Data analysis software verification
Benchmark test 4 using D2_4 signal.

Function of test

The function of this test is to check the computation of signal statistics and in the frequency domain auto spectral density (ASD) (some times referred to as Power Spectral Density (PSD)) functions for a selected section of some real world data.

D2_4 Signal Details

The D2_4 signal is real data taken from a load measuring wheel transducer. The data is supplied as ASCII values and is already scaled to the correct levels. A single signal is supplied which is the vertical force measured over a rough road. The total signal includes the initial and final static data when the vehicle was at rest.

The file supplied for this benchmark is.

EIS_DATA_D2_4_V1.TXT

Which contains data acquired at 630 samples per second.
The units are: kN
And the signal description is: Wheel vertical load

Analysis parameters to be used

The data are supplied in ASCII form and the file represents one signal. When loaded into an analysis package the data should be set to a sample rate of 630 samples per second and the units to kN.

The analysis should be performed on the section of the signal from 28.5 seconds to 154.00 seconds.

Four auto spectral analyses should be performed as follows:

Two Auto Spectral Density analyses of the specified section of data as supplied the first at a frequency spacing of 0.30762 Hz and the second at a frequency spacing of 0.078125 Hz, which are equivalent to 2048 and 8192 FFT transform sizes)

The selected section of data should then be normalized to zero mean and a further two Auto Spectral Density analyses performed at the same effective bandwidths.

In all four cases a Hanning window should be used with an overlap of 50% of block sections. The equation for a Hanning window is:

w(n) = 0.5* (1.0 - cos (2*PI*n/N)) n = 0,1,….,N

This window gives an effective noise bandwidth of 1.5 times the frequency spacing.

Reference results

The reference results quoted below have been computed using DATS for Windows Version 5.0.31

Imported signal

The imported signal is shown in Figures 1 & 2.

Basic Statistics

The basic statistics for the selected section of data are:

Maximum value 14.4652 kN Located at 150.5820 Sec

Minimum value -0.2512 kN Located at 102.2680 Sec

Mean value 4.8347 kN

Root mean square value 5.1625 kN

Standard deviation 1.8103 kN

Number of points 79066

NOTE maximum and minimum signal locations are referred to the original signal start.

Auto Spectral Density (ASD) results.

Results of the spectral density analyses are detailed in the table below.

Reference results are supplied in ASCII form in datasets named:

EIS_DATA_RESULT_{ident}_V1.TXT

Where Ident is as specified in the table below.

It is recommended that spot checks on the ASD results be carried out at 4 spot points in each of the spectra as shown in the table.

Figures

Spacing of points

Signal Condition

Reference points

Point No.

Value

Point No.

Value

Point No.

Value

Point No.

Value

ASD_1

3 & 4

0.30762 Hz

Signal including mean

1

X=0.0

Y=101.6

8

X=2.1533

Y=0.6630

17

X=4.922

Y=0.4079

28

X=8.306

Y=0.2172

ASD_2

5 & 6

0.0769 Hz

Signal including mean

1

X=0.0

Y=406.9

29

X=2.153

Y=0.9391

65

X=4.922

Y=0.6862

110

X=8.383

Y=0.3299

ASD_3

7 & 8

0.30762 Hz

Signal with mean removed

1

X=0.0

Y=0.1066

8

X=2.153

Y=0.6630

17

X=4.922

Y=0.4079

28

X=8.306

Y=0.2172

ASD_4

9 & 10

0.0769 Hz

Signal with mean removed

1

X=0.0

Y=0.2775

29

X=2.153

Y=0.9391

65

X=4.922

Y=0.6862

110

X=8.383

Y=0.3299

Figure 1 Original signal

Figure 2 Selected section of signal

Figure 3 ASD of selected section of signal including mean at 0.30762 Hz frequency spacing.

Figure 4 ASD of selected section of signal including mean at 0.30762 Hz frequency spacing.

Figure 5 ASD of selected section of signal including mean at 0. 0769Hz frequency spacing.

Figure 6 ASD of selected section of signal including mean at 0. 0769Hz frequency spacing.

Figure 7 ASD of selected section of signal with mean removed at 0.30762 Hz frequency spacing.

Figure 8 ASD of selected section of signal with mean removed at 0.30762 Hz frequency spacing.

Figure 9 ASD of selected section of signal with mean removed at 0. 0769Hz frequency spacing.

Figure 10 ASD of selected section of signal with mean removed at 0.0769 Hz frequency spacing.

Acceptable tolerance in computed results

The tolerance on the results of the specified analyses should as follows:

Signal Statistics

Number of samples processed should be exact.

Other results should be accurate to 4 significant figures. (This is considered to be acceptable for normal analysis purposes)

Auto spectral densities

As will be noted from the plots the signals reach a noise floor above approximately 100 Hz and it is recommended that comparisons with the reference results should only be made in the range 0 to 60 Hz.

Due to differences in computational algorithms it is not anticipated that exact agreement will be attained. However, good agreement should be achieved for the significant peaks in respect to both amplitude and frequency.

Typical Benchmark 4 erroneous results and their causes

If good agreement is not achieved for the basic statistics then the tests specified in groups A-C should be run to check that good agreement for basic statistics for deterministic signals can be obtained to ensure that the computation of the statistics is correct. If results from groups A-C are correct then the length of data in the selected section and its position within the original data should be checked.

Overlaying the supplied reference spectra on the locally derived spectra best checks computed spectra.

Possible causes of differences are:

Incorrect application of or failure to apply the Hanning window.
Difference in overlapping of spectral segments.
Incorrect scaling of first and last point in the spectra.
Differences in methods employed for normalizing to zero mean.
Incorrect handling of an incomplete block at end of data.

Results return documents.

In order to aid the working party in the development of benchmark data users are invited to submit the results obtained when employing the tests. These submissions will be assessed by the working party and summaries may be used in presentations and publications of the working party’s activities.

If you wish to submit results please use the document contained in Appendix A.

Appendix A

Benchmark 4. Analysis results return.

Name: Organisation: Date:

Address:

Email: Tel: Fax:

Analysis Package used: Version:

Computer Hardware and operating system details

Processor: Speed: Memory size: Mb:

Operating System: Version:

Results for basic statistics

Minimum value Located at

Maximum value Located at

Mean Value

Root Mean Square Value

Standard Deviation Value

Number of points

Spectral Density Results

Comparison of reference points

	Point	Values	Point	Values	Point	Values	Point	Values
ASD_1	1	X= Y=	8	X= Y=	17	X= Y=	28	X= Y=
ASD_2	1	X= Y=	29	X= Y=	65	X= Y=	110	X= Y=
ASD_3	1	X= Y=	8	X= Y=	17	X= Y=	28	X= Y=
ASD_4	1	X= Y=	29	X= Y=	65	X= Y=	110	X= Y=

Please detail any differences found and supply the data in ASCII form in datasets named

{Identifier}_DATA_RESULT_ASD_n.TXT

where Identifier is your name and n is the number for the result as in the table above.

Comments:

Suggestions for further benchmark tests:

Return results to: Dr. B. J .May 1, Westhall Road, Mickleover, Derby. DE3 0PA. UK

Email: verification@e-i-s.org.uk Tel/Fax: +44 (01332) 737034

NOTES:

1. Numeric precision

All results should be quoted to 4 significant figures.

2. Trailing zeros

Trailing zeros may be suppressed.

3. Use of results

The working party may make use of the information received in Analysis results returns for the purpose of promoting the work of the party and for informing the Data Analysis community of the variation of results obtained.

When results are used for presentations no reference will be made to either the source or analysis package employed.