Accurate measurement of micro-climates that include temperature and relative humidity is the bedrock of the control and management of plant life in protected cultivation systems.
Agricultural products are crucial to the sustenance of humans and livestock. However, their production is faced with several challenges such as extreme weather conditions, soil erosion, pests, and disease outbreaks, which all have far-reaching effects on crop productivity and growth rate 
. Protected cultivation systems such as greenhouses offer optimal production of agricultural products throughout the year by the appropriate control of micro- and macro-environments suitable for plant growth 
. Furthermore, protected cultivation systems result in higher income compared to open-field cultivation as a result of their higher returns per unit area 
. Hence, their adoption is increasing across continents 
. Despite these benefits, the operation of greenhouses is non-linear in nature due to changing atmospheric conditions 
and therefore requires intricate monitoring and control to obtain optimal yield. In other words, maintaining suitable temperature, which directly affects the humidity, is essential in greenhouse environmental control as these affect crop growth as well as quality and quantity 
. Specifically, while effective temperature control improves plant growth and minimizes the energy consumed by the system, an appropriate relative humidity range is required to prevent fungal infection and control transpiration 
To facilitate monitoring and control in protected cultivation systems, the integration of different advanced sensing technologies becomes eminent 
. Basically, sensors installed in greenhouses range from those used to monitor and control micro-climatic conditions such as temperature and relative humidity to soil-related parameters such as moisture, PH, and several others, which are vital for maintaining optimal conditions for favorable crop productivity and growth. In terms of micro-climates, previous studies have shown that monitoring and controlling the temperature and relative humidity within a greenhouse is complex and challenging due to drastic variations in daily and seasonal atmospheric conditions 
Generally, sensors are installed arbitrarily in protected systems based on factors such as grower resources, the size of the facility, and technical know-how 
. Furthermore, in conventional settings, as many sensors as possible are usually installed to facilitate the necessary measurements. However, the use of multiple randomly/inappropriately placed sensors fails to provide measurements that are true estimates of greenhouse micro-climates. In addition, employing a large number of sensors results in large quantities of data that require efficient data management. In other words, the quality of information and consequently the estimation accuracy of micro-climates depend heavily on the number of sensors and their locations/placements. Therefore, optimizing the number of sensors and their locations, though a challenging task, is crucial as it forms the basis for accurate measurement of micro-climates and consequently optimal control of the cultivation system. Additionally, it reduces the overall operating cost of protected cultivation systems.
In the literature, methods have been proposed based on approximate models of partial differential equations (PDEs), such as the error covariance matrix of the Kalman filter or the finite difference method 
. However, these methods were applied without any general systematic procedure to linear systems modeled based on a small number of sensors. Meanwhile, it is important to know that distributed processes, such as in protected cultivation systems, are intrinsically non-linear with infinite dimensions. Therefore, such methods are not appropriate for highly non-linear protected cultivation systems that feature high-dimensional representations. Consequently, different methods, such as genetic algorithms 
, Harris hawks optimization 
, the Fisher information matrix 
, the exponential-time exact algorithm 
, the system reliability criterion 
, and Bayesian optimization 
, have been proposed for optimal sensor placement in different application domains.
In terms of optimal sensor placement in protected cultivation systems (greenhouses), Yeon Lee et al. 
proposed a combination of an error-based and entropy-based approach for the optimal location of temperature sensors. In the work, based on the reference temperature obtained by averaging the temperature data obtained from all the measurement locations, sensor locations with measurements statistically close to reference values were selected. Furthermore, the entropy method was used to realize locations that are greatly influenced by external environmental conditions. Based on these two methods, optimal sensor locations that provide representative data of the entire greenhouse condition, as well as understanding regions with high variations in temperature, were realized. In order to maximize the coverage area (a non-occlusion coverage scheme) in a vegetable-cultivating greenhouse, Wu et al. 
proposed a hierarchical cooperative particle swarm optimization algorithm for directional sensor placement. Specifically, the decision variables were modeled in terms of the global effective coverage of each sensor and consequently the orientation angles of each sensor. The model demonstrated the capability to avoid occlusion between covered objects and also improved sensor utilization in general. However, the limitation of the aforementioned works is that their investigations were performed for a limited period of time and do not capture all the different planting seasons as well as different weather conditions. Recently, Uyeh et al. 
proposed a reinforcement learning (RL)-based approach for optimal sensor location in greenhouses using a robust dataset that covers different planting seasons. From the analysis, it was evident that the optimal locations for temperature and relative humidity are different. Specifically, the RL-based model was able to rank the sensor locations based on their importance in estimating the greenhouse micro-climates, for each temperature and relative humidity. However, it was also reported that the ranking of sensor locations for effective measurement of greenhouse micro-climates varies during the different months of the year with the change in the external weather conditions.
Although the assertion that the optimal sensor locations change from month to month is intuitive and supported by a number of recent literature 
, the implication is that it would be required to move the sensors every month throughout the growing seasons or to have a huge number of sensors within the cultivation system. This need to relocate the sensors every month is tedious, expensive, and not ideal for a typical grower. Hence based on the data collected from a greenhouse used to cultivate strawberries in 
, a framework based on the multi-channeled dense neural network (DNN) is proposed to be used to predict temperature and relative humidity values corresponding to the optimal sensor locations of each month without the need of moving the sensor from one location to another. Specifically, temperature and relative humidity values measured from the fixed locations (say the optimal locations of February) are used to predict the temperature and relative humidity values corresponding to the optimal locations of the other months referred to as target months (March, April, May, June, July, and October). The prediction of the temperature and relative humidity values corresponding to the optimal locations corresponding to the target month will help better estimate the micro-climates of the greenhouse. The effectiveness of the proposed model to predict temperature and relative humidity is demonstrated in terms of the resulting RMSE values. Furthermore, it is shown that the true and predicted sensor values are highly correlated based on Pearson’s correlation coefficient. Overall the results obtained show that the proposed framework is efficient and applicable in predicting micro-climates within protected cultivation systems and also comes with the advantage of cost reduction.In addition, as the prediction is performed for each month using the same fixed locations, the proposed framework alleviates the issue related to shifting of the sensors with the change in the external weather conditions. In other words, the novel framework proposed in this paper becomes an initiative basis in the research community for modeling dynamic optimal sensor placement in cultivation systems based on fixed sensors. Finally, it is important to note that the choice of the multi-channel DNN employed in this work is motivated by its simplicity in terms of implementation and deployment since it is well suited to several low-precision hardware for deep learning compared to other variants.
2. Greenhouse Micro-Climate Prediction
The prediction of micro-climates in protected cultivation systems under different setups has been studied in the literature 
. The prediction models often employed range from very basic deterministic models 
to more advanced learning networks such as ANN 
, multi-layer perceptron neural network (MLP-NN) 
, and extreme learning machine (ELM) 
. Although these works propose the use of learning or deterministic models for micro-climate predictions, most of them applied these models to achieve different goals. For example, the deterministic model proposed in 
was aimed at predicting crop temperature from measured air temperature, air density, and other related sensor-measured environmental conditions. The authors argued that rather than the air temperature, the crop temperature is responsible for crop growth and development. In 
, a dynamic model based on energy and mass transport processes, such as the mechanism of conduction, convection, radiation, etc., was employed to realize a prediction model capable of predicting the temperature of air in plant communities. Although the use of such models is very dependent on the structure of the greenhouse model, the authors claimed that the proposed model can be extended for a general greenhouse micro-climate prediction model. In terms of the use of learning networks, Liu et al. 
proposed the use of ELM for predicting temperature and relative humidity from historical samples of indoor temperature and humidity. In order words, the learning model is aimed at predicting current micro-climates based on previously sampled or measured micro-climates. This is beneficial in situations where the cost of continually measuring micro-climates in terms of energy and communication protocols is high and needs to be minimized. In 
, where MLP-NN and ANN were employed, respectively, the aim of the models was to predict indoor or internal micro-climates based on measured external micro-climates such as temperature, relative humidity, wind speed, etc. Although the aforementioned works have considered the prediction of micro-climates in the greenhouse setting, the aims of their predictions are different from ours, where researchers predict the measurements of micro-climates at varying optimal sensor locations using input data from fixed-placed sensors.
Generally, it can be observed that most of the aforementioned models are relatively not computationally expensive. This is because the choice of model or learning networks for such applications is usually motivated by the nature of the underlying data (real-valued vectors) and the need for quick prediction or low inference time. In a similar fashion, researchers employ a simple multi-channel learning model that extracts global features from all the input data, which are consequently fed into the channels’ response for extracting local features corresponding to micro-climate measurements from different sensor locations.