Decision & abrupt change detection

Transcription

1 Decision & abrupt change Statistical tools P. Grenoble INP, ense3, gipsa-lab

2 The estimation problem p X θ (x) f ( ) Physical system unknown parameter θ Measurements X = [X(0),, X(k)] Decision ˆΘ = f (X) θ: unknown parameter to estimate, deterministic X: measurement vector, random p X θ (x): stochastic model linking θ and X f ( ): estimator of θ ˆΘ: estimated parameter, random 2 / 5

3 The problem p X H (x H j ) g( ) Physical system unknown event H = H 0 Measurements X = [X(0),, X(k)] Decision Ĥ = g (X) = H0 H: unknown event to detect discrete random variable = H 0 = 2 hypothesis with "a priori" probabilities P Hj = Prob [H = H j ] X: measurement vector, random p X H (x H j ): stochastic model linking H and X g( ): decision function for H Ĥ: detected event, random 3 / 5

4 Spark Plug Ignition System Pressure Sensor Ampl. Missing Cogs Cog-wheel Inductive Sensor LP Filters Data Acquisition Computer One problem Cylinder pressure based combustion engine monitoring 5IonizationCurrentInterpretation 29 completeness of combustion before exhaust valve opening to insure that spark retard is not excessive. 4. Cylinder pressure-based control can also simplify and speed the tedious cold-start calibration process. Figure 31. MPR vs. IMEP at 4000 rpm and Zero Brake Torque. Depending on OBDII requirements and system Figure 4 The measurement situation. The pressure sensor requirements is used only for for misfire, the system may be validation. calibrated to simply detect total misfires or may be calibrated more aggressively to detect partial-burn Internal combustion engine cycles. Partial-burn cycles may also contribute to catalyst 5 Ionization Current Interpretation degradation. An MPR of 1.0 was chosen as an example of a partial-burn threshold in figures 28 through 31. Figure 32. Typical Cylinder Pressure Waveforms for the Cold Start with Greater and Less Fuel Evaporation. Cylinder pressure signal The ionization current is affected by several parameters other than the 65 cylinder pressure. Aiming at ignition control, using the ionization current and the peak COLD START CONTROL The cold start is a critical pressure algorithm, special care must be taken when extracting the pressure information from the ionization current. portion of 60the FTP test and is responsible for the majority of HC emissions generated for this test. In order to tolerate 55 the incomplete evaporation of fuel with acceptable driveability, open-loop fueling calibrations for 5.1 Connection between ionization and pressure 50 the cold start must be biased rich. This typically results in As mentioned earlier, and displayed in Figure 5, the pressure a has 40 most to 50 influence percent HC emissions penalty relative to a 45 on the post-flame phase of the ionization current. Problems occur cold when start searching with ideal fuel delivery. Open-loop spark timing for the peak pressure position: a peak search is not feasible since the flame-front control is 40 also used during the cold start. Since the gasphase peaks ina/f the flame and combustion burn rates depend on the phase often consists of more than one peak, and the post-flame phase often appears without a peak. In Figure 6 an ionization current signal with two front and no peak in the post flame is displayed. It can be seen completeness that the ionization 35 of fuel evaporation, spark timing must be signal contains information about the pressure in the post-flame phase, despite the advanced to prevent partial burn cycles. This increases fact that the post-flame phase does not contain a peak. 30 Figure 33. Typical Pressure-Ratio Waveforms for the the catalyst 0 light-off 200 period and 400 further increases 600 HC Cold Start with Greater and Less Fuel emissions. Even with optimized spark turns and fueling Evaporation. calibrations for the cold start, many production vehicles suffer from poor driveability when the lowest volatility To demonstrate the basis for A/F control during the cold fuels are used. Maximum pressure value / enginestart, turns Figures 32 and 33 show typical cylinder pressure Cylinder pressure sensing and Pressure-Ratio waveforms and calculated pressure ratios, respectively, Management can improve engine control during the cold for combustion with greater fuel evaporation and start in several ways: combustion with less fuel evaporation. For fixed spark timing, reduced burn rate for combustion with less fuel 1. Method 2 Dilution Control (see page 5) can be used evaporation causes a significantly later burn with to control the gas-phase A/F slightly lean of incomplete heat release by the 55 CAD ATDC sample stoichiometric. This prevents over fueling and point. This produces reduced PRM10 (and PRM25) and reduces HC emissions. reduced FPR (MPR) as shown in Figure Closed-loop (C/L) spark-timing control using PRM10 and PRM25 can provide precise spark retard KNOCK DETECTION The Spark-Plug-Boss Sensor is control and improve catalyst heating. located a short distance directly above each combustion 3. Spark retard is needed for catalyst heating but chamber. The mechanical load path between the excessive retard will increase HC emissions due to combustion chamber and the sensor is very stiff and incomplete combustion. MPR measured during the provides good response to knock-induced structural expansion stroke can be used to indicate vibrations over a wide range of frequencies. Valve train noise, such as noise created at valve closing, occurs Pa The maximum pressure value per turn combustion quality can be used to monitor the condition of the engine. 4 / 5

5 Necessary statistical tools : maximum likelihood principle θ unknown p X θ (x) likelihood: v(θ) = p X θ (x obs ) measurements X maximum likelihood estimator: ˆθ MV = arg max v(θ) θ : likelihood ratio principle H { H0 unknown p X H (x H j ) likelihood ratio: RV(x) = p X H(x ) p X H(x H 0) measurements X GLRT detector: RV(x) > < H 0 s threshold s determined by Bayes (P Hj ), Neyman-Pearson (P F ), or experimental approach unknown (nuisance) parameters replaced by their maximum likelihood estimates 5 / 5