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In this paper, we discuss the application of the constitutive relation error (CRE) to model updating and validation in the context of uncertain measurements. First, a parallel is drawn between the CRE method and a general theory for inverse problems proposed by Tarantola. Then, an extension of the classical CRE method considering uncertain measurements is proposed. It is shown that the proposed mechanics‐based approach for model validation is very effective in filtering noise in the experimental data. The method is applied to an industrial structure, the SYLDA5, which is a satellite support for Ariane5. The results demonstrate the robustness of the method in actual industrial situations.

In recent years, the mechanical industries began to apply many investments in research and technological development to obtain efficient methods to analyze the integrity of structures and prevent disasters and/or accidents, ensuring people’s lives and preventing economic losses. Any structure, whether mechanical or aeronautical, before being put into use undergoes a structural integrity assessment and testing. In this case, non-destructive evaluations are performed, aiming to estimate the degree of safety and reliability of the structure. For this, there are techniques traditionally used such as ultrasonic inspection, X-ray, acoustic emission tests, among other techniques. The traditional techniques may even have a good instrumental apparatus and be well formulated for structural integrity assessment; however, these techniques cannot meet growing industrial needs, even more so when structures are in motion. The purpose of this paper is to demonstrate artificial immune systems (AISs), ate and strengthen the emergence of an innovative technological tool, the biological immune systems and AISs, and these are presented as computing methods in the field of structural health monitoring (SHM).

The concept of SHM is based on a fault detection mechanism used in industries, and in other applications, involving the observation of a structure or a mechanical system. This observation occurs through the dynamic response of periodic measurements, later related to the statistical analysis, determining the integrity of the system. This study aims to develop a methodology that identifies and classifies a signal in normal signals or in faults, using an algorithm based on artificial immunological systems, being the negative selection algorithm, and later, this algorithm classifies the failures in probabilities of failure and degree of fault severity. The results demonstrate that the proposed SHM is efficient and robust for prognosis and failure detection.

The present study aims to develop different fast access methodologies for the prognosis and detection of failures, classifying and judging the types of failures based on AISs. The authors declare that the present study was neither published in any other vehicle of scientific information nor is under consideration for publication in another scientific journal, and that this paper strictly followed the ethical procedures of research and publication as requested.

This study is original by the fact that conventional structural integrity monitoring methods need improvements, which intelligent computing techniques can satisfy. Intelligent techniques are tools inspired by natural and/or biological processes and belong to the field of computational intelligence. They present good results in problems of pattern recognition and diagnosis and thus can be adapted to solve problems of monitoring and identifying structural failures in mechanical and aeronautical engineering. Thus, the proposal of this study demonstrates and strengthens the emergence of an innovative technological tool, the biological immune system and the AIS, and these are presented as computation methods in the field of SHM in rotating systems – a topic not yet addressed in the literature.

The purpose of this study is to review the existing fatigue and vibration-based structural health monitoring techniques and highlight the advantages of combining both approaches.

Fatigue monitoring requires a fatigue model of the material, the stresses at specific points of the structure, a cycle counting technique and a fatigue damage criterion. Firstly, this paper reviews existing structural health monitoring (SHM) techniques, addresses their principal classifications and presents the main characteristics of each technique, with a particular emphasis on modal-based methodologies. Automated modal analysis, damage detection and localisation techniques are also reviewed. Fatigue monitoring is an SHM technique which evaluate the structural fatigue damage in real time. Stress estimation techniques and damage accumulation models based on the S-N field and the Miner rule are also reviewed in this paper.

A vast amount of research has been carried out in the field of SHM. The literature about fatigue calculation, fatigue testing, fatigue modelling and remaining fatigue life is also extensive. However, the number of publications related to monitor the fatigue process is scarce. A methodology to perform real-time structural fatigue monitoring, in both time and frequency domains, is presented.

Fatigue monitoring can be combined (applied simultaneously) with other vibration-based SHM techniques, which might significantly increase the reliability of the monitoring techniques.

The determination of the vibration induced by an aircraft impact on an industrial structure requires dynamic studies. The determination of the response by using classical finite element method associated with explicit numerical schemes requires significant calculation time, especially during the transient stage. This kind of calculation requires several load cases to be analyzed in order to consider a wide range of scenarios. Moreover, a large frequency range has to be appropriately considered and therefore the mesh has to be very fine, resulting in a refined time discretization. The purpose of this paper is to develop new ways for calculating the shaking of reinforced concrete structures following a commercial aircraft impact (see Figure 1). The cutoff frequency for this type of loading is typically within the 50-100 Hz range, which would be referred to as the medium-frequency range.

Taking into account this type of problem and assuming that the structure is appropriately sized to withstand an aircraft impact, the vibrations induced by the shock bring about shaking of the structure. Then these vibrations can travel along the containment building, as directly linked with the impact zone, but also in the inner part of the structure due to the connection with the containment building by the raft. So the excited frequency range, due to the impact of a commercial aircraft, contains two frequency ranges: low frequencies (less than ten wavelengths in the structure) and medium frequencies (between ten and 100 wavelengths). The strategy, which is presented in this paper, is inscribed in the context of the verification of inner equipment under this kind of shaking. The non-linear impact zone is assumed to have been delimited with classical finite element simulations. In this paper the authors only focus on the response of the linear part of the structure. This phenomenon induces a non-linear localized area around the impact zone.

So the medium frequencies can therefore induce significant displacements and stresses at the level of equipment and thus cause damage if the structure is not dimensioning to this frequency range.

In this context the use of finite elements method for the resolution of the shaking implies a spatial discretization in correlation with the number of wavelengths to represent, and thus a long computation time especially for medium frequencies. That is why in the case of a coarse mesh the medium-frequency range is ignored. For example, a concrete structure with a characteristic dimension of about 30 and 1 m of thickness, may not represent frequencies higher than 16 Hz with a mesh size of 1 m (assuming ten elements per wavelength).

The paper includes implications for proper dimensioning civil engineering structures subjected to a load case containing a large frequency range.

This paper shows the gain of the strategy using appropriate method to medium frequencies compared to conventional method such as finite elements.

This paper aims to present an approach for calibrating the numerical models of dynamical systems that have spatially localized nonlinear components. The approach implements the extended constitutive relation error (ECRE) method using multi-harmonic coefficients and is conceived to separate the errors in the representation of the global, linear and local, nonlinear components of the dynamical system through a two-step process.

The first step focuses on the system’s predominantly linear dynamic response under a low magnitude periodic excitation. In this step, the discrepancy between measured and predicted multi-harmonic coefficients is calculated in terms of residual energy. This residual energy is in turn used to spatially locate errors in the model, through which one can identify the erroneous model inputs which govern the linear behavior that need to be calibrated. The second step involves measuring the system’s nonlinear dynamic response under a high magnitude periodic excitation. In this step, the response measurements under both low and high magnitude excitation are used to iteratively calibrate the identified linear and nonlinear input parameters.

When model error is present in both linear and nonlinear components, the proposed iterative combined multi-harmonic balance method (MHB)-ECRE calibration approach has shown superiority to the conventional MHB-ECRE method, while providing more reliable calibration results of the nonlinear parameter with less dependency on a priori knowledge of the associated linear system.

This two-step process is advantageous as it reduces the confounding effects of the uncertain model parameters associated with the linear and locally nonlinear components of the system.

To propose and develop an identification method of material parameters from dynamics test in the presence of extensively corrupted measurements.

The method we propose, which is based on the use of the error in constitutive relation for identification problems in the framework of transient dynamics, leads to nonstandard wave propagation problems. For solving this numerical difficulty, we used the transition matrix method for short‐duration tests and the combined Riccati constant/transition matrix approach for long‐duration tests.

A numerical strategy adapted to the problem. Results obtained appears to be insensitive to perturbation of measurements up to a very high level of perturbation.

Only simple case of elastic bar have been treated so far.

Without any a priori information on the level of perturbation, this method is robust with respect to the perturbation. A coupling of two resolution methods allows to deal with problem of arbitrary duration.

This paper deals with numerical techniques dedicated to the predictive calculation of complex structures undergoing medium‐frequency vibrations. This field presents challenging difficulties. The first difficulty is the development of an efficient computational method because with the traditional finite element method (FEM), as the frequency increases, it becomes more expensive to control the pollution error. The second difficulty is the availability of sufficiently realistic joint models to take into account damping phenomena because in vibration problems dissipation controls the magnitude of the response directly.

We use the Variational Theory of Complex Rays (VTCR), an approach which effectively avoids the difficulties encountered with traditional FE techniques. Using two‐scale shape functions which verify the dynamic equation and the constitutive relation within each substructure, the VTCR can be viewed as a means of expressing the power balance at the different interfaces between substructures in variational form. New joint models which include heterogeneous mass, stiffness and damping are introduced to deal with the second difficulty.

This paper focuses on a new, substructured version of the VTCR which enables us to separate the realistically modeled substructures from the less accurate joints. The equations of the substructures are enforced exactly, whereas the interface equations are verified approximately through the minimization of an L² residual. We show that this new formulation gives good results compared to the traditional VTCR or the FEM.

Although the examples presented in this paper are very simple, this new formulation shoult encounter no difficulties when dealing with more complex assemblies composed of several plates, beams, shells,…

This new, substructured VTCR approach provides more flexibility in the improvement of joint models, for example by carrying out experimental measurements on real structures.

A new approach called the “variational theory of complex rays” (VTCR) is developed for calculating the vibrations of weakly damped elastic structures in the medium‐frequency range. Here, the emphasis is put on the most fundamental aspects. The effective quantities (elastic energy, vibration intensity, etc.) are evaluated after solving a small system of equations which does not derive from a finite element discretization of the structure. Numerical examples related to plates show the appeal and the possibilities of the VTCR.

Denoising of the vibration signal is crucial to identify a structure's damage. Based on noise frequency character, the “real” vibration signal can be gotten. The purpose of this paper is to propose a novel method for denoising a signal based on the wavelet transform.

The vibration signal with noise which can be collected by wireless network is decomposed by wavelet transform. In order to select optimal level of wavelet decomposition, based on noise's frequency, power spectral density is used. A soft thresholding method based on minimum mean‐variance is used for vibration signal de‐noising with Gaussian noise.

A novel method has been described in his paper. Based on the relationship between vibration signal's character and noise frequency, the way to get rid of noise is combined wavelet transform with power spectral density.

In order to select optimal level of wavelet decomposition, based on noise's frequency, power spectral density is used. A soft thresholding method based on minimum mean‐variance is used for vibration signal denoising with Gaussian noise.

This paper aims to focus on the assessment of the ability of computer models with imperfect functional forms and uncertain input parameters to represent reality.

In this assessment, both the agreement between a model’s predictions and available experiments and the robustness of this agreement to uncertainty have been evaluated. The concept of satisfying boundaries to represent input parameter sets that yield model predictions with acceptable fidelity to observed experiments has been introduced.

Satisfying boundaries provide several useful indicators for model assessment, and when calculated for varying fidelity thresholds and input parameter uncertainties, reveal the trade-off between the robustness to uncertainty in model parameters, the threshold for satisfactory fidelity and the probability of satisfying the given fidelity threshold. Using a controlled case-study example, important modeling decisions such as acceptable level of uncertainty, fidelity requirements and resource allocation for additional experiments are shown.

Traditional methods of model assessment are solely based on fidelity to experiments, leading to a single parameter set that is considered fidelity-optimal, which essentially represents the values which yield the optimal compensation between various sources of errors and uncertainties. Rather than maximizing fidelity, this study advocates for basing model assessment on the model’s ability to satisfy a required fidelity (or error tolerance). Evaluating the trade-off between error tolerance, parameter uncertainty and probability of satisfying this predefined error threshold provides us with a powerful tool for model assessment and resource allocation.