A Formalism for Expressing the Probability Density Functions of Interrelated Quantities

Lira, Ignacio; Grientschnig, Dieter

doi:10.2478/msr-2013-0015

Cited by 6 publications

(7 citation statements)

References 9 publications

(14 reference statements)

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“…Cavitation number depends on the geometry of the region where cavitation is expected to occur [14], [17], [18], so it can only be determined by measurement.…”

Section: Cavitation Numbermentioning

confidence: 99%

Methods of Experimental Investigation of Cavitation in a Convergent - Divergent Nozzle of Rectangular Cross Section

Jablonská

Kozubková

Himr

et al. 2016

Measurement Science Review

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Cavitation is a phenomenon with both positive and negative effects and with dynamic manifestations in hydraulic, food, chemical and other machinery. This article deals with the detection and dynamic behavior of cavitation clouds in water flows through a rectangular cross-section convergent-divergent nozzle. Cavitation was measured by methods applicable in engineering practice. Pressure, flow rate, noise, vibration, and amount of air dissolved in the liquid were measured and cavitation region was recorded with a high-speed camera. Evaluation of acquired images in connection with measured pressure pulsations and mechanical vibrations was performed with the use of the FFT method. In certain cases, dimensionless parameters were used to generalize the measurements. The results will be used to specify multiphase mathematical cavitation model parameters.

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“…Cavitation number depends on the geometry of the region where cavitation is expected to occur [14], [17], [18], so it can only be determined by measurement.…”

Section: Cavitation Numbermentioning

confidence: 99%

Methods of Experimental Investigation of Cavitation in a Convergent - Divergent Nozzle of Rectangular Cross Section

Jablonská

Kozubková

Himr

et al. 2016

Measurement Science Review

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“…where m < n. Using bold letters as a short notation for the totality of items in a set, these equations can be condensed into f .X / D 0. If the functions f .i / are compatible, independent of one another and sufficiently well-behaved, selections of n m quantities exist that suffice to express the complete state of knowledge (Lira & Grientschnig, 2013). Such a subset of quantities represents a coordinate system or parameterization.…”

Section: Terms and Symbolsmentioning

confidence: 99%

Combining Probability Distributions by Multiplication in Metrology: A Viable Method?

Grientschnig

Lira

2014

Int Statistical Rev

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In measurement science quite often the value of a so-called 'output quantity' is inferred from information about 'input quantities' with the help of the 'mathematical model of measurement'. The latter represents the functional relation through which outputs and inputs depend on one another. However, subsets of functionally independent quantities can always be so defined that they suffice to express the entire information available. Reporting information in terms of such a subset may in certain circumstances require aggregating probability distributions whose arguments are interrelated quantities. The option of aggregating by multiplication of distributions is shown to be susceptible of yielding inconsistent results when the roles of inputs and outputs are assigned differently to the quantities. Two alternatives to this practice that do not give rise to such discrepancies are discussed, namely (i) logarithmic pooling with weights summing to one and (ii) linear pooling, of which the former appears to be slightly more favourable for applications in metrology. An example illustrates the inconsistency of results obtained by distinct ways of multiplying distributions and the manner in which these results differ from a logarithmically pooled distribution.

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“…The answer to this question was given in [6], a summary of which is provided in Section II. But before going into details let us clarify the meaning of the question.…”

Section: Introductionmentioning

confidence: 99%

“…The sequence of our treatment is as follows. In Section II we summarize the formalism in [6] for expressing the PDFs for interrelated quantities. The formalism is based on the change-of-variables theorem, and its output is a joint PDF for some or all of the quantities that were initially unknown.…”

Section: Introductionmentioning

confidence: 99%

Deriving PDFs for Interrelated Quantities: What to Do If There Is “More Than Enough” Information?

Lira

Grientschnig

2014

IEEE Trans. Instrum. Meas.

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The GUM and its supplements one and two have come to be regarded as de facto standards for evaluating measurement uncertainty. The latter documents have stressed the benefits of deriving probability density functions (PDFs) for the output quantities instead of just evaluating the standard and expanded uncertainties associated with their best estimates. Those supplements, however, present a brute force numerical method for obtaining the output PDFs. In this paper, we rely instead on the use of the change-of-variables theorem as a way of obtaining analytical expressions for PDFs in the form of integrals that, at least in principle, can be numerically evaluated. But more importantly, the GUM supplements do not include situations in which the available information is more than enough, in the sense that by separately considering its various components one may arrive at concurrent PDFs for the quantity or quantities of interest. In some situations these PDFs will be largely similar, so that implementing some form of merging method would perhaps be reasonable. But it may also happen that significant discrepancies between those PDFs are apparent, in which case a modification of the measurement model might make all information appear to be consistent. Herein we review two procedures for merging concurrent and not too dissimilar PDFs. We also discuss some elements to be considered if extending the measurement model appears to be a better alternative.

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A Formalism for Expressing the Probability Density Functions of Interrelated Quantities

Cited by 6 publications

References 9 publications

Methods of Experimental Investigation of Cavitation in a Convergent - Divergent Nozzle of Rectangular Cross Section

Methods of Experimental Investigation of Cavitation in a Convergent - Divergent Nozzle of Rectangular Cross Section

Combining Probability Distributions by Multiplication in Metrology: A Viable Method?

Deriving PDFs for Interrelated Quantities: What to Do If There Is “More Than Enough” Information?

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