Patent Publication Number: US-10310497-B2

Title: Equipment condition and performance monitoring using comprehensive process model based upon mass and energy conservation

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of U.S. patent application Ser. No. 12/904,009, filed Oct. 13, 2010, which is a continuation of U.S. patent application Ser. No. 10/305,657, filed Nov. 26, 2002, now abandoned, which claims priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application No. 60/338,052, filed Nov. 30, 2001, each of which is incorporated by reference herein in its entirety. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to the field of equipment condition and process performance monitoring and, in particular, to systems and methods for monitoring such condition and performance using data reconciliation techniques predicated upon mass and energy conservation. 
     BACKGROUND OF THE INVENTION 
     Complex industrial systems such as, for example, power generation systems and chemical, pharmaceutical and refining processing systems, have experienced a need to operate ever more efficiently in order to remain competitive. This need has resulted in the development and deployment of process modeling systems. These modeling systems are used to construct a process model, or flowsheet, of an entire processing plant using equipment or component models provided by the modeling system. These process models are used to design and evaluate new processes, redesign and retrofit existing process plants, and optimize the operation of existing process plants. 
     Existing flowsheet modeling techniques have been directed to discrete units of plant equipment, rather than to entire plant processes. In certain approaches the operation of individual items of plant equipment predicted by a flowsheet model is attempted to be reconciled with measurements of the equipment&#39;s actual operation. Data relating to such actual operation is typically acquired by flow sensors and the like positioned on or near the item of equipment. Such flow sensors vary in their accuracy depending on the material in the stream being monitored, the condition of the stream, and the specific sensing technology employed within the flow sensor. Moreover, the performance of flow sensors may be degraded by obstructions, wear or outright failure. The attendant inaccuracies in the operational data produced by the flow sensors may corrupt the reconciliation of such data with the equipment performance predicted by the flowsheet model, thereby resulting in undesirable erroneous predictions or process control adjustments. 
     The data reconciliation process often involves minimization of the sum of squared errors between predicted and measured operational parameters. However, the relative accuracy of the sensors used in deriving the error terms is generally not taken into account, which tends to introduce inaccuracies into the reconciliation process. That is, a sensor whose behavior changes due to failure or deterioration may cause incorrect adjusted estimates to be attributed to related sensors during the reconciliation process. Since conventional flowsheet models are not predicated upon operation of entire plant processes, it can be difficult to gauge when predicted operation of individual equipment is inconsistent with realistic operation of an overall process. 
     Equipment condition has also been attempted to be monitored using flowsheet models directed to individual units of equipment. However, it is generally difficult to determine whether a change in output or other monitored parameter of an individual unit of equipment is properly attributed to a change in the equipment itself or to a change in the applicable process “upstream” of the equipment unit. 
     In the field of power generation systems, this limitation of existing modeling techniques has proven to be particularly undesirable as concerns with deregulation and operational costs have resulted in efforts to improve system reliability and performance. As is well known, the Rankine cycle power plant, which typically utilizes water as the processed fluid, has been pervasive in the power generation industry for many years. In a Rankine cycle power plant, electrical energy is derived from heat energy through the heating of the processed fluid as it travels through tubular walls and thereby forms a vapor. The vapor is generally superheated to form a high pressure vapor, which is input to a turbine generator to produce electricity. 
     Other improvements in the efficiency of Rankine cycle power systems have been achieved through technological enhancements, which have enabled the temperatures and pressures of processed fluids to be increased. When reconciliation techniques such as those described above are employed to monitor the performance of such power systems, such techniques are often applied to individual units of equipment or indicia of performance (e.g., turbine efficiency). A dramatic change in such indicia signals that the applicable unit(s) of equipment may be not be operating properly. Again, however, such approaches are premised upon models of only subsets of the equipment utilized in the overall power generation process, and thus are not subject to the constraints which could be imposed upon the Rankine cycle of the process. This makes such approaches inherently uncertain, because it will not be known whether changes in monitored parameters of isolated equipment units are due to equipment degradation or to changes in upstream conditions. 
     SUMMARY OF THE INVENTION 
     In general, the present invention relates to a method and apparatus capable of monitoring performance of a process and of the condition of equipment units effecting such process. A process model predicated upon mass and energy balancing is developed on the basis of a plurality of generally nonlinear models of the equipment units. At least one or more of such equipment models are characterized by one or more adjustable maintenance parameters. As is described below, data relating to mass and energy transfer within the process is collected and is reconciled with the mass and energy characteristics of the process predicted by the model. In accordance with one aspect of the invention, the condition of the equipment units and process performance may be inferred by monitoring the values of the maintenance parameters over successive data reconciliation operations. 
     In a particular aspect the present invention relates to a method for monitoring the condition of a plurality of units of equipment used to effect a process involving one or more resource flows of mass and energy. The method includes measuring one or more quantities related to the resource flows (e.g., temperature, pressure, flow rate) in order to generate respective first and second measured resource flows. A model of the process is formulated so as to include a plurality of generally nonlinear equipment models corresponding to the plurality of units of equipment, wherein at least a first of the nonlinear equipment models includes a first maintenance parameter. A value of at least the first maintenance parameter is adjusted such that predictions of the flow rates are reconciled with the first and second measured resource flows. In addition, changes in the value of the first maintenance parameter are adjusted over time in order to enable detection of changes in the condition of at least one of the plurality of units of equipment. 
     In another aspect, the present invention relates to a method of processing signals representative of a process effected by one or more equipment units in operative communication through one or more resource flows. The method includes measuring flow rates of at least first and second of the resource flows in order to generate respective first and second measured resource flow signals. A model of the process is formulated based upon conservation of a process parameter characterizing the first and second resource flows, wherein the model includes at least a first maintenance parameter. The method further contemplates adjusting a first value of the first measured resource flow signal, a second value of the second measured resource flow signal, and the first maintenance parameter such that the process parameter is conserved consistent with the model. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a better understanding of the nature of the features of the invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  illustratively represents the network architecture of a system within which one embodiment of the present invention may be incorporated. 
         FIG. 2  illustrates an architecture of a client unit which may be used with an exemplary embodiment of the present invention. 
         FIG. 3  is a block diagram representative of the internal architecture of a server unit operative in accordance with the present invention. 
         FIG. 4  further illustrates certain additional components comprising a modeling engine of a simulation module. 
         FIG. 5  further illustrates one embodiment of the interaction between the modeling engine and a solution engine of the simulation module. 
         FIGS. 6A, 6B, and 7-9  illustratively represent a mathematical basis for a data reconciliation operation performed in accordance with one aspect of the present invention. 
         FIG. 10  depicts a relationship of the data reconciliation module to other system functionality within a general process control system. 
         FIG. 11  provides a high-level illustrative representation of the operation of a simulation module. 
         FIG. 12  provides a high-level illustrative representation of the operation of an optimization module. 
         FIG. 13  illustratively represent one manner in which instrument errors and component degradation may be identified in accordance with the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  illustratively represents the network architecture of a system  100  within which one embodiment of the present invention may be incorporated. The system operates on a process  101 , which may comprise any process including, without limitation, chemical processes, energy processes and distribution processes. In the case of a process  101  geared toward power generation, the math model will preferably reflect the Rankine cycle of the power generation operation. In implementations involving chemical and other processes, the material in the process can be treated as a fluid that is moved within the process in streams. A process is normally made up of more than one unit of equipment, where each unit carries out some specific processing function, such as reaction, distillation, or heat exchange. Equipment units are interconnected and/or in fluid communication via streams. A plurality of plant sensors  107  are selected and configured to measure values of the regulatory variables applicable to the equipment units used to perform the process  101 . These regulatory variables, e.g., pressure, temperature, level, and flow, are controlled to maintain process equipment operating at a designated stationary state. These variables may also be adjusted by the operator to move the process equipment to another stationary state (e.g., to increase production). 
     As is described below, in one aspect the method of the present invention contemplates reconciling predicted operation of an entire plant process and data measured by plant sensors  107 . In this regard the inventive method forces reconciliation of such measured plant data and predicted operational data derived from a comprehensive model of the entire plant process based upon generally nonlinear models of individual units of equipment. Each such nonlinear model is characterized by one or more parameters, some or all of which are designated as maintenance parameters. The maintenance parameters associated with the model of a particular unit of equipment will generally be selected so as to be reflective of the “health” or operational soundness of the equipment unit. For example, one of the maintenance parameters for a heat-exchanger could be a heat transfer coefficient while one of the maintenance parameters for a pump could be a pump curve scaling factor. 
     In an exemplary embodiment reconciliation between the plant operation predicted by the comprehensive plant model and the measured plant data is effected so as to establish an overall mass and energy balance. This approach is believed to be different from prior techniques, which have tended to be confined to optimization of discrete portions of an overall plant process without regard to maintenance of overall mass and energy balance. In an exemplary embodiment, the result of the reconciliation process of the present invention transforms the signals generated by the plant sensors into corrected measurement signals and adjusts the values of maintenance parameters within predefined ranges based upon estimated equipment variances. 
     Such simultaneous modification of both measured values and maintenance parameters over an entire process is believed to represent a significant departure from prior reconciliation techniques. 
     It has also been found that the changes in maintenance parameters across successive reconciliation operations may provide an indication of the condition of the equipment unit with which the maintenance parameter is associated. Such monitoring of maintenance parameters over time is believed to represent a novel approach to gauging equipment condition. This approach is facilitated by utilization of a comprehensive plant model comprised of a set of generally nonlinear models of individual equipment models. Prior modeling techniques involving only a portion of a plant process would not enable meaningful information to be gleaned from such monitoring of maintenance parameters over time, since it would be unclear as to whether changes in the monitored maintenance parameters were due to deterioration in equipment condition or to changes in upstream process conditions. 
     The system  100  may include a local area network (LAN)  102  that is connectable to other networks  104 , including other LANs or portions of the Internet or an intranet, through a router  106  or similar mechanism. One example of such a LAN  102  may be a process control network to which process control devices, such as process controller  114 , and plant sensors  107  are connected. Process control networks are well known in the art and are used to automate industrial tasks. The network  104  may be a corporate computing network, including possible access to the Internet, to which other computers and computing devices physically removed from the process  101  are connected. In one embodiment, the LANs  102 ,  104  conform to Transmission Control Protocol/Internet Protocol (TCP/IP) and Common Object Request Broker Architecture (COBRA) industry standards. In alternative embodiments, the LANs  102 ,  104  may conform to other network standards, including, but not limited to, the International Standards Organization&#39;s Open Systems Interconnection, IBM&#39;s SNA®, Novell&#39;s Netware®, and Banyon VINES®. 
     The system  100  includes a server  108  that is connected by network signal lines to one or more clients  112 . In an exemplary embodiment the server  108  includes a UNIX or Windows NT-based operating system. The server  108  and clients  112  may be uniprocessor or multiprocessor machines, and may otherwise be configured in a wide variety of ways to operate consistent with the teachings of the present invention. The server  108  and clients  112  each include an addressable storage medium such as random access memory and may further include a nonvolatile storage medium such as a magnetic or an optical disk. 
     The system  100  also includes a storage medium  110  that is connected to the process control network  102  or corporate control network  104 . In the exemplary embodiment the storage medium  110  may be configured as a database from which data can be both stored and retrieved. The storage medium  110  is accessible by devices, such as servers, clients, process controllers, and the like, connected to the process control network  102  or the corporate control network  104 . 
     Suitable servers  108  and clients  112  include, without limitation, personal computers, laptops, and workstations. The signal lines may include twisted pair, coaxial, telephone lines, optical fiber cables, modulated AC power lines, satellites, and other data transmission media known to those of skill in the art. A given computer may function both as a server  108  and as a client  112 . Alternatively, the server  108  may be connected to the other network  104  different from the LAN  102 . Although particular computer systems and network components are shown, those of skill in the art will appreciate that the present invention also works with a variety of other networks and components. 
       FIG. 2  illustrates an architecture of the client  112  which may be used with one preferred embodiment of the present invention. The client  112  provides access to the functionality provided by the server  108 . The client  112  includes a GUI  202  and an optional module interface  204 . The Graphical User Interface (GUI)  202  is used to build and specify model applications. One embodiment of the GUI  202  incorporates user interface features such as tree views, drag-and-drop functionality, and tabbed windows to enhance the intuitiveness and usability of the interface. The GUI  202  further enables access to other encapsulated GUIs such as process unit GUIs, non-process unit GUIs, and stream GUIs as described below. 
     Access to the GUI  202 , as well as other architectural objects to be discussed in detail below, are through the optional module interface  204 . In one embodiment, the module interface  204  is the Interface Definition Language (IDL) as specified in the CORBA/IIOP  2 . 2  specification. In one embodiment, the module interface  204  provides a uniform interface to the architectural objects, such as the GUI  202 . The module interface  204  allows the actual implementation of the architectural objects, such as the GUI  202 , to be independent of the surrounding architecture, such as the operating system and network technology. One of ordinary skill in the art will recognize that the module interface  204  may conform to other standards, or even be non-existent. 
       FIG. 3  is a block diagram representative of the internal architecture of the server  108 , which may be physically implemented using a standard configuration of hardware elements. As shown, the server  108  includes a CPU  330 , a memory  334 , and a network interface  338  operatively connected to the LAN  102 . The memory  334  stores a standard communication program (not shown) to realize standard network communications via the LAN  102 . The memory  334  further stores a solver  302  accessible by a modeling engine  304  through an access mechanism  306 , and a modeling engine framework  308 . The solver, modeling engine  304 , and modeling engine framework  308  collectively comprise a simulation module  340 , the operation of which is further described below. The optional module interface  204  provides uniform access to, and implementation independence and modularity for both the modeling engine  304  and the modeling engine framework  308 . As is discussed below, the memory  334  also stores a data reconciliation module  350  containing a set of computer programs which, when executed, effect certain mass and energy balance reconciliation processes of the present invention. 
     The modeling engine  304  provides an environment for building and solving process models. The solver  302  provides a solution algorithm for solving a process model generated by the underlying modeling engine  304 . In one embodiment, the solver  302  may contain one or more solution engines  310  which are used in solving different process models. For example, one solver that may be used is Opera, a solver available from the Simulation Sciences unit of Invensys Systems, Inc. as part of the ROMeo System. In one embodiment, the solver  302  comprises a solution engine  310  implemented as a generalized matrix solver utilizing a Harwell subroutines. As is well known in the art, the Harwell library is an application independent library of mathematical subroutines used in solving complex mathematical equation sets. In one embodiment, the access mechanism  306  is specific to the solution engine  310  contained in the solver  302  and the modeling engine  304  used in generating the math model. 
     The modeling engine framework  308  is an interpretive layer providing user-friendly access to the modeling engine  304 . In one embodiment, the modeling engine framework  308 , working in conjunction with the GUI  202 , provides a user the ability to add new unit models, modify existing unit models, and generally interact with the modeling engine  304  without having to know the specifics of the modeling engine  304 . 
       FIG. 4  further illustrates certain additional components comprising the modeling engine  304  in one preferred embodiment. The modeling engine  304  comprises model elements  402 , a flowsheet manager  404 , and an event handler  406 . The model elements  402  include individual units and streams from which a user builds a flowsheet model. For example, a pump is a unit that the user may include in a flowsheet model. 
     A unit represents a device that may be found in a process plant. The unit may be a process or an on-process unit. A process unit is an item of operating hardware such as a heat exchanger, a compressor, an expander, a firebox, a pipe, a splitter, a pump, and the like. As mentioned above, each unit is represented by a generally nonlinear model characterized by one or more parameters. Each parameter of a given model will typically pertain to mass or energy transfer characteristics of the equipment unit represented by the model. Some or all of these parameters may be considered maintenance parameters, and will generally be considered as such to the extent that monitoring the changes in their respective values over time may enable inference of the condition of the applicable unit of equipment. 
     A non-process unit is something other than an item of operating hardware. For example, a non-process unit may be a penalty. A penalty unit assigns a progressively increasing weight to a measured output temperature value beyond the optimum output temperature. For example, the penalty unit may account for the increased cleanup costs associated with operating the furnace at a higher than optimum output temperature. Another example of a non-process unit may be a measurement from measuring devices such as flow meters, thermocouples, and pressure gauges. 
     In one embodiment, each unit typically has one or more entry or exit ports and is associated with a model. The model is a collection of variables and equations, collectively known as a calculation block. A unit model represents the operation of the unit in terms of its associated calculation block. As an example, an equation for a measurement unit may be:
 
ModelVariable−Scan−Offset==0
 
where ModelVariable is a calculated value, Scan is a measured value, and Offset is the difference between ModelVariable and Scan. The above equation contains three variables: ModelVariable, Scan and Offset.
 
     As another example, the equations for a pump unit may be:
 
PresRise−Product:Pres+Feed:Pres==0, and
 
Head*GravConst*Feed:Prop[“WtDens”]1000*PresRise==0
 
where PresRise is a rise in pressure, Product:Pres is an output pressure, Feed:Pres is an input pressure, Head is a liquid height within a tank connected to the pump, GravConst is the gravity constant, Feed:Prop[“WtDens”] is a weight density of the liquid in the tank, and the PresRise is a rise in pressure of the pump. In the first equation, PresRise, Prod:Pres, and Feed:Pres are variables. In the second equation, Head, Feed:Prop[“WtDens”], and PresRise are variables. GravConst is a parameter, and thus requires a value to be assigned before the equation may be solved.
 
     A stream is used to connect a unit&#39;s entry or exit port to another unit&#39;s exit or entry port respectively. Furthermore, a feed stream is connected to the unit&#39;s entry port, whereas a product stream is connected to the unit&#39;s exit port. A stream model may have associated equations and variables. For example, a simplified stream model may be represented as follows:
 
 y=ax+b  
 
where “y” is a measurement that is allowed to assume values within a predefined range, and “x”, “a” and “b” are parameters representative of equipment condition (i.e., “a” and “b” will generally change over time due to equipment wear), and “x” is a calculated value. During the reconciliation operation, the values of “y”, “a” and “b” and similar values within all other equipment models of the applicable process are allowed to change until the overall process model reflects that mass and energy balance has been achieved throughout the process.
 
     In one exemplary embodiment, multi-dimensional data structures are used to store individual units and streams, and their associated variables and equations. The data structures may also store other information such as, but not limited to, the type of unit or stream, whether a variable requires a user-provided value, the variable&#39;s lower bound, upper bound, solution value, or status. One of ordinary skill in the art will recognize that the data structures may be in the form of an array, linked list, or as elements within other data structures. 
     The flowsheet manager  404  provides access to instances of unit models, stream models, and other information associated with a flowsheet model. In one embodiment, the information associated with a flowsheet model may be stored in the storage medium  110 . Preferably, the storage medium  110  stores at least one flowsheet model, including an equation, of an actual plant process. The flowsheet manager  404  may then communicate with the storage medium  110  to provide a user access to the information contained in the storage medium  110  in a manageable format. Further details regarding creation, modification and alteration of flowsheet models are provided in, for example, copending U.S. patent application Ser. No. 09/193,414, filed Nov. 17, 1998 and entitled INTERACTIVE PROCESS MODELING SYSTEM; U.S. Pat. No. 6,442,515, which is entitled PROCESS MODEL GENERATION INDEPENDENT OF APPLICATION MODE; and U.S. Pat. No. 6,323,882, which is entitled METHOD AND SYSTEMS FOR A GRAPHICAL REAL TIME FLOW TASK SCHEDULER, each of which is hereby incorporated by reference in its entirety. 
       FIG. 5  further illustrates one embodiment of the interaction between the modeling engine  304  and the solution engine  310  of the simulation module  340 . As is described in the above copending patent applications, the modeling engine  304  additionally comprises a model generator  502 , a residual generator  504 , and a derivative generator  506 . The modeling engine  304  provides the open form of model equations to the solution engine  310 . The solution engine  310 , in turn, solves the equations. In an alternative embodiment, a closed form of the model equations may be provided by the modeling engine  304 . 
     The model generator  502  creates a math model of the flowsheet for input to the solution engine  310 . In the exemplary embodiment, the math model is a large set of equations and variables that comprehensively models the entire process  101 . The math model will typically be in the form of a matrix which represents the equations contained in the flowsheet model in the form f(x)=0. Standard equations and variables associated with a corresponding unit model or stream model are provided in a previously compiled standard library  508 . The equations may comprise mass, material, equilibrium, thermodynamic, and physical property related equations applicable to the process  101  in its entirety. 
     As is described below, the data reconciliation module  350  uses the math model and measurements from the sensors  107  in computing reconciled model parameters and sensor measurements capable of being used to effect closed loop control of the process  101 . This computation is effected by adjusting (within the range of sensor accuracy) the measurements from the sensors  107  and the parameters of the math model until a solution is determined. 
     Again, in the exemplary embodiment the math model reflects mass and energy balance throughout the process  101  in its entirety; that is, the math model takes into account substantially all of the mass and energy associated with the process  101 . This is effected in part by specifying the input and output relationships with respect to mass and energy for each equipment model. In addition, equality constraints are applied as appropriate to those models representative of equipment units between which mass/energy is transferred. As a consequence, the data reconciliation module  1022  operates upon a set of equations which characterize mass and energy flow for the entire process  101 . This differs from conventional approaches, in which mass and/or energy balance is computed on only a localized basis. 
     The exemplary embodiment also contemplates that the accuracy of every sensor  101  used to measure parameters associated with the process  101  is characterized. This characterization generally involves determining the variance of each sensor  107 , which reflects the range over which the value of the variable measured by the sensor  107  can vary during the reconciliation process and still be consistent with expected calibration accuracy. Determination of the variance of each sensor  107  thus facilitates identification faulty or malfunctioning sensors, since an adjustment in the value of the sensor during the reconciliation process outside of such variance indicates that the sensor has been providing an erroneous measurement value. Similarly, variances are ascribed to one or more parameters associated with each model element  402  representative of a unit of equipment or characteristic of the process  101 . If adjustments made to such parameters during the reconciliation process result in ostensible operation of a unit of equipment outside of an expected range, then there exists a substantial likelihood of significant equipment degradation or malfunction. The present invention thus advantageously facilitates identification of faulty or inoperative units of equipment contributing to operation of the process  101 . 
       FIGS. 6A, 6B, and 7-9  provide an illustrative representation of a mathematical basis for a data reconciliation process effected in accordance with the present invention. Turning to  FIG. 6A , there is shown a simplified flow system  600  having an input flow stream  602  designated as relating in what follows to a mathematical variable X 3 . As shown, the simplified flow system  600  includes first and second output flow streams  604  and  608  designated as relating to the mathematical variables X 1  and X 2 , respectively. The discussion below is intended to elucidate a number of mathematical concepts underlying various features of the present invention. 
     Although the flow streams represented by  FIG. 6B  will often be associated with mass or matter in ‘bulk’, the streams could also be representative of a thermodynamic quantity (e.g., energy) or a specific component of a material being processed. As shown, the first flow stream  602  is separated into the second and third flow streams  604  and  608  at a process node. Depending upon the context of the flow system  600 , the node may correspond to various physical realizations (e.g., a three-way connector). Although the node may operate to maintain a substantially constant rate of flow, in a more complex arrangement the node may be representative of an overall process effected by a plurality of components. In the latter case, the sum of the flows of the output flow streams  604  and  608  may not equilibrate with the flow of the input flow stream as frequently as in simpler manifestations of the node. 
     In the case when the node is implemented straightforwardly to partition the input flow stream  602 , conservation of mass requires that
 
 X   1   +X   2   −X   3 =0  Equation (1)
 
In order to account for the possibility of a nonlinear relationship between the input flow stream  602  and the output flow streams  604  and  608 , the output flow streams  604  and  608  may be expressed as function of parameters P 1  and P 2  as follows:
 
 X   1   =F 1( P 1, X   3 )  Equation (2)
 
 X   2   =F 2( P 2, X   3 )  Equation (3)
 
In equations (2) and (3) the functions F 1  and F 2  could, for example, represent valve curves dependent upon the parameters P 1  and P 2 .
 
     Referring again to Equation (1), when actual measured values X′ 1 , X′ 2 , and X′ 3  of the three flows X 1 , X 2 , and X 3  are utilized it is likely that mass will not be conserved and Equation (1) will not be satisfied. In geometric terms, the measurements X′ 1 , X′ 2 , and X′ 3  may be considered to define a point in space while equation (1) may be viewed as defining a planar surface. That is, all sets of flows X 1 , X 2 , and X 3  in the plane satisfy equation (1). Any given set of measured flows values X′ 1 , X′ 2 , and X′ 3  will generally not conserve mass, and hence will generally spatially correspond to a point outside of the plane. 
     Turning now to  FIG. 7 , the process of data reconciliation in accordance with the present invention is illustratively represented in geometric terms. As shown, a point P N  defined by a measured set of flows X′ 1 , X′ 2 , and X′ 3  is translated from a location out of a plane P of flow values X 1 , X 2 , and X 3  satisfying equation (1). Although in the context of  FIG. 7  this translation is effected by simply adjusting the parameters the values of the measured flows X′ 1 , X′ 2 , and X′ 3 , in an exemplary embodiment both the parameters P 1  and P 2  of Equations (2) and (3) and the values of the measured flows X′ 1 , X′ 2 , and X′ 3  are adjusted in order to move the point P N  into the plane P. Once point P N  has been translated onto the plane P, it may be characterized as having been reconciled (i.e., the measured values X′ 1 , X′ 2 , and X′ 3  and parameters P 1  and P 2  have been modified to the extent necessary to satisfy Equations (1)-(3)). Mathematically, this reconciliation process may be equivalently represented as the determination of an offset reconciliation vector V 1  and its addition to the vector extending between the origin and the point P N . 
       FIG. 8  represents the manner in which a set of measured flow values may be reconciled either through a least squares minimization process in which both the parameters P 1  and P 2  and measured flow values are themselves adjusted. As shown, at a time t 1  a set of reconciled flows may exist which define a point P R, t1  on the plane P of flow values satisfying equation (1). At a subsequent point in time (t 2 ), a set of measured flows X′ 1, t2 , X′ 2, t2 , and X′ 3, t2  are seen to define a point P M, t2  off of the plane P. In accordance with the invention, the values of the parameters P 1  and P 2  and the values of the measured flows X′ 1, t2 , X′ 2, t2 , and X′ 3, t2  are each modified to the extent of the uncertainty inhering in each such value until the point P M, t2  is “translated” to the plane P. This reconciliation may be effected in accordance with the least-squares expression of equation (4), which in the exemplary implementation is minimized through perturbation of both measured values X′ and model parameters: 
                       Min             Tuning   ⁢           ⁢   Parameters     ⁢           &amp;               Measured   ⁢           ⁢   Values             ⁢          Offset        2       =                  X   ′     _     -     x   _            2     =         1     σ   1   2       ⁢       (       X   1   ′     -     x   1       )     2       +       1     σ   2   2       ⁢     (       X   2   ′     -     x   2       )       +       1     σ   3   2       ⁢       (       X   3   ′     -     x   3       )     2                   Equation   ⁢           ⁢     (   4   )                 
where the weighting factor, a, present in Equation (4) takes into account both the uncertainty and inaccuracy in the measured values X′ of the sensors  107  and in the parameters (i.e., P 1 , P 2  of Equations (2) and (3)) associated with the model elements  402 . In particular, uncertainty in the readings from the sensors affects the value of X′ within each offset term, while uncertainty in the values of the parameters affects the value of x within each offset term. The least squares objective function illustrated of Equation (4) is formulated such that each individual offset (i.e., (X′ 1 −x 1 ) 2 , (X′ 2 −x 2 ) 2 , (X′ 3 −x 3 ) 2 ) is multiplied by the reciprocal of the standard deviation (or variance) obtained during steady state conditions from a historical set of data for the relevant measured data value. The approach exemplified by Equation (4) aids in reducing the predictable noise effects introduced by the uncertainty and/or inaccuracy inherent with the sensors  107  or equipment maintenance parameters.
 
     In the exemplary embodiment, Equation (4) is solved under conditions of “steady state” operation. “Steady state operation” essentially corresponds to the case where (1) a process is substantially regular and uniform in its operation over a given time interval, (2) momentum, mass, and energy entities flowing into the process are substantially equal to the momentum, mass, and energy entities flowing out of the process, and (3) momentum, mass, and energy do not otherwise accumulate within the process unless stipulated by the relevant equipment model. 
       FIG. 9  illustratively represents a process of successive reconciliation in accordance with the present invention. As shown, at a time t 0  a set of reconciled flows (x 1 , x 2 , x 3 ) may exist which define a point P R, t0  on a plane P 1  of flow values satisfying equation (1). That is,
 
 x   1   +x   2   −x   3   Equation (5)
 
where,
 
 x   1   =F 1( p   1 )  Equation (6)
 
 x   2   =F 1( p   2 )  Equation (7)
 
 x   3   =F 1( p   3 )  Equation (8)
 
At a subsequent point in time (t 1 ), a set of measured flows X′ 1, t1 , X′ 2, t1 , and X′ 3, t1  are seen to define a point P M, t1  off of the plane P 1 . Consistent with the invention, the values of the parameters p 1 , p 2  and p 3 , as well as the values of the measured flows X′ 1, t1 , X′ 2, t1 , and X′ 3, t21  are modified by the simulation module  340  to the extent of their respective uncertainties until the point P M, t1  defines a point (P R, t1 ) on the plane P 1 . As noted above, this reconciliation may be effected in accordance with the least-squares expression of equation (4). As a consequence of this reconciliation, the model parameters p 1 , p 2  and p 3  are incremented by the quantities dp 1 , dp 2  and dp 3 , respectively, thereby yielding modified model parameters as of time t 1 :
 
 p′   1   =p   1   +dp   1  
 
 p′   2   =p   2   +dp   2  
 
 p′   3   =p   3   +dp   3  
 
As shown in  FIG. 9 , at later point in time (t 2 ) a set of measured flows X′ 1, t2 , X′ 2, t2 , and X′ 3, t2  are seen to define a point P M, t2  off of the plane P 1 . The values of the parameters p′ 1 , p′ 2  and p′ 3 , as well as the values of the measured flows X′ 1, t2 , X′ 2, t2 , and X′ 3, t22  are then modified by the simulation module  340  as described above until the point P M, t2  defines a point (P R, t2 ) on the plane P 1 .
 
     In accordance with one aspect of the invention, the behavior of the parameters p 1 , p 2 , and p 3  over time (e.g., days and months) can be monitored in order to detect equipment wear and enable anticipation of probable equipment failure. In particular, certain equipment parameters are identified as maintenance parameters and set as “free variables” to be monitored over time. The observed changes in these maintenance parameters may then provide an indication of equipment deterioration or imminent failure. In general, the maintenance parameters will be selected from among those equipment model parameters indicative of the capability of a given equipment unit to conduct mass and energy as intended. Significant changes in the values of such parameters as a result of the reconciliation process will generally be indicative of an adverse change in the state of the applicable equipment. 
       FIG. 10  depicts the relationship of the data reconciliation module  1022  to other system functionality within a general process control system  1000 . In specific embodiments the control system  1000  may be utilized in the control of, for example, power generation processes, chemical processes, refineries and transportation systems. The material operated upon by the process can often be treated as a fluid, which are moved within the process in streams. A process is typically comprised of multiple elements connected by way of streams. Each element effects a certain function (e.g., reaction, distillation, or heat exchange). 
     Referring to  FIG. 10 , the data reconciliation module  1022  operates together in a system  1000  with a set of regulation devices  1004  under the control of the process controller  114 . The regulation devices  1004  and the process controller  114  collectively control equipment-related variables such as pressure, temperature, level, and flow (commonly known as “PTLF” variables) in order to maintain the process  101  in a certain desired state. In particular, the regulation devices  1004  respond to output signals from the process controller  114  to produce an accordingly predetermined operation representing the strength of the output signal. Both the process controller  114  and PTLF-based regulation devices  1004  are familiar to those skilled in the art. The values of various PTLF variables may be adjusted in an operator setpoint adjustment operation  1010  in order to move the equipment involved in the process  101  to another stationary state. 
     In the controlled system  1000  of  FIG. 10 , various aspects of the process  101  are monitored by the sensors  107 . To this end, the sensors  107  produce output signals representative of the values of various PTLF or other characteristics of the process  101 . The output signals from the sensors  107  correspond to process variables operated upon by the system  1000 . Based upon these output signals, a steady state detection operation  1014  determines when the process  101  enters a steady state condition (described above). Once a steady-state condition has been achieved, the raw sensor output signals are screened against the upper and lower limits defining predefined acceptable ranges in a screen measurements operation  1018 . In a particular implementation default values may be substituted for those raw sensor signals discarded during the screen measurements operation  1018 . The remaining sensor output signals, and any substituted default signals, are then processed in the data reconciliation module  1022 . 
     The data reconciliation module  1022  utilizes the sensor signals from the screen measurements module  1018  and predicted process data provided by the simulation module  340  in creating reconciled measurement signals for utilization during a subsequent optimization operation  1026 . The predicted operational data (e.g., pressure, level, temperature, and flow) created by the simulation module  340  is generated by the solver  302  on the basis of the model of the process  101  established by the modeling engine  304 . Prior to performing the optimization operation  1026 , the reconciled measurement data generated by the reconciliation module  1022  is communicated to a constraint projection module  1030 . The reconciliation operation effected by the reconciliation module  1022  results in creation of an improved set of process measurement data for use during the optimization operation  1026 , thereby reducing the likelihood of inappropriate control of the process  101 . 
       FIG. 11  provides a high-level illustrative representation of the operation of the simulation module  340 . As is illustrated by  FIG. 11 , the simulation module  340  may also be utilized to simulate the state of the process  101  in response to varying load conditions and setpoints of the regulation devices  1004 . As mentioned above, in the exemplary embodiment the data reconciliation module  1022  provides updated model parameters and data to the simulation module  340  at the conclusion of each data reconciliation operation (step  1102  of  FIG. 11 ). This is done in order to cause the simulation model  340  to more accurately predict the characteristics of the process  101  measured by the sensors  107 . Periodic calibration of the model parameters (step  1106 ) compensates for changes in the behavior of the process  101  relative to the simulated operation computed by the simulation module  340 . This enables the simulation results produced by the simulation model  340  to be refined as its model parameters are periodically adjusted in connection with each iteration of the data reconciliation module  1022 . Various “what if” scenarios may then be investigated by adjusting parameters (e.g., ambient conditions, set-point, and process load) associated with the simulation model  340  (step  1110 ). In particular, simulated data under these new ambient conditions and/or set points is then produced by the simulation model  340  and may be reported to operators of the process  101  (step  1114 ). 
     Referring again to  FIG. 10 , the reconciled process measurement data is processed during the optimization operation  1026  upon being furnished by the constraint projection module  1030 . In the exemplary embodiment the optimization operation  1026  is also comprised of the modeling engine  304  and the solver  302 . That is, the mass and energy balance equations incorporated within the modeling engine  304  may also be used for optimization after undergoing the reconciliation effected by the data reconciliation module  1022 . 
       FIG. 12  provides a high-level illustrative representation of an exemplary optimization operation  1026 . In a step  1202 , the variables of the applicable mass and energy balance equations are initialized with values generated during a prior iteration of the simulation module  340 . A cost-based objective function is then formulated in which certain of these variables of interest are set to an independent state (step  1206 ). The independent variables are then incremented until the cost-based objective function is minimized (step  1210 ), and the operational results reported (step  1214 ). 
       FIG. 13  illustratively represent one manner in which instrument errors and component degradation may be identified through use of a data reconciliation module  1022  in accordance with the present invention. As is illustrated by  FIG. 13 , in a step  1302  the variables of the mass and energy balance equations included within the data reconciliation module  1022  are set in accordance with measurements of the parameters applicable to the monitored process. A weighted least squares (WLS) objective function is then formulated in which various parameters of the applicable equipment models (i.e., the equipment maintenance parameters) are set to a default state (step  1306 ). As mentioned above, the maintenance parameters associated with a particular unit of equipment will generally be selected to be parameters to reflective of the “health” or operational soundness of the equipment unit. By monitoring the change in such maintenance parameters over time it is thus possible to monitor the condition of selected units of equipment. In this way equipment maintenance or replacement may be scheduled when a change in the maintenance parameter(s) for a particular unit of equipment indicate that the equipment has experienced degradation or is likely to fail or malfunction. 
     Referring again to  FIG. 13 , the parameters characterizing the monitored process (including the maintenance parameters) are incremented until the WLS objective function is minimized (step  1310 ), and the reconciled data reported (step  1314 ). In addition, an instrument error report may be generated when the values of one or more maintenance or other parameters associated with an equipment unit diverge from one or more corresponding predefined ranges (step  1318 ). Such a divergence could, for example, indicate either that the sensor responsible for measuring the parameter has malfunctioned or that condition of the applicable unit of equipment has significantly degraded. 
     The foregoing description, for purposes of explanation, used specific nomenclature to provide a thorough understanding of the invention. However, it will be apparent to one skilled in the art that the specific details are not required in order to practice the invention. In other instances, well-known circuits and devices are shown in block diagram form in order to avoid unnecessary distraction from the underlying invention. Thus, the foregoing descriptions of specific embodiments of the present invention are presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed, obviously many modifications and variations are possible in view of the above teachings. The embodiments were chosen and described in order to best explain the principles of the invention and its practical applications, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated. It is intended that the following Claims and their equivalents define the scope of the invention.