# Applying an Adaptive Neuro-Fuzzy Inference System to Path Loss Prediction in a Ruby Mango Plantation

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## Abstract

**:**

## 1. Introduction

- An accurate semi-deterministic path loss prediction for a uniform Ruby mango plantation with an ANFIS engine, which consists of two inputs, namely, the distance between the transceivers of WSN nodes and vegetation height together, and an output of path loss prediction.
- The validation of the model using RMSE, MAE, and MAPE against benchmark models.

## 2. Related Path Loss Models

#### 2.1. ITU-R Model

#### 2.2. COST 235 Model

#### 2.3. FITU-R Model

_{t}is the height of the transmit antenna (m), h

_{r}is the height of the receive antenna (m), and d is the distance between the transmit and receive antennas (m). If the excess loss is considered, then (6) becomes

#### 2.4. Log-Distance Model

## 3. Proposed ANFIS Model

_{1}, A

_{2}, and B

_{1}, B

_{2}. The output parameters are p

_{j}, q

_{j}, and r

_{j}, with n rules:

_{1}is ${A}_{1}^{1}$ and x

_{2}is ${B}_{1}^{1}$ THEN f

_{1}= p

_{1}x

_{1}+ q

_{1}x

_{2}+ r

_{1}

_{1}is ${A}_{2}^{2}$ and x

_{2}is ${B}_{2}^{2}$ THEN f

_{2}= p

_{2}x

_{1}+ q

_{2}x

_{2}+ r

_{2}

_{1}is ${A}_{i}^{n}$ and x

_{2}is ${B}_{i}^{n}$ THEN f

_{n}= p

_{n}x

_{1}+ q

_{n}x

_{2}+ r

_{n}

- where, ${A}_{i}^{j}$ and ${B}_{i}^{j}$ are the fuzzy description of the input sets, and fj are the crisp description of the outputs.

**Layer 1:**This layer comprises antecedent parameters obtained via fuzzy determination from the Crisp input x to membership value ${\mu}_{{A}_{i}}$ or ${\mu}_{{B}_{i}}$ using the following membership function:

_{i}derived from the input x. The membership function may be a triangular, inverted bell, or other shape.

**Layer 2:**This layer comprises the T-norm operator or fuzzy rule base, which associates fuzzy values from each dimension and sends the product as an output signal:

**Layer 3:**This layer involves normalizing the firing strength or weighted layers so that all conditions from all rules can be combined into a single value:

**Layer 4:**The layer comprises consequent parameters obtained as follows:

**Layer 5:**This layer comprises the overall output, which includes all incoming signals and their defuzzification:

_{2}emissions from the energy sector and global temperature increases was investigated using ANFIS, ANN, and fuzzy time series models. This research aimed to avoid strict assumptions and study the complex relationships between variables [29]. A time series forecasting model using a hybrid method of an autoregressive adaptive network fuzzy inference system (AR-ANFIS) was studied. The AR-ANFIS was trained by using particle swarm optimization, and fuzzification was performed using the fuzzy C-Means method [30]. Multivariate time series prediction using a neuro-fuzzy model was proposed. Gaussian membership functions and a learning algorithm were used in the consequent layer [31]. The reviewed literature included training and optimization methods using complex functions and learning algorithms. This technique increases the complexity of the analysis. However, in this study path loss is determined based on a trajectory with a linear relationship between the variables. Therefore, this research uses linear relationships in layer 4 as consequent parameters. This is enough to create an accurate model. This section uses numerical data, which consist of distances, the height of the antenna, and the signal strength of electromagnetic waves. A collection of related datasets consists of a training dataset and a testing dataset. The training dataset is used to generate fuzzy rules and adjust the fuzzy set using a neural network. In general, the principle of fuzzy rules is to optimize the input set of rules in a given operating environment. Traditional methods use experts’ expertise to modify fuzzy rules. The ability to predict the results depend on the expert’s expertise. Furthermore, fuzzy rules can be created by simulating real situations to learn to create rules, which is inconvenient in the case of electromagnetic wave propagation. In this research, the fuzzy tuning setup has been developed using a neural network to achieve more accurate predictions. Adapting fuzzy rules will require training from the training data to optimize fuzzy sets and fuzzy rules, as detailed in the section above.

## 4. Experimental

#### 4.1. Study Site

#### 4.2. Measurement Setup

**Spreading factor:**The SF is the ratio between the symbol rate and chip rate. A higher SF increases the sensitivity and transmission range with a lower packet error rate (PER) and RSSI, but it increases the airtime of the transmitted packet. Therefore, a lower SF should result in a higher PER and minimum RSSI.

**Bandwidth:**A higher BW increases the transmission range and data rate and thus decreases the airtime, but it also decreases the sensitivity by integrating additional noise. A lower BW increases the sensitivity but decreases the data rate. A typical LoRa network operates at a BW of 125, 250, or 500 kHz.

**Coding rate:**A LoRa network sets a CR to protect against bursts of interference. The CR is usually set to 4/5, 4/6, 4/7, or 4/8. A higher CR better protects the system against decoding errors by transmitting more redundant data bits but increases the airtime.

## 5. Results and Discussion

#### 5.1. ANFIS Model and Validation

**Rule 1**: IF x

_{1}is mf1 and x

_{2}is mf1, THEN y is mf1

**Rule 2**: IF x

_{1}is mf1 and x

_{2}is mf2, THEN y is mf2

**Rule 3**: IF x

_{1}is mf1 and x

_{2}is mf3, THEN y is mf3

**Rule 4**: IF x

_{1}is mf1 and x

_{2}is mf4, THEN y is mf4

**Rule 5**: IF x

_{1}is mf1 and x

_{2}is mf5, THEN y is mf5

**Rule 6**: IF x

_{1}is mf2 and x

_{2}is mf1, THEN y is mf6

**Rule 7**: IF x

_{1}is mf2 and x

_{2}is mf2, THEN y is mf7

**Rule 8**: IF x

_{1}is mf2 and x

_{2}is mf3, THEN y is mf8

**Rule 9**: IF x

_{1}is mf2 and x

_{2}is mf4, THEN y is mf9

**Rule 10**: IF x

_{1}is mf2 and x

_{2}is mf5, THEN y is mf10

**Rule 11**: IF x

_{1}is mf3 and x

_{2}is mf1, THEN y is mf11

**Rule 12**: IF x

_{1}is mf3 and x

_{2}is mf2, THEN y is mf12

**Rule 13**: IF x

_{1}is mf3 and x

_{2}is mf3, THEN y is mf13

**Rule 14**: IF x

_{1}is mf3 and x

_{2}is mf4, THEN y is mf14

**Rule 15**: IF x

_{1}is mf3 and x

_{2}is mf5, THEN y is mf15

**Rule 16**: IF x

_{1}is mf4 and x

_{2}is mf1, THEN y is mf16

**Rule 17**: IF x

_{1}is mf4 and x

_{2}is mf2, THEN y is mf17

**Rule 18**: IF x

_{1}is mf4 and x

_{2}is mf3, THEN y is mf18

**Rule 19**: IF x

_{1}is mf4 and x

_{2}is mf4, THEN y is mf19

**Rule 20**: IF x

_{1}is mf4 and x

_{2}is mf5, THEN y is mf20

**Rule 21**: IF x

_{1}is mf5 and x

_{2}is mf1, THEN y is mf21

**Rule 22**: IF x

_{1}is mf5 and x

_{2}is mf2, THEN y is mf22

**Rule 23**: IF x

_{1}is mf5 and x

_{2}is mf3, THEN y is mf23

**Rule 24**: IF x

_{1}is mf5 and x

_{2}is mf4, THEN y is mf24

**Rule 25**: IF x

_{1}is mf5 and x

_{2}is mf5, THEN y is mf25

#### 5.2. Data Analysis of Proposed Model

#### 5.3. Comparison with Empirical Path Loss Models

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**ANFIS with two inputs: (

**a**) structure, (

**b**) antenna height as input 1, and (

**c**) log-distance as input 2.

Antenna Height (m) | $\mathit{P}\mathit{L}\left({\mathit{d}}_{0}\right)$ (dB) | PLE (NLOS) | A | B | C |
---|---|---|---|---|---|

0.3 | 26.57 | 3.79 | 0.98 | 0.39 | 0.34 |

1.2 | 23.2 | 3.84 | 0.8 | 0.39 | 0.35 |

2.2 | 17.54 | 4.33 | 0.98 | 0.39 | 0.33 |

2.7 | 22.1 | 3.71 | 1.0 | 0.39 | 0.3 |

No. | Total Height | Trunk Height | Trunk Diameter | Canopy Depth | Canopy Diameter |
---|---|---|---|---|---|

Tree 1 | 3.82 | 0.56 | 0.4 | 3.4 | 5.5 |

Tree 2 | 4.66 | 0.66 | 0.56 | 4.0 | 6.0 |

Tree 3 | 4.79 | 0.49 | 0.45 | 4.3 | 5.6 |

Tree 4 | 5.15 | 0.65 | 0.64 | 4.5 | 6.5 |

Tree 5 | 4.77 | 0.47 | 0.63 | 4.3 | 6.2 |

Tree 6 | 3.96 | 0.46 | 0.46 | 3.5 | 4.7 |

Tree 7 | 4.85 | 0.65 | 0.54 | 4.2 | 6.0 |

Tree 8 | 3.97 | 0.47 | 0.43 | 3.5 | 5.0 |

Average | 4.50 | 0.55 | 0.51 | 3.96. | 5.69 |

No. | Parameters | Value | Unit |
---|---|---|---|

1 | Power amplifier (PA) | 18 | dBm |

2 | Antenna gain | 2.2 | dBi |

3 | Frequency | 433 | MHz |

4 | Bandwidth (BW) | 125 | kHz |

5 | Spreading factor | 7 | - |

6 | Code rate (CR) | 4/5 | - |

7 | Offset factor (K) | 28 | dBm |

Antenna Height (m) | ANFIS Validation | |
---|---|---|

0.3 (Trunk) | 3.17 | 3.31 |

1.2 (Canopy_bottom) | 1.34 | 1.58 |

2.2 (Canopy_middle) | 1.65 | 1.57 |

2.7 (Canopy_top) | 2.61 | 2.60 |

Antenna Height (m) | AME | |||||
---|---|---|---|---|---|---|

Exponential Decay Equation (6) | Log-Distance Equation (11) | ITU-R | COST235 | FITU-R | ANFIS | |

0.3 (Trunk) | 0.11 | 5.73 | 19.33 | 5.41 | 20.26 | 0.32 |

1.2 (Canopy_bottom) | 0.28 | 3.14 | 15.91 | 7.91 | 15.69 | 0.01 |

2.2 (Canopy_middle) | 1.71 | 5.36 | 17.64 | 5.76 | 17.24 | 0.06 |

2.7 (Canopy_top) | 0.77 | 7.3 | 16.82 | 6.54 | 16.47 | 0.02 |

Antenna Height (m) | MAE | |||||
---|---|---|---|---|---|---|

Exponential Decay Equation (6) | Log-Distance Equation (11) | ITU-R | COST235 | FITU-R | ANFIS | |

0.3 (Trunk) | 6.17 | 6.32 | 19.63 | 10.19 | 20.55 | 2.43 |

1.2 (Canopy_bottom) | 2.66 | 3.36 | 16.39 | 7.91 | 16.49 | 1.03 |

2.2 (Canopy_middle) | 4.71 | 5.52 | 19.08 | 6.86 | 19.09 | 1.27 |

2.7 (Canopy_top) | 0.77 | 7.61 | 17.69 | 7.45 | 17.84 | 2.08 |

Antenna Height (m) | MAPE | |||||
---|---|---|---|---|---|---|

Exponential Decay Equation (6) | Log-Distance Equation (11) | ITU-R | COST235 | FITU-R | ANFIS | |

0.3 (Trunk) | 11.91 | 8.89 | 25.09 | 15.49 | 26.20 | 3.81 |

1.2 (Canopy_bottom) | 5.8 | 4.9 | 22.3 | 14.04 | 22.73 | 1.64 |

2.2 (Canopy_middle) | 12.48 | 7.51 | 27.57 | 17.11 | 28.22 | 1.76 |

2.7 (Canopy_top) | 11.08 | 10.51 | 24.42 | 15.5 | 25.28 | 3.16 |

Antenna Height (m) | RMSE | |||||
---|---|---|---|---|---|---|

Exponential Decay Equation (6) | Log-Distance Equation (11) | ITU-R | COST235 | FITU-R | ANFIS | |

0.3 (Trunk) | 7.74 | 8.59 | 21.65 | 11.77 | 22.59 | 3.17 |

1.2 (Canopy_bottom) | 3.69 | 4.08 | 16.96 | 8.61 | 17.1 | 1.34 |

2.2 (Canopy_middle) | 6.7 | 7.05 | 19.84 | 8.63 | 19.87 | 1.65 |

2.7 (Canopy_top) | 6.52 | 9.1 | 18.62 | 9.09 | 18.53 | 2.61 |

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**MDPI and ACS Style**

Phaiboon, S.; Phokharatkul, P.
Applying an Adaptive Neuro-Fuzzy Inference System to Path Loss Prediction in a Ruby Mango Plantation. *J. Sens. Actuator Netw.* **2023**, *12*, 71.
https://doi.org/10.3390/jsan12050071

**AMA Style**

Phaiboon S, Phokharatkul P.
Applying an Adaptive Neuro-Fuzzy Inference System to Path Loss Prediction in a Ruby Mango Plantation. *Journal of Sensor and Actuator Networks*. 2023; 12(5):71.
https://doi.org/10.3390/jsan12050071

**Chicago/Turabian Style**

Phaiboon, Supachai, and Pisit Phokharatkul.
2023. "Applying an Adaptive Neuro-Fuzzy Inference System to Path Loss Prediction in a Ruby Mango Plantation" *Journal of Sensor and Actuator Networks* 12, no. 5: 71.
https://doi.org/10.3390/jsan12050071