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DIAGNOSIS OF CAM PROFILE SWITCHING OF AN AUTOMOBILE GASOLINE ENGINE David Antory1, Paul J. King 2, R. Peter Jones1,3 and Ross McMurran1 International Automotive Research Centre, University of Warwick, Coventry, CV4 7AL, U.K. Powertrain Electronics Controls Simulation, Jaguar Cars Limited, Coventry, CV3 4BJ, U.K. 3 School of Engineering, University of Warwick, Coventry, CV4 7AL, U.K. 1 2 Abstract: The investigation on cam profile switching (CPS) in an automotive gasoline engine is presented. The performance of the CPS system is monitored and analysed to allow a diagnostic technique to be developed to determine whether the engine valves have operated to their correctly commanded position. The proposed diagnostic was developed from tests undertaken on a gasoline engine. The proposed approach is capable of performing accurate and reliable condition monitoring and diagnosis using Principal Component Analysis techniques. The results of the diagnostic are presented later in the paper. Keywords: Automobiles, Detection, Diagnosis, Engines, Process Monitoring. 1. INTRODUCTION Vehicles sold throughout the world are subject to an increasing stringent set of emission thresholds. To achieve certification, all sensors and vehicle subsystems that may affect vehicle exhaust emissions have to be monitored by an On-Board Diagnostic (OBD) system that is part of the Engine Management System or any other embedded controller. This was requirement was introduced in the US in 1988 for OBD1, for open and short circuit faults, and 1994 for OBD2, for changes in sensor and actuator responses, for Europe this legislation, EOBD, was introduced on any vehicle built after January 2000. Both sets of legislation link the performance of the different diagnostics to emission thresholds. In the event of component or sub-system failure, a check engine light must be illuminated as an indication to a driver there is a problem so corrective action can be taken to minimise the pollution caused by that fault. As the emissions thresholds are continually reduced more sophisticated techniques have to be employed to meet these increasing tightening thresholds. Condition monitoring and diagnosis (CMD) has already been applied to a number of industrial systems to great effect. CMD process can support the performance and the robustness of any systems by monitoring their entire operational conditions to make sure that the outcome of the process is achieved without any significant disturbances. While they may add complexity in terms of understanding the technologies behind them, they can also give an advantage to the CMD purposes. By taking the measurement signals from the sensors and actuators using an existence data-acquisition system, a dedicated CMD model can be built. The use of automotive data has recently been discussed (Mills, 2005). The model for the CMD system is generated from the collection of the measurement signals to represent the chosen systems/sub-systems. This type of model falls within a category of data-driven model. One of the popular datadriven techniques is Principal Component Analysis (PCA). It is a well-known technique for data compression and feature extraction. It has gained considerable attention and has been successfully applied in many industrial chemical and semiconductor processes (Kourti and MacGregor, 1995; MacGregor, 2005) and recently has been applied in the automotive engine diagnostics (Antory, 2005). This paper presents results of a collaborative research project between IARC and Jaguar and Land Rover on the investigation of a Cam Profile Switching (CPS) diagnostic for a gasoline engine. CPS allows for different valve lift and cam durations to operate on an engine. This has the following benefit for the driver of improving engine torque and fuel economy, more detailed discussion on CPS is given in Section 3. Further background information on CPS can be found in a number of papers (Milovanovic et al., 2005; Rask and Sellnau, 2004; Xu et al., 2003; Alger et al., 2003; Sellnau and Rask et al., 2003; Brüstle C. and Schwarzenthal D., 1998). The CMD model for CPS system was validated using measurements signals collected from a gasoline engine connected to a dynamometer in an engine test cell facility. Good results were obtained and detail analysis was performed. It was shown that the proposed approach was capable of performing a reliable CMD process to diagnose faults for a gasoline engine CPS system. The paper is organised as follows: The next section discusses the condition monitoring and diagnosis methods, followed by discussion of the experimental data associated with this case study in Section 3. Section 4 details the implementation of the proposed method where the process monitoring is performed and is analysed. Finally, Section 5 summarises and concludes the paper. 2. CONDITION MONITORING & DIAGNOSIS METHOD This section discusses briefly the fundamental theory of the proposed condition monitoring and diagnosis methods. 2.1. Principal Component Analysis (PCA) PCA is a one of the most popular data-driven method that has gained significant interests in large industrial processes. This is due to its simplicity and powerful approach to capture redundant information in the process. PCA relies on eigenvalue-eigenvector decomposition in the data. By capturing the most important variation in the data, a better monitoring process can be achieved. By forming a data matrix, X ∈ ℜ m×n , in which m samples are stored as row vectors, of n (n << m) process variables stored as column vectors, the application of PCA generates a reduced set of new independent ‘artificial’ variables, principal component (PC) scores T and PC loadings P. This transformation captures important variation and can be written as follows: k X = t 1pΤ1 + t 2pT2 + L + t k pTk + E = ∑ t i pTi + E i =1 (1) Here, X is a sum of vector products of PC score ti, stored as column vectors in T, and PC loading pi, stored as column vectors in P. The determination of k (< n) is crucial as it represents the significant variation of the first k eigenvectors of the correlation matrix Sxx defined as follows: S xx = 1 X T X ∈ ℜ n×n (m − 1) (2) X is scaled to zero mean-centred and unit variance to eliminate different unit scales of the process variables. E is the residual matrix which describes unimportant variation and noise in the original data, X. Eq(1) shows that the important variation stored in the estimation k ˆ = t pT can be used to determine the matrix, X ∑i i i =1 residual, E, as follows: ˆ E=X−X (3) PCA transformation produces loading vectors, pi, which describe the coefficient of the linear relationships between the process variables, and score vectors, ti, which represent the variation in these variables. The PCA model is built by determining k reduced set of PCs that describe significant process variation. The loading vectors, pi, are the eigenvectors of the correlation matrix, Sxx, defined as follows: S xx p i = λi p i (4) where λi is the eigenvalue associated with the eigenvector pi of the correlation matrix, which measures the amount of variance captured by the { ti , pi } pairs, which are arranged in descending order of λi . This means that the first k pairs capture the largest amount of variation subsequently they contain the largest amount of information from the original data. This transformation enhances the ability of PCA to extract information from the original data by eliminating redundant information. The reduced set of variables is then used for modelling and analysis. 2.2. Monitoring Statistics Two monitoring statistics are generated as a mean to evaluate the performance of the PCA model. The first monitoring statistic is the Hotelling’s T2 or T2 statistic (in short). T2 statistic is simply the sum of normalised squared scores divided by their variance, uses to measure significant variation of the process. Prior to determining the T2, the reduced set of PC score, t, is obtained by projecting the new observed data xnew onto the plane defined by the PCA loadings P. This process is summarised as follows: t = x new P (5) k T 2 = t T Λ −1t = ∑ i =1 t i2 (6) λi Λ −1 is a diagonal matrix of the inverse of the k largest eigenvalues λi of correlation matrix Sxx and ti is the ith score. The statistical thresholds for T2 are calculated using the F-distribution written as follows: k (m − 1) Tα = Fα (k , m − k ) (m − k ) 2 (7) The second monitoring statistic is known as the Q statistic. It gives the measurement uncertainty between the PCA model and the observed data to determine how well the newly observed data conforms to the model. The mismatch between measured and estimated model results in the residual, e. The Q statistic is simply the sum squared of the residual e. This process is summarised as follows: e = x − tP T = x[I n − PP T ] (8) n Q = e T e = ∑ e 2j (9) j =1 where ej is the jth residual. The statistical thresholds for the Q statistic (Jackson and Mudholkar, 1979) are calculated using the following equation: 1 ⎛ h0 cα 2θ 2 θ h (h − 1) ⎞ h0 Qα = θ1 ⎜ + 2 0 20 + 1⎟ ⎜ ⎟ θ θ 1 1 ⎝ ⎠ (10) where: and n ∑ λi , i = k +1 θ2 = n ∑ λi2 , i = k +1 3. CAM PROFILE SWITCHING The description of CPS system and the design of experiment for this case study are now discussed. 3.1. System Description Tα2 is the threshold value with α , the significance level of confidence, typically sets into 95% or 99%, m is the number of samples used to build the PCA model, k is the number of PCs retained and Fα (k , m − k ) is the upper 100 α % critical point of the F-distribution with k and (m - k) degrees of freedom. θ1 = The information collected from the above observations can then be used for condition monitoring and diagnosis purposes. This approach produced a reduced set that often contains more robust information of the process than the original data. Details information about PCA can be found in (Kourti and MacGregor, 1995; MacGregor, 2005) θ3 = n ∑ λ3i , i = k +1 h0 = 1 − 2θ1θ 3 3θ 22 cα is the normal deviate corresponding to the (1 − α ) percentile. To support the interpretation of the monitoring statistics, the corresponding contribution plot for the T2 and Q 2 statistics, can be generated from TCP = tΛ −1 P T for T2 and using Eq.(8) for Q statistics. Volumetric efficiency (Stone, 1999) of an engine is measure of how an engine can draw in and expel air, basically how well the engine breathes. The more air that can be draw into the combustion chamber the more fuel that can be injected to maintain a desired Air Fuel Ratio. This then results in a higher torque output from the engine. There are a number of different approaches to improving the volumetric efficiency one that has been used recently by engine manufacturers is to make use of Variable Valve Timing (VVT) to alter the phasing and timing of the inlet and /or exhaust cams of the engine. Cam Profile Switching or CPS allows for different valve lifts and cam profiles to optimise the engine's volumetric efficiency over a range of the engines operating envelope. Typically at low engine speeds the best setting for the valves is achieved by having a low lift and short cam durations for high engine speed high valve lifts is required for longer cam durations. 3.2. Design of Experiment There are a number of different failure modes that the OBD system will have to detect for a CPS system. In this paper the focus has been limited to the situation where all of the valves are in the wrong lift position for their commanded position. Instead of the valves being set to their Low lift position for low engine speed operation they are locked in their High lift position. The tests points chosen are based upon standard set of test points which are known to cover the steady-state conditions of the emission drive cycles for both the US and European regulator bodies. Table 1 lists these test conditions. To generate each of the different test conditions the following approach was used. Brake Mean Effect Pressure (BMEP), which is a measure average force applied to the crank wheel, was adjusted via an Engine Dynamometer with the engine speed being controlled by the throttle. The controller on the engine test bed is run in Speed/Load mode to maintain a specific operating condition Compensation provides information as to how well the EMS is controlling the Air Fuel Ratio to 14.6. Table 1 Design of experiment Table 3 Variance captured by PCA Operating Condition Test 1 2 3 4 5 6 7 8 9 10 11 Engine Speed (rpm) 2000 2000 1000 1000 1500 1500 1500 1500 2500 2000 2500 BMEP (bar) 2.0 5.0 2.0 4.0 1.0 2.62 5.0 7.5 4.0 7.5 7.5 The data was collected under two different sets of conditions the first being a nominal (fault-free) set of data and the second which had the fault deliberately introduced to the CPS system. The normal set of data was logged during steady-state operation and the failure data was collected just at the point when the CPS failure occurred. For the PCA model 1000 points for each test condition were taken from both sets. The summary of the engine variables logged is given in Table 2. Table 2 Engine variables of the CPS system Variable Number 1 2 3 4 5 6 7 8 9 PC Engine Variable Engine speed (rpm) Intake Air Flow (g/s) Manifold Pressure (kPA) Engine Load (g/s) AFR Feedback Compensation 1 AFR Feedback Compensation 2 Oxygen Sensor 1 Oxygen Sensor 2 Throttle Opening (%) 1 2 3 4 5 6 7 8 9 Eigenvalu e 4.4264 2.0637 1.2239 0.7254 0.3917 0.0833 0.0715 0.0131 0.0010 Variance Captured 49.18 22.93 13.59 8.06 4.35 0.93 0.79 0.15 0.01 Total Variance Captured 49.18 72.11 85.71 93.77 98.12 99.05 99.84 99.99 100 4. PROCESS MONITORING & ANALYSIS The CMD model for the CPS system was built using the nominal (fault-free) data from all 11 sets of data. This data was transformed using PCA, Table 3 shows the amount of variance captured by each of the 9 Principal Components. The first 4 principal components (PCs) capture a total of 93.77% of the original data, a CPS model was developed based upon this reduced set. This means that the original 9 variables can be represented by a mapped set of 4 independent variables for the CMD purposes. Once the number of PCs has been identified, the next step was to generate two monitoring statistics, Q and T2, using Eq.(6) and (9) respectively. Each monitoring statistic was developed with their 99% and 95% confidence limits for Eq.(7) and (10). The resulting model was validated on a different set of data with the Q and T2 monitoring statistics falling below the 95% limit. This gives confidence that the model can then be taken forward and used to detect failure conditions. Fig. 1 illustrates the models performance against a set of failure data specifically using the Q statistic. This violation can be seen over most of the operating points 1000-2000 and 8000-9000 which represented data Set 2 and Set 9 has failed to be identified at these points as 12 10 Q Statistic Engine Speed and Engine Load are measures of the test conditions which have been used to define the test condition. Note that Engine Load in this case is an inferred measurement of load calculated internally calculated within the Engine Management System (EMS). Air Flow is a measure of the mass airflow through the throttle and Manifold Pressure is generated as a function of the difference in mass airflows coming into and exiting the manifold. Oxygen Sensor measures the Air Fuel Ratio in the Exhaust. Air Fuel Ratio 8 6 4 2 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Sample Number Fig. 1. Q monitoring statistic for faulty data with 99% and 95% confidence limits. 11000 they lay well below the confidence limits. This situation can be explained as follows. It may well be that the operating condition of (2000 rpm, 5 bar) and (2500 rpm, 4 bar) conformed to the CPS model but they may contain high variation which violate normal operating condition. To assist the interpretation of this situation and also to complement the monitoring process, a T2 monitoring statistic was then used, as shown in Fig. 2. situation, as shown in Fig. 3. The two ellipse confidence limits are generated with 95% and 99% confidence limits respectively. The second type detects the abnormality using a joint monitoring of the Q and T2 statistics, as shown in Fig. 4. Here A3 represents normal condition. A1 is the worst condition where the fault is detected by both Q and T2 statistics. A2 and A4 are the conditions where the fault is apparently dominant only 1100 1000 900 2 T Statistic 800 700 600 500 400 300 200 100 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 Fig. 4. A joint bivariate scatter plot of the Q and T2 monitoring statistics with 99% confidence limits. Sample Number 2 Fig. 2. T monitoring statistic for faulty data with 99% and 95% confidence limits. It is clearly shown that the validation set strongly violates the T2 confidence limits, even for the points 1000-2000 and 8000-9000 missed in the Q metric. When this situation was monitored, they failed to stay below the T2 statistical limits due to the dominant fault signatures in the process. It is important to note that Q and T2 monitoring statistics are used to complement each other in performing the detection process of any abnormality. 10 PC2 (22.930%) 5 towards Q or T2 statistic respectively. Once fault has been successfully detected the next step is to determine which component of the systems (i.e. process variables or measurement signals) is effected most by the fault signatures. This will allow a closer look on how those process variables behave under fault condition, in comparison to normal operating condition. Contribution plots for both Q and T2 statistics can be used for this purpose. Initially a random selection contribution plots were investigated to determine if there was a consistent pattern across all of the data. This was found to be the case so attention was focussed on the section of data 7200 to 7400 (with the fault condition occurring at approximately 7250). Fig. 5 and Fig. 6 depict the representation of these contribution plots for Q and T2. 0 -5 -10 -15 -6 -4 -2 0 2 4 6 PC1 (49.182%) Fig. 3. Bivariate scatter plot of the first-two PC scores with two ellipse confidence limits (99% and 95%). Another type of detection process can be performed using bivariate scatter plots. Two types of scatter plots are utilised here. The first type uses the first-two principal component (PC) scores to detect abnormal In Fig 6 it can be clearly seen that both Oxygen Sensor signals (7 and 8) are the most dominant variables in the T2 metric, with Oxygen Sensor 1 (7) reducing to 50% of the effect of Oxygen Sensor 2 at iteration 7400. Looking at Fig 5 the Air Fuel Compensation 1 (5) is also a significant which suggests that after the initial loss of control that Oxygen Sensor 1 is being slowly brought under control. Air Fuel Compensation 2 has yet to react to insertion of a failure of the CPS system this might be down to calibration or sensor dynamics effects. In Fig 5 Engine Speed (1), Manifold Pressure (3) and to a lesser extent Engine Load (4) have been effected by the failure. This is unsurprising since there has been a significant change in Volumetric Efficiency, and the torque output, of the engine. Further investigation is required to determine which of these variables are still significant once the steady-state has been reached on the engine test bed. Contribution to Q Statistic 1.5 1 0.5 0 -0.5 -1 This research is funded by the Advantage West Midlands through the Premium Automotive Research & Development programme based at the International Automotive Research Centre (www.iarc.warwick.ac.uk), Warwick Manufacturing Group, University of Warwick, Coventry, U.K. The assistance and support of Francis McKinney and Peter Earp of Jaguar and Land Rover is gratefully acknowledged. -1.5 -2 REFERENCES 7200 7250 7300 Time Instance 7350 7400 8 9 6 7 4 5 3 1 2 Number of Variable Fig. 5. Contribution to Q statistic for faulty data. Engine Speed (1), Manifold Pressure (3) and AFR Feedback Compensation 1 (5) shows dominant contribution. Contribution to T Statistic 5. 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