Method for generating corrected measurement values during the process of determining the concentration and mass flow of an exhaust gas component in an exhaust gas flow

Abstract

The invention relates to a method for generating corrected measurement values during the process of determining the concentration of an emission component in an exhaust gas flow, said method being usable online for an OBD and / or OBM process, even when sensors present in certain regions supply measurement values with a high degree of inaccuracy. According to the invention, the concentration (I) of the emission component X in the exhaust gas flow is first measured via a sensor (14), and simultaneously the concentration (II) of the emission component X is determined via an exhaust gas model (24) which is stored in a computing unit (20) and via which expected concentrations of the emission component X in the exhaust gas flow are read or calculated on the basis of environmental data using physical models or map-based algorithms. An estimated concentration (III) of the emission component X is then derived from the concentration measurement of the sensor (14) and the concentration determination via the exhaust gas model (24) by means of a Kalman filter using the equation (IV), wherein K1 forms a weighting factor of the Kalman filter. FIG 1: (I)%%%c_X_sens (II)%%%c_X_mod (III)%%%c_X_corr (IV)%%%c_X_corr = c_X_mod + K1 · (c_X_sens - c_X_mod)

Description

PP34053WO / bg AVL List GmbH 24.07.2024 Method for generating corrected measured values ​​when determining the concentration and mass flow rate of an exhaust gas component in an exhaust gas stream. The invention relates to a method for generating corrected measured values ​​when determining the concentration of an emission component in an exhaust gas stream, as well as a method for generating corrected measured values ​​when determining the mass flow rate of an emission component in an exhaust gas stream. To comply with legally prescribed limit values ​​for certain exhaust gas components, their concentrations and resulting mass flow rates in the exhaust gas stream are determined both in corresponding test units and in the vehicle. Various methods are known for this purpose. Most often, sensors are used to measure the concentrations online and subsequently determine the mass flow rates.These sensors can be used in test units to verify compliance with legal limits, but they can also be used in vehicles to intervene in vehicle control via the control unit or, in the case of implausible readings, to prompt the vehicle owner to visit a workshop. In addition to sensor measurements, exhaust gas models are also used in vehicles to calculate concentrations from the available values ​​collected by the control unit. This is achieved through upstream measurements on test units, allowing a mass flow rate of a relevant exhaust component to be assigned to defined driving conditions. For this purpose, the readings from the lambda sensor, the composition of the fuel used, and other engine data can be used, for example. PP34053WO / bg AVL List GmbH 24.07.2024 As part of the EURO 7 regulations, on-board monitoring is mandatory, which obliges vehicle manufacturers, for example, to provide monitoring capabilities for nitrogen compounds in the exhaust. The current NO xHowever, sensors only exhibit an accuracy with a deviation of approximately 10%. Larger errors occur primarily under very cold conditions, i.e., before the sensor has heated up, but also in the presence of NH3 due to cross-sensitivity. Furthermore, it is not yet certain that aging will not distort the sensor data. Therefore, the task is to provide a method for generating corrected measured values ​​when determining the concentration and mass flow rate of an exhaust gas component in an exhaust stream. This method would eliminate the sensor measurement errors during on-board diagnostics and / or on-board monitoring by generating corrected measured values ​​that could then be used in these processes.This problem is solved by a method for generating corrected measured values ​​when determining the concentration of an exhaust gas component in an exhaust gas stream, comprising the features of main claim 1, and by a method for generating corrected measured values ​​when determining the mass flow rate of an exhaust gas component in an exhaust gas stream, comprising the features of main claim 9. In the inventive method for generating corrected measured values ​​when determining the concentration of an emission component in an exhaust gas stream, a concentration is first determined. ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X in the exhaust stream via a PP34053WO / bg AVL List GmbH 24.07.2024 corresponding sensor measured. At the same time a concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^The concentration of emission component X is determined using an exhaust gas model. This determined concentration is also referred to as a measured value. This exhaust gas model is stored in a vehicle's processing unit. The processing unit uses the exhaust gas model to read or calculate an expected concentration of emission component X in the exhaust stream, based on environmental data, via physical models or map-based algorithms. These algorithms or models are first developed through tests in a test center using sophisticated testing equipment that delivers highly accurate measurement data for various driving conditions, engines, and fuels. Accordingly, two measured values ​​for the concentration of the emission component are available at any given time: a measured value from the sensor and a calculated or read-out value from the exhaust gas model.If these two measurements differ, a decision must then be made as to which of them is more likely to correspond to the actual value. For this purpose, an estimated concentration is used. ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component from the concentration measurement of the sensor and the concentration determination via the exhaust gas model using a Kalman filter via the equation The Kalman factor is determined, with K1 representing a weighting factor for the Kalman filter. This weighting factor, which ranges between 0 and 1, determines, based on the potential deviations of the measured values, which of the measured values ​​has a higher probability of being correct. For example, in an area where the sensor is known to have potentially large measurement errors due to insufficient temperature, the measured values ​​of the exhaust gas model are assigned a higher probability of being correct. In this case, the Kalman factor approaches 0. In areas where the sensor provides reliable measured values, the opposite is true, and the Kalman factor approaches 1. Simultaneously, PP34053WO / bg AVL List GmbH 24.07.2024 By applying continuous weighting and not simply assigning a correct measurement to one of the measured values ​​at a time, the measured values ​​are also smoothed. Accordingly, a corrected measured value is generated which, for all operating conditions, provides a measured value with a very high probability that exhibits only minor error deviations. A method according to the invention, based on the same principle, is also used to generate corrected measured values ​​when determining the mass flow rate of an emission component in an exhaust gas stream. Here, too, a concentration is first determined. The emission component X in the exhaust stream is measured via a sensor, and a second concentration is determined. ^^^^ ^^^^ ^^^^ ^^^^The emission component X is determined via an exhaust gas model stored in a computing unit, which uses physical models or map-based algorithms to read or calculate expected concentrations of emission component X in the exhaust gas stream as a function of environmental data. Additionally, an exhaust gas mass flow rate is also determined in this case. ^^^^ ^^^^ℎFor example, it can be measured via an exhaust gas mass flow sensor, which may be used to determine the mass flow of the exhaust component and which itself also has a potential deviation that is taken into account in further calculations. In principle, it is not absolutely necessary to have a physical sensor. The exhaust gas mass flow can also be advantageously calculated based on an input mass flow, for example. It can also be advantageous if the exhaust gas mass flow is determined based on a pressure sensor or by so-called "in-vehicle models." An estimated mass flow is also used here below. ^^^^, ^^^^ ^^^^ ^^^^ ^^^^ the emission component X from, for example, the concentration measurement of the sensor or a calculated concentration measurement and the concentration determination via the exhaust gas model using the Kalman filter via the equation PP34053WO / bg AVL List GmbH July 24, 2024 ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ =^^^^ ^^^^ ^ ^^^ ^^^^ ^^^^ℎ ∙ ^^̇^^ ^^^^ ^^^^ℎ ∙� ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ + ^^^^2 ∙� ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ − ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ determined, where K2 forms a weighting factor of the Kalman filter and M x represents the molar mass of the emission component X and M exh represents the molar mass of the exhaust gas. This equation essentially corresponds to the equation according to claim 1, wherein is used to determine the Conversion to mass flow rate is performed. However, the Kalman factor K2 differs from the Kalman factor K1 because its calculation also requires consideration of the standard deviation of the exhaust gas mass flow sensor. This method makes it possible to determine the mass flow rate of the exhaust gas component in the exhaust stream with a very small deviation from the actual value and to smooth the results by taking into account the standard deviations of all models and measured values ​​when generating the corrected mass flow rate. When measured exhaust gas mass flow rates are mentioned within the scope of the invention, it is not strictly necessary that these be measured by a physical sensor in the exhaust system. The corresponding exhaust aftertreatment system can, in particular, be without a dedicated exhaust gas mass flow sensor. In this case, the exhaust gas mass flow rates are advantageously calculated using values ​​from other sensors.Within the scope of the invention, a measured exhaust gas flow value is therefore also, in particular, an arbitrarily determined exhaust gas flow value. Preferably, in the inventive method for generating the corrected concentration measurement value, the weighting factor K1 is replaced by 2. � ^^^^ ^^^^ ^^^^ ^^^ � the formula ^^^^1 = ^ ^^^^ ^^^^ calculated, whereby Standard deviation of the concentration determined via the exhaust gas model PP34053WO / bg AVL List GmbH July 24, 2024 ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ which represents emission component X in the exhaust stream, ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the standard deviation of the concentration measured by the sensor ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ 2 represents the emission component X in the exhaust stream, and… ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the variance of the concentration determined via the exhaust gas model ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X in the exhaust stream and the variance of the concentration measured by the sensor The emission component X in the exhaust gas stream is represented. The standard deviations or variances used are usually manufacturer data from the sensor manufacturers or must be determined. The deviations of the measured values ​​of the exhaust gas model depend on the sensor data used there and thus indirectly again depend on manufacturer data or standard deviations due to model errors, which can also be determined experimentally. By using the aforementioned Kalman factor, measured values ​​with small standard deviations are always assigned a higher weighting, so that reliable corrected measured values ​​are created. Furthermore, it is advantageous if a characteristic map of the standard deviation of the concentration measured by the sensor is included in the processing unit. ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ The emission component X in the exhaust stream is stored as a function of various parameters, so that the variance of the concentration measured by the sensor ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^the emission component X in the exhaust gas stream according to the rules of error propagation through the sum of the individual variances via the formula is determined. This takes into account that an error in the sensor's measured value can depend on various factors. These include, for example, temperature fluctuations at the sensor, the magnitude of the measured concentrations, the aging of the sensor, or cross-sensitivities to other factors. PP34053WO / bg AVL List GmbH 24.07.2024 Emission components. The more dependencies a sensor has, the greater its potential measurement error, which is taken into account by this calculation. Accordingly, in a preferred embodiment of the invention, the sensor temperature is measured and a characteristic map of the standard deviation of the concentration measured by the sensor is generated in the processing unit. ^^^^ ^^^^ ^^^^ ^^^^ ^^^^the emission component X in the exhaust gas stream as a function of temperature T sens of the sensor and the measured concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ stored so that the variance of the concentration measured by the sensor ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X in the exhaust gas stream according to the rules of error propagation by the sum of the individual variances using the formula This is particularly useful if it is known that the largest deviations arise from the temperature and concentration of the sensor. Additionally, it is useful if the processing unit includes a second characteristic curve of the standard deviation of the concentration measured by the sensor. ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X in the exhaust gas stream as a function of temperature T sens of the sensor and the measured concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^The system incorporates a parameter that takes sensor aging into account. An interpolation function, using the sensor's age as input, compares the sensor's characteristic curves. Thus, depending on the sensor's age, different characteristic curves are accessed, each with varying standard deviations. This ensures that additional measurement deviations caused by sensor aging are considered when determining the corrected measurement value. PP34053WO / bg AVL List GmbH 24.07.2024 In a particularly preferred embodiment of the method, a variance of the concentration of the emission component X determined via the exhaust gas model is calculated according to the rules of error propagation using the formula, in which a Accuracy error ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ due to model flaws and a precision error ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ä ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^This takes into account parameter errors and measurement errors used in the model calculation. This means that the standard deviations of the exhaust gas model are not merely estimated, but rather, depending on the exhaust gas model used, not only are known deviations due to inaccuracies in the model considered, but also the fact that the measured values ​​from which the model derives its values ​​vary in accuracy depending on the additional sensors used. For example, if a calculated concentration value depends on the values ​​of an oxygen sensor, lambda sensor, or the composition of the fuel used, the errors that may arise from these factors are also taken into account, thus weighting the reliability of the determined measurements differently. This leads to a further improvement in the calculation of the corrected concentration value.Furthermore, it is advantageous to calculate the variance of the estimated concentration of the emission component X. This is done using the formula. Diese Gleichung entsteht ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ – assuming that each normally distributed variable A has variance σ 2 for ^^^^ ∙ ^^^^ the variance ^^^^ 2 ∙ ^^^^ 2 This exhibits [variance]. In this way, a variance of the corrected measurement can be determined, and thus the accuracy of this corrected measurement can also be estimated. PP34053WO / bg AVL List GmbH 24.07.2024 In a further embodiment of the invention, this is used to determine, in addition to the estimated concentration of the emission component, a bandwidth with a lower threshold and an upper threshold of the concentration of the emission component X, which indicates that an actual concentration lies within the determined interval with a probability of 95%. indem als unterer Schwellwert ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ = ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ − 1,96 berechnet wird und als oberer Schwellwert 2 + 1,96 ∙ � � ^^^^ ^^^^ ^^^^ berechnet In addition to the determined corrected measurement value, this standard deviation can also be output and used for evaluation purposes. In a further development of the method for generating corrected measurement values ​​when determining the mass flow rate of an emission component in an exhaust gas stream, the weighting factor is... the variance of the mass flow determined via the exhaust gas model ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X in the exhaust stream the variance of the mass flow determined by the sensor ^^̇^^ ^^^^ ^^^^ ^^^^ The emission component X in the exhaust gas stream is represented. The applicable Kalman factor here depends on the measured mass flows and concentrations of the exhaust gas model and the sensor. This Kalman factor therefore does not correspond to the Kalman factor used for concentration correction. In addition to the standard deviations present there, errors in the exhaust gas mass measurement must also be taken into account, which are also included in the calculation of the variance. Nevertheless, the use of the aforementioned Kalman factor smooths the corrected value. PP34053WO / bg AVL List GmbH 24.07.2024 The mass flow rate of the exhaust gas component is determined by taking into account a weighting according to the existing standard deviations of the existing measurement uncertainties. Preferably, when calculating the variance of the mass flow rate of the emission component X from the sensor data, a standard deviation of the measured values ​​of the exhaust gas mass flow sensor or the calculated or determined exhaust gas mass flow values ​​and the measured values ​​of the sensor is taken into account by calculating the variance of the mass flow rate of the emission component X. Dependence of the variance of the concentration ^^^^ ^^^^ 2 ^ ^^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X in the exhaust mass flow, for example, from the sensor data and a variance of the exhaust mass flow ^^^^ ^^̇^^ 2 ^ ^^^ ^^^^ℎ is calculated approximately according to the rules of error propagation by partial differentiation. Variance is calculated according to the rules of error propagation by partial differentiation of the variance to be determined. 2 = ^^^^ ^^̇^^ ^^^^ ^^^^ℎ ∙ of the resulting The mass flow rate depends on the deviation between the values ​​of the exhaust gas mass flow sensor and the concentration measurement sensor. If the formula for calculating the mass flow rate is included in this equation... Massenstroms eingesetzt, wonach ^^̇^^ ^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ = ^^^ ^^^^ ∙ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ∙ ^^̇^^ ^^^^ ^^^^ℎ ist, wobei ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ der zu berechnende Massenstrom der Abgaskomponente X ist, ^^^^ ^^^^ the molar mass of the exhaust gas component is, ^^^^ ^^^^ ^^^^ℎ the molar mass of the exhaust gas flow is, ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the concentration measured by the sensor and ^^̇^^ ^^^^ ^^^^ℎ the exhaust mass flow rate measured by a mass flow sensor or otherwise determined, is obtained by further The following equation results from the transformation PP34053WO / bg AVL List GmbH 24.07.2024 from which the variance of The mass flow rate is calculated, and the Kalman factor K2 can thus be determined from it. Preferably, the variance of the mass flow rate of the emission component X is calculated from the model data in the same way, taking into account a standard deviation of the values ​​from the exhaust gas mass flow sensor and the model data determined for the concentration. Dependence of the variance of the concentration the emission component X in the exhaust mass flow from the model data and the variance of the exhaust mass flow ^^^^ ^^̇^^ 2 ^ ^^^ ^^^^ℎ approximately calculated in the same way according to the rules of error propagation by partial differentiation Thus, the weighting factor K2 is obtained using the formula that the concentration determined via the exhaust gas model ^^^^ ^^^^ ^^^^ ^^^^ ^^^^of molecule X in the exhaust stream, ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the standard deviation of the concentration measured by the sensor ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ of molecule X in exhaust stream 2, and… ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ – the variance of the concentration determined via the exhaust gas model of molecule X in the exhaust gas stream the variance of the concentration measured by the sensor of molecule X in the exhaust stream, ^^̇^^ ^^^^ ^^^^ℎ represents the exhaust gas mass flow and ^^^^ 2 ^ ^̇^^ ^^^^ ^^^^ℎ This represents the variance of the exhaust gas mass flow. It thus becomes possible to continuously calculate a corrected mass flow from the possible deviations specified by the manufacturers. PP34053WO / bg AVL List GmbH 24.07.2024 calculates the K2 factor, which takes into account the possible deviations of the determined sensor data and model data. The factor K2 is continuously recalculated during the measurements. Additionally, it is advantageous to calculate a variance of the estimated mass flow rate of the emission component X by: This serves to identify the uncertainty associated with the corrected value for the mass flow rate of the exhaust gas component. This formula is derived from the equation by Changeover By inserting the Formula ^^̇^^ ^ ^^^ ^^^^ ^^^^ ^^^^ ^^^^ = ∙ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ∙ ^^̇^^ ^^^^ ^^^^ℎ or rather ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ = ∙ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ∙ ^^̇^^ ^^^^ ^^^^ℎ This results in ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ = ^^^^2 ∙ ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ + (1 − ^^^^2) ∙ ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^, which in turn results in the aforementioned variance. The variance calculated in this way can advantageously be used to determine, in addition to the determined estimated mass flow rate of the emission component, a bandwidth with a lower threshold and an upper threshold for the mass flow rate of the emission component X, which indicates that an actual mass flow rate lies within the determined interval with a probability of 95%, by calculating the following as the lower threshold: ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ = ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ − 1,96 und als oberer Schwellwert 2 ^^̇^^ ^^^^ ^^^^ ^^^^ = + 1,96 ∙ ^^^^ ^^^^� berechnet wird. So kann mit einer A 95% probability can be determined that the corrected measurement value lies within the interval thus calculated. This can be used for on-board diagnostics and / or on-board monitoring in the vehicle, as well as for vehicle control. PP34053WO / bg AVL List GmbH 24.07.2024 On the one hand, this ensures compliance with the requirements of the EU7 standard by allowing on-board diagnostics and / or on-board monitoring to determine measured values, particularly those relating to harmful exhaust gas components, with greater accuracy, thus enabling a more realistic verification of whether the vehicle meets the relevant standards. Additionally, these measured values ​​can be used for vehicle control, preventing unnecessary sensor error messages that arise solely from high standard deviations in certain areas. The inventive method is described below using a non-limiting embodiment in which a corrected mass flow rate of a nitrogen oxide in the exhaust gas stream is to be determined. The figure schematically depicts an internal combustion engine with an exhaust system and sensors.The figure shows an internal combustion engine 10, which has an exhaust system 12 in which a NO. x A sensor 14, an NH3 sensor 16, and an exhaust gas mass flow sensor 18 are arranged and connected to a processing unit 20. The processing unit 20 contains characteristic maps 22 of the NOₓ sensor. x - Sensor 14, depending on the temperature of sensor 14, the measured concentration, and, for example, depending on existing cross-sensitivities, i.e., the measured values ​​of the NH3 sensor 16 or a water sensor. Furthermore, an exhaust gas model 24 is stored in the processing unit 20. This exhaust gas model 24 calculates an expected NOx concentration from values ​​of sensors not shown, such as a lambda sensor, an air mass meter, the composition of the fuel used, the amount of fuel injected, or other load data. PP34053WO / bg AVL List GmbH 24.07.2024 During the on-board analysis, for example, the NOx - Sensor 14 a concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ measured at 500 ppm. A characteristic curve is known from the manufacturer's data, from which it can be read that the NO x -Sensor 14 in this area via a temperature sensor 26 at the NO x -Sensor 14 measured temperature of, for example, 300°C, a deviation ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ of up to 10% of the measured value, which corresponds to 50 ppm. Further dependencies, such as cross-sensitivities to other exhaust gas components, can also be taken into account here and change the deviation accordingly. The exhaust gas mass flow sensor 18 measures a mass flow rate ^^̇^^ ^^^^ ^^^^ℎ at a rate of 500 kg / h. The manufacturer specifies an inaccuracy in this range. ^^̇^^ ^^^^ ^^^^ℎ a maximum of 5%, which equates to 25 kg / h. At the same time, the exhaust gas model 24 yields a concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^determined based on the prevailing conditions, for example 400 ppm, whereby this value is subject to possible sensor inaccuracies from which the NO x -Concentration is calculated, as well as an inaccuracy due to possible errors in the model ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ of up to 15%, which equates to 60 ppm. Using this information, a corrected measurement for the mass flow present in the exhaust gas stream should now be calculated in unit 20. ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ The nitrogen oxides are calculated. For this purpose, a Kalman filter is used, through which... an estimated corrected mass flow rate ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ is calculated. In order to use this formula, the Kalman factor must be taken from PP34053WO / bg AVL List GmbH July 24, 2024 first be calculated, in which the standard deviation of the mass flow determination via the exhaust gas mass flow sensor 18 and the NO x -Sensor 14 and The standard deviation of the mass flow rate determination using exhaust gas model 24 is represented. The variance mass flow rate determination via the NO x The readings of NOx sensor 14 and exhaust gas mass flow sensor 18 depend on the possible inaccuracies of both NOx sensor 14 and exhaust gas mass flow sensor 18. Therefore, ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ a function of the exhaust gas mass flow ^^̇^^ ^^^^ ^^^^ℎ and concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ The variance can be approximated by partial differentiation according to the rules of error propagation: The known equation is now incorporated into this formula. used to calculate a mass flow rate, so that after substitution and cancellation the following results: The variance ^^^^ ^^^^ 2 ^ ^^^ ^^^^ ^^^^ ^^^^ The exhaust gas model results in the same way. Since the mass flow rate of the exhaust gas model also depends on the calculated sensor data for concentration as well as on the values ​​of the exhaust gas mass flow sensor (18). It should be noted that the inaccuracies of the concentration depend on both PP34053WO / bg AVL List GmbH 24.07.2024 Inaccuracies of the model itself as well as inaccuracies of the data used for calculating the concentration in the model, and both must be taken into account in the characteristic map. Substituting equations (6) and (7) into (2) and simplifying yields: ^^^^2 Substituting the above values ​​yields the following: If we now insert this value into formula (1), we get: ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ = ^^^^ ^^^^ ^^^^ ^^^^ ^ ^^^ ^^^^ ^^^^ℎ ∙ ^^̇^^ ^^^^ ^^^^ℎ ∙� ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ + 0.5614 ∙� ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ − ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^The molar mass of exhaust gas is, for example, approximately 29 g / mol, while that of a mixture of nitrogen oxides is approximately 35 g / mol. This results in: 456,14 ^^^^ ^^^^ ^^^^ = 275 ^^^^ / ℎ. The concentration can also be calculated accordingly. ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ = 400 ^^^^ ^^^^ ^^^^ + 0,545 ∙ ( 500 ^^^^ ^^^^ ^^^^ − 400 ^^^^ ^^^^ ^^^^ ) = 454,5 ^^^^ ^^^^ ^^^^ und somit näher The corrected value is based on the sensor's reading, as it has a higher accuracy in this range. It becomes clear that when the Kalman factor approaches 1, the corrected value corresponds to the sensor's reading, while when the factor approaches 0, the corrected value corresponds to the reading of the exhaust gas model. PP34053WO / bg AVL List GmbH 24.07.2024 Furthermore, the variance of the corrected concentration and the corrected mass flow rate can be calculated in the same way. The variance of the corrected concentration is: = 58,57 ^^^^2 / ℎ²The equations result from a rearrangement of equation (1) and the known calculation of the variance, where a variable y has a variance σ 2 This leads to a variance of ^^^^² ∙ ^^^^² for the variable ^^^^ ∙ ^^^^. From this, an upper threshold and a lower threshold can be calculated, within whose interval the corrected measurement value lies with a probability of 95%. A normal distribution curve is assumed for this calculation. The lower threshold for the concentration is then calculated as follows: ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ 1,96 ∙�1487 ^^^^ ^^^^ ^^^^ 2 = 378 ^^^^ ^^^^ ^^^^ und der obere Schwellwert zu: ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ = ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ + 1,96 = 454,5 ^^^^ ^^^^ ^^^^ + 1,96 ∙�1487 ^^^^ ^^^^ ^^^^2 = 530 ^^^^ ^^^^ ^^^^ PP34053WO / bg AVL List GmbH 24.07.2024 Accordingly, the actual value of the nitrogen oxide concentration lies within an interval between 378 ppm and 530 ppm with a probability of 95%. Performing the same calculation for the mass flow rate yields: Accordingly, the actual mass flow rate of nitrogen oxides lies within a range of 260 g / h to 290 g / h with a probability of 95%. These values ​​are all continuously calculated in the processing unit from the available measurement data, including the Kalman factors. This results in a continuous output of corrected measured values ​​and ranges within which the measured values ​​are highly likely to lie. All this data can then be used for on-board diagnostics and / or on-board monitoring. It should be clear that the described procedure can be carried out for all exhaust gas components for which sensors and exhaust gas models are available. In particular, the checks of ammonia concentrations and mass flows, as well as particulate flows in the exhaust gas, which will be required in the future by the EU7 emissions standard, should be mentioned here.Of course, this method can also be used to monitor carbon dioxide, carbon monoxide, water or sulfur compounds.

Claims

PP34053WO / bg AVL List GmbH 24.07.2024 PATENT CLAIMS 1. Method for generating corrected measured values ​​when determining the concentration of an emission component in an exhaust gas stream, with the following steps: - Measuring a concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ of the emission component X in the exhaust gas stream via a sensor (14), - determining a concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ of the emission component X via an exhaust gas model (24) which is stored in a computing unit (20) and via which expected concentrations of the emission component X in the exhaust gas stream are read or calculated as a function of environmental data via physical models or map-based algorithms, - determining an estimated concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X from the concentration measurement of the sensor (14) and the concentration determination via the exhaust gas model (24) using a Kalman filter via the equation where K1 forms a weighting factor of the Kalman filter.

2. A method for generating corrected measured values ​​when determining the concentration of an emission component in an exhaust gas stream according to claim 1, characterized in that the weighting factor K1 is given by the formula ^^^^1 � ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ � +� ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ � is calculated, where the standard deviation of the concentration determined via the exhaust gas model (24) ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X in the exhaust stream, ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the standard deviation of the measured values ​​via the sensor (14) PP34053WO / bg AVL List GmbH 24.07.2024 Concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X in the exhaust gas stream, and the variance of the concentration determined via the exhaust gas model (24) ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X in the 2 exhaust gas stream and� ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^� the variance of the concentration measured by the sensor (14) ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ of the emission component X in the exhaust gas stream.

3. Method for generating corrected measured values ​​when determining the concentration of an emission component in an exhaust gas stream according to claim 1 or 2, characterized in that in the computing unit (20) a characteristic map of the standard deviation of the concentration measured by the sensor (14) ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X in the exhaust gas flow is stored as a function of various parameters, so that the variance of the concentration measured by the sensor (14) ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ of the emission component X in the exhaust gas flow according to the rules of error propagation by the sum of the individual variances using the formula 4. A method for generating corrected measured values ​​when determining the concentration of an emission component in an exhaust gas stream according to claim 3, characterized in that the sensor temperature is measured and in the computing unit (20) a characteristic map of the standard deviation of the concentration measured by the sensor (14) ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ of the emission component X in the exhaust gas stream as a function of the temperature T sens of the sensor (14) PP34053WO / bg AVL List GmbH 24.07.2024 and the measured concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ is stored so that the variance of the concentration measured by the sensor (14) ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ of the emission component X in the exhaust gas flow according to the rules of error propagation by the sum of the individual variances by the formula 5. Method for generating corrected measured values ​​when determining the concentration of an emission component in an exhaust gas stream according to claim 4, characterized in that in the computing unit (20) a second characteristic field of the standard deviation of the concentration measured by the sensor (14) ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ of the emission component X in the exhaust gas stream as a function of the temperature T sens of the sensor (14) and the measured concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ is stored, in which an aging of the sensor (14) is taken into account, wherein an interpolation function is used to weigh up between the sensor characteristic maps by input of the sensor aging.

6. Method for generating corrected measured values ​​when determining the concentration of an emission component in an exhaust gas flow according to one of claims 1 to 5, characterized in that a variance of the concentration of the emission component X determined via the exhaust gas model (24) is calculated according to the rules of 2 2Error propagation via the formula� ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ � =� ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^� + � ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ä ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^� 2 b erechnet wird, bei der ein Genauigkeitsfehler ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ due to errors in the model and a precision error ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ä ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ PP34053WO / bg AVL List GmbH 24.07.2024 due to parameter errors and measured value errors used in the model calculation.

7. A method for generating corrected measured values ​​when determining the concentration of an emission component in an exhaust gas stream according to one of claims 1 to 6, characterized in that a variance of the estimated concentration of the emission component X is calculated by:

8. Method for generating corrected measured values ​​when determining the concentration of an emission component in an exhaust gas stream according to claim 7, characterized in that in addition to the estimated concentration of the emission component, a bandwidth with a lower threshold value and an upper threshold value of the concentration of the emission component X is determined, which indicates that an actual concentration lies with a probability of 95% within the determined interval by calculating as the lower threshold value: ^ ^^^ ^^^^ ^^^^ ^^^^ ^^^^ = ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ − 1,96 ∙ ^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^� 2 � � ^^^ und als oberer Schwellwert berechnet wird: 1,96 9. Method for generating corrected measured values ​​when determining a mass flow of an emission component in an exhaust gas stream, comprising the following steps: - Measuring a concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X in the exhaust gas stream via a sensor (14), PP34053WO / bg AVL List GmbH 24.07.2024 - Determining a concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ of the emission component X via an exhaust gas model (24) which is stored in a computing unit (20) and via which expected concentrations of the emission component X in the exhaust gas flow are read or calculated as a function of environmental data via physical models or map-based algorithms, - measuring an exhaust gas mass flow ^^̇^^ ^^^^ ^^^^ℎ via an exhaust gas mass flow sensor (18), - determining an estimated mass flow ^^̇^^ ^^^^, ^^^^ ^^^^ ^^^^ ^^^^ the emission component X from the concentration measurement of the sensor (14) and the concentration determination via the exhaust gas model (24) using the Kalman filter via the equation: ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ = ^ ^^^ ^^^^ ^^^^ℎ ∙ ^^̇^^ ^^^^ ^^^^ℎ ∙� ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ + ^^^^2 ∙� ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ − ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ , where K2 is a weighting factor of the Kalman filter and M xis the molar mass of the emission component X and M exh represents the molar mass of the exhaust gas.

10. Method for generating corrected measured values ​​when determining a mass flow of an emission component in an exhaust gas flow according to claim 9, characterized in that the weighting factor K2 is determined by the formula 2 � ^^^^ � ^^^^2 = ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ 22= 1 2 is calculated, where � ^^^^ ^^̇^^ ^^^^ � +� ^^^^ ^^̇^^ ^^^^ � � ^^^^ ^^̇^^ e ^ ^^ � ^ ^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ 1+ ^ ^^^^ ^^^^ ^^^^ ^^^^ 2 � ^^^^ ^^̇^^ ^^^^ � ^ ^^^ ^^^^ ^^^^ Variance of the mass flow determined via the exhaust model (24) ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X in the exhaust stream represents 2 and � ^^^^ ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ � the variance of the mass flow determined by the sensor (14) ^^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X in the exhaust gas stream. PP34053WO / bg AVL List GmbH 24.07.2024 11. Method for generating corrected measured values ​​when determining a mass flow of an emission component in an exhaust gas flow according to claim 10, characterized in that when calculating the variance of the mass flow of the emission component X from the sensor data, a standard deviation of the measured values ​​of the exhaust gas mass flow sensor (18) and the measured values ​​of the sensor (14) are taken into account by the variance of the mass flow of the emission component X Dependence of the variance of the concentration ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ the emission component X in the exhaust gas mass flow from the sensor data and a variance of the exhaust gas mass flow is approximately calculated according to the rules of error propagation by partial derivative from:

12. Method for generating corrected measured values ​​when determining a mass flow of an emission component in an exhaust gas flow according to claim 10 or 11, characterized in that when calculating the variance of the mass flow of the emission component X from the model data, a standard deviation of the measured values ​​of the exhaust gas mass flow sensor (18) and the model data determined for the concentration are taken into account by a variance of the mass flow of the emission component Dependence of the variance of the concentration the emission component X in the exhaust gas mass flow from the model data and the variance of the exhaust gas mass flow ^^^^ ^^̇^^ 2 ^ ^^^ ^^^^ℎ is approximately calculated according to the rules of error propagation by partial derivative from: PP34053WO / bg AVL List GmbH July 24, 2024 13. Method for generating corrected measured values ​​when determining a mass flow of an emission component in an exhaust gas flow according to claims 9 to 12, characterized in that the weighting factor K2 is determined by the formula Standard deviation of the concentration determined by the exhaust gas model (24) of the molecule X in the exhaust stream, the standard deviation of the concentration measured by the sensor (14) ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ of the molecule X in the exhaust stream, and 2 � ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ � the variance of the concentration determined via the exhaust gas model (24) ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ of the molecule X in the exhaust stream and the variance of the concentration measured by the sensor (14) ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ of the molecule X in the exhaust stream, ^^̇^^ ^^^^ ^^^^ℎ represents the exhaust gas mass flow and� ^^^^ 2 ^ ^̇^^ ^^^^ ^^^^ℎ�represents the variance of the exhaust gas mass flow.

14. A method for generating corrected measured values ​​when determining a mass flow of an emission component in an exhaust gas flow according to one of claims 9 to 13, characterized in that a variance of the estimated mass flow of the emission component X is calculated by: PP34053WO / bg AVL List GmbH 24.07.2024 15. Method for generating corrected measured values ​​when determining a mass flow of an emission component in an exhaust gas flow according to claim 14, characterized in that in addition to the determined estimated mass flow of the emission component, a bandwidth with a lower threshold value and an upper threshold value of the mass flow of the emission component X is determined, which indicates that an actual mass flow lies with a probability of 95% within the determined interval by calculating as the lower threshold value: ^ ^̇^^ ^^^^ ^^^^ ^^^^ ^^^^ und als oberer Schwellwert berechnet wird:

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