asme background noise correction

8/11/2019 ASME Background Noise Correction

1/9

THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS

345

E

7th

81 New

York.. N.Y. 10017

The

Society

shaH not

be responsible

for statements

or opinions advanced in

apers or discussion at meetings of the Society or of its Divisions 01 Sections,

94WA/NCA7

or printed

in

its pubtieations. Discussion is printed only if the paper

is

pub

ffi

lished in an ASME Journal. Papers are available from ASME for

15

months

after the meeting.

Printed in U.S.A.

CORRECTING SOUND LEVEL MEASUREMENTS FOR BACKGROUND NOISE

Michael

A.

Staiano

Staiano Engineering, Inc.

Rockville, Maryland

ABSTRACT

This paper

examines

the

uncertainty associated with

background noise correct ions and their validity for high

background noise measurements,

and considers confi

dence bounds for low-background noise situations. A

ocrrection scheme is proposed which ocnsists of repeti

tive measurements of the

source-signal-with-back

ground and background noise alone then the ocmputa

tion of a signal estimate and confidence interval. The

procedure

assumes

that

both the source of interest and

background noise are uncorrelated, random

processes

which

are stationary over

the duration

of

the

measure

ments.

For

useful results, the numbers of measure

ments must be selected to provide calculated ocnfidence

intervals which acceptably ocntain the prediction error.

These

requirements are

strongly influenced by

the

var

iability of the

measured

processes.

When

background

noise

is

relatively low,

the

technique is useful primarily

for quantifying measurement confidence bounds.

INTRODUCTION

Sound levels measured

to

quantify the noise emissions

of a specific source may be contaminated by background

noise.

Good

measurement practice requires that sound

pressure levels be measured both with and without the

operation

of

the source

of

interest. f the sound pres

sure level with

the source

is

at

least 15 dB

greater than

the background noise alone,

the

sound

pressure levels

measured

with the

source

(and background noise)

are

essentially those due

to

the source alone-the preferred

condition,

but one

frequently

unobtainable

in

field

measurements.

f

the background sound pressure levels

and

those

with the source operating differ by 4-15 dB,

the sound pressure level due to the source alone may be

calculated by applying ocrrections.(ANSI) If the sound

pressure level measured with

the

sound source operat

ing

is

no more than 3 dB above

the

background noise,

the sound pressure level due to the source

of

interest is

less

than

or

equal to

the background sound pressure

level. In this circumstance, correction for background

noise is discouraged by all measurement standards since

the correction

is

large and unreliable . . . (Hassall)

Unfortunately,

in many cases,

background noise

is

within 4 dB

of

sound levels measured with

the

desired

source-at least in some frequency bands.

In

these

cases,

the alternatives

are: forego

any

information

quantifying

the

source emissions, use

the sound

levels

measured with the background noise

influence

as an

upper-bound source emission approXimation, or pro

ceed with a background noise correction to obtain an

estimate

of

source sound levels. Even when background

noise is relatively low, some uncertainty is introduced by

the background noise correction. This

paper

examines

the

validity of

background

noise corrections in high

background-noise measurements and the quantification

of confidence intervals for low-background-noise situa

tions.

EXISTING BACKGROUND NOISE CORRECTIONS

The background noise correction scheme, such as that

provided for in ANSI S1.13, consists of the logarithmic

subtraction

of

the measured background noise sound

pressure level from that

of

the measured total

of

the

background and source sound pressure levels. That is,

Presented at the

1994

International

Mechanical Engineering

Congress

;

Exhibition,

of the Winter Annual

Meeting

Chicago, illinois

-

November

6-11, 1994


2/9

. .... -

\

, \

.

-

\

\

\

\

1

-.

L_

_ _____

= _ ~

o 2

(-:l9 J

FIGURE 1. BACKGROUND NOISE CORRECTION

per

Equation

{3}

{l}

where S is

the

estimated source-signal sound pressure

level,

T

is

the

measured signal-with-noise sound pres

sure

level,

and N

is

the measured background-noise

sound pressure lev'el. With a little manipulation, this

expression can be reformulated as:

S =T-K

{2}

where

K

is a background noise correct ion factOr (dB),

K= -1010g[1- 1 O - T - N / l ~ _

{3}

This correction factor is

plotted

in Figure 1 versus the

difference in

the

sound levels measured with and with

out the source operating,

T

-

N).

As T -

N) goes to

o

dB,

K

goes

to

infinity. For most measurement proce

dures, the curve in Figure

1

is truncated at

T

-

N) < 4

dB.

A

background noise correct ion for small values

of

T - N) would still be quite acceptable

if

the

sound lev

els with and

without the source

could

be

measured ex

actly. Unfortunately, all measurements have some un

certainty,

and

this

unsureness propagates through the

correction procedure. Even where (T - N) > 4 finite

errors

can

be

generated due to the uncertainty. The

ambiguity

entailed

by

the

background-noise correction

becomes

very

large

as

the difference

in

the measure

ments becomes small.

SAMPLING OF

SOUND LEVELS

Data representing a physical phenomenon can be p r e ~

sented in terms

of

a finite-length amplitude-time record.

The collection of all

of

these time-history records de

fines

the

process

describing the phenomenon.

The

properties

of the

data can

be

computed

by averaging

over this ensemble of records. When the average value

at

some

relative time in

each

record remains conStant

with average values at

other

relative times,

the

process

is

stationary

and

the properties computed over short

time intervals do nOI vary significantly from interval to

interval.

Physical data

are often

conveniently described by

meaDS

of

statistics

quamifying the steady and fluctuating

components of a time history_ (Bendat and Piersol) The

static component

is described by

the

mean, i.e., the

average

of

all values. The dynamic component is de

scribed by the variance, i.e.,

the

mean

square

variation

about the mean. (The standard deviation is the positive

square

rOOI of

the variance.)

The

process statistics may

be

estimated

from a

sample of time histories. For

a

process x with n independent observations (i.e., sample

size), the sample mean is

x=< x./n, i

= 1

- n

{4}

I

and the sample variance is

{5}

A st.atistic computed from

one

sample will seldom

ex-

actly equal the parameter

of

interesL Therefore, confi

dence intervals are

used

to describe how c l o ~ e the value

of a

st21tistic is likely to

be

to the value

of

the parameter

and itS probability of being that close. Where the

mean

value, J I

,of a

process

x

is desired, it

is

estimated from

the sample

mean,

x

and

expressed as being

contained

within a range. xd II: with a chance it is not. In other

words: J I lies

w i h i ~ x

daJ2

wilh 1

- a) confidence.

[ ( l - a ) % ~ will be used

to

symbolize confidence in per

cent, more strictly written as "100(1 -

a)%."J

In situa

tions where the process standard deviation, ax,

is

un

known (essentially aU cases of interest), the sample

standard deviation, s , and Student'S t distribution are

used to define the corffidence bands,

provided rhe pro ess

is Gaussian as

follows

Dixon

and Massey)

- dt)

o

-

f) ,v,

x

t n

sin

. :s

J I

:s x

t ,,(d

s

10

{6}

cr X

1

-crl" X

where tidf)

is the

value of the Student's-t distribution

for

df

degrees

of

freedom (df

=

n - 1) and probability.

Since the t-distribution is symmetrical,

t (dt) =

-I

(df).

a

k

d e f i n e d a ~ o v e ,

the confidence inten-'al describes a

range about the

sample

mean, x d

cr12

, in .whiCh

the

process mean

is

expected to be found. ThiS

protects

against positive and negative extremes larger and small

2


3/9

OQ

70

Z

0

I

...

s

I

50

1

I

'0

-

-.

a Signal, S; Noise,

N;

and Total, T b. Signal Est., Sm; Upper Bnd., Se ; Lower Snd., Se-

FIGURE

2.

EFFECT OF MEASUREMENT UNCERTAINTY

hypothetical case of T known exactly and (T-N) known with =:3 dB uncertainty

er than the specified value-considering

the

symmetri

cal, two-sided shape

of

the sample mean distribution. In

many Situations, concern may be limited to the mean

value being DOt

more

than or

not

less than some magni

tude, i.e., one-sided tests

establishing

only

upper

or

lower bounds, respectively. For example, if an upper

bound limit is desired, then the appropriate confidence

interval

is}J.

:5:

X

d

l

.

Many proxcesses reSUlt in

sound

level distributions

which

are

non-Gaussian. However, the Central Limit

Theorem in statistics allows

the

sampling distribution of

the mean of ny r ndom v ri ble to be assumed normal

provided the

sample

size is sufficiently large. The as

sumption

of

normality

is

reasonable in many cases for n

> 4 and quite accurate in

most

cases for n > 10. (Ben

dat and Piersol)

PROPOSED ORRE TION S HEME

Many acoustical measurement situations involve ran

clam processes,

such as in environmental

or

community

noise evaluations. The

statistical

techniques described

above are readily

applicable

to

these

requirements. In

building or

industrial noise measurements, noise

sources

are

often highly

periodic-for

example,

the

blade-passage frequency of a fan,

the

hum of an electri

cal

motor,

or the

firing

fate

of a

diesel engine. For

these

evalua{jons,

deterministic

techniques are

most

suitable. However,

if

the sources

are

operated under

fluctuating

loading

conditions or

are

combined

with

numerous

other noise

sources in

an

uncorrelated

man

ner,

the assumption of

a random process may become

applicable.

Even

such apparently steady sinusoidal

noise sources as a motor-pump

set

or fan may exhibit

low-magnitude-but significant-noise emission fluctu

ations such

as due to

electrical-power and

pump-load

variations for the pump set or inflow

turbulence

to the

fan. Furthermore, as noise propagation distances in

crease, steady source noise emissions

will

become modi

fied by propagation conditions. In environmental

measurements, large amplitude fluctuations may be in

trOduced by

varying

atmospheric conditions and turbu

lence even over moderate propagation distances (e.g.,

fan

blade-passage noise has been observed

by

the author

to fluctuate over a 9-dB range at a 500-ft distance).

Implementation of a background noise correction re

qUires repetitive measurements of

.he

source signal with

background noise and of the background noise alone to

increase confidence in the measured magnitUdes of the

sound pressure

levels Which define T

and

N

and

to

de

termine the variability associated with their measure

ment.

From the

variabilities

(and

numbers of meas

urements), confidence interval bounds can be defined._

The source-signal magnitude

at

any instant, S., is

the

"decibel

difference in

the T.

and

N. amplitudes, per

Equation {l}. Over time, i l c .an be r ~ p r s n t by the

level

of

the ari hmeric mean

of

the antilogarithm differ

ences (i.e., the level

of

the expected SOurce sound pres

sures-squared). Confidence

intervals can

bederived

from

the

measurement means

and standard

deviations-assuming both the

source

of

interest

and

the background noise are uncorre13ted,

random

proc

esses.

The

difficulty that arises is {hat

T

and

N

cannot

bath

be measured simultaneou sly. However, jf

the

source and background are stationary over the time pe-

riod spanned by the measurements, T and N

can

be

measured separately and the source magnitude, $, com

puted.

The measurement

errors

for

T

and

N

are

such

that

they resull in upper and lower bound estimates

of

the

signal

which-when

expressed in

decibels-are

asym

3


4/9

TABLE

1.

GAUSSIAN RANDOM NUMBERS TEST RESULTS

n

11EAN

ERROR c

I . for

a - -ERR

C. L for a

OK

S N

Mean

SD

95.0

99.0

99.5 95.0

99.0 99.5 TRlS

(dB) (dB)

(dB)

(dB)

(dB) (dB)

(%)

(%) (%)

(%)

6 10.1

0.5 2.0

2.0

2.9 3.3 75

91

94 100

30 10.0

0.0 0.9

0.9

1.2 1.4

81

91

91 100

100 10.1

0.1

0.5

0.5

0.7

0.8

91

94

94

100

6 0.0

-0.4

2.9

3.3

4.6 5.1

80

87

97 94

30

-0.1

0.1

1.1

1.5

2.1 2.3 91

97

97

100

100

0.1

-0.1 0.6

0.9

1.2 1.3

94 97 100 100

6

-9.8

5.1

5.9

6.5 8.2 8.8

36

55

59

69

30 -9.7

-0.6

6.7

7.2 8.4 8.7

67 67

71

75

100

-10.0

0.5 5.9

4.7

5.6 5.9 64

89

89

88

metric, i.e., the upper-bound eSlimate

is

more tightly

constrained than the lower bound. This

is

illustrated in

Figures 2 which shows the two-sided, upper- and lower

bound estimates (Se+ and S . respectively) of

a

signal

for various magnitudes of signal-tO-noise ratio. Thus,

signal estimates may

be obtained

for

(T - N differences

less than 4 dB with relatively confined upper bounds

Correction

Procedure. A correction procedure is

proposed consisting of the following steps:

1. Perform n discrete measurementS of source sig

nal with background noise, T., and of back

ground noise alone, N., (for

a

total of 2n meas

urements). )

2.

Arbitrarily pair

T.

and N. measurementS,

(T.,

J J 1

N

.).

I

3.

COmpute

the

sound-pressures-squared (or each

measuremenl,

p

2

=

O(XiIlO).

{7}

4.

(11culate the

~ r e s s u r e s s q u r e d

differences,

8.

=

p1j2 -

P

N

. . {8}

I I .

5.

Kepe.at Steps 2-4 for the n measurement pairs

and determine the mean 8) and standard devia

tion

(5,s)

over the measurements.

6.

Estimate the signal magnitude

as

S =: 10

log (8).

{9}

7.

Calculate the signal estimate upper bound as

Sl-a:

=

10

log (8 + k1-o-s

S

) {l0}

where k}

=

} (df)/n

Y2

.",ith

t (dC) the value

1

of

Student s-t d'istribution

for-- d[

degrees of

freedom and

l a

probability (i.e., confidence).

LImitations. Fundamental to this approaCh is the as

sumption that not only are the signal and noise uocone

lated, but that the measurements of the background

noise with and without the source signal are uncorrelat

ed. In most situations of in terest, this premise

is

rea

sonable since the au!Ocorre)ation function for random

noise

goes to zero rapidly with increasing

intra

measurement time delay. (Bendat and Piersol) Even

narrow frequency bands of random noise may be ana

lyzed

provided the sampling interv'al between the meas

urements is sufficiently

long.

A

required condition is the stability of the background

noise magnitude during the measurementS. Stationarity

of

the background sound pressure levels can be tested

by performing background measurements before and

after the with-source measurementS. If necessary, be

fore and after background sound levels can be averaged,

or the

computation

aborted

if

excessive drift

is

ob

served.

EVALUATION OF PROCEDURE

The prOced-ure

was

tested by simulating its implemen-

tation in a number of uials. ach tri f1l consisted of the

repetitive sampling of noise and signal-with-noise six or

more times

(to

evaluate the effect of sample size) and

(he

computation of the expected signal value and upper

bound estimate (for various confidence intervals). For

each trial, the signal-estimation error was determined by

subtracting the actual signal magnitude from that

ex

pected using the correction procedure; and the actual

magnitude

was

compared

to

the upper-bound estimates.

This process was repeated for

32

trials using random

numbers and eight trials using experimental measure

ments.

The results of the trials were examined with respect 0

four considerations:

Accuracy is defined in terms of the mean error

experienced in eslimating a kno'W l1 signaL

Consistency

of Ihe estimates is quantified by the

standard deviation of the errors.

4


5/9

TABLE2. RAYLEIGH-LIKERANDOMNUMBERSTESTRESULTS

n

MEAN ---ERROR--- ---C.I.

for a

- - - -ERR C.I.

for a

OK

SiN

Mean

SO

95.0 99.0

99.5

95.0 99.0

99.5

TRLS

(dB)

(dB) (dB)

(dB)

(dB) (dB)

( )

( ) (%)

(%)

6

9.8

0.3

0.9

1.1 1.7

2.0

78

97

97

100

30

9.9 -0.2 0.5

0.5

0.7

0.8

97 100

100 100

100

10.0

0.0 0.2

0.3

0.4

0.4

84 97

97

100

6 0.2

-0_2

1.3

1.7 2.5

2.9

84 94

97 100

30

-0.0 0.2 0.5

0.8

1.1

1.2

84 91 94 100

100

-0.0

-0.0 0.4

0.5 0.6

0.7

91

97

97 100

6 -9.7

1.6

5.6

6.2 7.8

8.4

54

62

77 81

30

-9.8

-0.0 3.1

4.4

5.5

5.8

77 91

95

69

100

-10.0

-0.8

2.9

3.4

4.2 4.5

84 87

94

_00

Assurance

that

the

estimate

upper-bound con

tains the

actual magnitude

determines the

lidity of the procedure. It is quantified by the

fraction of the trials for which the confidence

interval

is

greater than or equal to the error,

Success

is

considered

to

exist when the mean of

the s i g n a l ~ w i t h n o i s e measurements is greater

than or equal to the

mean

of the noise-alone

measurements. (As signal-to-noise

ratio

de

creases, the probability increases of a 0 90 of time for nominal SIN 2: 0 dB and

confidence 1 0: 2:

99

(except

SIN

0 dB and

n= 6),

and confidence interval contains error

about

90 of

time for

SIN =:;

-10 dB

with 1 0: 2:

99%

and

n

=

100;and

S u c c e s s ~

94 successful trials for

nominal

SiN

2:

0

dB

and about 90% success rate for

SIN

10

dB.

From these testS, the correction procedure was deter

mined to provide useful estimates even for very poor

signal-to-noise

ratios (i.e., -10 dB). For high signal-to

noise ratios (about

+

10 dB), even

six

measurementS are

adequate; for poor signal-to-noise (about 0 dB), at least

30 measurements are necessary;

and,

for very poor sig

nal-to-noise ratios, 100 measurementS and 99 confi

dence intervals are needed to obtain marginally accept

able consistency and assurance.

Rayleigh-Like Distribution. Environmental

sound

levels

often do not

distribute

normally butexhibit a

Rayleigh distribution. Such a

distribution

is positively

skewed with

3

finite

lower bound but

an

asymptotic

upper bound. A rna thema Iica I expression was de

veloped to generate random numbers eXhibiting a Ray

leigh-like distribution. When random

numbers

with

sound-Level-like magnitudes were created with

the

se

lection

ora

suitable constant, the resultant distributions

5


6/9

"

'

.,

I .

-----

' ' I

~ ~ ~ ~ V ~

---I

,

1 1 T J : t ? ~ ~

,

,I

,

1 11

I: . .

'''

1;:-

--

-,

a. 15-min time history b. 2-min segment of "l.vhite noise" excitation

FIGURE

3.

EXPERMENTAL MEASUREMENTS-SPEAKER-EXCITATION TIME HISTORIES

TABLE

3. SAMPLING ERROR

IN BSENCE OF

BACKGROUND NOISE (over eight trials)

n ----ERROR (dB) for SAMPLING

TYPE--

~ r i o d i c -----Random----

mean SO

mean

SD

6

1.8 3.8

10 1.4 2.7

30

0.1

1.9

56

0.2 1.1

-0.1 1.6

-0.2

1.5

-0.0

0.5

+0.2

0.4

yielded standard deviations of about 1.6 dB if normally

distributed,

L -L :::: 4

dB).

As

for the Gaussian

raD

10 90

dam numbers, values

ofT and N

were generated

to

);eJd

nominal +10 dB, 0 dB, and 10 dB signal-to-noise ratios

for tests with 6,30, and 100 repetitive measurements.

The results, summarized in Table 2, are:

Accuracy-mean

error

magnitudes typically

:s

0.8 dB;

Consistency-standard deviation

of

errors gen

erally

less

than about

3 dB;

Assurance-> 90%

for nominal SIN

0 dB

and greater than about 90% for SiN


7/9

TABLE 4. PERIODICALLY SAMPLED MEASUREMENTS TEST RESULTS

n

MEAN ERROR ---e.

1. for

-

-ERR :: C.

I .

for

OK

SiN

Mean

SD

95.0 99.0 99.5 95.0 99.0 99.5 TRLS

(dB)

(dB)

(dB) (dB)

(dB) (dB)

( )

( )

( )

( )

6 11. 6 1.8 3.2 1.2 1.8

2.1

38 38 38

100

10 12.0

1.3

2.6 1.0

1.5

1.7 50 63

63

100

30

12.6

0.0

1.9

0.6

0.9

1.0

75

75

75

100

56

12.7 0.2

1 1

0.5

0.8

0_8

75

75 75

100

6

1.2

1.5

3.8

1.3 1.9 2.2

38 38

63

100

10 1.6

1.4 2.7 1.1

1.5

1.7

50 63 63 100

30

2.3

0.1

2.2 0.7 0.9

1.0

63

63

63

100

56

2.4

0.3

1.3

0.5

0.7

0.8 63

63

63

100

6

-8.8

2.3

3_9

3.0

4.2

4_7

63 75 75

100

10

-8.5

1.4

2.7

2.7

3.6

3.9 63

63

88

100

30

-7.8

0.5 2.3

1.7

2.2 2.4

63 75

75

100

56

-7.7

0.7 1.2 1.2 1.6 1.8 63

75

75 100

The measured

data were sampled such

that

effeCtively

trials

of

6, 10,30, and 56 L (1 s)

measurements

were

obtained for each s o u r c e l ~ k g r o u n d

noise

condition.

The sampling

was

done both periodically

(every 2 sec)

and randomly. For

each

number of measurements,

er

rors

and

95.0, 99.0 and

99.5%

con fidence

interval

bounds over 8 trials

were computed.

(The two traffic noise

recordings were employed such

that one

recording consistently was added to

the

white

noise

and

the other recording

consistently

represemed

the

excitation-alone, actual -magnitude

measuremem.

[The separate

recordings were used to preclude possible

false

favorable results

that

may

have arisen

from com

paring an excitation to itself.]

The error

associated v.ith

the sampling

alone, i.e.,

aside

from

the presence of

background noise, can be determined

by

estimating

the

magnitude

of one

recording

from

the other

using

the

correction procedure with infinitesimal

background

noise. The results of

this

comparison are

given in

Ta

ble

3.

With periodic sampling, the error is relatively

large [> 1

dB]

for n :s 10; with

random sampling

the

error is

small

0.2 dB]

for

all n.

The resultant

tests

had actual signal-lo-noise ratios

ranging from

-9

to

+

13 dB, relatively high

compared

to

the

nominal

magnitudes. The differences

between

the

nominal and actual

SIN

ratios

are

the result of the man

ual

setting

of

amplifier gains.

Periodic Sampling The

results, summarized in Ta

ble 4,

are:

Accuracy mean error magnitudes =

1.4

dB for

n 10 and about

2

dB for n

= 6;

Consiscency standard

deviation

of

errors

asme background noise correction

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