Convolutional Neural Network-Based Detection of Booming Noise in Internal Combustion Engine Vehicles Using Simulated Acoustic Spectrograms

Abstract

In this work, we tested the use of Convolutional Neural Networks (CNNs) to classify booming noise inside vehicles. Instead of relying only on long experimental campaigns, we generated a synthetic dataset from Sound Quality Equivalent (SQE) models that were originally built from real acoustic measurements collected with sensors. By applying smoothing functions and Hann windows, we were able to vary the intensity of the booming effect across different mission profiles. The CNNs were trained on spectrograms derived from these signals, with labels informed by psychoacoustic evaluations. The best model reached about 95.5% accuracy in the binary task (booming vs. no booming) and around 93.3% when using three classes (severe, mild, none). Tests with data from three different car models showed that the method can generalize across platforms. These results suggest that CNNs may become a practical tool for NVH analysis, offering a simpler and cheaper complement to traditional end-of-line testing, and one that could be adapted for real-time embedded systems.

1. Introduction

Growing public concern over the long-term health effects of noise exposure has led to increased attention on controlling sound emissions from mechanical systems, especially in the automotive industry. Among the key focus areas are both the noise emitted to the environment and the sounds experienced inside the vehicle cabin, as they affect not only legal compliance but also user comfort. As a result, substantial engineering efforts are directed toward enhancing interior acoustic conditions. The continuous effort to improve acoustic comfort has led to the development of the Noise, Vibration and Harshness (NVH) field, dedicated to studying and reducing unwanted vibrations and sound effects across the entire frequency range. Within this area, one of the most difficult issues is the occurrence of low-frequency “booming” noise, typically linked to resonances excited by the powertrain and often perceived by passengers as especially unpleasant.

Traditional NVH techniques such as Transfer Path Analysis (TPA), Operational Deflection Shape (ODS) and modal testing provide physically consistent insights into how noise is transmitted from excitation sources to interior targets [1]. However, these methods require extensive instrumentation, controlled test environments and specialized operators, which makes their systematic application in end-of-line (EOL) or high-volume production settings difficult. NVH problems remain relevant in internal combustion engine (ICE) vehicles, where the engine continues to be a dominant source of interior noise [2]. Among these issues, low-frequency booming noise is particularly disturbing to passengers and is commonly associated with driveline resonances excited by engine orders [3]. In industrial practice, booming assessment still depends heavily on subjective jury evaluations, which are time-consuming, operator-dependent and hard to standardize across plants. These limitations motivate the development of objective, scalable and data-driven tools for booming detection. In practice, this phenomenon is still detected mainly through subjective bench tests, a process that demands time and effort and often produces inconsistent results.

In parallel, recent advances in Machine Learning (ML) and Deep Learning (DL) have shown that Convolutional Neural Networks (CNNs) can learn discriminative features directly from time-frequency representations of acoustic signals. CNN-based models have demonstrated strong performance in several audio-classification tasks and have also been explored for booming detection. However, their wider application in NVH engineering remains constrained by the practical difficulty of acquiring and annotating sufficiently large, high-quality datasets from real vehicles.

This study addresses the lack of labeled data for booming detection by proposing a methodology that combines vehicle sound synthesis, digital twins, and CNN-based classification. The approach is built on five main elements:

• Synthetic datasets are automatically generated from real vehicle recordings using Sound Quality Equivalent (SQE) models, where booming events are deliberately introduced;
• Booming detection is carried out on spectrograms of synthesized engine sounds across different mission profiles;
• Several CNN architectures are trained and compared in both binary and three-class classification tasks;
• The models are validated with spectrograms derived from both smoothed and non-smoothed acoustic orders, representing distinct booming conditions;
• The overall aim is to provide NVH engineers with a scalable, objective, and data-driven tool that can support production testing.

The article is organized as follows. Section 2 reviews the state of the art, describing the origin of booming noise in ICE vehicles, conventional NVH assessment methods, and recent DL approaches for sound classification. Section 3 explains the materials and methods, from data acquisition and sound decomposition to SQE modeling, sound synthesis, and the creation of training datasets. Section 4 presents the results of the CNN classifiers, including binary (Yes/No) and three-class (Severe/Mild/None) tasks, their performance across different vehicles, and a short analysis of misclassifications. Finally, Section 5 highlights the main contributions and discusses future work, such as adding real vehicle data, testing the approach on embedded platforms, and exploring multimodal extensions.

2. Previous Work and Theoretical Concepts

Understanding how booming noise arises and how it can be detected is a necessary step toward developing effective solutions. This section summarizes earlier studies and introduces key concepts, with emphasis on Transfer Path Analysis (TPA), order-based spectrogram methods, and psychoacoustic metrics.

2.1. Analysis Methods for Booming Noise—TPA

Interior noise in ICE vehicles arises from both airborne and structureborne sources. Booming noise, in particular, is predominantly structureborne and often linked to the second engine order. TPA is widely used to trace noise propagation using frequency response functions (FRFs) along structural paths [4]. To characterize the intensity of booming noise, the corresponding Sound Pressure Level (SPL) can be calculated using the expression [5]:

$$p_k\left(\omega \right)={{\displaystyle \sum }}_{i=1}^{n}FR{F}_{ik}\left(\omega \right)·F_i\left(\omega \right), i=1,2,\dots ,n$$

(1)

where $p_k\left(\omega \right)$ denotes the interior noise at the target point k, $FR{F}_{ik}\left(\omega \right)$ refers to the frequency response function along the structural path $i$, the term $F_i\left(\omega \right)$ represents structural excitation, product $FR{F}_{ik}\left(\omega \right)·F_i\left(\omega \right)$ quantifies an individual contribution, and $n$ denotes the number of structural paths.

In a vehicle, noise energy travels through various subsystems and paths, making its transmission complex. Each transfer path’s frequency response can be expressed by [5]:

$$FR{F}_{ik}\left(\omega \right)={{\displaystyle \prod }}_{j=1}^{m}FR{F}_{ikj}\left(\omega \right), j=1,2,\dots ,m$$

(2)

In this context, $FR{F}_{ikj}\left(\omega \right)$ denotes the frequency response function corresponding to structural path $i$ within subsystem $j$, and $m$ represents the total number of subsystems considered in the analysis.

Experimental TPA helps to identify vibration paths into the vehicle cabin and quantify noise contributions. Reference [5] showed that driveline torsional resonance can transmit considerable energy to the rear suspension, which in turn excites body and cavity vibrations that passengers perceive as booming.

2.2. Signal-Based Approaches to Booming Noise Characterization: Spectrogram and Waterfall Analysis

Spectrograms offer a simple means of identifying booming noise in both time and frequency domains by tracking how frequency content changes over time. They are computed using the Short-Time Fourier Transform (STFT), which applies the Fast Fourier Transform (FFT) to overlapping windowed segments of a signal. The FFT efficiently computes the Discrete Fourier Transform (DFT) for each block [6]. The STFT is given by:

$$STFT\left\{x_n\right\}\left(m,\omega \right)\equiv X_k\left(m\right)={{\displaystyle \sum }}_{n=0}^{L-1}{x}_n·w_{n-m}·e^{- {\displaystyle \frac{j2\pi kn}{L}}}$$

(3)

where $x_n$ denotes the discrete-time signal being analyzed, and $w_{n-m}$ corresponds to the windowing function, typically a Hann or Gaussian window, applied during transformation. The parameter L defines the total length of the signal segment under consideration.

It is important to note that, due to the uncertainty principle, there is a fundamental trade-off between time and frequency resolution, meaning that both cannot be optimized simultaneously: wide windows favor frequency resolution while narrow windows favour time resolution [6]. In booming noise analysis, spectrograms often use revolutions per minute (RPM) on the x-axis to track engine orders, meaning harmonics of crankshaft rotation, calculated by [2]:

$$f_0=k·{\displaystyle \frac{N}{60}} \left[\mathrm{Hz}\right]$$

(4)

where $N$ stands for crankshaft speed in RPM, $k$ indicates the order, and $f_0$ is the frequency associated with that specific order $k$.

In a four-stroke, four-cylinder engine, four combustion events occur every two crankshaft revolutions, corresponding to the second engine order. With growing emphasis on efficiency and emissions, engine downsizing has led to increased torsional excitations tied to the engine firing rate [3], which is given by:

$$EFR= {\displaystyle \frac{N}{60·\epsilon }}·N_{cyl} \left[\mathrm{Hz}\right]$$

(5)

where $\epsilon$ takes the value 1 for two-stroke engines and 2 for four-stroke engines, and $N_{cyl}$ denotes the number of cylinders. Thus, for a typical four-stroke engine with four cylinders, this yields:

$$EFR={\displaystyle \frac{N}{60·2}}·4={\displaystyle \frac{N}{30}} \left[\mathrm{Hz}\right]$$

(6)

By combining Equations (4) and (6), it follows that the Engine Firing Rate (EFR) coincides with the second engine order. This order is linked to higher torsional excitation, a factor known to promote booming noise inside the cabin. For this reason, the second engine order is often used as a practical reference when studying this type of acoustic disturbance.

2.3. Approaches to Booming Noise Assessment: Sound Quality Metrics and Perceptual Analysis

To assess in-cabin sound perception, NVH specialists often rely on psychoacoustic indicators such as loudness, sharpness and roughness, which provide insight into the subjective experience of vehicle noise [7]. Among the different psychoacoustic metrics, loudness is particularly relevant for describing booming noise because it reflects the combined influence of sound pressure level (SPL), frequency content, and duration [8]. Under dynamic driving conditions, the Time-Varying Zwicker Loudness metric is often used [9]. Previous studies [10,11,12,13] have also introduced psychoacoustic-based booming metrics, which show a strong correlation with subjective evaluations.

2.4. Booming Noise in ICE Vehicles, Traditional NVH Methods, and CNN-Based Classification

Booming noise is a low-frequency resonance, usually linked to the second or third engine orders interacting with the vehicle’s structural dynamics, and it has a strong impact on passenger comfort. Kim et al. [14] looked at booming in electric vehicles and suggested structural measures to reduce it. Altinsoy [15] focused on combustion engines, with particular attention to psychoacoustic factors. Common NVH techniques such as Transfer Path Analysis (TPA), Operational Deflection Shape (ODS), and modal analysis can be very precise, but in practice they require elaborate test setups and costly equipment. To make these methods more practical, Song et al. [16] proposed a data-driven version of TPA aimed at improving fault detection. Song et al. [16] suggested a data-driven adaptation of TPA to improve fault detection, while Kim et al. [14] also pointed out that finite element (FE) validation, although accurate, can be expensive to apply. More recently, CNNs have emerged as a scalable alternative for booming detection by classifying spectrogram representations of sound. Chu et al. [17] and Tsalera et al. [18] showed that CNNs, especially when combined with data augmentation and pre-trained architectures, form a solid basis for transfer learning in this domain.

2.5. Related Work and Proposed Solution

Recently, researchers have started combining physical modeling with artificial intelligence (AI), and this mixed approach is drawing more attention. For instance, Souza et al. [19] combined Multibody Dynamics with an artificial neural network (ANN) to estimate tonal prominence in electric vehicles (EVs), avoiding the need for direct acoustic measurements. Although their study focused on tonal noise, the idea is similar to the synthetic approach used in this work.

Table 1. Comparison of the most relevant related works.

Article	Main Contribution	Advantages Over This Work	Limitations Compared to This Work
Kim et al. (2023) [14]	FE and modal analysis of tailgate-induced booming in EVs.	Provides a physically validated approach for structural improvements.	No AI; limited to structural methods and EV context.
Altinsoy (2022) [15]	Psychoacoustic study of booming perception in ICE/HEVs based on listening tests.	Strong perceptual grounding; real-world relevance.	Requires human evaluation; no automation or classification.
Song et al. (2025) [16]	Big data + TPA/OTPA framework for NVH optimization in vehicle production.	Production-scale applicability; sensor fusion.	Still dependent on large sensor setups; no classification approach.
Chu et al. (2023) [17]	CNN with MFCC and augmentation for environmental sound classification.	Lightweight architecture; high accuracy with little data.	Uses generic datasets; not tailored for vehicle interior sounds
Tsalera et al. (2021) [18]	Transfer learning with pre-trained CNNs for audio classification (GoogLeNet, YAMNet).	Efficient training; flexible use of vision models.	Not domain-specific; tested mostly on urban and domestic sounds.
Souza et al. (2024) [19]	MBD + ANN to predict tonal sound prominence in EV powertrains.	Bypasses need for real measurements; ideal for early design.	Focus on tonal sounds in EVs; no classification of booming phenomena.

reviews the main studies on the topic, comparing their contributions, strengths, and limitations in relation to booming noise detection, and helps to frame the research gap addressed in this article.

Despite progress in NVH assessment, some important limitations are still evident:

• Traditional methods such as TPA, ODS, and modal testing give accurate and physically consistent results, but they demand extensive instrumentation, are expensive, and not practical for real-time or end-of-line (EOL) testing;
• Psychoacoustic studies provide valuable insight into how noise is perceived, but they depend on human evaluation, take time, and are difficult to standardize in production;
• CNN-based sound classification has achieved good results, yet it often relies on public datasets like UrbanSound8K or ESC-50, which are not specific to in-vehicle acoustics;
• The use of synthetic NVH data for supervised DL, particularly for booming noise classification, remains mostly unexplored.

The method was organized in four main steps:

Step 1—Signal creation: synthetic booming signals were produced from engine orders, combining digital twins of ICE vehicles with simple modulation techniques.

Step 2—Labeling: signals were grouped into three categories (Severe, Mild, None) according to psychoacoustic thresholds that relate order gain and spread (∆RPM).

Step 3—CNN training: different networks were trained with spectrograms generated under several mission profiles to separate booming from non-booming cases.

Step 4—Validation: the models were checked for stability by comparing smoothed and non-smoothed orders, testing on different vehicles, and benchmarking against other architectures.

The system developed in this work is intended as a practical tool for automatic booming noise detection. It is objective, inexpensive, and scalable, which makes it suitable for end-of-line testing and also promising for future use on embedded platforms.

3. Materials and Methods

This section describes the six-step methodology used to detect booming noise using CNNs. The workflow includes data acquisition, signal decomposition, SQE model construction, synthetic data generation, database labeling, and deep-learning classification.

3.1. Overview of the Proposed Workflow

The methodology is composed of six sequential stages: (i) acquisition of interior acoustic and RPM signals; (ii) signal decomposition into engine orders and broadband noise; (iii) construction of SQE models; (iv) generation of synthetic sounds through controlled manipulation of the second engine order (random modulation, Hann-window shaping and smoothing); (v) creation of labeled spectrograms and database preparation; and (vi) CNN training and validation.

3.2. Experimental Setup

This subsection corresponds to Step (1) in the workflow shown in Figure 1.

The dataset was collected at the Aldenhoven Test Center (Germany) using three internal combustion engine vehicles. Vehicles 1 and 2 came from the same manufacturer, while Vehicle 3 was from another. All tests were carried out under realistic driving conditions to keep the measurements consistent and to reduce surface noise. The vehicles were equipped with four-cylinder, four-stroke engines, with an engine firing rate (EFR) corresponding to the second engine order.

Table 2. Key parameters of the test track layout used during data acquisition.

Parameter	Value	Unit	Notes
Surface type	Asphalt	—	Uniform across the full circuit
Straight section length (each)	400 × 2	m	Two identical straights
Lane length—Lane 1/2/3	2074/2097/2120	m	Measured along central line
Lane width—Lane 1/2/3	3.75/3.75/4.00	m	Lane 3 slightly wider for high-speed tests
Curve radius—North/South	186.5/113.5	m	North is wider than south
Max cornering speed—Lane 3 (north/south curve)	117/96	km/h	Under free cornering conditions

summarizes the main features of the test track.

The dataset, gathered over several campaigns, was later used for two purposes:

• Developing SQE models specific to each vehicle;
• Applying coherence-based methods to separate structure-borne and airborne noise contributions.

A standard test matrix for vehicle acoustic characterization generally comprises multiple operating scenarios, including: (i) full acceleration (run-up) tests across all gears; (ii) coast-down sequences; (iii) constant-speed runs; (iv) engine rundown; and (v) free-driving conditions. In the present study, only the run-up condition in second gear with full throttle application was adopted for all vehicles under analysis.

Several sensors were employed during data acquisition. For this study, two elements were especially important: a binaural microphone placed at the driver’s seat to capture the in-cabin sound, and a tachometer to record the engine speed. These recordings were then used to build SQE-based synthetic datasets, which allowed the training of CNN models consistent with real vehicle dynamics.

The measured acoustic and engine-speed signals obtained from this experimental setup constitute the input data for the subsequent signal decomposition and order-based analysis described in the following subsection.

3.3. Signal Decomposition and Dominant Order Identification

This subsection corresponds to Step (2) in the workflow. Starting from the raw acoustic and tachometer signals acquired during the experimental campaigns, the objective of this step is to extract the dominant engine-order components that are later used to construct the SQE models. The goal is to decompose the recorded acoustic signal into its engine-order components and identify the dominant orders responsible for booming.

3.3.1. TVDFT Order Tracking

The Time-Varying Discrete Fourier Transform (TVDFT) was applied to track the harmonic structure of the signal as a function of engine speed. This method enables high-resolution isolation of the engine orders across the full RPM range.

3.3.2. Dominant Engine Order Identification

From the tracked-order representation, the second engine order was identified as the most relevant contributor to low-frequency booming noise, based on structural resonance behavior and psychoacoustic characteristics.

Once the data were collected, they were processed using Simcenter Testlab, a Siemens platform that integrates testing, analysis, and modeling tools tailored for NVH studies. For vehicle 2, tachometer data are shown in Figure 2, while Figure 3 and Figure 4 display amplitude over time captured by microphones at the driver’s left and right ears. As no significant differences were observed between sides, or between seats in other vehicles, only the left ear microphone signals were used for further analysis.

Using tachometer and left-ear microphone captured data, the spectrogram of a representative vehicle, namely vehicle 1, was analyzed (Figure 5). Most of the high-amplitude content appeared at low frequencies, following the engine orders (diagonal lines) and also below 50 Hz, where broadband noise was present but not considered in this study. Across all vehicles, the second engine order was the dominant component, especially in the 1350–2000 RPM range, which points to possible booming. To isolate the relevant sound features, we applied high-pass and order-based filters. By listening to the recordings, we noticed that booming was strongest at low RPMs. We used this observation to decide which engine orders to decompose in Simcenter Testlab.

The identified dominant engine orders and broadband noise components obtained in this step form the basis for the SQE model construction described in the next subsection.

3.4. SQE Model Construction

This subsection corresponds to Step (3) in the workflow shown in Figure 1. Using the decomposed engine-order and broadband noise components extracted in the previous step, SQE models were constructed to enable controlled sound synthesis and systematic booming manipulation.

Sound decomposition was carried out using the Simcenter Vehicle Sound Simulator, 2023, developed by Siemens Industry Software, FARNBOROUGH. This tool supports a wide range of NVH-related applications, including the study of virtual vehicle prototypes and the early-stage integration of noise and vibration considerations (frontloading). It also enables the creation of vehicle libraries for benchmarking and sound target definition, supports the evaluation of new components within existing platforms, and facilitates comparison between alternative configurations. Additionally, it is useful for assessing both interior and exterior sound characteristics, as well as implementing active noise enhancement strategies.

In this study, Simcenter Testlab was employed to build vehicle sound libraries by decomposing the interior acoustic signals into engine-order harmonics and broadband noise components. This decomposition was performed using an order tracking algorithm based on the Time-Variant Discrete Fourier Transform (TVDFT) [20,21], which enables the separation of tonal content from stochastic background noise.

After extracting the relevant engine orders, we transferred the data to Simcenter Testlab for processing. Figure 6 and Figure 7 show the main order components for Vehicles 1 and 3. In both cases, the second engine order at low RPM was the most evident source of booming noise. The broadband noise profiles can be seen in Figure 8 and Figure 9.

Based on these decomposed components (orders and broadband noise), the SQE model was constructed as described below.

3.4.1. SQE Model Creation

The SQE model reconstructs the interior sound by combining the extracted engine orders and broadband noise components using a top-down modeling strategy.

In this work, the SQE model was built from the decomposed engine orders and broadband noise extracted from the second-gear full-throttle run-up recordings.

The decomposition follows a simplified additive sound model, in which the total interior acoustic signal is represented as the sum of tonal engine-order components and broadband noise contributions. This makes it possible to analyze or adjust each component separately. In this study, a top-down approach was chosen, which means the decomposition can be done from a single recording without the need to isolate sources. For model construction, data from second-gear runs at 100% throttle were used, covering an observed RPM interval between ~1300 and 4600.

After defining the SQE modeling strategy and constructing the vehicle-specific sound models, mission profiles were generated to synthesize realistic run-up scenarios, as described in the following subsection.

3.4.2. Generation of Mission Profiles

Driving conditions in the SQE model are mapped onto a 3D grid. Each block stands for a driving condition defined by RPM, throttle, and gear. This setup makes it possible to interpolate and synthesize vehicle sounds across the full operating range, even for conditions that were not measured directly. This makes it suitable for predicting sound behavior in dynamic driving.

After the SQE model is set up for a vehicle, the next step is to define the mission profiles. These profiles describe different run-up conditions and are generated randomly from anchor points of engine speed (RPM) and time. Using these inputs, the simulation program produces acceleration scenarios that are realistic and varied.

Table 3. Input anchor points for mission profile generation.

Phase	Time [s]	Engine Speed [RPM]
Start	0.0	1.05
Finish	6.5	4.57

presents an example of the RPM-time anchors used as input to generate a representative mission profile.

Using the input anchors in Table 3, random velocity profiles were generated to simulate different run-up behaviors and increase the variability of the dataset. During synthesis, the SQE models follow these profiles, so each sound reflects a different driving dynamic. This randomization gives a closer match to real conditions, where acceleration patterns naturally change from driver to driver. Examples of the generated mission profiles, shown as RPM over time, are given in Figure 10.

These mission profiles increase dataset diversity by exposing the SQE model to realistic variability in acceleration behavior, while preserving the measured vehicle-specific sound characteristics.

3.5. Synthetic Acoustic Data Generation

This subsection corresponds to Step (4) in the workflow shown in Figure 1. After building the SQE model and generating mission profiles, synthetic booming scenarios were created by controlled manipulation of the second engine order. The modified orders were then recombined with the broadband noise component to synthesize full interior sounds representative of different booming severities. All SQE modeling and synthesis steps were implemented in a custom MATLAB 2019 program, which generated the final acoustic signals used in the subsequent database creation stage.

Synthetic signals were generated from the SQE models to support the creation of a labeled database suitable for CNN training. Booming events were deliberately introduced during synthesis by manipulating selected engine orders and also generated the synthesized acoustic signals used in the subsequent stages.

3.5.1. SQE Model Adjustment for Booming Simulation

In the RPM ranges typically associated with booming noise, the second engine order shows a marked rise in amplitude, becoming the predominant contributor to the interior sound. The corresponding curve displays a bell-shaped profile across these intervals.

After creating the SQE models and their mission profiles, we modified them to simulate booming noise in the synthesized vehicle sounds. This was done by changing specific engine order components, which made it possible to add booming effects in a controlled way and increase the variability of the dataset. The changes included:

• Low-frequency random modulations were added to the engine-order signals to reproduce the amplitude variations normally observed during run-ups. This made the synthesized profiles better reflect the natural variability of real driving. Figure 11 illustrates a comparison between original and modified second-order curves for the three vehicles.
• RPM values outside the main operating range (below 1500 RPM and above 4230 RPM) were left out of the modification process, since the analysis targets the region where booming is most noticeable. Depending on how much noise was injected, the resulting signals either stayed close to the original waveform or diverged from it more strongly.
• A Hann window was applied to the second-order signal to reproduce the booming effect by shaping its amplitude envelope. The window width (ΔRPM) and gain (G) were chosen randomly to add variation between instances. Details of the parameter ranges are provided in

  Table 4. Limits of parameters G and ΔRPM used in second-order amplitude modulation with a Hann window.

  Parameter	Range [min, max]
  G	[0.0, 1.5]
  ΔRPM	[0, 560] RPM

  . The window spans 1500–4230 RPM. Below that, peaks are perceived as engine strength. Figure 12 illustrates three cases: (a) a peak near 1800 RPM simulates booming; (b) a sharp spike mimics transient noise; (c) a low-amplitude window has little effect.

• The second-order curves were smoothed with a function available in the synthesis software to reduce abrupt variations and make them more uniform across vehicles. Figure 13 gives an example of this effect for all three test cars. When smoothing is combined with random fluctuations (Figure 14), the acoustic profile looks more consistent, with fewer dips and softer bell-shaped patterns. This tends to reduce booming at low RPM. In contrast, applying a Hann window to the smoothed curves (Figure 15) has the opposite effect, making the booming more pronounced—a useful feature for training CNNs to detect moderate and high-amplitude events. However, applying a Hann window to these smoothed curves (Figure 15) amplifies booming, which is beneficial for training CNNs to detect moderate-to-high amplitude events.

Following the manipulation of the SQE model to incorporate the previously described variations, a quantitative criterion was established to identify the presence of booming noise. Based on the application of a smoothing function and Hann window, parameterized by gain G and window width RPM, experimental tests indicated that booming was consistently perceived when G > 0.5 and ∆RPM > 280 RPM. These thresholds were thus adopted as the classification metric in the subsequent analysis.

The selection of the modulation parameters and the corresponding classification thresholds was not arbitrary. These criteria originate from a prior development stage of the SQE-based booming simulator, in which extensive exploratory simulations were combined with controlled listening evaluations. Multiple combinations of G, ΔRPM, smoothing, and random low-frequency fluctuations were systematically assessed through subjective listening tests. These evaluations showed that low gain values or narrow windows mainly affected perceived engine strength or transient events, while sustained booming sensations were consistently perceived only when both the gain and window width exceeded minimum values. Based on these perceptual observations, the thresholds G > 0.5 and ΔRPM > 280 RPM were adopted to distinguish clear booming phenomena from non-booming or borderline cases.

3.5.2. Final Sound Synthesis

To synthesize vehicle sound, both the manipulated SQE model (orders) and the broadband noise model are combined according to the mission profile. The synthesis frequency must satisfy the Nyquist criterion. Since broadband noise contains higher frequencies than engine orders, a synthesis rate of 44,100 Hz was selected. For broadband noise, a “Narrow Band” synthesis approach was used [22], which introduces random fluctuations. Figure 16 shows separate synthesized signals (orders in blue, noise in orange), and their combination is presented in Figure 17.

The synthesized acoustic signals generated through this process were subsequently transformed into time–frequency representations and labeled to create the dataset used for CNN training, as described in the following subsection.

3.6. Label Creation and Database Preparation

This subsection corresponds to Step (5) in the workflow. Labels (Severe, Mild, None) were assigned according to the psychoacoustic criteria defined from the gain G and window width ΔRPM used during the synthetic data generation stage.

Each synthesized signal was converted into a spectrogram using the STFT. A Hann window was applied to each signal segment, with overlapping windowed blocks to ensure adequate time-frequency resolution for booming noise analysis.

The spectrograms were generated using a fixed engine-speed range between 1500 and 4230 RPM, corresponding to the operational interval where booming is perceptually relevant. The RPM resolution was set to 15 RPM, matching the resolution of the extracted engine orders. The amplitude color scale was fixed between 60 and 105 dB to ensure consistency across all samples and alignment with the classification criteria.

High-frequency components were excluded from the spectrograms, as booming noise is predominantly a low-frequency phenomenon associated with the second engine order. This choice reduced data dimensionality and emphasized the most relevant acoustic features for CNN-based classification.

These preprocessing choices ensured that the generated spectrograms preserved the structural characteristics of booming noise while remaining suitable for convolutional feature extraction.

The labeling strategy adopted in this work is grounded on psychoacoustic observations obtained during the development of the SQE-based booming simulator. During this exploratory phase, multiple combinations of gain G, window width ΔRPM, smoothing, and random low-frequency fluctuations were systematically evaluated through controlled listening sessions conducted by experienced NVH engineers.

These informal perceptual assessments consistently showed that low gain values or narrow modulation windows mainly affected perceived engine strength or transient tonal events, while sustained booming sensations were reliably perceived only when both gain and modulation width exceeded minimum values. Based on these observations, the thresholds G > 0.5 and ΔRPM > 280 RPM were selected to distinguish clear booming phenomena from non-booming or borderline cases.

Although no formal jury-based listening campaign with statistical analysis was conducted, the adopted thresholds reflect practical NVH engineering experience and established psychoacoustic trends reported in the literature. The proposed labeling strategy should therefore be interpreted as a pragmatic and operational approximation of human booming perception, suitable for large-scale data generation and supervised learning, rather than as a replacement for standardized subjective evaluation procedures.

3.7. CNN Training and Validation

This subsection corresponds to Step (6) in the workflow. At this stage, the labeled spectrograms obtained from the synthetic data generation pipeline serve as input to the CNN-based classification framework.

The labeled spectrograms were used to train CNN architectures of varying depth and kernel configuration. Models were trained for both binary (Yes/No) and three-class (Severe/Mild/None) classification, and validated across different synthetic sets.

The selection of the CNN configurations was guided by the characteristics of the input data and the objectives of the proposed framework rather than by the pursuit of maximum architectural complexity. The input spectrograms represent low-frequency acoustic phenomena with relatively smooth time-frequency patterns, for which shallow to moderately deep convolutional architectures are well suited. Preliminary experiments showed that increasing network depth beyond a limited number of convolutional layers did not yield consistent performance improvements and increased the risk of overfitting due to the controlled size of the synthetic dataset.

Furthermore, compact CNN architectures offer advantages in terms of training stability, computational efficiency, and interpretability, which are important for practical NVH applications and potential integration into industrial workflows. For these reasons, the adopted configurations represent a balanced trade-off between model complexity and generalization capability, rather than an exhaustive exploration of deep-learning architectures.

3.8. CNN Architecture and Training Configuration

For reproducibility purposes, the CNN architecture and training configuration adopted in this work are detailed below. The design choices were guided by the characteristics of the input data, namely low-frequency spectrogram representations of in-cabin sound, and by the need to balance classification performance with robustness against overfitting.

The CNN architecture and hyperparameters were selected based on a systematic exploratory study, which evaluated different numbers of convolutional layers, regularization strategies, and training configurations. The final architecture, consisting of six convolutional layers, was found to provide the best compromise between classification accuracy and generalization across vehicles. Training was carried out using fixed batch-size values and a learning-rate decay strategy to ensure stable convergence. Separate models were trained for binary and three-class classification tasks.

Table 5. CNN architecture and training parameters.

Component	Configuration
Input	Grayscale spectrogram images
Convolutional layers	6 convolutional layers
Filters	Increasing depth across layers following a doubling scheme
Kernel size	3 × 3
Activation function	ReLU
Padding	Same
Pooling	Max pooling (stride = 2)
Regularization	Dropout (0.5) and L2 regularization (λ = 0.0001)
Fully connected layer	1 dense layer
Output layer	Softmax (3-class)/Sigmoid (binary)
Loss function	Categorical cross-entropy/Binary cross-entropy
Optimizer	Stochastic Gradient Descent with momentum
Learning rate	Initial value with decay applied during training
Batch size	32
Number of epochs	50
Validation strategy	Hold-out validation set (separate from training data)
Framework	MATLAB 2019

presents this information in detail.

The adopted CNN architecture follows a compact design, suitable for learning low-frequency time-frequency patterns from spectrogram representations while reducing the risk of overfitting. Hyperparameters were selected based on preliminary exploratory experiments and standard practices in audio-based deep learning. Training was performed using fixed learning-rate and batch-size values to ensure stable convergence. Separate models were trained for binary and three-class classification tasks.

4. Results and Discussion

This section reports the classification results of the CNN system on both smoothed and non-smoothed spectrogram datasets. Two tasks were considered: a binary one that separates booming from non-booming (Yes/No), and a three-class one that distinguishes between No, YesMild, and YesSevere. We also break down the results by vehicle type and discuss common misclassification patterns.

4.1. Pre-Processing Pipeline for Spectrogram-Based Classification

After synthesizing the acoustic signals, we turned them into spectrograms for CNN training. In setting up the spectrograms, we made three simple choices:

• Y-axis in RPM: The vertical axis was plotted in engine speed (RPM) rather than frequency. This way the second engine order stands out more clearly, as it is the one most associated with booming.
• Fixed scales: All spectrograms used the same limits for RPM and amplitude. The RPM range was 1500–4230 with steps of 15 RPM, matching the extracted orders. The amplitude was set between 60 and 105 dB, based on order-two levels across the vehicles. Using the same scales kept the data comparable and consistent with the thresholds used later.
• Low-frequency cut: High frequencies were left out because booming mainly occurs at low frequencies. This reduced the processing load and improved the clarity of the features.

Figure 18 shows examples of these spectrograms. For each vehicle, the left image is a booming case and the right one is non-booming. In some vehicles, such as Vehicle 2, the difference is small to the eye, which shows why CNNs are needed to separate the cases reliably.

The next step was to balance the dataset across the classes.

For the binary task:

• Yes → ΔRPM > 280 and G > 0.5
• No → all other cases

For the three-class task:

• YesSevere → ΔRPM > 280 and 1 < G < 1.5
• YesMild → ΔRPM > 280 and 0.5 < G < 1
• No → all other cases

To avoid class imbalance and keep the training process stable, the datasets were built so that each class had roughly the same number of samples.

4.2. CNN Architecture and Hyperparameter Configuration

The CNN architectures used in this work are shown in Figure 19. Each network has several convolutional layers with max-pooling layers in between, which extract spatial and frequency features from the spectrograms step by step. After the last pooling layer, the network switches to fully connected layers that generate the predictions. Two architectural choices were adopted: batch normalization was applied after each convolutional layer, and a dropout layer was added after the last pooling layer. The goal of these adjustments is to improve generalization and ensure stable training.

During the first training runs, signs of overfitting were observed, which is a common issue in deep learning models trained on limited or highly structured datasets. To mitigate this effect, dropout regularization was applied following standard practices [23,24]. The adopted training strategy builds upon the authors’ previous experience in training convolutional neural networks for complex engineering pattern-recognition tasks [25,26,27,28].

Batch normalization was also included to keep training stable and to allow for higher learning rates. For activation functions, ReLU was used in the convolutional layers and Softmax in the output layer [29,30], making sure the probabilities add up to one. Max pooling was used [31,32,33] to capture the high-energy spots in the spectrograms, since booming shows up as bright regions. Some hyperparameters were tuned by hand, especially the learning rate. If the rate is too small, training becomes slow and the model may get stuck in a local minimum. If it is too large, the network may not converge. To deal with this, a decay schedule was used so that the rate decreased step by step during training. Although many parameters affect performance, small variations matter little once a balanced setup is reached. The values used are listed in

Table 6. Selected hyperparameters and optimization settings for CNN training.

Category	Parameter	Value
Optimization	Optimizer	SGD with momentum
	Momentum	0.9
	Initial learning rate	0.001
	Decay schedule	×0.1 every 10 epochs
	Mini-batch size	32
Architecture	Convolution kernel	3 × 3
	Filters per layer nn	8 × 2 (n − 1)
	Padding	Same
	Convolution stride	1
	Max-pooling (kernel, stride)	2 × 2, stride 2
Regularization	Dropout	50%
	L2 coefficient (λ)	0.0001

. Stochastic gradient descent with momentum was chosen as the optimizer. The table summarizes the hyperparameters used in the CNN training. Experimental testing guided the choice of values, with the goal of achieving stable training, good generalization, and solid accuracy.

The number of layers in a CNN matters a lot. If the network is too shallow, it fails to pick up the right features and accuracy in training stays poor. When it gets too deep, another problem shows up: the model learns the training set by heart and does not generalize, so test accuracy drops. More layers also mean more time to train and higher demand on the hardware. In the end, the depth has to be set so that accuracy, generalization, and computing effort are kept in check.

4.3. Training Set Size Estimation

Before deciding on the depth of the architecture (number of convolutional and fully connected layers), we first checked how much training data was needed to obtain stable results. The aim was to avoid underfitting while still keeping the computational cost reasonable. For the binary task (Yes/No), we tested a small CNN with three convolutional layers and one fully connected layer. In total, 1250 samples were produced: 1000 for training and 250 for testing. Both sets had balanced class distributions. Figure 20 shows the accuracy and loss curves across 100 epochs. Training and testing are plotted separately to illustrate how the model behaved over time.

Even with regularization, some overfitting was still visible. To reduce it, the dataset was expanded to 12,500 samples: 10,000 for training and 2500 for testing, keeping an 80/20 split. Both sets were built with balanced class distributions.

Figure 20 shows the accuracy and loss curves for this larger dataset. To make the results comparable with the first experiment (1250 training samples), the number of epochs was kept at 10. In Figure 21, the training and validation curves are much closer, which indicates that overfitting was reduced. Accuracy also improved. For this reason, the rest of the study used the larger dataset (10,000 training samples). Two notes are worth adding: (i) although the curves did not fully converge, they were stable enough to compare the two dataset sizes; and (ii) the small oscillations in validation accuracy, often in the form of local minima, come from the mini-batch training process. These oscillations decrease over time thanks to learning rate decay and do not affect the overall trend.

4.4. Evaluation of Convolutional Layer Depth

After fixing the training set size, we tested how the number of convolutional layers affected performance. The aim was to find a depth that offered a good balance between accuracy and generalization. To make the results reliable, each setup was run five times and the average accuracy was taken. Training was limited to 10 epochs per run, which was enough for the networks to reach a stable phase and allowed fair comparisons between different architectures (see Figure 22). The average results for the various depths are shown in Figure 23.

The results show that the network with six convolutional layers gave the best average test accuracy. Accuracy increased steadily from three to six layers, but dropped when a seventh was added. In most cases, the mean accuracy of a given setup was close to the maximum from the previous, shallower model. The exception was the seven-layer network, where the mean accuracy was closer to the previous minimum. This pattern supports the choice of six layers as a good compromise between performance and complexity. To check this further, and because the test accuracy showed small fluctuations with a slight upward trend, the six-layer model was also trained for 30 epochs. Figure 23 illustrates a representative test under these conditions. Although the learning curve shows continued improvement initially, signs of overfitting emerge, and no substantial gains in accuracy are observed compared to the results from shorter training runs.

A similar evaluation procedure was applied to the ternary classification task (YesSevere/YesMild/No), although this scenario introduced additional complexity due to the increased number of classes and finer distinctions between them. Training began with 6 convolutional layers, and deeper architectures were also tested. Results illustrated in Figure 24 indicate that the best performance was achieved with 6 layers. Due to fluctuations and a still-rising test accuracy curve, the final accuracy was calculated after 30 epochs. Figure 25 shows an example, where overfitting is evident and the test accuracy stops improving significantly.

4.5. Test Results on Non-Smoothed Orders

Here we report the results of testing the models on non-smoothed order data. The networks are the same as those trained in the previous section, where smoothed signals were used for training. The goal was to see how well the models generalize when the test data differ from the training distribution. The outcomes for the Yes/No classification task are shown in

Table 7. Accuracy results for smoothed and non-smoothed test cases across CNN architectures.

Network ID	Convolutional Layers	Epochs	Accuracy (Smoothed Test Set)	Accuracy (Non-Smoothed Test Set)
1	3	10	94.20%	84.51%
2	4	10	94.76%	84.78%
3	5	10	95.72%	86.11%
4	6	10	96.20%	85.25%

. This table compares model performance when tested on non-smoothed input data, after training on smoothed orders. The analysis includes four network configurations with increasing convolutional depth.

To look closer at the drop in performance on non-smoothed data, we analyzed Network 3, which gave the best accuracy in this setting. Classification accuracy was checked separately for each vehicle to see where the differences came from. The results are in

Table 8. Test accuracy of Network 3 on non-smoothed cases, broken down by vehicle.

Network ID	Overall Accuracy (Non-Smoothed)	Vehicle 1	Vehicle 2	Vehicle 3
3	86.11%	81.33%	93.37%	83.73%

. They show that accuracy for Vehicle 2 is clearly higher than for the other two, meaning the model generalizes better on that subset. Overall, the table illustrates how classification performance varies across the three vehicles when using the best architecture (Network 3) on non-smoothed data.

Table 9. Accuracy results for ternary classification on smoothed vs. non-smoothed cases.

Network ID	Convolutional Layers	Epochs	Accuracy (Smoothed Test Set)	Accuracy (Non-Smoothed Test Set)
6	6	10	93.44%	70.34%
7	7	10	92.92%	78.16%

compares classification performance across two network configurations for the YesSevere/YesMild/No task. Models were trained on smoothed inputs and evaluated on both smoothed and non-smoothed datasets.

Network 7 gave the best results for the ternary task (YesSevere/YesMild/No) on non-smoothed data, so we looked at its performance by vehicle. The outcomes are shown in

Table 10. Classification accuracy (%) of Network 7 on raw (unsmoothed) datasets.

Dataset	Vehicle 3	Vehicle 2	Vehicle 1	Overall
Accuracy	75.10	90.55	69.02	78.20

. As in the binary case, Vehicle 2 again reached higher accuracy than the other two models.

4.6. Performance Evaluation Under a Regression-Based Formulation

Although the problem is sometimes described using discrete booming severity levels for interpretability, the proposed CNN model is formulated as a regression task. The network outputs a continuous value associated with the estimated booming intensity, rather than directly predicting discrete class labels.

For this reason, classical classification metrics such as precision, recall, F1-score, and confusion matrices are not directly applicable in this context, as they require discrete class predictions. Model performance was therefore evaluated using accuracy-based indicators derived from thresholding the continuous output, together with loss convergence analysis across training iterations and epochs.

Table 11. Regression-based performance indicators for the CNN model.

Metric	Description
Overall accuracy	Percentage of samples whose predicted booming intensity falls within the correct perceptual range after thresholding
Training loss	Mean regression loss during training iterations
Validation loss	Mean regression loss on validation data
Convergence stability	Consistency of accuracy and loss across epochs

summarizes the regression-based performance indicators adopted in this study, including overall accuracy after thresholding, loss evolution, convergence stability, and vehicle-wise performance. These indicators provide a comprehensive view of model behavior while remaining consistent with the regression-based formulation of the problem.

Overall, this evaluation strategy allows the assessment of predictive consistency and robustness across different network configurations and vehicles, while avoiding the misuse of classification-specific metrics in a regression framework.

Given the regression-based formulation of the problem, performance is summarized using indicators that reflect predictive consistency and convergence rather than discrete class separation.

4.7. Validation of Results

To test the robustness of the models, we looked at the misclassified cases in more detail. The analysis covered both smoothed and non-smoothed test sets for the Yes/No task.

Network 4 was taken as the example for smoothed data, and Network 3 for non-smoothed inputs. Figure 26 shows 30 misclassified samples from Network 4, chosen at random. In the scatter plot, the horizontal line marks the gain G threshold and the vertical line marks the ΔRPM threshold. Many points appear close to these limits, forming an “L”-shaped distribution. Most of the errors occurred right on the boundary, close to the decision thresholds, and none could be considered severe.

Complementing this, Figure 27 presents the distribution of misclassified samples across different engine speed intervals, based on the starting point of the Hann window. Most of the errors occurred in the lower RPM range.

Figure 28 displays a similar scatter plot for 30 misclassified cases from Network 7, which was applied to the non-smoothed ternary classification task. In this case, the misclassifications are more widely spread across the parameter space, and some errors deviate significantly from the decision boundary, indicating the presence of more critical misclassification instances. Lastly, Figure 29 shows the corresponding histogram of misclassified cases per RPM range. As with Network 4, most errors are concentrated at lower engine speeds.

4.8. Comparison with Traditional Booming Detection Approaches

Traditional booming noise detection and assessment methods in the automotive NVH field typically rely on a combination of physical measurements, order analysis, and expert-driven subjective evaluation. Common approaches include the inspection of order-tracked spectra, sound pressure level thresholds in predefined frequency bands, coherence analysis between engine speed and interior noise, and jury-based listening tests conducted on measured or synthesized signals. While these methods are well established and effective, they are generally time-consuming, require expert interpretation, and are difficult to scale for large datasets or early design-stage evaluations.

In contrast, the proposed approach leverages SQE-based synthetic sound generation combined with CNN-based classification to automate the detection of booming phenomena. Rather than relying on manually defined spectral thresholds or expert listening alone, the method learns discriminative patterns directly from time–frequency representations of sound. This enables rapid evaluation of a large number of synthetic scenarios and supports data-driven generalization across different vehicles and operating conditions.

It should be noted that the objective of the proposed method is not to replace traditional NVH analysis tools, but to complement them by providing an automated screening mechanism. The CNN-based framework can be used to pre-filter potential booming cases, which may then be further analyzed using conventional order-based inspection and expert listening. This complementary role positions the proposed method as a scalable and efficient extension of existing booming detection workflows rather than a direct substitute.

4.9. Influence of Vehicle-Specific Factors on Model Performance

The observed variation in classification performance across different vehicles reflects inherent vehicle-specific NVH characteristics rather than limitations of the proposed methodology. Each vehicle presents distinct structural dynamics, interior cavity responses, and engine-body coupling mechanisms, which directly influence the manifestation of booming phenomena in the low-frequency range.

Since the proposed framework is trained on SQE-based synthetic data derived from vehicle-specific measurements, the learned representations naturally capture these differences. Variations in performance can therefore be attributed to differences in the amplitude, bandwidth, and RPM localization of the second engine order, as well as to the interaction between tonal and broadband components in each vehicle.

Importantly, this behavior highlights the ability of the proposed approach to generalize across vehicles while remaining sensitive to their individual acoustic signatures. Rather than enforcing a vehicle-agnostic representation, the method preserves physically meaningful differences, which is desirable in practical NVH applications. Future work may include a more detailed correlation between classification performance and vehicle-specific physical parameters, such as structural resonance frequencies or interior modal characteristics.

4.10. Limitations and Generalization Considerations

The scope of the present study is intentionally focused on four-cylinder internal combustion engine vehicles and on a single, well-defined driving condition, namely second-gear full-throttle run-up. This choice was motivated by the fact that low-frequency booming phenomena are most strongly excited under these conditions, making them particularly suitable for controlled analysis and methodological validation.

By restricting the study to a homogeneous engine configuration and a repeatable operating scenario, the proposed framework minimizes variability unrelated to the booming mechanism itself and allows a clearer assessment of the sound synthesis, labeling strategy, and CNN-based detection pipeline. This controlled setup is consistent with common NVH development practices, where specific operating conditions are selected to isolate and study critical acoustic phenomena.

While other engine architectures, powertrain types, and driving conditions may exhibit different NVH characteristics, the regression-based formulation and the modular SQE-driven data generation approach adopted in this work are not inherently limited to the selected configuration. Extending the framework to additional vehicle types and operating scenarios is therefore considered a natural and straightforward direction for future work.

The proposed approach relies primarily on SQE-based synthetic datasets, which was a deliberate methodological choice rather than a limitation of data availability. In the automotive NVH domain, SQE techniques are widely adopted to generate controlled and repeatable sound scenarios while remaining grounded in real in-vehicle measurements. Since the synthetic signals used in this work are directly derived from measured vehicle recordings, the generated datasets preserve the essential physical and perceptual characteristics of real booming phenomena.

Validation using raw in-vehicle recordings was therefore employed mainly as a qualitative consistency check, rather than as a large-scale training resource. The main objective of the proposed framework is not to replace experimental NVH testing, but to complement it by enabling scalable and systematic evaluation of booming scenarios that would be impractical to capture exhaustively through measurements alone. The authors acknowledge that generalization is influenced by the diversity of vehicles used to construct the SQE models, and extending the framework to a broader range of vehicle architectures and operating conditions constitutes a natural direction for future work.

5. Conclusions

This work investigated the use of CNNs to classify booming noise in ICE vehicles using spectrogram images. Booming noise is one of the most intrusive in-cabin NVH phenomena, yet lacks standardized quantification metrics. A method was developed to simulate booming by altering the engine order 2 profile with Hann windows, generating bell-shaped patterns across 1500–4230 RPMs. This enabled the creation of a large, diverse, labeled dataset without real-world recordings. The synthetic data effectively trained multiple CNN architectures. Binary classification achieved 96.2% accuracy; ternary classification exceeded 93% with smoothed data. Accuracy dropped when using non-smoothed profiles, especially at low RPMs where pressure amplitudes are higher. The results show that CNNs can pick up useful features, but they are also sensitive to noise in some conditions. The method itself is scalable, repeatable, and low-cost, which makes it practical for end-of-line testing or even on-board use. There are, however, some limitations. The approach depends on precise RPM tracking and on labels that are mathematically derived, which do not always match human perception. Even so, the low complexity and fast inference of 2D-CNNs on grayscale spectrograms make them a good fit for embedded systems. Future work will focus on validating the models with real vehicle data collected in controlled conditions. Because the models are lightweight, they could run on small devices like Raspberry Pi or Jetson Nano for real-time NVH monitoring.