# Airborne Kite Tether Force Estimation and Experimental Validation Using Analytical and Machine Learning Models for Coastal Regions

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## Abstract

**:**

## 1. Introduction

- The proposed approach is based on field data collection, processing, and analysis. The field tests are conducted under steady and turbulent wind conditions, which is explained rigorously.
- Tether force estimation using the physical model of a kite is proposed and is simulated using MATLAB SIMULINK.
- Two machine learning models—ANN and LSTM—are trained with the known data from the field tests and the models are tested with unknown data to predict the tether force.
- The proposed methods are experimentally validated and the performance of each method is evaluated.

## 2. Problem Description

#### 2.1. Kite Constraints

**Hypothesis 1.**

**Assumption 1:**

**Assumption 2:**

**Assumption 3:**

**Assumption 4:**

#### 2.2. Kite Dynamics

#### 2.3. Kite Field Test Conditions

## 3. Tether Force Estimation Methods

#### 3.1. Wind Window and Crosswind Power

#### 3.2. Kite Kinematics and Aerodynamic Force

#### 3.3. Experimental Setup

#### 3.3.1. Kite Telemetry System

#### 3.3.2. On-Air Kite Unit

#### 3.3.3. On-Ground Kite Unit

#### 3.3.4. Force Measurement Unit

#### 3.3.5. Field Data Collection

#### 3.4. Kite Tether Force Estimation

#### 3.4.1. Kite Inclination Effects

#### 3.4.2. Kite Tether Force Estimation Using Physical Model (PM)

#### 3.4.3. Kite Force Estimation Using Deep Neural Networks

#### 3.4.4. Artificial Neural Network (ANN)

#### 3.4.5. Long Short-Term Memory (LSTM)

## 4. Results

#### 4.1. PM Simulation Results

#### 4.2. Tether Force Validation

#### 4.2.1. Physical Model (PM) Validation

#### 4.2.2. Artificial Neural Network (ANN) Model Validation

#### 4.2.3. Long Short-Term Memory (LSTM) Model Validation

#### 4.2.4. Comparison and Validations of Models

#### RMSE Method

#### MAE Method

#### ${R}^{2}$ Method

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Kite power generation technique: kite travels in a figure-eight trajectory, which pulls the tether wound on the drum and rotates the generator to produce electric power.

**Figure 2.**Kite’s position and orientation represented in the spherical coordinate system and the forces experienced by the kite [26]. (

**a**) Kite’s orientation and position. (

**b**) Angle of attack of the kite.

**Figure 3.**Wind window: an imaginary boundary in which the kite can be flown to produce power; the red area indicates the maximum power zone, the yellow area shows the moderate power zone, and the green area indicates the low power zone.

**Figure 4.**Kite reference frame [25]: The left figure shows the position of the kite at point K in a three-dimensional plane with the forces acting on the kite. The right figure shows the orientation of the kite in terms of the Euler form.

**Figure 5.**Experimental setup: (

**a**) pictorial representation of the system used for estimating the tether force with a block diagram of the system, (

**b**) Actual experimental setup used in the experimental tests.

**Figure 7.**Sensor system on the kite: (

**a**) block diagram of the system, (

**b**) PCB implementation of the sensor system, (

**c**) PCB enclosed within the box for protection, (

**d**) Sensor system installed on the kite using velcro.

**Figure 8.**Sensor system on the ground: (

**a**) Block diagram of the kite data receiver system on the ground, (

**b**) Implementation of the sensor data receiver circuit in the PCB, (

**c**) Back side of the PCB with LCD, (

**d**) Wind speed and direction sensors at the testing site.

**Figure 9.**Measurement of tether force using lad-cell, (

**a**) shows the pictorial representation of the setup, (

**b**) shows the actual setup mounted on the wooden board in which the tether is passed through the pulleys.

**Figure 10.**Wind window with shaded area indicating area swept by the kite in the figure-eight trajectory ($\varphi $ degrees); ${W}_{de}$ represents the wind direction vector; K represents kite tether vector; N, E, and S are the north, east, and south reference vectors; $\chi $ is the angle between east and ${W}_{de}$; $\psi $ is the angle between east and the kite tether vector; $\beta $ is the angle between ${W}_{de}$ and the kite tether vector.

**Figure 11.**The figure-eight trajectory followed by the kite during the test. The GPS and altitude data were used to plot the trajectory of the kite in 3 dimensions. (

**a**) Top view: lat vs. lon. (

**b**) 3D view: lat-lon vs. altitude. (

**c**) Side view: lat vs. altitude. (

**d**) Yaw vs. Force. (

**e**) Roll vs. Force. (

**f**) Pitch vs. Force.

**Figure 12.**Simulation of tether force in MATLAB SIMULINK: (

**a**) From left, the data from the field test are given as a numeric matrix and the kite’s data block filters the data to calculate the lift and drag forces; the force–simulated block calculates the tether force. (

**b**) Shows a plot of the lift force vs. drag force from the simulated tether force.

**Figure 13.**The flow of the estimation of the tether force using the DNN methods: The field test data were imported to the models and then normalised so that they could be used in the ANN and LSTM models; the predicted data in the normalised form were then inverted to the actual values; the performance was evaluated using the RMSE, MAE, and ${R}^{2}$ methods.

**Figure 14.**The basic architecture of the ANN: the input layer is fed with the kite’s orientation data on altitude and wind speed; there are four hidden layers between the input and output and the output of the ANN was the tether force (${F}_{t}$).

**Figure 15.**The basic structure of a Long Short-Term Memory (LSTM) unit: ${X}_{t}$ is the current input; ${h}_{t-1}$ is the last output; ${C}_{t-1}$ is the memory from the last LSTM unit; ${h}_{t}$ is the current output; ${C}_{t}$ is the next cell state; ’b’ is the bias; ’$\sigma $’ block is a sigmoid layer; ’$tanh$’ block is a tanh layer; ’×’ and ’+’ are the scaling and addition operators, respectively.

**Figure 16.**Tether force simulation for three test cases: (

**a**–

**c**) polar plots of the YRP vs. force; the sweep represents the angles (${0}^{\circ}$ to ${360}^{\circ}$) and the magnitude represents the tether force, (

**d**–

**f**) time-series plots of the YRP and the tether force under the steady wind conditions.

**Figure 17.**Tether force simulation for three test cases: (

**a**–

**c**) polar plots of the YRP vs. force; the sweep represents the angles (${0}^{\circ}$ to ${360}^{\circ}$) and the magnitude represents the tether force, (

**d**–

**f**) time-series plots of the YRP and the tether force under turbulent wind conditions.

**Figure 18.**Validation of the physical model with the experimental data: (

**a**–

**c**) steady wind conditions, (

**d**–

**f**) turbulent wind conditions.

**Figure 19.**Experimental validation of predicted tether force from ANN: (

**a**–

**c**) test results for steady wind conditions, (

**d**–

**f**) test results for turbulent wind conditions.

**Figure 20.**LSTM model test results comparison with the experimental data: (

**a**–

**c**) steady wind condition data for the three tests, (

**d**–

**f**) turbulent wind condition data for the three tests.

**Figure 21.**Combined analysis of tether force estimation methods–physical, ANN, and LSTM methods: (

**a**–

**c**) the three tests under steady wind conditions, (

**d**–

**f**) the three tests under turbulent wind conditions.

**Figure 22.**Scatter plots of the physical, ANN, and LSTM models: (

**a**–

**c**) the performance of the models under steady wind conditions, (

**d**–

**f**) the performance of the models under turbulent wind conditions.

**Figure 23.**Performance analysis of PM, ANN, and LSTM models under steady wind conditions: (

**a**) RMSE method, (

**b**) MAE method, (

**c**) ${R}^{2}$ method.

**Figure 24.**Performance analysis of PM, ANN, and LSTM models under turbulent wind conditions: (

**a**) RMSE method, (

**b**) MAE method, (

**c**) ${R}^{2}$ method.

Kite Parameters | |
---|---|

No. of Lines | 4 lines |

Surface Area | 12 ${\mathrm{m}}^{2}$ |

No. of Struts | 3 |

Canopy Material | Ripstop Nylon |

Weight (Deflated) | 3.5 kg |

Type of kite | Supported leading-edge kite (SLE) |

**Table 2.**Kite telemetry system: on-air kite unit specifications and on-ground kite unit specifications.

Sl No | Part Name | On-Air Kite Unit | On-Ground Kite Unit |
---|---|---|---|

1 | Wireless Module | NRF24L01 2.4 GHz | NRF24L01 2.4 GHz |

2 | Micro-Controller Unit (MCU) | ATMEGA328p, 8 bit, 16 MHz, 32 KB flash, 2 KB SRAM, 14 I/O pins | ATMEGA328p, 8 bit, 16 MHz, 32 KB flash, 2 KB SRAM, 14 I/O pins |

3 | Sensors (20 Hz Sampling) | IMU-BNO055 Altimeter-BME280 GPS—Neo M8N | Loadcell with HX711 ADC Anemometer (Cup type) Wind direction (Encoder) |

4 | Data Logging | NA | SD card module |

5 | Power Source | 18650 Li-ion battery (Two in series—8 V) | 12 V, 7.5 Ah Lead Acid Battery |

**Table 3.**Data logged in the field tests consisting of orientation in quaternion form, altitude, GPS data, load-cell values, wind speed, and wind direction.

Data Point | Q_{w} | Q_{x} | Q_{y} | Q_{z} | Altitude (m) | Latitude | Longitude | Load-Cell Analog Value | Wind Speed (m/s) | Wind Direction (Degrees) |
---|---|---|---|---|---|---|---|---|---|---|

1 | 0.04 | −0.36 | 0.82 | 0.44 | 0.43 | 130091287 | 747885344 | 354,420 | 3.58 | 15 |

2 | 0.06 | −0.37 | 0.82 | 0.44 | 0.17 | 130091287 | 747885344 | 611,959 | 3.63 | 6 |

3 | 0.13 | −0.4 | 0.78 | 0.47 | 0.96 | 130091263 | 747885311 | 778,686 | 3.58 | 3 |

4 | 0.22 | −0.44 | 0.73 | 0.48 | 1.95 | 130091232 | 747885259 | 1,012,329 | 3.58 | 7 |

5 | 0.26 | −0.45 | 0.72 | 0.46 | 2.41 | 130091214 | 747885219 | 1,020,015 | 3.53 | 13 |

6 | 0.3 | −0.45 | 0.73 | 0.42 | 4.98 | 130091167 | 747885097 | 955,023 | 3.55 | 17 |

7 | 0.31 | −0.44 | 0.75 | 0.4 | 5.93 | 130091147 | 747885017 | 976,031 | 3.6 | 14 |

8 | 0.27 | −0.41 | 0.79 | 0.36 | 7.14 | 130091131 | 747884937 | 984,059 | 3.6 | 9 |

9 | 0.2 | −0.37 | 0.85 | 0.32 | 8.16 | 130091119 | 747884748 | 947,582 | 3.63 | 8 |

10 | 0.17 | −0.34 | 0.89 | 0.27 | 10.05 | 130091119 | 747884655 | 788,606 | 3.63 | 11 |

11 | 0.15 | −0.32 | 0.9 | 0.25 | 10.66 | 130091148 | 747884473 | 607,128 | 3.68 | 13 |

12 | 0.16 | −0.32 | 0.9 | 0.22 | 12.23 | 130091164 | 747884386 | 550,783 | 3.7 | 6 |

13 | 0.19 | −0.33 | 0.91 | 0.18 | 13.89 | 130091212 | 747884234 | 461,953 | 3.65 | 6 |

14 | 0.2 | −0.34 | 0.9 | 0.17 | 15.53 | 130091240 | 747884159 | 399,323 | 3.65 | 15 |

15 | 0.2 | −0.34 | 0.91 | 0.15 | 16.33 | 130091300 | 747884055 | 405,638 | 3.65 | 12 |

S No. | Items | Detail of ANN | Detail of LSTM |
---|---|---|---|

1 | Target | Tether force | Tether force |

2 | Input Variable | ${Q}_{w}$, ${Q}_{x}$, ${Q}_{y}$, ${Q}_{z}$, Altitude, Wind Speed | ${Q}_{w}$, ${Q}_{x}$, ${Q}_{y}$, ${Q}_{z}$, Altitude, Wind Speed |

3 | Training Parameters | Learning rate: 0.0001, Number of epochs: 1000 | Learning rate: 0.0001, Dropout: 0.2, Mini-Batch Size: 8, Number of epochs: 1000 |

4 | Training dataset | Steady Wind Case (30,000) Dynamic Case (30,000) | Steady Wind Case (30,000) Dynamic Case (30,000) |

5 | Test dataset | Steady Wind Case (1000) Dynamic Case (1000) | Steady Wind Case (1000) Dynamic Case (1000) |

6 | Network layer | 4 (hidden layers) | 6 $\left(\begin{array}{c}\hfill \mathrm{F}\mathrm{u}\mathrm{l}\mathrm{l}\mathrm{y}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}1:\mathrm{B}\mathrm{i}-\mathrm{d}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{L}\mathrm{S}\mathrm{T}\mathrm{M}1:\\ \hfill \mathrm{F}\mathrm{u}\mathrm{l}\mathrm{l}\mathrm{y}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}2:\mathrm{D}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{o}\mathrm{u}\mathrm{t}1:\mathrm{B}\mathrm{i}-\mathrm{d}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{L}\mathrm{S}\mathrm{T}\mathrm{M}2:\\ \hfill \mathrm{F}\mathrm{u}\mathrm{l}\mathrm{l}\mathrm{y}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}3:\mathrm{D}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{o}\mathrm{u}\mathrm{t}2:\mathrm{F}\mathrm{u}\mathrm{l}\mathrm{l}\mathrm{y}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}4\end{array}\right)$ |

7 | Number of neurons in each layer | 100:50:25:5 | 100:50:50:25:25:5 |

8 | Training Method | Adam | Adam |

9 | Loss function | mse | mse |

10 | Training Type | Regression | Regression |

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**MDPI and ACS Style**

Castelino, R.V.; Kashyap, Y.; Kosmopoulos, P. Airborne Kite Tether Force Estimation and Experimental Validation Using Analytical and Machine Learning Models for Coastal Regions. *Remote Sens.* **2022**, *14*, 6111.
https://doi.org/10.3390/rs14236111

**AMA Style**

Castelino RV, Kashyap Y, Kosmopoulos P. Airborne Kite Tether Force Estimation and Experimental Validation Using Analytical and Machine Learning Models for Coastal Regions. *Remote Sensing*. 2022; 14(23):6111.
https://doi.org/10.3390/rs14236111

**Chicago/Turabian Style**

Castelino, Roystan Vijay, Yashwant Kashyap, and Panagiotis Kosmopoulos. 2022. "Airborne Kite Tether Force Estimation and Experimental Validation Using Analytical and Machine Learning Models for Coastal Regions" *Remote Sensing* 14, no. 23: 6111.
https://doi.org/10.3390/rs14236111