*TROY, Mich. — This is the first of three articles by Fabio Squadrani, Senior Manager, Braking Systems in Applus IDIADA on the use of Artificial Intelligence â€“ AI â€“ to detect brake noise.*

#### 1. INTRODUCTION

Recently, computational power has dramatically increased, allowing AI (artificial intelligence) to become more and more attractive to approach engineering problems. In this study, it is shown how to use a machine learning algorithm and to detect high frequency brake noise (squeal). Currently this detection is made in data acquisition systems in real time or in post processing by an algorithm, which is based in logical or Boolean conditions. Artificial Intelligence could allow a machine (DAQ) to detect the noise imitating human behavior. No Boolean conditions will have to be set prior to the test; the ML algorithm will have to be trained to detect the noise by itself.

Three main sections will be presented to the reader. First, the mathematical background of the study will be explained, then a specific explanation of the machine learning techniques used to define and train the detection algorithm will be provided. Finally, some validation data will also be provided.

#### 2. MATHEMATICAL BACKGROUND

**2.1. Spectrogram calculation**

This work consists in detecting brake noise or squeal in an automated way by using a machine learning algorithm. The recognition of the squeal is based on three steps:

This work consists in detecting squeal in an automated way by using a machine learning algorithm. The recognition of the squeal is based on three steps:

- To import the microphone data for each wheel
- To compute the spectrogram
- To develop the machine learning algorithm

The spectrogram is a visual way (usually on a logarithmic scale, such as decibel) of representing the Short-Time Fourier Transformation (STFT) magnitude. The STFT is a sequence of Fast Fourier Transforms (FFTs) of windowed data segments, where the windows are usually allowed to overlap in time.

In our study, we compute the spectrogram by using the Hanning window with an overlap in time, typically between 50%-80%. The Hanning window is defined as:

where M is the number of points in the output window. We establish that the value M is equal to length of the Fast Fourier Transform, we use a power of 2 as values of M. To compute the spectrogram, we often use the sampling frequency f_s equal to 40000 Hz. In general, the sampling frequency is a variable value, but it needs to satisfy the conditions of Nyquist-Shannon theorem, in fact f_s must be at least the double of 20000 Hz.

The spectrogram is a two-dimensional graph, with a third dimension represented by a colormap. In particular, the horizontal axis represents the time and the vertical axis represents the frequency, with the lowest frequencies at the bottom and the highest frequencies at the top. The third dimension indicates the amplitude of a frequency at a particular time and it is represented by the intensity of color of each point in the image.

The spectrogram can be represented as an array with m rows and n columns, where m is the dimension of the array of sample frequencies and n is the dimension of the array of the segment times. The sampling is done in according with the Nyquist-Shannon sampling theorem.

In our work, we express the spectrogram in acoustic decibel. Here we explain the methodology to obtain this.

We consider an array *F* of frequencies of dimension *mx1* that is defined such that

where is the sampling frequency. Now we apply a filter for each entry of the frequency vector *F.*

Therefore, we consider the filter, which is a function of *F *and it is defined in the following way,

for each *i=1,â€¦,m* and indicates the entry of frequency vector *F. *We obtain an array of dimension *mx1.*

The last step is to compute the linear decibel and to join it with the filter.Â Therefore, after computing the Short Time Fourier Transformation magnitude of the sound, we obtain an array T with m rows and n columns. To obtain the linear decibel we compute for each entry of T the following formula,

where indicates the entry of the array *T* and *ref *is the reference frequency, we establish Â Hz.

Therefore, we compute the acoustic decibel in the following way

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