ANNEX VII
The measurement data for the calculation of the individual mode results are shown below. In this example, CO and NOx are measured on a dry basis, HC on a wet basis. The HC concentration is given in propane equivalent (C3) and has to be multiplied by 3 to result in the C1 equivalent. The calculation procedure is identical for the other modes. P (kW) | Ta (K) | Ha (g/kg) | GEXH (kg) | GAIRW (kg) | GFUEL (kg) | HC (ppm) | CO (ppm) | NOx (ppm) 82,9 | 294,8 | 7,81 | 563,38 | 545,29 | 18,09 | 6,3 | 41,2 | 495 and The following example calculation is given for CO; the calculation procedure is identical for the other components. The emission mass flow rates of the individual modes are multiplied by the respective weighting factors, as indicated in Annex III, Appendix 1, Section 2.7.1, and summed up to result in the mean emission mass flow rate over the cycle: CO | = | | = | 30,91 g/h The engine power of the individual modes is multiplied by the respective weighting factors, as indicated in Annex III, Appendix 1, Section 2.7.1, and summed up to result in the mean cycle power: | = | | = | 60,006 kW Assume the following values have been determined on the random point: nZ | = | 1 600 min-1 MZ | = | 495 Nm NOx mass,Z | = | 487,9 g/h (calculated according to the previous formulae) P(n)Z | = | 83 kW NOx,Z | = | 487,9/83 = 5,878 g/kWh Assume the values of the four enveloping modes on the ESC to be as follows: nRT | nSU | ER | ES | ET | EU | MR | MS | MT | MU 1 368 | 1 785 | 5,943 | 5,565 | 5,889 | 4,973 | 515 | 460 | 681 | 610 Particulate measurement is based on the principle of sampling the particulates over the complete cycle, but determining the sample and flow rates (MSAM and GEDF) during the individual modes. The calculation of GEDF depends on the system used. In the following examples, a system with CO2 measurement and carbon balance method and a system with flow measurement are used. When using a full flow dilution system, GEDF is directly measured by the CVS equipment. Assume the following measurement data of mode 4. The calculation procedure is identical for the other modes. GEXH (kg/h) | GFUEL (kg/h) | GDILW (kg/h) | GTOTW (kg/h) | CO2D (%) | CO2A (%) 334,02 | 10,76 | 5,4435 | 6,0 | 0,657 | 0,040 carbon balance method flow measurement method The GEDFW flow rates of the individual modes are multiplied by the respective weighting factors, as indicated in Annex III, Appendix 1, Section 2.7.1, and summed up to result in the mean GEDF over the cycle. The total sample rate MSAM is summed up from the sample rates of the individual modes. | = | | = | 3 604,6 kg/h | = | 0,226 + 0,122 + 0,151 + 0,152 + 0,076 + 0,076 + 0,076 + 0,136 + 0,151 + 0,121 + 0,076 + 0,076 + 0,075 | = | 1,515 kg Assume the particulate mass on the filters to be 2,5 mg, then Assume one background measurement with the following values. The calculation of the dilution factor DF is identical to Section 3.1 of this Annex and not shown here. Sum of DF | = | | = | 0,923 | = | | = | 60,006 kW Assume the values calculated for mode 4 above, then This value is within the required value of 0,10 ± 0,003. Since Bessel filtering is a completely new averaging procedure in European exhaust legislation, an explanation of the Bessel filter, an example of the design of a Bessel algorithm, and an example of the calculation of the final smoke value is given below. The constants of the Bessel algorithm only depend on the design of the opacimeter and the sampling rate of the data acquisition system. It is recommended that the opacimeter manufacturer provide the final Bessel filter constants for different sampling rates and that the customer use these constants for designing the Bessel algorithm and for calculating the smoke values. Due to high frequency distortions, the raw opacity signal usually shows a highly scattered trace. To remove these high frequency distortions a Bessel filter is required for the ELR-test. The Bessel filter itself is a recursive, second-order low-pass filter which guarantees the fastest signal rise without overshoot. Assuming a real time raw exhaust plume in the exhaust tube, each opacimeter shows a delayed and differently measured opacity trace. The delay and the magnitude of the measured opacity trace is primarily dependent on the geometry of the measuring chamber of the opacimeter, including the exhaust sample lines, and on the time needed for processing the signal in the electronics of the opacimeter. The values that characterise these two effects are called the physical and the electrical response time which represent an individual filter for each type of opacimeter. The goal of applying a Bessel filter is to guarantee a uniform overall filter characteristic of the whole opacimeter system, consisting of: physical response time of the opacimeter (tp), electrical response time of the opacimeter (te), filter response time of the applied Bessel filter (tF). The resulting overall response time of the system tAver is given by: and must be equal for all kinds of opacimeters in order to give the same smoke value. Therefore, a Bessel filter has to be created in such a way, that the filter response time (tF) together with the physical (tp) and electrical response time (te) of the individual opacimeter must result in the required overall response time (tAver). Since tp and te are given values for each individual opacimeter, and tAver is defined to be 1,0 s in this Directive, tF can be calculated as follows: By definition, the filter response time tF is the rise time of a filtered output signal between 10 % and 90 % on a step input signal. Therefore the cut-off frequency of the Bessel filter has to be iterated in such a way, that the response time of the Bessel filter fits into the required rise time. Figure a Traces of a step input signal and the filtered output signal Step input signal Signal [-] Bessel filtered output signal Time [s] In Figure a, the traces of a step input signal and Bessel filtered output signal as well as the response time of the Bessel filter (tF) are shown. Designing the final Bessel filter algorithm is a multi step process which requires several iteration cycles. The scheme of the iteration procedure is presented below. Characteristics of opacimeter tp, te [s] Regulation tAver [s] Data acquisition system sample rate [Hz] Required overall Bessel filter response time tF Step 1 fc = fc,new Design of Bessel filter algorithm fc, E, K Step 2 Application of Bessel filter on step input Step 3 t(10 %), t(90 %) Calculation of iterated filter response time tF,iter = t(90 %) - t(10 %) Step 4 Adjustment of cut-off frequency fc,new = fc × (1 + Δ) Deviation between tF and tF,iter Step 5 Iteration Check for iteration criteria no |Δ| ≤ 0,01 yes Step 6 Final Bessel filter constants and algorithm Yi = … Step 7 In this example a Bessel algorithm is designed in several steps according to the above iteration procedure which is based upon Annex III, Appendix 1, Section 6.1. For the opacimeter and the data acquisition system, the following characteristics are assumed: physical response time tp 0,15 s electrical response time te 0,05 s overall response time tAver 1,00 s (by definition in this Directive) sampling rate 150 Hz fc | = | Δt | = | 1/150 = 0,006667 s Ω | = | E | = | K | = | This gives the Bessel algorithm: where Si represents the values of the step input signal (either ‘0’ or ‘1’) and Yi represents the filtered values of the output signal. The Bessel filter response time tF is defined as the rise time of the filtered output signal between 10 % and 90 % on a step input signal. For determining the times of 10 % (t10) and 90 % (t90) of the output signal, a Bessel filter has to be applied to a step input using the above values of fc, E and K. The index numbers, the time and the values of a step input signal and the resulting values of the filtered output signal for the first and the second iteration are shown in Table B. The points adjacent to t10 and t90 are marked in bold numbers. In Table B, first iteration, the 10 % value occurs between index number 30 and 31 and the 90 % value occurs between index number 191 and 192. For the calculation of tF,iter the exact t10 and t90 values are determined by linear interpolation between the adjacent measuring points, as follows: where outupper and outlower, respectively, are the adjacent points of the Bessel filtered output signal, and tlower is the time of the adjacent time point, as indicated in Table B. |Δ| ≤ 0,01 is required. Since 0,081641 > 0,01, the iteration criteria is not met and a further iteration cycle has to be started. For this iteration cycle, a new cut-off frequency is calculated from fc and Δ as follows: This new cut-off frequency is used in the second iteration cycle, starting at step 2 again. The iteration has to be repeated until the iteration criteria is met. The resulting values of the first and second iteration are summarised in Table A. Table A Values of the first and second iteration Parameter | 1. Iteration | 2. Iteration fc | (Hz) | 0,318152 | 0,344126 E | (-) | 7,07948 E-5 | 8,272777 E-5 K | (-) | 0,970783 | 0,968410 t10 | (s) | 0,200945 | 0,185523 t90 | (s) | 1,276147 | 1,179562 tF,iter | (s) | 1,075202 | 0,994039 Δ | (-) | 0,081641 | 0,006657 fc,new | (Hz) | 0,344126 | 0,346417 As soon as the iteration criteria has been met, the final Bessel filter constants and the final Bessel algorithm are calculated according to step 2. In this example, the iteration criteria has been met after the second iteration (Δ = 0,006657 ≤ 0,01). The final algorithm is then used for determining the averaged smoke values (see next Section 2.3). Table B Values of step input signal and Bessel filtered output signal for the first and second iteration cycle Index i [-] | Time [s] | Step input signal Si [-] | Filtered output signal Yi [-] 1. Iteration | 2. Iteration - 2 | - 0,013333 | 0 | 0,000000 | 0,000000 - 1 | - 0,006667 | 0 | 0,000000 | 0,000000 0 | 0,000000 | 1 | 0,000071 | 0,000083 1 | 0,006667 | 1 | 0,000352 | 0,000411 2 | 0,013333 | 1 | 0,000908 | 0,001060 3 | 0,020000 | 1 | 0,001731 | 0,002019 4 | 0,026667 | 1 | 0,002813 | 0,003278 5 | 0,033333 | 1 | 0,004145 | 0,004828 ~ | ~ | ~ | ~ | ~ 24 | 0,160000 | 1 | 0,067877 | 0,077876 25 | 0,166667 | 1 | 0,072816 | 0,083476 26 | 0,173333 | 1 | 0,077874 | 0,089205 27 | 0,180000 | 1 | 0,083047 | 0,095056 28 | 0,186667 | 1 | 0,088331 | 0,101024 29 | 0,193333 | 1 | 0,093719 | 0,107102 30 | 0,200000 | 1 | 0,099208 | 0,113286 31 | 0,206667 | 1 | 0,104794 | 0,119570 32 | 0,213333 | 1 | 0,110471 | 0,125949 33 | 0,220000 | 1 | 0,116236 | 0,132418 34 | 0,226667 | 1 | 0,122085 | 0,138972 35 | 0,233333 | 1 | 0,128013 | 0,145605 36 | 0,240000 | 1 | 0,134016 | 0,152314 37 | 0,246667 | 1 | 0,140091 | 0,159094 ~ | ~ | ~ | ~ | ~ 175 | 1,166667 | 1 | 0,862416 | 0,895701 176 | 1,173333 | 1 | 0,864968 | 0,897941 177 | 1,180000 | 1 | 0,867484 | 0,900145 178 | 1,186667 | 1 | 0,869964 | 0,902312 179 | 1,193333 | 1 | 0,872410 | 0,904445 180 | 1,200000 | 1 | 0,874821 | 0,906542 181 | 1,206667 | 1 | 0,877197 | 0,908605 182 | 1,213333 | 1 | 0,879540 | 0,910633 183 | 1,220000 | 1 | 0,881849 | 0,912628 184 | 1,226667 | 1 | 0,884125 | 0,914589 185 | 1,233333 | 1 | 0,886367 | 0,916517 186 | 1,240000 | 1 | 0,888577 | 0,918412 187 | 1,246667 | 1 | 0,890755 | 0,920276 188 | 1,253333 | 1 | 0,892900 | 0,922107 189 | 1,260000 | 1 | 0,895014 | 0,923907 190 | 1,266667 | 1 | 0,897096 | 0,925676 191 | 1,273333 | 1 | 0,899147 | 0,927414 192 | 1,280000 | 1 | 0,901168 | 0,929121 193 | 1,286667 | 1 | 0,903158 | 0,930799 194 | 1,293333 | 1 | 0,905117 | 0,932448 195 | 1,300000 | 1 | 0,907047 | 0,934067 ~ | ~ | ~ | ~ | ~ In the scheme below the general procedure of determining the final smoke value is presented. Speed A Load step 1 Speed B Load step 1 Speed C Load step 1 Speed A Load step 2 Speed B Load step 2 Speed C Load step 2 Speed A Load step 3 Speed B Load step 3 Speed C Load step 3 Raw opacity values N [%] Conversion to light absorption coefficient k [1/m] k = -(1/LA) × ln(1-N/100) Filtering with Bessel filter Selection of maximum k-value (peak) for each speed and load step Ymax1,A Ymax1,B Ymax1,C Ymax2,A Ymax2,B Ymax2,C Ymax3,A Ymax3,B Ymax3,C Cycle validation for each speed Calculation of mean smoke value for each speed SVA = (Ymax1,A + Ymax2,A + Ymax3,A)/3 SVB = (Ymax1,B + Ymax2,B + Ymax3,B)/3 SVC = (Ymax1,C + Ymax2,C + Ymax3,C)/3 Calculation of the final smoke value SV = 0,43 × SVA + 0,56 × SVB + 0,01 × SVC In Figure b, the traces of the measured raw opacity signal, and of the unfiltered and filtered light absorption coefficients (k-value) of the first load step of an ELR-Test are shown, and the maximum value Ymax1,A (peak) of the filtered k trace is indicated. Correspondingly, Table C contains the numerical values of index i, time (sampling rate of 150 Hz), raw opacity, unfiltered k and filtered k. Filtering was conducted using the constants of the Bessel algorithm designed in Section 2.2 of this Annex. Due to the large amount of data, only those sections of the smoke trace around the beginning and the peak are tabled. Figure b Traces of measured opacity N, of unfiltered smoke k and of filtered smoke k Peak = 0,5424 m-1 Opacity N Unfiltered smoke k Filtered smoke k Opacity N [%] Smoke k [1/m] Time [s] The peak value (i = 272) is calculated assuming the following data of Table C. All other individual smoke values are calculated in the same way. For starting the algorithm, S-1, S-2, Y-1 and Y-2 are set to zero. LA (m) | 0,430 Index i | 272 N ( %) | 16,783 S271 (m-1) | 0,427392 S270 (m-1) | 0,427532 Y271 (m-1) | 0,542383 Y270 (m-1) | 0,542337 This value corresponds to S272 in the following equation. In the following equation, the Bessel constants of the previous Section 2.2 are used. The actual unfiltered k-value, as calculated above, corresponds to S272 (Si). S271 (Si-1) and S270 (Si-2) are the two preceding unfiltered k-values, Y271 (Yi-1) and Y270 (Yi-2) are the two preceding filtered k-values. | = | | = | This value corresponds to Ymax1,A in the following equation. From each smoke trace, the maximum filtered k-value is taken for the further calculation. Assume the following values Speed | Ymax (m-1) Cycle 1 | Cycle 2 | Cycle 3 A | 0,5424 | 0,5435 | 0,5587 B | 0,5596 | 0,5400 | 0,5389 C | 0,4912 | 0,5207 | 0,5177 Before calculating SV, the cycle must be validated by calculating the relative standard deviations of the smoke of the three cycles for each speed. Speed | Mean SV (m-1) | Absolute standard deviation (m-1) | Relative standard deviation (%) A | 0,5482 | 0,0091 | 1,7 B | 0,5462 | 0,0116 | 2,1 C | 0,5099 | 0,0162 | 3,2 In this example, the validation criteria of 15 % are met for each speed. Table C Values of opacity N, unfiltered and filtered k-value at beginning of load step Index i [-] | Time [s] | Opacity N [%] | Unfiltered k-value [m-1] | Filtered k-value [m-1] - 2 | 0,000000 | 0,000000 | 0,000000 | 0,000000 - 1 | 0,000000 | 0,000000 | 0,000000 | 0,000000 0 | 0,000000 | 0,000000 | 0,000000 | 0,000000 1 | 0,006667 | 0,020000 | 0,000465 | 0,000000 2 | 0,013333 | 0,020000 | 0,000465 | 0,000000 3 | 0,020000 | 0,020000 | 0,000465 | 0,000000 4 | 0,026667 | 0,020000 | 0,000465 | 0,000001 5 | 0,033333 | 0,020000 | 0,000465 | 0,000002 6 | 0,040000 | 0,020000 | 0,000465 | 0,000002 7 | 0,046667 | 0,020000 | 0,000465 | 0,000003 8 | 0,053333 | 0,020000 | 0,000465 | 0,000004 9 | 0,060000 | 0,020000 | 0,000465 | 0,000005 10 | 0,066667 | 0,020000 | 0,000465 | 0,000006 11 | 0,073333 | 0,020000 | 0,000465 | 0,000008 12 | 0,080000 | 0,020000 | 0,000465 | 0,000009 13 | 0,086667 | 0,020000 | 0,000465 | 0,000011 14 | 0,093333 | 0,020000 | 0,000465 | 0,000012 15 | 0,100000 | 0,192000 | 0,004469 | 0,000014 16 | 0,106667 | 0,212000 | 0,004935 | 0,000018 17 | 0,113333 | 0,212000 | 0,004935 | 0,000022 18 | 0,120000 | 0,212000 | 0,004935 | 0,000028 19 | 0,126667 | 0,343000 | 0,007990 | 0,000036 20 | 0,133333 | 0,566000 | 0,013200 | 0,000047 21 | 0,140000 | 0,889000 | 0,020767 | 0,000061 22 | 0,146667 | 0,929000 | 0,021706 | 0,000082 23 | 0,153333 | 0,929000 | 0,021706 | 0,000109 24 | 0,160000 | 1,263000 | 0,029559 | 0,000143 25 | 0,166667 | 1,455000 | 0,034086 | 0,000185 26 | 0,173333 | 1,697000 | 0,039804 | 0,000237 27 | 0,180000 | 2,030000 | 0,047695 | 0,000301 28 | 0,186667 | 2,081000 | 0,048906 | 0,000378 29 | 0,193333 | 2,081000 | 0,048906 | 0,000469 30 | 0,200000 | 2,424000 | 0,057067 | 0,000573 31 | 0,206667 | 2,475000 | 0,058282 | 0,000693 32 | 0,213333 | 2,475000 | 0,058282 | 0,000827 33 | 0,220000 | 2,808000 | 0,066237 | 0,000977 34 | 0,226667 | 3,010000 | 0,071075 | 0,001144 35 | 0,233333 | 3,253000 | 0,076909 | 0,001328 36 | 0,240000 | 3,606000 | 0,085410 | 0,001533 37 | 0,246667 | 3,960000 | 0,093966 | 0,001758 38 | 0,253333 | 4,455000 | 0,105983 | 0,002007 39 | 0,260000 | 4,818000 | 0,114836 | 0,002283 40 | 0,266667 | 5,020000 | 0,119776 | 0,002587 Values of opacity N, unfiltered and filtered k-value around Ymax1,A (≡ peak value, indicated in bold number) Index i [-] | Time [s] | Opacity N [%] | Unfiltered k-value [m-1] | Filtered k-value [m-1] 259 | 1,726667 | 17,182000 | 0,438429 | 0,538856 260 | 1,733333 | 16,949000 | 0,431896 | 0,539423 261 | 1,740000 | 16,788000 | 0,427392 | 0,539936 262 | 1,746667 | 16,798000 | 0,427671 | 0,540396 263 | 1,753333 | 16,788000 | 0,427392 | 0,540805 264 | 1,760000 | 16,798000 | 0,427671 | 0,541163 265 | 1,766667 | 16,798000 | 0,427671 | 0,541473 266 | 1,773333 | 16,788000 | 0,427392 | 0,541735 267 | 1,780000 | 16,788000 | 0,427392 | 0,541951 268 | 1,786667 | 16,798000 | 0,427671 | 0,542123 269 | 1,793333 | 16,798000 | 0,427671 | 0,542251 270 | 1,800000 | 16,793000 | 0,427532 | 0,542337 271 | 1,806667 | 16,788000 | 0,427392 | 0,542383 272 | 1,813333 | 16,783000 | 0,427252 | 0,542389 273 | 1,820000 | 16,780000 | 0,427168 | 0,542357 274 | 1,826667 | 16,798000 | 0,427671 | 0,542288 275 | 1,833333 | 16,778000 | 0,427112 | 0,542183 276 | 1,840000 | 16,808000 | 0,427951 | 0,542043 277 | 1,846667 | 16,768000 | 0,426833 | 0,541870 278 | 1,853333 | 16,010000 | 0,405750 | 0,541662 279 | 1,860000 | 16,010000 | 0,405750 | 0,541418 280 | 1,866667 | 16,000000 | 0,405473 | 0,541136 281 | 1,873333 | 16,010000 | 0,405750 | 0,540819 282 | 1,880000 | 16,000000 | 0,405473 | 0,540466 283 | 1,886667 | 16,010000 | 0,405750 | 0,540080 284 | 1,893333 | 16,394000 | 0,416406 | 0,539663 285 | 1,900000 | 16,394000 | 0,416406 | 0,539216 286 | 1,906667 | 16,404000 | 0,416685 | 0,538744 287 | 1,913333 | 16,394000 | 0,416406 | 0,538245 288 | 1,920000 | 16,394000 | 0,416406 | 0,537722 289 | 1,926667 | 16,384000 | 0,416128 | 0,537175 290 | 1,933333 | 16,010000 | 0,405750 | 0,536604 291 | 1,940000 | 16,010000 | 0,405750 | 0,536009 292 | 1,946667 | 16,000000 | 0,405473 | 0,535389 293 | 1,953333 | 16,010000 | 0,405750 | 0,534745 294 | 1,960000 | 16,212000 | 0,411349 | 0,534079 295 | 1,966667 | 16,394000 | 0,416406 | 0,533394 296 | 1,973333 | 16,394000 | 0,416406 | 0,532691 297 | 1,980000 | 16,192000 | 0,410794 | 0,531971 298 | 1,986667 | 16,000000 | 0,405473 | 0,531233 299 | 1,993333 | 16,000000 | 0,405473 | 0,530477 300 | 2,000000 | 16,000000 | 0,405473 | 0,529704 Assume the following test results for a PDP-CVS system V0 (m3/rev) | 0,1776 Np (rev) | 23 073 pB (kPa) | 98,0 p1 (kPa) | 2,3 T (K) | 322,5 Ha (g/kg) | 12,8 NOx conce (ppm) | 53,7 NOx concd (ppm) | 0,4 COconce (ppm) | 38,9 COconcd (ppm) | 1,0 HCconce (ppm) | 9,00 HCconcd (ppm) | 3,02 CO2,conce (%) | 0,723 Wact (kWh) | 62,72 Assuming a diesel fuel of the composition C1H1,8 Assume the following test results for a PDP-CVS system with double dilution MTOTW (kg) | 4 237,2 Mf,p (mg) | 3,030 Mf,b (mg) | 0,044 MTOT (kg) | 2,159 MSEC (kg) | 0,909 Md (mg) | 0,341 MDIL (kg) | 1,245 DF | 18,69 Wact (kWh) | 62,72 Assume the following test results for a PDP-CVS system with double dilution MTOTW (kg) | 4 237,2 Ha (g/kg) | 12,8 NOx conce (ppm) | 17,2 NOx concd (ppm) | 0,4 COconce (ppm) | 44,3 COconcd (ppm) | 1,0 HCconce (ppm) | 27,0 HCconcd (ppm) | 3,02 CH4 conce (ppm) | 18,0 CH4 concd (ppm) | 1,7 CO2,conce ( %) | 0,723 Wact (kWh) | 62,72 GC method NMC method Assuming a methane efficiency of 0,04 and an ethane efficiency of 0,98 (see Annex III, Appendix 5, Section 1.8.4) Assuming a G20 reference fuel (100 % methane) of the composition C1H4: where: Sλ | = | λ-shift factor; inert % | = | % by volume of inert gases in the fuel (i.e. N2, CO2, He, etc.); O2 * | = | % by volume of original oxygen in the fuel; n and m | = | refer to average CnHm representing the fuel hydrocarbons, i.e: where: CH4 | = | % by volume of methane in the fuel; C2 | = | % by volume of all C2 hydrocarbons (e.g. C2H6, C2H4, etc.) in the fuel; C3 | = | % by volume of all C3 hydrocarbons (e.g. C3H8, C3H6, etc.) in the fuel; C4 | = | % by volume of all C4 hydrocarbons (e.g. C4H10, C4H8, etc.) in the fuel C5 | = | % by volume of all C5 hydrocarbons (e.g. C5H12, C5H10, etc.) in the fuel; diluent | = | % by volume of dilution gases in the fuel (i.e. O2 *, N2, CO2, He etc.). | Example 1: | G25: CH4 = 86 %, N2 = 14 % (by volume) | Example 2: | GR: CH4 = 87 %, C2H6 = 13 % (by vol) | Example 3: | USA: CH4 = 89 %, C2H6 = 4,5 %, C3H8 = 2,3 %, C6H14 = 0,2 %, O2 = 0,6 %, N2 = 4 %
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Source: EUR-Lex (Cellar) · retrieved 2026-11-01 · Text as adopted (Official Journal); later amendments are not incorporated in this text.