Estimation of Energy Expenditure Using a Patch-Type Sensor Module with an Incremental Radial Basis Function Neural Network

Conventionally, indirect calorimetry has been used to estimate oxygen consumption in an effort to accurately measure human body energy expenditure. However, calorimetry requires the subject to wear a mask that is neither convenient nor comfortable. The purpose of our study is to develop a patch-type sensor module with an embedded incremental radial basis function neural network (RBFNN) for estimating the energy expenditure. The sensor module contains one ECG electrode and a three-axis accelerometer, and can perform real-time heart rate (HR) and movement index (MI) monitoring. The embedded incremental network includes linear regression (LR) and RBFNN based on context-based fuzzy c-means (CFCM) clustering. This incremental network is constructed by building a collection of information granules through CFCM clustering that is guided by the distribution of error of the linear part of the LR model.


Introduction
More than one-third of adults and almost 17% of youth were obese in 2009-2010 [1]. Excess nutrient and energy imbalances are considered to be a major cause of chronic diseases, such as diabetes and obesity [2], indicative of the need for a better understanding on how energy expenditure (EE) can be assessed and quantified. Body fitness and athletic performance can also be evaluated by monitoring energy expenditure and physical activities [2,3]. The conventional method to estimate energy expenditure is by using a gas system that can measure the oxygen consumption (VO 2 ) and carbon dioxide (VCO 2 ) in the exhaled air. The method uses a gas system and is highly accurate. However, the people tested have to wear a mask during physical activities that imposes practical limitations, since the tube needed to connect to the gas analyzer has a finite length. Furthermore, the equipment is expensive and cumbersome. Researchers have tried to develop a small sensor and algorithm to estimate the energy expenditure.
To estimate energy expenditure, two commonly used methods include the monitoring of heart rate (HR) and sensing of movements. Spurr et al. developed the FlexHR method that uses the resting metabolic rate (RMR) and exercise activity to estimate energy expenditure [4]. The FlexHR point is the highest HR in the RMR compared to the lowest HR during exercise. If the HR is lower than the FlexHR, then energy expenditure is estimated based on the RMR, whereas if it is higher, then the estimation is based on the linear relationship between energy expenditure and VO 2 . This method has been extensively applied in research lately. However, the accuracy of the elicited results requires them to be fitted to a linear regression model to develop the estimation formula. Another method The main scope of this study is to estimate the EE of walking and running which are the most common activities for adults in modern lifestyles. The rest of this paper is organized as follows: in Section 2, we illustrate the system architecture that includes the entire generation of the system and the structure of the patch-type sensor. The embedded incremental RBFNN is described in detail in Section 3. Section 4 then provides the experimental design and results in accordance to a two-part protocol. First, the experiment is conducted using a submaximal treadmill protocol in a laboratory. Then, we instructed the participants to walk and run on a school playground as naturally as possible. Finally, conclusions are summarized in Section 5.

General System Description
The function of the entire system is wireless monitoring of the energy expenditure of the participants using a cheap and lightweight sensor. The users can be monitored at any time during the day and upon engagement in different physical activities. The system includes one inverse triangle patch-type sensor and a portable computer to display the heart rate and movement index (MI). The sensor node is small in size (6 × 9 cm 2 ) and lightweight (41 g) and can be patched on the chest of the user for collecting physiological data. The physiological data include HR, MI, humidity, and temperature. The sensor has the ZigBee RF module that can wirelessly transmit the information to a personal computer. The analysis software is embedded in the portable computer. The physician could check the physiological condition of the user using the portable computer.

Sensor Module
The sensor board consisted of a three-axis accelerometer, three ECG electrodes, a voltage converter, and a Li-ion charger. Two quasi-triangular flexible PCB boards are combined in the sensor, as shown in Figure 2. The MI is the summation of the motion indices along all the three axes x, y, and z. It can detect the movement acceleration signal in the range of −6 g to 6 g. The agility was examined using physical training protocols, such as the zigzag run, a 20 m shuttle run, the Burpee test, and a side-step test. The movement detection was strongly correlated to conventional agility tests (R 2 = 0.80-0.91). The results verified its applicability to the evaluation of the exercise state of the users. The HR detection was designed based on the use of a bandpass filter for R-wave detection. Motion artifacts were incurred and led to an error rate that was less than 2% with a commercial stress ECG monitor (CASE System, GE Medical, Westborough, MA, USA). The sensor node included 3.3 V Li-ion rechargeable batteries with a continuous operation period of two hours. The distances for transmission can achieve more than 400 m in an open field using the ZigBee telecommunication. The technical details of the sensor design can be found in a previously published study [26]. The main scope of this study is to estimate the EE of walking and running which are the most common activities for adults in modern lifestyles. The rest of this paper is organized as follows: in Section 2, we illustrate the system architecture that includes the entire generation of the system and the structure of the patch-type sensor. The embedded incremental RBFNN is described in detail in Section 3. Section 4 then provides the experimental design and results in accordance to a two-part protocol. First, the experiment is conducted using a submaximal treadmill protocol in a laboratory. Then, we instructed the participants to walk and run on a school playground as naturally as possible. Finally, conclusions are summarized in Section 5.

General System Description
The function of the entire system is wireless monitoring of the energy expenditure of the participants using a cheap and lightweight sensor. The users can be monitored at any time during the day and upon engagement in different physical activities. The system includes one inverse triangle patch-type sensor and a portable computer to display the heart rate and movement index (MI). The sensor node is small in size (6 × 9 cm 2 ) and lightweight (41 g) and can be patched on the chest of the user for collecting physiological data. The physiological data include HR, MI, humidity, and temperature. The sensor has the ZigBee RF module that can wirelessly transmit the information to a personal computer. The analysis software is embedded in the portable computer. The physician could check the physiological condition of the user using the portable computer.

Sensor Module
The sensor board consisted of a three-axis accelerometer, three ECG electrodes, a voltage converter, and a Li-ion charger. Two quasi-triangular flexible PCB boards are combined in the sensor, as shown in Figure 2. The MI is the summation of the motion indices along all the three axes x, y, and z. It can detect the movement acceleration signal in the range of −6 g to 6 g. The agility was examined using physical training protocols, such as the zigzag run, a 20 m shuttle run, the Burpee test, and a side-step test. The movement detection was strongly correlated to conventional agility tests (R 2 = 0.80-0.91). The results verified its applicability to the evaluation of the exercise state of the users. The HR detection was designed based on the use of a bandpass filter for R-wave detection. Motion artifacts were incurred and led to an error rate that was less than 2% with a commercial stress ECG monitor (CASE System, GE Medical, Westborough, MA, USA). The sensor node included 3.3 V Li-ion rechargeable batteries with a continuous operation period of two hours. The distances for transmission can achieve more than 400 m in an open field using the ZigBee telecommunication. The technical details of the sensor design can be found in a previously published study [26].

Incremental RBFNN
The overall design process of the incremental RBFNN is shown in Figure 3. The development of the incremental RBFNN consists of two phases. First, we design the linear regression (LR) phase, which is treated as the preliminary global model representing the linear part of the data. Next, the modeling error obtained by the LR is compensated by the local RBFNN. In the design of RBFNN, the hidden layer is constructed using fuzzy granulation realized via CFCM clustering. For simplicity, we assume that the incremental RBFNN under consideration has two inputs, 1 x and 2 x . We firstly design the LR model in the input-output space. On the basis of the original data set and error obtained by the LR model, the nonlinear data sets are formed in a collection of input-error pairs. The contexts are produced from the input-error pairs and are characterized by the triangular membership functions.

RBFNN
The RBFNN is attractive in that it can be used for functional approximations, prediction, interpolation, and nonlinear modeling [27], which makes it useful in many applications. The RBFNN has a three-layer structure: an input layer that feeds feature vectors into the network, a hidden layer

Incremental RBFNN
The overall design process of the incremental RBFNN is shown in Figure 3. The development of the incremental RBFNN consists of two phases. First, we design the linear regression (LR) phase, which is treated as the preliminary global model representing the linear part of the data. Next, the modeling error obtained by the LR is compensated by the local RBFNN. In the design of RBFNN, the hidden layer is constructed using fuzzy granulation realized via CFCM clustering.

Incremental RBFNN
The overall design process of the incremental RBFNN is shown in Figure 3. The development of the incremental RBFNN consists of two phases. First, we design the linear regression (LR) phase, which is treated as the preliminary global model representing the linear part of the data. Next, the modeling error obtained by the LR is compensated by the local RBFNN. In the design of RBFNN, the hidden layer is constructed using fuzzy granulation realized via CFCM clustering. For simplicity, we assume that the incremental RBFNN under consideration has two inputs, 1 x and 2 x . We firstly design the LR model in the input-output space. On the basis of the original data set and error obtained by the LR model, the nonlinear data sets are formed in a collection of input-error pairs. The contexts are produced from the input-error pairs and are characterized by the triangular membership functions.

RBFNN
The RBFNN is attractive in that it can be used for functional approximations, prediction, interpolation, and nonlinear modeling [27], which makes it useful in many applications. The RBFNN has a three-layer structure: an input layer that feeds feature vectors into the network, a hidden layer For simplicity, we assume that the incremental RBFNN under consideration has two inputs, x 1 and x 2 . We firstly design the LR model in the input-output space. On the basis of the original data set and error obtained by the LR model, the nonlinear data sets are formed in a collection of input-error pairs. The contexts are produced from the input-error pairs and are characterized by the triangular membership functions.

RBFNN
The RBFNN is attractive in that it can be used for functional approximations, prediction, interpolation, and nonlinear modeling [27], which makes it useful in many applications. The RBFNN has a three-layer structure: an input layer that feeds feature vectors into the network, a hidden layer that calculates the outcome of radial basis functions, and an output layer that calculates a linear combination of basic functions. The receptive fields w i of the ith hidden unit in the hidden layer are calculated as follows: where x is a multi-dimensional input vector, and φ i is the ith radial basis function in the hidden layer. Additionally, v i is the center of the Gaussian basis function associated with ith hidden unit, and σ i is a width parameter of ith hidden unit. The output of the hidden units is normalized between 0 and 1. The output of RBFNN is determined as follows: where g i is the weight from the hidden unit to output E. From the above equation, we can determine on whether the performance is highly depended on the receptive fields and on the connections of the neuron in the output layer of network. The RBFNN is a two-layer feed-forward network. The training process of the RBFNN is divided into two stages: (a) first, the centers from the input to the hidden layer are determined; and (b) the weights are then determined from the hidden to the output layer.
Once we have formed the receptive field, the optimization of the weights of the neuron in the output layer becomes straightforward [28,29]. Since the centers and widths are fixed after they are chosen, the RBFNN often results in an unsatisfactory performance when the input patterns are not particularly clustered. Therefore, the CFCM clustering is used in conjunction with the RBFNN to determine good locations for the radial basis functions.

Local RBFNN Based on CFCM Clustering
CFCM clustering partitions a collection of input vectors into several fuzzy groups and estimates a cluster center in each context, such that a cost function of dissimilarity measure is minimized.
In what follows, we shall briefly describe the CFCM clustering algorithm. The given data belong to corresponding membership values. The partition matrices were induced by the lth context and are denoted and defined as follows where w lk is a membership value of the kth data point implied by the lth context. The underlying objective function can be expressed in the standard format as follows: where m is any real number greater than 1, u ik is the degree of membership of x k in the kth cluster, and ||·|| is a distance function between any measured data and the ith center cluster. The minimization of the objective function is realized by iteratively updating the values of the partition matrix and the prototypes, as shown above. The update of the partition matrix u ik and the cluster center v i is computed as follows where u ik pertains to the partition matrix induced by the lth context. The prototypes produced for the Euclidean distance are calculated in accordance to The cluster centers of Equation (6) estimated by CFCM clustering are used in the hidden layer of RBFNN described in Section 3.1.
The main design procedure of incremental RBFNN consists of the following steps: where Y is the final output of the incremental RBFNN, as shown in Figure 3. The z and E are the outputs of the LR and the local RBFNN, respectively. Therefore, the modeling error based on LR as the global model is compensated by the local RBFNN, based on specialized CFCM clustering using the concept of information granules.

Experimental Design and Results
To evaluate the function of incremental RBFNN and realize the final goal applied under free-living conditions, the design of the experiment consisted of two parts, namely, a laboratory, and a field test.

Laboratory-Based Experiment
The participants were tested on a treadmill using the submaximal Bruce protocols in the laboratory, as shown in Figure 4. The treadmill's initial velocity was set at 9.72 m·s −1 , and with a 10% gradient. The incline of the treadmill was increased by 2% at three-minute intervals. The participants walked and ran until they felt exhausted. For men, the test time lasted approximately 12 min, whereas for women the test time lasted approximately 9-10 min. The HR and MI were recorded in real-time by the patch-type sensor. The VO 2 and EE were measured by the gas system. The physical characteristics of the subjects are listed in Table 1.  HR and MI are the two major factors used to estimate EE. Thus, they were considered as two inputs to the incremental RBFNN. The total number of data pairs is 252. In order to solve the data scarcity problem, we divided the data set into training and test datasets as a commonly used solution. The training datasets were randomly selected from approximately 60% of the entire dataset, and the testing dataset from the remaining 40%. The data were normalized between 0 and 1. Ten iterations were used for all experiments. The training data were used for the construction of the incremental RBFNN. However, the testing data were used for the verification of the network. Thus, the resultant network is not biased towards the training dataset, and it is likely to have a better generalization capacity to new data. The nonlinear data we called "error" can be calculated using the RMSE Euclidean value, as shown in Equation (8).
where N is the length of the training or testing datasets, EEk is the estimated EE, and EEk' is the measured EE.
The error values constituted the context dataset. These contexts are generated through the triangular membership functions, and are equally spaced along the domain of an output variable. The membership matrix is initialized between 0 and 1, as shown in Figure 5 (context p = 3).   HR and MI are the two major factors used to estimate EE. Thus, they were considered as two inputs to the incremental RBFNN. The total number of data pairs is 252. In order to solve the data scarcity problem, we divided the data set into training and test datasets as a commonly used solution. The training datasets were randomly selected from approximately 60% of the entire dataset, and the testing dataset from the remaining 40%. The data were normalized between 0 and 1. Ten iterations were used for all experiments. The training data were used for the construction of the incremental RBFNN. However, the testing data were used for the verification of the network. Thus, the resultant network is not biased towards the training dataset, and it is likely to have a better generalization capacity to new data. The nonlinear data we called "error" can be calculated using the RMSE Euclidean value, as shown in Equation (8).
where N is the length of the training or testing datasets, EE k is the estimated EE, and EE k ' is the measured EE.
The error values constituted the context dataset. These contexts are generated through the triangular membership functions, and are equally spaced along the domain of an output variable. The membership matrix is initialized between 0 and 1, as shown in Figure 5 (context p = 3).  HR and MI are the two major factors used to estimate EE. Thus, they were considered as two inputs to the incremental RBFNN. The total number of data pairs is 252. In order to solve the data scarcity problem, we divided the data set into training and test datasets as a commonly used solution. The training datasets were randomly selected from approximately 60% of the entire dataset, and the testing dataset from the remaining 40%. The data were normalized between 0 and 1. Ten iterations were used for all experiments. The training data were used for the construction of the incremental RBFNN. However, the testing data were used for the verification of the network. Thus, the resultant network is not biased towards the training dataset, and it is likely to have a better generalization capacity to new data. The nonlinear data we called "error" can be calculated using the RMSE Euclidean value, as shown in Equation (8).
where N is the length of the training or testing datasets, EEk is the estimated EE, and EEk' is the measured EE.
The error values constituted the context dataset. These contexts are generated through the triangular membership functions, and are equally spaced along the domain of an output variable. The membership matrix is initialized between 0 and 1, as shown in Figure 5 (context p = 3).   The centers can be generated by fuzzy c-means clustering based on each of the contexts. Given "p" contexts and "c" centers per context, c × p clusters can be obtained. Figure 6 shows the cluster centers generated by the three contexts and the three clusters. The cluster centers can be the same as those of the RBFN hidden layer. Therefore, the RBFN model can be constructed as follows: HR and MI are used as the inputs of the input layer, nine units as the hidden layer-based on the number of contexts-and the clusters, and the EE as the output layer. The centers can be generated by fuzzy c-means clustering based on each of the contexts. Given "p" contexts and "c" centers per context, c × p clusters can be obtained. Figure 6 shows the cluster centers generated by the three contexts and the three clusters. The cluster centers can be the same as those of the RBFN hidden layer. Therefore, the RBFN model can be constructed as follows: HR and MI are used as the inputs of the input layer, nine units as the hidden layer-based on the number of contexts-and the clusters, and the EE as the output layer. The estimation of the performance was evaluated by the RMSE as the number of context, and the cluster increased from three to six and from two to six, respectively. Table 2 shows the RMSE results for the training and testing data. The result elicited from the best fitting model is shown in bold (p = 3, c = 3). The comparison of the RMSE with previous work is shown in Table 3. The RBFNN we used was a 2-10-1 network, employed a BP algorithm, and 1000 epochs with a learning rate of 0.01. The linguistic model (LM) we used consisted of three contexts and three clusters which were determined by trial and error. The CFCM-RBFNN used the hidden layer that increased from 3 to 20 in the experimental design.  The estimation of the performance was evaluated by the RMSE as the number of context, and the cluster increased from three to six and from two to six, respectively. Table 2 shows the RMSE results for the training and testing data. The result elicited from the best fitting model is shown in bold (p = 3, c = 3). The comparison of the RMSE with previous work is shown in Table 3. The RBFNN we used was a 2-10-1 network, employed a BP algorithm, and 1000 epochs with a learning rate of 0.01. The linguistic model (LM) we used consisted of three contexts and three clusters which were determined by trial and error. The CFCM-RBFNN used the hidden layer that increased from 3 to 20 in the experimental design.

Field Test
The final goal is to realize the accurate estimation of EE under free-living conditions. After the laboratory tests, all of the participants were encouraged to complete four exercise tests in the open field. The first was comfortable walking, the second jogging, the third was a quick walk, and the last was slow running. Each test course was performed in approximately two minutes in an oval track field. The experimental procedure was designed to progress as naturally as possible. The structure of the RBFNN thus constituted the reference basis of the experimental laboratory test. The data obtained for walking, jogging, fast walking, and slow running, respectively consisted of 157, 60, 63, and 99, sample pairs. The prediction performance is shown in Figure 7. As indicated in the Figure 7, the experimental results revealed that the proposed network showed good prediction and generalization performance in all cases of normal walking, brisk walking, slow running, and jogging, for the training and testing datasets, respectively. Table 4 lists a comparison of the RMSE data collected using the RBFNN and LM methods.

Field Test
The final goal is to realize the accurate estimation of EE under free-living conditions. After the laboratory tests, all of the participants were encouraged to complete four exercise tests in the open field. The first was comfortable walking, the second jogging, the third was a quick walk, and the last was slow running. Each test course was performed in approximately two minutes in an oval track field. The experimental procedure was designed to progress as naturally as possible. The structure of the RBFNN thus constituted the reference basis of the experimental laboratory test. The data obtained for walking, jogging, fast walking, and slow running, respectively consisted of 157, 60, 63, and 99, sample pairs. The prediction performance is shown in Figure 7. As indicated in the Figure 7, the experimental results revealed that the proposed network showed good prediction and generalization performance in all cases of normal walking, brisk walking, slow running, and jogging, for the training and testing datasets, respectively. Table 4 lists a comparison of the RMSE data collected using the RBFNN and LM methods.

Conclusions
This study has shown that the incremental RBFNN is effective for estimating the EE. The significant advantage of this model is that it starts from the linear regression model and then uses a refined

Conclusions
This study has shown that the incremental RBFNN is effective for estimating the EE. The significant advantage of this model is that it starts from the linear regression model and then uses a refined version of this regression model by adding granular patches. This leads to a final model that is quite different compared to the preliminary version of the linear model. The other important design is related to the application of the CFCM clustering for the calculation of the center value, which is a process that can reduce the iteration times and optimize the network structure. The output space can be optimized by the context number and the number of clusters. The experimental results have been compared with the LM, RBFN, and CFCM-RBFNN, which indicate that the sensor module that is based on the incremental RBFNN, has the ability to estimate the EE during walking and running both in laboratory and free-living settings. Moreover, in future work, the same approach of the incremental modeling could be explored in other domains, such as pattern recognition and classification, which could be especially useful for application to the e-health monitoring field.