Abstract— Greenhouse climate is a nonlinear time variant multi-input multi-output system with delay time and non-minimum phase. Because of the variety of parameters and strong coupling, developing a physical model based on thermodynamic principles is rather difficult. Having the ability of universal approximations, Artificial Neural Networks (ANN) can be well adapted to model the nonlinear behavior of greenhouse climate. However, a random selection of the initial parameters makes their convergence slow and suboptimal. Fuzzy logic makes it possible to solve this problem due to its capability to handle both numerical data and linguistic information. In this paper, a hybrid neuro-fuzzy approach based on fuzzy clustering is proposed in modeling a greenhouse climate built upon the experimental data. In the first stage, the nearest neighborhood method generates the necessary fuzzy rules automatically. Then, the cluster centers were used as the initial condition for the applied neural network trained and optimized using the Self-Organized Feature Mapping (SOFM) algorithm. The simulation results have shown the efficiency of the proposed model.
I. INTRODUCTION Crop production in greenhouses has experienced a large
expansion recently [1]. Greenhouses are used for the main purpose of improving the environmental conditions in which plants are grown. The goal in a greenhouse climate control is to further improve these conditions in order to optimize the plant production process. The greenhouse climate is one of the key factors affecting plant production, and it is influenced by many elements such as the outside weather, the actuators, and the crop itself [2-3]. Modern greenhouse and computerized climate control modules have become inseparable nowadays [4]. The functions of the computerized climate control can be summarized as follows: (a) It takes care of maintaining a protected environment despite fluctuations of external climate, and (b) It acts as a program memory, which can be operated by the growers as a tool to control their crops [5]. The main advantages of using computerized climate control are energy conservation, better productivity of plants, and reduced human intervention [6].
Greenhouses are considered as complex processes. In fact, they are nonlinear, multi-input multi-output (MIMO) systems which present time-varying behaviors, and they are subject to pertinent disturbances depending generally on meteorological
conditions. All these make it difficult to describe a greenhouse with analytic models and to control them with classical controllers [7-13].
Many conventional methods for controlling a greenhouse climate are not effective since they are based on either on-off control methods, or PID approaches. This results in a loss of energy, labor, and productivity [14]. To maintain a steady climate, a more complex control system must be used [6]. The requirements for climate control the energy consumption or maximize economic profit have instigated many researchers in this area. Today, there are numerous papers dealing with modeling, short term climate control, and long horizon control devised either to minimize [1, 15]. In [7], a model of a greenhouse using the energy balance has been presented. The proposed model is then used to perform a simulation on the greenhouse climate (temperature and humidity) with optimal control for part of a day. In [8] the author has proposed a greenhouse model including the crop transpiration. They then made a comparison between optimal and predictive control on the considered greenhouse for part of a day. In [9] the authors have described the application of model predictive control (MPC) for temperature regulation in agricultural processes (a greenhouse). In [10], the authors have proposed the application of fuzzy logic to identify and control some multi-dimensional systems. They describe a method to reduce the complexity of a fuzzy controller and they show an application on a real system (a greenhouse). In [11], a recurrent neural network based on an Elman structure [12-13] is trained to emulate the direct dynamics of the greenhouse.
Modern control techniques have been developed in various branches [15, 16]. During the last two decades, considerable effort was devoted to develop adequate greenhouse climate and crop models, for simulation, control and management purposes [17-18]. A proper model for a greenhouse climate is an essential tool for its control [19-22]. The model can be designed in two ways. One method is based on the physical laws involved in the process and the other on the analysis of the input-output data of the process. In the first method, the thermodynamic properties of the greenhouse system are employed. However, the parameters of the equations are time-variant and weather-dependent, so it is difficult to obtain accurate mathematical models of the greenhouse climate. The second approach is based on the theory of system identification [19]. Conventional methods based on system identification
such as ARX approaches can not properly model the nonlinear behavior of greenhouse climate. Intelligent methods seem to be the most proper choices for the modeling of this type of systems. Because of the properties of universal approximation, they can model nonlinear systems with trained data by arbitrary fitness.
In contrast with a neural network identifier, a fuzzy identifier has some essential advantages which are described in the following. Due to its capability to handle both numerical data and linguistic information, it is feasible to apply fuzzy logic system for greenhouse climate modeling and then provide prediction for choosing optimal controlling decision. The present paper describes simulation results of a hybrid fuzzy clustering model optimized by SOFM algorithm for predicting a greenhouse climate. The proposed method uses in a first stage a fuzzy clustering technique to determine both the premises and consequent parameters of the fuzzy rules. In the second stage, these parameters are adapted by using the SOFM algorithm.
II. APPLICATION OF FUZZY CLUSTERING IN GREENHOUSE
CLIMATE MODELING Having the capability of universal approximations, neural
networks can properly model the nonlinear behavior of greenhouse climate. In comparison with a neural network identifier, a fuzzy identifier has two main advantages:
(1) The initial values of fuzzy identifier have physical meanings, so it can be selected in a proper way. On the contrary, the initial values of neural network identifier are usually selected randomly. Because the back propagation learning algorithm adopted by two kinds of identifier belongs to gradient algorithm, the selection of initial parameters influences the convergence speed of algorithm to a great extent.
(2) Since the Fuzzy identifier is composed of a set of "if- then'' rules, it provides the path for using linguistic information. Important information about the unknown nonlinear system is probably contained in the linguistic information.
In short, the linguistic information is applied to construct an initial identifier. The fuzzy identifier based on this initial identifier tracks the real system faster.
The adjustment of rule numbers is very important in designing fuzzy systems. A few number of fuzzy rules lead to a weak estimation while a large one may complicate the problem more than needed. Also it imposes higher computational costs. In our work, we derive the number of rules as an essential parameter of fuzzy estimator by applying the Nearest Neighborhood Fuzzy Clustering (NNFC) Algorithm.
Data clustering can be used to classify the measurement data into different groups [23]. Clustering is the partitioning of data into subsets or groups based on similarities between the data. In the nearest neighborhood fuzzy clustering, the first selected data forms the first cluster, and the first rule is written in the rule base. If the next data belongs to a neighborhood of this cluster, a new cluster is not formed, while the impact factor of that particular rule increases. On the other hand, if the next data does not belong to a neighborhood of this cluster, a second cluster is formed for which a new rule is devised.
In order to obtain results comparable with those of other papers, the modeling procedure considered was based on the experimental data collected from a research greenhouse in [17], which was then followed by a thorough simulation. Figs. 1-4 show the input-output signals. It can be noted that this greenhouse climate has been considered as a six-input (outside temperature, soil temperature, outside humidity, radiation emitted from the sun, ventilation power, and heater power) and a two-output (greenhouse air temperature and humidity) system. The measured air temperature and absolute humidity levels are plotted in Fig. 1 for two days of validation data set, April 5 and 6, 1998. Fig. 2 shows the normalized thermal disturbances (included in outside temperature and soil temperature) and Fig. 3 shows the nonthermal disturbances (included in outside humidity and sun radiation) for the same two days. For the same period of time, Fig. 4 shows the normalized power consumption for the actuators including the ventilation and heater. In the simulations performed, the experimental collected data have been divided in two parts: the first half of the data sets pertaining to the first day (April 5 1998) was used for the training purpose and the second half of data sets related to the second day (April 6 1998) was used for the testing purpose.
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Figure1. Normalized measured greenhouse air temperature and humidity for April 5 and 6, 1998
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Figure 2. Normalized thermal disturbances
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Each data is composed of both input and output parameters. If we show data vector by ψ then: ]...[,][ 321 xxxXyX ==ψ where X is n dimensional input vector and y is the system output. Greenhouse temperature and humidity models are developed, separately.
In temperature modeling, y refers to the present value of greenhouse temperature, while x refers to the last values of greenhouse temperature, present and last values of control signals (ventilation power and heater power) and disturbances (sun radiation, soil temperature, outside temperature, greenhouse humidity and outside humidity).
Similarly, in humidity modeling, y refers to the present value of greenhouse humidity, while x refers to the last values of greenhouse humidity, present and last values of actuators' status or control signals (ventilation power and heater power) and disturbances (sun radiation, soil temperature, outside temperature, greenhouse humidity and outside humidity). So, either for temperature or humidity modeling, dimension (n) of the input signal (x) is greater than seven (n>7).
In the following, we introduce a universal algorithm named "nearest neighborhood fuzzy clustering" for automatically
generating fuzzy rules. For simplicity, the nearest neighborhood fuzzy clustering approach is explained by assuming n=2 which can be demonstrated in the paper by Fig. 5.
This algorithm begins by selecting data from data set respectively. First selected data (s1) generates the first cluster (w1) and the corresponding fuzzy rule is automatically generated as follows:
If x=x(s1) then y=y(s1)
where x is the input vector, and y is the system output. Assume that, second selected data, s2 dose not belong to w1, i.e. the distance between s2 and center of nearest cluster (w1) is greater than predefined distance (r). Therefore, a new cluster (w2) is constructed and another rule added to rule base as follows:
If x=x(s2) then y=y(s2)
Additionally, if difference between the distance of third selected data (s3) to nearest cluster center (w1) is less than predefined distance (r), it does not construct a new fuzzy rule. Instead, this data object (s3) is additionally assigned to this cluster (w1) and importance factor of the corresponding rule increases in the estimate process.
The algorithm continues until all data are assigned to a cluster. For n>2, the nearest neighborhood fuzzy clustering is the same.
As with the work in reference [24], we constructed a fuzzy estimation system that approximates the function that is inherently represented in the training data set. The singleton fuzzification, Gaussian membership functions, product inference, and center-average defuzzification, as well as the fuzzy system were used here as in [24]. The model is represented as (1):
∑
∑
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=M
l
lcl
M
l
lcl
k xxkB
xxkA
xf
1
1
)2^
exp()(
)2^
exp()()(
σ
σ (1)
where x is the input vector, lcx is the center of th cluster, σ
is the width of the membership functions, M is the number of clusters (rules), )(1 kB is the number of members of the th cluster, and )(1 kA is the summation of outputs of the th cluster. The simulation results of using such a model are demonstrated in Fig. 6 and Fig. 7. Due to the high similarity of humidity modeling approach and temperature modeling, and for brevity, humidity modeling approach has been avoided in the coming sections.
III. FUZZY MODELING OF GREENHOUSE CLIMATE
As it can be understood, this approach is strongly affected by initial parameter adjustment. For example, sigma increment causes smoother model. Strongly large sigma selection leads to model with grater order than the real system, otherwise the small sigma selection causes the fuzzy model be unable to track the quick variations of process. As it can be seen in Figs. 6-7,
the modeling fitness is insufficient for accurate predictions of behavior of system outputs. So as to overcome this problem, it was handled by a minor modification of the algorithm.
Figure 6. Simulation results of temperature modeling with nearest neighborhood clustering algorithm with the fitness of 64%
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Figure 7. Humidity modeling with nearest neighborhood clustering algorithm
The variations can be divided in two parts. The first of which is related to the mathematics. The simulation results have been improved by applying hemographical functions rather than exponential. However, the best results were obtained from the exponential function by using larger powers. Although the modeling results are improved, the fitness is yet inadequate. The main reason for this insufficient result is for the nonoptimal selection of the clusters in this approach.
To remedy the problem, the nearest neighborhood clustering algorithm was used along with adapting cluster centers. In this approach, as it can be seen in Fig. 8, the center of each cluster is shifted towards the center of the data as these data were introduced. As such, new cluster centers are being generated each corresponding to its own new rule while deleting the rule corresponding to the “older” cluster. Hence, in the random selection of data sets, if we show the k th data by
)(kx and the 1+k th data by )1( +kx , then the modified cluster centers in the algorithm will be as follows:
)1)(/())1()(*)(()1( +++=+ kBkxkBkxkx lllc
lc (2)
Based on the Least Square Error, one can infer that the average of the data for each cluster is represented more properly as the center of that cluster. Simulation results verify this theory quite clearly, as demonstrated by Fig. 9. This figure shows the modeling results of the greenhouse temperature according to the rule base obtained from such an algorithm based on (3):
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pxxkA
xf
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)^
exp()(
)^
exp()()(
σ
σ (3)
In this equation, p is greater than 3 and smaller than 4, and, σ is adjusted based on p. Other variables are the same as (1).
( )1lcx k +
1x
2x
( )lcx k
( )1x k +
Figure 8. Automatically generating fuzzy rules by adaptive
nearest neighborhood fuzzy clustering algorithm
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Figure 9. Simulation results of temperature modeling with nearest
neighborhood clustering algorithm with the fitness of 77%
IV. OPTIMIZATION OF FUZZY CLUSTERING MODEL WITH SOFM ALGORITHM
Artificial neural network is a mathematical or computational model mimicking biological neural networks [25]. An ANN is a set of interconnected groups of artificial neurons that are linked by a mathematical model for information processing. It consists of an interconnected group of artificial neurons and processes information using a connectionist approach to computation. More practically, neural networks are nonlinear statistical data modeling tools. They can be used to model complex relationships between inputs and outputs or to find patterns in data through training. Therefore, they are quite useful in solving problems where the system is nonlinear and a functional relation between inputs and outputs is hard to describe [25].
There are numerous algorithms available for training neural network models [23]. Most algorithms used for training ANN employ the gradient descent method. There are three major learning networks: supervised learning, unsupervised learning and reinforcement learning. Usually, any special type of neural network is accompanied by a special learning method [23]. Self-Organized (unsupervised) learning consists of repeatedly modifying synaptic weights of a neural network in response to activation patterns and in accordance with prescribed rules, until a final configuration develops [26].
Self-Organized Feature Mapping (SOFM) algorithms are based on competitive learning and their principal goal is to transform an incoming signal pattern of arbitrary dimension into a one- or two-dimensional discrete map, and to perform this transformation adaptively in a topologically ordered fashion [26]. The algorithm is summarized as follows:
content and organizational editing before formatting. Please take note of the following items when proofreading spelling and grammar:
A. Initialization Choose random values for the initial weight vectors (0)jw .
The only restriction is that the (0)jw be different for j=1, 2,…,
, where is the number of neurons in the lattice. It may be desirable to keep the magnitude of the weights small.
Another way of initializing the algorithm is to select the weight vectors from the available set of input vectors 1{ }N
i ix = in a random manner.
B. Sampling Draw a sample X from the input space with a certain
probability; the vector X represents the activation pattern that is applied to the lattice. The dimension of vector X is equal to m.
C. Similarity Matching Find the best-matching (winning) neuron ( )i x at time step
n by using the minimum-distance Euclidean criterion:
jj
wnxxi −= )(minarg)( lj ,...,2,1= (4)
D. Updating Adjust the synaptic weight vectors of all neurons by using
the update formula:
))()((*)(*)()()1( )( nwnxnhnnwnw jxjijj −+=+ η (5)
where ( )nη is the learning-rate parameter, and , ( )j i xh is the neighborhood function centered around the winning neuron ( )i x . Both ( )nη and , ( )j i xh are varied dynamically during learning for best results.
E. Continuation Continue with step A until no noticeable changes in the
feature map are observed which indicates convergence of the algorithm.
The center of clusters gained from fuzzy clustering approach is not optimal, based on the Least Square Error. Having the ability of selecting the best features of data set, The SOFM algorithm is used in order to optimize the modified proposed fuzzy approach. In fact, these two approaches are complementary.
Once the SOFM algorithm has converged, the feature map computed by the algorithm displays important statistical characteristics of the input space [27]. As it has been explained, the selection of the initial parameters of the SOFM algorithm is random. The initial parameters have a significant effect on the results and convergence speed of the SOFM algorithm. It is therefore possible that a certain choice of the initial parameters may lead to slow convergence [28-29]. Clustering results can be good candidate for setting the initial parameters of the SOFM algorithm. The proposed method uses, in a first stage, a fuzzy clustering technique to determine both the premises and consequent parameters of the fuzzy rules. These parameters are used as initial parameters of the SOFM algorithm, i.e. the number of neurons in the SOFM algorithm ( ) equals to the number of rules gained from NNFC algorithm. Moreover, the initial values of weight vectors ( (0)jw ) in the SOFM
algorithm correspond to the center of each cluster lcx in the
NNFC algorithm.
Hence, not only more proper rules are used, but also better variance and rule numbers are applied as the initial parameters for the SOFM algorithm. In the second stage, these parameters are adapted by using the SOFM algorithm, and so rules are generated automatically. In addition, use of the fast convergence clustering algorithm leads to a higher speed for the proposed hybrid algorithm rather than the SOFM algorithm. Finally, the rules from the SOFM are applied based on equation (3) for modeling the greenhouse temperature. As observed in Fig. 10, simulation results show the effectiveness of the proposed procedure and verify the theory for this approach.
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Figure 10. Temperature modeling with hybrid nearest neighborhood clustering and SOFM algorithm with the fitness of 90%
V. CONCLUSION In order to design optimal controller for saving energy,
precise prediction of greenhouse temperature and humidity is needed for compensating the negative effects of the inherent delay time of the greenhouse climate. In this paper, a hybrid model composed of a fuzzy approach (Clustering) and artificial neural networks (SOFM) is proposed to predict the greenhouse climate. Automatically generated rule base of the fuzzy approach is optimized with the neural networks. Using the clustering algorithm, significantly improves the converge speed of the highly slow self-organized algorithm. The simulation results show the efficiency of the proposed approach for modeling greenhouse climate and they verify the theory for the algorithm.
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