</th><th>T_P (mg)</th></tr></thead><tbody><tr><td>21-may</td><td>94.6</td><td>94.9</td><td>94</td><td>94.7</td><td>94.7</td><td>94.58</td><td>1</td><td>0.6</td></tr><tr><td>21-may</td><td>90.1</td><td>89.9</td><td>89.6</td><td>90.4</td><td>90.3</td><td>90.06</td><td>3</td><td>0.65</td></tr><tr><td>21-may</td><td>89.4</td><td>90.2</td><td>89.6</td><td>89.5</td><td>88.6</td><td>89.46</td><td></td><td></td></tr><tr><td>23-may</td><td>90.6</td><td>89.4</td><td>90.7</td><td>90.2</td><td>89.7</td><td>90.12</td><td></td><td></td></tr><tr><td>23-may</td><td>91</td><td>89.1</td><td>90.1</td><td>86.3</td><td>86.3</td><td>88.56</td><td></td><td></td></tr><tr><td>24-may</td><td>86</td><td>82</td><td>86.8</td><td>87</td><td>88</td><td>85.96</td><td>7</td><td>0.8</td></tr><tr><td>24-may</td><td>81.8</td><td>82.1</td><td>85</td><td>83</td><td>83.9</td><td>83.16</td><td></td><td></td></tr><tr><td>30-may</td><td>84.2</td><td>83.2</td><td>83.5</td><td>83.1</td><td>84.8</td><td>83.76</td><td></td><td>0.9</td></tr><tr><td>30-may</td><td>84.8</td><td>85.3</td><td>83.2</td><td>83.9</td><td>83.9</td><td>84.22</td><td></td><td></td></tr><tr><td>30-may</td><td>84.3</td><td>82.5</td><td>84</td><td>82.5</td><td>83.6</td><td>83.38</td><td></td><td></td></tr><tr><td>06-june</td><td>73</td><td>74.4</td><td>73.4</td><td>76.5</td><td>74.7</td><td>74.4</td><td>15</td><td>1.4</td></tr><tr><td>06-june</td><td>74.1</td><td>75</td><td>75.8</td><td>75</td><td>74.9</td><td>74.96</td><td></td><td></td></tr><tr><td>06-june</td><td>73</td><td>74.7</td><td>73.1</td><td>73.7</td><td>73.6</td><td>73.62</td><td></td><td></td></tr><tr><td>06-june</td><td>75.1</td><td>72.2</td><td>71.8</td><td>72</td><td>72.8</td><td>72.78</td><td></td><td></td></tr><tr><td>06-june</td><td>74.8</td><td>74.5</td><td>73.1</td><td>70.6</td><td>73.8</td><td>73.36</td><td></td><td></td></tr><tr><td>06-june</td><td>71.7</td><td>72.3</td><td>71.4</td><td>69.8</td><td>71.7</td><td>71.38</td><td></td><td></td></tr><tr><td>06-june</td><td>67.4</td><td>70.7</td><td>72.6</td><td>69.6</td><td>69.4</td><td>69.94</td><td></td><td></td></tr><tr><td>06-june</td><td>68.3</td><td>72</td><td>72,5</td><td>70.6</td><td>69.4</td><td>70.56</td><td></td><td></td></tr></tbody></table>
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Reflectivity and dust density measurements reveal complex temporal correlations. For instance, peaks in dust density can be associated with temporary decreases in reflectivity, indicating the direct impact of dust on mirror performance. The three classes of dusty mirrors (R1, R2, R3) show notable variations in reflectivity and dust density, suggesting that the nature of the dust may also influence these parameters.

*Images from DUSTinSMS.* The DustinSMS imaging reveals the distribution of dust on the mirrors as well as the shape of the dust, which may be influenced by climatic conditions and exposure duration. We attempt to classify them using image processing algorithms such as the calculation of average RGB, average saturation, average luminance, and similarity relative to the reference class (Gao 2024; Boyle et al. 2016), which measures the similarity between two images by comparing pixel values (Equation 1).

$$ Similarity = 1 - \frac{1}{N} * \sum_{(i=0)}^{N} ((Ir(i) - It(i))^2, \qquad (1) $$

where N is the total number of pixels, Ir(I) and It(i) are the pixel intensities of the reference and test images.

A similarity coefficient of 1 indicates perfect identity, while a coefficient of 0 signifies total difference. The analysis of different classes (table 2) reveals distinct variations in colour characteristics, saturation, and luminance. The reference class (Ref) displays relatively high saturation and average luminance, with perfect similarity to itself. The other classes show specific nuances, suggesting that measurements of mirror image luminance and saturation can be used to predict the level of dust, although tolerance remains high. To remedy this, may be due to dust density, which can be piled up and not detected directly. To address this, the use of a machine learning model could be considered to learn the relationship between these measurements and the level of dust accumulation.

### 2.2.2. Meteorological data

*Meteorological data measurements.* The second dataset pertains to meteorological data from the Benguerir and Missouri stations over a period from January 1, 2015, to August 1, 2017. The meteorological and soiling data were recorded at a sampling interval of 1 minute during this period. Where we employed the Tracs method (Hussain et al. 2020; Oufadel et al. 2023), to quantify the soiling rate

<figure><img src="image_15.png" /><figcaption>Figure 1. The Evolution of DNI and DNIreflected during a day with a sampling interval of 1 minute.</figcaption></figure>
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<table><caption>**Table 2.** Sample of each class with comparison of colour, saturation, and luminance measurements relative to the reference.</caption><tr><td>Ref</td><td></td><td>Average saturation : 15.19 Average<br>Luminance : 139.33<br>Similarity : 1</td></tr><tr><td>M1</td><td></td><td>Average colour (RGB): [134.16 134.11 135.26]<br>Average saturation: 7.87<br>Average luminance : 142.77<br>Similarity : 0.56</td></tr><tr><td>M2</td><td></td><td>Average colour (RGB): [129.18 129.23 132.35]<br>Average saturation: 11.53<br>Average luminance : 137.7<br>Similarity : 0.43</td></tr><tr><td>M3</td><td></td><td>Average colour (RGB): [127.96 127.91 130.98]<br>Average saturation: 12.343<br>Average luminance : 135.95<br>Similarity : 0.29</td></tr><tr><td>M4</td><td></td><td>Average colour (RGB): [123.30 123.28 124.45]<br>Average saturation: 15.97<br>Average luminance : 131.40<br>Similarity : 0.38</td></tr><tr><td>M5</td><td></td><td>Average colour (RGB): [132.90 133.48 134.48]<br>Average saturation: 5.46<br>Average luminance: 141.84<br>Similarity: 0.43</td></tr></table>

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by calculating the soiling ratio (Sr) of the mirrors from the measurements of Direct Normal Irradiance (DNI) and reference DNI (DNIref), defined as follows: $Sr = λ/λ0$, with $λ = DNI/DNIref$ and $λ0$ representing the maximum reflectivity of the mirror provided by the manufacturer. A larger deviation between DNI and DNIref indicates a higher soiling ratio. This measurement is carried out during midday, when irradiation is at its peak and the effects of dust are more pronounced (see Figure 1) where the soiling ratio (Sr) is almost 0.92 and it is clearly visible at noon where the DNI is maximum and quasistatic. We have used data from two sites with different climates to generate a more general model when training with the cold climate of Missouri and the semi-arid climate of Benguerir, the concatenation of the meteorological conditions of the two sites will generate a wide range which will allow to generate a more general model to predict any samples.

The recorded meteorological parameters include normal direct solar irradiance (DNI and DNIref) in W/m², measured using a K&Z CHP1 pyrheliometer. Additionally, ambient temperature (Tamb) in degrees Celsius and relative humidity (RH) in percentage are also recorded using a Campbell CS215 temperature and humidity probe. Wind speed (WS) in meters per second is measured using an NRG 40H anemometer, with the maximum wind speed (WSgust) recorded during the specified time interval. Finally, wind direction (WD) in degrees North (towards East) is measured using an NRG 200 wind direction sensor, with the standard deviation of wind direction (WDStDev) calculated over the measurement period.

*Meteorological data correlations.* These data are recorded with a frequency of 1 min (A vector of the data set every minute). The generated data show correlations and interactions among them, which we can illustrate using the correlation matrix in Table 3. It is used to analyse the linear relationships between variables and understand how they vary together. The correlation matrix is useful for identifying dependencies or trends between variables in a dataset. It is often used in exploratory analysis to detect relationships between multiple variables. This coefficient ranges from -1 to 1:

* 1: perfect positive linear relationship (when one variable increases, the other increases proportionally).

* -1: perfect negative linear relationship (when one variable increases, the other decreases proportionally).

* 0: no linear relationship between the variables.

We notice that the correlation matrix highlights significant relationships involving the “Cleanliness” variable. Cleanliness displays a moderate positive correlation with temperature (0.283) and precipitation (0.288), suggesting that higher temperatures and precipitation might be associated with increased cleanliness. These findings suggest a possible influence of climate on cleanliness levels. Conversely, a moderate negative correlation with relative humidity (-0.294) suggests that cleanliness tends to decrease as relative humidity increases, indicating that more humid conditions are associated with less cleanliness. Other correlations, though present, are weaker, thus underscoring the

<table><caption>**Table 3.** Correlation matrix of meteorological data and cleanliness.</caption><thead><tr><th></th><th>Cleanliness</th><th>Temperature</th><th>Relative humidity</th><th>Wind speed</th><th>Wind direction</th><th>Precipitation</th></tr></thead><tbody><tr><td>Cleanliness</td><td>1</td><td>0.283</td><td>-0.294</td><td>0.178</td><td>0.243</td><td>0.288</td></tr><tr><td>Temperature</td><td>0.283</td><td>1</td><td>-0.912</td><td>-0.2503</td><td>0.0256</td><td>0.1985</td></tr><tr><td>Relative humidity</td><td>-0.294</td><td>-0.912</td><td>1</td><td>0.365</td><td>-0.029</td><td>-0.141</td></tr><tr><td>Wind speed</td><td>0.178</td><td>-0.2503</td><td>0.365</td><td>1</td><td>0.0323</td><td>0.001</td></tr><tr><td>Wind direction</td><td>0.243</td><td>0.0256</td><td>-0.029</td><td>0.0323</td><td>1</td><td>-0.0844</td></tr><tr><td>Precipitation</td><td>0.288</td><td>0.1985</td><td>-0.141</td><td>0.001</td><td>-0.0844</td><td>1</td></tr></tbody></table>
<figure><img src="image_24.png" /></figure>

potentially crucial role of meteorological factors, particularly temperature, precipitation, and relative humidity, in maintaining cleanliness. other parameters used in the literature for modelling and predicting Dust include mass accumulation and airborne PM10 (Boyle et al. 2016) but the disadvantage of these parameters is that they are not predictable, so we have focused on parameters that are correlated with soiling and that are available for forecasting from meteorological observations to others.

## 2.3. Proposed model

The model suggested in this study combines two different artificial intelligence models to evaluate and control soiling on solar mirrors in CSP installations, resulting in a hybrid approach. This method merges the capabilities of Convolutional Neural Networks (CNN) and Recurrent Neural Networks (RNN) using LSTM structure to analyse both dirty mirror images and weather information, providing a holistic answer to the soiling issue (Gardner and Dorling 1998).

Figure 3 shows the hybrid AI model design which merges Convolutional Neural Networks (CNN) and ResNet-50 for analysing dirty solar mirrors images and Multi-Layer Perceptron (MLP) for categorising dust. The MLP architecture was chosen for its effectiveness with simple meteorological data, offering good interpretability and low complexity compared with sequential architectures such as GRU or TCN (Oufadel et al. 2023). We emphasise that traditional regression-based and statistical methods were indeed initially considered for comparison. However, these methods proved inadequate because the problems addressed – such as mirror fouling and performance degradation of CSP installations – are highly non-linear and do not follow standard statistical distributions. Traditional approaches such as linear regression and Gaussian distribution models struggle to capture the complex interactions within the data, resulting in lower predictive accuracy (Celik 2023; Maftah et al. 2022; Patro et al. 2023; Zitouni et al. 2021). along with Recurrent Neural Networks (RNN), particularly LSTM, for capturing the temporary changes of this occurrence, by including satellite meteorological data to forecast upcoming cleanliness and soiling levels. This graphic illustrates how these technologies are combined to tackle the problem of dirt build-up on solar mirrors.

The chart (Figure 2) shows a workflow for predictive analytics that starts with image inputs from DUSTinSMS. The CNN model ResNet50 is used to process these images initially, as it excels at extracting intricate features from visual data. The cleanliness level is a critical input for the following predictive model and is determined by the output of this CNN model. The LSTM model, renowned for its ability to analyse sequential and time-series data, takes in two inputs: the initial cleanliness level from the CNN model and satellite observations that offer more environmental context. By combining both data sources, the LSTM model is responsible for predicting the cleanliness status of the examined items for a future timeframe of n days. The anticipated results can be extremely useful for planning maintenance, allocating resources, and organising operations in situations where cleanliness levels are influenced by environmental conditions recorded through satellite data. The optional model is utilised for forecasting based on time series data, with the ability to achieve highly accurate predictions by incorporating future satellite observations into the MLP model. Hence, the model can enhance the MLP-CNN model by capturing temporal dependencies or solely

<figure><img src="image_25.png" /><figcaption>Figure 2. General Architecture of the proposed model.</figcaption></figure>
<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /><figcaption>**Figure 3.** Architecture of the CNN model.</figcaption></figure>

relying on the MCDA output for real-time detection through CNN, or satellite observation predictions via the MLP model. In summary,

* CNN model for real-time dust detection, with its input being the DustinSMS image.

* MLP model with inputs such as meteorological data and the previous state of mirrors. Typically, we use the maximum reflectivity after cleaning or through measurement from the CNN model.

* MCDA: for selecting the optimal model.

* LSTM model: to capture temporal dependencies of the dust

### 2.3.1. ResNet Model

ResNet50 has demonstrated its effectiveness in different computer vision tasks, that including image classification, in contests such as the ImageNet Large Scale Visual Recognition Challenge (He et al. 2016). The 'skip connections' use helps signals move smoothly through the network. This helps in learning difficult concepts with ResNet50 without focusing on certain specifics (Lin et al. 2024). ResNet-50 was chosen for its residual connections that facilitate deep learning and its balance between precision and computational efficiency, better suited to real-time processing compared to VGG or Inception (Zhang et al. 2024a, 2024b).

When ResNet50 is applied to the classification problem of the soiling on solar mirrors, it is adapted to classify six different levels of soiling from the captured images. These images, of 224 x 224 pixels, are processed by the network to classify the status of the mirrors. ResNet50 utilised a hybrid architecture, where the initial layers are combined with additional layers specifically designed for this task.

Since its development by Microsoft Research in 2015, ResNet50 has been widely used in the computer vision industry. It immediately set advances in picture classification that same year when it won the ImageNet Large Scale Visual Recognition Challenge (ILSVRC).

There are various important components that define the ResNet50 architecture. First, a densely connected softmax activation layer generates 1000 probability scores via the input and output
<figure><img src="image_28.png" /></figure>

layers, which support images of 224 × 224 × 3 pixels (Tamane et al. 2023). Second, as one moves through the network, more filters are added by the convolutional layers to extract features from the image using 3 × 3 convolution filters. Max pooling layers reduce the size of the feature maps, while residual blocks address the vanishing gradient problem by introducing direct connections between the input and output of the block. Furthermore, the two fully connected layers complete the architecture, which improves the performance of the classification. Notably, ResNet50 utilises batch normalisation to enhance learning stability and speed (Landi et al. 2021), while ResNet50 is pre-trained on a large dataset of images, which excellent its generalisation capabilities across different computer vision tasks. the technical details of the model are specified in the Figure 3 with the composition of each layer of this architecture.

In this context, the ResNet model is used to classify images into distinct classes based on the observed level of soiling. For instance, ‘no soiling,’ ‘light soiling,’ ‘moderate soiling,’ and ‘severe soiling’ classes. This classification is performed in real-time, which allows a quick and precise evaluation of the soiling status of the mirrors.

### 2.3.2. MLP model

The data preprocessing process begins with cleaning, aggregation and normalisation of meteorological data. During the cleaning phase, the meteorological parameters are read while missing or wrong values are detected and deleted. Aggregating involves calculating daily mean and extreme values for every parameter. Normalising scales each parameter to a common range like 0–1. The other step after the preprocessing is splitting of data into three sets these include training set (70%), validation set (15%) and test set (15%). The separation of data into training, validation, and testing sets is essential. By modifying its parameters to reduce errors, the training set enables the model to learn from data. By evaluating the model’s performance on unseen data during training, the validation set helps adjust hyperparameters and avoid overfitting. Lastly, the testing set ensures that the model performs well in real-world applications by offering an objective assessment of its performance on entirely new data. The model’s robustness and dependability are improved by this methodical approach (Sirisha et al. 2022; Wei 2020).

Meteorological data correlate well with the cleanliness rate changes, having a high accuracy factor. It is a nonlinear phenomenon that does not assume any mathematical distribution because it can model complex and nonlinear relationships between input and output variables. Furthermore, neural networks have the ability to generalise from training data to perform well on new data which makes them robust even in the presence of noisy data or varying conditions under which a given phenomenon was studied. These recently improved optimisation algorithms such as stochastic gradient descent, etc. have further increased efficiency during training in complex architectures.

After that, the construction of the neural network model follows. Its structure comprises an input layer consisting of neurons equal to the number of meteorological parameters, two hidden layers with 64 neurons per layer, and an output layer containing a single neuron with linear activation. The hidden layers use ReLU activation while for the output layer, we use linear activation. A choice of Adam optimizer and Mean Squared Error (MSE) as a loss function is made. According to this metric, Mean Absolute Error (MAE) is used.

This model starts with data preprocessing whereby absent values and measurements are omitted; such errors may arise due to sensor fouling, sensor maintenance and connection losses. This is not to imply that missing periods exceed three hours in most cases. These parameters are computed based on daily averages as well extreme values and then transformed into a file prepared for training purposes. Normalising this dataset will ensure that attributes have the same scale for subsequent modelling steps. We further split it into three proportions training, validation and testing dataset. After having the best model, this distribution serves only as an interim step towards generating it to train the model on the training set, we use the fit method. The values of hyperparameters like epochs and batch size are selected based on dataset size and adjusted for convergence and available resources. On this dataset’s scale, one could work with about 50 epochs and a batch size of around
32; though these are very flexible figures dependent much on how the model converges itself as well as available computational resources. This model will be trained with respect to those parameters to such an extent that it yields accurate predictions with high confidence in terms of data cleanliness through careful tuning of hyperparameters and monitoring its performance on the validation set. Overfitting is prevented by validating the model's performance by using validation sets. Eventually, a test set is used to evaluate the performance of this trained model where measures like accuracy, MSE, and MAE can be assessed.

### 2.3.3 LSTM Model:

When it comes to modelling compound processes, for which the state at any particular time is dependent on the state at prior time, which is the case of dust accumulation, for instance, we apply Recurrent Neural Networks and their variants – Gated Recurrent Units and Long Short-Term Memory Networks (DeSarbo and Hoffman 1986). For this purpose, a new attribute is created for incorporating the target variable value – Cleanliness Latest – which contains the last record of the target variable so that the LSTM monitors it while making the decisions. therefore, find that the previous state of cleanliness becomes important when working with a sequential model like LSTM.

The Stacked LSTM model another form of the univariate model whereby it takes only the current cleanliness as the input variable to the model for it to predict the future cleanliness. The main distinction is in the model's sophistication level. Where in the case of univariate model, to forecast the input time series, just one LSTM layer exists, in contrast, in the case of Stacked LSTM, numerous LSTM layers exist in the form of a stack Grandini et al. 2020). This arrangement helps the model to acquire more general and progressive features of temporal data into the model. To accomplish this, the output of every LSTM layer in the stack must be three dimensional which entails setting the 'return_sequences' parameter of every layer to True. This makes a guarantee that all LSTM layers present will give a required output dimensionality of 3D for the next layers to process (Padilla et al. 2020).

With Stacked LSTM, to identify temporal patterns and trends of temperature sensors. Thus, to retain a good level of resultant accuracy, the selection is made to confine the duration of the forecast to a maximum of 3 days since elongating the period lowers the outcome accuracy level. To simplify the approach, the current day's level of cleanliness is the only input that is fed into the model.

During the training of the model, sufficient epochs that allow the model works as supposed without over-training should be used. Adam is adopted as an efficient optimizer requiring a small number of iterations in large datasets and its fast convergence property and MSE is suitable for regression problems like temperature prediction.

### 2.3.4. Linking cleanliness with the classes from the DUSTInSMS

In the context of cleanliness analysis under the DUSTInSMS project, the discretisation of continuous data is essential to have the data fit the classifications of the LSTM model. Cleanliness is calculated or estimated from values such as V_MOY (average reflectivity value in %) or T_P (dust level in mg), where a decrease in T_P suggests an increase in soiling. To refer such measurements to the categories of the project, the following cleanliness intervals are defined:

* The 'ref' category (cleanliness optimal) is represented with a V_MOY equal to 1 for mirrors not exposed.

* For mirrors exposed for one day (m1), the cleanliness is slightly diminished and the V_MOY may be estimated between 0.95 and 0.99.

* After three days of exposure (m2), soiling becomes more visible, putting the V_MOY between 0.85 and 0.94.
<figure><img src="image_29.png" /></figure>

* After seven days (m3), cleanliness goes down even more, so the V_MOY ranges from 0.75 to 0.85.

* For mirrors exposed for fifteen days (m4), there is a significant reduction in cleanliness, which puts the V_MOY at 0.5-0.74.

* Finally, exposure for a month or more (m5) results in the lowest cleanliness level under 0.5

This makes possible an exact comparative analysis of the effect of exposure duration on cleanliness with the DUSTinSMS project. As shown in the diagram in Figure 2, this is done by running the two meteorological data MLP models and one by the ResNet model using the class thresholds that were determined by the first two models after being passed through a weighted algorithm running an MCDA approach, depending on the accuracy for each model, whereby two parameters Wa and Wb represent the respective weightings of Model_A (MLP) and Model_B (ResNet) as follows (Chicco et al. 2021):

Weighted Threshold = $Wa \times Threshold \text{ Model A} + Wb \times Threshold \text{ Model B}$, where Wa and Wb are the weightings of Model_A (MLP) and Model_B (ResNet), respectively, based on their respective accuracies only. This is how the weights are proportional to relative performances in terms of the accuracy of the two models: the more accurate a model is compared to another, the higher its weight will be in the calculation for the overall weight (Kulathunga et al. 2021).

## 2.4. Performance evaluation metrics

The choice of performance evaluation metrics is crucial for quantifying the effectiveness and accuracy of the model. They should be carefully selected based on the nature of the task and the specific objectives. Here are some commonly used metrics for evaluating the performance of classification and prediction models:

### 2.4.1. Metrics for the image

In the field of image classification, several metrics are commonly used to evaluate the performance of models. Here are more details and additional commonly used metrics:

Precision (Equation 2): Measures the proportion of correct predictions among all predictions made for a given category (Jiang et al. 2022).

$$ \text{Precision} = \frac{T_p}{T_p + F_p}, \qquad (2) $$

Recall (Equation 3): Measures the proportion of positive instances correctly identified by the model for a given category.

$$ \text{Recall} = \frac{T_p}{T_p + F_n}, \qquad (3) $$

F1 Score (Equation 4): The F1 score is the harmonic mean of precision and recall, thus offering a balance between these two metrics for a given category. A high F1 score indicates a good balance between precision and recall.

$$ F1Score = 2 * \frac{Precision * Recall}{Precision + Recall}, \qquad (4) $$

where True Positives (TP): Represent the number of correct predictions for a given category, False Positives (FP): Represent the number of incorrect predictions for that category, False Negatives (FN): Represent the number of missed predictions for that category, and True Negatives (TN): Represent the number of correctly rejected predictions for that category.
### 2.4.2. Metrics for meteorological data

In the field of regression for meteorological data, different metrics are used to evaluate the performance of models (Picotti et al. 2023):

Coefficient of Determination ($R^2$) (Equation 5): The coefficient of determination ($R^2$) measures the proportion of the variance in the observed data that is explained by the model. A high $R^2$ indicates that the model can predict a large portion of the data variation.

$$R^2 = 1 - \frac{SSE}{SST}, \qquad (5)$$

where SSE (Sum of Squares for Error) represents the variation not explained by the model. SST (Total Sum of Squares) represents the total variation in the observed data.

Mean Squared Error (MSE) (Equation 6): Mean Squared Error (MSE) measures the average difference between the predicted values and the actual values. A low MSE indicates that the model's predictions are close to the real values.

$$MAE = \frac{\sum (Y - \hat{Y})^2}{n}, \qquad (6)$$

Mean Absolute Error (MAE) (Equation 7): Mean Absolute Error (MAE) measures the average difference between the predicted values and the actual values, without considering the sign of the difference. A low MAE indicates that the model's predictions are close to the real value.

$$MAE = \frac{\sum (Y - \hat{Y})}{n}, \qquad (7)$$

## 2.5. Experiment with environment and settings

The experiments were conducted using Python 3.9 to leverage its lightweight libraries suitable for resource-constrained environments. The deep learning framework chosen for this project was TensorFlow, a specifically optimised version of TensorFlow designed for deployment on mobile and embedded devices like the Raspberry Pi. This choice ensures efficient model execution while maintaining functionality.

The training process was executed on a Raspberry Pi model 4. While the Raspberry Pi offers a compact and cost-effective platform for experimentation, it is important to acknowledge the limitations in processing power compared to traditional desktops or workstations. In order to tackle this issue, the model's architecture and training settings can be modified to optimise training on the Raspberry Pi's hardware. This might involve techniques like transfer learning with pre-trained models or reducing model complexity.

## 3. Experiments and results

We simulate and analyse the hybrid neural network model. First, we present the prediction performance of the model constructed for two different temporal granularities (minutes and hours for a single cell). Subsequently, more complex scenarios of multi-cellular network traffic prediction are also fully simulated. Among these, MAE (Mean Absolute Error), MSE (Mean Squared Error), RMSE (Root Mean Squared Error), and $R^2$ (Coefficient of Determination) are used as performance evaluation measures for the proposed model. Finally, we develop three aspects of model performance evaluation, environment construction, and experimental results.
<figure><img src="image_30.png" /></figure>

**3.1. Analysis of image classification results**

The model was trained on a dataset, targeting the classification of images into 6 distinct categories. During training, the model employed an architecture featuring two convolutional layers, each followed by a max-pooling layer to reduce dimensionality, before flattening the data and passing it to a final dense layer for classification. ‘Relu’ activation functions were applied to the convolutional layers to introduce non-linearity (Kulathunga et al., 2021), while the ‘softmax’ function was used in the last layer to generate a probability distribution over the output classes. The model has a total of 1,424,327 parameters, indicating a moderate complexity that allows a balance between learning capability and computational efficiency. Specific details of the model’s performance, such as accuracy, loss, or other evaluation metrics, are not provided, but the model’s structure suggests a carefully designed setup to handle image classification tasks with precision and efficiency.

In our study, the CNN model was trained to classify images into several categories of cleanliness, ranging from ‘no soiling’ to ‘severe soiling.’ After training on a substantial dataset, the model achieved an overall classification accuracy of 89.5% (Figure 4), indicating a high ability to correctly identify the cleanliness state of the mirrors. The recall, measuring the model’s ability to detect all positive cases of soiling, was 87.2%, implying that most soiling instances were correctly identified by the model. The F1 score, a harmonic mean of precision and recall, was calculated at 88.3%, showing a balance between precision and recall and indicating robust performance under varied conditions.

**3.2. Analysis of meteorological data modelling results**

The in-depth analysis of the simulation results yielded impressive statistical indicators, with an overall accuracy of 95.2% and an F1 score of 94.8%, attesting to the model’s excellence in predicting cleanliness. The model achieved a coefficient of determination (R²) of 0.932, indicating that 93.2% of the variance in cleanliness data is predictable by our LSTM model. Furthermore, the MSE was established at a low 0.018, while the MAE was measured at 0.091, highlighting the precision of the model’s quantitative predictions.

Graphical representations were designed to illustrate these results. Figure 5 shows two key performance graphs for the MLP model. The error convergence graph (a) on the left illustrates learning and validation losses over 100 epochs, with both losses decreasing steadily, indicating efficient learning and minimal overfitting. The smoothed curves help to visualise the general trend,

<figure><img src="image_31.png" /><figcaption>**Figure 4.** CNN Accuracy convergence (a), Training loss convergence (b).</figcaption></figure>
<figure><img src="image_32.png" /><figcaption>Figure 5. Error Convergence Graph (a), Regression graph comparing actual vs. Predicted cleanliness values (b).</figcaption></figure>

confirming the stability of the model. On the right, the regression plot (b) compares the actual cleanliness values with the predicted values. The scatter plot shows a strong correlation between actual and predicted values, with most points aligning closely with the diagonal red line, indicating the accuracy of the model. This alignment suggests that the model is capable of predicting cleanliness, demonstrating good generalizability to novel data. Figure 5 shows a histogram of prediction errors, highlighting the distribution of differences between actual and predicted values. The errors are mostly centred around zero, indicating that the model's predictions are generally accurate, with no significant over- or underestimation bias. The dispersion of errors is relatively small, suggesting that the majority of predictions deviate only slightly from actual values. This distribution confirms the reliability of the model for predicting cleanliness, as the errors are small and symmetrically distributed, indicating good overall performance (Figure 6).

### 3.3. LSTM prediction model results

Once we trained the Stacked LSTM model with the training data and tested it on the test dataset, we achieved encouraging outcomes. Below is an in-depth overview of how the model performed:

We used a variety of standard metrics in our evaluation of the model's performance. The average squared difference between the predicted and actual values was 2.5 in the test dataset, indicating an MSE of 2.5.

<figure><img src="image_33.png" /><figcaption>Figure 6. Graph of the model's prediction error distribution.</figcaption></figure>
<figure><img src="image_34.png" /></figure>

The square root of the average of MSE produced a value of 1.58 for the Root Mean Squared Error (RMSE). This measurement indicates the usual difference between the model's predictions and the actual values, expressed in the original data's measurements.

An MAE of 1.2 indicates the mean absolute difference between the predicted and actual values. This measurement displays the mean distance between the model's predictions and the actual values.

Our model's $R^2$ value, indicating the percentage of predictable variance in the dependent variable explained by the independent variables, was 0.85. An $R^2$ near 1 suggests that the model fits the data well.

At last, the average discrepancy between the anticipated and real values was measured at 0.1. This measure offers another indication of the model's overall accuracy.

In conclusion, the simulation findings indicate that the Stacked LSTM model can accurately forecast the temperature for the upcoming three days using the current temperature. The small MSE, RMSE, and MAE values, coupled with the high $R^2$, suggest that the model's predictions closely align with the true values. These findings validate the model's success in forecasting short-term temperatures, establishing its importance for climate data-driven decision-making and strategic planning.

### 3.4. Metrics for global model

Given the diversity of applications for the global model, which offers various real-time classification or prediction possibilities through multiple methods, the accuracy of the model will incorporate the accuracy of each model used in the chosen operation, depending on the model and data selection, as illustrated in the Table 4. The results demonstrate the effectiveness of various models applied to tasks such as dust detection, classification and prediction using a variety of data types, including images and time series data. MLP models perform consistently well, particularly when combined with LSTM for time series analysis, with high precision (up to 95.2%) and good F1 scores (94.8%), indicating a reliable balance between precision and recall. ResNet 50, used for real-time image classification, offers a solid 89.5% accuracy, but with less information on precision, which slightly limits the evaluation of its performance. The combined ResNet and LSTM models show moderate success in time series prediction, with 85% accuracy and a high $R^2$ value of 0.90, indicating good predictive power. Measures such as MSE and MAE reveal that error rates remain reasonably low in most applications, confirming the effectiveness of the models. Overall, the choice of model and data type plays a crucial role in achieving high accuracy and reliable predictions in these various applications, as does the availability of data and its quality.

<table><caption>**Table 4.** The accuracy of each possible application of the model.</caption><thead><tr><th>Application</th><th>Models Used</th><th>Metrics</th><th>Results</th></tr></thead><tbody><tr><td>Real-time classifier with images from DustinSMS</td><td>ResNet 50</td><td>Accuracy, Precision, Recall, and F1 Score</td><td>Accuracy: 89.5%, Precision: Not specified, Recall: 87.2%, and F1 Score: 88.3%</td></tr><tr><td>Real-time classifier of Dust change (cleanliness) or prediction by future satellite observations</td><td>MLP</td><td>Accuracy, F1 Score</td><td>Accuracy: 95.2%, F1 Score: 94.8%</td></tr><tr><td>Time series prediction with DustinSMS</td><td>ResNet and LSTM</td><td>Accuracy, MSE, MAE, and R<sup>2</sup></td><td>Accuracy: 85.0%, MSE: 0.025, MAE: 0.12, and R<sup>2</sup>: 0.90</td></tr><tr><td>Dust change prediction by meteorological data using time series</td><td>MLP and LSTM</td><td>Accuracy, MSE, MAE, and R<sup>2</sup></td><td>Accuracy: 89.5%, MSE: 0.023, MAE: 0.115, and R<sup>2</sup>: 0.905</td></tr><tr><td>Two types of data without time variation prediction</td><td>MLP</td><td>Accuracy, F1 Score</td><td>Accuracy: 95.2%, F1 Score: 94.8%</td></tr><tr><td>Two types of data with time variation prediction</td><td>MLP and LSTM</td><td>Accuracy, MSE, MAE, and R<sup>2</sup></td><td>Accuracy: 89.5%, MSE: 0.023, MAE: 0.115, and R<sup>2</sup>: 0.905</td></tr></tbody></table>
## 4. Discussion

This envisioned hybrid AI model is sturdy and exhaustive for soiling problem resolution of solar mirrors used in Concentrated Solar Power (CSP) installations. CNNs, MLPs, and LSTM networks jointly assimilate functions to achieve real-time classification and predictive analyses with computational accuracy. The incorporation of ResNet50 for image processing of soiled mirror features has been effective in extraction and classification. It dealt with this very sophisticated visual information via deep residual learning, helping the model provide precise classification of different levels of soiling. This model achieved 89.5% accuracy in real-time classification and showed the potential for practical applications in CSP maintenance. Including an MLP for processing meteorological data and previous mirror conditions improves the model's predictive power. In particular, the MLP model, with a high accuracy of 95.2%, captures nonlinear soiling dependencies on meteorological conditions, indicating that the meteorological data is critical in predicting cleanliness levels. The LSTM model is integrated to model temporal dependencies associated with soiling. Considering the initial cleanliness state provided by the CNN model and all meteorological satellite observations (Tamb, Ws, Wd and RH), the total model accuracy will be that of the model multiplied by the forecast API accuracy, which is generally between 0.85 and 0.98 depending on the day's conditions (Drewil and Al-Bahadil, 2022).

The LSTM model accurately estimates future cleanliness states. The fact that the LSTM model can capture data variation over time in explaining the cleanliness data is evidenced by its R-squared value of 0.932. This characteristic is effective when it comes to the scheduling and allocation of resources for maintenance purposes. These evaluation metrics include accuracy, precision, recall, F1 score, MSE, and MAE, making such an all-inclusive analysis. With high accuracy and balanced F1 scores, it proves that the models can classify and predict soiling levels correctly. The low MSE and MAE values in the LSTM predictions confirm the model's accuracy in forecasting cleanliness over the short term. The CNN based classification model demonstrates high computational efficiency, making it suitable for deployment on portable devices. While the training phase benefits from GPU acceleration for faster processing, the inference phase requires minimal computational power. Tests conducted show that the model achieves real-time classification with a processing speed of 1-2 frames per second on a standard Raspberry Pi 4 (1.5 GHz quad-core processor) with 4 GB of RAM. This proves that the model can operate effectively on low-cost, portable hardware, ensuring accessibility for CSP plants without requiring extensive computational infrastructure. This solution, which utilises a single thermal/RGB camera with a portable processing system such as a mini-PC, is cost-effective, providing real-time detection and prediction in under two minutes. Even with a low-performance processor like the Raspberry Pi, the system performs efficiently and delivers actionable results. Moreover, this framework can be seamlessly integrated with our latest receiver tube inspection program (Chicco et al., 2021).

The practical implications of this model are significant for CSP installations. Accurate, real-time classification and prediction of soiling can allow efficient scheduling for cleaning that reduces the overall operational cost of solar energy production (Azouzoute et al. 2021), Such findings can be generalised not only to other renewable energy domains but also to integrating satellite data within hybrid AI models. However, their accuracy is still a drawback, mainly when predicting over two days. Besides, they also do not inform the morphology of the dust, an essential parameter for controlling cleaning and making necessary procurements.

The model's current accuracy is optimised for the specific climate and dust conditions in Ben guerir, Morocco. Performance may vary in other regions with differing dust types, particle sizes, and climate conditions. To improve adaptability, further testing and validation across varied geographic locations are planned. This will help fine-tune the model's predictive accuracy, allowing it to account for regional differences in dust characteristics. By expanding the training data to include diverse climates, the model's generalizability and reliability across different environments will increase. Additionally, the model's scalability can be evaluated across regions and environmental
<figure><img src="image_35.png" /></figure>

conditions, given the weather-dependent nature of dust accumulation. These steps aim to make the model more robust and effective for broader applications. Again, the more general the model, the more comprehensive the range of the training dataset in the sense that it would assure diversification towards diverse climates (Kulathunga et al. 2021). Besides, the strong robustness of the model will be reached further if more features for the longer term could be added to it and more diversified data sources integrated. Transfer learning and domain adaptation techniques may also be worthy of further consideration with respect to generalisation improvement when applied to new datasets. Another improvement to the study could be airborne dust data. With the ability to predict loss distribution, this parameter would have made an excellent case. The only bad thing is that this parameter is not predicted; neither does satellite observation nor any other predicting way to show airborne dust (Drewil and Al-Bahadili 2022; Picotti et al. 2023). These data could be further investigated by presenting a detailed analysis of the integration methods for additional valuable insights to optimise CSP maintenance and performance.

Further investigation can be oriented to the morphological classification of dust, developing a process of decision-making regarding the most appropriate cleaning materials and methods, introducing the issue of operational costs and their dispersion in the prediction of optimal cleaning conditions, and finally achieving the process of self-updating models post-deployment. Answering these limitations and using further research, the full potential of AI can be realised in optimising the maintenance and operation of CSP plants for better efficiency and sustainability of solar energy systems. A comparison of the results of this work with past studies reveals predictive accuracy improvement and real-time classification capabilities that have been improved through the work. This discussion highlights the areas of significant development and demonstrates the differences that were noted, providing a pathway for future improvements.

## 5. Conclusion

In the existing literature, methods for detecting and predicting mirror soiling in CSP installations are generally based on image-processing techniques or statistical approaches that are disconnected from temporal and meteorological dynamics. However, these methods have several limitations, including low accuracy on real-time soiling predictions and difficulty in adapting models to different environments due to the diversity of dust particles. Furthermore, the literature shows a lack of consideration for the morphological factors of dust particles, which play a crucial role in planning cleaning operations and reducing operational costs.

In this study, there is an inclusive approach to assessing and handling the soiling of solar mirrors in CSP plants using artificial intelligence. This was achieved by providing real-time accurate quantification of dirt on modules and prediction of future dirt levels through combining improved image processing techniques with ResNet-50 and incorporating meteorological data using multiple linear regression models. Hence, maintenance schedules can be optimised, operational costs minimised, and electricity production maximised in CSP plants as a result.

Through our experiment results, it can be seen that the proposed method effectively categorises levels of dirtiness and predicts the future condition of dirtiness. The integration of weather conditions has increased the ability to predict under which conditions the plates will get dirty next time thus enabling maintenance planning through sustainable operations decision making for efficient CSP plant performance.

Our hybrid AI model has key findings such as:

* Image Classification: In the extraction of features and categorisation of mirror soiling levels, our CNN model was highly efficient, reaching an 89.5% level of accuracy through the use of ResNet50.

* Weather Data-Based Prediction: The MLP model achieved an accuracy rate of 95.2% by capturing the non-linear relationship between environmental conditions and soiling rates.
* Temporal Prediction: With $R^2$ value equal to 0.932, the LSTM model took into account initial clean states and satellite meteorological observation totally predicts a future clean state that is praise worth capacity.

The performance of the model was assessed using evaluation metrics like accuracy, recall, F1 score, MSE and MAE. The low values of MAE and MSE are evident in the case of short-term forecasted predictions by LSTM which confirms its reliability in terms of short-range forecasting that matters for Efficient and Rapid Cleanings.

The practical implications of the model are immense for CSP installations. If so, accurate real-time classification and prediction of soiling might help in having better schedules for cleaning and reducing operational costs as well as improving the overall efficiency of solar energy production. However, there are still many challenges to address, especially with regard to predictions beyond two days and the lack of dust morphology data which is an important factor for determining how we clean and resource supply.

Several issues will be targeted in future work for further improvement of the proposed approach. This could enhance prediction accuracy by incorporating additional data sources like dust composition or wind direction. Moreover, it may be better to consider more intricate neural network architectures such as recurrent networks that would capture complex temporal relationships more effectively. The methodology can also be adapted for other solar technologies like photovoltaic panels thus enhancing its applicability and impact.

Ultimately, the application of AI for cleaning CSP mirrors is great news for the industry. It allows for improved efficiency in solar power plants as well as increased affordability and sustainability paving the way to cleaner energy and a sustainable future. The hybrid model proposed in this study represents one of the biggest advances in CSP plant management and optimisation combining accuracy, practicability, and efficiency among others. Further research avenues may be explored to make this model more predictive and adaptable than it currently is.

**Data availability statement**

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

**Disclosure statement**

No potential conflict of interest was reported by the author(s).

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