Data Fusion for Magnetic Sensor Based on Fuzzy Logic Theory

Transcription

1 2 Fourth International Conference on Intelligent Computation Technology and Automation Data Fusion for Magnetic Sensor Based on Fuzzy Logic Theory ZHU Jian, CAO Hongbing, SHEN Jie, LIU Haitao Shanghai Institute of Microsystem and Information Technology, CAS, Shanghai, 25, China Abstract Data fusion of s is a useful technique to obtain more comprehensive information about the monitoring targets in wireless networks (WSN). This paper proposes a data fusion algorithm based on fuzzy logic theory to monitor a parking space in the parking lot using magnetic s and point out the probability of occupancy of the corresponding parking space. Simulation results show that our algorithm gathers more accurate information about the monitoring targets to support right decisions and has the ability of anti-interference. Keywords-WSN; magnetic ; target monitoring; decision-making; data fusion; fuzzy logic theory I. INTRODUCTION Currently due to recent advances in microelectronic and wireless communication techniques, Wireless networks (WSN) has been used widely, especially in military surveillance, facility and environmental monitoring []. In many applications of WSN such as target monitoring or classification, the characteristics of monitoring targets are complex and y data is uncertain, incomplete and inconsistent, so we could not get comprehensive understanding of these targets just using data from single source. Consequently multi-source data fusion (MSDF) is adopted to meet this need [2]. Multi-source data fusion refers to combining information from different sources in order to obtain more accurate descriptions of the targets [3]. Recently, This paper was supported in part by the National Key Special Program of China under Grant No. 29ZX36-3 and National Basic Research Program of China (973 Program) (2CB329 ) researchers have explored some MSDF algorithms [4], of which Kalman filter, Bayesian inference theory, Dempster-Shafer (D-S) theory and neural network are the most common ones. However, Kalman filter and D-S theory are computationally expensive, Bayesian inference theory needs a prior probability, neural network has the defects such as finite sample study and the black-box structure questions [5] and each of them could not deal with the problems of uncertainty of uncertainty [4], for instance, problems described by human linguistic variables. In this paper, we proposed a multi-source data fusion algorithm that is based on fuzzy logic theory to combine information from three sources and then outputs a probability as the result for decision-making. Fuzzy logic theory is capable of processing imprecise data [6] from multi-source and provides a simple and effective method for uncertainty analysis. It requires much less computation than those common algorithms. The most important characteristic of fuzzy logic theory is its simulation of human cognition, i.e. it is able to deal with problems described by human linguistic variables. The remainder of this paper is organized as follows. In Section II, background and motivation will be discussed. In Section III basic fuzzy logic theory will be introduced and data fusion algorithm will be presented. In Section IV simulation and performance evaluation will be described. At last conclusions will be made in Section V. II. BACKGROUND AND MOTIVATION In order to make cars park on the proper parking space, staff of the parking lot should make sure that whether the specified parking space has been occupied. Lots of methods have been proposed to solve the problem. Our solution is / $26. 2 IEEE DOI.9/ICICTA

2 using magnetic s based on geomagnetic induction. The magnetic node, which is fixed on the ground of the parking space (Fig. ), consists of a magnetic for monitoring the parking space, a microcontroller (MCU) and an RF chip for wireless communication. Each parking space has a magnetic node which composes wireless networks (WSN). These magnetic nodes are grouped into clusters. They send monitoring or processing results to the corresponding cluster head (CH) through wireless communication and the CHs after aggregating the information from nodes send final results to the control center for decision-making. The magnetic has three axes for monitoring changes in geomagnetic field and outputs acquired data in digital signal mode. The signal is shown in Fig. 2 and each axis of the has its own data waveform in the figure. The X-axis of Fig. 2 refers to time axis and Y-axis refers to amplitude axis of the signal. The data is acquired when a car is parking and fluctuations of the signal indicate that geomagnetic field has changed when there is some metal object such as a car. What we should do is that based on the data acquired by the, we should point out that whether the parking space monitored by the has been occupied. A traditional way to accomplish that is simply setting thresholds for y data. When the thresholds are exceeded, we say that the corresponding parking space is occupied. However this way has some defects. First of all, it s difficult to set a proper threshold for each axis of the. A lot of experiments have to be carried out for finding the proper thresholds. Figure. The position of magnetic node on the parking space Figure 2. amplitude Acquired data of three axes of the magnetic when there is a car on the parking space Even if we get the thresholds, interference may cause wrong decisions. In addition, traditional algorithms don t have the ability to deal with problems described by linguistic terms like little, greatly and etc. On the contrary, fuzzy logic theory is quite qualified for such problems which we will face in our applications. For this reason our algorithm based on fuzzy logic theory is proposed, combining data from 3 axes of the to obtain more accurate information about the corresponding parking space without setting any thresholds. III. A. Fuzzy Logic Theory time DATA FUSION ALGORITHM Fuzzy logic theory was first introduced by Zadeh in 965 [7]. In his thesis he proposed the concept of fuzzy sets and membership functions to deal with problems which are imprecise, uncertain or expressed by vague and linguistic terms. In classical set theory, each element either belongs to a crisp set or not. Thus the membership degree of each element to a crisp set is or. Contrary to crisp sets, Zadeh s fuzzy sets [7] have extended the value of membership degree from binary value to any value in the interval of [, ]. As a result, we can say that the degree that an element belongs to the specified fuzzy set is.5 for example. Let A be a fuzzy set in the universe of discourse U then A can be described by x y z μ : [,], () A where μ Α is the membership function of the fuzzy set A. μ Α can take any value in the interval of [,]. μ Α represents 88

3 the membership degree of u in A, in other words, μ Α means how much the element u in the universe of discourse U belongs to the fuzzy set A. If μ Α (u) is close to, it is very likely that u belongs to A and vice versa. If U is discrete and finite and U= {u,u 2,,u n }, A can be represented by [8] ( u ) μa μ A( u2) μ A( un) A = (2) u u u 2 B. Data Fusion Algorithm In this subsection we will describe our algorithm based on fuzzy logic theory. Unlike those traditional algorithms that output binary results with less information, our algorithm making use of the data acquired by the as the input will output a probability of the occupancy of the corresponding parking space for decision makers. Based on this output, an early-warning mechanism can be set up to reduce wrong decisions further. Our algorithm makes use of the principle of geomagnetic induction which can be explained informally as the following: a metal object like a car coming into geomagnetic field will result in great change in geomagnetic field. The amplitude of the signal in Fig. 2 indicates the extent of the change. The larger the amplitude is, the greater the change is. The first step of our algorithm is fuzzification. Fuzzification refers to the process of transforming crisp values into linguistic variables by membership functions [9]. Here crisp values come from s, and membership functions associate crisp values with linguistic variables of fuzzy sets by assigning values to each crisp value. Assume that X represents the data coming from X-axis of the, while Y and Z represent data of Y-axis and Z-axis of the respectively. Let X={x,x 2,,x n }, Y={y,y 2,,y n }, Z={z,z 2,,z n }. Because X, Y and Z are similar, we just study on X. Each single element x i in X is acquired at a fixed frequency and the data of three axes is acquired synchronously. The inputs of our algorithm are {x i,y i,z i }which are acquired at the same time. Then we calculate the average value of the first M elements of X, n the smooth interval of the whole signal. Therefore M between 2 and 5 is recommended. Consequently in practical applications, at the very beginning of the system when there is no car on any of the parking spaces and the signal is smooth, we should wait for a short period for getting the average value and the short period can be considered as the start time of the system. This process is called background value acquisition. After background value acquisition, we calculate the absolute values of differences between x and each element of X. Let X = { x x x },,, where x n i = x i x. 2 Note that X is the crisp set and the corresponding fuzzy sets are Low which means both of x i and the change of geomagnetic field are small, Medium which means both are moderate and High which means both are great. There are many kinds of membership functions with different shapes such as triangular function, trapezoidal function and Gaussian function. Given its better performance, we choose Gaussian function for the fuzzy sets as membership functions which are shown in Fig 3, Fig. 4 and Fig. 5. The expected output of our algorithm which leads to right decisions is the probability of occupancy of corresponding parking space. Thus The corresponding crisp set is [, ], and the fuzzy sets are VL, L, M, H, VH, which means the probability is very low, low, moderate, high, very high respectively. Here we choose triangular function and trapezoidal function as the member functions shown in Fig. 6 for simplifying computations. Figure Low Medium High xdiff Membership functions for data of X-axis of the magnetic M x i= i M x =.Here we must note that M should not be too great and the M elements should be at the beginning and in 89

4 Figure 4. Low Medium High ydiff Membership functions for data of Y-axis of the magnetic while Mamdani method is the most common one and has been used widely in various practical engineering applications []. Finally, we should transform the fuzzy inference results into crisp values and this process is called defuzzification [9]. In our algorithm, we should transform the final inference result into a probability which indicates the occupancy of the corresponding parking space. Table. Examples of fuzzy inference rules of our algorithm Low Medium High IF THEN operator, operator probability Low And Low And Low VL Low And Low And Medium L Low And Medium And Medium M Figure 5. Membership functions for data of Z-axis of the magnetic Figure 6. Membership functions for output of our algorithm, i.e. the probability of occupancy of the corresponding parking space Next step, we come to fuzzy inference system and rule evaluation. The fusion of data from 3 axes is implemented here. Fuzzy inference system contains a library of fuzzy rules (i.e. if... then...) which are based on studying the input and output of the system or expert knowledge [9]. These fuzzy rules simulate human reasoning and produce fuzzy outputs. As mentioned above, we have 3 inputs of our algorithm which are {x i,y i,z i }, by computing we obtain { x, y, z } as the inputs of the fuzzy inference system. Then i i i we make fuzzy rules by combining the three inputs. There are totally 27 rules and some of them are shown as examples in Table. It is clear that each rule has an output. In order to get the final inference result, we should aggregate the outputs of all rules with respect to the input { x, y, z }. There are some methods to accomplish this i i i zdiff VL L M H VH output Medium And Medium And High H High And High And High VH There are also some methods to do this and centroid [9] method is widely adopted.the centroid method is represented as the following [6] p μ = μ ( p) * ( ) pdp p dp. (3) where p refers to the final result of our algorithm, i.e. the probability, and μ is the new function for the probability after aggregation of the outputs of all rules with respect to the input{ x, y, z }. To sum up finally, Fig. 7 shows the i i i process of our algorithm. Magnetic IV. Data of X-axis Data of Average Y-axis value Data of Z-axis calculation Figure 7. Absolute value calculation Fuzzification and Rules making Experience and expert knowledge Rule inference Rules defuzzification The general process of our algorithm Probabil ity/crisp value SIMULATIONS AND PERFORMANCE EVALUATION For our simulations, the input data are shown in Fig. 2. Because the geomagnetic field changes slowly, the frequency of data acquisition is low and 2Hz is chosen in our work. Additionally the data of the three axes is acquired synchronously as mentioned before. 9

5 Look at the X-axis of Fig. 2, approximately in the interval of [, ], the signal is flat, because the system is at the very beginning and there is no car driving in, thus no change in geomagnetic field. We calculate the average value mentioned above in this interval. Approximately in the interval of [, 23], a car is driving in and continue moving slowly on the parking space, so we can see fluctuations on the signal which indicate that there is a great change in the geomagnetic field. Approximately in the interval of [23, 33], the signal appears smooth again because the car stops on the parking space. Approximately in the interval of [33, 4], the signal returns to the original state when the car has driven out. We perform our algorithm simulations in the following steps. A. Comparing our algorithm with threshold-setting algorithm First of all we set a threshold for y data of each axis. By setting proper thresholds, the algorithm based on thresholds outputs when there is a car parking on the corresponding parking space and when there is no car. It outputs and alternately when the car is moving slowly on the parking space. On the contrary, without setting any thresholds, our algorithm outputs a low (about 8%) and high probability (about 87%) to indicate that there is no car and the car is parked respectively. It also outputs a moderate probability (about 46%) indicating that a car is moving slowly on the parking space and has not stopped, so an early-warning mechanism can be started, which can reduce false alarm rate. However, when there is some interference in the y data, threshold-setting algorithm may lead to wrong decisions. The interference is added to data of X-axis and Y-axis, which is shown in Fig. 8. Threshold-setting algorithm simply outputs when there is some interference while our algorithm outputs a low probability (about 26%); therefore it is clear that the former may lead to wrong decisions. B. Fusing data of 3 axes, 2 axes and axis of the In this subsection, we perform our algorithm simulations using data from 3 axes, 2 axes, and axis of the and make comparisons among them. Firstly we just use data from X-axis to monitor the parking space. Secondly we use data from X-axis and Y-axis. We find that without setting any thresholds, our algorithm using data from only one axis has a performance similar to threshold-setting algorithm. It outputs less information about the monitoring target because it does not output a middle state about the monitoring target.i.e. the probability indicating that the car is moving slowly on the parking space. Figure 8. amplitude time Interference added in the interval of [6,8] in data of X-axis and Y-axis of the magnetic Furthermore, when there is some interference which is shown in Fig. 8, fusion of data from one or two axes cannot well deal with that because they cannot get comprehensive information about the monitoring target and both output a higher probability (about 44%) for interference than our algorithm fusing data of three axes (about 26%). The final simulation results are shown in Table. 2 V. CONCLUSIONS In this paper, we proposed a data fusion algorithm based on fuzzy logic theory to monitor parking spaces in the parking lot and points out whether the specified parking space has been occupied. Our algorithm, making use of geomagnetic induction, fuses data of 3 axes from the magnetic. Simulation results show that without setting any thresholds the algorithm can output more accurate and comprehensive information than traditional methods such as threshold-setting algorithm. It also has a better performance than algorithms fusing data from fewer x y z 9

6 sources for its capacity to obtain more comprehensive information about the target and get rid of interference. Therefore our algorithm is a promising method for monitoring targets with low false alarm rate in WSN. REFERENCES [] F. Zhao and L. Guibas, Wireless Sensor Networks: An Information Processing Approach (Morgan Kaufmann Series in Networking). San Mateo, CA: Morgan Kaufmann, 24 [2] Fu Hua, Liu Yin-ping and Xiao Jian, Applications of State Estimation in Multi- Information Fusion for the Monitoring of Open Pit Mine Slope Deformation, Journal of Coal Science & Engineering, Vol. 4, No. 2, pp , 28. [3] L. A. Klein, Sensor and data fusion concepts and applications (Tutorial Texts in Optical Engineering), SPIE Optical Engineering Press, pp. 4:3, 993. [4] Bahador Khaleghi, Saiedeh N. Razavi, Alaa Khamis, Fakhreddine O. Karray and Mohamed Kamel, Multi Data Fusion: Antecedents and Directions, Proc. International Conference on Signals, Circuits and Systems (SCS 9), Nov, 29, pp. -6, doi:.9/icscs [5] Feng HAN, Lei Zhu and Xiao-jun ZHI, Measurement of multi- data fusion method based on fuzzy theory, Journal of Applied Optic, Vol. 3, Nov. 29, pp [6] T. J. Ross, Fuzzy logic with engineering applications. New York: McGraw-Hill Inc, 997 [7] L. A. Zadeh, Fuzzy sets, Information Control, vol. 8, pp , 965. [8] Wen Xin et al., Analysis and applications of MATLAB fuzzy logic toolbox. Beijing: Science Press, 23. [9] Ashraf M. Aziz, Effects of fuzzy membership function shapes on clustering performance in multi-multitarget data fusion systems, Proc. IEEE International Conference on Fuzzy Systems, Aug. 29, pp , doi:.9/fuzzy [] Sercan Gök, Adnan Yazici, Ahmet Cosar and Roy George, Fuzzy decision fusion for single target classification in wireless networks, Proc. IEEE International Conference on Fuzzy Systems, July 2, pp. -8, doi:.9/fuzzy Table 2. Final results of simulations of our algorithm and other algorithms for comparison Algorithms [] Events [2] No car (probability [3] ) The car s moving slowly on the parking space(probability [3] ) The car s parked (probability [3] ) Interference (probability [3] ) Threshold-setting /(alternately) Fusion of data from X-axis of magnetic 7.6% 87.2%/7.5%(alternately) 85.5% 43.8% Fusion of data from X-axis and Y-axis of magnetic 7.6% 45.4%/8.4%/85.6%(alternately) 85.8% 43.8% Fusion of data from three axes of magnetic (our algorithm) 7.6% 46.3%(mostly) 86.2% 25.8% []: the algorithms proposed to point out occupancy of the specified parking space [2]: different conditions under which the simulations are performed [3]: the probability of occupancy of the corresponding parking space 92