A Guaranteed Blind and Automatic Probability Density Estimation of Raw Measurements

Barbé, Kurt; Fuentes, Lee Gonzales; Barford, Lee; Lauwers, Lieve

doi:10.1109/tim.2014.2304858

Cited by 10 publications

(7 citation statements)

References 19 publications

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“…where P (x ij |s k ) is crucial for determining the category of a new instance. The estimation methods for P (x ij |s k ) mainly include parametric estimations such as histogram computation, k-nearest neighbor estimation, maximum likelihood estimation, and Bayesian estimation [2]- [11]. These methods depend on the assumption that attributes are conditionally independent.…”

Section: 42mentioning

confidence: 99%

Evaluation strategy and mass balance for making decision about the amount of aluminum fluoride addition based on superheat degree

Yue¹,

Gui²,

Chen³

et al. 2020

Journal of Industrial &Amp; Management Optimization

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The purpose of aluminum fluoride (AlF 3) addition is to adjust the superheat degree (SD) in the aluminum reduction process. Determining the appropriate amount of AlF 3 to add has long been a challenging industrial issue as a result of its inherent complexity. Because of the decreasing number of experienced technicians, the manual addition of AlF 3 is usually inexact, which easily leads to an unstable cell condition. In this paper, an evaluation strategy based on the SD for AlF 3 addition is proposed. An extended naïve Bayesian classifier (ENBC) is designed to estimate the states of SD and its trends that represent the current and potential cell condition respectively, and then the process is graded by evaluating the estimated results based on fuzzy theory. The reduction process is divided into a few situations based on the evaluation grades, and mass balance is introduced to determine the amount of AlF 3 addition in each situation. The results of experiments show that the proposed strategy is feasible, and the effectiveness of AlF 3 addition is improved compared to the existing method. Moreover, automatic AlF 3 addition is promising based on the proposed strategy.

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Section: 42mentioning

confidence: 99%

Evaluation strategy and mass balance for making decision about the amount of aluminum fluoride addition based on superheat degree

Yue¹,

Gui²,

Chen³

et al. 2020

Journal of Industrial &Amp; Management Optimization

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show abstract

“…In the following, simple linear interpolation is adopted that is shown to provide acceptable results. Many other published techniques can be found in the scientific literature [12]- [14].…”

Section: ) Known Test Parametersmentioning

confidence: 99%

Measuring the Noise Cumulative Distribution Function Using Quantized Data

Carbone

Schoukens

Kollár

et al. 2016

IEEE Trans. Instrum. Meas.

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This paper considers the problem of estimating the cumulative distribution function and probability density function of a random variable using data quantized by uniform and nonuniform quantizers. A simple estimator is proposed based on the empirical distribution function that also takes the values of the quantizer transition levels into account. The properties of this estimator are discussed and analyzed at first by simulations. Then, by removing all assumptions that are difficult to apply, a new procedure is described that does not require neither the transition levels, nor the input sequence used to source the quantizer to be known. Experimental results obtained using a commercial 12-bit data acquisition system show the applicability of this estimator to real-world type of problems.

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“…If the input to the nonlinear system is Gaussian, the model can be approximated through a Bussgang decomposition [3], where the idea is to use the best linear approximation of the nonlinearity and to characterize the second moment of the resulting error. In the situation where the output model is completely unknown one has to use empirical methods like histograms [4]. In the case that the system parameter only modulates the output mean and leaves the variance constant, it is possible to use a pessimistic replacement strategy by assuming an equivalent Gaussian model.…”

Section: Motivationmentioning

confidence: 99%

Measurement-driven quality assessment of nonlinear systems by exponential replacement

Stein

Nossek

Barbé

2016

2016 IEEE International Instrumentation and Measurement Technology Conference Proceedings

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Abstract-We discuss the problem how to determine the quality of a nonlinear system with respect to a measurement task. Due to amplification, filtering, quantization and internal noise sources physical measurement equipment in general exhibits a nonlinear and random input-to-output behaviour. This usually makes it impossible to accurately describe the underlying statistical system model. When the individual operations are all known and deterministic, one can resort to approximations of the input-to-output function. The problem becomes challenging when the processing chain is not exactly known or contains nonlinear random effects. Then one has to approximate the output distribution in an empirical way. Here we show that by measuring the first two sample moments of an arbitrary set of output transformations in a calibrated setup, the output distribution of the actual system can be approximated by an equivalent exponential family distribution. This method has the property that the resulting approximation of the statistical system model is guaranteed to be pessimistic in an estimation theoretic sense. We show this by proving that an equivalent exponential family distribution in general exhibits a lower Fisher information measure than the original system model. With various examples and a model matching step we demonstrate how this estimation theoretic aspect can be exploited in practice in order to obtain a conservative measurement-driven quality assessment method for nonlinear measurement systems.Index Terms-nonlinear systems, Fisher information, Cramér-Rao lower bound, exponential family, Saleh model, Rician model, regression, Wiener system, measurement uncertainty I. MOTIVATION The characterization of nonlinear systems and the development of appropriate processing algorithms forms a problem for engineering tasks like signal processing or system identification while the increasing demand on low-cost, energy-efficient and fast measurement devices makes it inevitable to operate such systems outside their linear regime. In order to provide high processing accuracy under these circumstances, it is important to investigate nonlinear models and to develop generic approaches and methods for such kind of problems. The key challenge for efficient solutions to nonlinear measurement problems lies in the fact that access to an appropriate model p(z; θ) is required. In theory, this probabilistic description establishes the statistical relationship of the system parameter θ ∈ R and the output measurement z ∈ R. This allows to formulate efficient signal processing algorithms and to describe the achievable performance by analytical tools. However, in practice the system model p(z; θ) is rarely known exactly and therefore has to be established by numerical calculations or approximated by physical measurements.If the analytical form of the system model p(z; θ) is known but to complicated to work with, one can resort to an direct approximation of the distribution function like performed in [1] for the Rician model. When the nonlinear...

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A Guaranteed Blind and Automatic Probability Density Estimation of Raw Measurements

Cited by 10 publications

References 19 publications

Evaluation strategy and mass balance for making decision about the amount of aluminum fluoride addition based on superheat degree

Evaluation strategy and mass balance for making decision about the amount of aluminum fluoride addition based on superheat degree

Measuring the Noise Cumulative Distribution Function Using Quantized Data

Measurement-driven quality assessment of nonlinear systems by exponential replacement

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