In control and monitoring of manufacturing processes, it is key to understand model uncertainty in order to achieve the required levels of consistency, quality, and economy, among others. In aerospace applications, models need to be very precise and able to describe the entire dynamics of an aircraft. In addition, the complexity of modern real systems has turned deterministic models impractical, since they cannot adequately represent the behavior of disturbances in sensors and actuators, and tool and machine wear, to name a few. Thus, it is necessary to deal with model uncertainties in the dynamics of the plant by incorporating a stochastic behavior. These uncertainties could also affect the effectiveness of fault diagnosis methodologies used to increment the safety and reliability in real-world systems. Determining suitable dynamic system models of real processes is essential to obtain effective process control strategies and accurate fault detection and diagnosis methodologies that deliver good performance. In this paper, a maximum likelihood estimation algorithm for the uncertainty modeling in linear dynamic systems is developed utilizing a stochastic embedding approach. In this approach, system uncertainties are accounted for as a stochastic error term in a transfer function. In this paper, we model the error-model probability density function as a finite Gaussian mixture model. For the estimation of the nominal model and the probability density function of the parameters of the error-model, we develop an iterative algorithm based on the Expectation-Maximization algorithm using the data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.

We present an algorithm for a class of statistical inference problems. The main idea is to reformulate the inference problem as an optimization procedure, based on the generation of surrogate (auxiliary) functions. This approach is motivated by the MM algorithm, combined with the systematic and iterative structure of the Expectation-Maximization algorithm. The resulting algorithm can deal with hidden variables in Maximum Likelihood and Maximum a Posteriori estimation problems, Instrumental Variables, Regularized Optimization and Constrained Optimization problems. The advantage of the proposed algorithm is to provide a systematic procedure to build surrogate functions for a class of problems where hidden variables are usually involved. Numerical examples show the benefits of the proposed approach.

Aims. The study of accurate methods to estimate the distribution of stellar rotational velocities is important for understanding many aspects of stellar evolution. From such observations we obtain the projected rotational speed (vsini) in order to recover the true distribution of the rotational velocity. To that end, we need to solve a difficult inverse problem that can be posed as a Fredholm integral of the first kind.Methods. In this work we have used a novel approach based on maximum likelihood (ML) estimation to obtain an approximation of the true rotational velocity probability density function (PDF) expressed as a sum of known distribution families. In our proposal, the measurements have been treated as random variables drawn from the projected rotational velocity PDF. We analyzed the case of Maxwellian sum approximation, where we estimated the parameters that define the sum of distributions.Results. The performance of the proposed method is analyzed using Monte Carlo simulations considering two theoretical cases for the PDF of the true rotational stellar velocities: (i) an unimodal Maxwellian probability density distribution and (ii) a bimodal Maxwellian probability density distribution. The results show that the proposed method yielded more accurate estimates in comparison with the Tikhonov regularization method, especially for small sample length (N = 50). Our proposal was evaluated using real data from three sets of measurements, and our findings were validated using three statistical tests.Conclusions. The ML approach with Maxwellian sum approximation is a accurate method to deconvolve the rotational velocity PDF, even when the sample length is small (N = 50).

This paper considers the identification of a linear dynamic system driven by a non-Gaussian noise distribution. The noise is approximated by a finite Gaussian mixture, whilst the parameters of the system and the parameters that approximate the noise distribution are simultaneously estimated using the principle of Maximum Likelihood. To this end, a global optimization algorithm is utilized to solve the resulting non-convex optimization problem. It is shown that our approach improves the accuracy of the estimates, when compared with classic estimation techniques such as the prediction error method (PEM), in terms of covariance of the estimation error, while also obtaining an approximation of the noise distribution. The benefits of the proposed technique are illustrated by numerical simulations.