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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

A new application of neurocomputing for data approximation and classification is introduced to process data in a wireless sensor network. For this purpose, a simplified dynamic sliding backpropagation algorithm is implemented on a wireless sensor network for transportation applications. It is able to approximate temperature and humidity in sensor nodes. In addition, two architectures of “radial basis function” (RBF) classifiers are introduced with probabilistic features for data classification in sensor nodes. The applied approximation and classification algorithms could be used in similar applications for data processing in embedded systems.

There are different means of transporting products between cities and countries worldwide. According to the type and importance of the transported products, certain requirements are considered in the selection and supervision of transportation systems [

Different approaches exist to approximate data, including stochastic approximation, polynomial interpolation, differential and integral equations, “least squares”, and “neural network” [

Data classification is a secondary neural network application that is especially useful when the data classes are only partially known [

In our study, to wirelessly process the data, the data are first approximated by a dynamic backpropagation mechanism and then classified by a probabilistic radial basis function (RBF) network implemented on a wireless sensor network, seen in

Presently, knowledge-based approaches are applied to intelligent transportation. ANN-based diagnosis, real-time traffic signal control, and road signal analysis are some applications of ANN found in transportation systems [

The data must first be approximated. Different techniques are applied in wireless sensor network for data approximation depending on application. Then, the approximated data could be used either for data fusion or fault diagnosis purposes [

Probabilistic features also make the neural network an important model for data classification [

As mentioned, we propose an application of two joint mechanisms for wireless data approximation and classification in food transportation. For this purpose, the Imote2 kit is used to record temperature and relative humidity and to process the recorded data. The kit consists of three main components, including a radio/processor board, a sensor board, and a battery board [

The sensor nodes are positioned in different locations throughout the inside of the food transportation truck. A reefer unit inside the truck establishes the desired environmental conditions [_{1}” records the temperature and humidity of the reefer unit. Sensors “_{ACP}_{2}” are located in the middle of the truck, and “_{3}”is in front of the door, farthest from the reefer unit. The task of finding the best sensor positions for optimum data approximation will be addressed in the next section of this paper.

The sensor nodes are programmed in Microsoft^{®} .NET Micro Framework using Visual Studio. Compared to the .NET Framework, the .NET Micro Framework is limited [

Otherwise, when the actual record of 5th sample is reliable, the last four samples (namely, the 2nd, 3rd, 4th, and 5th samples) are used for training and to approximate the 6th value using the 3D approximation algorithm and it continues to predict next values. This procedure, called the sliding backpropagation algorithm, depends solely on the last four reliable values. By gradually receiving each piece of data from the other sensor nodes, the approximation mechanism updates all of the network weights; this sliding “weight update” stems from the “least squares” (LS) approximation approach that uses members of a small group of related previous equation sets [

In (1),
_{1}-th neuron in the first hidden layer, and _{i}

_{1}-th neuron in the first hidden layer after the outputs of all hidden neurons in first layer are calculated. In a similar manner, the weighted inputs (

By calculating and summing the outputs of each neuron in the second hidden layer, the output of network (_{j}

To train the network, a “gradient descent” algorithm is applied to minimize the error function (E) between the desired and actual outputs of the network.

In (6), D_{j} and Y_{j} refer to the desired and actual outputs. The output error e_{j}(k) is calculated for each sample (k) and is defined as the difference between the desired and network outputs in the output layer. The output error is minimized by updating the weight values towards decreasing the error function. The weight changes are proportional to the negative gradients of the error function and current weights (according to

After calculating the weight changes, the weights between the second hidden layer and the output layer are updated. Similarly, the remaining weights are consequently updated according to (8):

Like the applied ANN algorithm, the LS approach relates the records of the “under approximation sensor node” and the last four records of other sensor nodes by an over-determined matrix as shown in (9):

In (9), the current and previous values of parameters _{ACP}_{1} and _{2} are recorded and used to find the approximation coefficients (
_{ACP}_{1} and _{2}) and the updated approximation coefficients (_{3} (the value of the “under approximation sensor node”) is calculated.

This procedure continues and the coefficients are constantly updated based on the last four instantaneous equations. To calculate the values of the other sensors, the same algorithm is applied by replacing the sensor names and values.

The simplified probabilistic RBF algorithm is used to classify data. The probabilistic RBF algorithm is applied primarily to calculate the “probability density function” for assigning the network output to predefined classes. Sometimes, according to reading errors or weaknesses in approximation, the approximation exceeds the desired accuracy in wireless sensor network. Further research is needed to determine if this excess stems from an inaccurate approximation, or from a fault or failure inside the system that causes error and uncertainty. For data classification, an alternative could be using the classical RBF classifier including three output layers, however, for increasing the accuracy of data classification, more training data should be used in this case. In classical RBF, when the number of training sets is not enough, the algorithm could infer incorrect classes.

Probabilistic neural networks are feed-forward networks derived from “Bayesian decision networks” [

The training algorithm of the RBF network is a “Gradient descent” algorithm which is applied for mapping input set to predefined classes. An appropriate number for center should be assigned to each neuron in the hidden layers. There are different choices for assigning number of centers. The number of centers could be equal, less or more, than number of inputs.

When the number of input sets is more than the number of centers, it takes more time for the calculation, because the calculated weight values needs training algorithms for updating all weight values each time. The assumption of considering fewer input sets than centers is quite unrealistic. In this research, equal numbers of centers and input sets are considered. Thus, the “Gradient descent” training algorithm is not necessary to update the weight values each time; it is applied whenever the training error exceeds the training accuracy. The training set must be a thorough representation of the data. Probabilistic neural networks handle data that have spikes and points outside the norm better than the classical RBF network.

To train the probabilistic neural network, the radial basis function Φ_{i}_{i}

In (11), _{i}_{i}_{i}_{i}

Different nonlinear functions, such as “multi-quadratic” and “spline”, are used to calculate the output of each hidden neuron. In this paper, the “Gaussian function” is used as the nonlinear function for the hidden neurons, which results in a nonlinear mapping between the inputs and classes.

The output layer compares the data using the competitive neural layer which leads to selecting the highest value.

In (12), _{k}

_{ACP}_{1}, _{2} and _{3}, as shown in _{1}” show the temperature of the reefer unit, which fluctuates over time according to the unit’s on/off cycles. The reefer unit could cool down or warm up the truck according to set points, illustrated in

In this research, first the “data request” message from ACP is sent for each sensor node every 2 seconds respectively according to predefined scenario; every two seconds the ACP collects data from each node and it takes 6 seconds to collect data from all sensor nodes by ACP. It means that the ACP starts 3D approximation and classification after collecting data from all three sensor nodes (3D denotes approximation of data for each sensor node using the other three nodes). Otherwise, the algorithm is able to switch to 2D (2D denotes approximation of data for each sensor node using two other faultless nodes) or even 1D approximation depending on the available received records in ACP [_{ACP}_{1}, _{2} and _{3}) are illustrated in

The ACP receives the first four temperature and humidity records of different points as input vector for training. The network creates a mapping between the input and target vectors during the training phase. The target vector corresponds to the previous and current values of the “under approximation sensor node”. Three possible ways to approximate data include:

Mapping (_{1}, _{2}, _{ACP}_{1}, _{2}, _{ACP}_{3}, _{3}) to approximate the temperature and humidity of “node 3” by ACP.

Mapping (_{1}, _{3}, _{ACP}_{1}, _{3}, _{ACP}_{2}, _{2}) to approximate the temperature and humidity of “node 2”.

Mapping (_{2}, _{3}, _{ACP}_{2}, _{3}, _{ACP}_{1}, _{1}) to predict the temperature and humidity of “node 1”.

The residual term is defined as the difference between the actual data and the approximation. This residual could be calculated for both temperature and humidity records individually:

_{Actual}_{Actual}_{Network}_{Network}

The accuracy of approximation is determined according to the experimental results in normal situation when the records are reliable. The approximation residual doesn’t exceed sum of the maximum reading error and training error. For example, the maximum reading error of temperature sensor is ±0.3 °C and the maximum training error is less than ±0.15 °C (sum is ±0.45 °C). The maximum ANN approximation error is considered ±0.5 °C which is observed in experimental results.

The maximum reading error of humidity sensor is ±2.5 RH% and the maximum training error is less than ±2RH% (sum is ±4.5 RH%). The maximum ANN approximation error is considered ±5 RH%. As seen in

The accuracies of the approximations of the temperature and humidity records are compared with accuracies of the approximations using the pure LS approach. For a more precise comparison, the “root mean squared errors” (RMSE) of the temperature and humidity approximations are calculated for each sensor node using the same actual values that were used in the sliding backpropagation approximation [

_{Actual}_{App.}

As previously mentioned, any temperature or humidity change found in the various positions of the truck is related to the reefer unit. A primary research task is to find the optimal position for the data approximation platform (AP). Three main alternatives are available as shown in

There are 6 zones, labeled A through F, which could be used to place sensor nodes. Previously, the AP was placed in the middle of the truck for data approximation. Currently, discovering the location exhibiting optimum performance is investigated.

For this purpose, all three alternatives were tested by positioning the three sensor nodes as three individual approximation platforms. Thus, the following three main cases were tested:

D as approximation platform for A, B, and C;

E as approximation platform for A, B, and C;

F as approximation platform for A, B, and C.

Then, the approximation residual and RMSE of each sensor node was calculated for each individual case. Finally, the average approximation residual was calculated separately for each of the three cases. This average returns the arithmetic mean of the arguments as the “average root mean squared error” (ARMSE). According to (14), the _{i}

Finally, by using point E as AP, the approximation accuracy at point B increases and the accuracies at points A and C suffice. Thus, the optimal position for data approximation is in the middle of the truck at point E. The temperature and humidity changes at the farthest points, such as point C, are not instantaneously synchronized with the reefer unit, so that the accuracy of data approximation when the AP is located at point D is greater than when the AP is located at point F.

After approximating temperature and humidity, an evaluation of the reliability of the records is necessary. The approximation residual and RMSE were used to detect any abnormal data change due to faults or failures in the wireless sensor network, such as battery problems or accidental door openings in truck. However, the approximation residual seldom exceeds the approximation accuracy in the absence of any fault or failure due to inaccurate sensor readings or insufficient data mapping. When the approximation residual exceeds the approximation ranges, the cause of this excess, such as a fault or failure in the system or weakness in approximation, must be determined. Three main residual ranges are defined to evaluate the reliability of the records. If the absolute value of the residual is used, the following cases could be defined for temperature and humidity approximation residuals:

Normal situation: 0 ≤ |Δ

Unknown situation: 0.5 ≤ |Δ

Abnormal situation: 1 ≤ |Δ

These cases are not especially accurate at the borders of classes, in which case the use of probabilistic features is required. Using probabilistic features could clarify the temperature and humidity residuals at the borders of the classes. The probabilistic RBF network is trained by samples which have the statistical requirements of the aforementioned cases, including:

Class 1: Normal;

Class 2: Unknown;

Class 3: Abnormal.

After training, the probabilistic RBF network is mapped to one of the classes instead of any new given input.

In (16), _{1}, _{2}) returns the correlation factor between sets _{1} and _{2} including their elements (_{1} and _{2}) and average values (_{1}and _{2}) [

As shown, temperature and humidity are evaluated separately and the results are combined. Although the temperature and humidity are not independent variables but the temperature and humidity sensors could be defective separately on sensor board and the main task of the approximation and classification algorithm is detecting any abnormal condition in wireless sensor network.

The applied 2D RBF mechanism is seen in

Two different 2D RBF architectures are used because it is assumed that sensor defection could occur separately for either the temperature or humidity sensors. The results of the classification of the temperature and humidity data are combined at the end of the classification process. The networks are trained using

A further alternative to classify data employs a 3D RBF network only in unknown areas in which the absolute approximation residual exceeds the limits but remains less than 1 °C for temperature and 10% RH for humidity records (0.5 ≤ |Δ

The training data in

In this paper, a neurocomputing approach was introduced and implemented for data approximation and classification. First, an optimized backpropagation network was defined for temperature and humidity approximation in a wireless sensor network. The results proved that the new applied approximation mechanism could predict the data more accurately than the “least squares” (LS) method. In addition, the goal of finding the optimal position of the approximation platform was discussed. The best position for this platform is in the middle of the truck, where the average “root mean squared error” (ARMSE) of data approximation is minimized. This position also correlates sufficiently with the other nodes to be used as a classification platform as well. To evaluate the reliability of the records, two types of probabilistic radial basis function networks were introduced. The networks were trained with accurate input sets and different classes. By feeding new input, the probabilistic classifiers were able to classify the data. The applied mechanism is applicable in similar projects for the purpose of data fusion in wireless sensor networks.

This research was supported by the German Research Foundation (DFG), as part of the Collaborative Research Centre 637 on “Autonomous Cooperating Logistic Processes”.

ANN for data approximation and classification.

Architecture of the wireless sensor nodes.

Applied ANN approximation mechanism.

Applied RBF classification mechanism.

Actual temperature of reefer unit and sensor nodes.

Actual humidity of reefer unit and sensor nodes.

Approximation residual of each sensor node.

RMSE of ANN approximations.

RMSE of LS approximations.

Allocation of approximation platform.

Performance of different approximation platforms (Temperature).

Performance of different approximation platforms (Humidity).

Classification range.

2D RBF classification diagram.

Classification range.

3D RBF classification diagram.

Training 2D RBF classifier for temperature records.

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Training 2D RBF classifier for humidity records.

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Training 3D RBF classifier.

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