Document ID: chunk:federal_register_of_legislation:F2023L00129:reg:13:p11
Version: federal_register_of_legislation:F2023L00129
Segment Type: reg
Provision Reference: reg 13 (pt 11/56)
Character Range: 324482–327469

starting shall be omitted. Actual cycle work shall be determined over the test cycle by synchronously using actual speed and actual torque values to calculate instantaneous values for engine power. Instantaneous engine power values shall be integrated over the test cycle to calculate the actual cycle work Wact (kWh). If auxiliaries/equipment are not fitted in accordance with paragraph 6.3.1., the instantaneous power values shall be corrected using equation 4 in paragraph 6.3.5.

 The same methodology as described in paragraph 7.4.8. shall be used for integrating actual engine power.

 The actual cycle work Wact is used for comparison to the reference cycle work Wref and for calculating the brake specific emissions (see paragraph 8.6.3.).

 Wact shall be between 85 per cent and 105 per cent of Wref

7.8.7. Validation statistics of the test cycle

Linear regressions of the actual values (nact, Mact, Pact) on the reference values (nref, Mref, Pref) shall be performed for both the WHTC and the WHSC.

To minimize the biasing effect of the time lag between the actual and reference cycle values, the entire engine speed and torque actual signal sequence may be advanced or delayed in time with respect to the reference speed and torque sequence. If the actual 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:

y  =  a1x + a0 (11)

 Where:
y   is the actual value of speed (min-1), torque (Nm), or power (kW)
a1  is the slope of the regression line
x  is the reference value of speed (min-1), torque (Nm), or power (kW)
a0  is the y intercept of the regression line

 The standard error of estimate (SEE) of y on x and the coefficient of determination (r²) shall be calculated for each regression line.

 It is recommended that this analysis be performed at 1 Hz. For a test to be considered valid, the criteria of Table 2 (WHTC) or Table 3 (WHSC) shall be met.
       Table 2
       Regression line tolerances for the WHTC
                                            Speed                                     Torque                                                        Power
Standard error of estimate (SEE) of y on x  maximum 5 per cent of maximum test speed  maximum 10 per cent of maximum engine torque                  maximum 10 per cent of maximum engine power

Slope of the regression line, a1            0.95 to 1.03                              0.83 - 1.03                                                   0.89 - 1.03

Coefficient of determination, r²            minimum 0.970                             minimum 0.850                                                 minimum 0.910

y intercept of the regression line, a0      maximum 10 per cent of idle speed         ±20 Nm or 2 per cent of maximum torque whichever is greater  ±4 kW or 2 per cent of maximum power whichever is greater

       Table 3
       Regression