Engine emission control

Abstract

Method of training a machine learning model to estimate engine emission data in an exhaust system (fig.1, 106) of a vehicle (fig.1, 100) in cold-start conditions, when a corresponding engine emission

Description

TECHNICAL FIELD The present invention relates to a method of training a machine learning model to estimate engine emission data in an exhaust system of a vehicle. Aspects of the invention relate to a method, to a virtual sensor device, and to an engine emission control system. BACKGROUND TO THE INVENTION Engine control systems and exhaust gas purification technologies, such as catalytic converters, are known in the automotive industry for reducing pollution from an internal combustion engine. Such control systems are typically configured to control one or more parameters of the engine operation, such as an air-fuel ratio of the intake mixture, to improve a purification effect of the catalytic converter and provide efficient combustion, whilst taking temperature, load, and other operating conditions into account. For example, such methods may control the air-fuel ratio of the intake mixture for optimal catalyst performance based on a nitrogen oxide or an oxygen storage amount (OSA) of the catalytic converter. The control systems commonly use closed-loop controllers that rely on feedback measurements obtained by a set of engine emission sensors arranged in the exhaust system of the vehicle. The engine emission sensors are configured to determine measurements indicative of the performance of the catalytic converters, such as the contents and / or characteristics of the exhaust gas, and may include nitrogen oxide sensors, air / fuel ratio sensors and / or oxygen sensors, amongst others. For example, such sensors may include an air / fuel ratio sensor arranged in front of the catalytic converter of the catalyst, and / or a rear oxygen sensor (also known as a lambda sensor), for calculating the OSA of the catalytic converter. However, the engine emission sensors are susceptible to error and damage from moisture in the exhaust system following a cold-start of the engine, i.e. when starting the engine with relatively low engine, cooling water, and / or oil temperatures compared to their normal operating temperatures. For example, cold-starts typically occur when the ambient temperature is less than approximately 20°C and the vehicle has been shutdown (i.e. engine off) for a prolonged period, e.g. for a few hours or overnight, such that residual engine heat has dissipated. The engine emission sensors are therefore typically only activated after an initial warm-up period, following a cold-start, which allows for removal of any moisture in the exhaust system, protecting the sensors from damage. Thereafter, the senor(s) are activated to monitor the exhaust gasses and generate engine emission data for controlling the engine operation. However, the warm-up period required to suitably heat the components, and remove the moisture, may last between 100 to 300 seconds, particularly where sensors are arranged downstream in the exhaust system and exposed to relatively low exhaust gas temperatures. During the warm-up period, the engine emission data is therefore unavailable or incomplete for feedback-based control and, instead, existing engine emission control systems typically rely on predefined control strategies, such as open-loop control loops, for managing the engine operation. The use of predefined control strategies for controlling the engine operation during the warm-up period is sub-optimal and, as a result, relatively high levels of polluting emissions are observed during the warmup period. This issue is particularly problematic in relation to short journeys, and urban driving scenarios, where a cold start is most frequently encountered. It is against this background that the present invention has been devised. SUMMARY OF THE INVENTION According to an aspect of the invention, there is provided a method of training a machine learning model to estimate engine emission data in an exhaust system of a vehicle. In particular, estimating engine emission data in cold-start conditions, when a corresponding engine emission sensor of a sensor system of the vehicle is inactive. The machine learning model is trained to estimate the engine emission data based on inputs received from one or more active sensors of the sensor system during the cold-start conditions. The method comprises: obtaining test data for one or more test cycles in cold-start conditions using a test apparatus representative of the exhaust system and a corresponding sensor system, the obtained test data comprising engine emission data obtained by activating the engine emission sensor during the one or more test cycles; and training the machine learning model to estimate the engine emission data during cold-start conditions based on the obtained test data by (iteratively): estimating engine emission data using the machine learning model, the estimated engine emission data being determined based on the test data obtained by one or more sensors, other than the engine emission sensor, of the corresponding sensor system; comparing the estimated engine emission data from the machine learning model to the test data obtained by the activated engine emission sensor; and updating the machine learning model based on the comparison. In this manner, the trained machine learning model is able to supplement the engine emission data ordinarily determined by the engine emissions sensor with estimates obtained during inactive periods of that sensor, i.e., during cold-start conditions. Engine emission data can therefore be determined even in cold-start conditions, enabling closed-loop control of the engine emissions. The training method uses test data obtained from a test apparatus that corresponds to a production version of the vehicle but further includes the capability of activating the engine emission sensor, e.g. by heating, when the engine emission sensor would ordinarily be inactive, e.g. in cold-start conditions. The one or more test cycles may, for example, corresponding to Real-Driving Emissions tests simulating driving on public roads, for example involving urban, rural, and / or highway driving scenarios. It shall be appreciated that ‘cold-start conditions’ refer to conditions in which the engine emission sensor is inactive, for example when the engine emission sensor is below a minimum activation temperature, as shall be described in more detail. In an example, the method further comprises determining the test data using the test apparatus by: activating the engine emission sensor of the corresponding sensor system; operating the test apparatus according to the one or more test cycles; and determining test data for each test cycle using the plurality of sensors of the corresponding sensor system. The machine learning model may, for example, comprise a recurrent neural network and a gated recurrent unit. Optionally, updating the machine learning model based on the comparison comprises: minimising a loss function quantifying a difference between the estimated engine emission data and the test data determined by the activated engine emission sensor. In an example, updating the machine learning model based on the comparison further comprises: back propagating the loss determined by the loss function; and updating one or more weightings of the neural network using a gradient descent optimisation technique. Optionally, the method further comprises: obtaining test data for one or more test cycles in warm conditions using the test apparatus and the corresponding sensor system; and training the machine learning model to estimate the engine emission data during warm conditions based on the obtained test data. In this manner, the trained machine learning model is further able to estimate the engine emission data in warm conditions. It shall be appreciated that warm conditions, refer to those conditions where the engine emission sensor is active for example having been heated to a minimum activation temperature of said sensor by the exhaust gases. The test data may, for example, be obtained for a range of emission test cycles or real-driving emissions tests. In an example, the engine emission sensor may be heat-activated. For example, the test data may be obtained for the one or more cold-start conditions by heating the engine emission sensor to an active state (e.g., by heating to a temperature greater than or equal to an activation temperature of said engine emission sensor). The plurality of sensors of the sensor system may, for example, comprise a further engine emission sensor that remains active during the cold start conditions. That is, another engine emission sensor arranged in another position in the exhaust system and / or measuring another engine emission parameter, such that the further engine emission sensor can remain active during the cold start conditions. The engine emission data determined by the further engine emission sensors may be provided as an input to the machine learning model for estimating the engine emission data of the inactive engine emission sensor during cold-start conditions. Accordingly, the obtained test data may further include engine emission data obtained by the further engine emission sensor. The engine emission sensor may, for example, be configured to determine engine emission data indicative of catalytic performance of a catalytic converter arranged in the vehicle exhaust system. For example, the engine emission sensor may be configured to determine engine emission data indicative of an oxygen storage amount or a nitrogen oxide storage amount of the catalytic converter. Optionally, the engine emission sensor may take the form of: an air-fuel sensor arranged upstream of the catalytic converter in the vehicle exhaust system; an oxygen sensor arranged downstream of the catalytic converter in the vehicle exhaust system; an engine out emissions sensor; or a nitrogen oxide sensor arranged downstream of the catalytic converter in the vehicle exhausts system. The engine emission sensor may, for example, take the form of an oxygen sensor arranged downstream of the catalytic converter in the exhaust system and the further engine emission sensor may take the form of an oxygen sensor or an air-fuel sensor arranged upstream of the catalytic converter in the exhaust system. In an example, the plurality of sensors of the sensor system may comprise one or more of the following: an engine speed sensor; a vehicle speed sensor; a pressure sensor arranged in an intake manifold of the vehicle; an air-mass flow rate sensor arranged in the intake manifold; and / or a fuel pressure sensor. Accordingly, the inputs to the machine learning model for estimating the engine emission data may therefore include engine speed, vehicle speed, intake manifold pressure, intake air mass, and fuel pressure, determined by the sensors of the sensor system. In some examples, the air-fuel measurements of the air-fuel sensor may also be used as inputs to the machine learning model. Other inputs to the machine learning model may also include a fuel injection timing, a target equivalence ratio, a rich spike fuel cut-off time, and intake charging efficiency, for example. Optionally, the machine learning model may be trained to estimate engine emission data for one of a plurality of performance drift classifications of the catalytic converter. That is, one of a plurality of categories or classifications of the catalytic converter according to its performance drift or degradation relative to a newly manufactured device. The test apparatus used to obtain the test data may comprise a catalytic converter associated with that performance drift classification. In other words, the machine learning model may be trained for a particular performance drift classification based on test data obtained from a test apparatus that includes a catalytic converter with corresponding performance. Optionally, the plurality of performance drift classifications of the catalytic converter may comprise: a fresh classification, a worn classification, and / or a best part unacceptable classification. According to another aspect of the invention there is provided a virtual sensor device comprising a machine learning model trained to estimate engine emission data according to the method described in a previous aspect of the invention. According to yet another aspect of the invention, there is provided an engine emission control system for a vehicle. The engine emission control system comprises a virtual sensor device as described in a previous aspect of the invention. According to a still further aspect of the invention, there is provided a vehicle comprising a virtual sensor device as described in a previous aspect of the invention. Within the scope of this application it is expressly intended that the various aspects, embodiments, examples and alternatives set out in the preceding paragraphs, in the claims and / or in the following description and drawings, and in particular the individual features thereof, may be taken independently or in any combination. That is, all embodiments and / or features of any embodiment can be combined in any way and / or combination, unless such features are incompatible. The applicant reserves the right to change any originally filed claim or file any new claim accordingly, including the right to amend any originally filed claim to depend from and / or incorporate any feature of any other claim although not originally claimed in that manner. BRIEF DECRIPTION OF THE DRAWINGS One or more embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which: Figure 1 is a schematic illustration of a plan view of a vehicle, in accordance with an embodiment of the invention, with an overlay of an exemplary engine emission control system; Figure 2 schematically illustrates an exemplary embodiment of the control system shown in Figure 1; Figure 3 schematically illustrates an exemplary control loop implemented by the control system shown in Figure 2; Figure 4 schematically illustrates an exemplary neural network for estimating engine emission data in the control system shown in Figure 2; Figure 5 is a plot illustrating measurements from a rear oxygen sensor of the control system shows in Figure 2 and corresponding estimates from a trained sensor model of a virtual sensor device of that control system; Figure 6 is a plot illustrating measurements from a rear oxygen sensor of the control system shows in Figure 2 and corresponding estimates from a validated sensor model of a virtual sensor device of that control system; Figure 7 is a schematic illustration of an exemplary method of sensor model selection for a virtual sensor device of the control system shown in Figure 2; Figure 8 is a plot showing exemplary measurements of a rear oxygen sensor of the control system, shown in Figure 2, for use in the sensor model section method of Figure 7; Figure 9 schematically illustrates an exemplary method, in accordance with an embodiment of the invention, of operating the engine emission control system shown in Figure 1; and Figure 10 schematically illustrates an exemplary method, in accordance with an embodiment of the invention, of diagnosing sensor faults in the control system shown in Figure 2. DETAILED DESCRIPTION Embodiments of the present invention relate to systems and methods for engine emission control, seeking to improve a purification effect of a catalytic converter of a vehicle, such as a passenger car. For this purpose, such systems include one or more engine emission sensors for determining engine emission data indicative of the exhaust gas characteristics, and one or more virtual sensor devices for estimating engine emission data when the engine emission sensor(s) are inactive, e.g. during cold-start conditions of the engine. The estimated engine emission data is utilised to provide closed loop control of the engine operation, even when the engine emission sensor(s) are inactive or unavailable. It is envisaged that embodiments of the invention will therefore lead to a reduction of polluting emissions from the vehicle, particularly in urban driving scenarios where coldstarts are frequently encountered. Embodiments of the invention shall now be discussed in more detail with reference to Figures 1 to 10. Figure 1 shows a plan view of a vehicle 100, in accordance with an embodiment of the invention, with a schematic overlay of an engine emission control system 102 for managing the operation of an internal combustion engine (ICE) 104 of the vehicle 100. The control system 102 may therefore act as, or form part of, an overall engine management system of the vehicle 100, for example. In this example, the vehicle 100 takes the form of a passenger car. However, this example is not intended to be limiting on the scope of the invention and, in other examples, the vehicle 100 may take various other forms, such as a bus, or truck, amongst other passenger vehicles. Moreover, whilst the vehicle 100 is shown to include a conventional combustion powertrain in Figure 1, it shall be appreciated that the vehicle 100 may include alternative powertrain arrangements with an ICE in other examples, such as a hybrid powertrain arrangement. The ICE 104 may take the form of a petrol-fuelled, diesel-fuelled, or gaseous-fuelled engine, and the invention is not intended to be particularly limited in this respect. Moreover, in the following description it shall be appreciated that the references to the ICE 104 are intended to refer to the combustion system, more generally. The references to the ICE 104 are therefore intended to further encompass sub-systems for managing the engine operation and the intake mixture, including the fuel injection system that delivers fuel to the engine for example. The ICE 104 is connected to an exhaust system 106, as shown in Figure 1, through which exhaust gases are expelled from the ICE 104. The exhaust gasses output from the ICE 104 may contain pollutants though, such as nitrogen oxides, carbon monoxide, and hydrocarbons. To mitigate such emissions, the exhaust system 106 of the vehicle 100 further includes exhaust gas purification technologies, such as one or more catalytic converters 110, as shown in Figure 1. The catalytic converter(s) 110 are configured to catalyse redox reactions of the exhaust gases, and thereby convert toxic compounds and pollutants into less harmful forms. For example, a three-way catalytic converter may be used for: (i) the reduction of nitrogen oxides into nitrogen and oxygen, (ii) the oxidation of carbon monoxide into carbon dioxide, and (iii) the oxidation of hydrocarbons into carbon dioxide and water. It shall be appreciated that the catalytic converter(s) 110 will vary depending on the nature and configuration of the ICE 104 though, and the exhaust gases generated by its operation. In examples, the catalytic converter(s) 110 may therefore include a two-way catalytic converter and / or a three-way catalytic converter for treating the exhaust gases of a petrol-fuelled engine. In other examples, the catalytic converter(s) 110 may include a diesel oxidation catalyst and / or a selective catalytic reduction (SCR) system for treating the exhaust gases of a diesel-fuelled engine. Other variations are also envisaged. Moreover, in examples, the arrangement of such catalytic converter(s) 110 within the exhaust system 106 may vary. However, for the purposes of the following description, the catalytic converter(s) 110 are considered to include a close-coupled (CC) catalytic converter 110a and an under-floor (UF) catalytic converter 110b. The CC catalyst 110a is installed close to the ICE 104 so as to minimise heat losses from the exhaust gasses and maximise the oxidation of hydrocarbons. Meanwhile, the UF catalyst 110b is arranged downstream in the exhaust system 106 and may serve as the main catalyst for the conversion of the remaining hydrocarbons along with the carbon monoxide and nitrogen oxides. The control system 102 is configured to monitor emissions from the ICE 104 in the exhaust system 106 and to manage or control the operation of the ICE 104 accordingly to reduce, or mitigate, the polluting emissions expelled from the exhaust system 106. Various engine emission control systems are known in the automotive industry for controlling and reducing the emissions from an ICE based on feedback measurements obtained by engine emission sensors arranged in the exhaust system. For example, such control systems typically adjust an air-fuel ratio of the intake mixture of the engine for optimal performance of the catalytic converters using a feedback-based control system, e.g. based on feedback measurements indicative of a nitrogen oxide or an oxygen storage amount of the catalytic converter(s). The engine emission sensors used therefore provide engine emission data that is indicative of the exhaust gas contents and / or characteristics, and the performance of the catalytic converters more generally. Such engine emission sensors may include nitrogen oxide sensors, air / fuel ratio sensors, and / or oxygen sensors, amongst others. For example, the engine emission sensors may include an air / fuel ratio sensor arranged in front of one of the catalysts, and / or an oxygen sensor arranged to the rear of the catalyst, for calculating an oxygen storage amount (OSA) of that catalyst. However, the engine emission sensors are susceptible to damage and error due to moisture in the exhaust system during cold-starts of the engine, i.e. when starting the engine with relatively low engine, cooling water, and / or oil temperatures relative to their normal operating temperatures (e.g. with temperatures less than or equal to approximately 20°C). To mitigate the risk of damage, the sensors are typically only activated once they have been heated to a minimum activation temperature, which may correspond to a dew point of the moisture. The sensors are therefore inactive during an initial warm-up period following engine start-up, and the sensors arranged further downstream in the exhaust system, such as the rear oxygen sensor, are associated with longer warm-up periods due to their exposure to lower exhaust gas temperatures. In the absence of engine emission data during the warm-up period, existing engine emission control systems typically rely on predefined control strategies for controlling the engine operation during engine cold-starts. As a result, relatively high levels of polluting emissions are observed during the warmup period. This issue is particularly problematic in relation to short journeys, and urban driving scenarios, where a cold start is most frequently encountered. To mitigate this issue, the control system 102 of the present invention further includes one or more virtual sensor devices (not shown in Figure 1), trained to estimate engine emission data, such as the oxygen amount at the rear of the catalyst, during such warm-up periods (when the physical engine emission sensor(s) of the control system 102 are inactive). The control system 102 is further configured to use the estimated engine emission data in a feedback control loop for managing the engine operation, e.g. by controlling the air-fuel ratio of the intake mixture. In this manner, the control system 102 is able to use the estimated engine emission data as a stand-in for the inactive engine emission sensors. As a result, the control system 102 is able to precisely control the operation of the ICE 104 for optimal performance of the catalytic converter(s) 110, significantly reducing the polluting emissions expelled from the exhaust system 106, particularly during cold-start conditions. An exemplary control system 102, in accordance with embodiments of the present invention, shall now be discussed in more detail with additional reference to Figures 2 and 3. As shown in Figure 2, the control system 102 includes a sensor system 112 and one or more controller(s) 114 for controlling the operation of the ICE 104 based on the information received from the sensor system 112. The controller(s) 114 may be considered as part of a main engine control unit (ECU) of the vehicle 100, for example. The sensor system 112 is configured to provide a range of data indicative of the engine emissions and corresponding operating conditions of the ICE 104. Such data is provided to the controller(s) 114 to inform feedback-based control of the ICE 104. For example, the controller(s) 114 may use signals from the sensor system 112 for precise control of an airfuel ratio of the intake mixture in accordance with one or more known methodologies. In examples, the sensor system 112 may therefore take various suitable forms for providing data that is indicative of the contents and / or characteristics of the exhaust gases in the vehicle exhaust system 106, along with information that is indicative of the operating conditions of the ICE 104 and / or the exhaust system 106. In Figure 2, the sensor system 112 is shown to include one or more operational sensor(s) 115 for determining operational data that is indicative of the operating conditions of the ICE 104, such as the throttle position, engine speed, engine load, intake air flow, and ambient temperature, amongst others. For example, the operational sensor(s) may include an air mass flow rate sensor for measuring a mass flow rate of the air in an intake manifold of the ICE 104, a fuel temperature sensor, a fuel tank pressure sensor, an acceleration pedal position sensor, an engine speed sensor, a vehicle speed sensor, an intake manifold pressure sensor, an exhaust gas recirculation temperature sensor, a knock sensor, and an engine pressure sensor, amongst others. Suitable operational sensors and their arrangements for informing feedback-based control of the ICE 104 are well-known in the art and are not described in detail here to avoid obscuring the invention. Additionally, in order to determine the engine emission data, the sensor system 112 is shown to include one or more engine emissions sensors 116 and one or more virtual sensor devices 118. The engine emission sensor(s) 116 are physical sensors arranged in the exhaust system 106 for measuring parameter(s) of the exhaust gas in the exhaust system 106. In examples, the engine emission sensor(s) 116 may include one or more nitrogen oxide sensors, oxygen sensors, temperature sensors, air-fuel sensors, and / or engine out emissions (EOE) sensors, amongst others. Indeed, suitable engine emissions sensors and their arrangements for controlling engine emissions are well-known in the art and are not described in detail here to avoid obscuring the invention. For the purposes of the following description, the engine emission sensor(s) 116 are considered to include a front air-fuel ratio sensor 116a and a rear oxygen sensor 116b. The front air-fuel ratio sensor 116a is arranged upstream of the CC catalyst 110a for measuring the air-fuel ratio of the exhaust gasses emitted from the ICE 104 and may take the form of a linear, wide-band, sensor. The rear oxygen sensor 116b is arranged downstream of the CC catalyst 110a, between the CC catalyst 110a and the UF catalyst 110b, for measuring the oxygen amount downstream of the CC sensor 110b. The rear oxygen sensor 116b may take the form of a binary sensor, for example, for detecting oxygen full and empty states of the CC catalyst 110a. In combination, the engine emission data provided by the front air-fuel ratio sensor 116a and the rear oxygen sensor 116b may therefore be indicative of an oxygen storage amount of the CC catalyst 110a. As noted above, a number of the identified engine emission sensors 116 are typically heat-activated devices that are only activated after the dew point, or minimum activation temperature, is reached. This serves to protect the sensors in the exhaust system 106 from damage and erroneous readings caused by condensed moisture in the exhaust gas. For example, oxygen sensors and air-fuel sensors are designed to measure precise variables like oxygen content and airflow, but humidity introduces moisture into the air that can condense on the sensor surfaces, leading to inaccurate measurements, inappropriate control, and / or the risk of damage. To mitigate these issues, such sensors are typically only activated after a warm-up period, during which the exhaust gases heat the exhaust system and remove the moisture. However, the warm-up period can last between 100 to 300 seconds for the sensors to reach their minimum activation temperature, particularly in relation to sensors arranged downstream in the exhaust system (such as the rear oxygen sensor 116b) where the exhaust gas temperatures are lower. The control system 102 therefore further includes the virtual sensor device(s) 118 for providing engine emission data estimates following a cold-start of the ICE 104 (when measurement data from one or more of the physical engine emission sensor(s) 116 is unavailable). The virtual sensor device(s) 118 are computer-implemented devices configured to estimate engine emission data based on the indicated operating conditions of the ICE 104, such as the engine speed, engine load, intake air flow, and ambient temperature, provided by the operational sensors 115. The virtual sensor device(s) 118 therefore use the sensor data that is available during a cold-start of the ICE 104 to estimate the engine emission data ordinarily provided by the inactive engine emission sensor(s) 116. For example, the control system 102 may include a virtual sensor device 118 corresponding to each engine emission sensor 116 that is inactive for an initial warm-up period following a cold-start of the ICE 104, e.g. inactive for a threshold period following a cold-start. In examples, each virtual sensor device 118 may be configured to generate outputs corresponding to a respective physical engine emission sensor 116, for example on a one-to-one basis. For the sake of simplicity, a first virtual sensor device 118a is shown in Figure 2, which is configured to estimate oxygen measurements in the manner of the rear oxygen sensor 116b. In this regard, the rear oxygen sensor 116b is relatively far downstream in the exhaust system 106 and therefore associated with a relatively long warm-up period (e.g. 100 to 300 seconds), while the air-fuel sensor 116a is arranged close to the ICE 104 and may therefore be associated with a negligible warm-up period, such that it is effectively active upon start-up. For context, the warm-up period of the oxygen sensor may be approximately 100 seconds for ambient temperatures of approximately 20°C, 200 seconds for ambient temperatures of approximately 0°C, and 300 seconds for ambient temperatures of approximately -10°C, while the warm-up period of the air-fuel sensor 116a may be a maximum of approximately 10 seconds in any such conditions. However, it shall be appreciated that, in other examples, the virtual sensor device(s) 118 may include alternative or additional virtual sensor devices. For example, virtual sensor devices may be included for estimating the air-fuel measurements in the manner of the airfuel sensor 116a in addition to, or as an alternative to, virtual sensor devices for estimating other parameters measured by respective engine emission sensors, such as the nitrogen oxide amounts upstream and downstream of a catalyst. Each virtual sensor device 118 includes one or more machine learning models, also referred to as ‘sensor models’, that are trained using machine learning algorithm(s) to estimate engine emission data based on the sensor data received from the active sensors of the sensor system 112. It shall be appreciated that the operational sensors 115 remain active during cold-start conditions of the vehicle 100 and are therefore able to provide the operational data as an input to the sensor model(s) for estimating the engine emission data during cold-starts of the ICE 104. Some of the engine emission sensor(s) 116, such as the front air-fuel sensor 116a, may similarly remain active during cold-start conditions of the vehicle 100 and provide input data for estimating the engine emissions. To give an example, the first virtual sensor device 118a may include a sensor model configured to estimate the amount of oxygen in the exhaust gas (in the manner of the physical oxygen sensor 116b) based on sensor inputs indicative of the following: engine speed, vehicle speed, intake manifold pressure, intake air mass, and fuel pressure determined by the operational sensors 115 of the sensor system 112. In some examples, the air-fuel measurements of the air-fuel sensor 116a may also be used as inputs to the sensor model of the first virtual sensor device 118a for further improving the accuracy of the oxygen estimates since such measurements may become available within a relatively short period following engine startup, e.g. within 10 seconds. Other inputs to the sensor model may also include a fuel injection timing, a target equivalence ratio, a rich spike fuel cut-off time, and intake charging efficiency, for example. In turn, the controller(s) 114 are configured to determine one or more control signals for controlling the operation of the ICE 104 based on the operational data and the engine emission feedback from the sensor system 112. For example, the controller(s) 114 may operate a feedback-based control loop for precise control of the air-fuel ratio of the intake mixture using the operational data determined by the operational sensors 115, and engine emission feedback from the front air-fuel ratio sensor 116a, the rear oxygen sensor 116b, and / or the first virtual sensor device 118a. In this context, the first virtual sensor device 118a provides engine emission feedback that is lacking in cold-start conditions, enabling feedback-based control. The control signal(s) determined by the controller(s) 114 are therefore output to respective systems for managing the operation of the ICE 104, thereby mitigating the pollution exhausted to the environment. For example, control signal(s) may be output to a fuel injection system to control an amount of fuel injection in the intake mixture according to a target air-fuel ratio, where the target air-fuel ratio may be based, at least in part, on the engine emission feedback. For this purpose, the controller(s) 114 may include an input module 120, a processor module 122, a memory module 124, and an output module 126, as shown in Figure 2. That is, Figure 2 shows an exemplary embodiment of a controller 114 of the control system 102, including four functional elements, units or modules. Each of these units or modules may be provided, at least in part, by suitable software running on any suitable computing substrate using conventional or customer processors and memory. Some or all of the units or modules may use a common computing substrate (for example, they may run on the same server) or separate substrates, or different combinations of the modules may be distributed between multiple computing devices. The example architecture of the controller 114 is not intended to be limiting on the scope of the invention though and, in other examples, it shall be appreciated that the architecture may take other suitable forms. The input module 120 is electrically connected to the sensor system 112 and configured to receive the engine emission data, the estimated engine emission data, and the operational data (indicative of the operating conditions of the ICE 104), amongst other inputs. The processor module 122 is configured to process the data received at the input module 120 and determine one or more control signals for adjusting the operation of the ICE 104 based on the received data. In particular, the processor module 122 is configured to generate control signal(s) for managing the operation of the ICE 104 based on the received engine emission data, estimated engine emission data, and operational data. For example, such control signals may be configured to control the air-fuel ratio of the intake mixture by adjusting the operation of a fuel injector system and / or an Evaporative Emission Control (EVAP) system of the vehicle 100. For example, a purge valve may be operated accordingly to control the amount of fuel vapour to be purged from the charcoal canister and burned in the ICE 104. For this purpose, the processor module 122 may be configured to implement one or more control methods or closed loop control strategies, as shall be described in more detail. The memory module 124 may store one or more sets of instructions and / or parameters, along with historical data, that may be accessed by the processor module 122, for example, to determine the control signal(s). The output module 126 is configured to output the determined control signal(s) for controlling the ICE 104. For example, the output module 126 may be configured to output control signal(s) to the fuel injector to control the amount of fuel in the intake mixture. Additionally, or alternatively, the output module 126 may be configured to output control signal(s) to the EVAP system for controlling the amount of fuel vapour introduced from the fuel tank I charcoal cannister. As shall be appreciated by the skilled person, these exemplary outputs are not intended to be particularly limiting on the scope of the invention though. In this manner, the controller(s) 114 manage the operation of the ICE 104 to mitigate the pollution emitted from the exhaust system 106, and optimise the performance of the catalytic converter(s) 110. The controller(s) 114 may use various feedback-based control methods that are known in the art for this purpose, and manage the operation of the ICE 104 based on feedback measurements obtained by the engine emission sensors 116 in a conventional manner, further using the virtual sensor device(s) 118 to provide such feedback measurements when the engine emission sensor(s) 116 are inactive, e.g. in cold-start conditions. For example, such control systems may control the fuel addition to an intake mixture of the engine using a target air-fuel ratio, and adjust the target air-fuel ratio for optimal performance of the catalytic converters based on the feedback measurements from the engine emission sensors 116 and / or the virtual sensor device(s) 118. In this context, the virtual sensor device(s) 118 of the present invention provide a significant advantage and allow for known closed loop control strategies to be extended to cold-start conditions. To give an example, Figure 3 schematically shows an exemplary closed loop control strategy that may be implemented by the controller(s) 114 to control the emissions from the ICE 104. The example control strategy is not intended to be limiting on the scope of the invention though and, in other examples, it shall be appreciated that the controller(s) 114 may implement other closed loop control strategies for controlling the operation of the ICE 104 based on the engine emission feedback., e.g. determining a nitrogen oxide or an oxygen storage amount of the catalytic converter(s) and using such parameters as indicators of the catalyst performance for adjusting the target air-fuel ratio of the intake mixture. In the example shown in Figure 3, an intake manifold 302 is depicted for delivering an intake mixture of air and fuel to the ICE 104 for combustion. In this example, the air flow inside the intake manifold 302 is measured by a mass air flow sensor 115a, and controlled by an adjustable throttle 304. The mass air flow sensor 115a is one example of an operational sensor 115 used in the control loop, though it shall be appreciated that the control loop may use operational data from other operational sensors 115 not shown in Figure 3 for the sake of simplicity. Fuel addition to the intake mixture is provided by a fuel injection system 306 and an EVAP system 308 arranged in the intake manifold 302. The intake mixture is supplied to the ICE 104 and the exhaust gasses generated by combustion in the ICE 104 are output to an exhaust manifold 310, shown to extend from an outlet of the ICE 104. To continue the previous example, the exhaust manifold 310 is shown to include the CC catalyst 110a and UF catalyst 110b for treating the exhaust gasses, as they pass from the ICE 104 to an outlet 312 at an opposing end of the exhaust manifold 310. The engine emission sensors 116 are shown to include the front air-fuel ratio sensor 116a, arranged in front of the CC catalyst 110a, and the rear oxygen sensor 116b, arranged at the rear of the CC catalyst 110a. In this example, the feedback measurements from the engine emission sensors 116 are provided to an oxygen storage amount calculator 314, which compares the air-fuel measurements output from the front air-fuel sensor 116a with the oxygen content measured by the rear oxygen sensor 116b to calculate the oxygen storage amount (OSA) of the CC catalyst 110a. The OSA may be calculated as a binary value, e.g. indicating an oxygen empty or full state of the CC catalyst 110a, or as a non-binary value, e.g. a measured value of the OSA. The calculated OSA of the CC catalyst 110a is indicative of the performance of the CC catalyst 110a, i.e. the capacity of the CC catalyst 110a for catalysing redox reactions of the exhaust gases. Accordingly, the calculated OSA is fed back to a ‘A’ or air-fuel ratio target setting module 316, which is configured to determine a target air-fuel ratio for the intake mixture. For example, the A target setting module 316 may process the calculated OSA along with operational data, such as the engine speed, engine load, ambient temperature, and other parameters, received from the operational sensors 115 to determine an optimum target air-fuel ratio of the intake mixture for effective performance of the CC catalyst 110a. Methods are well-known in the art for determining the OSA amount and an air-fuel ratio target for the intake mixture based on such inputs though and so such methods are not described in detail here to avoid obscuring the invention. In any case, the determined target air-fuel ratio is output to respective control modules, such as a fuel injection control moule 318 and a purge valve control module 320, along with the operational data, to determine respective control signals for achieving the target air-fuel ratio. In particular, in this example, the controller(s) 114 are configured to determine a purge valve control signal and a fuel injector control signal for controlling the intake mixture according to the target air-fuel ratio. The fuel injector control signal controls a fuel injection amount from the fuel injection system 306 and the purge valve control signal controls the amount of fuel vapour released from the EVAP 308 by the purge valve. In this manner, the control system 102 is able to precisely control the air-fuel ratio to preserve fuel efficiency, optimise the exhaust purification, and achieve efficient combustion. Advantageously though, in embodiments of the present invention the closed loop control strategy further incorporates feedback measurements from the virtual sensor device(s) 118, which provide engine emission data estimates when the respective engine emission sensors 116 are inactive, e.g. during cold-start conditions. The virtual sensor device(s) 118 estimate the engine emission data based on sensor data received from the sensors that are active in such conditions, which include the operational sensor(s) 115 and may include one or more of the engine emission sensor(s) 116. To continue the previous example, the virtual sensor device(s) 118 shown in Figure 3 may take the form of the first virtual sensor device 118a, which is configured to estimate the oxygen content of the exhaust gas at the rear of the CC catalyst 110a. The first virtual sensor device 118a therefore acts as a stand-in for the rear oxygen sensor 116b during cold-start conditions and is configured to estimate the oxygen content based on operational data such as the indicated engine speed, engine load, ambient temperature and mass air flow rate determined by the operational sensors 115 of the sensor system 112. As shown in Figure 3, the air-fuel measurements of the air-fuel sensor 116a may also be used as inputs to the first virtual sensor device 118a for further improving the accuracy of the oxygen estimates, since such measurements may become available within a relatively short period following engine startup (e.g. within 10 seconds). The estimated oxygen content is output from the first virtual sensor device 118a during cold-start conditions, and provided to the OSA calculator 314, which compares the air-fuel measurements output from the front air-fuel sensor 116a with the estimated oxygen content to calculate the oxygen storage amount (OSA) of the CC catalyst 110a, substantially as described previously. In this manner, the virtual sensor device 118 provide feedback measurements of the engine emissions for closed-loop control of the ICE 104, facilitating more accurate control of the ICE 104, particularly during cold-start conditions. This example is not intended to be particularly limiting on the scope of the present invention though, and other known methods for controlling the intake mixture based on such outputs may be used. Moreover, it shall be appreciated that the engine emission data outputs from the engine emission sensor(s) 116 and the virtual sensor device(s) 118 may be used in combination, and / or interchangeably, for controlling the ICE 104 according to their availability. For example, the control system 102 may use the engine emission data determined by the physical engine emission sensor(s) 116 whenever such sensors are active. Meanwhile, the estimated engine emission data from the virtual sensor devices 118 may be reserved for inactive periods of the physical engine emission sensors 116, for example following a cold-start of the ICE 104. Following an initial warm-up period, one or more engine emission sensors 116 may therefore be activated and start to provide direct measurements of the engine emissions. At which point, the control system 102 may revert to controlling the ICE 104 based on the outputs from the engine emissions sensors 116, replacing or otherwise refining the estimates from the virtual sensor devices 118. For example, when engine emission data is available from the engine emission sensors 116 and the virtual sensor devices 118, the estimated engine emission data may be used in conjunction with the measurements to verify the results, update the virtual sensor devices 118, and I or perform fault diagnosis, as shall be described in more detail. The virtual sensor device(s) 118 that enable the closed-loop control strategies described above shall now be discussed in more detail. In order to estimate the engine emission data, such as the rear oxygen amount, each virtual sensor device 118 includes one or more sensor models featuring a neural network trained to estimate the engine emission data based on the sensor data that is available during a cold-start of the ICE 104. This includes data obtained from the sensors of the sensor system 112 that are not susceptible to the moisture effects in cold-starts and remain active. To give an example, the inputs to the sensor model(s) of the first virtual sensor device 118a may include sensor inputs indicative of the air-fuel ratio in front of the CC catalyst 110a, engine speed, vehicle speed, intake manifold pressure, intake air mass, and fuel pressure. Other inputs to the sensor model(s) may include a fuel injection timing, a target equivalence ratio, a rich spike fuel cut-off time, and intake charging efficiency, for example. For each sensor model, the neural networks may be trained by one or more machine learning techniques that are known in the art and may, for example, include a recurrent neural network (RNN) and a gated recurrent unit. In particular, the recurrent neural network may take various suitable forms for relating operational data inputs to respective estimates of the engine emission data, as outputs. In general, the RNN architecture of each sensor model will therefore include an input layer for processing the operational data as inputs, an output layer for generating the engine emission data estimates and a specified number of hidden layers, comprising gated recurrent unit cells. The connection weights between respective nodes of adjacent layers are determined and refined by the training process, which involves a comparison of the estimated engine emission outputs to test data obtained by physical engine emission sensors for corresponding operational data. By way of example, Figure 4 shows an exemplary neural network 400 of the first virtual sensor device 118a for estimating the rear oxygen amount. The neural network 400 takes the form of an RNN and includes an input layer 402, an output layer 404, and three hidden layers 406. The input layer 402 is shown to include twelve inputs 408 in this example, including air-fuel measurements of the air-fuel sensor 116a, a fuel injection timing, a target equivalence ratio, a rich spike fuel cut-off time, an intake air mass, a vehicle speed, an intake manifold pressure, an engine speed, an cylinder intake charging efficiency, a saturation limit of the air-fuel ratio (so that the air-fuel ratio does not exceed 17), and a balance of oxygen for the CC catalyst 110a (i.e. the intake air mass multiplied by the difference of the air-to-fuel measurements to stoichiometric conditions). Such inputs are provided by the sensor system 112 or provided by other controllers of the vehicle 100 and are standardised before entering the neural network 400. Each hidden layer 406 is shown to include thirty cells 410 in this example. The cells 410 are gated recurrent unit cells and the neural network 400 a lookback length of 300 timesteps in this example. The output layer 404 has a single output, being a standardised estimate of the rear oxygen amount. This example is provided by way of reference only though and is not intended to be limiting on the scope of the invention. The test data used to train each sensor model is obtained using a test apparatus corresponding to the production vehicle 100. The test apparatus therefore includes a sample engine and exhaust system, with one or more engine emission sensors arranged therein, corresponding to the ICE 104 and exhaust system 106 described previously. Accordingly, corresponding reference numerals are used in the following description to refer to corresponding features. The test apparatus may differ from the production version of the vehicle 100 in that the test apparatus is advantageously further configured to heat, and thereby activate, the engine emission sensors 116 when the ICE 104 is subjected to cold-start conditions. In this manner, the test apparatus is able to obtain test data that would not typically be available in real-world operation of the production vehicle 100. For example, the test apparatus may include one or more heating devices (not present in the production version of the vehicle 100) configured to heat the engine emissions sensors 116 in the test apparatus to the minimum activation temperature. The engine emissions sensors 116 can therefore be activated when the ICE 104 is started and tested in cold-start conditions, producing corresponding engine emission data that can be used to train the respective sensor models. The temperature of the test environment may be suitably controlled and adjusted such that test data can be obtained for a range of ambient temperatures that may be encountered in real-world use of the production vehicle 100. The test procedure itself may therefore include a range of engine test cycles, and combinations of operating conditions, that may be encountered during real-world operation of the production vehicle 100. In examples, such operating conditions will include cold-start conditions, such as ambient temperatures of approximately 20°C, 0°C, and / or -10°C, amongst others, and may further include one or more warm-start conditions (during which the physical engine emission sensors 116 are active without additional heating). The operational data is recorded, for example by corresponding operational sensor(s) of the sensor system 112, and the resulting engine emission data is recorded by the engine emission sensors 116 for use in training the sensor model(s) of the virtual sensor device(s) 118. In particular, the determined test data is used as the ground truth for training the sensor models to estimate the engine emission data for respective conditions indicated by the operational data. To give an example, the testing may involve Real-Driving Emissions (RDE) tests simulating driving on public roads for a plurality of test trips involving urban, rural, and / or highway (HW) driving scenarios, which may be carried out in a prescribed order. Table 1 below shows an example set of test trips simulated in order to acquire sufficient training data for training the sensor model(s) of the first virtual sensor device 118a . Test Trip Approximate Duration (s) Trip Type RDE#1 6000 urban-rural-HW RDE#2 6000 urban-rural-HW RDE#3 2000-3000 urban-rural-HW (any order) RDE#4 2000-3000 urban-rural-HW (any order) RDE#5 2000-3000 urban-rural-HW (any order) RDE#6 2000-3000 urban-rural-HW (any order) RDE#7 2000-3000 urban-rural-HW (any order) RDE#8 2000-3000 urban-rural-HW (any order) RDE#9 2000-3000 urban-rural-HW (any order) RDE#10 2000-3000 urban-rural-HW (any order) RDE#U 2000-3000 urban-rural-HW (any order) RDE#12 2000-3000 any RDE#13 2000-3000 any RDE#14 2000-3000 urban RDE#15 2000-3000 urban RDE#16 2000-3000 urban RDE#17 2000-3000 urban Table 1 The exemplary test trips presented in Table 1 have been found to generate sufficient training data for training the sensor models, such as for the first virtual sensor device 118a, though it shall be appreciated that alternative or additional test trips may be used in other example. Furthermore, in order to validate the sensor models, further validation test trips may include: any number of repetitions of the same test trips used for training in addition to at least four test trips not completed for training purpose. At least one of those additional test trips may feature urban, rural and highway driving scenarios (in that order) for a period of at least 6000 seconds, preferably at least 9000 seconds. Methods of training a neural network on this basis are well-known in the art and are not described in detail here to avoid obscuring the invention. For context though, it shall be appreciated that the initial weights and biases of the neural network may be generated randomly (or initialised from a related sensor model) and the resulting engine emission data estimates may be computed for respective operational data inputs. The estimated engine emission data may then be compared to the test data obtained by the engine emission sensors 116 during testing in order to compute the loss. The weights of the neural network may subsequently be updated by back propagating the loss determined by the loss function and updating one or more weightings of the neural network, for example using a gradient descent optimisation technique. Here, it shall be appreciated that the loss function minimizations may therefore be achieved through gradient descent-based methods (including stochastic gradient descent—typically in conjunction with a backpropagation algorithm, such as backpropagation through time). This process may be repeated across the test data, and the sensor model may be validated accordingly, for example by evaluating the trained model on a validation set of test data, as in the example above. To continue the previous example, the neural network 400 has a total number of 15151 trainable parameters (weights &biases) and a combination of loss functions may be used for updating the weights and biases. For example, a first loss function may determine the mean squared error between the measured rear oxygen amount and the estimated rear oxygen amount. A second loss function may be used for sensitivity analysis and may: (i) classify the measured rear oxygen amounts into respective air-fuel ratio zones or slices (e.g. including first and second lean zones, a stoichiometric zone and a rich zone) and determine the distance of the corresponding estimates of the rear oxygen amount from the respective zones. A third loss function may similarly be used for sensitivity analysis and determine an average time between: (i) the measured rear oxygen amount crossing a threshold from one air-fuel ratio zone to an adjacent air-fuel ratio zone and (ii) the estimated rear oxygen amount crossing the same threshold. The parameters may be updated in 50 training iterations, for example, each having a batch size of 3000 measurements / estimates. For this purpose, the training algorithms may have a learning rate of a learning rate of 0.003 and a learning rate decay of 0.005. Such a training method is not intended to be limiting on the scope of the invention though and is provided for exemplary purposes only. Figure 5 shows a plot illustrating a comparison of the test data against the estimated rear oxygen amount (as respective voltage signals) for a trained sensor model of the first virtual sensor device 118a. Various evaluation methods and thresholds that are known in the art may be used for validating the sensor model, once trained. To give an example, one condition for validating the sensor model may be that the loss distribution is less than or equal to a threshold value, which may be 0.125, for example, or preferably less than or equal to 0.075. Another condition for validating the sensor model may be a coefficient of determination that is compared to a respective threshold, which may be greater than or equal to 0.85, for example, and preferably greater than or equal to 0.925. Other thresholds and conditions may be configured according to the needs of the application, as shall be appreciated by the skilled person. The trained sensor model of each virtual sensor device 118 is therefore configured to receive a respective set of sensor inputs, including operational data, and estimate the engine emission data of one or more corresponding engine emission sensor(s) 116 based thereon. For example, the first virtual sensor device 118a includes a sensor model trained to estimate an oxygen content of the exhaust gas at the rear of the CC catalyst 110a based on the engine speed, vehicle speed, intake manifold pressure, intake air mass, and fuel pressure received from the sensor system 112, along with other inputs such as a fuel injection timing, a target equivalence ratio, a rich spike fuel cut-off time, and intake charging efficiency. For corresponding operating conditions, the sensor model is therefore able to estimate the oxygen amount determined by the oxygen sensor 116b with sufficient accuracy for controlling the intake mixture of the ICE 104. By way of example, Figure 6 shows a plot illustrating a comparison of the validation test data against the estimated rear oxygen amount (as respective voltage signals) for a validated sensor model of the first virtual sensor device 118a. It shall be appreciated that the virtual sensor device(s) 118 of the control system 102 may each be implemented on a control unit or a computational device having one or more electronic processors. Each virtual sensor device 118 may therefore include a single sensor model, trained substantially as described above, for determining corresponding estimates of the engine emission data determined by a respective one of the engine emission sensors 116. However, the performance of each catalytic converter 110 will deteriorate over time, e.g. due to usage, wear and degradation. For example, the performance of a catalytic converter is correlated to its storage capacity, i.e. how much nitrogen oxide or oxygen the catalytic converter is able to store, and the storage capacity reduces over usage cycles. This deterioration is known as performance drift. As a result, the emissions from the exhaust system 106 will therefore vary, quite significantly in some cases, according to the performance drift of the catalytic converter(s) 110, and the effects on the engine emissions can be categorized accordingly. For example, a new or fresh classification will generally be associated with relatively low levels of pollution and a relatively high storage capacity (greater than or equal to a respective threshold), while a worn classification will be associated with higher levels of pollution for the same operating conditions and a relatively low storage capacity (less than that threshold). A best part unacceptable classification will then be associated with even higher pollution levels and even lower or zero storage capacity (less than a lower threshold). The inventors have found that the accuracy of the trained sensor models may therefore be impaired in systems where performance drift has a significant effect on the emissions. For example, a sensor model that is trained to provide accurate engine emission data estimates for a new or fresh catalytic converter 110 will have diminished accuracy as the catalytic converter(s) 110 become worn during use. To mitigate the performance drift issue, the inventors have found that individual sensor models of a virtual sensor device 118 can be trained for respective performance drift classifications of the catalytic converter(s) 110, e.g. based on corresponding sets of test data. That is, test data acquired from the test apparatus for a corresponding performance drift classification, e.g. a corresponding storage capacity of oxygen I nitrogen oxides. To further improve the accuracy of the engine emission data estimates, and the resulting control over the engine emissions, the virtual sensor device(s) 118 of the present invention may therefore each include a plurality of sensor models, each sensor model being trained for a respective performance drift classification of the catalytic converter(s) 110. For example, each virtual sensor device 118 may include a plurality of virtual sensor models, such as a fresh model, an aged model, and / or a best part unacceptable (BPU) model, where each sensor model is trained in the manner described above based on test data obtained for a sample system having a respective performance drift classification. That is, the fresh model may be trained based on test data obtained from a newly manufactured vehicle with limited, if any, wear and tear on components and a storage capacity that is greater than or equal to a first threshold. The aged model may be trained based on test data obtained from a vehicle that exhibits signs of wear, and performance degradation, with a storage capacity that is less than the first threshold but greater than or equal to a second threshold. The BPU model may be trained based on data obtained from a model of a vehicle that has the best parts available, but fails to achieve the market standard, having a storage capacity that is less than the second threshold. For context, the first threshold may be a value of 0.75, for example, such that oxygen storage capacities greater than or equal to 0.75 are indicative of a fresh model. The second threshold may be a value of 0.5, or even 0.45, for example, such that oxygen storage capacities less than the second threshold are indicative of a BPU model, while values between the first and second threshold may be indicative of an aged model. These examples are not intended to be limiting on the scope of the invention though, and the skilled person shall appreciate that other thresholds may be determined by testing and validation with physical sensors. In such examples, the virtual sensor device 118 may therefore further include suitable logic for selecting the sensor model that best matches the current performance of the catalytic converter(s) 110, in use. The selection may be based on a comparison of the estimated engine emission data to the actual engine emission data determined by the engine emission sensor(s) 116. For example, such comparison may be rendered possible during warm conditions when the engine emission sensor(s) 116 are also active. The selected sensor model is then used for estimating the engine emission data during the next coldstart. For example, the selection may be performed while the engine emission sensor(s) 116 are active, or shortly thereafter, in order to select a sensor model for the next coldstart of the ICE 104. Various mathematical methods are known in the art for model selection and accuracy assessment, and the invention is not intended to be particularly limited in this respect. By way of example, Figure 7 schematically shows an exemplary method 700, in accordance with an embodiment of the invention, for selecting the sensor model of a virtual sensor device 118. For the purposes of continuity, the senor model selection process 700 is demonstrated with reference to the first virtual sensor device 118a, described previously, but this example is not intended to be limiting on the scope of the invention and it shall be appreciated that the same process may be applied in a corresponding manner for other virtual sensor device(s) 118. In step 702, the engine emission sensor(s) 116 determine engine emission data during one or more engine operations. For example, the engine emission data may be determined during ordinary driving of the vehicle 100, or when performing a particular engine operation (e.g. an engine calibration process). To continue the previous example, the front air-fuel ratio sensor 116a and the rear oxygen sensor 116b of the vehicle 100 may therefore be operated to determine respective measurements of the air-fuel ratio and oxygen content whilst driving the vehicle 100. At the same time, the operational sensors 115 of the vehicle 100 are configured to determine the operational data, which is indicative of the engine operating conditions, such as the engine load, engine speed, and ambient temperature, for use in estimating corresponding engine emissions. In step 704, two or more sensor models of the virtual sensor device(s) 118 are therefore operated to determine corresponding estimates of the engine emission data based on the operational data, and optionally data from the front air-fuel ratio sensor 116a, determined in step 702. For example, the measured engine speed, engine load, and ambient temperature, may be provided as inputs to multiple sensor models of the first virtual sensor device 118a to determine corresponding estimates of the oxygen content at the rear of the CC catalyst 110a. The sensor models may for example include the fresh sensor model, the aged sensor model, and / or the BPU model, of the first virtual sensor device 118a, and corresponding estimates may be determined by each sensor model. However, performance drift is a progressive effect, and it shall be appreciated that, in some examples, the engine emission data may only be estimated using current sensor models and sensor models associated with the next or subsequent performance classifications. For example, the input data may be provided to the aged sensor model (currently being used) and the BPU model of the first virtual sensor device 118a, but not the fresh model. Alternatively, the input data may be provided to each sensor model, but only the engine emission data estimates from a current sensor model and a sensor model associated with the next or subsequent performance classification may be used in the subsequent steps. In step 706, the modelling accuracy of each sensor model is determined by comparing the estimated engine emission data, determined in step 704, to the measurements determined by the respective engine emission sensor(s) 116, in step 702. For example, the oxygen amounts measured by the rear oxygen sensor 116b may therefore be compared to the respective estimates of the worn and BPU models of the first virtual sensor device 118a to determine the respective modelling accuracies. The estimates may be compared to the measured data, in step 706, using one or more mathematical methods that are known in the art for model selection and accuracy assessment, include regression analysis, mean squared error analysis, and / or sensitivity analysis for analysing a dynamic response, amongst other known methods. To give an example, Figure 8 shows an exemplary plot of a voltage signal 802 output from the rear oxygen sensor 116b, during a sample engine operating profile. The voltage level is indicative of the oxygen content in the exhaust gasses at the rear of the CC catalyst 110a. As shown in Figure 8, the voltage readings may be split into four zones (Zones A to D) indicative of the performance of the CC catalyst 110a. For example, Zone A corresponds to a first lean slice, with voltage values of 0 to approximately 0.21, which corresponds to an OSA of the CC catalyst 110a being equal to an oxygen storage capacity (OSC) of the CC catalyst 110a. Zone B corresponds to a second lean slice, with voltage values of approximately 0.21 to 0.65, which corresponds to an OSA greater than 50% of the OSC of the CC catalyst 110a. Zone C corresponds to a stoichiometric region, with voltages values of 0.65 to 0.69, which corresponds to an ideal performance of the CC catalyst 110a with a stable OSA equal to approximately 50% of the OSC of the CC catalyst 110a. Zone D corresponds to a rich slice, with voltage values of 0.69 to 1, which corresponds to an OSA of the CC catalyst 110a being less than 50% of the OSC or negligible capacity. Respective thresholds 804 are set at the boundaries between adjacent zones, and the accuracy of the respective sensor models may be determined, in step 706, by calculating an amount or proportion of time that the respective sensor model estimates fall in the same performance region (Zone A to D) as the voltage signal 802, as well as the respective distances of the estimates and the voltage signal 802 to the upper or lower thresholds 804 of that zone. These accuracy indicators may be determined as an addition, or an alternative, to other mathematical methods of regression analysis and mean squared error analysis for comparing the accuracy of the estimates of each sensor model to the measured values. For example, the dynamic response of each sensor model may be assessed based on the respective engine emission data estimates obtained when the engine emission sensors 116 indicate sudden changes in the catalyst performance or individual parameters thereof. For example, the controller(s) 114 may determine a dynamic response parameter, such as a response time, of each sensor model of the first virtual sensor device 118a when the rear oxygen sensor 116b indicates a step or sudden change in the oxygen content, and compare the determined response times to one another. Additionally or alternatively, the controller(s) 114 may compare the engine emission data obtained from the rear oxygen sensor 116b and the respective sensor models directly, for example by applying one or more fitting functions, such as a linear fitting function, to assess the correlations between the measured oxygen content and the respective sensor model estimates. The relative correlation strengths may then be compared to assess the relative accuracy of the sensor models. Returning to Figure 7, in step 708, the sensor model with the greatest indicated accuracy is selected for estimating the engine emission data during the next cold-start condition of the ICE 104. In this manner, the selected model is able to provide accurate estimates of the engine emission data, taking into account the current condition and capabilities of the catalytic converter(s) 110, for use in controlling the ICE 104 It shall be appreciated that the model selection may be performed periodically, for example at a prescribed frequency, or whenever data is available from the physical engine emission sensors 116, to ensure that the selection keeps track with the performance drift of the catalytic converter(s) 110 overtime. In some examples, the model selection process may be triggered in response to detecting a sensor fault, as shall be described in more detail. By updating the virtual sensor device(s) 118 in this way, accuracy and robustness can be improved and maintained over time. The virtual sensor device(s) 118 are therefore able to provide the control system 102 with accurate engine emission data estimates during coldstart conditions allowing for closed-loop control of the ICE 104. A method of controlling the ICE 104 shall now be discussed with additional reference to Figure 9. Figure 9 schematically illustrates an exemplary method 900, in accordance with an embodiment of the invention, of controlling the ICE 104 using the control system 102. The exemplary method 900 includes, but is not limited to, cold-start conditions and therefore provides a general-purpose method of controlling the ICE 104. At the start of the method 900, the ICE 104 may therefore have been started from a coldstart condition, e.g. having been shutdown overnight and started from an ambient temperature of less than or equal to 20°C. In step 902, the controller(s) 114 therefore receive data from the active sensors of the sensor system 112, as the ICE 104 is operated during driving of the vehicle 100. The data received in step 902 includes operational data determined by the operational sensors of the sensor system 112, which remain active even during cold-start conditions. The determined operational data is indicative of the operating conditions of the ICE 104, and may include a throttle position, an ambient temperature, an engine load, and an engine speed, amongst other engine operating parameter(s) that are indicative of the operating conditions of the ICE 104. The data received, in step 902, may further include engine emission data determined by the active ones of the engine emission sensor(s) 116. Here, it shall be appreciated that one or more of the engine emission sensor(s) 116 may be active during cold-start conditions, e.g. due to their relative proximity to the ICE 104, while one or more of the other engine emission sensors are inactive, at least for an initial warm-up period. During such periods, no engine emission data is therefore received from the inactive engine emission sensor(s) 116, but engine emission data may be received from any engine emission sensor(s) 116 that are active. To continue the previous example, the front air-fuel ratio sensor 116a may therefore be active upon start-up of the ICE 104, providing measurements indicative of the air-fuel ratio upstream of the CC catalyst 110a, while the rear oxygen sensor 116b may be inactive for the initial warm-up period not providing any feedback measurements. In step 904, the control system 102 determines whether to operate one or more of the virtual sensor device(s) 118 to estimate engine emission data due to the inactivity of a respective engine emission sensor 116. For example, the control system 102 may determine whether the controller(s) 114 received engine emission data, in step 902, from each of the engine emissions sensors 116, and thereby identify any inactive engine emission sensor(s) 116. If one or more of the engine emissions sensor(s) 116 are determined to be inactive, in step 904, the control system 102 is configured to operate respective ones of the virtual sensor device(s) 118, in step 906, to estimate corresponding engine emission data for the operating conditions determined in step 902. In particular, in the absence of corresponding measurements from a respective engine emission sensor 116, one or more of the virtual sensor device(s) 118 are operated, in step 906, to estimate respective outputs of the engine emission data based on the sensor data received in step 902. To continue the previous example, the front air-fuel sensor 116a may therefore output a voltage signal indicative of the air-fuel ratio upstream of the CC catalyst 110a, in step 902, while the rear oxygen sensor 116b may be inactive. In step 904, the control system may therefore determine that the rear oxygen sensor 116b is inactive and operate the first virtual sensor device 118a to estimate the oxygen amount downstream of the CC catalyst 110b, in step 906, based on the sensor data determined in step 902. Here it shall be appreciated that the sensor data, determined in step 902, is provided as an input to the first virtual sensor device 118a and may include operational data, such as the engine speed, engine load, ambient temperature, and other parameters indicative of the operating conditions of the ICE 104. In some examples, the sensor data provided as an input to the first virtual sensor device 118a may further include the air-fuel ratio determined by the front air-fuel ratio sensor 116a in step 902. To continue the previous example, the data provided as an input to the first virtual sensor device 118a, in step 906, may include the engine speed, vehicle speed, intake manifold pressure, intake air mass, and fuel pressure, as well as a fuel injection timing, a target equivalence ratio, a rich spike fuel cut-off time, and intake charging efficiency. Here it shall be appreciated that, in step 906, the first virtual sensor device 118a may use one of a plurality of sensor models for estimating the oxygen content, where that sensor model has previously been selected according to the current performance drift classification of the CC catalyst 110a, substantially as described previously. The virtual sensor device(s) 118 therefore accurately estimates the engine emission data as a stand-in for any inactive engine emission sensors during the cold-start conditions, allowing for closed-loop control of the ICE 104. In step 908, the control system 102 is configured to determine one or more control signal(s) for managing the operation for the ICE 104 using the engine emission data determined by the engine emission sensor(s) 116 and / or the virtual sensor device(s) 118, in steps 902 and 906. As discussed previously with reference to Figure 3, the control system 102 may therefore use the engine emission data, in combination with the operational data determined in step 902, in a closed-loop control system for controlling the operation of the ICE 104, e.g. by determining one or more control signal(s) for controlling the air-fuel ratio of the intake mixture. For example, the engine emission data may be processed by the controller(s) 114 to determine the oxygen storage amount of the CC catalyst 110a, amongst other parameters, which may be used, in turn, for setting the target air-fuel ratio and controlling the intake mixture of the ICE 104. The control signal(s) output from the controller(s) 114 may therefore include a first signal control signal for controlling an amount of fuel injection from the fuel injector(s) and / or a second control signal for controlling an amount of fuel vapor introduced into the intake mixture via the purge valve, substantially as described previously, according to the target air-fuel ratio. In step 910, the control system 102 outputs the determined control signal(s) to the ICE 104 and thereby manages the operation of the ICE 104 to mitigate the amount of pollution emitted from the vehicle 100. For example, the output control signal(s) may cause a reduction of the amount of fuel injected into the intake mixture where the determined oxygen content in the exhaust system 106 is determined or estimated to be too low (i.e. higher than a target reference value). The process 900 may then be repeated iteratively, for example at a prescribed frequency for controlling the operation of the ICE 104. It shall be appreciated that the controller(s) 114 may therefore determine the control signal(s) based on the estimated engine emission data whenever the corresponding engine emission sensor(s) 116 are inactive, and the controller(s) 114 may switch to determining the control signal(s) based on the engine emission data received from the engine emission sensor(s) 116 whenever such sensors are active. In this manner, the virtual sensor device(s) 118 may act as a temporary stand-in for the respective engine emission sensor(s) 116 during the warm-up period and, when the engine emission sensor(s) 116 are active, the estimated engine emission data may therefore be ignored and discontinued, or used in conjunction with the measured data to control the ICE 104. In this manner, the method 900 serves to reduce polluting emissions from the ICE 104, particularly during cold-start conditions, by enabling feedback-based control even when the physical engine emission sensor(s) 116 are inactive. It is noted that the steps of the method 900 described are merely exemplary in nature and are not intended to limit the energy management method. As such, it is understood that the steps involved may be altered, reordered, added and removed as will be appreciated by the person skilled in the art. In order to provide additional robustness to the control system 102, the inventors have further devised methods of diagnosing faults of the virtual sensor device(s) 118 using the engine emission sensors 116, and vice versa. In particular, the inventors have devised fault detection methods that involve comparisons of the estimated engine emission data, determined by the virtual sensor device(s) 118, and the measurements obtained from the engine emission sensors 116, and analysis of the disparities therebetween. Figure 10 illustrates an exemplary method 1000 of fault detection for the virtual sensor device(s) 118. In step 1002, the control system 102 receives engine emission data from the engine emission sensor(s) 116, e.g. during ordinary driving of the vehicle 100 in warm conditions or following an initial warm-up period. In step 1004, the control system 102 receives corresponding estimates of the engine emission data from the virtual sensor device(s) 118. For example, the virtual sensor device(s) 118 may be provided with the operational data determined by the operational sensors of the sensor system 112, in step 1002, which is input to the virtual sensor device(s) 118, in step 1004, for determining corresponding estimates of the engine emission data. In step 1006, the control system 102 compares the estimated engine emission data to the engine emission data received from the engine emission sensors 116 to detect a fault of the virtual sensor device(s) 118. Here, it shall be appreciated that the engine emission sensors 116 are expected to provide reliable engine emission data that is usable to detect faulty estimates in the virtual sensor device(s) 118 and thereby detect failures. The engine emission sensors 116 are therefor used as a true source of engine emission data for detecting a sensor fault associated with the virtual sensor device(s) 118. The estimated and measured engine emission data may therefore be compared, in step 1006, using one or more mathematical methods that are known in the art for detecting faults when comparing corresponding data sets from first and second sources. Such methods may include regression analysis, mean squared error analysis, and / or sensitivity analysis, substantially as described previously in relation to the model selection process, with additional comparison to respective thresholds for fault detection. For instance, the dynamic response of each virtual sensor device 118 may be assessed against respective fault thresholds based on the estimated engine emission data obtained when the engine emission sensors 116 indicate sudden changes in the catalyst performance or individual parameters thereof. For example, the controller(s) 114 may determine a dynamic response parameter, such as a response time, of the first virtual sensor device 118a when the engine emission sensors 116 indicate an oxygen full or empty state of the CC catalyst 110a, and compare the response time to a fault threshold. In another example, the controller(s) 114 may determine the response time of the first virtual sensor device 118a when the rear oxygen sensor 116b indicates a step or sudden change in the oxygen content. In each case, a fault may be detected if the response time is greater than or equal to the fault threshold. Additionally, or alternatively, the controller(s) 114 may compare the engine emission data obtained from the engine emission sensor(s) 116 and respective virtual sensor devices 118 directly. For example, the engine emission sensor(s) 116 and respective virtual sensor devices 118 may each be operated to determining engine emission data for corresponding operating conditions and one or more fitting functions, such as a linear fitting function, may be applied to the determined engine emission data to assess the relationship or correlation between the respective sets of data. The determined function, or parameters thereof, may then be compared against prescribed fault limits. For example, a determined correlation coefficient may be compared to minimum and maximum fault limits indicating a respective reach or lean fault bias of the virtual sensor device 118. In another example, a determined constant of the linear regression function may be compared to maximum and minimum fault limits indicating lean or rich shifts in the of the virtual sensor device 118 causing faults. Additionally, or alternatively, the error between the engine emission data determined by the engine emission sensors 116 and the respective virtual sensor devices 118 may be compared to fault thresholds, for example being indicative of short or open circuit / grounded conditions of the sensors. A faulty virtual sensor device 118 can therefore be detected by comparing the estimated engine emission data to the respective measurements obtained by the engine emission sensors 116. In step 1008, the control system 102 may therefore check whether a sensor fault has been detected based on the comparison in step 1006. If no fault is detected, the method 1000 may proceed to receives engine emission data from the engine emission sensor(s) 116, in step 1002, for the next iteration. However, if a sensor fault is detected, in step 1008, the control system 102 may proceed to execute one or more fault response commands, in step 1010, such as deactivating the faulty virtual sensor device 118, initiating a model selection process of the faulty virtual sensor device 118, notifying a user of the sensor fault, and / or adjusting the control of the ICE 104. For example, the control system 102 may be configured to output a control command to initiate a new model selection method, substantially as described in the method 700, to determine whether the fault is due to a change in the performance of the CC catalyst 110a, and / or a new sensor model is required. Alternatively, or additionally, the control system 102 may output a control command to deactivate the faulty virtual sensor device 118 so that the respective engine emission data estimates are not used for controlling the ICE 104 until the fault is removed. The faulty sensor device may also be notified to a user of the vehicle 100, for example by issuing an alert through one or more human-machine interface devices of the vehicle 100. In this manner, the method 1000 provides additional robustness and sensor fault detection to mitigate unintended operation of the ICE 104. It will also be appreciated that various changes and modifications can be made to the examples described above without departing from the scope of the present invention. In the example above, the engine emission sensors 116 are used as the true source of engine emission data for determining a faulty virtual sensor device 118, since physical engine emission sensors 116 are typically more reliable. However, in other examples, it shall be appreciated that the method 1000 may also be used to detect faults of the physical engine emission sensors 116 based on the estimates of the virtual sensor devices 118 (e.g. where the virtual sensor devices satisfy certain confidence thresholds). It shall be appreciated that the sensor fault detection may be performed in substantially the same manner but using virtual sensor device as the true source of engine emission data for determining deviations of the measured engine emission data constituting a fault of the engine emission sensor(s) 116. 5 Additionally, whilst the sensor system 112 in the example above includes both engine emission sensor(s) 116 and corresponding virtual sensor device(s) 118 it shall be appreciated that, in other examples, there may be no need for the physical engine emissions sensors 116 on board the vehicle 100 and, instead, the engine emission data may be provided solely by a set of virtual sensor device(s) 118.

Claims

1. A method of training a machine learning model to estimate engine emission data in an exhaust system of a vehicle in cold-start conditions, when a corresponding engine emission sensor of a sensor system of the vehicle is inactive, the machine learning model being trained to estimate the engine emission data based on inputs received from one or more active sensors of the sensor system during the cold-start conditions, the method comprising:obtaining test data for one or more test cycles in cold-start conditions using a test apparatus representative of the exhaust system and a corresponding sensor system, the obtained test data comprising engine emission data obtained by activating the engine emission sensor during the one or more test cycles; andtraining the machine learning model to estimate the engine emission data during cold-start conditions based on the obtained test data by:estimating engine emission data using the machine learning model, the estimated engine emission data being determined based on the test data obtained by one or more sensors, other than the engine emission sensor, of the corresponding sensor system;comparing the estimated engine emission data from the machine learning model to the test data obtained by the activated engine emission sensor; andupdating the machine learning model based on the comparison.

2. A method according to claim 1, further comprising determining the test data using the test apparatus by:activating the engine emission sensor of the corresponding sensor system; operating the test apparatus according to the one or more test cycles; and determining test data for each test cycle using the plurality of sensors of the corresponding sensor system.

3. A method according to claim 1 or claim 2, wherein the machine learning model comprises a recurrent neural network and a gated recurrent unit.

4. A method according to claim 3, wherein updating the machine learning model based on the comparison comprises: minimising a loss function quantifying a differencebetween the estimated engine emission data and the test data determined by the activated engine emission sensor.

5. A method according to claim 4, wherein updating the machine learning model based on the comparison further comprises:back propagating the loss determined by the loss function; andupdating one or more weightings of the neural network using a gradient descent optimisation technique.

6. A method according to any preceding claim, further comprises:obtaining test data for one or more test cycles in warm conditions using the test apparatus and the corresponding sensor system; andtraining the machine learning model to estimate the engine emission data during warm conditions based on the obtained test data.

7. A method according to any preceding claim, wherein the test data is obtained for a range of emission test cycles.

8. A method according to any preceding claim, wherein the engine emission sensor is heat-activated, and wherein the test data is obtained for the one or more cold-start conditions by heating the engine emission sensor to an active state.

9. A method according to any preceding claim, wherein the plurality of sensors of the sensor system comprises a further engine emission sensor that remains active during the cold start conditions, the engine emission data determined by the further engine emission sensors being provided as an input to the machine learning model for estimating the engine emission data of the inactive engine emission sensor during cold-start conditions.

10. A method according to any preceding claim, wherein the engine emission sensor is configured to determine engine emission data indicative of catalytic performance of a catalytic converter arranged in the vehicle exhaust system.

11. A method according to claim 10, wherein the engine emission sensor is configured to determine engine emission data indicative of an oxygen storage amount or a nitrogen oxide storage amount of the catalytic converter.

12. A method according to claim 11, wherein the engine emission sensor takes the form of:an air-fuel sensor arranged upstream of the catalytic converter in the vehicle exhaust system;an oxygen sensor arranged downstream of the catalytic converter in the vehicle exhaust system;an engine out emissions sensor; ora nitrogen oxide sensor arranged downstream of the catalytic converter in the vehicle exhausts system.

13. A method according to claim 12, when dependent on claim 9, wherein the engine emission sensor takes the form of an oxygen sensor arranged downstream of the catalytic converter in the exhaust system and the further engine emission sensor takes the form of an oxygen sensor or an air-fuel sensor arranged upstream of the catalytic converter in the exhaust system.

14. A method according to any of claims 10 to 13, wherein the plurality of sensors of the sensor system comprises one or more of the following:an engine speed sensor;a vehicle speed sensor;a pressure sensor arranged in an intake manifold of the vehicle;an air-mass flow rate sensor arranged in the intake manifold; and / or a fuel pressure sensor.

15. A method according to any of claims 10 to 14, wherein the machine learning model is trained to estimate engine emission data for one of a plurality of performance drift classifications of the catalytic converter, the test apparatus used to obtain the test data comprising a catalytic converter associated with that performance drift classification.

16. A method according to claim 15, wherein the plurality of performance drift classifications of the catalytic converter comprise: a fresh classification, a worn classification, and / or a best part unacceptable classification.

17. A virtual sensor device comprising a machine learning model trained to estimate engine emission data according to the method of any preceding claims.

18. An engine emission control system for a vehicle, the control system comprising a plurality of sensors including an engine emission sensor in an exhaust system of the vehicle, the engine emission sensor being configured to measure engine emission data indicative of catalytic performance of a catalytic converter arranged in the exhaust system;5 and a virtual sensor device, according to claim 17, for estimating engine emission data when the engine emission sensor is inactive.41

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