# Difference between revisions of "Basic Statistical Analysis of LWR Pin Power Data"

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== 1D Axial Power Results == | == 1D Axial Power Results == | ||

+ | The axial ''power difference'' is defined by the formula below. | ||

+ | |||

+ | <math>C(k) = \sqrtThe axial power difference is defined by the formula below. | ||

+ | |||

+ | <math>C(k) = \sqrt[2]{\frac{\sum_{ijl}(C{\cdot}W)}{{\sum_{ijl}}W}}</math> | ||

+ | |||

+ | The average axial power difference is defined as | ||

+ | |||

+ | <math>\frac{\sum_k[C(k){\cdot}dz]}{{\sum_k}dz}</math> | ||

+ | |||

+ | where the dz, the axial weight, is <math>dz = mesh(k+1) - mesh(k)</math>. Here mesh is a 1D array containing the actual physical distance between each axial level k. | ||

+ | |||

+ | The RMS axial power difference is defined by the formula below. | ||

+ | |||

+ | <math>\sqrt[2]{\frac{\sum_k[C(k)^{2}{\cdot}dz]}{{\sum_k}dz}}</math>[2]</pre>{\frac{\sum_{ijl}(C{\cdot}W)}{{\sum_{ijl}}W}}</math> | ||

+ | |||

+ | The average axial power difference is defined as | ||

+ | |||

+ | <math>\frac{\sum_k[C(k){\cdot}dz]}{{\sum_k}dz}</math> | ||

+ | |||

+ | where the ''dz'', the ''axial weight'', is <math>dz = mesh(k+1) - mesh(k)</math>. Here ''mesh'' is a 1D array containing the actual physical distance between each axial level k. | ||

+ | |||

+ | The RMS axial power difference is defined by the formula below. | ||

+ | |||

+ | <math>\sqrt[2]{\frac{\sum_k[C(k)^{2}{\cdot}dz]}{{\sum_k}dz}}</math> | ||

+ | |||

== 2D Radial Power Results == | == 2D Radial Power Results == | ||

== 3D Assembly Power Results == | == 3D Assembly Power Results == |

## Revision as of 14:38, 28 February 2015

This article details the basic mathematical formulas used to statistically compare pin power data sets from a reference and an alternate LWR.

Due to the migration of our articles from MediaWiki to Markdown, the formulas are not showing up properly. Unfortunately, Markdown does not have a lot of support for mathematical characters. We will soon be migrating back to MediaWiki pages, at which point this article will be back to normal.

## Contents

## Pin Power Dataset Representation

First, let's view the pin power dataset of each LWR as a 4D matrix *P(i, j, k, l)* where

Variable | Represents |
---|---|

i | pin row |

j | pin column |

k | axial level |

l | assembly number |

In order to compare two of these pin power datasets, we shall define the following 4D pin power datasets:

Variable | Represents |
---|---|

A | reference power data set |

B | alternate power data set |

C | power difference data set |

where

_C = B - A _ (a **basic power difference**)

or

_C = (B - A) / A _ (a **relative power difference**)

In addition, each element in *C* can be weighted by a 4D matrix *W*.

## Derived Quantities

There are four general derived quantities used in pin power analysis. The first is the *simple difference* which is simply the dataset C. The second is the absolute difference which is the absolute value of *C* or |*C*|. The third is the average difference is a weighted average calculated with the following formula.

<math>\frac{\sum(C{\cdot}W)}{{\sum}W}</math>

Finally, the *root-mean-square difference* is a weighted RMS difference determined by the formula below.

<math>\sqrt[2]{\frac{\sum(C^{2}{\cdot}W)}{{\sum}W}}</math>

The following sections detail how to calculate the above quantities over a variety of dimensions to develop statistical results from pin power differences.

## 1D Axial Power Results

The axial *power difference* is defined by the formula below.

<math>C(k) = \sqrtThe axial power difference is defined by the formula below.

<math>C(k) = \sqrt[2]{\frac{\sum_{ijl}(C{\cdot}W)}{{\sum_{ijl}}W}}</math>

The average axial power difference is defined as

<math>\frac{\sum_k[C(k){\cdot}dz]}{{\sum_k}dz}</math>

where the dz, the axial weight, is <math>dz = mesh(k+1) - mesh(k)</math>. Here mesh is a 1D array containing the actual physical distance between each axial level k.

The RMS axial power difference is defined by the formula below.

<math>\sqrt[2]{\frac{\sum_k[C(k)^{2}{\cdot}dz]}{{\sum_k}dz}}</math>[2]</pre>{\frac{\sum_{ijl}(C{\cdot}W)}{{\sum_{ijl}}W}}</math>

The average axial power difference is defined as

<math>\frac{\sum_k[C(k){\cdot}dz]}{{\sum_k}dz}</math>

where the *dz*, the *axial weight*, is <math>dz = mesh(k+1) - mesh(k)</math>. Here *mesh* is a 1D array containing the actual physical distance between each axial level k.

The RMS axial power difference is defined by the formula below.

<math>\sqrt[2]{\frac{\sum_k[C(k)^{2}{\cdot}dz]}{{\sum_k}dz}}</math>