# Commission Delegated Regulation (EU) 2017/654 of 19 December 2016 supplementing Regulation (EU) 2016/1628 of the European Parliament and of the Council with regard to technical and general requirements relating to emission limits and type-approval for internal combustion engines for non-road mobile machinery, Division 7.8.3.5: Validation statistics (see Appendix 2 of Annex VII)

Extent: E+W+S+N.I.

Linear regression between the reference and the feedback values shall be calculated for speed, torque and power.
To minimize the biasing effect of the time lag between the reference and feedback cycle values, the entire engine speed and torque feedback signal sequence may be advanced or delayed in time with respect to the reference speed and torque sequence. If the feedback signals are shifted, both speed and torque shall be shifted by the same amount in the same direction.
The method of least squares shall be used, with the best-fit equation having the form set out in equation (6-19):
y = a 1 x + a 0
(6-19)
where:
y is the feedback value of speed (min– 1), torque (Nm), or power (kW)
a 1 is the slope of the regression line
x is the reference value of speed (min– 1), torque (Nm), or power (kW)
a 0 is the y intercept of the regression line.
The standard error of estimate (SEE) of y on x and the coefficient of determination (r 2) shall be calculated for each regression line in accordance with Appendix 3 of Annex VII.
It is recommended that this analysis be performed at 1 Hz. For a test to be considered valid, the criteria of Table 6.2 shall be met.
Table 6.2
Regression line tolerances
Speed
Torque
Power
Standard error of estimate (SEE) of y on x
≤ 5,0 percent of maximum test speed
≤ 10,0 % of maximum mapped torque
≤ 10,0 % of maximum mapped power
Slope of the regression line, a 1
0,95 to 1,03
0,83 - 1,03
0,89 - 1,03
Coefficient of determination, r 2
minimum 0,970
minimum 0,850
minimum 0,910
y intercept of the regression line, a 0
≤ 10 % of idle
± 20 Nm or ± 2 % of maximum torque whichever is greater
± 4 kW or ± 2 % of maximum power whichever is greater
For regression purposes only, point deletions are permitted where noted in Table 6.3 before doing the regression calculation. However, those points shall not be deleted for the calculation of cycle work and emissions. An idle point is defined as a point having a normalized reference torque of 0 % and a normalized reference speed of 0 %. Point deletion may be applied to the whole or to any part of the cycle; points to which the point deletion is applied have to be specified.
Table 6.3
Permitted point deletions from regression analysis
Where:
n ref is the reference speed (see section 7.7.2.),
n idle is the idle speed,
n act is the actual (measured) speed,
T ref is the reference torque (see section 7.7.2.),
T act is the actual (measured) torque,
T maxmappedtorque is the highest value of torque on the full-load torque curve mapped in accordance with section 7.6.
Event
Conditions ( n = engine speed, T = torque)
Permitted point deletions
Minimum operator demand (idle point)
n ref = n idle
and
T ref = 0 %
and
T act > ( T ref – 0,02 T maxmappedtorque )
and
T act < ( T ref + 0,02 T maxmappedtorque )
speed and power
Minimum operator demand
n act ≤ 1,02 n ref and T act > T ref
or
n act > n ref and T act ≤ T ref'
or
n act > 1,02 n ref and T ref < T act ≤ ( T ref + 0,02 T maxmappedtorque )
power and either torque or speed
Maximum operator demand
n act < n ref and T act ≥ T ref
or
n act ≥ 0,98 n ref and T act < T ref
or
n act < 0,98 n ref and T ref > T act ≥ ( T ref – 0,02 T maxmappedtorque )
power and either torque or speed

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Source: https://www.legislation.gov.uk/eur/2017/654/annex/VI/division/7/division/7.8/division/7.8.3/division/7.8.3.5 (the official version)
Page: https://openlegislation.uk/eu-regulation-2017-654/annex-VI/division-7/division-7.8/division-7.8.3/division-7.8.3.5
Contains public sector information licensed under the Open Government Licence v3.0. Source: legislation.gov.uk, The National Archives.