Physical model has been implemented for centuries to evaluate the illuminance quality in the interior of buildings (Bodart et al. 2007). The models are usually made of card, wood or plastics. The accuracy of evaluation highly depends on measurement position, model geometry and manufacturing details, especially the surfaces reflectance, fenestration and glazing transmittance. The experiment is usually undertaken under the real sky conditions or Commission Internationale de L'Eclairage (CIE) artificial sky.

Littlefair (Littlefair 2002) proposed a scale model to predict daylight level within an atrium building. It evaluated the performance of an atrium and the illuminance level of neighbouring space. Kim et al. (Kim and Chung 2011) built a 1:20 scale model for measuring indoor illuminance of Seoul Art Museum installed with toplights. With the scale model, the building details, including façade, textures, furniture and inner layout or figures, can be considered. A case study has been done by Aghemo et al (Aghemo et al. 2008) to simulate daylight environment of a high school classroom with various shading system in Italy. By simulating different sky conditions and sun paths, the best shading scheme can be determined. Some rules should be followed in order to get accurate results (Bodart et al. 2007; Littlefair 2002). General regulations include using original building structure and geometry, preventing light leaking, and choosing the same material property. Further, specialized rules include using appropriate model size and scale varying from 1:500 to 1:1 based on different modelling purpose, the test sensor size and position in the model, etc. The advantage of this method is able to analyse the daylighting performance quantitatively and qualitatively at the same time. Normally, the daylight factor can be measured by photocells and visual impact could be directly presented. However, several studies have revealed that it is difficult to completely match the results from the physical models to those from the actual buildings. Further, it has been found that the daylighting performance in physical models tends to be overvalued. Therefore, using the scaled physical model alone would not be a reliable option.

The use of mathematical formulae is another useful method in predicting daylighting performance. This approach may be applied at three different levels, basic metrics, empirical formulae, date regression model.

Daylight factor (DF) is one of the most accepted and basic daylighting performance indicator, as defines below,

where is the average illuminance on all room surfaces, is the vertical illuminance on the window, LT is the light transmittance of glass, is the area of the window, is the total area of the indoor surfaces, and R is the area-weighted mean reflectance of all indoor surfaces (Li and Lam 2001). DF is the most widely used metrics of daylighting and adopted as a design criteria in relevant industry standards and guides (Kittler 2007). As the DF is defined for the overcast sky condition, it does not need to consider the building orientation and location, so it is easy to be determined analytically. However, the solar angles and redirection of sunlight are not considered in the formulation of the DF. This often causes problems if the DF metrics is used for prediction under other sky conditions rather than the overcast sky.

The DF value is generally for certain point, to estimate the average illuminance on a working plane. Littlefair (Littlefair 2002) introduced the concept of average daylight factor () and gave an empirical formula,

where W is the glazing area (m²), T is the transmittance of the glazing and θ is the angle of visible sky at the centre of the window. A is the total area of room surfaces, including roof, floor, walls and windows (m²). R is the average reflectance of these surfaces. Similar to Eq. (1), this formula for daylight is easy to use but it summarises the overall daylighting performance. Love and Navvab (1994) proposed a new metrics as an indicator of daylighting performance, which is the vertical-to-horizontal illuminance ratio (VH ratio) (Love and Navvab 1994), that is, the ratio between the illuminance value on a vertical window and outdoors horizontal illuminance value as given by Equation 3. They found that the VH ratio is more stable than the DF under real sky conditions, so more suitable to be used to estimate the illuminance and determine the glare.

Besides these basic formulae, advanced mathematical equations can also be extrapolated based on measurement or theoretical derivation. Kim et al. (Kim and Kim 2007) used multiple linear regression method to build a mathematical model to forecast the fluctuation of external daylight illuminance. Kazanasmaz (Kazanasmaz 2013) used the fuzzy logic model to examine the uniformity of daylight illuminance in an office. In recent years, for advanced daylight guide and transmission systems, some mathematical models were put forward to predict the daylighting performance of a system. Su et al. (Su et al. 2012) proposed a regression model to forecast the output lumen value of a light pipe. Moreover, both (Swift and Smith 1995) and (Dutton and Shao 2007) explore the mathematical model to predict the transmission of light pipes.

Compared to physical model and mathematical formulae, computer optical simulation combines the benefits of both illuminance calculation and interior visualization (Littlefair 2002). Moreover, it does not require any physical materials, which is economic, and environment friendly while significantly saves time. Computer simulation can also be much more accurate in certain cases. Radiosity and raytracing are the fundamental methods to calculate illuminance in computer simulation. Radiosity analyses simple surfaces with diffuse element method while raytracing technique deals with complex surfaces with specular reflection (Kazanasmaz et al. 2009). The common computer modelling tools include RADIANCE, LightTools, Photopia, TracePro, EnergyPlus, IES, DAYSIM, Ecotect, Relux, Dialux, Lightsolve, ADELINE, CODYRUN, SkyCalc, Autodesk, SPOT Pro, Lightscape, RadioRay, Microstation, etc.

Those computer software packages have been used extensively in the recent years to predict daylighting performance and evaluate daylighting designs. For instance, Jovanović et al. used DAYSIM to calculate DF, daylight autonomy (DA) and useful daylight illuminance (UDI) (Jovanović 2014). Li et al. used RADIANCE to simulate the illuminance value in different categories of buildings (Li and Tsang 2008). Similar studies could be found in literatures (Apian-Bennewitz et al. 1998; Kim and Chung 2011; Krüger and Dorigo 2008; Lim et al. 2012). Meanwhile, numerical software is also used to guide daylighting design. Andersen et al. employed Lightsolve to simulate the annual daylighting performance, which provided an ideal and reliable design guide for daylighting design in buildings (Andersen et al. 2013). Similarly, Gagne et al. used Lightsolve Viewer (LSV) for daylighting design and set up an interactive expert system to explore geometries of daylighting and performance goal in initial design stage (Gagne et al. 2011). Kota et al. (Kota et al. 2014) integrated BIM tool in Revit with Radiance and DAYSIM to simulate the daylighting situation.

In addition, some studies integrated two or more different types of numerical tools to simulate the daylighting level and predict energy saving. It has been reported in (Bodart and De Herde 2002), which coupled ADELINE to simulate daylighting and TRNSYS to simulate thermal condition and found that 50% to 80% artificial lighting could be reduced by daylighting which can save 40% energy cost. Chen et al. used Ecotect and RADIANCE to simulate the daylighting value and distribution (Chen et al. 2014). Meanwhile, EnergyPlus was used to determine the potential energy saving and some studies can be found in (Arranz et al. 2014; Galasiu and Atif 2002; Loutzenhiser et al. 2007; McHugh et al. 2004; Sabry et al. 2014; Tian et al. 2014).

Moreover, simulation techniques have been intensively used in recent years in evaluation of new daylighting systems and technologies. Acosta et al. (Acosta et al. 2013) employed Lightscape to simulate three different shapes of lightscoop skylights in order to choose a proper shape. Dutton et al. (Dutton and Shao 2007) used Photopia raytracing to predict the lightpipe transmittance. Ullah et al. (Ullah and Shin 2014) used LightTools and Dialux to simulate inner illuminance quality in multi-floor office buildings with installation of an innovative daylighting system which combines LED light with a highly concentrated optical fibre-based daylighting guide system. Page et al. (Page et al. 2007) used the raytracing method in RANDIANCE to simulate the visual comfort and performance of an office building installed with electrochromic glazing coupled with an anidolic daylighting system.

Different from conventional computational methods, ANNs simulation does not require building up any physical model. During the past three decades, ANNs has been used as an alternative approach to conventional prediction methods in many research areas. ANNs is a powerful tool in solving complex and non-linear problems in a number of fields by the means of simulation, identification, prediction, optimization, classification and control.

The ANNs simulation is a self-learning and self-training platform or programme. According to different network structures, ANNs models can be classified into 4 categories: Feedforward Neural Network, Feedback Neural Network, Self-organizing Map and Random Neural Network (as shown in Figure 2). Most of categories are straightforward applications of optimization theory and statistical estimation (Esen et al. 2009). ANNs can model multi-variable problems while extracting the non-linear complex relationships between the variables by means of training data. In the meantime, the performance of ANNs could be evaluated by some routine statistics indexes as shown in Table 1, which represent the accuracy of forecasting. These indexes would be used in section 3 to evaluate the ANN prediction ability.

Due to different strengths and requirements, different networks could be used in various fields. Almost all relevant researches in literature used the backpropagation (BP) neural network and its variants, which belongs to feedforward neural network category. BP neural network model is illustrated in Figure 3. It is one of the widest applications of ANNs and it is quite convenient and accurate. In fact, it is hard to determine the fastest training algorithm for a given problem. Instead, the most suitable one is always determined by the method of trials and errors. The BP neural network is normally composed of three components (Esen et al. 2008). These parts usually consist of one input layer, some hidden layers and one output layer, as shown in Figure 3. Within each layer, there are a certain number of neurons. The procedure for developing an ANNs model includes 3 phases including modelling, training and validating. First, modelling involves analysing data, identifying input parameters and selecting network architecture and internal rules. The prepared data can then be trained, for example, by using BP learning algorithm to establish a model. After the training of data and the establishment of the model, it should be validated before application. BP algorithm is a gradient descent method. The principle is that they are processing elements (PEs) and each connection of them has an associate weight. Each time it reduces the total error by changing the weights along its gradient to improve the performance of the network (Nasr et al. 2003). The process of an ANNs simulation starts with weighted summation activation of the neuron through its incoming connections; it is then followed by passing through an activation function and this activated value is the output of the neuron (Kalogirou 2001). Specifically, training BP model should assign random values to the weight terms () in all nodes initially. For the output layer for the case of the logistic-sigmoid activation (as shown in Figure 4), the error can be computed as follows:

For a node in a hidden layer:

where the subscript k is a summation over all nodes in the direction of the output layer. The subscript j is the weight position in each node. Moreover, δ and α for each node are used to calculate an incremental change to each weight via:

where ε is the learning rate which determines the size of the weight adjustments during each training iteration and m is the momentum factor which is applied to the weight change used in the previous training iteration. The values of ε and m are determined prior to the training cycle and controls the speed and stability of the simulation (Kalogirou 2003).

In light of non-linear problems, the sigmoid function is the most common logical transfer function in BP algorithm. It includes tansig and logsig algorithms (sometimes purelin algorithm is also used as the transfer function, but it is linear function which is less commonly used) (Hosseini 2016). They are both an “S” shaped transfer function, logsig ranging from 0 to 1 and tansig ranging from -1 to 1, which can be expressed in Figure 4.

Normally, 70% to 90% of dataset is used in training the model and the remaining dataset is used to test and validate the model. Relevant application of ANNs predictions in daylighting would be elaborated in Section 3.

These prediction methods all have their advantages and disadvantages in different aspects, while they may also be used together for some specific problems. In this section, the strengths and shortcomings for each prediction method are summarized in Table 2.

One of the criteria to assess the daylighting design is based on how much energy could be saved. Fonseca et al. (Fonseca et al. 2013) compared ANNs modelling and multivariate linear regression (MLR) in predicting energy saving by employing daylighting. The office simulated was located in Florianopolis climate in Brazil. The data was from 216 parameter groups in 3 types with different room depth (Figure 10). Cross-validation (Figure 11) was used to train and validate the ANN model due to limited data. The data was simulated by EnergyPlus (energy) and Daysim/RADIANCE (lighting). The ANN network architecture here adopted 6 input variables, 1 hidden layer with 10 nodes and 1 output variable structure. The 6 input parameters include quantitative variables (room depth, room orientation, solar heat gain coefficient, and window-to-wall ratio) and qualitative variables (vertical and horizontal shading coefficient). 90% of parameter groups to train the ANNs model while the rest 10% were for validation. Multifold cross-validation presents an excellent performance to solve the issue of limited data sets. From the comparison of their coefficients of determination, that is, R² = 0.9867 for ANN and 0.8028 for MLR, it is clear that ANN can provide much more accurate prediction of daylighting energy saving.

Electric lighting consumes about 20%~30% of office building electricity (de Bakker et al. 2017). Proper lighting design with utilization of daylighting can directly reduce the lighting energy consumption and also indirectly reduce air conditioning energy consumption which would be used to neutralize the heat released by artificial lighting. Wong et al. (Wong et al. 2010) used ANNs modelling to develop the daylighting design for an office building in subtropical zone. The daily electricity consumption for cooling, heating, artificial lighting, etc. was the output of the ANNs model (Figure 12). In this study, EnergyPlus simulations were first run followed by ANNs modelling – 70% and 30% of the data obtained from EnergyPlus was used to train and validate the ANNs model, respectively. Different from other researches, a commercial software named NeuroShell 2 was chosen as the prediction tool. A new coefficient Nash-Sutcliffe efficiency coefficient (NSEC) which can be expressed as in Equation 7, which is similar to the R² and was adopted to access the accuracy of the model.

where is the daily electricity consumption obtained in ANNs, and are the daily electricity consumption and the mean electricity consumption respectively simulated in EnergyPlus, n is the total number of data used in ANNs training and testing. NSEC was introduced to evaluate the model performance, which were 0.994, 0.940, 0.993 and 0.996 respectively. Logistic sigmoid was chosen as the active function. 3 groups of random input data generated by using Monte Carlo methods were employed to assess the accuracy of ANNs model. Statistical analysis involved MBD, RMSE, NMBE and CVRMSE. It was concluded that ANNs could well describe the non-linear relationship between input and output variables; it is especially useful at mass end use situations (e.g., cooling in summer and heating in winter). Moreover, ANNs model can optimize design parameters without carrying out experiments and avoid considerable time consuming. In order to get the relative minimum consumption of the total electricity, different combinations of input parameters were put into the ANNs model to predict the total electricity consumption value. The minimum energy consumption value can be obtained from the ANNs model in a mesh graphic (Figure 13) and the corresponding best input parameters for best design can also be determined.

According to (Dounis and Caraiscos 2009), if daylighting and HVAC (heating, ventilating and air conditioning) system are separately considered, it often causes conflicts between energy efficiency and environmental comfort. Hence, to set up an integrated control process, which could simultaneously satisfy all requirements as mentioned above, is essential. Due to the complex geometrical conditions and complex operations, ANNs would be an ideal option. Daylighting integrated with HVAC system is a nonlinear problem. The integrated daylighting and HVAC (IDHAVC) model (as shown in Figure 14) was set by Kim et al. (Kim et al. 2016) to predict the building energy performance. It was an integrated meta-model (Figure 15), which included regression models (indoor artificial illuminance model, lighting energy consumption model) and ANN models (temperature, indoor daylighting illuminance, total energy consumption). The building was located in Seoul, Korea and ANN were trained with data generated from EnergyPlus for three months. The ANNs model consisted of 4 variables for indoor daylighting illuminance and 11 variables for temperature and total energy consumption respectively. Levenberg-Marquardt (LM) algorithm was adopted to train the ANNs model. The number of hidden layers were fixed at three and the neurons in each hidden layers were optimized by Genetic Algorithm (GA). 70% of the data generated by EnergyPlus were used to train the model, 15% were used to test and the rest 15% for validation to avoid overfitting. The prediction accuracy is measured through R² which is bigger than 0.98. This optimization model was achieved via minimizing energy consumption but still keeping the same thermal and visual comforts of occupants. It was shown that 13.7% energy could be saved compared with original model.

Excessive daylighting could cause overheating problem in buildings, which increases the consumption of cooling energy. It is essential, in daylighting design, to estimate the daylighting control system to avoid unwanted sun light and thermal discomfort. According to different strategies for the control of lighting systems, daylight-linked lighting controls can be divided into daylight-linked switching and daylight-linked dimming (Li et al. 2010). Daylight-linked switching can control the light by switching between ‘On’ and ‘Off’ states based on available daylight. There may also be multi-level switching. For instance, based on the level of available daylight in a particular control zone, 33%, 50%, and 66% of light in the zone may be switched off. Dimming system controls the lamp outputs continuously using dimmable electronic ballasts. Dimming requires dimmable ballasts to maintain the illuminance level of the lamps, so it is more expensive than switching system. However, integrating energy efficient lamps with lighting control can significantly reduce electrical energy consumption (Lam, 2003) and also improve vision efficiency (Öztürk 2008). Adding lighting control system is widely common strategies in retrofitting project of lighting. Based on simulation studies, which predict the effect of retrofitting investment save the unexpected money and time. However, traditional simulations need a large number of data and a lot of time. ANN as a surrogate model was developed by Hu et al. to simulate lighting retrofitting in a building located in Chicago (Hu et al. 2015). It successfully solves the issue of time wasting and uncertainty retrofitting parameters. This model could predict the lighting and HVAC energy consumption under different combinations of lamp types, control strategies, weather conditions and occupants’ pattern. This created model could save a large number of repeating modelling runs. Surrogate modelling (SUMO) toolbox was firstly introduced into ANNs modelling. Weather condition, LED wattage and occupancy level and control strategies were all considered as input parameters in the modelling. The results of the ANNs modelling showed a reliable relationship between the input building parameters and the output lighting energy consumption. Meanwhile, it has shown that the minimum lighting electricity energy consumption could be achieved by using occupancy plus daylighting control replacing exciting manual control and change the T12 lamp to LED lamp. Another advantage of this model is the HVAC energy consumption could be obtained at the same time, which has 98% precision and considerably saves time.

Venetian blinds is another form of daylighting control, which can significantly control direct solar radiation and glare as well as overheating. Based on ANNs modelling, an illuminance-based slat angle selection (ISAS) model was developed to predict the optimum slat angles of split blinds to achieve the required illuminance (Hu and Olbina 2011). The input variables were the horizontal illuminance and the sun angle while the output was the illuminance level at a sensor point. The automated split-controlled blinds divided the whole blinds into three equal parts from the top to the bottom (Figure 16). EnergyPlus was employed to simulate the working plane illuminance at the sensors’ positions in an office located in Gainesville, Florida, USA. The illuminance data obtained from the EnergyPlus simulation, combined with weather parameters, were used to train the ANNs model which was subsequently validated. Once the ANNs model was established, the illuminance predicted by the ANNs model was employed to optimise the slats angle and to find the optimum value. Similar to most other researches, a multi-layer feedforward ANNs model with BP learning algorithm was derived. Illuminance at sensor points located at 3 positions of the blind, i.e., top, middle and bottom, were predicted. It was shown that the model prediction performance in terms of comparison between the prediction illuminance and measured value could reach 94.7%, this demonstrated high accuracy in forecasting illuminance level in sensor point. Then the illuminance forecasted by ANNs were input to a mathematical model to optimize the slat angles of blind to achieve the aim of daylighting control (the process is shown in Figure 17). Another advantage of ANNs model is that it could solve the real-time blind control problems. Since the external illuminance data could directly feed in the ANN model and determine the optimum slat angle of blinds, this really solves the difficulties in controlling the daylight in real conditions as a result of the dynamical change nature of solar irradiation.

Almost all articles in daylighting prediction by ANNs modeling are searched and reviewed. A summary of ANNs application in predicting daylighting with detailed input and output parameters is presented in Table 8.

Table 9 summarizes the strengths and weaknesses of ANNs across seven domains, including prediction performance, computational efficiency, variable handling and so forth. The strengths of each domain are highlighted, such as high accuracy, rapid computational speed, strong multivariable coupling capability, while the weaknesses include limited interpretability, lack of theoretical guidance for architectural design, and insufficient exploration of advanced algorithms, among other issues. This comparative overview serves as a guide for understanding the trade-offs involved in deploying ANNs, depending on whether the focus is on predictive accuracy, computational speed, system integration, or real-time control capability.