# Mathematical Framework for Wearable Devices in the Internet of Things Using Deep Learning

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## Abstract

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## 1. Introduction

#### 1.1. Literature Survey

#### 1.2. Research Gap and Motivation

#### 1.3. Contributions

- Maximize the monitoring device’s distance, so all infections are identified without connecting to the frame;
- Minimize all errors present in the infection identification and data transmission process, thus increasing the efficiency of the device;
- Integrate a deep learning model for reducing the loss of designed devices with a unique representation of mathematical models.

#### 1.4. Paper Organization

## 2. System Model

## 3. Optimization Algorithm

#### Step-by-Step Implementation of DL Using Adversarial Networks

- Select the captured images and measure the communication module energy representation values using different data sets in a systematic way for computing the throughput, by using Equation (3);
- Verify the value of ${S}_{i}$ and ${E}_{cm}$ using the probability value set;
- If the complexities of identification are higher, ${S}_{i}$ is not at $({S}_{i}<N)$ do;
- Divide the probability of different events using the number of affected users ${H}_{i}$ and $event{s}_{i}$, which ensures different ecological conditions using Equation (5) ${H}_{i}$ with $1\le i\le N$ into N number of affected points;//Training sample phase
- Update the infected region and total region areas using a spreading ratio matrix with minimized loss function using sample and prediction loss as shown in Equation (9);//Loss phase
- Select the number of loss functions with wearable signal representation values of different training samples with separate image analyses in a single output $trai{n}_{s}\left(i\right)$, as defined in Equation (8);
- Update the object representation values of the relative positions and identified position, followed by measurement of the data quality index, and compute the relative weight of all parameters ${\gamma}_{i}$, as defined in Equation (7);
- Identified infections at each point are updated by using the probability of the generator and data that is designed for the image signals;

## 4. Experimental Outcomes

#### 4.1. Scenario 1

#### 4.2. Scenario 2

#### 4.3. Scenario 3

#### 4.4. Scenario 4

#### 4.5. Scenario 5

#### 4.6. Performance Analysis

#### 4.7. Robustness Characteristics

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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References | Background | Objectives |
---|---|---|

[16] | Overview of medical devices and application platform for wearable devices | Minimize the cost of implementation |

[17] | Detection of interruptions that are present in monitoring systems for wireless devices | Minimize the number of IoT data interruption |

[18] | Possible developments in wireless network applications for medical healthcare | Minimization of cost |

[19] | Fabrication design of wearable devices for different applications | Minimization of congestion |

[20] | Design of wideband antennas for wireless communication transfer | Maximization of coverage |

Proposed | Deep learning approach for wearable devices | Multi-objective framework with minimization of loss, energy and errors |

Variables | Description |
---|---|

${A}_{i}$ | Identified area of infection |

${P}_{i}$ | Different types of patients with infections |

${t}_{i}$, ${h}_{i}$ | Time period and infirmaries of identification |

${\rho}_{i}$ | Demand for persistence in a particular area |

${E}_{1}+\dots +{E}_{i}$ | Energies of different wearable devices |

${\delta}_{i}$ | Work functionality of devices |

${t}_{ph}$ | Time period of mobile-connecting devices |

${E}_{cm}$ | Energy of communication module |

${p}_{cm}$ | Power delivered to the communication module |

${\beta}_{i}$ | Throughput of the device module |

${d}_{n}$ | Size of data to be transmitted |

${H}_{i}$ | Group of affected users |

$event{s}_{i}$ | Occurrence of different events |

${I}_{r}$, ${T}_{r}$ | Individuals in infected regions and total covered regions |

${\gamma}_{i}$ | Relative weights of all parameters |

${D}_{q}$ | Data quality index |

$pro{b}_{g}$, $pro{b}_{d}$ | Probability of generator and data |

${l}_{s}$, ${l}_{p}$ | Sample loss and prediction loss periods |

${T}_{o}$ | Object representation target |

${S}_{1}..{S}_{i}\dots {S}_{n}$ | Wearable signal-representation matrix |

Key Features | Existing [3] | Proposed |
---|---|---|

Package size | 4 × 5.2 × 1.3 | 2 × 2 × 0.7 |

Sensor power | High power greater than 5 volts | Ultra-low power with a three-axis accelerometer |

Noise density | 50 | 22 |

Current consumption | 0.89 mA | 0.55 mA |

Maximum distance | 2.5 m | 5.7 m |

Sensitivity | 15 | 2 |

Gain bandwidth | 4 kHz | 8 kHz |

Memory unit | 100 GHz | 500 GHz |

Run mode | 12 microamperes | 30 microamperes |

Number of Infected Areas | Demand | Distance [3] | Distance (Proposed) |
---|---|---|---|

120 | 32 | 1.3 | 1.6 |

180 | 44 | 1.7 | 2.8 |

260 | 57 | 2 | 3.4 |

340 | 61 | 2.2 | 4.9 |

400 | 65 | 2.5 | 5.7 |

Period | Number of Energy Modules | Waiting Period [3] | Waiting Period (Proposed) |
---|---|---|---|

10 | 100 | 2.33 | 1.25 |

20 | 300 | 2.21 | 1.16 |

30 | 500 | 2.17 | 1.1 |

40 | 700 | 2.06 | 1 |

50 | 900 | 2 | 0.8 |

Number of Affected Users | Probability of Occurrence | Percentage of Sensitivity [3] | Percentage of Sensitivity (Proposed) |
---|---|---|---|

1000 | 40 | 31 | 20 |

2000 | 27 | 26 | 14 |

3000 | 35 | 21 | 10 |

4000 | 56 | 17 | 5 |

5000 | 73 | 15 | 2 |

Relative Weights | Percentage of Data Quality | Quality of Service [3] | Quality of Service (Proposed) |
---|---|---|---|

10 | 45 | 60 | 75 |

15 | 54 | 62 | 79 |

20 | 69 | 63 | 82 |

25 | 75 | 63 | 84 |

30 | 82 | 63 | 84 |

Number of Sample Loss | Number of Predicted Loss | Total Loss [3] | Total Loss (Proposed) |
---|---|---|---|

89 | 51 | 117 | 76 |

124 | 87 | 203 | 87 |

153 | 99 | 245 | 103 |

205 | 125 | 305 | 128 |

279 | 154 | 400 | 142 |

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**MDPI and ACS Style**

Mirza, O.M.; Mujlid, H.; Manoharan, H.; Selvarajan, S.; Srivastava, G.; Khan, M.A.
Mathematical Framework for Wearable Devices in the Internet of Things Using Deep Learning. *Diagnostics* **2022**, *12*, 2750.
https://doi.org/10.3390/diagnostics12112750

**AMA Style**

Mirza OM, Mujlid H, Manoharan H, Selvarajan S, Srivastava G, Khan MA.
Mathematical Framework for Wearable Devices in the Internet of Things Using Deep Learning. *Diagnostics*. 2022; 12(11):2750.
https://doi.org/10.3390/diagnostics12112750

**Chicago/Turabian Style**

Mirza, Olfat M., Hana Mujlid, Hariprasath Manoharan, Shitharth Selvarajan, Gautam Srivastava, and Muhammad Attique Khan.
2022. "Mathematical Framework for Wearable Devices in the Internet of Things Using Deep Learning" *Diagnostics* 12, no. 11: 2750.
https://doi.org/10.3390/diagnostics12112750