Page 28 - Noisy-User-Manual-2017-en

26 2 Program concepts

2.2 Determining the percentile confidence
intervals

2.2.1 Problem
For detailed measurement of noise level trends, use can be be made not only
of the mean value but also of percentile levels (statistical levels) as
distribution measurement variables, for example, LAF1 or LAF95. By reason
of the usually stochastic fluctuations of the noise level trend and the
necessarily finite measurement duration, the measuring certainty of percentile
levels is inevitably limited. This is also true for all other measurement
variables and all parameters derived from them.
Appropriately, the measurement uncertainty is marked by a two-sided
confidence interval, i.e., a figure comprising the percentile value; with a
specified probability, e.g., 80% or higher, the true percentile value is within
this confidence interval [1]. In this way, the limit of the measurement
certainty of the percentile can be quantified directly out of the stochastic
curve, i.e., without repeating the measurements [2].
Due to the necessary computing workload, this quality parameter can be
realized in practical measuring applications only by means of a computer-
based, user-friendly measuring and evaluation process in accordance with
today's PC standards. To meet this requirement, Wölfel Monitoring Systems
GmbH + Co. KG developed the NOISY software. The new measuring
technology was then submitted to a field test [3].

2.2.2 Basic algorithm: Percentile confidence intervals
The upper and lower confidence limit Lq,o and Lq,u of a percentile level Lq
are determined by means of

L q, o  L  L  L q, u t  n 1;1 /2 dL ˆ    q 2 s 2  q 2 s 2   
q
q
w
w
u
u
dq
T 

i.e., based on data that can be observed and data that have to be specified [2].
Here, q stands for the exceedance ratio (0<q<1); T stands for the measurement
time; n stands for the number of the time intervals ui or wi present in T, which
are assumed to be stochastically independent, in which the noise level falls
below or exceeds the percentile, with n > 5; dL/dq stands for the increase of