IRJET- Expert Independent Bayesian Data Fusion and Decision Making Model for Multi-Sensor Systems Sm

International Research Journal of Engineering and Technology (IRJET) Volume: 06 Issue: 03 | Mar 2019

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Expert Independent Bayesian Data Fusion and Decision Making Model for Multi-Sensor Systems Smart Control Mumbere Muyisa Forrest1, Masivi Osée Muhindo2, Kasereka Masivi Samuel3 1School

of Software, Central South University, Changsha 410000, China. d’Informatique de Gestion, ISP/Muhangi, Butembo, DRC. 3Departement of Computer Science, Invertis University, India.

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Abstract- Internet of Things (IoT) and its applications have increased the number of multi-sensors computer applications. Then, the necessity of multi-sensor data merging and expert independent decision algorithms is real. This paper proposes a novel multi-sensor system smart control model based on Bayesian. Proposed “study on intelligent” algorithms are expect-dependent trainable predicting the system only from anterior and actual data.

Simulations test on a three sensors system (sol temperature, air temperature, and moisture) an overall prediction precision of more than 96%. However, a real life customizable implementation of the proposed algorithm is needed.

system was able to stand between the source data and the human and helped him to make decisions based on the fused output. The big challenge with these methods is the amount of data and processing need for training the decision making algorithm.

Therefore, Bayesian approach, including Bayesian analysis, Statistic, and recursive operators stood as one of reliable alternatives. Used already for data fusion [7] Bayesian approach is being accepted to be one of the most classical fusion approach. Furthermore, the authors in [8] demonstrated that the data fusion based on Bayes estimation can weaken the possible sensor errors, resulting from the sensor faults and noise inference. The most appealing advantage of Bayes parameters estimation algorithms is the small amount of training needed for classification [9] [10] and its impendence toward system experts.

Keywords: Naïve Bayes, Data fusion, Multi-sensor, System smart control, Expert independent training.

1. INTRODUCTION

This paper introduces the Naïve Bayes theorem in the decision algorithm from merged data collected from sensors with different characteristics. The algorithm should to make decision in control systems under multisensor context. The proposed method includes system parameters learning and time-based system state prediction and is expected [11] (a) to easy design process with less free parameters to set, (b) to easy result application to a large variety of tasks, (c) to use a small amount of data for learning process (d) to be computationally fast when making decisions.

The meteoric rise of Internet of Things (IoT) has increased the number of sensors in almost all computer applications and hence increases the necessity of multisensor systems smart control algorithms. These algorithms are not only required to merge sensed data from a good number of sensors into a common representational format, but also to make relevant decisions. Despite the fact that suggested principles, procedures, theories and tools are approximately the same [1], decision algorithms depend on the number of sensors [2] [3] in the application context [4].

Furthermore, sensors characteristics increase exponentially the complexity of the system decision algorithm.

3. PROPOSED MATHEMATICAL METHOD In this paper, Bayesian inference is used to draw conclusions about features (parameters) in system control based on a sample from the same system. Both parameters and sample data are treated as random quantities [12]. The proposed algorithm computes the distribution for the system parameters from the likelihood function which defines the random process that generates the data, and a prior probability distribution for the parameters.

2. RELATED WORKS AND OBJECTIVES Data fusion and decision making and related challenges [4] have been addressed by researchers for decades.

Since then, two major approaches have emerged: artificial intelligence methods and probabilistic based methods. Artificial approaches, with the main focus on machine learning, fuzzy logic, have been reputed to yield higher accuracy compared to other techniques [2][5]. In this line, [6] proposed a generic data fusion system which established a relationship between the source of data and the type of processing in order to extract maximum possible information from data collected. The

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By assuming that all the variables are observed with no missing data and that all classes have equal prior probabilities [13], the proposed method estimates the probability of a system feature by the frequency of

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occurrence of the same feature database { }.

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in the feature

| )

(

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( ): Posterior probability of class membership. ( | ) : Likelihood which is the probability of the predicator given class. : class prior probability Using (9), any new case X can be labeled by a class level with the highest posterior probability. Then after normalization, the decision distribution is : ( ) (10) ( ) -

The conditional likelihood of this feature is computed by (1) and the density probability of the set of data D is computed by (2). Since occurs whenever and , (3) is deducted from (2), then the logarithmic notation of (3) gives (4). (

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√

Where :

∏

(1)

∏

4. PROPOSED COMPUTATIONAL MODEL ∏

(2)

∏∏

∏∏

The proposed computational protocol sketched in Figure 1, uses the following steps: (a) getting data from sensors (b) split training set from test data (c) learning/training the model (d) predict class using Naive Bayes model.

(3)

∏∏∏

Naive Bayes Model

(4)

∑∑∑

Since [6] demonstrates that (4) formula can be simplified to (5), the Maximum Likelihood (ML) approach used in this paper is expressed by (6). ̂ ̂(

{

∑ |

)

̂

} ∑

Sensors data capturing g

(5)

Figure 1: Naïve Bayes protocol for state estimation A.

∏ (

(

| )

Table 1. Adequate range values for the system C.

(7)

Sensor S1 Values

(8)

| )

B. ( | )

( )∏ (

| )

(9)

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S2

S3

Learning & training the model

The proposed model is “study on intelligent” say it was trained from data collected from sensors [15]. Hence, the state of the system depends on values provided by

Where:

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Collecting data from sensors

During this step, the system collects data from a given number of sensors. Each sensor can be in one of the three states: low, adequate or high. Each sensor is assumed to be independent in terms of data types and collecting rate [14] [15]. The example provided in Table 1 gives the ranges for the training system of three sensors.

This classifier was improved by Naive Bayes to handle an arbitrary number of independent variables by constructing the posterior probability for the feature { } among a set given a set of variables, { } by (7). Assuming of possible outcomes that the variables are statistically independent, the likelihood is decomposed to a product of terms in (8).

Then from (8) the estimation computed by (9). )

Posterior probability Predicted State

(6)

With being the number of features in the database whose variable is in the state and parents are in the configuration .

(

Training data Test data

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D. Decision

different sensors: at time t, Ct depends on the state of S1t, S2t, S3t, Snt. From example (Table 1), the System State had 27 different probable classes. Each class is composed by 3 different states provide by the 3 sensors.

The class C1can be represented by: S1low, S2adequate, S3high, meaning that at a given time t, sensor 1 sent a value lower than 16, sensor 2 sent a value between 20 and 25 and sensor 3 sent a value higher than 120. The learning process used it this paper can be summarized by algorithm 1 as follow:

The proposed Bayesian classifier (Algorithm 2) is a probabilistic model based on the Bayes rule [17] in which each element ) is associated to a class with a maximum a posteriori. ( |

) ( )

( | )

Algorithm 1: Training process Input: K (Training set) For each class c in K do Compute mean(k) and std(k) End for Output: mean, std

( | )

(15)

( | )

Algorithm 2: Testing Input: k(Learned features) For each class li do Calculate P(li|k) End for { Output: class)

During the training stage, the mean and standard deviation values of the features for each class were computed.

C.

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}(estimated

The probabilities for the objective existing in each class are computed and the highest is chosen as the estimated class.

Classification

5. SIMULATION RESULTS

Assuming that system parameters are distributed according to the Gaussian density, two parameters were computed. First the parent node without parents . It probability is the frequency of the class in the training database. Since all the classes have the same probability at this stage:

The proposed computational model was evaluated and its goodness was tested using the following evaluation parameters: accuracy, precision, recall, f1 score drawn from a confusion matrix. Furthermore, imbalanced data set results were compared to balanced data set results

( )

A.

Confusion matrix

( ) ∑

(11)

( )

∑ ( ) Where: : The size of the database ( ): The number of observation belonging to the class Second, the probability of the children nodes were computed by using the Normal law in conditional probability of node considering the parent (12) then combine the different values computed in the previous step (13). in (13) being constant hence easy to compute, (13) was rewritten as (14).

Figure 2. Confusion matrix for imbalanced data set Figure 2, shows a confusion matrix, with an accuracy rate of 87% for imbalanced data. In Figure 3, the false negative and the false positive have been minimized by balancing the data in the training set; the result shows that the accuracy of the model has improved from 87.33% to 96.33%.

(12) ( | ( | ( )

(

) ) ( | )

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| )

( | )

( | )

(13) (14)

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96.33%. Accuracy is misled by the class with high support, thus reducing the overall accuracy as shown in (a).

Precision, recall, f1-score Precision 120

precision

100 80 60

Precision

40 20

Cl as s Cl 1 as s Cl 2 as s Cl 3 as s Cl 4 as s Cl 5 as s Cl 6 as s Cl 7 as s Cl 8 as Cl s 9 as s Cl 10 as s Cl 11 as s Cl 12 as s Cl 13 as s Cl 14 as s 15

0

Figure 3. Confusion matrix with balanced data sent.

classes

Comparative Accuracy

(a)

After varying the percentage of the learning set and the test set, we create 9 different set of data. Figure 3 show the relationship between the size of the learning set and the test set.

Precision 105 100 95 Precision 90

Accuracy 85

87.5

Cl a

ss Cl 1 as s Cl 2 as s Cl 3 as s Cl 4 as s Cl 5 as s Cl 6 as s Cl 7 as s Cl 8 as Cl s 9 as s Cl 10 as s Cl 11 as s Cl 12 as s Cl 13 as s Cl 14 as s 15

80

Accuracy %

87

(b)

86.5 Accuracy

Figure 5: Precision (a) Precision for imbalance data set (b) Precision for balanced data set.

86

85.5

Figure 5 shows that the balanced data set achieves high precision than the imbalance data set, reaching 6 times a precision of 100%, on the other hand, the highest precision for classes in the imbalance data set reached hardly reached 100%. Figure 5 represents the sensitivity of balanced and imbalance data set.

85 10%

20%

30%

40%

50%

60%

70%

80%

90%

Training set

(a) Accuracy 100

Accuracy %

95

In term of sensitivity, the balanced data set, produce a higher rate of sensitivity than the imbalance data set.

F1-score conveys the balance between the precision and the recall, when dealing with imbalance classes, classification alone cannot be trusted to select a well performing model. Figure 8, shows the relationship between precision, recall and f1-score.

90 85

Accuracy

80 75 70 10%

20%

30%

40%

50%

60%

70%

80%

90%

Training set

(b) Figure 4: Relation between the size of the learning set and accuracy. (a) Imbalance data set (b) Balanced data set.

Better result are obtained when the size of the training set ranges between 40 to 65 % as shown in (a) and (b) in Figure 4. On the other hand taking the same number of data for each class in the training set (balanced data set) can improve the accuracy of the system from 87.3% to

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Recall 120

120

100 Score in %

100 80

Score

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60

Recall

80 Precision 60

Recall f1-score

40

40 20

20 0

Cl a

ss

Cl 1 as s Cl 2 as s Cl 3 as s Cl 4 as s Cl 5 as s Cl 6 as s Cl 7 as s Cl 8 as Cl s 9 as s Cl 10 as s Cl 11 as s Cl 12 as s Cl 13 as s Cl 14 as s 15

C la ss C 1 la ss C 2 la ss C 3 la ss C 4 la ss C 5 la ss C 6 la ss C 7 la ss C 8 la s C s9 la ss C 10 la ss C 11 la ss C 12 la ss C 13 la ss C 14 la ss 15

0

Classes

classe

(a)

(a)

Precision, recall, f1-score

Recall

105

102

100

Classes

100

Score

98

Precision

95

Recall 90

96

f1-score

Recall 94

85

92

80

Cl a

ss Cl 1 as s Cl 2 as s Cl 3 as s Cl 4 as s Cl 5 as s Cl 6 as s Cl 7 as s Cl 8 as Cl s 9 as s Cl 10 as s Cl 11 as s Cl 12 as s Cl 13 as s Cl 14 as s 15

90 88 Cl a

ss

Cl 1 as s Cl 2 as s Cl 3 as s Cl 4 as s Cl 5 as s Cl 6 as s Cl 7 as s Cl 8 as Cl s 9 as s Cl 10 as s Cl 11 as s Cl 12 as s Cl 13 as s Cl 14 as s 15

score %

(b)

Classe

Figure 8: Precision (a) Precision for imbalance data set (b) Precision for balanced data set.

(b) Figure 6: Recall (a) Precision for imbalance data set (b) Precision for balanced data set.

For imbalance class in the training set, the support of a class has a positive impact on the precision of the class; however, classes with a very high accuracy can create an accuracy paradox problem by predicting the value of the majority class for all predictions and achieve high classification accuracy.

The support of the class in the training set has a positive impact on the precision of the class, especially when we have imbalance class in the training set. Figure 7 shows the relationship between the support and the precision.

C al ss lC a ss 2 lC a ss 3 lC a ss 4 lC a ss 5 lC a ss 6 lC a ss 7 lC a ss 8 lC a ss C 9 al ss 01 alC ss 11 alC ss 21 alC ss 31 alC ss 1 4 alC ss 51

Classes

1

f1-score

0 100

80 70 60

200

50 40 30 20

erocS

Score

100 90

f1-score

Precision

300

Support

400 500 600

10 0 Cl a

ss

Cl 1 as s Cl 2 as s Cl 3 as s Cl 4 as s Cl 5 as s Cl 6 as s Cl 7 as s Cl 8 as Cl s 9 as s Cl 10 as s Cl 11 as s Cl 12 as s Cl 13 as s Cl 14 as s 15

Support & Precision

(a)

Classe

Support & Precision

(a) 30

f1-score

25 102

20 Score

100

score

98 96

support

10

94

f1-score

5

92

0 Cl as s Cl 1 as s Cl 2 as s Cl 3 as s Cl 4 as s Cl 5 as s Cl 6 as s Cl 7 as s Cl 8 as Cl s 9 as s Cl 10 as s Cl 11 as s Cl 12 as s Cl 13 as s Cl 14 as s 15

90 88 86 Cl 1 as s Cl 2 as s Cl 3 as s Cl 4 as s Cl 5 as s Cl 6 as s Cl 7 as s Cl 8 as Cl s 9 as s Cl 10 as s Cl 11 as s Cl 12 as s Cl 13 as s Cl 14 as s 15

Classes

ss Cl a

Precision

15

(b)

classe

Figure 9: Relationship between the support and the precision. (a) Relationship between the support and precision for imbalance data set (b) Relationship between the support and precision for balanced data set.

(b) Figure 7: f1 score (a) Precision for imbalance data set (b) Precision for balanced data set.

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6. DISCUSSIONS AND CONCLUSION

Since the trained and proposed model is “study on intelligent”, the algorithm reduces the reliance on experts. It is a “previous system data” dependent model.

This means that any non-expert can train and use the system. A few expertise is only required during the training step of the system. However, a real life customizable implementation of the proposed algorithm is needed.

7. REFERENCES [1] H. Mitchell, Multi-Sensor Data Fusion: An Introduction, Berlin: Springer.

[2] D. Hall and J. Llinas, Handbook of Multisensor Data Fusion, New York, 2001.

[3] M. Wang and all, "City Data Fusion: Sensor Data Fusion in the Internet of Things," International Journal of Distributed Systems and Technologies, June2015.

[4] F. Aiam and All, "Data Fusion and IoT for Smart Ubiquitous Environments: A Survey. ,," IEEE. [5] B. Yang, X. Liu and X. Z. Y. Li, "Stochastic Blocmodeling and variational Bayes Learning for Signed Network Analysis," in IEEE Transactions on Knowledge and Data Engineering, May 2017.

[6] D. Hall and A. Garga, "Pitfalls in data fusion(and how to avoid them)," Proceedings of the Second International Conference on Information Fusion (Fusion ’99), vol. 1, pp. 429-439, 1999.

[7] H. Holzapfel, K. Nickel and R. Stiefelhagen, "Implementation and evaluation of a constraintbased multimodal fusion system for speech and 3D pointing gestures," Proc. 6th Int. Conference Multimodal interfaces- ICMI ’04, p. 175, 2004.

[8] F. Shen and R. Yan, "A Thermostatic Control Strategy Based on Multi-sensor Data Fusion and Fuzzy PID Method," in Tenth Internation Conference on Sensing Technology, 2016.

[9] J. He, S. Bai and X. Wang, "An Unobtrusive Fall Detection and Alerting System Based on Kalman Filter and Bayes Network Classifier," Sensors 2017, vol. 14, p. 1393, 2017.

[10] R. Mahler, Unified Bayes Multi target Fusion of

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Ambigous Data Sources, Boston, USA: Kimasi, 2003.

[11] A. Ashari, I. Paryudi and A. Tjoa, "Performance Comparison between Naive Bayes, Decision tree and K-Nearest Neighbor in Searching Alternative Design in an Energy Simulation Too," IJACSA, International Journal of Advanced Computer Science and Applications, vol. IV, no. 11, 2013.

[12] X. Meng, G. Bai, X. Shu and D. Bao, "A study of intelligent fault diagnosis in engine room by Bayes method;, 2002.," IEEE; Intelligent Control and Automation. Proceedings of the 4th World Congress, 2002.

[13] G. Myburgh and A. V. Niekerk, "Impact of training set size on object-based land cover classification: A Comparison of three classifiers," International Journal of Applied Geospacial Research, vol. V, no. 3, pp. 49-67, July 2014.

[14] D. J. Hand and K. Yu, "Idiot’s bayes : Not so stupid after all?," International statistical Review, 2001.

[15] M. Godec, C. Leistner, A. Saffari and H. Bischof, "OnLine Random Naïve Bayes for Tracking," IEEE, Pattern Recognition (ICPR), 2010 20th International Conference, 2010.

A novel multi-sensor system smart control model based on Bayesian data was proposed. The proposed algorithm is able to predict the state of a system taking into account the actual and the anterior data collected from different types of sensors. For test seek, a three sensors system (sol temperature, air temperature, and moisture) was set and the algorithm performance was measured.

Simulation tests have proved that the proposed algorithm can predict at an overall rate of more than 96% the actual state of the system.

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BIOGRAPHIES Mumbere Muyisa Forrest is a MSc holder in Information Technology and a Lecturer of IT courses at Université Adventiste de Lukanga and Institut de Commerce de Beni in RDC. He is currently preparing his PhD in Software Engineering in School of Software at Central South University, Changsha 410000, China.

Dr MASIVI is a Computer Science PhD holder from University of the Philippines Los Banos. He is currently Associate Professor lecturing IT and Computer Science courses at Rusangu University (Zambia) and ISP/Muhangi (RDC).

Kasereka Masivi Samuel is a MSc holder in Information Technology and a Lecturer of courses at Université Adventiste de Lukanga and Université de Bunia in DRC. He is currently preparing his PhD in Computer Science at Invertis University, India.

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