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Dufek, Janorcid.org/0000-0002-7943-7517

Open this publication in new window or tab >>Optimal time step length and statistics in Monte Carlo burnup simulations### Dufek, Jan

### Mickus, Ignas

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2020 (English)In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 139, article id 107244Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2020
##### Keywords

Efficiency, Monte Carlo burnup calculations, Optimisation, Statistics, Time step length
##### National Category

Physical Sciences
##### Identifiers

urn:nbn:se:kth:diva-267784 (URN)10.1016/j.anucene.2019.107244 (DOI)2-s2.0-85076440384 (Scopus ID)
#####

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##### Note

KTH, School of Engineering Sciences (SCI), Physics, Nuclear Engineering.

KTH, School of Engineering Sciences (SCI), Physics, Nuclear Engineering.

Monte Carlo burnup simulations continue to be seen as computationally very expensive numerical routines despite recent developments of associated methods. Here, we suggest a way of improving the computing efficiency via optimisation of the length of the time steps and the number of neutron histories that are simulated at each Monte Carlo criticality run. So far, users of Monte Carlo burnup codes have been required to set these parameters at will; however, an inadequate choice of these free parameters can severely worsen the computing efficiency. We have tested a large number of combinations of the free parameters on a simplified and fast solver, and we have observed that the computing efficiency was maximized when the computing cost of all Monte Carlo neutron transport calculations (summed over all time steps) was approximately comparable to costs of other procedures (all depletion simulations, the loading and processing of neutron cross sections, etc.). In this technical note, we demonstrate these results, and we also derive a simple theoretical model of the convergence of Monte Carlo burnup simulations that conforms to these numerical results. Here, we also suggest a straightforward way to automatise the selection of the optimal values of the free parameters for Monte Carlo burnup simulations.

QC 20200304

Available from: 2020-03-04 Created: 2020-03-04 Last updated: 2020-03-04Bibliographically approvedOpen this publication in new window or tab >>Stochastic-deterministic response matrix method for reactor transients### Mickus, Ignas

### Roberts, Jeremy A.

### Dufek, Jan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, article id 107103Article in journal (Refereed) In press
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2019
##### National Category

Energy Engineering
##### Identifiers

urn:nbn:se:kth:diva-263309 (URN)10.1016/j.anucene.2019.107103 (DOI)2-s2.0-85073812774 (Scopus ID)
#####

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##### Note

KTH, School of Engineering Sciences (SCI), Physics, Nuclear Engineering.

Department of Mechanical and Nuclear Engineering, Kansas State University.

KTH, School of Engineering Sciences (SCI), Physics, Nuclear Engineering.

Presented is a stochastic-deterministic, response matrix method for transient analyses of nuclear systems. The method is based on the response matrix formalism, which describes a system by a set of response functions. We propose an approach in which these response functions are computed during a set of Monte Carlo criticality calculations and are later used to formulate a deterministic set of equations for solving a space-time dependent problem. Application of the response matrix formalism results in a set of loosely connected equations, which leads to a favourable linear scaling of the problem. The method offers a simplified approach compared to previously proposed response matrix methods by avoiding phase-space expansions in sets of basis functions. We describe the method starting with the fundamental neutron transport considerations, provide a demonstration on two absorber movement transients in a 3 × 3 assembly PWR mini-core geometry, and compare the solutions against time-dependent Monte Carlo simulations.

QC 20191108

Available from: 2019-11-05 Created: 2019-11-05 Last updated: 2019-11-08Bibliographically approvedOpen this publication in new window or tab >>Optimal neutron population growth in accelerated Monte Carlo criticality calculations### Mickus, Ignas

### Dufek, Jan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 117, p. 297-304Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2018
##### Keywords

Monte Carlo criticality; Fission source; Convergence; Bias; Efficiency
##### National Category

Energy Engineering
##### Identifiers

urn:nbn:se:kth:diva-225829 (URN)10.1016/j.anucene.2018.03.046 (DOI)000431469900029 ()2-s2.0-85044790843 (Scopus ID)
#####

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##### Note

KTH, School of Engineering Sciences (SCI), Physics, Nuclear Engineering.

KTH, School of Engineering Sciences (SCI), Physics, Nuclear Engineering.

We present a source convergence acceleration method for Monte Carlo criticality calculations. The method gradually increases the neutron population size over the successive inactive as well as active criticality cycles. This helps to iterate the fission source faster at the beginning of the simulation where the source may contain large errors coming from the initial cycle; and, as the neutron population size grows over the cycles, the bias in the source gets reduced. Unlike previously suggested acceleration methods that aim at optimisation of the neutron population size, the new method does not have any significant computing overhead, and moreover it can be easily implemented into existing Monte Carlo criticality codes. The effectiveness of the method is demonstrated on a number of PWR full-core criticality calculations using a modified SERPENT 2 code.

QC 20180412

Available from: 2018-04-09 Created: 2018-04-09 Last updated: 2019-11-06Bibliographically approvedOpen this publication in new window or tab >>Correlation of errors in the Monte Carlo fission source and the fission matrix fundamental-mode eigenvector### Dufek, Jan

### Holst, Gustaf

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2016 (English)In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 94, p. 415-421Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2016
##### Keywords

Correlation, Eigenvector, Error, Fission matrix, Fission source, Monte Carlo, Correlation methods, Errors, Mesh generation, Monte Carlo methods, Correlation of errors, Criticality calculations, Error correlation, Fission matrixes, Fission source distribution, Fission sources, Strong correlation, Unbiased estimation, Eigenvalues and eigenfunctions
##### National Category

Physical Sciences
##### Identifiers

urn:nbn:se:kth:diva-186898 (URN)10.1016/j.anucene.2016.04.013 (DOI)000377231600046 ()2-s2.0-84964504934 (Scopus ID)
#####

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##### Note

KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.

KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.

Previous studies raised a question about the level of a possible correlation of errors in the cumulative Monte Carlo fission source and the fundamental-mode eigenvector of the fission matrix. A number of new methods tally the fission matrix during the actual Monte Carlo criticality calculation, and use its fundamental-mode eigenvector for various tasks. The methods assume the fission matrix eigenvector is a better representation of the fission source distribution than the actual Monte Carlo fission source, although the fission matrix and its eigenvectors do contain statistical and other errors. A recent study showed that the eigenvector could be used for an unbiased estimation of errors in the cumulative fission source if the errors in the eigenvector and the cumulative fission source were not correlated. Here we present new numerical study results that answer the question about the level of the possible error correlation. The results may be of importance to all methods that use the fission matrix. New numerical tests show that the error correlation is present at a level which strongly depends on properties of the spatial mesh used for tallying the fission matrix. The error correlation is relatively strong when the mesh is coarse, while the correlation weakens as the mesh gets finer. We suggest that the coarseness of the mesh is measured in terms of the value of the largest element in the tallied fission matrix as that way accounts for the mesh as well as system properties. In our test simulations, we observe only negligible error correlations when the value of the largest element in the fission matrix is about 0.1. Relatively strong error correlations appear when the value of the largest element in the fission matrix raises above about 0.5. We also study the effect of the error correlations on accuracy of the eigenvector-based error estimator. The numerical tests show that the eigenvector-based estimator consistently underestimates the errors in the cumulative fission source when a strong correlation is present between the errors in the fission matrix eigenvector and the cumulative fission source (i.e., when the mesh is too coarse). The error estimates are distributed around the real error value when the mesh is sufficiently fine.

QC 20160518

Available from: 2016-05-18 Created: 2016-05-16 Last updated: 2017-11-30Bibliographically approvedOpen this publication in new window or tab >>Monte Carlo criticality calculations accelerated by a growing neutron population### Dufek, Jan

### Tuttelberg, Kaur

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2016 (English)In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 94, p. 16-21Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2016
##### Keywords

Monte Carlo criticality, Fission source, Convergence, Bias, Convergence acceleration
##### National Category

Other Engineering and Technologies not elsewhere specified
##### Research subject

Physics
##### Identifiers

urn:nbn:se:kth:diva-192580 (URN)10.1016/j.anucene.2016.02.015 (DOI)000377231600003 ()2-s2.0-84959300318 (Scopus ID)
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##### Note

KTH, School of Engineering Sciences (SCI).

Tallinn University of Technology.

We propose a fission source convergence acceleration method for Monte Carlo criticality simulation. As the efficiency of Monte Carlo criticality simulations is sensitive to the selected neutron population size, the method attempts to achieve the acceleration via on-the-fly control of the neutron population size. The neutron population size is gradually increased over successive criticality cycles so that the fission source bias amounts to a specific fraction of the total error in the cumulative fission source. An optimal setting then gives a reasonably small neutron population size, allowing for an efficient source iteration; at the same time the neutron population size is chosen large enough to ensure a sufficiently small source bias, such that does not limit accuracy of the simulation.

QC 20160919

Available from: 2016-09-15 Created: 2016-09-15 Last updated: 2019-09-04Bibliographically approvedOpen this publication in new window or tab >>Optimised Iteration in Coupled Monte Carlo - Thermal-Hydraulics Calculations### Hoogenboom, J. Eduard

### Dufek, Jan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2016 (English)In: SNA + MC 2013 - JOINT INTERNATIONAL CONFERENCE ON SUPERCOMPUTING IN NUCLEAR APPLICATIONS + MONTE CARLO / [ed] Caruge, D Calvin, C Diop, CM Malvagi, F Trama, JC, E D P SCIENCES , 2016, article id UNSP 03406Conference paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

E D P SCIENCES, 2016
##### Keywords

Monte Carlo, thermal-hydraulics, coupling schemes
##### National Category

Other Physics Topics
##### Identifiers

urn:nbn:se:kth:diva-214918 (URN)10.1051/snamc/201403406 (DOI)000408930200114 ()
##### Conference

Joint 8th International Conference on Supercomputing in Nuclear Applications (SNA) / 4th Monte Carlo Meeting (MC), OCT 27-31, 2013, Paris, FRANCE
#####

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##### Note

KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics. KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.

This paper describes an optimised iteration scheme for the number of neutron histories and the relaxation factor in successive iterations of coupled Monte Carlo and thermal-hydraulic reactor calculations based on the stochastic iteration method. The scheme results in an increasing number of neutron histories for the Monte Carlo calculation in successive iteration steps and a decreasing relaxation factor for the spatial power distribution to be used as input to the thermal-hydraulics calculation. The theoretical basis is discussed in detail and practical consequences of the scheme are shown, among which a nearly linear increase per iteration of the number of cycles in the Monte Carlo calculation. The scheme is demonstrated for a full PWR type fuel assembly. Results are shown for the axial power distribution during several iteration steps. A few alternative iteration method are also tested and it is concluded that the presented iteration method is near optimal.

QC 2017-09-25

Available from: 2017-09-25 Created: 2017-09-25 Last updated: 2017-09-25Bibliographically approvedOpen this publication in new window or tab >>Neutron batch size optimisation methodology for Monte Carlo criticality calculations### Tuttelberg, Kaur

### Dufek, Jan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 75, p. 620-626Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Monte Carlo criticality, Source convergence, Source bias, Error propagation, Dominance ratio, Optimisation
##### National Category

Physical Sciences
##### Identifiers

urn:nbn:se:kth:diva-159613 (URN)10.1016/j.anucene.2014.09.011 (DOI)000347493400075 ()2-s2.0-84907887324 (Scopus ID)
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##### Note

KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.

KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.

We present a methodology that improves the efficiency of conventional power iteration based Monte Carlo criticality calculations by optimising the number of neutron histories simulated per criticality cycle (the so-called neutron batch size). The chosen neutron batch size affects both the rate of convergence (in computing time) and magnitude of bias in the fission source. Setting a small neutron batch size ensures a rapid simulation of criticality cycles, allowing the fission source to converge fast to its stationary state; however, at the same time, the small neutron batch size introduces a large systematic bias in the fission source. It follows that for a given allocated computing time, there is an optimal neutron batch size that balances these two effects. We approach this problem by studying the error in the cumulative fission source, i.e. the fission source combined over all simulated cycles, as all results are commonly combined over the simulated cycles. We have deduced a simplified formula for the error in the cumulative fission source, taking into account the neutron batch size, the dominance ratio of the system, the error in the initial fission source and the allocated computing time (in the form of the total number of simulated neutron histories). Knowing how the neutron batch size affects the error in the cumulative fission source allows us to find its optimal value. We demonstrate the benefits of the method on a number of numerical test calculations.

QC 20150209

Available from: 2015-02-09 Created: 2015-02-05 Last updated: 2017-12-04Bibliographically approvedOpen this publication in new window or tab >>PERFORMANCE OF THE EXPLICIT EULER AND PREDICTOR-CORRECTOR-BASED COUPLING SCHEMES IN MONTE CARLO BURNUP CALCULATIONS OF FAST REACTORS### Mickus, Ignas

### Dufek, Jan

### Tuttelberg, Kaur

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Nuclear Technology, ISSN 0029-5450, E-ISSN 1943-7471, Vol. 191, no 2, p. 193-198Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Monte Carlo, fast reactor, burn up calculations
##### National Category

Physical Sciences
##### Identifiers

urn:nbn:se:kth:diva-173285 (URN)10.13182/NT14-48 (DOI)000359754800008 ()2-s2.0-84942465735 (Scopus ID)
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##### Note

KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.

KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.

We present a stability test of the explicit Euler and predictor-corrector based coupling schemes in Monte Carlo burnup calculations of the gas fast reactor fuel assembly. Previous studies have identified numerical instabilities of these coupling schemes in Monte Carlo burnup calculations of thermal-spectrum reactors due to spatial feedback induced neutron flux and nuclide density oscillations, where only sufficiently small time steps could guarantee acceptable precision. New results suggest that these instabilities are insignificant in fast-spectrum assembly burnup calculations, and the considered coupling schemes can therefore perform well in fast-spectrum reactor burnup calculations even with relatively large time steps. Note: Some figures in this technical note may be in color only in the electronic version.

QC 20150909

Available from: 2015-09-09 Created: 2015-09-09 Last updated: 2020-03-05Bibliographically approvedOpen this publication in new window or tab >>Description of a stable scheme for steady-state coupled Monte Carlo-thermal-hydraulic calculations### Dufek, Jan

### Eduard Hoogenboom, J.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2014 (English)In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 68, p. 1-3Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Coupling scheme, Monte Carlo calculations, Thermal-hydraulic feedback
##### National Category

Energy Engineering
##### Identifiers

urn:nbn:se:kth:diva-142297 (URN)10.1016/j.anucene.2013.12.017 (DOI)000333790800001 ()2-s2.0-84892690634 (Scopus ID)
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##### Funder

EU, FP7, Seventh Framework Programme, 295971
##### Note

KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.

We provide a detailed description of a numerically stable and efficient coupling scheme for steady-state Monte Carlo neutronic calculations with thermal-hydraulic feedback. While we have previously derived and published the stochastic approximation based method for coupling the Monte Carlo criticality and thermal-hydraulic calculations, its possible implementation has not been described in a step-by-step manner. As the simple description of the coupling scheme was repeatedly requested from us, we have decided to make it available via this note.

QC 20140305

Available from: 2014-03-05 Created: 2014-02-28 Last updated: 2017-12-05Bibliographically approvedOpen this publication in new window or tab >>Development and comparison of spectral methods for passive acoustic anomaly detection in nuclear power plants### Riber Marklund, Anders

### Dufek, Jan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2014 (English)In: Applied Acoustics, ISSN 0003-682X, E-ISSN 1872-910X, Vol. 83, p. 100-107Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Acoustic anomaly detection, Sodium fast reactor, Signal processing
##### National Category

Other Physics Topics
##### Identifiers

urn:nbn:se:kth:diva-148338 (URN)10.1016/j.apacoust.2014.03.014 (DOI)000337645900011 ()2-s2.0-84899010916 (Scopus ID)
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##### Note

KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.

KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.

We have developed spectral signal processing methods for passive acoustic anomaly detection in nuclear power plants. Furthermore, we compared the developed and existing methods by applying them to stationary sounds recorded in a controlled environment. Our new methods show significant improvement, in particular concerning robustness against false alarms. The results also demonstrate that clear detection of a given sound at a given signal-to-noise ratio is highly dependent on the distribution of characteristic frequency content in the spectrum in relation to the background noise and the spectral uncertainty. Since the frequency monitoring principle used here is quite rigid, we stress the need for research on more flexible methods, also taking into account differences between experiments and real reactor systems.

QC 20140805

Available from: 2014-08-05 Created: 2014-08-05 Last updated: 2017-12-05Bibliographically approved