In the frequency domain, broadband mechanical sources are typically identified frequency by frequency using Tikhonov-like regularization strategies.However, such an approach does not exploit the spectral characteristics of the sources to be identified, which can be detrimental to the quality of the identification, especially in the vicinity of the resonance frequencies of the structure.Based on this observation, mixed-norm regularization has been developed and applied with some success.However, this comes at the price of an increase in the computational cost, since the problem is solved for all frequencies at once.In order to reduce the computational cost of the identification procedure, while taking into account the spectral characteristics of the sources to identify, an original frequency-domain Bayesian filter is presented in this contribution.More precisely, the proposed strategy is a frequency-domain application of the Bayesian filtering theory to which Kalman filters belong.To evaluate the identification ability of the proposed approach, a numerical experiment is conducted on a simply-supported beam excited by a broadband point mechanical point force.A comparison with sparse regularization applied at each frequency independently is also proposed.

Air inlets coupled with mechanically controlled ventilation systems are widely used to renew polluted indoor air. They are generally positionned at the top of windows inducing a reduction of the sound insulation. As the harmful consequences of noisy environments on human health are more and more highlighted, it becomes necessary to maximize the sound insulation while ensuring a sufficient fresh air flow. To this end, efficient numerical simulation appears to be a promising way for studying air inlet acoustic behavior: many parameters can be considered without the need to carry out costly and time-consuming laboratory tests. This work aims at developing a reliable numerical model reproducing the acoustic laboratories used by manufacturers for the measurements of air inlet sound reduction index. The low frequency range is studied in the present paper as the measurement uncertainties arising from experimental conditions are the greatest at these frequencies. In order to make the calculations computationally efficient, the proposed model uses a sub-structuring approach called the Patch Transfer Function (PTF) method, and combines analytical or numerical solutions, depending on the subdomain considered. Each subsystem of complex geometries is discretized using finite elements. Conversely, the PTF of simple geometries are analytically computed from a modal decomposition, enriched with a quasi-static correction numerically computed. As empirical improvements pointed out the benefits of the addition of melamine foams, porous material modeling is introduced in the study based on an equivalent fluid model.

During their lifetime, structures are usually subjected to some mechanical shocks that generate high levels of vibration that can damage the structure itself as well as the embedded devices. However, the characteristics of these shocks (location, time history, maximum intensity, etc.) are often unknown due to the inaccessibility of the excitation region for direct force measurements or the inability to instrument the system. Therefore, inverse methods have been developed to quantify these complex excitations. Recently, a Bayesian formulation of the input-state estimation problem for linear systems has been proposed by the authors, which unifies most of the state-of-the-art filters. In this paper, we present two novel Bayesian filters derived from this framework: (a) the Correlated Dual Kalman Filter (CDKF), which is one of the filters that naturally follows from the unified Bayesian formulation, and (b) the Component Bayesian Filter (CBF), which promotes spatial sparsity of the input vector. Essentially, these filters differ in the prior distributions used to convey information about the spatial distribution of the input vector to be identified. The performance of these filters is evaluated through a numerical experiment and a real-world application aimed at reconstructing a sparse and transient excitation acting on a linear structure. A comparison of these original filters with other Bayesian filters proposed in the literature is also proposed. In particular, the numerical experiment allows to study the performance of the proposed filters in different scenarios, such as the number of sensors, the measurement noise level or the sensor configuration, while the real-world application allows to test them in operational conditions. More specifically, it is shown that filters promoting the spatial sparsity of the input vector, such as CBF, lead to a consistent identified excitation profile when acceleration measurements are the only available data.

This paper introduces a novel strategy for point force localization in the frequency domain, based on metamodeling techniques and independent of the excitation level. More precisely, the ability of well-established techniques, such as Polynomial Chaos expansion or Universal Kriging, in providing accurate surrogate models for locating a point force through an optimization procedure is evaluated. The proposed methodology is applied in a purely data-driven context. Obtained results highlight the good performance of the proposed strategy for relatively small data sets, as well as its robustness to noise in both training and deployment phases.

The present paper introduces a novel Bayesian filter for estimating mechanical excitation sources in the time domain from a set of vibration measurements. The proposed filter is derived from a very general Bayesian formulation, unifying most of the state-of-the-art recursive filters developed in the last decade for solving input-state estimation problems. More specifically, the proposed Bayesian filter allows promoting the spatial sparsity of the estimated input vector, by assuming that the predicted input vector is a random vector with independent and identically distributed components following a generalized Gaussian distribution. To properly estimate the most probable parameters of the latter probability distribution, a nested Bayesian optimization is implemented. The validity of the proposed approach, called Sparse adaptive Bayesian Filter, is assessed both numerically and experimentally. In particular, the comparisons performed with some state-of-the-art filters show that the proposed strategy outperforms the existing filters in terms of input estimation accuracy and avoids the so-called drift effect.

The acoustic performances of building elements such as windows are carried out in laboratory according to standards. In addition to the high cost of the experimental tests, the measurements at low frequencies face some difficulties such as the lack of reproducibility, the rooms' modal behaviour effect and the diffuseness of the acoustic field. To separately study each source of deviation from the ideal experimental situation, four numerical configurations, based on experimental conditions, are proposed to characterize the transmission loss (TL) of an Insulation Glazing Unit (IGU) below 500 Hz. The effect of the emitting and receiving rooms with a comparison to the ideal configuration which has a free field on both sides of the IGU are investigated. The numerical model used for the IGU is calibrated from an Experimental Modal Analysis. As expected, TL results show that there is a significant effect of the modal behavior and the acoustic properties of the rooms at low frequencies. Numerical results are compared to those obtained from experimental tests and a good agreement in the all frequency range of interest is observed. In addition, parametric studies are carried out to investigate the influence of the variation of some properties of the studied structure such as the structural damping and the panel's thickness. (C) 2021 Elsevier Ltd. All rights reserved.

Input estimation remains an important problem for the structural dynamics community as evidenced by the abundant literature dedicated to this topic in the recent years. Generally speaking, inverse methods can be classified into two groups. The first group includes methods that are specifically designed to solve the inverse problem in the time or frequency domains. In the time domain, one can cite Kalman-like approaches [1?3] or dynamic programming [4?6], while, in the frequency domain, methods based on the filtering of the equation of motion of structures, such as beams, cylindrical shells or This paper implements a generalized multiplicative regularization for estimating the mechanical loads acting on a linear structure. The proposed strategy extends the ordinary multiplicative regularization, previously published by the authors, by introducing an extra tuning parameter, which is determined through an original iterative procedure. To assess the practical interest and the overall performances of the proposed approach, numerical and real-world applications are proposed. Obtained results illustrate the influence of the extra tuning parameter according to the measurement noise level and highlight the benefits brought by the generalized multiplicative regularization in terms of solution accuracy. (c) 2021 Elsevier Ltd. All rights reserved.

This work focuses on the numerical prediction of the sound transmission of wooden windows in the low frequency range. In this context, the finite element method is used to solve the multiphysics problem. This choice is justified by the fact that this approach is suitable for the resolution of fluid-structure interaction problems in low frequencies, due in particular to its flexibility in taking into account the coupling between domains and the geometrical and material complexities of the structures. To reach the desired objective, experimental modal analyses of the main components of a window, and then of a complete one, are performed in order to calibrate the numerical models. Then, a configuration that combines free-fields on both sides of the structure is employed to evaluate the intrinsic acoustic response of the window. The numerical results for a symmetric and an asymmetric glazing are compared to experimental ones to evaluate the efficiency and validity of the developed models.

This paper introduces a multi-parameter multiplicative regularization for force reconstruction problems. This approach allows exploiting the local prior information available on the sources to identify, while determining the related regularization parameters in an elegant and efficient manner. The aim of this paper is to assess the applicability of a multi-parameter regularization strategy compared to a single parameter formulation for reconstructing the external sources acting on a mechanical structure. A particular attention is also paid to the practical resolution of the regularization problem by implementing an original Iteratively Reweighted algorithm derived from the direct application of the first-order optimality condition. The performance of the proposed algorithm in terms of solution accuracy is compared with a more classical implementation based on an Iteratively Reweighted Least-Squares procedure. The interest of the proposed multi-parameter strategy is assessed numerically. Obtained results demonstrates that consistent reconstructions are obtained for high and moderate measurement noise level whatever the formulation considered (i.e. single or multi-parameter) provided that the suitable resolution algorithm is implemented. For very and extremely noisy input data, the single parameter strategy is more robust than the multi-parameter approach.

In a paper, recently published in Mechanical Systems and Signal Processing, a multiplicative mixed-norm regularization has been introduced for solving space-frequency force reconstruction problems. Originally, the solution is obtained from an Iteratively Reweighted Least-Squares (IRLS) algorithm. However, as shown in this communication, such an algorithm exhibits a lack of robustness regarding the measurement noise level. For this reason, a novel iterative resolution algorithm, based on the first-order optimality condition, is introduced. From a numerical experiment, it is shown that the proposed algorithm exhibits a better robustness than the IRLS algorithm initially implemented for solving force reconstruction problems in the frequency domain. (C) 2020 Elsevier Ltd. All rights reserved.

The acoustic performances of building elements such as windows are performed in laboratory according to standards. In addition to the high cost of the experimental tests, the measurements at low frequencies, face some difficulties such as the lack of reproducibility, the diffuseness of the acoustic field and the effect of the modal behaviour of the rooms. To overcome this, a numerical analysis of the transmission loss of a double-glazing structure is developed in this work. To this end, four numerical configurations, based on experimental conditions, are proposed. The differences concern the modeling of the emitting and receiving rooms. The numerical model used for the double-glazing was calibrated through the Experimental Model Analysis. Results show that there is a significant effect of the rooms on the transmission loss at low frequencies and so of its properties such as the acoustic absorption. A comparison with experimental results is also established to validate the chosen configuration with which parametric analyses are carried out, however, results are not presented in this paper.

Kalman-type filtering tends to become one of the favorite approaches for solving joint input-state estimation problems in the structural dynamics community. This article focuses on the applicability of the Augmented Kalman Filter (AKF) for reconstructing mechanical sources, addressing a set of practical issues that are frequently encountered in the engineering practice. In particular, this paper aims to help the reader to better apprehend some of the advantages and limitations of the application of the AKF in the context of purely input estimation problems. The present paper is not a simple collection of test cases, since it introduces a novel state-space representation of dynamical systems, based on the generalized-α method, as well as further insights in the tuning of Kalman filters from the Bayesian perspective. In this work, the various practical situations considered lead us to recommend to employ collocated acceleration measurements, when reconstructing excitation sources from the AKF. It is also demonstrated that the violation of some of the feasibility conditions proposed in the literature doesn't necessarily imply the failure of the estimation process.

Tikhonov and LASSO regularizations are commonly used to solve force reconstruction problems in time domain. Unfortunately, these particular forms of additive regularization are not well adapted to tackle both localization and time reconstruction problems simultaneously, since they are generally restricted to the reconstruction of sources sharing the same space and time characteristics. To alleviate this limitation, a multiplicative space-time regularization is introduced. The proposed regularization strategy takes advantage of one's prior knowledge of the space-time characteristics of excitation sources. It also introduces a novel reconstruction model based on the generalized-a method, which is unconditionally stable and second-order accurate. The validity of the proposed method is assessed numerically and experimentally. In particular, comparisons with standard regularization terms point out the practical benefit in exploiting both spatial and temporal prior information simultaneously in terms of quality and robustness of reconstructed solutions. (C) 2018 Elsevier Ltd. All rights reserved.

In a paper, recently published in Mechanical Systems and Signal Processing, we have proposed a full Bayesian inference for reconstructing mechanical sources acting on a linear and time invariant structure. The main interest of this approach is to propose an estimation of all the parameters of the model and quantify the posterior uncertainty associated to each parameter. Since all the necessary information about the problem is available, statistical measures, such as the mean, the median and the mode of the solution, can be easily estimated. In many practical situations, however, one only wants to determine the most probable parameters given the available data. Consequently, it is not relevant to implement a full Bayesian inference to only extract a point estimate. To overcome this potential issue, this paper introduces an optimal Bayesian regularization aiming at computing the Maximum a Posteriori estimate of the Bayesian formulation previously introduced by the authors. In doing so, the most probable parameters are obtained without heavy computations. The validity of the proposed method is assessed numerically and experimentally. In particular, obtained results highlight the ability of the proposed regularization strategy in computing solutions with a minimal amount of prior information on the sources to identify. (C) 2019 Elsevier Ltd. All rights reserved.

In time domain, force reconstruction problems are commonly solved from Tikhonov and LASSO regularizations. Practically, these approaches can lead to inaccurate reconstructions, if the sources to identify don’t share the same space-time characteristics or the corresponding force vector doesn’t exhibit the desired structure. To alleviate this potential drawback, we have recently introduced a multiplicative space-time regularization that allows exploiting one’s prior knowledge of the spatial distribution of the sources as well as their time history. In this contribution, the proposed regularization strategy is compared to the multiplicative Tikhonov and LASSO regularizations through an experimental application to point out the practical interest of exploiting simultaneously both spatial and temporal prior information in terms of quality and robustness of the reconstructed excitation sources.

The multiplicative ℓq-regularization has been recently introduced in structural dynamics for solving force reconstruction problems. Practically, the resolution of this regularization strategy requires the implementation of an iterative procedure. To this end, an Iteratively Reweighted Least-Squares algorithm has been originally implemented. The core idea of this algorithm is to replace the direct resolution of the inverse problem by an equivalent iterative procedure having an explicit and unique solution at each iteration. However, the exploitation of this very general idea allows defining other Iteratively Reweighted schemes. The present paper aims at comparing the overall performances of three particular Iteratively Reweighted algorithms for solving force reconstruction problems derived from a more general and original iterative procedure. The numerical applications proposed in this contribution highlight the ability of the considered algorithms in providing consistent regularized solutions with respect to various parameters such as the measurement noise level or the tolerance chosen to stop the iterative process.

Compared to numerous theoretical studies, the problem of experimentally realizing supported conditions on plane panels has received very little attention. A technique to setup a simply supported rectangular plane panel for laboratory vibroacoustic tests is described. Several application cases are reported, including three panels built in Groupe d'Acoustique de l'Universite de Sherbrooke (GAUS, Sherbrooke, Canada), three panels built at Laboratoire de Mecanique des Structures et des Systemes Couples (LMSSC, Paris, France) and one at Laboratoire Vibrations Acoustique (LVA, Lyon, France). Covered subjects include vibration and sound radiation under deterministic and random excitations (diffuse acoustic field, turbulent boundary layer), similitude laws and passive control of vibrations using piezoelectric patches or viscoelastic treatments. All obtained results highlight the interest of having access to a laboratory tool that behaves closely to an exact mathematical model, and confirm that such a tool can be reproduced and generalized between laboratories.