Division 7.8.3.5 Validation statistics (see Appendix 2 of Annex VII)
United Kingdom
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:
is the feedback value of speed (min– 1), torque (Nm), or power (kW)
is the slope of the regression line
is the reference value of speed (min– 1), torque (Nm), or power (kW)
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.
F1Table 6.3
Permitted point deletions from regression analysis
| Where: n refis the reference speed (see section 7.7.2.), is the idle speed, is the actual (measured) speed, is the reference torque (see section 7.7.2.), is the actual (measured) torque, 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 |