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Ensuring the early detection of structural issues in aircraft is crucial for preserving human lives. One effective approach involves identifying cracks in composite structures. This paper employs experimental modal analysis and a multi-variable Gaussian process regression method to detect and locate cracks in glass fiber composite beams.

The present study proposes Gaussian process regression model trained by the first three natural frequencies determined experimentally using a roving impact hammer method with crystal four-channel analyzer, uniaxial accelerometer and experimental modal analysis software. The first three natural frequencies of the cracked composite beams obtained from experimental modal analysis are used to train a multi-variable Gaussian process regression model for crack localization. Radial basis function is used as a kernel function, and hyperparameters are optimized using the negative log marginal likelihood function. Bayesian conditional probability likelihood function is used to estimate the mean and variance for crack localization in composite structures.

The efficiency of Gaussian process regression is improved in the present work with the normalization of input data. The fitted Gaussian process regression model validates with experimental modal analysis for crack localization in composite structures. The discrepancy between predicted and measured values is 1.8%, indicating strong agreement between the experimental modal analysis and Gaussian process regression methods. Compared to other recent methods in the literature, this approach significantly improves efficiency and reduces error from 18.4% to 1.8%. Gaussian process regression is an efficient machine learning algorithm for crack localization in composite structures.

The experimental modal analysis results are first utilized for crack localization in cracked composite structures. Additionally, the input data are normalized and employed in a machine learning algorithm, such as the multi-variable Gaussian process regression method, to efficiently determine the crack location in these structures.

One of the biggest problems in an R&D process is the acquisition of information about the structure dynamic loads, which are needed to reliably prove the structure's durability. This paper aims to present an innovative method for simulating stationary Gaussian random processes, which is based on the conditional probability density function (PDF) approach.

The basic information on the structure dynamic loads is first obtained by short‐duration measurements on prototypes or the structure itself. These data are then used to simulate the expected structure load states during operations. A theoretical background is presented first, which is followed by the application of the method.

The results show that the spectral characteristics of the original and simulated Gaussian random processes are very similar, if the influential range of the conditional PDF is properly chosen.

The method can be applied for simulating random loads of structures, and excitations of dynamic systems, for example.

The innovative simulation approach could be helpful to engineers in the early phases of the new product development process.

A method for approximation of the Shannon entropy of Gaussian photon‐counting processes with infinite history was constructed on the memory function of these processes, described by autoregressive‐integrated moving average (ARIMA) models. Most frequently, photon‐counting processes are stationary or nonstationary multidimensional Gaussian discrete‐time stochastic ones which justify the use of the ARIMA models. Starting from the memory function, a memory time‐equivalent finite autoregressive representation of a given process with infinite history, i.e. a stationary finite‐order Gaussian Markov chain, was determined, then corresponding autocorrelation matrices were calculated from the truncated memory function using the Yule‐Walker equations, and an autocorrelation‐based formula for approximation of the entropy of the process through the entropy of its stationary Markovian representation was given. An ARMA(1,1) process together with its stationary (MA(1)) or nonstationary (IMA(0,1,1)) boundary cases were considered to demonstrate opposite changes in the entropy as the memory time increases at a fixed variance of the process: the entropy was found to decrease for stationary processes and increase for nonstationary ones. It was also found on experimental examples (perturbed human neutrophils and yeast cells) that those changes can be reversed by opposite changes in the process variance. The method allows us to determine, at any desired accuracy, the Shannon entropy of time‐discrete stochastic processes, and reveals new aspects of the relationship between the process' stationarity, memory, entropy and heteroskedasticity.

We propose a generic algorithm for numerically accurate likelihood evaluation of a broad class of spatial models characterized by a high-dimensional latent Gaussian process and non-Gaussian response variables. The class of models under consideration includes specifications for discrete choices, event counts and limited-dependent variables (truncation, censoring, and sample selection) among others. Our algorithm relies upon a novel implementation of efficient importance sampling (EIS) specifically designed to exploit typical sparsity of high-dimensional spatial precision (or covariance) matrices. It is numerically very accurate and computationally feasible even for very high-dimensional latent processes. Thus, maximum likelihood (ML) estimation of high-dimensional non-Gaussian spatial models, hitherto considered to be computationally prohibitive, becomes feasible. We illustrate our approach with ML estimation of a spatial probit for US presidential voting decisions and spatial count data models (Poisson and Negbin) for firm location choices.

In the dynamical analysis of engineering systems, running a detailed high‐resolution finite element model can be expensive even for obtaining the dynamic response at few frequency points. To address this problem, this paper aims to investigate the possibility of representing the output of an expensive computer code as a Gaussian stochastic process.

The Gaussian process emulator method is discussed and then applied to both simulated and experimentally measured data from the frequency response of a cantilever plate excited by a harmonic force. The dynamic response over a frequency range is approximated using only a small number of response values, obtained both by running a finite element model at carefully selected frequency points and from experimental measurements. The results are then validated applying some adequacy diagnostics.

It is shown that the Gaussian process emulator method can be an effective predictive tool for medium and high‐frequency vibration problems, whenever the data are expensive to obtain, either from a computer‐intensive code or a resource‐consuming experiment.

Although Gaussian process emulators have been used in other disciplines, there is no knowledge of it having been implemented for structural dynamic analyses and it has good potential for this area of engineering.

We discuss the problem of the classification of continuous‐amplitude stochastic signals by their variety. It is shown in this context that continuous Gaussian processes must be characterized by three parameters which are intimately related to the ability of the process to carry information. Finally, conservation laws for the variety of stochastic signals under feedback are given, and the relation of variance and variety is discussed.

This paper aims to present an approach for the probabilistic characterization of the response of linear structural systems subjected to random time-dependent non-Gaussian actions.

Its fundamental property is working directly on the probability density functions of the actions and responses. This avoids passing through the evaluation of the response statistical moments or cumulants, reducing the computational effort in a consistent measure.

It is an efficient method, for both its computational effort and its accuracy, above all when the input and output processes are strongly non-Gaussian.

This approach can be considered as a dynamic generalization of the probability transformation method recently used for static applications.

A method is evoked which produces a non‐stationary (and possibly non‐Gaussian) stochastic process with given statistics to second order. The method is useful either for simulation solution of stochastic differential equations or stochastic modeling of system performance.

Recently, Stein et al. (2016) studied theoretical properties and parameter estimation of continuous time processes derived as solutions of a generalized Langevin equation (GLE). In this paper, the authors extend the model to a wider class of memory kernels and then propose a bond and bond option valuation model based on the extension of the generalized Langevin process of Stein et al. (2016).

Bond and bond option pricing based on the proposed interest rate models presents new difficulties as the standard partial differential equation method of stochastic calculus for bond pricing cannot be used directly. The authors obtain bond and bond option prices by finding the closed form expression of the conditional characteristic function of the integrated short rate process driven by a general Lévy noise.

The authors obtain zero-coupon default-free bond and bond option prices for short rate models driven by a variety of Lévy processes, which include Vasicek model and the short rate model obtained by solving a second-order Langevin stochastic differential equation (SDE) as special cases.

Bond and bond option pricing plays an important role in capital markets and risk management. In this paper, the authors derive closed form expressions for bond and bond option prices for a wider class of interest rate models including second-order SDE models. Closed form expressions may be especially instrumental in facilitating parameter estimation in these models.

The purpose of this study is to research the influence of wire’s surface topography on interwire contact performance of simple spiral strand.

The mechanical model of the simple spiral strand imposed by a tensile load is first established, into which the surface topography, Poisson’s ratio effect and radial deformation are incorporated simultaneously. Meanwhile, the Gaussian and non-Gaussian rough surfaces of the steel wires are obtained with the fast Fourier transform (FFT) and digital filter technology. Then, the rough interwire contact performance of the simple spiral strand is calculated by using conjugate gradient method and FFT.

As compared with smooth wire surface, both the longitudinal orientation for the Gaussian wire surface and large kurtosis or small skewness for the non-Gaussian surface yield a small contact pressure and stress.

This study conducts detailed discussion of the influence of wire’s surface topography on the interwire contact performance for the simple spiral strand and gives a beneficial reference for the design and application of a wire rope.