This paper explores stochastic maintenance for a large fleet of structures, focusing on the example of bridges. The approach involves replacing the states of degradation of a facility with a probability distribution over the states. Even though the degradation state of each individual structure may be available, it is often more convenient to work with the proportions of structures in each degradation state. This is particularly useful when incorporating constraints such as limited maintenance budgets or desired quality levels for the overall fleet. Probability distributions are commonly used when the initial state is unknown or when degradation is observed with error (i.e., under partial observation). However, the same methodology is applied here in a different context. Full information may be available, but using it directly can be too complex. Instead, partial information is used to reduce this complexity. The theory of Markov Decision Processes (MDPs) provides a framework for many applications in Operations Research and Management Science, and stochastic maintenance has become one such application. When working with probability distributions over states instead of individual states, the framework is referred to as a mean-field MDP. In this setting, the dynamic programming methodology for MDPs is extended to the mean-field case, tailored to fleets of structures. Both value iteration and policy iteration algorithms are considered to characterize the value function and determine the optimal (randomized) control policy.

In this paper, we derive the asymptotic properties of the generalized least squares estimator (GLSE) of autoregressive models endowed with fractional Gaussian noise (the so-called fractional autoregressive models). We establish the consistency and the asymptotic normality of the GLSE. Some simulation studies and a financial application are presented to corroborate our theoretical work.

A new method has been proposed to analyze acoustic emission (AE) signals obtained from a prestressed concrete viaduct to realize the cracking mechanisms that evolve during the passage of trucks/cars. This new method exploits the information contained in narrow partial powers (PPs) bands of the acquired AE signals. The narrow PP bands are found to be extremely sensitive to the evolving damage modes in concrete, both in the case of in situ and laboratory experiments. Results show that the classification of trucks is possible using the cracking information contained in the narrow PP bands of the acquired AE signals during the passage of trucks. AE-monitored laboratory bending experiments have been performed on reinforced concrete T-beams. The effectiveness of the proposed narrow PP bands in the discrimination of damage modes in the beams is found to be overwhelming. The proposed method has a unique advantage in visualizing the frequency content of a large number of AE signals by using the narrow PP-based heatmap. This study consists of simultaneous measurement of strain and AE during the passage of trucks/cars, and correspondence between the two types of data has also been presented. This research work shows that frequency information of AE signals can be used for monitoring of prestressed/RC concrete structures.

Fast and asymptotically efficient one-step and two-step estimation procedures for the parameters of the location-scale t and log(t) distributions are proposed. They are based on two possible initial guess estimators: the first one is the maximum likelihood estimator on a subsample, and the second one is a combination of the empirical median for the location, a slowly converging Hill estimator for the degree of freedom, and a maximum likelihood type estimator for the scale. Then, one or two steps of the Fisher scoring gradient descent method are done in order to correct the initial estimation and reach asymptotical efficiency. The performances of the estimation procedures are evaluated on samples of finite size in terms of root mean square error and computation time. An application in economics is also proposed.

A fast calibration procedure is presented for multivariate regression models with categorical explanatory variables. The marginal distributions are modeled using generalized linear models (GLMs), and the dependency structure between coordinates is captured via a parametric copula, yielding a flexible and interpretable framework for multivariate analysis. While the inference functions for margins (IFM) method, based on a two-step estimation separating marginals and copula, offers practical simplification over full maximum likelihood estimation (MLE), it remains computationally intensive in high-dimensional settings involving numerous covariates, modalities, or large sample sizes. To overcome this limitation, a one-step estimator is introduced, relying on a closed-form initial guess previously developed for univariate GLMs with categorical covariates. Compared to both full MLE and classical IFM-MLE, the proposed method significantly reduces computation time while maintaining similar asymptotic variance. The approach is validated through a simulation analysis and an application to real-world insurance data.

In this article, the one-step estimation procedure is presented for generalized linear models. In these models, the maximum likelihood estimator, which is asymptotically efficient, has no closed-form and gradient-descent methods are generally used for its numerical computation. Nevertheless, when the amount of data is large and/or the number of explanatory variables is high, then the computations can be very consuming. To overcome this difficulty, the one-step estimation procedure is used, which is based on an initial (inefficient) guess estimator and a single step of the Fisher scoring. The main advantage of this procedure is that only one iterative step is required to achieve the asymptotic efficiency. The results are validated numerically by means of Monte-Carlo simulations.The estimation procedure is used to fit generalized linear models for climate risk insurance data.

In this paper, we investigate the optimal design problem for asymptotically efficient estimation in the context of controlled Ornstein-Uhlenbeck processes. The study builds a connection between statistical optimal design and ergodic control theories. We focus on the estimation of an unknown drift parameter with continuous observations and the possibility of an additive admissible control. Two notions of statistical asymptotic efficiency are examined in the controlled setting. The first relies on maximizing the Fisher information with respect to controls on finite horizons, while the second is based on ergodic (infinite-horizon) controls. We establish that both definitions lead to the same asymptotic variance in the case of deterministic controls, and also provide results for stochastic controls.

The joint parametric estimation of the drift coefficient, the scale coefficient and the jump activity in stochastic differential equations driven by a symmetric stable L & eacute;vy process is considered, based on high-frequency observations. Firstly, the LAMN property for the corresponding Euler-type scheme is proven and lower bounds for the estimation risk in this setting are deduced. When the approximation scheme experiment is asymptotically equivalent to the original one, these bounds can be transferred. Secondly, a one-step procedure is proposed which is shown to be fast and asymptotically normal and even asymptotically efficient when the scale coefficient is constant. The performances in terms of asymptotical variance and computation time on samples of finite size are illustrated with simulations.

This work presents an acoustic emission (AE) based method, named a series of narrow partial power bands (SN2PB), to monitor the damage mechanisms within reinforced concrete beams during quasi-static bending tests. Unlike conventional time-domain methods, which give a global view of the involved cracking modes, SN2PB has the advantage of obtaining information on cracking modes within each AE hit in reduced frequency bands. SN2PB is applied by dividing the frequency content of each AE signal into narrow bands. Results show that the same AE signal can contain shear and tension cracking signatures at the lower and upper frequency bands, respectively. This work shows also the presence of a transitional domain between the two distinct bands. Changes and fluctuations corresponding to the involved mechanisms during the entire mechanical tests are therefore followed and visualized in the form of a heatmap. Moreover, the densities of the shear and tensile mechanisms at an instant are also determined using a Gaussian Mixture Model. Results show that the separation obtained using the SN2PB method is more advantageous than that of the conventional method based on the average frequency and the RA parameter.

This paper considers the joint estimation of the parameters of a first-order fractional autoregressive model. A one-step procedure is considered in order to obtain an asymptotically-efficient estimator with an initial guess estimator with convergence speed lower than n and singular asymptotic joint distribution. This estimator is computed faster than the maximum likelihood estimator or the Whittle estimator and therefore allows for faster inference on large samples. The paper also illustrates the performance of this method on finite-size samples via Monte Carlo simulations.

The parameters of generalized linear models (GLMs) are usually estimated by the maximum likelihood estimator (MLE) which is known to be asymptotically efficient. But the MLE is computed using a Newton-Raphson-type algorithm which is time-consuming for a large number of variables or modalities, or a large sample size. An alternative closed-form estimator is proposed in this paper in the case of categorical explanatory variables. Asymptotic properties of the alternative estimator is studied. The performances in terms of both computation time and asymptotic variance of the proposed estimator are compared with the MLE for a Gamma distributed GLM.

In the last decade, research and corporate have shown a dramatically growing interest in the field of machine learning, mostly due to the performances of deep neural networks. These increasingly complex architectures solved a wide range of problems. However, training these sophisticated architectures require many computation on advanced hardware. With this paper, we introduce a new approach based on the One-Step procedure that may fasten their training. In this procedure, an initial guess estimator is computed on a subsample that is then improved with only one step of the Newton gradient descent on the whole dataset. To show the efficiency of this framework, we consider regression and classification tasks using simulated and real datasets. We consider classic architectures, namely multi-layer perceptrons and show, on our examples, that the One-Step procedure is often halving the computation time to train the neural networks while preserving the performances.

In 2000, Ludovic Menguy and Joël Gilbert generalized the Burgers equation in order to incorporate thermoviscous losses due to boundary layers on the walls.This allowed studying the nonlinear propagation in brass instruments.Later, Joël Gilbert and colleagues were involved on the study of high-level noise sources from which emerged the study of nonlinear propagation of noise in tubes.This is the subject of the present paper.The problem is solved numerically using a fractional step method together with a convexification method.This one is suited to nonlinear propagation of acoustic signals containing a large number of pre-shocks and shocks which coalesce during the propagation.Model predictions and experimental data are compared and shown to be in a good agreement.It is shown that the Gaussianity of narrowband noise at the inlet of the tube is not conserved during nonlinear propagation.

In this paper, we investigate the asymptotic properties of Le Cam's one-step estimator for weak Fractionally AutoRegressive Integrated Moving-Average (FARIMA) models. For these models, noises are uncorrelated but neither necessarily independent nor martingale differences errors. We show under some regularity assumptions that the one-step estimator is strongly consistent and asymptotically normal with the same asymptotic variance as the least squares estimator. We show through simulations that the proposed estimator reduces computational time compared with the least squares estimator. An application for providing remotely computed indicators for time series is proposed.

Fast and asymptotically efficient methods for the estimation of the parameters in self-excited counting Hawkes processes are considered. They are based on the Le Cam one-step estimation procedure. An initial guess estimator is given to estimate both the intensity baseline and the parameters of the kernel of the Hawkes process which characterize the influence of an event on the intensity. Then, the estimation is corrected by a single step of a Newton-type gradient-descent algorithm on the loglikelihood function. Asymptotic properties of the one-step estimators are studied. Monte Carlo simulations show the performance of the procedures for finite size samples in terms of computing time and efficiency. The methodology is finally used to study the claim frequency in building insurance.

The parameters of generalized linear models are generally estimated by the maximum likelihood estimator (MLE), computed using a Newton–Raphson type algorithm that can be time-consuming for a large number of variables or modalities, or a large sample size. Explicit estimators exist for these models but they are not always asymptotically efficient, especially for simple effects models, although they are fast to calculate compared to the MLE. The article proposes a fast and asymptotically efficient estimation of the parameters of generalized linear models with categorical explanatory variables. It is based on a one-step procedure where a single step of the gradient descent is performed on the log-likelihood function initialized from the explicit estimators. This work presents the theoretical results obtained, the simulations carried out and an application to car insurance pricing.

A generic, fast and asymptotically efficient method for parametric estimation is described. It is based on the projected stochastic gradient descent on the log-likelihood function corrected by a single step of the Fisher scoring algorithm. We show theoretically and by simulations that it is an interesting alternative to the usual stochastic gradient descent with averaging or the adaptative stochastic gradient descent.

Road bridges are facing the effects of both their ageing and the increase of the traffic loads, which justifies the necessity of combining Weigh-In-Motion (WIM) with Structural Health Monitoring (SHM) solutions. An operational case study located in southern Italy is described, on which a single Monitoring System achieves both results: to perform Bridge-WIM by using the bridge deck as a scale for the detection and qualification of the traffic load, and to assess the structural health of the asset through combined strain and vibration analysis. The system uses a low number of sensors and is not intrusive for the pavement, making it an efficient and comprehensive solution for the asset manager. The Salso viaduct is a concrete structure with nine simple-supported 32 m long spans, composed of four main prestressed concrete beam girders and a reinforced concrete slab. The system has been installed on two spans with twelve sensors, among them eight optical strand strain gauges and four accelerometers. Two cameras identify the weighed vehicles. Moreover, each truck crossing the bridge triggers strain and vibration records and these data are further analyzed for the SHM of the concrete structure. The performance of the Bridge-WIM system was assessed according to the COST323 specification and the OIML R-134 recommendation. It reached the COST323 accuracy class A(5) and the OIML class 10 for the gross vehicle weights. The OIML class 5 was reached for the fully loaded trucks.