Models in Motorsports – The ones that win you the race! (part 1)

TL;DR: The motorsport industry is a large source of time series data. Models can be trained for classification, forecasting or to aid the design of control systems. This blog post looks at the application of time series models in motorsports.

Introduction to Time Series

As described by the name, time series represents a collection of data points gathered at constant time intervals. Many data sets appear as time series: a monthly sequence of sold items of an online electronics store, a weekly series of road accidents, daily rainfall recordings, hourly sensor observations from automated industrial processes, and many others [1]. Examples of time series are prevalent in many areas including marketing and sales, business, economics, finance, engineering, and many natural sciences such as geophysics and meteorology.

Large volumes of time series data can also be discovered in the motorsport industry where hundreds of millions of dollars are spent by each team every year on analytic tools and technologies for optimizing race performance and improving lap times [2]. An average of 100-200 IoT sensors are installed on each race car or motorcycle to measure an endless number of system and environmental parameters [3, 4]. These sensors are used to monitor almost everything from tyre pressure and vibrations to downforce, drag, engine temperature, weather conditions, driver audio communication signals, and the location of the competitors on the race track.

The analysis of time series data is of enormous importance in the motorsport industry where the capacity of detecting patterns, analysing vehicle performance on different race tracks and conditions, and forecasting future events based on past observations has a potential to maximize the physical capabilities of the vehicle, minimize lap times and increase profits for everyone involved.

Understanding Time Series Datasets

Before we go into the details of time series analysis and discovering the secret for winning races, we first need to understand the nature of time series datasets. An intrinsic feature of time series is that adjacent observations are time dependent [1]. Trends can also be seen in many time series datasets, especially in the motorsport industry where accelerometer and gyroscope drift is common in many internal measurement unit (IMU) sensors. Furthermore, many time series also have some type of seasonality trends, i.e. variations in the observations that are specific to a certain time frame. For example, if we observe the environment temperature time series from a race occurring in summer, we will notice higher temperature values when compared to the values observed from a race held in winter conditions. Similar patterns can be seen in the temperature time series for races which start in the late afternoon and continue into the evening. Additionally, irregular variations are also common in many time series datasets from the motorsport industry where unsystematic fluctuations in the time series can be caused by unexpected events such as sudden engine malfunction, failure of mechanical components, collisions, or extreme weather conditions.

Time series modelling and applications

Due to the inherent properties of time series, there are multiple steps that need to be followed when analysing time series datasets [1, 5]. Furthermore, this also demands the creation and implementation of stochastic and dynamic models for the vast applications involving time series data.

There are four key areas of application where stochastic and dynamic modelling could be used to model time series data collected from complex drive-by-wire and ride-by-wire systems, in which the steering and throttle control is electrical or electro-mechanical [1].

Models for forecasting

Forecasting is the process of predicting a value at some future time t + d given the observations at time t, where d is the look ahead time. Forecasting can play a very important role in many competitive races where it can be used to predict the optimal pit stop times, as well as the most optimal choice of tyres and gearbox settings based on the smart real-time information regarding the race track conditions, environmental conditions and the human input to the system [2]. Additionally, forecasting could also be applied for the selection of mechanical components for achieving optimal lap times, as well as for selecting the optimal parameters of the traction control system which will allow maximum speeds during dangerous cornering. Time series forecasting can also be used for determining the optimal racing strategy for each driver or rider taking into account their personal driving/riding style, track and weather conditions, location and distance of adjacent competitors and overall team strategy.

All of the above forecasting applications require an accurate dynamic model to capture the linear and nonlinear interrelationships between the different input variables for achieving accurate and reliable predictions in a timely manner. Although current forecasting and modelling techniques have already resulted in tremendous improvements in race performance for high-funded F1 teams such as McLaren, the future advancements in time series modelling techniques and feature selection/reduction methods and expected to result in much higher speeds, shorter lap times and better placings even for the less funded teams.

Modelling of system dynamics

The modelling of system dynamics involves defining the relationship between output and input observations which is required for the design of optimal control systems for anti-lock brake control, anti-jerk control, traction control, as well as launch control and anti-wheelie control for motorcycles.

For linear systems, this process involves deriving a transfer function representation of the system (a function than captures the linear relationship between the system output y(t) and input x(t), i.e. TF = y(t)/x(t) ) which is essential for the design of linear optimal and robust control methods such as the linear quadratic regulator (LQR) and H-infinity methods.

Obtaining an accurate representation of the plant dynamics is exceptionally important in many complex systems where the relationship between the output and input is highly nonlinear. Examples of nonlinear dynamics can be seen in many electric vehicle and motorbike subsystems including the wheel slip dynamics, anti-lock braking system (ABS) and the drivetrain system. An accurate representation of the nonlinear relationships present in the above mentioned subsystems such as nonlinear friction, hysteresis, backlash and dead zone will allow the design of nonlinear controllers for achieving improved control performance [6-8].

Another useful application of the linear and nonlinear representations of system dynamics is in forecasting. Moreover, if the dynamic relationship between the output y(t) and input x(t) of the system is known, past and current values of the input series x(t) can be used for forecasting the output series y(t).

Modelling of multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) systems is also very important in some instances where the system may have multiple control inputs and one to many outputs. A potential application of a dynamic MIMO model would be in the design of a traction control system where one could control power during loss of traction by retarding the ignition timing, cutting fuel, controlling the throttle plate or even by applying the brakes.

Examining the interrelationships between different input variables for developing appropriate multivariable dynamic models

In many forecasting applications, time series data may be available for a number of related input variables. Forecasting using this data requires dynamic models which capture the interrelationship between these dependent variables. For example, rainfall information, track surface information and tyre choice are all very relevant and highly correlated inputs that need to be included into the dynamic model intended for optimal pit stop time forecasting.

This type of analysis and modelling is also important and useful for developing appropriate multivariable dynamic models for complex highly-coupled systems such as the vehicle-track and bike-track systems. An accurate model representation of the coupling present in these systems is essential for the design of effective traction control and anti-lock brake control systems.

Modelling for the design of simple and advanced control methods

Time series analysis can also be a useful tool in the area of control system design. Moreover, dynamic models can be developed from empirical time series data and later used to infer the optimal feedforward or feedback control action for achieving optimal robust performance.

Time series modelling can also be used to improve the tracking performance and robustness of existing control methodologies which are currently used in some race cars and motorcycles. For example, time series forecasting can be applied to determine the optimal control inputs of a model predictive controller (MPC) used for anti-jerk control [9]. This has the potential to increase the speed of the vehicle or motorcycle with a high power engine setup during slow cornering.

Overview of Time Series Modelling Techniques

The modelling of time series datasets has been explored and applied to many different problems in vast applications areas. Simple linear models such as the Moving Averages (MA), Auto-Regressive Moving Averages (ARMA) and Auto-Regressive Integrated Moving Averages (ARIMA) are still commonly used for the modelling of time series datasets in many applications ranging from stock market forecasting solutions to epilepsy seizure prediction systems. However, despite the simplicity and reliability of these methods, they fail to capture the nonlinear interrelationships between system variables which may result in the loss of forecasting precision and reliability in many complex systems such as the drive-by-wire and ride-by-wire systems.

The time series modelling and forecasting problems discussed above can also be framed as supervised learning problems. This will allow access to a large set of standard linear and nonlinear machine learning algorithms for overcoming the numerous challenges in the motorsport industry. More on how to apply machine learning techniques to time series modelling and forecasting problems as the ones described in this blog post will be covered in more detail in our next blog post.

Resources

1. Box G.E.P, Jenkins G.M, Reinsel G.C, Ljung G.M, “Time Series Analysis: Forecasting and Control”, 5th Edition
2. Artificial Intelligence in Formula 1 Strategy – Part 1/2 Link
3. F1 telemetry: The data race Link
4. Fast Cars, Big Data – How Streaming Data Can Help Formula 1 Link
5. A comprehensive beginner’s guide to create a Time Series Forecast (with Codes in Python) Link
6. Saha S., Saha S., Ikkurti H.P., “A robust slip based traction control of electric vehicle under different road conditions”, Michael Faraday IET International Summit, 2015
7. Kuntanapreeda S., “Traction Control of Electric Vehicles Using Sliding-Mode Controller with Tractive Force Observer”, International Journal of Vehicular Technology, 2014
8. Antić D.S., Mitić D.B., Jovanović Z.D., Perić S.L., Milojković M.T., Nikolić S.S., “Sliding Mode Based Anti-Lock Braking System Control”, In: Complex Systems. Studies in Systems, Decision and Control, vol 55. Springer, Cham, 2016
9. Lu X. , Chen H., Zhang. H, Wang P., Goo B., “Design of model predictive controller for anti-jerk during tip-in/out process of vehicles”, Proceedings of the Chinese Control Conference, 2011