# FCS-MBFLEACH: Designing an Energy-Aware Fault Detection System for Mobile Wireless Sensor Networks

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Distributed Fault Detection Algorithm (FCS-MBFLEACH)

#### 3.1. Support Vector Machine

#### 3.1.1. Linear-SVM

#### 3.1.2. Nonlinear SVM

- (1)
- Performing computation in the feature space “Hilbert″ can be costly because it has more dimensions.
- (2)
- In general, the dimensions of this space are infinite, so working with this space is difficult.
- (3)
- In addition to the problem of increasing the computational cost, the generalization problem may also occur from very high dimensional spaces when analyzing and organizing data.

#### 3.2. One-Class SVM

_{i}” is a positive slack variable that is defined in the problem constraints. Given the weight vector “w” and the width of the origin “b” to solve the problem in Equation (14), the decision function or separator function is obtained as follows [19]:

#### 3.3. Fuzzy One-Class SVM

_{i}” relative to the target class and parameter “ξ

_{i}” is a fault rate in one-class SVM, the expression “${\mu}_{i}{\xi}_{i}$” is the fault rate with various weighting. Then, the optimization problem based on a constraint for the fuzzy one SVM is demonstrated as follows [19]

_{i}” equal to zero assigns, the result is obtained as follows [19]:

#### 3.4. MB-FLEACH Algorithm

#### 3.5. The Proposed Method

## 4. Experiments

- (1)
- The first scenario: The nodes are randomly distributed with 50 sensor nodes in a 100 square meter region so that the base station location changes randomly. It is given that the base station’s initial location is assigned in the 30 m × 30 m coordinate.
- (2)
- The second scenario: In this scenario, the density of the node changes. It is given that 100 nodes are randomly distributed in the same first scenario space so that the probability of the base station arriving at the next location is randomly determined based on the appropriate location of the base station with respect to the selected SCH.

#### 4.1. Learning Phase

#### 4.2. Testing Phase

## 5. Results

#### 5.1. Fault Detection Accuracy

#### 5.1.1. Fault Detection Accuracy for the First Scenario

#### 5.1.2. Fault Detection Accuracy for the Second Scenario

#### 5.2. False-Positive Rate

#### 5.2.1. False-Positive Rate for the First Scenario

#### 5.2.2. False-Positive Rate for the Second Scenario

#### 5.3. Average Remaining Energy

#### 5.4. Network Lifetime

#### 5.5. Network Lifetime for the First Scenario

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Optimized hyperplane for two-dimensional space (Linear-SVM) [23]. SVM: support vector machine.

**Figure 2.**Nonlinear SVM [22].

**Figure 3.**MB-FLEACH algorithm [4].

**Figure 7.**Average detection accuracy of sensor node faults with a density equal to five for the first scenario.

**Figure 8.**Average detection accuracy of sensor node faults with a density equal to 10 for the first scenario.

**Figure 9.**Average detection accuracy of sensor node faults with a density equal to five for the second scenario.

**Figure 10.**Average detection accuracy of sensor node faults with a density equal to 10 for the second scenario.

**Figure 11.**Average false positive rate for sensor node faults with a density equal to five for the first scenario.

**Figure 12.**The average false positive rate for sensor node faults with a density equal to 10 for the first scenario.

**Figure 13.**Average false positive rate for sensor node faults with a density equal to 5 for the second scenario.

**Figure 14.**Average false positive rate for sensor node faults with a density equal to 10 for the second scenario.

**Figure 15.**Average remaining energy for fault detection methods in different rounds for the first scenario.

**Figure 16.**Average remaining energy for fault detection methods in different rounds for the second scenario.

Parameter Values | |
---|---|

Platform | Windows 10 |

Tool used | Opnet vs. 14.5 |

Network size | 100 m × 100 m |

Maximum number of rounds | 800 |

Base station location | 30 m × 30 m |

Mobility of base station | Random |

Node distribution | Random |

Energy startup | 1 J |

Ɛ_{fs} | 15 pJ/bit/m^{2} |

Ɛ_{mp} | 0.0015 pJ/bit/m^{4} |

E_{elec} | 60 nJ/bit |

E_{DA} | 5 nJ/bit/signal |

Data packet size | 500 bytes |

Threshold distance (d_{0}) | 65 m |

Algorithms | Average Remaining Energy | |||||
---|---|---|---|---|---|---|

Scenario 1 | ||||||

Round 1 | Round 57 | Round 112 | Round 342 | Round 678 | Round 800 | |

One SVM | 0.7463 | 0.6231 | 0.4289 | 0.2893 | 0.1257 | 0.0893 |

Fuzzy one SVM | 0.8435 | 0.7825 | 0.6791 | 0.5102 | 0.3974 | 0.1948 |

MB-FLEACH | 0.9125 | 0.8516 | 0.7462 | 0.6318 | 0.5189 | 0.4215 |

FCS-MBFLEACH | 0.9786 | 0.9215 | 0.8217 | 0.7029 | 0.6248 | 0.4951 |

Algorithms | Average Remaining Energy | |||||
---|---|---|---|---|---|---|

Scenario 2 | ||||||

Round 1 | Round 57 | Round 112 | Round 342 | Round 678 | Round 800 | |

One SVM | 0.7921 | 0.7184 | 0.5249 | 0.4421 | 0.3514 | 0.2143 |

Fuzzy one SVM | 0.8714 | 0.8146 | 0.7536 | 0.5978 | 0.4852 | 0.3610 |

MB-FLEACH | 0.9412 | 0.8761 | 0.8053 | 0.6538 | 0.5549 | 0.4914 |

FCS-MBFLEACH | 0.9873 | 0.9352 | 0.8624 | 0.7348 | 0.6534 | 0.5827 |

**Table 4.**A comparison between the proposed algorithms in terms of remaining energy, as well as FND and HND criteria.

Algorithms | FND | HND | ||
---|---|---|---|---|

Scenario 1 | Scenario 2 | Scenario 1 | Scenario 2 | |

One SVM | 354 | 387 | 512 | 576 |

Fuzzy one SVM | 412 | 432 | 594 | 645 |

MB-FLEACH | 561 | 612 | 628 | 682 |

FCS-MBFLEACH | 673 | 718 | 732 | 791 |

**Table 5.**A comparison between the proposed algorithms in terms of detection accuracy and FPR criteria.

Algorithms | Detection Accuracy (%) with Density Equal to 5 | FPR with Density Equal to 5 | Detection Accuracy (%) with Density Equal to 10 | FPR with Density Equal to 10 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Scenario 1 for Fault Probability | Scenario 2 for Fault Probability | Scenario 1 for Fault Probability | Scenario 2 for Fault Probability | Scenario 1 for Fault Probability | Scenario 2 for Fault Probability | Scenario 1 for Fault Probability | Scenario 2 for Fault Probability | |||||||||

5 | 45 | 5 | 45 | 5 | 45 | 5 | 45 | 5 | 45 | 5 | 45 | 5 | 45 | 5 | 45 | |

One SVM | 88.48 | 51.29 | 92.51 | 52.74 | 0.25 | 0.65 | 0.23 | 0.56 | 85.51 | 48.84 | 90.42 | 48.75 | 0.22 | 0.57 | 0.20 | 0.51 |

Fuzzy one SVM | 90.90 | 57.20 | 93.01 | 56.65 | 0.18 | 0.59 | 0.16 | 0.54 | 89.20 | 54.75 | 91.58 | 52.69 | 0.15 | 0.48 | 0.12 | 0.43 |

MB-FLEACH | 95.44 | 67.44 | 95.87 | 70.06 | 0.07 | 0.41 | 0.05 | 0.38 | 92.64 | 58.36 | 93.82 | 66.19 | 0.05 | 0.36 | 0.03 | 0.35 |

FCS-MBFLEACH | 98.59 | 73.32 | 99.12 | 75.69 | 0.03 | 0.34 | 0.02 | 0.31 | 94.81 | 64.91 | 97.01 | 69.08 | 0.01 | 0.31 | 0.00 | 0.28 |

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**MDPI and ACS Style**

Shamshirband, S.; Joloudari, J.H.; GhasemiGol, M.; Saadatfar, H.; Mosavi, A.; Nabipour, N.
FCS-MBFLEACH: Designing an Energy-Aware Fault Detection System for Mobile Wireless Sensor Networks. *Mathematics* **2020**, *8*, 28.
https://doi.org/10.3390/math8010028

**AMA Style**

Shamshirband S, Joloudari JH, GhasemiGol M, Saadatfar H, Mosavi A, Nabipour N.
FCS-MBFLEACH: Designing an Energy-Aware Fault Detection System for Mobile Wireless Sensor Networks. *Mathematics*. 2020; 8(1):28.
https://doi.org/10.3390/math8010028

**Chicago/Turabian Style**

Shamshirband, Shahaboddin, Javad Hassannataj Joloudari, Mohammad GhasemiGol, Hamid Saadatfar, Amir Mosavi, and Narjes Nabipour.
2020. "FCS-MBFLEACH: Designing an Energy-Aware Fault Detection System for Mobile Wireless Sensor Networks" *Mathematics* 8, no. 1: 28.
https://doi.org/10.3390/math8010028