Abstract:
An apparatus, system, and method are disclosed for robustly estimating soot oxidation rates on a particulate filter. The invention uses empirically measured soot consumption rates as defined boundary rates, and operates between those rates using theoretical relationships between soot consumption and various operating conditions. The invention may also operate outside the defined boundaries by extrapolating the theoretical relationships beyond the defined boundary. The invention thereby overcomes the inflexibility of empirical modeling by allowing reasonable estimates at points that are not explicitly measured, and it overcomes the sensitivity of theoretical models to non-idealities that are experienced in real applications.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     1. Field of the Invention  
         [0002]     This invention relates to model implementation and more particularly relates to apparatuses, systems, and methods for combining theoretical and empirical knowledge as an improvement over a purely theoretical or purely empirical model.  
         [0003]     2. Description of the Related Art  
         [0004]     Modern diesel emissions regulations are driving engine manufacturers to use particulate filters in engine aftertreatment systems. These filters accumulate soot over time, and the soot must be removed from the filter periodically.  
         [0005]     There are two primary mechanisms for removing the soot. The engine naturally generates some NO 2  in the exhaust stream. At low temperatures, this NO 2  oxidizes some of the soot on the filter, releasing the soot—typically as CO or CO 2 . This mechanism is called “noxidation.” 
         [0006]     The noxidation mechanism is often insufficient to keep the particulate filter at acceptable soot levels. Therefore, a faster oxidation mechanism is sometimes required. One implementation of this mechanism is to raise the temperature of the exhaust stream to the point where simple O 2  will oxidize the soot. This temperature is higher than where the engine will typically run under normal loads and therefore must generally be triggered intentionally by the engine controls. This mechanism is called “oxidation.” 
         [0007]     The oxidation of soot through either mechanism—“oxidation” or “noxidation”—is called “soot consumption.” 
         [0008]     The oxidation mechanism consumes soot at a much higher temperature and much more quickly than the noxidation mechanism. If the soot level is too high in the particulate filter when the oxidation mechanism is initiated, oxidation can generate heat within the particulate filter much more quickly than the rate at which the heat can be dissipated. This causes local temperature spikes within the particulate filter, and can result in unnecessary wear on the particulate filter or even mechanical failure of the particulate filter. A runaway heat spike like this is called an “uncontrolled regeneration.” 
         [0009]     Before an oxidation-based regeneration is attempted, the controller must be as sure of the overall soot level as possible. The primary feedback mechanism to determine the soot level on the particulate filter is the use of a delta-pressure sensor across the particulate filter. With a known flow rate and pressure drop, the amount of soot on the particulate filter can be estimated. Even in the ideal case, this feedback mechanism is still only intermittently dependable for determining soot levels. First, whenever mass flow through the system is low, the delta-pressure based soot load estimate is known to be unreliable. Further, while soot is being consumed on the particulate filter, the delta-pressure sensor is known to become unreliable due to holes developing in the soot layer.  
         [0010]     An independent measure of the rate of soot consumption on the soot filter would help properly utilize the delta-pressure sensor for estimating soot loading on the particulate filter, and would help in optimizing and limiting heat generation within the particulate filter. Therefore, a model of soot generation and consumption rates and overall soot levels on the particulate filter is desirable to be used in some combination with the feedback mechanism.  
         [0011]     Purely empirical models of soot consumption rates are problematic. Any given system must have data for every possible operating point to build a data map. This is impossible, so some shortcuts must be taken and there will be operating points between and outside the data set which will yield poor results.  
         [0012]     Purely theoretical models are also problematic. Regarding the noxidation mechanism, the relation depends strongly upon the temperature of the particulate filter. The temperature within the particulate filter experiences gradients and localized variances which temperature measurements available for production engines cannot describe adequately. Therefore, practical observations of noxidation rates often vary considerably from the theoretically derived models.  
         [0013]     Regarding the oxidation mechanism, the relation depends even more strongly upon the temperature of the particulate filter than for noxidation. The oxidation mechanism is also more sensitive to soot loading than the noxidation mechanism, making any such model sensitive to soot loading and distribution errors. These combine to cause the achieved oxidation rates to be different—often lower—than theoretically derived models suggest.  
         [0014]     The value of interest for the use of these models—the soot loading on the particulate filter—is not the direct output of the model, but rather the integration of the model output over time. Therefore, errors from the models to the value of interest accumulate over time and become larger. Even in a theoretically sound model, the errors in oxidation and noxidation rates can accumulate to the extent that within one hour, the particulate filter can be completely full and appear completely clean to the model, or the particulate filter can be completely clean and appear completely full to the model. The inherent issues with the available soot load feedback mechanisms can force the system to not have a reliable feedback mechanism for many hours at a time. Therefore, current systems can have large stretches of time where no information is available about the current soot loading.  
         [0015]     From the foregoing discussion, it should be apparent that a need exists for an apparatus, system, and method that can overcome the limitations of both the theoretical and the empirical models for estimating soot consumption rates. Beneficially, such an apparatus, system, and method would be calibratible with just a few parameters, and from the types of measurements that are already typically made in the field.  
       SUMMARY OF THE INVENTION  
       [0016]     The present invention has been developed in response to the present state of the art, and in particular, in response to the problems and needs in the art that have not yet been fully solved by currently available modeling techniques. Accordingly, the present invention has been developed to provide an apparatus, signal bearing medium, method and system for calibrating a theoretical model to empirical knowledge that overcome many or all of the above-discussed shortcomings in the art.  
         [0017]     The apparatus, in one embodiment, is configured to store boundary soot consumption rates, and further configured to store relationship information between potential operating conditions of the system and the boundary soot consumption rates. In one embodiment, the apparatus is further configured to generate a condition index value from the current operating conditions of the system, and is further configured to generate a final output value of the current soot consumption rate utilizing the condition index value and the boundary soot consumption rates. The apparatus may include an empirical boundary conditions module for storing the boundary soot consumption rates, a defined relationship module for storing relationship information between potential operating conditions and the boundary soot consumption rates, a condition index module for determining the condition index value, and a final output value module for determining the final output value of current soot consumption rate. In one embodiment, the modules may be contained within a controller.  
         [0018]     The apparatus is further configured, in one embodiment, to determine a soot consumption rate via the O 2  based oxidation mechanism. In one embodiment, the oxidation estimate further includes storing an oxidation high rate and low rate, and interpolating or extrapolating between the low rate and the high rate using the condition index value. The apparatus is further configured, in one embodiment, to use the O 2  mass fraction, the current soot loading on the particulate filter, and the current temperature of the particulate filter as the current operating conditions for the condition index value. In one embodiment, the apparatus is further configured to use a range of values of: O 2  mass fraction, soot loading on the particulate filter, and temperature of the particulate filter—as the plurality of operating conditions for which the defined relationship module stores relationships to the boundary soot consumption rates.  
         [0019]     The apparatus is further configured, in one embodiment, to determine a soot consumption rate via the NO 2  based noxidation mechanism. In one embodiment, the noxidation estimate further includes storing a noxidation high rate and low rate, and interpolating or extrapolating between the low rate and the high rate using the condition index value. The apparatus is further configured, in one embodiment, to use the NO 2  mass flow, the current soot loading on the particulate filter, and the current temperature of the particulate filter as the current operating conditions for the condition index value. In one embodiment, the apparatus is further configured to use a range of values of: NO 2  mass flow, soot loading on the particulate filter, and temperature of the particulate filter—as the plurality of operating conditions for which the defined relationship module stores relationships to the boundary soot consumption rates.  
         [0020]     A system of the present invention is also presented to treat exhaust gas emitted as a byproduct of operation of an internal combustion engine. The system may be embodied in an exhaust gas after-treatment system. In particular, the system, in one embodiment, includes sensors for determining various operating conditions, a controller configured to store a high rate of soot oxidation and a low rate of soot oxidation based on defined operating conditions, to store relationships between a plurality of potential operating conditions and the high and low soot oxidation rates, to determine a conditions index determined according to current operating conditions, and to combine the conditions index with the high rate of soot oxidation and low rate of soot oxidation to determine a rate of soot consumption on the particulate filter. The system may further include a control unit for determining operating and ambient conditions, an internal combustion engine, a particulate filter, a catalytic component, a differential pressure sensor, and a reactant delivery mechanism.  
         [0021]     A method of the present invention is also presented for storing boundary soot consumption rates determined according to defined operating conditions, storing relationship information between a plurality of potential operating conditions and the boundary soot consumption rates, determining a condition index value determined according to current operating conditions and the stored relationship information, and combining the condition index value with the boundary soot consumption rates to produce a final output value of soot consumption rate. The method in the disclosed embodiments substantially includes the steps necessary to carry out the functions presented above with respect to the operation of the described apparatus and system.  
         [0022]     Reference throughout this specification to features, advantages, or similar language does not imply that all of the features and advantages that may be realized with the present invention should be or are in any single embodiment of the invention. Rather, language referring to the features and advantages is understood to mean that a specific feature, advantage, or characteristic described in connection with an embodiment is included in at least one embodiment of the present invention. Thus, discussion of the features and advantages, and similar language, throughout this specification may, but do not necessarily, refer to the same embodiment.  
         [0023]     Furthermore, the described features, advantages, and characteristics of the invention may be combined in any suitable manner in one or more embodiments. One skilled in the relevant art will recognize that the invention may be practiced without one or more of the specific features or advantages of a particular embodiment. In other instances, additional features and advantages may be recognized in certain embodiments that may not be present in all embodiments of the invention.  
         [0024]     These features and advantages of the present invention will become more fully apparent from the following description and appended claims, or may be learned by the practice of the invention as set forth hereinafter.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0025]     In order that the advantages of the invention will be readily understood, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments that are illustrated in the appended drawings. Understanding that these drawings depict only typical embodiments of the invention and are not therefore to be considered to be limiting of its scope, the invention will be described and explained with additional specificity and detail through the use of the accompanying drawings, in which:  
         [0026]      FIG. 1  is a schematic block diagram illustrating one embodiment of an engine system in accordance with the present invention;  
         [0027]      FIG. 2  is a schematic block diagram illustrating one embodiment of a control system in accordance with the present invention;  
         [0028]      FIG. 3  is a schematic block diagram illustrating one embodiment of an empirical boundary conditions module in accordance with the present invention;  
         [0029]      FIG. 4  is a schematic block diagram illustrating another embodiment of an empirical boundary conditions module in accordance with the present invention;  
         [0030]      FIG. 5  is a schematic block diagram illustrating one embodiment of a defined relationships module in accordance with the present invention;  
         [0031]      FIG. 6  is a schematic block diagram illustrating another embodiment of a defined relationships module in accordance with the present invention;  
         [0032]      FIG. 7  is a schematic block diagram illustrating one embodiment of the interactions of the current operating conditions, the defined relationships module, and the condition index module to produce a condition index value in accordance with the present invention;  
         [0033]      FIG. 7A  is a process flow diagram illustrating one embodiment of a method to generate a condition index value in accordance with the present invention;  
         [0034]      FIG. 8  is a schematic block diagram illustrating one embodiment of the interactions of the condition index value, the boundary soot consumption rates, and the final output value module to produce a final output value in accordance with the present invention;  
         [0035]      FIG. 9  is a graph illustrating one embodiment of the interactions of the condition index value and the boundary soot consumption rates to determine a final output value in accordance with the present invention;  
         [0036]      FIG. 10  is a process flow diagram illustrating one embodiment of a method of determining a soot consumption rate in accordance with the present invention; and  
         [0037]      FIG. 11  is a graph illustrating a method to use easily obtainable information to more easily practice the present invention.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0038]     Many of the functional units described in this specification have been labeled as modules, in order to more particularly emphasize their implementation independence. For example, a module may be implemented as a hardware circuit comprising custom VLSI circuits or gate arrays, off-the-shelf semiconductors such as logic chips, transistors, or other discrete components. A module may also be implemented in programmable hardware devices such as field programmable gate arrays, programmable array logic, programmable logic devices or the like.  
         [0039]     Modules may also be implemented in software for execution by various types of processors. An identified module of executable code may, for instance, comprise one or more physical or logical blocks of computer instructions which may, for instance, be organized as an object, procedure, or function. Nevertheless, the executables of an identified module need not be physically located together, but may comprise disparate instructions stored in different locations which, when joined logically together, comprise the module and achieve the stated purpose for the module.  
         [0040]     Indeed, a module of executable code may be a single instruction, or many instructions, and may even be distributed over several different code segments, among different programs, and across several memory devices. Similarly, operational data may be identified and illustrated herein within modules, and may be embodied in any suitable form and organized within any suitable type of data structure. The operational data may be collected as a single data set, or may be distributed over different locations including over different storage devices, and may exist, at least partially, merely as electronic signals on a system or network.  
         [0041]     Reference throughout this specification to “one embodiment,” “an embodiment,” or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases “in one embodiment,” “in an embodiment,” and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment.  
         [0042]     Reference to a signal bearing medium may take any form capable of generating a signal, causing a signal to be generated, or causing execution of a program of machine-readable instructions on a digital processing apparatus. A signal bearing medium may be embodied by a transmission line, a compact disk, digital-video disk, a magnetic tape, a Bernoulli drive, a magnetic disk, a punch card, flash memory, integrated circuits, or other digital processing apparatus memory device.  
         [0043]     Furthermore, the described features, structures, or characteristics of the invention may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided, such as examples of programming, software modules, user selections, network transactions, database queries, database structures, hardware modules, hardware circuits, hardware chips, etc., to provide a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the invention may be practiced without one or more of the specific details, or with other methods, components, materials, and so forth. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the invention.  
         [0044]      FIG. 1  depicts one embodiment of an internal combustion engine system, such as a diesel engine system  100 , in accordance with the present invention. As illustrated, the engine system  100  may include a diesel engine  110 , a controller  130 , a catalytic component  140  to oxidize engine-out hydrocarbons, a catalytic component  142  to oxidize added hydrocarbons, adsorb NO x , or both, and a particulate filter  150  to trap soot particles from the soot generating source. The engine system  100  may further include various temperature sensors  124 , various pressure sensors  126 , an air intake  112 , a turbine compressor  120 , an air intake manifold  114 , an exhaust manifold  116 , an exhaust turbine  118  that may include a wastegate or variable geometry technology, an exhaust gas recirculation with a cooler  122 , an exhaust bypass valve  128 , exhaust bypass line  132 , a fuel tank  180  which supplies the engine  110  and potentially an external fueling pump  170 , an external fueling delivery mechanism  190 , an exhaust gas flow sensor  165 , and a sensor  160  detecting the differential pressure across the particulate filter  150 .  
         [0045]     It is readily understood by those in the art that many of the components may not be present in a given system, and that many of the sensors may be virtual calculations based on other parameters rather than a physical device on the system. Further, it is readily understood by those in the art that alternative locations for many of the components are equivalent to the illustrations for one embodiment shown in the engine system  100 , and all of these are intended to be included in the scope of the present invention.  
         [0046]      FIG. 2  shows a controller  200  in accordance with the present invention. A controller, which in one embodiment may be a controller  200  similar in configuration to the controller  130 , contains an empirical boundary conditions module  202 , a defined relationship module  204 , a condition index module  206 , and a final output value module  208 . The controller  200  obtains the current operating conditions  210  of the system from sensors, from another controller, over a datalink, or the like.  
         [0047]     As is known in the art, the controller  200  and components may comprise processor, memory, and interface modules that may be fabricated of semiconductor gates on one or more semiconductor devices mounted on circuit cards. Connections between the modules may be through semiconductor metal layers, substrate-to-substrate wiring, or circuit card traces or wires connecting the semiconductor devices.  
         [0048]     The current operating conditions  210  may include whatever parameters for which relationships are available in the defined relationships module  204 . For an estimate of the soot consumption rate via oxidation, the current operating conditions  210  might be the temperature of the particulate filter, the current soot loading on the particulate filter, and the oxygen mass fraction of the flow through the particulate filter. For an estimate of the soot consumption rate via noxidation, the current operating conditions  210  might be the temperature of the particulate filter, the current soot loading on the particulate filter, and the NO 2  mass flow rate through the particulate filter.  
         [0049]     The empirical boundary conditions module  202  is configured to store boundary soot consumption rates which reflect observed soot consumption rates. The empirical boundary conditions module  202  might store an oxidation high rate and an oxidation low rate. The defined relationship module  204  is configured to store soot consumption rates relative to the boundary soot consumption rates, and it is further configured to relate those rates to various operating conditions. In one embodiment, the defined relationship module  204  may store a range of particulate filter temperatures, and relate each temperature to a soot consumption rate as a percentage of the high soot consumption rate.  
         [0050]     The condition index module  206  may be configured to combine the current operating conditions  210  with the relationships defined in the defined relationship module  204  to generate a condition index value. The final output value module  208 , in one embodiment, is configured to relate the condition index value to a final output value of soot consumption rate.  
         [0051]      FIG. 3  shows an embodiment of the empirical boundary conditions module  202 . In the illustrated embodiment, the empirical boundary conditions module  202  includes a set of boundary soot consumption rates  302 , including an oxidation high rate  304 , and an oxidation low rate  306 . The empirical boundary conditions module  202 , in the illustrated embodiment, further includes a set of defined operating conditions  308 , including the particulate filter temperature  310 , the O 2  mass fraction  312 , and the soot loading  314 . In the illustrated embodiment, the defined operating conditions  308  are the values of the conditions which are associated with the oxidation high rate  304  and the oxidation low rate  306 . In one embodiment, the oxidation high rate  304  is 600 grams/hour, the oxidation low rate  306  is 1 gram/hour; the particulate filter temperature  310 , O 2  mass fraction  312 , and soot loading  314  associated with the oxidation high rate  304  are 550 degrees C., 0.12, and 120 grams, respectively; the particulate filter temperature  310 , O 2  mass fraction  312 , and soot loading  314  associated with the oxidation low rate  306  are 350 degrees C., 0.05, and 60 grams, respectively. These values are taken from the current best knowledge on a 15-liter diesel engine, and can be readily determined experimentally on another system by one skilled in the art.  
         [0052]      FIG. 4  shows an embodiment of the empirical boundary conditions module  202 .  FIG. 4  is substantially like  FIG. 3 , except that the boundary soot consumption rates  302  include a noxidation high rate  316  and a noxidation low rate  318 . The defined operating conditions, in one embodiment, differ only in that NO 2  mass flow  322  is shown rather than O 2  mass fraction, and that the particulate filter temperature  320  and soot loading  324  use a different number to emphasize that the particulate filter temperature estimate  320  for noxidation estimation might be different than the particulate filter temperature estimate  310  for oxidation estimation. The noxidation reaction occurs almost exclusively on a catalytic surface within the particulate filter  150 , while at higher temperatures the oxidation reaction can occur in the bulk away from the catalyst. Therefore, in one embodiment, the particulate filter temperature  320  is an estimation of the filter substrate temperature, while the particulate filter temperature  310  is an estimation of the bulk exhaust flow temperature at the center of the particulate filter  150 . The invention will perform acceptably even if the same estimate is used for both mechanisms in a particular embodiment.  
         [0053]     In one embodiment, the noxidation high rate  316  is 35 grams/hour, the noxidation low rate  306  is 0.175 gram/hour; the particulate filter temperature  320 , NO 2  mass flow rate  322 , and soot loading  324  associated with the noxidation high rate  316  are 325 degrees C., 2400 grams/hour, and 120 grams, respectively; the particulate filter temperature  320 , NO 2  mass flow rate  322 , and soot loading  324  associated with the noxidation low rate  318  are 250 degrees C., 120 grams/hour, and 60 grams, respectively. These values are taken from the current best knowledge on a 15-liter diesel engine, and can be readily determined experimentally on another system by one skilled in the art.  
         [0054]      FIG. 5  illustrates one embodiment of the relationships captured in the defined relationships module  204 . It is understood by those in the art that the exact relationships affecting reaction rates in a catalytic system are affected by dominant flow regimes, catalyst loading, mass transfer limited systems versus reaction rate limited systems, and the like. Therefore, for a given system, the relationship graphs as shown must be developed by fixing all of the relationships, and experimentally sweeping the value for which a desired relationship is required.  
         [0055]     The plurality of soot consumption ratios  502  plotted against the range of soot loading values  504 , in one embodiment, shows the soot consumption ratio to be linear with soot loading. The plurality of soot consumption ratios  506  plotted against the range of O 2  mass fraction values  508 , in one embodiment, shows the soot consumption ratio to be linear with O 2  mass fraction. The plurality of soot consumption ratios  510  plotted against the range of particulate filter temperature values  512 , in one embodiment, shows the soot consumption rate to be exponential with temperature. Table 1 lists the values indicated by the graphs of  FIG. 5  in one embodiment.  
                                                                       TABLE 1                           Example of Defined Relationship Module 204 calibration                Range of soot   Plurality of soot       Plurality of soot   Range of particulate       Soot consumption   loading values   consumption ratios   Range of O 2  mass   consumption ratios   filter temperature values       ratios 502   504   506   fraction values 508   510   512                    0.00   0   grams   0.08   0.01   0.001   300       0.17   20   grams   0.42   0.05   0.004   350       0.33   40   grams   0.67   0.08   0.016   400       0.50   60   grams   1.00   0.12   0.031   425       0.67   80   grams   1.25   0.15   0.063   450       1.00   120   grams           0.125   475       1.25   150   grams           0.25   500       1.50   180   grams           0.50   525                           1.00   550                  
 
         [0056]      FIG. 6  illustrates another embodiment of the relationships captured in the defined relationships module  204 . It is understood by those in the art that the exact relationships affecting reaction rates in a catalytic system are affected by dominant flow regimes, catalyst loading, mass transfer limited systems versus reaction rate limited systems, and the like. Therefore, for a given system, the relationship graphs as shown must be developed by fixing all of the relationships, and experimentally sweeping the value for which a desired relationship is required.  
         [0057]     The plurality of soot consumption ratios  602  plotted against the range of soot loading values  604 , in one embodiment, shows the soot consumption ratio to increase with the ¼ power of soot loading. The plurality of soot consumption ratios  606  plotted against the range of NO 2  mass flow values  608 , in one embodiment, shows the soot consumption ratio to increase with the square of NO 2  mass flow. The plurality of soot consumption ratios  610  plotted against the range of particulate filter temperature values  612 , in one embodiment, shows the soot consumption rate to resemble a bell curve with temperature. Table 2 lists the values indicated by the graphs of  FIG. 6  in one embodiment.  
                                                                       TABLE 2                           Example of Defined Relationship Module 204 calibration                Range of soot   Plurality of soot   Range of NO 2     Plurality of soot   Range of particulate       Soot consumption   loading values   consumption ratios   mass flow values   consumption ratios   filter temperature values       ratios 602   604   606   608   610   612                                        0.00   200       0   0   grams   0.08   120   0.071   225       0.193049   20   grams   0.42   240   0.143   250       0.229575   40   grams   0.67   480   0.286   275       0.254066   60   grams   1.00   960   0.857   300       0.273012   80   grams   1.25   1440   1.000   325       1   120   grams       1920   0.857   350       1.057371   150   grams       2400   0.286   375       1.106682   180   grams           0.143   400                           0.071   425                           0.00   450                  
 
         [0058]      FIG. 7  illustrates one embodiment of a condition index module  206  configured to calculate a condition index value  708  in accordance with the present invention. In one embodiment, the condition index module  206  utilizes information from the current operating conditions  210 , with the relationships defined in the defined relationship module  204  to calculate a condition index value  708 .  
         [0059]      FIG. 7A  illustrates one embodiment of a method to combine the current soot loading  706 , current O2 mass fraction  704 , and current particulate filter temperature  702 , with the various defined relationships to generate a condition index value  708 , in accordance with the present invention. In one embodiment, each operating condition and relationship is combined into an index contribution: a soot loading index contribution  710 , a mass fraction index contribution  712 , and a temperature index contribution  714 . In one embodiment, the index contributions are multiplied together in the product of all inputs  716 , to generate a condition index value  708 . In the present example, the relationships of Table 1 are used for illustration. Therefore, in one embodiment, each index contribution will be a value substantially between 0 and 1—although they need not be as indicated in Table 1—and therefore the condition index value  708  will be a value substantially between 0 and 1.  
         [0060]      FIG. 8  shows an embodiment of the final output module  208  generating a final output value  802  in accordance with the present invention. The final output module  208 , in one embodiment, is configured to take information from the boundary soot consumption rates  302 , and combine it with the condition index value  708  to generate a final output value  802 . In one embodiment, there is a low condition index value  708  associated with the oxidation low rate  306 , and a high condition index value  708  associated with the oxidation high rate  304 . In that embodiment, when the condition index value  708  is at the low value, the final output value is equal to the oxidation low rate  306 ; when the condition index value  708  is at the high value, the final output value is equal to the oxidation high rate  304 .  
         [0061]     One skilled in the art will readily be able to determine the appropriate final output value  802  for values of the condition index value  708  above the high value or below the low value, in light of this disclosure. For example, below the low index value the final output value  802  could be zero in one embodiment. Above the high index value the final output value  802  could be a linear extrapolation and yield a final output value  802  higher than the oxidation high rate  304 .  
         [0062]      FIG. 9  illustrates the operation of the final output module  208  as it is configured in one embodiment in accordance with the present invention. The axis  902  represents a soot consumption rate in units of grams per hour in one embodiment. The axis  916  represents the condition index value  708 , which is unitless in one embodiment. The condition index high value represented by  912  is associated with the oxidation high rate  304 . The condition index low value represented by  910  is associated with the oxidation low rate  306 .  
         [0063]     In one embodiment, the final output module  208  is configured to output a final output value  802  associated with a condition index value  708  along the operating line  914  whenever the condition index value  708  is between the low condition index  910  and the high condition index  912 . In one embodiment, the final output module  208  is further configured to extrapolate along operating line  906  above the high condition index  912 , and to extrapolate along operating line  908  below the low condition index  910 . In another embodiment, the final output module  208  is configured to output a final output value  802  equal to the oxidation high rate  304  whenever the condition index value  708  is higher than the high condition index  912 . In yet another embodiment, the final output module  208  is configured to output a final output value  802  of zero whenever the condition index value  708  is lower than the low condition index  910 . In another embodiment, the final output module  208  is configured to output a final output value  802  equal to the oxidation low rate  306  whenever the condition index value  708  is lower than the low condition index  910 .  
         [0064]     The schematic flow chart diagram that follows is set forth as a logical flow chart diagram. As such, the depicted order and labeled steps are indicative of one embodiment of the presented method. Other steps and methods may be conceived that are equivalent in function, logic, or effect to one or more steps, or portions thereof, of the illustrated method. Additionally, the format and symbols employed are provided to explain the logical steps of the method and are understood not to limit the scope of the method. Although various arrow types and line types may be employed in the flow chart diagram, they are understood not to limit the scope of the corresponding method. Indeed, some arrows or other connectors may be used to indicate only the logical flow of the method. For instance, an arrow may indicate a waiting or monitoring period of unspecified duration between enumerated steps of the depicted method. Additionally, the order in which a particular method occurs may or may not strictly adhere to the order of the corresponding steps shown.  
         [0065]      FIG. 10  illustrates one embodiment of a method  1000  of estimating the current soot consumption rate in the particulate filter  150 . The method starts at  1002 , and in one embodiment proceeds to store boundary soot consumption rates  1004 . Step  1004  occurs only one time during a calibration event, and it need not be executed again. The method continues to the store relationship information step  1006  in one embodiment. In one embodiment, the store relationship information step  1006  occurs only one time during a calibration event, and it need not be executed again. Step  1008  begins what is, in one embodiment, the main execution loop. Step  1008  is a survey of the current conditions, which as previously indicated may be reading values from sensors, datalinks, control modules, performing calculations, and the like. The method proceeds to the determine condition index value step  1010  in one embodiment. In one embodiment, the method then proceeds to produce a final output value of soot consumption rate  1012 .  
         [0066]     In one embodiment, the method will execute a loop until given an indication that operations should cease, as checked in step  1014 . One potential indicator that operations should cease might be the beginning of an engine shutdown procedure after a vehicle operator turns off the key switch. If the method is to continue operation, the controller  200  proceeds back to step  1008  in one embodiment. If there were a calculation of new relationship information or new boundary soot consumption rates in a given embodiment, the method would cycle back to step  1006  or  1004  to store the new relationship. When the decision in step  1014  to continue operation indicates that operations should cease, the method proceeds to  1016  and ends.  
         [0067]      FIG. 11  illustrates the best method of calibrating the oxidation high rate value in one embodiment. The vertical axis represents soot loading  1150  on the particulate filter. The horizontal axis represents the observed regeneration time  1160 . This graph is used as follows: 1) load up a particulate filter with a known amount of soot, 2) set the regeneration conditions at fixed values—in one embodiment this is a fixed temperature and oxygen mass fraction, 3) perform the regeneration until the design soot loading end point is reached. On the graph, this procedure will begin at the operating point  1108 , which is time zero, and a soot loading of the value at the point  1100 . On the graph, this procedure will end at the operating point  1110 , which is a finite time equal to the time value  1106 , and a soot loading equal to the value at  1102 .  
         [0068]     If the suggested correction from  FIG. 11  were not applied, the apparent operating curve for this regeneration would be  1114 —i.e. simply a line drawn through the starting and ending operating points. However, because the decrease in soot loading as the regeneration proceeds decreases the rate of soot consumption, the true operating curve is actually curve  1112 . The desired oxidation high rate is the slope of the line  1116  rather than the slope of the line  1114 . If all parameters except the soot loading have been held constant, the slope  1116  can be derived mathematically if the soot loading to soot consumption rate relationship is known, and this derivation is within the ordinary skill of one in the art in light of this disclosure. To enhance understanding, the equation for the corrected slope  1116  relative to the uncorrected slope  1114  is given for the case where the soot loading relationship is linear, like the embodiment shown in Table 1. The values in Equation 1 are taken from  FIG. 11 —i.e. the point  1100  is the beginning soot loading as used in the equation, the point  1102  is the ending soot loading, and the time point  1106  is the observed regeneration time.  
               CorrectedRate   ⁡     (     g   ⁢     /     ⁢   hr     )       =               (     1100   -   1102     )     /               [           ⁢     (       (       ln   ⁢     (   1100   )       -     ln   ⁢     (   1102   )         )     *     (     1100   /   1106     )         ]             (     1102   -   1100     )               Equation   ⁢           ⁢   1             
 
         [0069]     The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.