On the Uncertainty Identification for Linear Dynamic Systems Using Stochastic Embedding Approach with Gaussian Mixture Models

A Two-Filter Approach for State Estimation Utilizing Quantized Output Data

Filtering and smoothing algorithms are key tools to develop decision-making strategies and parameter identification techniques in different areas of research, such as economics, financial data analysis, communications, and control systems. These algorithms are used to obtain an estimation of the system state based on the sequentially available noisy measurements of the system output. In a real-world system, the noisy measurements can suffer a significant loss of information due to (among others): (i) a reduced resolution of cost-effective sensors typically used in practice or (ii) a digitalization process for storing or transmitting the measurements through a communication channel using a minimum amount of resources. Thus, obtaining suitable state estimates in this context is essential. In this paper, Gaussian sum filtering and smoothing algorithms are developed in order to deal with noisy measurements that are also subject to quantization. In this approach, the probability mass function of the quantized output given the state is characterized by an integral equation. This integral was approximated by using a Gauss–Legendre quadrature; hence, a model with a Gaussian mixture structure was obtained. This model was used to develop filtering and smoothing algorithms. The benefits of this proposal, in terms of accuracy of the estimation and computational cost, are illustrated via numerical simulations.

The Deterministic Nature of Sensor-Based Information for Condition Monitoring of the Cutting Process

Condition monitoring of the cutting process is a core function of autonomous machining and its success strongly relies on sensed data. Despite the enormous amount of research conducted so far into condition monitoring of the cutting process, there are still limitations given the complexity underlining tool wear; hence, a clearer understanding of sensed data and its dynamical behavior is fundamental to sustain the development of more robust condition monitoring systems. The dependence of these systems on acquired data is critical and determines the success of such systems. In this study, data is acquired from an experimental setup using some of the commonly used sensors for condition monitoring, reproducing realistic cutting operations, and then analyzed upon their deterministic nature using different techniques, such as the Lyapunov exponent, mutual information, attractor dimension, and recurrence plots. The overall results demonstrate the existence of low dimensional chaos in both new and worn tools, defining a deterministic nature of cutting dynamics and, hence, broadening the available approaches to tool wear monitoring based on the theory of chaos. In addition, recurrence plots depict a clear relationship to tool condition and may be quantified considering a two-dimensional structural measure, such as the semivariance. This exploratory study unveils the potential of non-linear dynamics indicators in validating information strength potentiating other uses and applications.

The Identification of the Uncertainty in Soil Strength Parameters Based on CPTu Measurements and Random Fields

The present paper responds to the challenge of modeling uncertainty in soil strength parameters concerning its spatial variability in a situation of limited soil information. Understanding this uncertainty allows for the management of the risk of geotechnical structure failure. In the present work, this uncertainty is identified based on signals from the cone penetration test (CPT) device. Signals are directly transformed using existing interpretation methods (typically used as a source of mean values of parameters for a given range of depths) to obtain depth-varying effective strength parameters of the soil. The process is performed by incorporating data from two case studies from different locations in similar soil materials. First, Keswick clay from Australia, for which the results of both CPT and laboratory tests are available, is examined. Second, to further verify the obtained results, the soil from Poland called Świerzna clay, for which only CPT signals were available, is also tested. As shown, the variability of the transformed signals can be a good source of information for identifying uncertainty in soil strength. It agrees well with literature data and can be used to identify random fields describing soil parameters.