Streamlining NVH analysis of loudspeaker performance

October 20, 2025

Introduction

In modern vehicle development, the acoustic quality of the passenger cabin has become a defining feature of perceived comfort and brand identity. Consumers increasingly expect immersive and high fidelity audio experiences, making the design of in-cabin sound systems a critical differentiator for manufacturers. However, integrating loudspeakers into the vehicle interior remains a challenging task due to designed space restrictions.

During the development cycle, loudspeakers are rarely given priority in packaging. Their placement is often determined after critical safety, structural, and ergonomic components have been fixed. As layouts evolve, speaker positions are repeatedly adjusted, each relocation altering the resulting acoustic field within the cabin. Reliable evaluation of these effects requires simulation, but current practices rely on manual and expert-driven workflows that do not scale well with the number of iterations demanded by modern design processes.

This context highlights the need for solutions that combine automation, repeatability, and accessibility. Beyond reducing engineering effort, such solutions can democratize acoustic analysis, empowering designers and engineers outside the simulation domain to explore alternatives early in the development process. The approach presented in this work addresses precisely this need: it streamlines acoustic studies through fully automated, tool-agnostic workflows.

Methodology

Advanced numerical simulation methods have been first introduced into the aerospace and automotive industry. Today, it is widely used in all industries [1] and virtual product development, and simulation-driven design is disseminating fast. Increasingly, advanced engineering analysis methods are used already in the early development phases to create digital prototypes for assessing the performance of products - already at concept level.

This trend can also be seen in the audio industry. For almost 20 years, advanced engineering analysis methods have been used on a regular basis for the multidisciplinary simulation of loudspeakers long before any hardware exists [2]. More recently, the complex listening environment of an automobile has been included in the simulation models as well [3].

Especially for the automotive industry, this is significant as there is a strong trend towards a fully digital development environment, where advanced engineering analysis methods are moved upfront in the development process, with the goal of increasing engineering efficiency and using fewer physical prototypes or even targeting a zero-prototype strategy.

Multidisciplinary simulation model

On transducer level, the simulation model needs to capture at least the following physical domains:

• Electromagnetics
• Mechanics (structural dynamics)
• Acoustics

Figure 1 shows the governing equation for each domain and the resulting coupled system. A detailed description of this model can be found in [4].

In the context of car audio we are dealing with system level simulations. I.e., the whole system including the interaction of the transducer with an enclosure and a listening space needs to be modelled. It must be noted, that also the electronics, especially digital signal processing, needs to be modelled as well. And also noteworthy is the use of geometrical acoustics for full bandwidth simulations. But this is beyond the scope of this paper and we refer to [5].

Because of the scale differences between the loudspeaker’s motor system (the air gap between voice coil and magnet is only several 1/10 of millimeters) and the passenger compartment (size is several meters), we use a mixture of 1D and 3D models. Typically, a 1D lumped parameter model (LPM) is used for the motor system, while finite elements (FEA) are used for the mechanical and acoustical domain (see Figure 1).

Such a simulation model can be seen in in Figure 2:

In this work we use a simplified car model that is also used for concept studies and training purposes [6].

Assessment of sound quality

There is a significant difference in the assessment of product performance between the audio industry and many other industries. While for most technical products its performance can be described by reference metrics or parameters, an audio system’s performance, i.e. the reproduced and perceived sound quality, cannot be described by a closed form definition with a distinct metric that could be measured or simulated. Typically, the assessment of sound quality is based on subjective methods by means of listening tests.

However, especially in the concept phase there are a couple of easy to calculate metrics that are used to optimize the product performance.

As the perception of sound in small spaces is related to sound power, like in an automobile’s interior, our metric is based on the localized sound power method [7]. This method uses an array of six microphones to measure sound pressure and perform a spatial averaging as an efficient approximation to the local sound power. The term “local” here means the proximity of a listener’s ears. As per definition, the location of the microphone covers the “99% ear ellipsoid”. That is the area where 99% of the driver’s ears are located (see Figure 3).

In the current work we focus on the so-called Front Center Speaker in the instrument panel (see Figure 4) and its frequency response at the driver location. We will use this virtual measurement to explore the effect of the location of the speaker and eventually optimize it with respect to sensitivity based on the localized sound power. In loudspeaker design and audio engineering, sensitivity refers to how efficiently a loudspeaker converts electrical power into acoustic sound.

A typical full bandwidth frequency response is given in Figure 5.

We will use the bandwidth from 100 Hz up to 2 kHz for demonstration purposes of the workflow. Also, this bandwidth is very important for reproduction of human voices and hence is of crucial interest.

Workflow implementation

The automated workflow has been implemented in pSeven Enterprise [8], a server-based process integration and design optimization (PIDO) platform. Within this environment, workflows are constructed from modular blocks that are configured through a dedicated GUI, each representing a distinct action within the tool chain. By connecting these blocks together, the entire simulation pipeline is encapsulated into a repeatable, parameter-driven process.

The workflow (Figure 6) begins with a script generation block, which produces a customized input file for MSC Apex. A template script is prepared in advance, and the block automatically replaces the X and Y coordinates of the loudspeaker position with user-defined values. This ensures that new configurations can be introduced without requiring manual editing or knowledge of MSC Apex scripting.

The second block is used to start up MSC Apex on a remote host connected to the pSeven Enterprise server. The generated script is executed, and the tool produces an updated finite element mesh that reflects the new loudspeaker position. Automating this step removes the need for repetitive geometry manipulation and meshing by hand, which is typically a bottleneck in acoustic studies.

The third block launches COMSOL Multiphysics, again in remote mode, and applies the updated mesh to the existing simulation project. The block replaces the previous mesh file with the newly generated one, executes the acoustic simulation, and exports the results in standardized data formats. In this way, the simulation setup remains consistent across iterations, while the geometry is dynamically updated based on the chosen loudspeaker coordinates.

The fourth block is responsible for post-processing. It parses the exported result file, extracts the relevant acoustic metrics, and returns a scalar value of the localized sound power to the user.

Once the workflow has been assembled, it can be executed repeatedly with different loudspeaker positions as input parameters. The entire process—geometry preparation, meshing, simulation, and post-processing — runs automatically without human intervention. This not only reduces the turnaround time for each study but also guarantees consistency across repeated runs. Furthermore, the modular structure of the workflow makes it straightforward to extend, for instance, additional post-processing steps can be added to compute new performance indicators, the COMSOL block can be replaced with another solver if required or a different tool to generate the mesh can be used.

If the user wants to run a calculation for a different geometric model or simulation project, they can do so by replacing the source files in the project.

Workflow extension

Web application

Once the workflow was finalized, it was published as a web application in pSeven Enterprise. End users no longer interact directly with the underlying workflow; instead, they access it through a simplified GUI that guides them in configuring runs and reviewing results. The interface allows users to enter input values (such as loudspeaker coordinates) through predefined fields and, once the run is complete, to directly inspect the post-processed graphs generated by the simulation. In this way, both setup and analysis are consolidated in a single environment, eliminating the need to handle scripts or raw output files.

A key advantage of this approach is that such interfaces in pSeven Enterprise can be created automatically from the workflow and require no manual coding effort. This makes it straightforward to provide intuitive applications tailored to specific tasks, while at the same time lowering the barrier for non-expert users to perform and interpret acoustic studies.

Optimization

In the next step, an additional workflow was assembled to automatically determine the optimal loudspeaker position. It integrates the Design Space Exploration (DSE) block that drives the simulation, which is incorporated via a dynamic reference link to the previously assembled workflow to ensure that any of its modifications are automatically propagated, maintaining consistency and reducing duplication.

Instead of running a single configuration, the DSE block varies the loudspeaker coordinates within the defined design space and calls the automated simulation workflow for each candidate. The resulting performance metrics are collected and evaluated by the optimization algorithm, which guides the search toward improved designs.

To evaluate the optimization workflow, the problem was formulated as follows: maximize the averaged sound power at the driver’s seat location by varying the loudspeaker coordinates within the range of –150 mm to +150 mm.

Surrogate-Based Optimization (SBO) [9] technique was selected as the optimization method, since it is well suited for problems where each function evaluation is computationally expensive. It builds an approximate model of the objective function and uses it to perform the search efficiently, reducing the number of required simulations.

The results, shown in Figure 9, indicate a 3.7% improvement in the objective function compared to the initial loudspeaker position. As expected, when other speakers in the simulation model and averaged sound power for other passengers were not considered, the optimal location of the Front Center Speaker suggested by the algorithm was found in the far corner opposite the driver.

The current study demonstrates the feasibility of the approach. More complex formulations, including multiple objectives and constraints, can be addressed in the same workflow, opening the way for systematic exploration of design alternatives.

Predictive modeling

To further accelerate design exploration, a Gaussian Processes (GP) model [10] was trained to approximate the relationship between loudspeaker position and the localized sound power at the driver’s seat. Once trained, the model can predict this performance metric for new configurations almost instantaneously, avoiding the need for a full simulation. In this paper, the model is trained on a pre-generated dataset; however, in production the dataset will continue to expand as users execute simulations, enabling periodic retraining and steadily improving the model’s accuracy and reliability.

The workflow for model training (Figure 10) consists of three components: The DSE block, the NVH analysis workflow and the Model builder. The DSE block generates a set of loudspeaker positions using LHS algorithm [11] and calls the simulation workflow for each configuration. The resulting dataset, containing input parameters and corresponding outputs, is then passed to the Model builder, which trains the predictive model (also called approximation model, surrogate model, ROM etc.).

Once the model was trained, validation on a separate test sample (Figure 11) yielded a coefficient of determination (R² = 0.98), confirming that the surrogate accurately captures the acoustic behavior within the studied design space.

Such predictive model can later be integrated into the same application built on top of the simulation workflow. Instead of launching a full simulation for every new loudspeaker position, the interface could query the surrogate to provide rapid feedback on the predicted localized sound power. High-fidelity simulations would then be reserved for selected cases, significantly reducing computation time while maintaining confidence in the results.

Conclusion

This article demonstrates how acoustic simulations for loudspeaker placement can be transformed into a repeatable, accessible, and extensible process. By integrating geometry adaptation, meshing, simulation, and result extraction into a single automated workflow, the methodology reduces manual effort and enables design teams to perform studies that would otherwise require specialist expertise.

Described workflows not only support routine evaluations whenever interior layouts change but also extend to advanced applications. Design optimization can guide the search for the best loudspeaker positions within defined constraints, while predictive modeling provides rapid approximations of acoustic performance without running full simulations. Together, these capabilities accelerate design iterations, reduce computational cost, and enhance the integration of acoustic considerations early in the development cycle.

A further advantage of the presented approach is its deployment in a web-native environment. Since workflows and applications are hosted centrally on the server, they can be accessed from any location through a standard web interface, while simulations themselves are executed on remote machines connected to the server. This setup also provides centralized resource management, ensuring that simulation tasks are efficiently scheduled and balanced across available hardware. As a result, multiple users can work in parallel without interfering with each other’s runs, enabling collaborative use of shared resources while maintaining consistent performance and reliability.

Overall, this methodology provides a foundation for simulation-driven framework for automotive audio engineering, enabling systematic exploration of design alternatives and supporting more informed, evidence-based design decisions.

References

[1] P. Newton, “The NAFEMS Simulation Capability Survey 2015”, NAFEMS (2015)

[2] A. J. Svobodnik, “Acoustic Matrix Methods for Woofers, Tweeters, Horns and Small Transducers”, Audio Engineering Society (2005)

[3] A. J. Svobodnik, “CAE as Key Technology for the Multidisciplinary Virtual Product Development of Automotive Audio Systems”, NAFEMS (2011)

[4] A. J. Svobodnik, “Multiphysical Simulation Methods for Loudspeakers - A (Never-)Ending Story?”, Audio Engineering Society (2014)

[5] A. J. Svobodnik, M. Levasseur, and C. Faller, “Fully Digital Development of Automotive Audio Systems”, Audio Engineering Society (2017)

[6] Mvoid Audio Technologies, “The Mvoid® Simulation Process Technology”, Automotive Audio Version, Version 2.4

[7] E. Geddes, H. Blind, “The Localized Sound Power Method”, Audio Engineering Society (1986)

[8] pSeven SAS: “pSeven Enterprise Help”, https://www.pseven.io/assets/files/documentation/pseven-enterprise/v2025.08/en/

[9] pSeven SAS: “Surrogate Based Optimization”, https://www.pseven.io/product/pseven-core/manual/v2025.06/guide/gtopt/sbo.html

[10] pSeven SAS: “Gaussian Processes”, https://www.pseven.io/product/pseven-core/manual/v2025.06/guide/gtapprox/techniques.html#gaussian-processes

[11] pSeven SAS: “Latin Hypercube Sampling”, https://www.pseven.io/product/pseven-core/manual/v2025.07/guide/gtdoe/techniques.html#latin-hypercube-sampling

Authors:
George Biryukov, Application Engineer, pSeven SAS
Alfred Svobodnik, CEO, Mvoid Group