Patent Publication Number: US-9416714-B2

Title: Non-intrusive exhaust gas sensor monitoring

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation-in-part of U.S. patent application Ser. No. 13/410,171, filed on Mar. 1, 2012, the entire contents of which are incorporated herein by reference for all purposes. 
    
    
     BACKGROUND AND SUMMARY 
     An exhaust gas sensor may be positioned in an exhaust system of a vehicle to detect an air/fuel ratio of exhaust gas exhausted from an internal combustion engine of the vehicle. The exhaust gas sensor readings may be used to control operation of the internal combustion engine to propel the vehicle. 
     Degradation of an exhaust gas sensor may cause engine control degradation that may result in increased emissions and/or reduced vehicle drivability. Accordingly, accurate determination of exhaust gas sensor degradation may reduce the likelihood of engine control based on readings from a degraded exhaust gas sensor. In particular, an exhaust gas sensor may exhibit six discrete types of degradation behavior. The degradation behavior types may be categorized as asymmetric type degradation (e.g., rich-to-lean asymmetric delay, lean-to-rich asymmetric delay, rich-to-lean asymmetric filter, lean-to-rich asymmetric filter) that affects only lean-to-rich or rich-to-lean exhaust gas sensor response rates, or symmetric type degradation (e.g., symmetric delay, symmetric filter) that affects both lean-to-rich and rich-to-lean exhaust gas sensor response rates. The delay type degradation behaviors may be associated with the initial reaction of the exhaust gas sensor to a change in exhaust gas composition and the filter type degradation behaviors may be associated with a duration after an initial exhaust gas sensor response to transition from a rich-to-lean or lean-to-rich exhaust gas sensor output. 
     Previous approaches to monitoring exhaust gas sensor degradation, particularly identifying one or more of the six degradation behaviors, have relied on intrusive data collection. That is, an engine may be purposely operated with one or more rich to lean or lean to rich transitions to monitor exhaust gas sensor response. However, these excursions may be restricted to particular operating conditions that do not occur frequently enough to accurately monitor the sensor. Further, these excursions may increase engine operation at non-desired air/fuel ratios that result in increased fuel consumption and/or increased emissions. Additionally, large amounts of background noise present in the collected samples may confound accurate determination of the sensor degradation. 
     As described in U.S. patent application Ser. No. 13/410,171, filed on Mar. 1, 2012, the entire contents of which are incorporated herein by reference for all purposes, the inventors herein have recognized the above issues and identified a non-intrusive approach that utilizes a robust parameter for determining exhaust gas sensor degradation. In one embodiment, a method of monitoring an exhaust gas sensor coupled in an engine exhaust comprises indicating exhaust gas sensor degradation, including asymmetric degradation, based on a time delay and line length of each sample of a set of exhaust gas sensor responses collected during a commanded change in air-fuel ratio. 
     The exhaust gas sensor time delay and line length may provide a robust signal that has less noise and higher fidelity than previous approaches. In doing so, the accuracy of the sensor degradation determination may be improved. In one example, the commanded change in lambda may be entry into or exit out of deceleration fuel shut-off (DFSO). During entry into DFSO, the engine may be commanded from stoichiometric operation to lean operation, and during exit out of DFSO, the engine may be commanded from lean operation to stoichiometric operation. As such, the exhaust gas sensor time delay and line length may be monitored during conditions that approximate lean-to-rich and rich-to-lean transitions to determine if any of the six discrete sensor degradation behaviors are present without intrusive excursions. 
     By determining degradation of an exhaust gas sensor using a non-intrusive approach with data collected during DFSO, exhaust gas sensor degradation monitoring may be performed in a simple manner. Further, by using the exhaust gas sensor output to determine which of the degradation behaviors the sensor exhibits, closed loop feedback control may be improved by tailoring engine control (e.g., fuel injection amount and/or timing) responsive to indication of the particular degradation behavior of the exhaust gas sensor to reduce the impact on vehicle drivability and/or emissions due to exhaust gas sensor degradation. 
     The inventors herein have also recognized that, in such approaches which indicate sensor degradation based on comparing measured time delays and line lengths to expected responses, the expected response may be difficult to predict. For example, changes in air mass, purge flow, and similar noises may contribute to inaccuracies in expected response determination and may result in reduced accuracy in sensor fault estimations. 
     In one example approach, in order to address these issues, a method of monitoring an upstream exhaust gas sensor coupled in an engine exhaust is provided. The method comprises indicating exhaust gas sensor degradation based on a downstream exhaust gas sensor responding before the upstream exhaust gas sensor during a commanded change in air-fuel ratio. 
     In this way, sensor degradation may be at least partially based on comparing the response of the upstream sensor with the downstream sensor so that sensor faults may be identified even during conditions where an expected sensor response determination is inaccurate, e.g., due to changes in air mass, purge flow, and similar noises. Further, the downstream sensor response may be used to adapt and refine an expected response for the upstream sensor so that sensor degradation may be indicated based on comparing measured time delays and line lengths to expected responses. 
     The above advantages and other advantages, and features of the present description will be readily apparent from the following Detailed Description when taken alone or in connection with the accompanying drawings. 
     It should be understood that the summary above is provided to introduce in simplified form a selection of concepts that are further described in the detailed description. It is not meant to identify key or essential features of the claimed subject matter, the scope of which is defined uniquely by the claims that follow the detailed description. Furthermore, the claimed subject matter is not limited to implementations that solve any disadvantages noted above or in any part of this disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a schematic diagram of an embodiment of a propulsion system of a vehicle including an exhaust gas sensor. 
         FIG. 2  shows a graph indicating a symmetric filter type degradation behavior of an exhaust gas sensor. 
         FIG. 3  shows a graph indicating an asymmetric rich-to-lean filter type degradation behavior of an exhaust gas sensor. 
         FIG. 4  shows a graph indicating an asymmetric lean-to-rich filter type degradation behavior of an exhaust gas sensor. 
         FIG. 5  show a graph indicating a symmetric delay type degradation behavior of an exhaust gas sensor. 
         FIG. 6  shows a graph indicating an asymmetric rich-to-lean delay type degradation behavior of an exhaust gas sensor. 
         FIG. 7  shows a graph indicating an asymmetric lean-to-rich delay type degradation behavior of an exhaust gas sensor. 
         FIG. 8A  shows a graph indicating an entry into DFSO without an air-fuel ratio disturbance. 
         FIG. 8B  shows a graph indicating an entry into DFSO with an air-fuel ratio disturbance. 
         FIG. 9  is a flow chart illustrating a method for indicating an air-fuel ratio disturbance according to an embodiment of the present disclosure. 
         FIG. 10  is a flow chart illustrating a method for monitoring air-fuel ratio during DFSO according to an embodiment of the present disclosure. 
         FIG. 11  is a flow chart illustrating a method for indicating exhaust gas degradation according to an embodiment of the present disclosure. 
         FIG. 12  shows example graphs of upstream and downstream exhaust gas sensor responses during commanded air/fuel ratio changes. 
         FIG. 13  shows an example method for indicating sensor degradation based on comparisons of upstream and downstream sensor responses. 
     
    
    
     DETAILED DESCRIPTION 
     The following description relates to systems and methods for determining degradation of an exhaust gas sensor. More particularly, the systems and methods described below may be implemented to determine an upstream exhaust gas sensor degradation based on comparisons of an upstream sensor response with a downstream sensor response during commanded air/fuel ratio changes, e.g., entry into or exit out of deceleration fuel shut-off (DFSO). For example, if the downstream sensor responds before the upstream sensor then the upstream sensor may be degraded. Further, the systems and methods described below may be implemented to determine exhaust gas sensor degradation based on recognition of any one of six discrete types of behavior associated with exhaust gas sensor degradation. The recognition of the degradation behavior may be performed during entry into or exit out of DFSO to non-intrusively monitor exhaust gas sensor response during rich-to-lean and lean-to-rich transitions. Further, gross air-fuel ratio disturbances that may confound the monitoring, such as a change in fuel vapors present in the intake (due to fuel vapor canister purge, for example) or from closed throttle transition, may be detected to increase accuracy of the degradation indication. 
       FIG. 1  is a schematic diagram showing one cylinder of multi-cylinder engine  10 , which may be included in a propulsion system of a vehicle in which an exhaust gas sensor  126  may be utilized to determine an air fuel ratio of exhaust gas produce by engine  10 . The air fuel ratio (along with other operating parameters) may be used for feedback control of engine  10  in various modes of operation. Engine  10  may be controlled at least partially by a control system including controller  12  and by input from a vehicle operator  132  via an input device  130 . In this example, input device  130  includes an accelerator pedal and a pedal position sensor  134  for generating a proportional pedal position signal PP. Combustion chamber (i.e., cylinder)  30  of engine  10  may include combustion chamber walls  32  with piston  36  positioned therein. Piston  36  may be coupled to crankshaft  40  so that reciprocating motion of the piston is translated into rotational motion of the crankshaft. Crankshaft  40  may be coupled to at least one drive wheel of a vehicle via an intermediate transmission system. Further, a starter motor may be coupled to crankshaft  40  via a flywheel to enable a starting operation of engine  10 . 
     Combustion chamber  30  may receive intake air from intake manifold  44  via intake passage  42  and may exhaust combustion gases via exhaust passage  48 . Intake manifold  44  and exhaust passage  48  can selectively communicate with combustion chamber  30  via respective intake valve  52  and exhaust valve  54 . In some embodiments, combustion chamber  30  may include two or more intake valves and/or two or more exhaust valves. 
     In this example, intake valve  52  and exhaust valves  54  may be controlled by cam actuation via respective cam actuation systems  51  and  53 . Cam actuation systems  51  and  53  may each include one or more cams and may utilize one or more of cam profile switching (CPS), variable cam timing (VCT), variable valve timing (VVT) and/or variable valve lift (VVL) systems that may be operated by controller  12  to vary valve operation. The position of intake valve  52  and exhaust valve  54  may be determined by position sensors  55  and  57 , respectively. In alternative embodiments, intake valve  52  and/or exhaust valve  54  may be controlled by electric valve actuation. For example, cylinder  30  may alternatively include an intake valve controlled via electric valve actuation and an exhaust valve controlled via cam actuation including CPS and/or VCT systems. 
     Fuel injector  66  is shown arranged in intake passage  44  in a configuration that provides what is known as port injection of fuel into the intake port upstream of combustion chamber  30 . Fuel injector  66  may inject fuel in proportion to the pulse width of signal FPW received from controller  12  via electronic driver  68 . Fuel may be delivered to fuel injector  66  by a fuel system (not shown) including a fuel tank, a fuel pump, and a fuel rail. In some embodiments, combustion chamber  30  may alternatively or additionally include a fuel injector coupled directly to combustion chamber  30  for injecting fuel directly therein, in a manner known as direct injection. 
     Ignition system  88  can provide an ignition spark to combustion chamber  30  via spark plug  92  in response to spark advance signal SA from controller  12 , under select operating modes. Though spark ignition components are shown, in some embodiments, combustion chamber  30  or one or more other combustion chambers of engine  10  may be operated in a compression ignition mode, with or without an ignition spark. 
     Exhaust gas sensor  126  is shown coupled to exhaust passage  48  of exhaust system  50  upstream of emission control device  70 . Sensor  126  may be any suitable sensor for providing an indication of exhaust gas air/fuel ratio such as a linear oxygen sensor or UEGO (universal or wide-range exhaust gas oxygen), a two-state oxygen sensor or EGO, a HEGO (heated EGO), a NOx, HC, or CO sensor. In some embodiments, exhaust gas sensor  126  may be a first one of a plurality of exhaust gas sensors positioned in the exhaust system. For example, additional exhaust gas sensors may be positioned downstream of emission control  70 . In some examples, a downstream exhaust gas sensor may be included in the engine exhaust at a position downstream of exhaust gas sensor  126 . For example, sensor  127  may be disposed in the exhaust downstream of emission control device  70 . However, in other examples, sensor  127  may be positioned between emission control device  70  and exhaust gas sensor  126 . Sensor  127  may be any suitable sensor for providing an indication of exhaust gas air/fuel ratio such as a linear oxygen sensor or UEGO (universal or wide-range exhaust gas oxygen), a two-state oxygen sensor or EGO, a HEGO (heated EGO), a NOx, HC, or CO sensor. As described in more detail below, in some examples, comparison of a response of downstream sensor  127  with a response of upstream sensor  126  may be used to determine degradation of the upstream sensor  127 . 
     Emission control device  70  is shown arranged along exhaust passage  48  downstream of exhaust gas sensor  126 . Device  70  may be a three way catalyst (TWC), NOx trap, various other emission control devices, or combinations thereof. In some embodiments, emission control device  70  may be a first one of a plurality of emission control devices positioned in the exhaust system. In some embodiments, during operation of engine  10 , emission control device  70  may be periodically reset by operating at least one cylinder of the engine within a particular air/fuel ratio. 
     Controller  12  is shown in  FIG. 1  as a microcomputer, including microprocessor unit  102 , input/output ports  104 , an electronic storage medium for executable programs and calibration values shown as read only memory chip  106  in this particular example, random access memory  108 , keep alive memory  110 , and a data bus. Controller  12  may receive various signals from sensors coupled to engine  10 , in addition to those signals previously discussed, including measurement of inducted mass air flow (MAF) from mass air flow sensor  120 ; engine coolant temperature (ECT) from temperature sensor  112  coupled to cooling sleeve  114 ; a profile ignition pickup signal (PIP) from Hall effect sensor  118  (or other type) coupled to crankshaft  40 ; throttle position (TP) from a throttle position sensor; and absolute manifold pressure signal, MAP, from sensor  122 . Engine speed signal, RPM, may be generated by controller  12  from signal PIP. Manifold pressure signal MAP from a manifold pressure sensor may be used to provide an indication of vacuum, or pressure, in the intake manifold. Note that various combinations of the above sensors may be used, such as a MAF sensor without a MAP sensor, or vice versa. During stoichiometric operation, the MAP sensor can give an indication of engine torque. Further, this sensor, along with the detected engine speed, can provide an estimate of charge (including air) inducted into the cylinder. In one example, sensor  118 , which is also used as an engine speed sensor, may produce a predetermined number of equally spaced pulses every revolution of the crankshaft. 
     Furthermore, at least some of the above described signals may be used in the exhaust gas sensor degradation determination methods described in further detail below. For example, the inverse of the engine speed may be used to determine delays associated with the injection-intake-compression-expansion-exhaust cycle. As another example, the inverse of the velocity (or the inverse of the MAF signal) may be used to determine a delay associated with travel of the exhaust gas from the exhaust valve  54  to exhaust gas sensor  126 . The above described examples along with other use of engine sensor signals may be used to determine the time delay between a change in the commanded air fuel ratio and the exhaust gas sensor response rate. 
     In some embodiments, exhaust gas sensor degradation determination may be performed in a dedicated controller  140 . Dedicated controller  140  may include processing resources  142  to handle signal-processing associated with production, calibration, and validation of the degradation determination of exhaust gas sensor  126 . In particular, a sample buffer (e.g., generating approximately 100 samples per second per engine bank) utilized to record the response rate of the exhaust gas sensor may be too large for the processing resources of a powertrain control module (PCM) of the vehicle. Accordingly, dedicated controller  140  may be operatively coupled with controller  12  to perform the exhaust gas sensor degradation determination. Note that dedicated controller  140  may receive engine parameter signals from controller  12  and may send engine control signals and degradation determination information among other communications to controller  12 . 
     Note that storage medium read-only memory  106  and/or processing resources  142  can be programmed with computer readable data representing instructions executable by processor  102  and/or dedicated controller  140  for performing the methods described below as well as other variants. 
     As discussed above, exhaust gas sensor degradation may be determined based on any one, or in some examples each, of six discrete behaviors indicated by delays in the response rate of air/fuel ratio readings generated by an exhaust gas sensor during rich-to-lean transitions and/or lean-to-rich transitions.  FIGS. 2-7  each show a graph indicating one of the six discrete types of exhaust gas sensor degradation behaviors. The graphs plot air/fuel ratio (lambda) versus time (in seconds). In each graph, the dotted line indicates a commanded lambda signal that may be sent to engine components (e.g., fuel injectors, cylinder valves, throttle, spark plug, etc.) to generate an air/fuel ratio that progresses through a cycle comprising one or more lean-to-rich transitions and one or more rich-to-lean transitions. In the depicted figures, the engine is entering into and exiting out of DFSO. In each graph, the dashed line indicates an expected lambda response time of an exhaust gas sensor. In each graph, the solid line indicates a degraded lambda signal that would be produced by a degraded exhaust gas sensor in response to the commanded lambda signal. In each of the graphs, the double arrow lines indicate where the given degradation behavior type differs from the expected lambda signal. 
       FIG. 2  shows a graph indicating a first type of degradation behavior that may be exhibited by a degraded exhaust gas sensor. This first type of degradation behavior is a symmetric filter type that includes slow exhaust gas sensor response to the commanded lambda signal for both rich-to-lean and lean-to-rich modulation. In other words, the degraded lambda signal may start to transition from rich-to-lean and lean-to-rich at the expected times but the response rate may be lower than the expected response rate, which results in reduced lean and rich peak times. 
       FIG. 3  shows a graph indicating a second type of degradation behavior that may be exhibited by a degraded exhaust gas sensor. The second type of degradation behavior is an asymmetric rich-to-lean filter type that includes slow exhaust gas sensor response to the commanded lambda signal for a transition from rich-to-lean air/fuel ratio. This behavior type may start the transition from rich-to-lean at the expected time but the response rate may be lower than the expected response rate, which may result in a reduced lean peak time. This type of behavior may be considered asymmetric because the response of the exhaust gas sensor is slow (or lower than expected) during the transition from rich-to-lean. 
       FIG. 4  shows a graph indicating a third type of degradation behavior that may be exhibited by a degraded exhaust gas sensor. The third type of behavior is an asymmetric lean-to-rich filter type that includes slow exhaust gas sensor response to the commanded lambda signal for a transition from lean-to-rich air/fuel ratio. This behavior type may start the transition from lean-to-rich at the expected time but the response rate may be lower than the expected response rate, which may result in a reduced rich peak time. This type of behavior may be considered asymmetric because the response of the exhaust gas sensor is only slow (or lower than expected) during the transition from lean-to-rich. 
       FIG. 5  shows a graph indicating a fourth type of degradation behavior that may be exhibited by a degraded exhaust gas sensor. This fourth type of degradation behavior is a symmetric delay type that includes a delayed response to the commanded lambda signal for both rich-to-lean and lean-to-rich modulation. In other words, the degraded lambda signal may start to transition from rich-to-lean and lean-to-rich at times that are delayed from the expected times, but the respective transition may occur at the expected response rate, which results in shifted lean and rich peak times. 
       FIG. 6  shows a graph indicating a fifth type of degradation behavior that may be exhibited by a degraded exhaust gas sensor. This fifth type of degradation behavior is an asymmetric rich-to-lean delay type that includes a delayed response to the commanded lambda signal from the rich-to-lean air/fuel ratio. In other words, the degraded lambda signal may start to transition from rich-to-lean at a time that is delayed from the expected time, but the transition may occur at the expected response rate, which results in shifted and/or reduced lean peak times. This type of behavior may be considered asymmetric because the response of the exhaust gas sensor is only delayed from the expected start time during a transition from rich-to-lean. 
       FIG. 7  shows a graph indicating a sixth type of degradation behavior that may be exhibited by a degraded exhaust gas sensor. This sixth type of behavior is an asymmetric lean-to-rich delay type that includes a delayed response to the commanded lambda signal from the lean-to-rich air/fuel ratio. In other words, the degraded lambda signal may start to transition from lean-to-rich at a time that is delayed from the expected time, but the transition may occur at the expected response rate, which results in shifted and/or reduced rich peak times. This type of behavior may be considered asymmetric because the response of the exhaust gas sensor is only delayed from the expected start time during a transition from lean-to-rich. 
     It will be appreciated that a degraded exhaust gas sensor may exhibit a combination of two or more of the above described degradation behaviors. For example, a degraded exhaust gas sensor may exhibit an asymmetric rich-to-lean filter degradation behavior (i.e.,  FIG. 3 ) as well as an asymmetric rich-to-lean delay degradation behavior (i.e.,  FIG. 6 ). 
       FIGS. 8A and 8B  show graphs illustrating an exhaust gas sensor response to a commanded entry into DFSO.  FIG. 8A  shows a graph  210  illustrating an entry into DFSO without an air-fuel ratio disturbance prior to the entry, and  FIG. 8B  shows a graph  220  illustrating an entry into DFSO with an air-fuel ratio disturbance prior to the entry. Turning to  FIG. 8A , the commanded lambda, expected lambda, and degraded lambda are shown similar to the lambdas described with respect to  FIGS. 2-7 .  FIG. 8A  illustrates a rich-to-lean and/or symmetric delay degradation wherein the time delay to respond to the commanded air-fuel ratio change is delayed. The arrow  202  illustrates the time delay, which is the time duration from the commanded change in lambda to a time (τ 0 ) when a threshold change in the measured lambda is observed. The threshold change in lambda may be a small change that indicates the response to the commanded change has started, e.g., 5%, 10%, 20%, etc. The arrow  204  indicates the time constant (τ 63 ) for the response, which in a first order system is the time from τ 0  to when 63% of the steady state response is achieved. The arrow  206  indicates the time duration from τ 0  to when 95% of the desired response is achieved, otherwise referred to as a threshold response time (τ 95 ). In a first order system, the threshold response time (τ 95 ) is approximately equal to three time constants (3*τ 63 ). 
     From these parameters, various details regarding the exhaust gas sensor response can be determined. First, the time delay, indicated by arrow  202 , may be compared to an expected time delay to determine if the sensor is exhibiting a delay degradation behavior. Second, the time constant, indicated by the arrow  204 , may be used to predict a τ 95 . The predicted τ 95  may be compared to a measured τ 95  to determine if an air-fuel ratio disturbance is present prior to the entry into DFSO. Specifically, as explained above, the time constant represents the amount of time to achieve 63% of the desired air-fuel ratio, and τ 95  can be predicted by multiplying the time constant by three. If the predicted τ 95  is not equal to the measured τ 95 , this indicates a disturbance in the air-fuel ratio, which will be explained in more detail with respect to  FIG. 8B . Finally, a line length, indicated by the arrow  206 , may be determined based on the change in lambda over the duration of the response, starting at τ 0 . The line length is the sensor signal length, and can be used to determine if a response degradation is present. The line length may be determined based on the equation:
 
line length=Σ√{square root over (Δ t   2 +Δλ 2 )}
 
     Turning to  FIG. 8B , a graph  220  showing an exhaust gas sensor response during an entry into DFSO including an air-fuel ratio disturbance is depicted. Similar to  FIG. 8A , the commanded lambda, expected lambda, and degraded lambda are shown. An air-fuel ratio disturbance, shown in the expected lambda signal at  208 , may cause a transient change in the air-fuel ratio that is not commanded by the controller. The air-fuel ratio disturbance may be caused by a fuel vapor canister purge, or other action that results in changes to the fuel present in the cylinders, such as a fuel error due to a closed throttle transition. Air-fuel ratio disturbances may also be caused by transient changes to the air flow into the cylinders. As a result of the disturbance, the determined time delay, indicated by arrow  202 ′, is shorter than the time delay of  FIG. 8A . This is because the lambda begins to change just after the commanded entry into DFSO, and hence the measured time between the commanded start of DFSO and when lambda changes by a threshold amount is shortened. As a result of this shortened time delay, the time constant, indicated by arrow  204 ′, is lengthened. Further, the line length, indicated by arrow  206 ′, is also increased compared to the line length of  FIG. 8A . Inclusion of this time delay and line length in a degradation determination may result in inaccurate degradation determination. To identify such a disturbance, the predicted τ 95  (3*τ 63 ) may be compared to the measured τ 95 . As shown in  FIG. 8B , the predicted τ 95 , which is three times the determined time constant (arrow  204 ′), is greater than the measured τ 95 . If the predicted τ 95  is different from the measured τ 95  by a threshold amount, such as 10%, the data collected during that commanded change in lambda may be discarded, reducing noise and improving the accuracy of the degradation determination. 
       FIGS. 9-11  are flow charts depicted methods for monitoring exhaust air-fuel ratio in order to determine if one or more sensor degradation behaviors are present. The exhaust gas air-fuel ratio may be determined by an exhaust gas sensor during a commanded air-fuel ratio change, such as during entry into or exit out of DFSO. However, in some embodiments, other commanded air-fuel ratio changes may be monitored, such as changes due to a catalyst regeneration or other actions. During the commanded AFR change, the lambda as measured by the sensor may be collected as the sensor responds to the commanded change, and the rate at which the sensor responds may be evaluated to determine a time delay and line length for the response. A set of responses may be collected, and the time delays and line lengths for all responses may be averaged and compared to an expected time delay and line length. Further, to improve accuracy of the monitoring, the AFR may be monitored to determine if a disturbance to the AFR occurs prior to the commanded change. If so, the lambda values collected during that commanded change may be discarded, as the AFR disturbance may confound the calculated time delay and line length. 
     Turning now to  FIG. 9  an example method  300  for indicating an air-fuel ratio disturbance is depicted according to an embodiment of the present disclosure. Method  300  may be carried out by a control system of a vehicle, such as controller  12  and/or dedicated controller  140 , to monitor air-fuel ratio during a commanded air-fuel ratio change via a sensor such as exhaust gas sensor  126 . 
     At  302 , method  300  includes determining engine operating parameters. Engine operating parameters may be determined based on feedback from various engine sensors, and may include engine speed, load, air/fuel ratio, temperature, etc. Further, engine operating parameters may be determined over a given duration, e.g., 10 seconds, in order to determine whether certain engine operating conditions are changing, or whether the engine is operating under steady-state conditions. Method  300  includes, at  304 , determining if the engine is entering into or exiting out of deceleration fuel shut-off (DFSO). During DFSO, the engine is operated without fuel injection while the engine rotates and pumps air through the cylinders. DFSO entry and exit conditions may be based on various vehicle and engine operating conditions. In particular, a combination of one or more of vehicle speed, vehicle acceleration, engine speed, engine load, throttle position, pedal position, transmission gear position, and various other parameters may be used to determine whether the engine will be entering or exiting DFSO. In one example, the DFSO entry conditions may be based on an engine speed below a threshold. In another example, the DFSO entry conditions may be based on an engine load below a threshold. In still another example, the DFSO condition may be based on an accelerator pedal position. Additionally or alternatively, entry into DFSO may be determined based on a commanded signal to cease fuel injection. Exit out of DFSO may be based on a commanded signal to begin fuel injection in one example. In another example, a DFSO event may be ended based on a driver tip-in, the vehicle speed reaching a threshold value, and/or engine load reaching a threshold value. 
     If it is determined at  304  that the engine is not entering or exiting DFSO, method  300  returns to  302  to continue to determine engine operating parameters. If DFSO entry or exit conditions are determined, method  300  proceeds to  306  to record the change in lambda over time during the DFSO entry or exit. When the engine enters or exits DFSO, the commanded air-fuel ratio changes, and the air-fuel ratio detected by the exhaust gas sensor can be stored in the memory of the controller or the dedicated controller during the transition into or out of DFSO. As used herein, the terms entry into and exit out of DFSO may include the time from when a commanded entry or exit is detected until a time when the air-fuel ratio detected by the sensor reaches the steady-state commanded value. 
     At  308 , it is determined if an air-fuel ratio disturbance is present prior to the entry or exit. As explained previously, the air-fuel ratio disturbance may be caused by, for example, additional fuel vapors present in the intake. These disturbances may confound the monitoring of the exhaust gas sensor response to the commanded DFSO entry or exit. In order to detect an AFR disturbance, the lambda at the commanded start or stop of DFSO is recorded at  310 . At  312 , the time since the start or stop of DFSO at which the lambda has increased by a threshold percentage is recorded. In one example, the threshold percentage may be a suitable small change in lambda that indicates the engine is responding to the commanded change, such as an increase of 10%, 20%, etc. This time may be referred to as τ 0 . At  314 , the time constant is determined (τ 63 ). As explained previously, the time constant may be the time from τ 0  at which 63% of the commanded response is reached. T 95  may be the time from τ 0  at which 95% of the commanded response is reached, and, in a first order system, is equivalent to three time constants. At  316 , the 3*τ 63  is compared to a measured τ 95 . 
     At  318 , it is determined if 3*τ 63  is approximately equal to the measured τ 95 . The predicted τ 95  (e.g., 3*τ 63 ) may deviate from the measured τ 95  by a suitable range, such as 5 or 10%. If 3*τ 63  is different from the measured τ 95  by an amount larger than this range, it indicates that the determined τ 0  is in response to an AFR disturbance, and not the actual τ 0  in response to the commanded DFSO entry or exit. Thus, method  300  proceeds to  320  to indicated that an AFR disturbance is present and discard the collected change in lambda. However, if 3*τ 63  is approximately equal to the measured τ 95 , an AFR disturbance is not present, and the collected change in lambda during the DFSO entry or exit may be added as a sample to a set of exhaust gas sensor responses at  322 . After discarding the collected lambda values at  320  or adding the collected lambda values to the set of responses at  322 , method  300  exits. 
       FIG. 10  illustrates a method  400  for monitoring air-fuel ratio during DFSO. Method  400  may be carried out by controller  12  and/or dedicated controller  140 . Method  400  includes, at  402 , determining if a threshold number of samples have been collected in the set of exhaust gas sensor responses. The samples may be collected during entry and exit of DFSO, as explained with respect to  FIG. 9 . The samples may include lambda values collected during the exhaust gas sensor response to the commanded entry or exit of DFSO. For example, each sample may include every lambda value collected during a response to a commanded entry into DFSO, e.g., the sample may include a lambda value collected every 10 ms, or a value collected every 100 ms, etc. The threshold may be a suitable threshold that balances data collection with accurate sensor modeling, and may include 10 samples, 20 samples, etc. 
     If the threshold number of samples has not been collected, method  400  returns. If the threshold number of samples has been collected, method  400  proceeds to  404  to determine an expected and measured time delay and line length for each sample collected during a DFSO entry. The measured time delay and line length may be calculated as described above with respect to  FIGS. 8A and 8B . The expected time delay between the change in the commanded air fuel ratio and the initial exhaust gas sensor response may be determined from several sources of delay. First, there is a delay contribution from the injection-intake-compression-expansion-exhaust cycle. This delay contribution may be proportional to the inverse of the engine speed. Secondly, there is a delay contribution from the time for the exhaust gas to travel from the exhaust port of the engine cylinders to the exhaust gas sensor. This delay contribution may vary with the inverse of the velocity or air mass flow rate of gas in the exhaust passage. Finally, there are delay contributions induced by processing times, the filtering applied to the exhaust gas sensor signal, and the time required for the filtered exhaust gas sensor signal to change the required delta lambda. 
     The expected line length may be calculated based on the time to reach the final value from the end of the time delay (start of the line length) and the final value, which may be determined based on air mass, velocity of exhaust through the sensor, and other parameters. 
     At  406 , the expected and measured time delay and line length for each sample collected during a DFSO exit is determined, similar to the time delay and line length for the DFSO entry described above. At  408 , all entry measured time delays are averaged, all entry measured line lengths are averaged, all entry expected time delays are averaged, and all entry expected line lengths are averaged. Similarly, at  410 , the exit measured and expected time delays and line lengths are averaged. Thus, an average measured time delay, an average measured line length, an average expected time delay, and an average expected line length are determined for both rich-to-lean transitions (e.g., entry into DFSO) and lean-to-rich transitions (e.g., exit out of DFSO). 
     At  412 , sensor degradation behavior type is determined based on the average time delays and line lengths calculated previously, which will be described in more detail with respect to  FIG. 11 . At  414 , it is determined if the sensor is exhibiting at least on type of sensor degradation. If no, method  400  exits, as the sensor is not degraded, and thus standard engine operation may continue. If yes, method  400  proceeds to  416  to adjust fuel injection amount and/or timing. To ensure adequate engine control to maintain engine emissions and fuel economy at a desired level, one or more engine operating parameters may be adjusted at  416 , if desired. This may include adjusting fuel injection amount and/or timing, and may include adjusting control routines that are based on feedback from the degraded sensor to compensate for the identified degradation. At  418 , if the degradation behavior exceeds a threshold, this may indicate the sensor is damaged or otherwise non-functional and as such an operator of the vehicle may be notified of the sensor degradation, for example by activating a malfunction indication light. Upon adjusting operating parameters and/or notifying a vehicle operator, method  400  exits. 
       FIG. 11  is a flow chart illustrating a method  500  for determining a sensor degradation behavior based on determined and expected time delays and line lengths during exit and entry into DFSO. Method  500  may be carried out by controller  12  and/or dedicated controller  140 , and may be executed during  412  of method  400  described above. At  502 , method  500  includes comparing measured entry time delay and exit time delay to the expected entry time delay and exit time delay. As explained with respect to  FIG. 10 , for both entry into and exit out of DFSO, the average measured time delay and average expected time delay may be determined. Each measured time delay may be compared to its respective expected time delay to determine a difference in the time delays. 
     At  504 , it is determined if both the entry and exit time delays are greater than their respective expected time delays by a threshold amount. The threshold amount may be a suitable amount, such as 5% or 10%, that allows for some variation in the exhaust gas sensor response that does not affect drivability or emissions, and allows for error in the expected time delays. If both the entry and exit time delays are greater than their respective expected time delays, a symmetric delay degradation behavior is indicated at  506 , and method  500  proceeds to  508 . If both are not greater than their respective expected time delays, method  500  also proceeds to  508  to determine if one of the entry or exit time delays is greater than its respective expected time delay. If no, method  500  proceeds to  512 . If yes, method  500  proceeds to  510  to indicate an asymmetric delay degradation. If the entry time delay is greater than expected, a rich-to-lean delay degradation is indicated. If the exit time delay is greater than expected, a lean-to-rich delay degradation is indicated. Method  500  then proceeds to  512 . 
     At  512 , the measured entry line length is compared to the expected entry line length, and the measured exit line length is compared to the expected exit line length. At  514 , it is determined if both the entry and exit line lengths are greater than their respective expected line lengths by a threshold amount, similar to the determination made at  504 . If both are greater than expected, method  500  proceeds to  516  to indicate a symmetric filter degradation, and then method  500  proceeds to  518 . If no, method  500  proceeds to  518  to determine if one of the entry or exit line lengths is greater than its respective expected line length. 
     If it is determined that one of the entry or exit line lengths is greater than expected, method  500  proceeds to  520  to indicate an asymmetric filter degradation. If the entry line length is greater than expected, a rich-to-lean filter degradation is indicated. If the exit line length is greater than expected, a lean-to-rich filter degradation is indicated. Method  500  then proceeds to  522 . Also, if the answer is no at  518 , method  500  proceeds to  522  to determine if at least one degradation behavior is indicated, based on the previous comparisons of the time delays and line lengths. If at least one degradation behavior is indicated, method  500  exits. If no degradation is indicated, method  500  proceeds to  524  to indicate no degradation behavior, and then method  500  exits. 
     Thus, the methods presented herein provide for determining exhaust gas sensor degradation based on a time delay and line length of a set of exhaust gas sensor responses collected during commanded changes in lambda. These commanded changes in lambda may be entry into and exit out of DFSO. Further, the collected lambda values during the commanded change in lambda may be monitored to determine if an air-fuel ratio disturbance is present prior to the commanded change in lambda. If so, those collected lambda values may be discarded so as to reduce noise that may confound the accurate degradation determination. The air-fuel ratio disturbance may be detected by determining a time constant of the sensor response, and estimating a threshold response time based on the time constant. If the estimated threshold response time is different from a measured response time, then a disturbance may be indicated. 
     As remarked above, expected sensor responses, e.g., expected lambda responses including expected time delays and line lengths as described above with regard to  FIGS. 2-11 , may be difficult to predict due to changes in air mass, purge flow, and other noise sources present during engine operation. Such inaccuracies in expected response determination may result in reduced accuracy in sensor fault estimations employing the methods described above. 
     In order to address these issues, signals from a downstream exhaust gas sensor, e.g., a HEGO sensor  127  positioned downstream of an UEGO sensor  126 , may be used to assist in identification of sensor faults. For example, if the downstream exhaust gas sensor is responding before the upstream sensor during a commanded air/fuel ratio change then a fault in the upstream sensor may be present. 
     For example,  FIG. 12  shows example graphs of upstream and downstream exhaust gas sensor responses during commanded air/fuel ratio changes. In the graphs shown in  FIG. 12 , DFSO flags indicating entry into or exit out of DFSO are shown as dotted lines, signals from an upstream exhaust gas sensor, e.g., sensor  126 , are shown as dashed lines, and signals from a downstream exhaust gas sensor, e.g., sensor  127 , are shown as solid lines. Each graph shown in  FIG. 12  shows lambda along the x-axis and time in seconds along the y-axis. 
     The graph at  1202  in  FIG. 12  shows upstream and downstream sensor response during an entry into DFSO for an upstream sensor with no fault or no degradation. As indicated by the DFSO flag in graph  1202 , entry into DFSO is commanded at t 0 . After a time delay  1214 , a threshold change, in this case a threshold amount of increase, in lambda at the upstream sensor is observed before the downstream sensor responds at t 1 . This threshold change in lambda observed indicates that a response to the commanded change in air-fuel ratio has begun to occur at the upstream sensor. In some examples, the time delay  1214  shown in graph  1202  may be used as a reference to adjust expected sensor response time delay for subsequent sensor degradation routines, e.g., using the methods described above with regard to  FIGS. 9-11 . 
     Graph  1202  shows the downstream sensor responding after the upstream sensor responds following the entry into DFSO at t 0 . For example, at time t 1  the downstream sensor responds to the commanded change in air-fuel ratio. This initial response of the downstream sensor at t 1  occurs after the initial response of the upstream sensor. At time t 1 , when the downstream sensor responds, a difference  1216  between measured lambda at the upstream exhaust gas sensor and measured lambda at the downstream exhaust gas sensor is observed or measured. In some examples, this difference  1216  shown in graph  1202  may be used as a difference threshold reference during subsequent entries into DFSO to determine sensor degradation. For example, as described below, if the difference between the measured lambda at the upstream exhaust gas sensor and measured lambda at the downstream exhaust gas sensor when the downstream sensor initially responds is less than this difference threshold reference then a sensor fault may be indicated. 
     The graph at  1204  in  FIG. 12  shows upstream and downstream sensor response during an entry into DFSO for an upstream sensor with a filter fault. As indicated by the DFSO flag in graph  1204 , entry into DFSO is commanded at t 0 . After a time delay  1214 , a threshold change in lambda at the upstream sensor is measured before the downstream sensor responds at t 1 . In graph  120 , 4 the time delay  1214  is substantially the same as the time delay  1214  shown in graph  1202  for the no fault sensor indicating that the sensor fault is not a delay fault in graph  1204 . However, at t 1  when the downstream sensor responds, the measured lambda for the upstream sensor has not reached or increased to a desired threshold lambda change indicating that there is a fault in the upstream sensor. For example, in graph  1204  at time t 1  when the downstream sensor responds, the difference  1216  between measured lambda at the upstream exhaust gas sensor and measured lambda at the downstream exhaust gas sensor is less than the difference threshold reference for the no-fault sensor shown in graph  1202  indicating that a fault is present. In this example, since no significant time delay is measured for the upstream sensor response, this may indicate that the fault is a filter fault. 
     The graph at  1206  in  FIG. 12  shows upstream and downstream sensor response during an entry into DFSO for an upstream sensor with a delay fault. As indicated by the DFSO flag in graph  1206 , entry into DFSO is commanded at t 0 . After a time delay  1214 , a threshold change in lambda at the upstream sensor is observed before the downstream sensor responds at t 1 . In graph  1206 , the time delay  1214  is greater than the time delay  1214  shown in graph  1202  for the no-fault sensor indicating that the sensor fault is a delay fault in graph  1206 . At t 1 , when the downstream sensor responds, the measured lambda for the upstream sensor has not reached a desired threshold lambda change indicating that there is a fault in the upstream sensor. For example, in graph  1206  at time t 1  when the downstream sensor responds, the difference  1216  between measured lambda at the upstream exhaust gas sensor and measured lambda at the downstream exhaust gas sensor is less than the difference threshold reference for the no-fault sensor shown in graph  1202  indicating that a fault is present. 
     The graph at  1208  in  FIG. 12  shows upstream and downstream sensor response during an exit out of DFSO for an upstream sensor with no fault or no degradation. As indicated by the DFSO flag in graph  1208 , exit out of DFSO is commanded at t 0 . After a time delay  1218 , a threshold change, in this case a threshold decrease, in lambda at the upstream sensor is observed before the downstream sensor responds at t 1 . This threshold change in lambda observed indicates that a response to the commanded change in air-fuel ratio is beginning to occur at the upstream sensor. In some examples, the time delay  1218  shown in graph  1208  may be used as a reference to adjust expected sensor response time delay for subsequent sensor degradation routines, e.g., using the methods described above with regard to  FIGS. 9-11 . 
     Graph  1210  shows the downstream sensor responding after the upstream sensor responds following the exit out of DFSO. For example, at time t 1  the downstream sensor responds to the commanded change in air-fuel ratio at t 0 . This initial response of the downstream sensor at t 1  occurs after the initial response of the upstream sensor. At time t 1 , when the downstream sensor responds, a difference  1220  between measured lambda at the upstream exhaust gas sensor and measured lambda at the downstream exhaust gas sensor is observed. In some examples, this difference  1220  shown in graph  1208  may be used as a difference threshold reference during subsequent exits out of DFSO to determine sensor degradation. For example, as described below, if the difference between the measured lambda at the upstream exhaust gas sensor and measured lambda at the downstream exhaust gas sensor when the downstream sensor initially responds is greater than this difference threshold reference during an exit out of DFSO then a sensor fault may be indicated. 
     The graph at  1210  in  FIG. 12  shows upstream and downstream sensor response during an exit out of DFSO for an upstream sensor with a filter fault. As indicated by the DFSO flag in graph  1210 , exit out of DFSO is commanded at t 0 . After a time delay  1218 , a threshold change in lambda at the upstream sensor is observed before the downstream sensor responds at t 1 . In graph  1210 , the time delay  1218  is substantially the same as the time delay  1218  shown in graph  1208  for the no fault sensor indicating that the sensor fault shown in graph  1210  is not a delay fault. However, at t 1  when the downstream sensor responds, the measured lambda for the upstream sensor has not decreased to a desired threshold lambda change indicating that there is a fault in the upstream sensor. For example, in graph  1210  at time t 1  when the downstream sensor responds, the difference  1220  between measured lambda at the upstream exhaust gas sensor and measured lambda at the downstream exhaust gas sensor is greater than the difference threshold reference for the no-fault sensor shown in graph  1208  indicating that a fault is present. In this example, since no significant time delay is measured for the upstream sensor response, this may indicate that the fault is a filter fault. 
     The graph at  1212  in  FIG. 12  shows upstream and downstream sensor response during an exit out of DFSO for an upstream sensor with a delay fault. As indicated by the DFSO flag in graph  1212 , exit out of DFSO is commanded at t 0 . After a time delay  1218 , a threshold change in lambda at the upstream sensor is observed before the downstream sensor responds at t 1 . In graph  1212 , the time delay  1218  is greater than the time delay  1218  shown in graph  1208  for the no-fault sensor indicating that the sensor fault shown in graph  1212  is a delay fault. At t 1 , when the downstream sensor responds, the measured lambda for the upstream sensor has not decreased to a desired threshold lambda change indicating that there is a fault in the upstream sensor. For example, in graph  1212  at time t 1  when the downstream sensor responds, the difference  1220  between measured lambda at the upstream exhaust gas sensor and measured lambda at the downstream exhaust gas sensor is greater than the difference threshold reference for the no-fault sensor shown in graph  1208  indicating that a fault is present. 
       FIG. 13  shows an example method  1300  for indicating sensor degradation based on comparisons of upstream and downstream sensor responses. Method  1300  utilizes a downstream sensor, e.g., sensor  127 , positioned in the exhaust of an engine at a location downstream of an upstream sensor, e.g., sensor  126 , to assist in identifying degradation in the upstream sensor. For example, during an entry into or exit out of deceleration fuel shut-off, an exhaust gas sensor degradation may be indicated based on the downstream exhaust gas sensor responding before the upstream exhaust gas sensor. In some examples, method  1300  may be used in conjunction with the methods described above with regard to  FIGS. 9-11 . For example, method  1300  may be used to initially diagnose a sensor fault and then the methods described above with regard to  FIGS. 9-11  may be used to further diagnose the fault, e.g., by determining the type of fault present. 
     At  1302 , method  1300  includes determining operating parameters. Engine operating parameters may be determined based on feedback from various engine sensors, and may include engine speed, load, air/fuel ratio, temperature, etc. Further, engine operating parameters may be determined over a given duration, e.g., 10 seconds, in order to determine whether certain engine operating conditions are changing, or whether the engine is operating under steady-state conditions. 
     Method  1300  includes, at  1304 , determining if the engine is entering into or exiting out of deceleration fuel shut-off (DFSO). During DFSO, the engine is operated without fuel injection while the engine rotates and pumps air through the cylinders. DFSO entry and exit conditions may be based on various vehicle and engine operating conditions. In particular, a combination of one or more of vehicle speed, vehicle acceleration, engine speed, engine load, throttle position, pedal position, transmission gear position, and various other parameters may be used to determine whether the engine will be entering or exiting DFSO. In one example, the DFSO entry conditions may be based on an engine speed below a threshold. In another example, the DFSO entry conditions may be based on an engine load below a threshold. In still another example, the DFSO condition may be based on an accelerator pedal position. Additionally or alternatively, entry into DFSO may be determined based on a commanded signal to cease fuel injection. Exit out of DFSO may be based on a commanded signal to begin fuel injection in one example. In another example, a DFSO event may be ended based on a driver tip-in, the vehicle speed reaching a threshold value, and/or engine load reaching a threshold value. 
     If it is determined at  1304  that the engine is not entering or exiting DFSO, method  1300  returns to  1302  to continue to determine engine operating parameters. If DFSO entry or exit conditions are determined, method  1300  proceeds to  1306 . 
     At  1306 , method  1300  includes recording change in lambda for the downstream exhaust gas sensor over time during the DFSO entry or exit. For example, a change in lambda for sensor  127  may be recorded. When the engine enters or exits DFSO, the commanded air-fuel ratio changes, and the air-fuel ratio detected by the downstream exhaust gas sensor can be stored in the memory of the controller or the dedicated controller during the transition into or out of DFSO. As used herein, the terms entry into and exit out of DFSO may include the time from when a commanded entry or exit is detected until a time when the air-fuel ratio detected by the sensor reaches the steady-state commanded value. 
     At  1308 , method  1300  includes recording change in lambda for the upstream exhaust gas sensor over time during the DFSO entry or exit. For example, change in lambda may be recorded for sensor  126 . When the engine enters or exits DFSO, the commanded air-fuel ratio changes, and the air-fuel ratio detected by the upstream exhaust gas sensor can be stored in the memory of the controller or the dedicated controller during the transition into or out of DFSO. In some examples, recording of the upstream lambda signal may be recorded when the downstream sensor initially responds so that the difference, e.g., difference  1216  or difference  1220  shown in  FIG. 12 , between the upstream and downstream sensor signals can be compared to diagnose upstream sensor faults. 
     At  1310 , method  1300  includes comparing the signals from the upstream and downstream sensors. For example, as described above with regard to  FIG. 12 , the signal from the upstream sensor may be compared with the signal from the downstream sensor to determine if a fault is present at the upstream sensor. For example, if the downstream sensor is responding before the upstream sensor then a fault may be present at the upstream sensor. 
     At  1312 , method  1300  may include adapting an expected upstream sensor response based on the downstream sensor response. For example, an expected upstream sensor response may be adjusted based on a comparison of the downstream exhaust gas sensor response with the upstream exhaust gas sensor response during the commanded change in air-fuel ratio. These adapted or adjusted expected sensor responses may be used during subsequent commanded changes in air/fuel ratio to diagnose sensor faults using the methods described above with regard to  FIGS. 9-11 . 
     For example, the expected upstream sensor response may include an expected time delay and an expected line length so that exhaust gas sensor degradation may be indicated based on a comparison of a time delay of an upstream exhaust gas sensor response during the subsequent commanded change in air-fuel ratio with the expected time delay and a comparison of a line length of an upstream exhaust gas sensor response during the subsequent commanded change in air-fuel ratio with the expected line length, as described above with regard to  FIG. 11 . As another example, the expected upstream sensor response may include an expected entry time delay during an entry into a deceleration fuel shut-off, an expected exit time delay during an exit out of a deceleration fuel shut-off, an expected entry line length during an entry into a deceleration fuel shut-off, and an expected exit line length during an exit out of a deceleration fuel shut-off, wherein the time delay is a duration from a commanded entry into or exit out of deceleration fuel shut-off to a threshold change in lambda, and wherein the line length is based on a change of lambda over time during the upstream exhaust gas sensor response. As described above with regard to  FIG. 11 , if a time delay of the upstream exhaust gas sensor response during a subsequent deceleration fuel shut-off entry exceeds the expected entry time delay, and a time delay of the upstream exhaust gas sensor response during a subsequent deceleration fuel shut-off exit does not exceed the expected exit time delay, then a rich-to-lean delay sensor degradation may be indicated. Further, if the time delay of the upstream exhaust gas sensor response during the subsequent deceleration fuel shut-off entry does not exceed the expected entry time delay, and the time delay of the upstream exhaust gas sensor response during the subsequent deceleration fuel shut-off exit exceeds the expected exit time delay, then a lean-to-rich delay sensor degradation may be indicated. 
     As another example, if a line length of the upstream exhaust gas sensor response during a subsequent deceleration fuel shut-off entry exceeds the expected entry line length, and a line length of the upstream exhaust gas sensor response during a subsequent deceleration fuel shut-off exit does not exceed the expected exit line length, then a rich-to-lean filter sensor degradation may be indicated. Further, if the line length of the upstream exhaust gas sensor response during the subsequent deceleration fuel shut-off entry does not exceed the expected entry line length, and the line length of the upstream exhaust gas sensor response during the subsequent deceleration fuel shut-off exit exceeds the expected exit line length, then a lean-to-rich filter sensor degradation may be indicated. 
     As still another example, if a time delay of the upstream exhaust gas sensor responses during a subsequent deceleration fuel shut-off entry exceeds the expected entry time delay and a time delay of the upstream exhaust gas sensor responses during a subsequent deceleration fuel shut-off exit exceeds the expected exit time delay, then a symmetric delay sensor degradation may be indicated. Further, if a line length of the upstream exhaust gas sensor responses during the subsequent deceleration fuel shut-off entry exceeds the expected exit line length and a line length of the upstream exhaust gas sensor responses during the subsequent deceleration fuel shut-off exit exceeds the expected entry line length, then a symmetric filter sensor degradation may be indicated. 
     At  1314 , method  1300  includes determining if sensor degradation is indicated. For example, exhaust gas sensor degradation may be indicated in response to a change in measured lambda at the upstream exhaust gas sensor less than a first threshold change when a change in measured lambda at the downstream exhaust gas sensor is greater than a second threshold change. Here, the second threshold change may indicate that a response to the commanded change in air-fuel ratio has started and the first threshold change may be a desired response based on the commanded change in air-fuel ratio. 
     As another example, exhaust gas sensor degradation may be indicated in response to a difference between measured lambda at the upstream exhaust gas sensor and measured lambda at the downstream exhaust gas sensor less than a difference threshold when a change in measured lambda at the downstream exhaust gas sensor is greater than a second threshold change during an entry into deceleration fuel shut-off. As still another example, exhaust gas sensor degradation may be indicated in response to a difference between measured lambda at the upstream exhaust gas sensor and measured lambda at the downstream exhaust gas sensor greater than a difference threshold when a change in measured lambda at the downstream exhaust gas sensor is greater than a second threshold change during an exit out of deceleration fuel shut-off. 
     At  1314 , sensor degradation behavior type may also be determined using the methods described above with regard to  FIGS. 9-11 . For example, sensor degradation behavior type may be determined based on the average time delays and line lengths as described above with respect to  FIG. 11 . 
     At  1316 , it is determined if the sensor is exhibiting at least on type of sensor degradation. If no, method  1300  exits, as the sensor is not degraded, and thus standard engine operation may continue. If yes, method  1300  proceeds to  1318  to adjust fuel injection amount and/or timing. To ensure adequate engine control to maintain engine emissions and fuel economy at a desired level, one or more engine operating parameters may be adjusted at  1318 , if desired. This may include adjusting fuel injection amount and/or timing, and may include adjusting control routines that are based on feedback from the degraded sensor to compensate for the identified degradation. 
     At  1320 , if the degradation behavior exceeds a threshold, this may indicate the sensor is damaged or otherwise non-functional and as such an operator of the vehicle may be notified of the sensor degradation, for example by activating a malfunction indication light. Upon adjusting operating parameters and/or notifying a vehicle operator, method  1300  exits. 
     It will be appreciated that the configurations and methods disclosed herein are exemplary in nature, and that these specific embodiments are not to be considered in a limiting sense, because numerous variations are possible. For example, the above technology can be applied to V-6, I-4, I-6, V-12, opposed 4, and other engine types. The subject matter of the present disclosure includes all novel and non-obvious combinations and sub-combinations of the various systems and configurations, and other features, functions, and/or properties disclosed herein. 
     The following claims particularly point out certain combinations and sub-combinations regarded as novel and non-obvious. These claims may refer to “an” element or “a first” element or the equivalent thereof. Such claims should be understood to include incorporation of one or more such elements, neither requiring nor excluding two or more such elements. Other combinations and sub-combinations of the disclosed features, functions, elements, and/or properties may be claimed through amendment of the present claims or through presentation of new claims in this or a related application. Such claims, whether broader, narrower, equal, or different in scope to the original claims, also are regarded as included within the subject matter of the present disclosure.