## 1 Introduction
[38] classified shading due to soiling into two types: soft shading resulted from the airborne materials, and hard shading due to accumulated soil on the PV surface. It was reported that soft shading affects the current whereas hard shading affects the voltage. Thus, cleaning on a daily basis was recommended for severe accumulation, and on a weekly basis in the dry season. Results from an experiment conducted in Belgium by [39] showed that there is a constant power loss of 3-4% for a 35\({}^{\circ}\) tilt angle due to dust effects. In addition, it was concluded that rainfall definitely helps in cleaning large particles but has only a slight effect on smaller ones. It was shown in [40] that cleaning dust using nylon brushes will not have a significant effect on the optical parameters of the glass surface. However, the cleaning efficiency is not high compared to water cleaning using soft wipers. The derivation of a mathematical model to calculate cleaning frequency for PV panels is done in [41]; the suggested model is a function of particle accumulation density, particle deposition velocity, and particle mass concentration. It was shown that for a reduction of power output of 5%, a cleaning frequency of 20 days is recommended for desert regions. It is worth mentioning that modeling PV efficiency as a linear function of dust accumulation and ambient temperature is valid and supported by observation and experiments published by other researchers [42; 43; 44; 45; 46]. A brief review of the energy yield losses caused by dust deposition on PV systems is reported in [42]. A number of experiments supporting the assumption of a linear approximation for efficiency reduction versus dust deposition is presented in this review. Another study focusing on the effect of tilt angle on soiled PV panels was conducted and proposed an empirical 2 nd polynomial correlation of power reduction as a function of the number of unclean days and tilt angle [43]. The coefficients of linear terms are significantly larger than those of the quadratic terms. The soiling losses are found to aggregate linearly with time in two studies performed in California, USA [44; 45]. A decrease in efficiency varying from 7.2% to 5.6% during 108 days of the dry period in the summer was noted [44]. In addition, it was stated that there were losses of 7.4% and 13.9% in efficiency for an average of 145 days of summer drought and more than 145 days of drought, respectively [45]. Experiments for a 3-month period in the Sahara area, Algeria, for PV modules for different dust densities were conducted in [46]. The reduction in efficiency was modeled by a polynomial expression of the 3 rd order, with the coefficient of linear term being very large compared to the coefficients of the quadratic and cubic terms by one and two orders of magnitudes, respectively. In short, and by revisiting the introduction above, it is obvious that the combined effect of dust accumulation and ambient temperature on PV systems depends on environmental and metrological conditions as well as the geographical location. It is important to investigate the effect of such parameters so that the power loss can be minimized. Additionally, many researchers have tried to find the best cleaning method and frequency. In this research, we build simple and accurate mathematical models based on the actual performance conditions to predict the behavior of a PV system and determine its optimum cleaning frequency. This work aims to add a significant contribution to the PV literature. In this work, we have experimentally collected PV system parameters during a 192-day period under real conditions. Based on the performance parameters, two models are developed to predict the system output behavior employing optimized artificial neural network (ANN) and optimized extreme learning machine (ELM) models [47].