# Patent

## Title
Virtual sensor system and method

## Abstract

A method is provide for providing sensors for a machine. The method may include obtaining data records including data from a plurality of sensors for the machine and determining a virtual sensor corresponding to one of the plurality of sensors. The method may also include establishing a virtual sensor process model of the virtual sensor indicative of interrelationships between at least one sensing parameters and a plurality of measured parameters based on the data records and obtaining a set of values corresponding to the plurality of measured parameters. Further, the method may include calculating the values of the at least one sensing parameters substantially simultaneously based upon the set of values corresponding to the plurality of measured parameters and the virtual sensor process model and providing the values of the at least one sensing parameters to a control system.

## Background
TECHNICAL FIELD
This disclosure relates generally to computer based process modeling techniques and, more particularly, to virtual sensor systems and methods using process models.
BACKGROUND
Physical sensors are widely used in many products, such as modern machines, to measure and monitor physical phenomena, such as temperature, speed, and emissions from motor vehicles. Physical sensors often take direct measurements of the physical phenomena and convert these measurements into measurement data to be further processed by control systems. Although physical sensors take direct measurements of the physical phenomena, physical sensors and associated hardware are often costly and, sometimes, unreliable. Further, when control systems rely on physical sensors to operate properly, a failure of a physical sensor may render such control systems inoperable. For example, the failure of a speed or timing sensor in an engine may result in shutdown of the engine entirely even if the engine itself is still operable.
Instead of direct measurements, virtual sensors are developed to process other various physically measured values and to produce values that were previously measured directly by physical sensors. For example, U.S. Pat. No. 5,386,373 (the '373 patent) issued to Keeler et al. on Jan. 31, 1995, discloses a virtual continuous emission monitoring system with sensor validation. The '373 patent uses a back propagation-to-activation model and a monte-carlo search technique to establish and optimize a computational model used for the virtual sensing system to derive sensing parameters from other measured parameters. However, such conventional techniques often fail to address inter-correlation between individual measured parameters, especially at the time of generation and/or optimization of computational models, or to correlate the other measured parameters to the sensing parameters.
Further, a modern machine may need multiple sensors to function properly. It may be difficult to decide which sensor function should be provided by a physical sensor, which sensor function should be provided by a virtual sensor, or which sensor function should be provided by a combination of a physical sensor and a virtual sensor. Moreover, it may be difficult to determine required precision and/or reliability of a particular physical sensor. A physical sensor with a high precision or high reliability, i.e., high quality, may be more expensive than a normal physical sensor. Using high quality sensors for all sensor functions may increase product cost significantly.
In other circumstances, a modern machine may be retrofitted to provide new functionalities on existing machines. The new functionalities may require new sensors to be installed on the existing machines, which may be practically impossible or may result in substantial cost for retrofitting with new hardware and software.
Methods and systems consistent with certain features of the disclosed systems are directed to solving one or more of the problems set forth above.
SUMMARY OF THE INVENTION
One aspect of the present disclosure includes a method of providing sensors for a machine. The method may include obtaining data records including data from a plurality of sensors for the machine and determining a virtual sensor corresponding to one of the plurality of sensors. The method may also include establishing a virtual sensor process model of the virtual sensor indicative of interrelationships between at least one sensing parameters and a plurality of measured parameters based on the data records and obtaining a set of values corresponding to the plurality of measured parameters. Further, the method may include calculating the values of the at least one sensing parameters substantially simultaneously based upon the set of values corresponding to the plurality of measured parameters and the virtual sensor process model and providing the values of the at least one sensing parameters to a control system.
Another aspect of the present disclosure includes a method for retrofitting a first machine lacking a supporting physical sensor with a virtual sensor created based on a second machine with a supporting physical sensor. The method may include obtaining data records including data from a plurality of sensors that are available on both of the first machine and the second machine, and from the supporting physical sensor on the second machine; and calculating correlation values between the supporting physical sensor and each of the plurality of sensors based on the data records. The method may also include selecting correlated sensors from the plurality of sensors based on the correlation values; creating a virtual sensor of the supporting physical sensor based on the correlated sensors; and using the virtual sensor in the first machine to provide functionalities that were provided by the supporting physical sensor on the second machine.
Another aspect of the present disclosure includes a computer system. The computer system may include a database and a processor. The database may be configured to store information relevant to a virtual sensor process model. The processor may be configured to obtain data records including data from a plurality of sensors for the machine and to determine a virtual sensor corresponding to one of the plurality of sensors. The processor may also be configured to establish the virtual sensor process model of the virtual sensor indicative of interrelationships between at least one sensing parameters and a plurality of measured parameters based on the data records and to obtain a set of values corresponding to the plurality of measured parameters. Further, the processor may be configured to calculate the values of the at least one sensing parameters substantially simultaneously based upon the set of values corresponding to the plurality of measured parameters and the virtual sensor process model and to provide the values of the at least one sensing parameters to a control system.
Another aspect of the present disclosure includes a machine having a retrofitted virtual sensor to provide functionalities of a corresponding physical sensor without the supporting physical sensor being installed on the machine. The machine may include a power source, a control system, and a virtual sensor system. The power source may be configured to provide power to the machine. The control system may be configured to control the power source. The virtual sensor system may correspond to the supporting physical sensor, and may include a virtual sensor process model indicative of interrelationships between at least one sensing parameters provided by a plurality of sensors and a plurality of measured parameters of the supporting physical sensor. Further, the virtual sensor system may be configured to obtain a set of values corresponding to the plurality of measured parameters and to calculate the values of the at least one sensing parameters substantially simultaneously based upon the set of values corresponding to the plurality of measured parameters and the virtual sensor process model. The virtual sensor system may also be configured to provide the values of the at least one sensing parameters to the control system to provide functionalities corresponding to the supporting physical sensor. The virtual sensor may be created by a process. The process may include obtaining data records including data from the plurality of sensors and the supporting physical sensor; and calculating correlation values between the supporting physical sensor and the plurality of sensors based on the data records. The process may also include selecting correlated sensors from the plurality of sensors based on the correlation values; and creating the virtual sensor of the supporting physical sensor based on the correlated sensors.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates an exemplary machine in which features and principles consistent with certain disclosed embodiments may be incorporated;
FIG. 2 illustrates a block diagram of an exemplary virtual sensor system consistent with certain disclosed embodiments;
FIG. 3 shows a flow chart of an exemplary sensor selection process consistent with certain disclosed embodiments;
FIG. 4 illustrates a logical block diagram of an exemplary computer system consistent with certain disclosed embodiments;
FIG. 5 illustrates a flowchart diagram of an exemplary virtual sensor model generation and optimization process consistent with certain disclosed embodiments;
FIG. 6 shows a flowchart diagram of an exemplary control process consistent with certain disclosed embodiments;
FIG. 7 shows a flow chart of an exemplary retrofitting process consistent with certain disclosed embodiments; and
FIG. 8 shows a flowchart diagram of another exemplary control process consistent with certain disclosed embodiments.



DETAILED DESCRIPTION
Reference will now be made in detail to exemplary embodiments, which are illustrated in the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts.
FIG. 1 illustrates an exemplary machine 100 in which features and principles consistent with certain disclosed embodiments may be incorporated. Machine 100 may refer to any type of stationary or mobile machine that performs some type of operation associated with a particular industry, such as mining, construction, farming, transportation, etc. and operates between or within work environments (e.g., construction site, mine site, power plants and generators, on-highway applications, etc.), such as trucks, cranes, earth moving machines, mining vehicles, backhoes, material handling equipment, farming equipment, marine vessels, aircraft, and any type of movable machine that operates in a work environment. Machine 100 may also include any type of commercial vehicle such as cars, vans, and other vehicles. Other types of machines may also be included.
As shown in FIG. 1, machine 100 may include an engine 110, an engine control module (ECM) 120, a virtual sensor system 130, physical sensors 140 and 142, and a data link 150. Engine 110 may include any appropriate type of engine or power source that generates power for machine 100, such as an internal combustion engine or fuel cell generator. ECM 120 may include any appropriate type of engine control system configured to perform engine control functions such that engine 110 may operate properly. ECM 120 may include any number of devices, such as microprocessors or microcontrollers, memory modules, communication devices, input/output devices, storages devices, etc., to perform such control functions. Further, ECM 120 may also control other systems of machine 100, such as transmission systems, and/or hydraulics systems, etc. Computer software instructions may be stored in or loaded to ECM 120. ECM 120 may execute the computer software instructions to perform various control functions and processes.
ECM 120 may be coupled to data link 150 to receive data from and send data to other components, such as engine 110, physical sensors 140 and 142, virtual sensor system 130, and/or any other components (not shown) of machine 100. Data link 150 may include any appropriate type of data communication medium, such as cable, wires, wireless radio, and/or laser, etc. Physical sensor 140 may include one or more sensors provided for measuring certain parameters of machine operating environment. For example, physical sensor 140 may include physical emission sensors for measuring emissions of machine 100, such as Nitrogen Oxides (NOx), Sulfur Dioxide (SO2), Carbon Monoxide (CO), total reduced Sulfur (TRS), etc. In particular, NOx emission sensing and reduction may be important to normal operation of engine 110. Physical sensor 142, on the other hand, may include any appropriate sensors that are used with engine 110 or other machine components (not shown) to provide various measured parameters about engine 110 or other components, such as temperature, speed, acceleration rate, etc.
Virtual sensor system 130 may include any appropriate type of control system that generate values of sensing parameters based on a computational model and a plurality of measured parameters. The sensing parameters may refer to those measurement parameters that are directly measured by a particular physical sensor. For example, a physical NOx emission sensor may measure the NOx emission level of machine 100 and provide values of NOx emission level, the sensing parameter, to other components, such as ECM 120. Sensing parameters, however, may also include any output parameters that may be measured indirectly by physical sensors and/or calculated based on readings of physical sensors. On the other hand, the measured parameters may refer to any parameters relevant to the sensing parameters and indicative of the state of a component or components of machine 100, such as engine 110. For example, for the sensing parameter NOx emission level, measured parameters may include environmental parameters, such as compression ratios, turbocharger efficiency, aftercooler characteristics, temperature values, pressure values, ambient conditions, fuel rates, and engine speeds, etc.
Further, virtual sensor system 130 may be configured as a separate control system or, alternatively, may coincide with other control systems such as ECM 120. Virtual sensor system 130 may also operate in series with or in parallel to ECM 120. Virtual sensor system 130 and/or ECM 120 may be implemented by any appropriate computer system. FIG. 2 shows an exemplary functional block diagram of a computer system 200 configured to implement virtual sensor system 130 and/or ECM 120. Computer system 200 may also include any appropriate computer system configured to design, train, and validate virtual sensor 130 and other component of machine 100.
As shown in FIG. 2, computer system 200 (e.g., virtual sensor system 130, etc.) may include a processor 202, a memory module 204, a database 206, an I/O interface 208, a network interface 210, and a storage 212. Other components, however, may also be included in computer system 200.
Processor 202 may include any appropriate type of general purpose microprocessor, digital signal processor, or microcontroller. Processor 202 may be configured as a separate processor module dedicated to controlling engine 110. Alternatively, processor 202 may be configured as a shared processor module for performing other functions unrelated to virtual sensors.
Memory module 204 may include one or more memory devices including, but not limited to, a ROM, a flash memory, a dynamic RAM, and a static RAM. Memory module 204 may be configured to store information used by processor 202. Database 206 may include any type of appropriate database containing information on characteristics of measured parameters, sensing parameters, mathematical models, and/or any other control information.
Further, I/O interface 208 may also be connected to data link 150 to obtain data from various sensors or other components (e.g., physical sensors 140 and 142) and/or to transmit data to these components and to ECM 120. Network interface 210 may include any appropriate type of network device capable of communicating with other computer systems based on one or more wired or wireless communication protocols. Storage 212 may include any appropriate type of mass storage provided to store any type of information that processor 202 may need to operate. For example, storage 212 may include one or more hard disk devices, optical disk devices, or other storage devices to provide storage space. Any or all of the components of computer system 200 may be implemented or integrated into an application specific integrated circuit (ASIC) or field programmable gate array (FPGA) device.
Machine 100 may require a plurality of measured parameters and/or sensing parameters. The measured parameters and/or sensing parameters may be provided by a plurality of sensors. The sensors may include physical sensors, such as physical sensors 140 and 142, virtual sensors, such as virtual sensor system 130, and/or a combination of a physical sensor and a virtual sensor. Further, physical sensors may include physical sensors with various qualities (e.g., accuracy, error, uncertainty, repeatability, hysteresis, reliability, etc.). Computer system 200 may perform a sensor selection process to determine the type of sensors and/or qualities of the physical sensors.
As shown in FIG. 3, computer system 200, or processor 202, may obtain data records containing data records or readings from the plurality of sensors (step 302). The data records may be provided from a test or current machine 100 having the plurality of sensors S1, S2, S3, . . . , and Sn, where n is an integer representing a total number of the sensors.
After obtaining the data records (step 302), processor 202 may measure a relationship between any two sensors (step 304). The relationship may include any appropriate relationship, such as statistical relationship or other mathematical relationship. The relationship may be measured by any appropriate physical or mathematical term.
For example, processor 202 may calculate correlations between any two sensors. A correlation, as used herein, may refer to a statistical measurement of a relationship between two or more variables (events, occurrences, sensor readings, etc.). A correlation between two variables may suggest a certain causal relationship between the two variables, and a larger correlation value may indicate a greater correlation. Processor 202 may calculate correlations based on the data records via any appropriate algorithm for calculating correlations.
Further, processor 202 may create a relation matrix for sensors S1, S2, S3, . . . , and Sn (step 306). The relation matrix may refer to a matrix reflecting the measured relationships between any two sensors. In the example above, processor 202 may use correlation between two sensors to reflect the relationship between the two sensor and may create a correlation matrix as the relation matrix. For example, processor 202 may create a correlation matrix as:




   
  
    
      
        
          
        
      
      
        
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The correlation matrix may include a total number of n2 elements, each representing a correlation value between two sensors. The value of any diagonal element is 1 in that the correlation value between a sensor and itself is 1. The correlation value between two sensors may represent relatedness between the two sensors. If the correlation value is equal to or greater than a predetermined threshold, processor 202 may determine that the two sensors are correlated. A sensor correlated to a second sensor may be represented by the second sensor to a certain degree.
Processor 202 may determine a score for each sensor (step 308). Processor 202 may determine a score for each sensor based on the relation matrix. For example, processor 202 may determine the score for each sensor as a total number of correlation values greater than or equal to a predetermined threshold, except for the self-correlation value. Processor 202 may determine the threshold by any appropriate way. In certain embodiments, processor 202 may use 0.6 as a threshold for calculating the score.
In the exemplary correlation matrix above, processor 202 may determine a score of 3 for S1, a score of 1 for S2, a score of 0 for S3, and a score of 2 for Sn. These scores may change if other sensors not explicitly listed are included, and are only for illustrative purposes. Other relationship measurements may also be used.
After determining the score for each sensor (step 308), processor 202 may separate the sensors into certain groups of sensors based on the scores (step 310). For example, processor 202 may separate S1, S2, S3, and Sn into three sensor groups and, more specifically, may separate S3 into a first sensor group, S2 and Sn into a second sensor group, and S1 into a third sensor group. Other number of sensor groups may also be used.
As the score of each sensor may reflect correlation with other sensors, the first sensor group may include sensors with no or significant less correlated sensors (e.g., S3 with a score of 0, etc.) than other sensor groups, i.e., with no or significant less amount of relationship. The second sensor group may include sensors with a certain range of correlated sensors (e.g., S2 and Sn with scores of 1 and 2, etc.), i.e., with a certain amount of relationship. The third group may include sensors with a total number of correlated sensors beyond a predetermined threshold (e.g., S1 with a score of 3, etc.), i.e., with a significant amount of relationship. Other scores or score ranges may also be used to separate the sensors.
Further, processor 202 may determine sensor types and configurations for the sensors based on the sensor groups (step 312). For example, with respect to the first sensor group, processor 202 may choose a high quality and/or expensive physical sensor as sensor S3, or may choose a high quality sensor with a redundant sensor (physical or virtual) as sensor S3 to ensure operations of sensor S3 in that it may be unable to obtain information provided by sensor S3 from any other sensors due to the significant less amount of relationship.
With respect to the second sensor group, processor 202 may choose an ordinary quality physical sensor with a virtual sensor backup as sensor S2 or sensor Sn in that certain information provided by sensor S2 or sensor Sn may be obtained from one or more correlated sensor (e.g., Sn for S2, or S1 and S2 for Sn, etc.). For sensors in the second sensor group, it may be desired to have a physical sensor providing measuring parameters directly. However, if the physical sensor fails, other sensors or the back up virtual sensor may provide enough information to continue operation of machine 100 without replacing the physical sensor, because the existence of the certain amount of relationship.
Further, with respect to the third sensor group, processor 202 may choose a virtual sensor for sensor S1 in that most or all of information provided by sensor S1 may be obtained from other correlated sensors (e.g., S2, S3, and Sn, etc.) because of the significant amount of relationships.
Processor 202 may use virtual sensors (e.g., virtual sensor system 130, etc.) for the various sensor groups. Processor 202 may use virtual sensor system 130 as backup sensors or as replacement sensors. Virtual sensor system 130 may include a process model to provide values of certain sensing parameters to ECM 120. FIG. 4 shows a logical block diagram of an exemplary virtual sensor system 130.
As shown in FIG. 4, a virtual sensor process model 404 may be established to build interrelationships between input parameters 402 (e.g., measured parameters) and output parameters 406 (e.g., sensing parameters). After virtual sensor process model 404 is established, values of input parameters 402 may be provided to virtual sensor process model 404 to generate values of output parameters 406 based on the given values of input parameters 402 and the interrelationships between input parameters 402 and output parameters 406 established by the virtual sensor process model 404.
In certain embodiments, virtual sensor system 130 may include a NOx virtual sensor to provide levels of NOx emitted from an exhaust system (not shown) of machine 100. Input parameters 402 may include any appropriate type of data associated with NOx emission levels. For example, input parameters 402 may include parameters that control operations of various response characteristics of engine 110 and/or parameters that are associated with conditions corresponding to the operations of engine 110.
For example, input parameters 402 may include fuel injection timing, compression ratios, turbocharger efficiency, aftercooler characteristics, temperature values (e.g., intake manifold temperature), pressure values (e.g., intake manifold pressure), ambient conditions (e.g., ambient humidity), fuel rates, and engine speeds, etc. Other parameters, however, may also be included. For example, parameters originated from other vehicle systems, such as chosen transmission gear, axle ratio, elevation and/or inclination of the vehicle, etc., may also be included. Further, input parameters 402 may be measured by certain physical sensors, such as physical sensor 142, or created by other control systems such as ECM 120. Virtual sensor system 130 may obtain values of input parameters 402 via an input 410 coupled to data link 150.
On the other hand, output parameters 406 may correspond to sensing parameters. For example, output parameters 406 of a NOx virtual sensor may include NOx emission level and/or any other types of output parameters used by NOx virtual sensing application. Output parameters 406 (e.g., NOx emission level) may be sent to ECM 120 via output 420 coupled to data link 150.
Virtual sensor process model 404 may include any appropriate type of mathematical or physical model indicating interrelationships between input parameters 402 and output parameters 406. For example, virtual sensor process model 404 may be a neural network based mathematical model that is trained to capture interrelationships between input parameters 402 and output parameters 406. Other types of mathematic models, such as fuzzy logic models, linear system models, and/or non-linear system models, etc., may also be used. Virtual sensor process model 404 may be trained and validated using data records collected from a particular engine application for which virtual sensor process model 404 is established. That is, virtual sensor process model 404 may be established according to particular rules corresponding to a particular type of model using the data records, and the interrelationships of virtual sensor process model 404 may be verified by using part of the data records.
After virtual sensor process model 404 is trained and validated, virtual sensor process model 404 may be optimized to define a desired input space of input parameters 402 and/or a desired distribution of output parameters 406. The validated or optimized virtual sensor process model 404 may be used to produce corresponding values of output parameters 406 when provided with a set of values of input parameters 102. In the above example, virtual sensor process model 404 may be used to produce NOx emission level based on measured parameters, such as ambient humidity, intake manifold pressure, intake manifold temperature, fuel rate, and engine speed, etc.
Returning to FIG. 2, the establishment and operations of virtual sensor process model 404 may be carried out by processor 202 based on computer programs stored on or loaded to virtual sensor system 130. Alternatively, the establishment of virtual sensor process model 404 may be realized by other computer systems, such as ECM 120 or a separate general purpose computer configured to create process models. The created process model may then be loaded to virtual sensor system 130 for operations.
Processor 202 may perform a virtual sensor process model generation and optimization process to generate and optimize virtual sensor process model 404. FIG. 5 shows an exemplary model generation and optimization process performed by processor 202.
As shown in FIG. 5, at the beginning of the model generation and optimization process, processor 202 may obtain data records associated with input parameters 402 and output parameters 406 (step 502). The data records may include information characterizing engine operations and emission levels including NOx emission levels. Physical sensor 140, such as physical NOx emission sensors, may be provided to generate data records on output parameters 406 (e.g., sensing parameters such as NOx levels). ECM 120 and/or physical sensor 142 may provide data records on input parameters 402 (e.g., measured parameters, such as intake manifold temperature, intake manifold pressure, ambient humidity, fuel rates, and engine speeds, etc.). Further, the data records may include both input parameters and output parameters and may be collected based on various engines or based on a single test engine, under various predetermined operational conditions.
The data records may also be collected from experiments designed for collecting such data. Alternatively, the data records may be generated artificially by other related processes, such as other emission modeling, simulation, or analysis processes. The data records may also include training data used to build virtual sensor process model 404 and testing data used to validate virtual sensor process model 404. In addition, the data records may also include simulation data used to observe and optimize virtual sensor process model 404.
The data records may reflect characteristics of input parameters 102 and output parameters 106, such as statistic distributions, normal ranges, and/or precision tolerances, etc. Once the data records are obtained (step 502), processor 202 may pre-process the data records to clean up the data records for obvious errors and to eliminate redundancies (step 504). Processor 202 may remove approximately identical data records and/or remove data records that are out of a reasonable range in order to be meaningful for model generation and optimization. After the data records have been pre-processed, processor 202 may select proper input parameters by analyzing the data records (step 506).
The data records may be associated with many input variables, such as variables corresponding to fuel injection timing, compression ratios, turbocharger efficiency, aftercooler characteristics, various temperature parameters, various pressure parameters, various ambient conditions, fuel rates, and engine speeds, etc. The number of input variables may be greater than the number of a particular set of input parameters 102 used for virtual sensor process model 404. That is, input parameters 102 may be a subset of the input variables. For example, input parameter 402 may include intake manifold temperature, intake manifold pressure, ambient humidity, fuel rate, and engine speed, etc., of the input variables.
A large number of input variables may significantly increase computational time during generation and operations of the mathematical models. The number of the input variables may need to be reduced to create mathematical models within practical computational time limits. Additionally, in certain situations, the number of input variables in the data records may exceed the number of the data records and lead to sparse data scenarios. Some of the extra input variables may have to be omitted in certain mathematical models such that practical mathematical models may be created based on reduced variable number.
Processor 202 may select input parameters 402 from the input variables according to predetermined criteria. For example, processor 202 may choose input parameters 402 by experimentation and/or expert opinions. Alternatively, in certain embodiments, processor 202 may select input parameters based on a mahalanobis distance between a normal data set and an abnormal data set of the data records. The normal data set and abnormal data set may be defined by processor 202 using any appropriate method. For example, the normal data set may include characteristic data associated with input parameters 402 that produce desired output parameters. On the other hand, the abnormal data set may include characteristic data that may be out of tolerance or may need to be avoided. The normal data set and abnormal data set may be predefined by processor 202.
Mahalanobis distance may refer to a mathematical representation that may be used to measure data profiles based on correlations between parameters in a data set. Mahalanobis distance differs from Euclidean distance in that mahalanobis distance takes into account the correlations of the data set. Mahalanobis distance of a data set X (e.g., a multivariate vector) may be represented as

MDi=(Xi−μx)Σ−1(Xi−μx)′  (1)

where μx is the mean of X and Σ−1 is an inverse variance-covariance matrix of X. MDi weights the distance of a data point Xi from its mean μx such that observations that are on the same multivariate normal density contour will have the same distance. Such observations may be used to identify and select correlated parameters from separate data groups having different variances.

Processor 202 may select input parameter 402 as a desired subset of input variables such that the mahalanobis distance between the normal data set and the abnormal data set is maximized or optimized. A genetic algorithm may be used by processor 202 to search input variables for the desired subset with the purpose of maximizing the mahalanobis distance. Processor 202 may select a candidate subset of the input variables based on a predetermined criteria and calculate a mahalanobis distance MDnormal of the normal data set and a mahalanobis distance MDabnormal of the abnormal data set. Processor 202 may also calculate the mahalanobis distance between the normal data set and the abnormal data (i.e., the deviation of the mahalanobis distance MDx=MDnormal−MDabnormal). Other types of deviations, however, may also be used.
Processor 202 may select the candidate subset of input variables if the genetic algorithm converges (i.e., the genetic algorithm finds the maximized or optimized mahalanobis distance between the normal data set and the abnormal data set corresponding to the candidate subset). If the genetic algorithm does not converge, a different candidate subset of input variables may be created for further searching. This searching process may continue until the genetic algorithm converges and a desired subset of input variables (e.g., input parameters 402) is selected.
Optionally, mahalanobis distance may also be used to reduce the number of data records by choosing a part of data records that achieve a desired mahalanobis distance, as explained above.
After selecting input parameters 402 (e.g., intake manifold temperature, intake manifold pressure, ambient humidity, fuel rate, and engine speed, etc.), processor 202 may generate virtual sensor process model 404 to build interrelationships between input parameters 402 and output parameters 406 (step 508). In certain embodiments, virtual sensor process model 404 may correspond to a computational model, such as, for example, a computational model built on any appropriate type of neural network. The type of neural network computational model that may be used may include back propagation, feed forward models, cascaded neural networks, and/or hybrid neural networks, etc. Particular type or structures of the neural network used may depend on particular applications. Other types of computational models, such as linear system or non-linear system models, etc., may also be used.
The neural network computational model (i.e., virtual sensor process model 404) may be trained by using selected data records. For example, the neural network computational model may include a relationship between output parameters 406 (e.g., NOx emission level, etc.) and input parameters 402 (e.g., intake manifold temperature, intake manifold pressure, ambient humidity, fuel rate, and engine speed, etc.). The neural network computational model may be evaluated by predetermined criteria to determine whether the training is completed. The criteria may include desired ranges of accuracy, time, and/or number of training iterations, etc.
After the neural network has been trained (i.e., the computational model has initially been established based on the predetermined criteria), processor 202 may statistically validate the computational model (step 510). Statistical validation may refer to an analyzing process to compare outputs of the neural network computational model with actual or expected outputs to determine the accuracy of the computational model. Part of the data records may be reserved for use in the validation process.
Alternatively, processor 202 may also generate simulation or validation data for use in the validation process. This may be performed either independently of a validation sample or in conjunction with the sample. Statistical distributions of inputs may be determined from the data records used for modeling. A statistical simulation, such as Latin Hypercube simulation, may be used to generate hypothetical input data records. These input data records are processed by the computational model, resulting in one or more distributions of output characteristics. The distributions of the output characteristics from the computational model may be compared to distributions of output characteristics observed in a population. Statistical quality tests may be performed on the output distributions of the computational model and the observed output distributions to ensure model integrity.
Once trained and validated, virtual sensor process model 404 may be used to predict values of output parameters 406 when provided with values of input parameters 402. Further, processor 202 may optimize virtual sensor process model 404 by determining desired distributions of input parameters 402 based on relationships between input parameters 402 and desired distributions of output parameters 406 (step 512).
Processor 202 may analyze the relationships between desired distributions of input parameters 402 and desired distributions of output parameters 406 based on particular applications. For example, processor 202 may select desired ranges for output parameters 406 (e.g., NOx emission level that is desired or within certain predetermined range). Processor 202 may then run a simulation of the computational model to find a desired statistic distribution for an individual input parameter (e.g., one of intake manifold temperature, intake manifold pressure, ambient humidity, fuel rate, and engine speed, etc.). That is, processor 202 may separately determine a distribution (e.g., mean, standard variation, etc.) of the individual input parameter corresponding to the normal ranges of output parameters 406. After determining respective distributions for all individual input parameters, processor 202 may combine the desired distributions for all the individual input parameters to determine desired distributions and characteristics for overall input parameters 402.
Alternatively, processor 202 may identify desired distributions of input parameters 402 simultaneously to maximize the possibility of obtaining desired outcomes. In certain embodiments, processor 202 may simultaneously determine desired distributions of input parameters 402 based on zeta statistic. Zeta statistic may indicate a relationship between input parameters, their value ranges, and desired outcomes. Zeta statistic may be represented as




  
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  ,




where xi represents the mean or expected value of an ith input; xj represents the mean or expected value of a jth outcome; σi represents the standard deviation of the ith input; σj represents the standard deviation of the jth outcome; and |Sij| represents the partial derivative or sensitivity of the jth outcome to the ith input.

Under certain circumstances, xi may be less than or equal to zero. A value of 3 σi may be added to xi to correct such problematic condition. If, however, xi is still equal zero even after adding the value of 3 σi, processor 202 may determine that σi may be also zero and that the process model under optimization may be undesired. In certain embodiments, processor 202 may set a minimum threshold for σi to ensure reliability of process models. Under certain other circumstances, σj may be equal to zero. Processor 202 may then determine that the model under optimization may be insufficient to reflect output parameters within a certain range of uncertainty. Processor 202 may assign an indefinite large number to ζ.
Processor 202 may identify a desired distribution of input parameters 402 such that the zeta statistic of the neural network computational model (i.e., virtual sensor process model 404) is maximized or optimized. An appropriate type of genetic algorithm may be used by processor 202 to search the desired distribution of input parameters 402 with the purpose of maximizing the zeta statistic. Processor 202 may select a candidate set values of input parameters 402 with predetermined search ranges and run a simulation of virtual sensor process model 404 to calculate the zeta statistic parameters based on input parameters 402, output parameters 406, and the neural network computational model. Processor 202 may obtain xi and σi by analyzing the candidate set values of input parameters 402, and obtain xj and σj by analyzing the outcomes of the simulation. Further, processor 202 may obtain |Sij| from the trained neural network as an indication of the impact of the ith input on the jth outcome.
Processor 202 may select the candidate set of input parameters 402 if the genetic algorithm converges (i.e., the genetic algorithm finds the maximized or optimized zeta statistic of virtual sensor process model 404 corresponding to the candidate set of input parameters 402). If the genetic algorithm does not converge, a different candidate set values of input parameters 402 may be created by the genetic algorithm for further searching. This searching process may continue until the genetic algorithm converges and a desired set of input parameters 402 is identified. Processor 202 may further determine desired distributions (e.g., mean and standard deviations) of input parameters 402 based on the desired input parameter set. Once the desired distributions are determined, processor 202 may define a valid input space that may include any input parameter within the desired distributions (step 514).
In one embodiment, statistical distributions of certain input parameters may be impossible or impractical to control. For example, an input parameter may be associated with a physical attribute of a device, such as a dimensional attribute of an engine part, or the input parameter may be associated with a constant variable within virtual sensor process model 404 itself. These input parameters may be used in the zeta statistic calculations to search or identify desired distributions for other input parameters corresponding to constant values and/or statistical distributions of these input parameters.
Further, optionally, more than one virtual sensor process model may be established. Multiple established virtual sensor process models may be simulated by using any appropriate type of simulation method, such as statistical simulation. Output parameters 406 based on simulation of these multiple virtual sensor process models may be compared to select a most-fit virtual sensor process model based on predetermined criteria, such as smallest variance with outputs from corresponding physical sensors, etc. The selected most-fit virtual sensor process model 404 may be deployed in virtual sensor applications.
Returning to FIG. 1, after virtual sensor process model 404 is trained, validated, optimized, and/or selected, ECM 120 and virtual sensor system 130 may provide control functions to relevant components of machine 100. For example, ECM 120 may control engine 110 according to NOx emission level provided by virtual sensor system 130, and, in particular, by virtual sensor process model 404.
In certain embodiments, virtual sensor system 130 may be used to replace corresponding physical sensors. For example, virtual sensor system 130 may replace one or more NOx emission sensors used by ECM 120. ECM 120 may perform a control process based on virtual sensor system 130. FIG. 6 shows an exemplary control process performed by ECM 120.
As shown in FIG. 6, ECM 120 may control and/or facilitate physical sensors 140 and/or 142 and engine 110 to measure relevant parameters, such as intake manifold temperature, intake manifold pressure, ambient humidity, fuel rate, and engine speed, etc. (step 602). After intake manifold temperature, intake manifold pressure, ambient humidity, fuel rate, and engine speed have been measured by, for example, corresponding correlated physical sensors 142, ECM 120 may provide these measured parameters to virtual sensor system 130 (step 604). ECM 120 may provide the measured parameters on data link 150 such that virtual sensor system 130 may obtain the measured parameters from data link 150. Alternatively, virtual sensor system 130 may read these measured parameters from data link 150 or from other physical sensors or devices directly.
As explained above, virtual sensor system 130 includes virtual sensor process model 404. Virtual sensor system 130 may provide the measured parameters (e.g., intake manifold temperature, intake manifold pressure, ambient humidity, fuel rate, and engine speed, etc.) to virtual sensor process model 404 as input parameters 402. Virtual sensor process model 404 may then provide output parameters 406, such as NOx emission level.
ECM 120 may obtain output parameters 406 (e.g., NOx emission level) from virtual sensor system 130 via data link 150 (step 606). In certain situations, ECM 120 may be unaware the source of output parameters 406. That is, ECM 120 may be unaware whether output parameters 406 are from virtual sensor system 130 or from physical sensors. For example, ECM 120 may obtain NOx emission level from data link 150 without discerning the source of such data. After ECM 120 obtains the NOx emission level from virtual sensor system 130 (step 606), ECM 120 may control engine 110 and/or other components of machine 100 based on the NOx emission level (step 608). For example, ECM 120 may perform certain emission enhancing or minimization processes.
In certain embodiments, machine 100 may be used to retrofit another machine 100. The term “retrofit,” as used herein, may refer to equipping a previously made machine 100 with virtual sensor system 130 to provide a new functionality or a new feature for the previously made machine 100 without a hardware device, such as a physical sensor, that is required to support the new functionality or the new feature. For example, a previously made machine 100 may lack a physical anti-lock sensor to provide anti-block functionality based on the physical anti-lock sensor. Computer system 200 may perform a retrofitting process to provide new functionality for machine 100 based on virtual sensor system 130. FIG. 7 shows an exemplary retrofitting process performed by computer system 200 or, more particularly, processor 202.
Processor 202 may obtain data records of physical sensors (step 702). For example, processor 202 may obtain data records from a current machine 100 having the physical sensors including the required physical anti-block sensor. Further, processor 202 may calculate a correlation between the physical anti-lock sensor to any other physical sensors of machine 100 (step 704).
Further, processor 202 may select physical sensors correlated to the physical anti-lock sensor based on the correlation values (step 706). For example, processor 202 may select any physical sensor with a correlation value beyond a predetermined threshold as a correlated physical sensor (e.g., 0.6, etc.). Other selection methods may also be used.
After selecting correlated physical sensors (step 706), processor 202 may create a virtual sensor based on the correlated physical sensors (step 708). For example, processor 202 may create virtual sensor system 130 as a virtual anti-lock sensor based on data records of the correlated physical sensors to provide anti-lock sensor output parameter or parameters, according to the process described above with respect to FIG. 5. In certain embodiments, processor 202 may include outputs or readings from the correlated physical sensors as input parameters to virtual sensor process model 404 and may include outputs or readings from the physical anti-lock sensor as output parameters of virtual sensor process model 404 when creating virtual sensor system 130. Because information provided by the physical anti-lock sensor may be provided by the correlated physical sensors, a desired precision may be obtained by virtual sensor system 130 created based on the correlated physical sensors.
Processor 202 may retrofit machine 100 with virtual sensor system 130 (step 710). Processor 202, or ECM 120, may execute computer programs implementing virtual sensor system 130 to provide anti-block sensing functionality for a previously made machine 100 without being equipped with a physical anti-lock sensor, according to the exemplary process described above with respect to FIG. 6.
In certain other embodiments, virtual sensor system 130 may be used in combination with physical sensors or as a back up for physical sensors. For example, virtual sensor system 130 may be used when one or more physical NOx emission sensors have failed. ECM 120 may perform a control process based on virtual sensor system 130 and corresponding physical sensors. FIG. 8 shows another exemplary control process performed by ECM 120.
As shown in FIG. 8, ECM 120 may control and/or facilitate physical sensors 140 and/or 142 and engine 110 to measure relevant parameters, such as intake manifold temperature, intake manifold pressure, ambient humidity, fuel rate, and engine speed, etc. (step 802). ECM 120 may also provide these measured parameters to virtual sensor system 130 (step 804). Virtual sensor system 130, especially virtual sensor process model 404, may then provide output parameters 406, such as NOx emission level.
Further, ECM 120 may obtain output parameters (e.g., NOx emission level) from virtual sensor system 130 via data link 150 (step 806). Additionally and/or concurrently, ECM 120 may also obtain NOx emission level from one or more physical sensors, such as physical sensor 142 (step 808). ECM 120 may check operational status on the physical sensors (step 810). ECM 120 may include certain logic devices to determine whether the physical sensors have failed. If the physical sensors have failed (step 810; yes), ECM 120 may obtain NOx emission level from virtual sensor system 130 and control engine 110 and/or other components of machine 100 based on the NOx emission level from virtual sensor system 130 (step 812).
On the other hand, if the physical sensors have not failed (step 810; no), ECM 120 may use NOx emission level from the physical sensors to control engine 110 and/or other components of machine 100 (step 814). Alternatively, ECM 120 may obtain NOx emission levels from virtual sensor system 130 and the physical sensors to determine whether there is any deviation between the NOx emission levels. If the deviation is beyond a predetermined threshold, ECM 120 may declare a failure and switch to virtual sensor system 130 or use a preset value that is neither from virtual sensor system 130 nor from the physical sensors.
In addition, ECM 120 may also obtain measuring parameters that may be unavailable in physical sensors 140 and 142. For example, virtual sensor system 130 may include a process model indicative of interrelationships between oxygen density in a certain geographical area (e.g., the state of Colorado, etc.) and space-based satellite and weather data. That is, virtual sensor system 130 may provide ECM 120 with measuring parameters, such as the oxygen density, that may be otherwise unavailable on physical sensors.
INDUSTRIAL APPLICABILITY
The disclosed systems and methods may provide efficient and accurate virtual sensor process models in substantially less time than other virtual sensing techniques. Such technology may be used in a wide range of virtual sensors, such as sensors for engines, structures, environments, and materials, etc. In particular, the disclosed systems and methods provide practical solutions when process models are difficult to build using other techniques due to computational complexities and limitations. When input parameters are optimized substantially simultaneously to derive output parameters, computation may be minimized. The disclosed systems and methods may be used in combination with other process modeling techniques to significantly increase speed, practicality, and/or flexibility.
The disclosed systems and methods may provide efficient methods to determine types and qualities of sensors in a product. By choosing appropriate types of sensors and appropriate qualities of sensors, product cost may be reduced and product quality may be increased. Further, a combination of physical sensors and virtual sensors may be established to further improve product quality and reliability.
The disclosed systems and methods may provide flexible solutions as well. The disclosed virtual sensor system may be used interchangeably with a corresponding physical sensor. By using a common data link for both the virtual sensor and the physical sensor, the virtual sensor model of the virtual sensor system may be trained by the same physical sensor that the virtual sensor system replaces. Control systems may operate based on either the virtual sensor system or the physical sensor, without differentiating which one is the data source.
The disclosed virtual sensor systems may be used to replace the physical sensor and may operate separately and independently of the physical sensor. The disclosed virtual sensor system may also be used to back up the physical sensor. Moreover, the virtual sensor system may provide parameters that are unavailable from a single physical sensor, such as data from outside the sensing environment.
Further, the disclosed virtual sensor systems may be used to retrofit a machine with new functionalities without installing or changing new hardware devices, while such new functionalities usually require new hardware devices, such as physical sensors, to be installed.
The disclosed systems and methods may also be used by machine manufacturers to reduce cost and increase reliability by replacing costly or failure-prone physical sensors. Reliability and flexibility may also be improved by adding backup sensing resources via the disclosed virtual sensor system. The disclosed virtual sensor techniques may be used to provide a wide range of parameters in components such as emission, engine, transmission, navigation, and/or control, etc. Further, parts of the disclosed system or steps of the disclosed method may also be used by computer system providers to facilitate or integrate other process models. Other embodiments, features, aspects, and principles of the disclosed exemplary systems will be apparent to those skilled in the art and may be implemented in various environments and systems.

## Claims

1. A method providing sensors for a machine, comprising:
obtaining data records including data from a plurality of sensors for the machine;
determining a virtual sensor corresponding to one of the plurality of sensors;
establishing a virtual sensor process model of the virtual sensor indicative of interrelationships between at least one sensing parameters and a plurality of measured parameters based on the data records;
obtaining a set of values corresponding to the plurality of measured parameters;
calculating the values of the at least one sensing parameters substantially simultaneously based upon the set of values corresponding to the plurality of measured parameters and the virtual sensor process model; and
providing the values of the at least one sensing parameters to a control system.

2. The method according to claim 1, wherein determining includes:
calculating correlation values between any two sensors of the plurality of sensors;
separating the plurality of sensors into a plurality of sensor groups based on the correlation values; and
determining the virtual sensor corresponding to the one of the plurality of sensors from a desired sensor group.

3. The method according to claim 2, wherein separating includes:
creating a correlation matrix with rows representing the respective plurality of sensors, columns representing the respective plurality of sensors, and each element representing a correlation value between the corresponding two sensors from a row and a column, respectively;
determining a score for each of the plurality of sensors based on the correlation matrix; and
separating the plurality of sensors into the plurality of sensor groups based on the score of each of the plurality of sensors.

4. The method according to claim 3, wherein the plurality of sensor groups include:
a first sensor group containing desired physical sensors;
a second sensor group containing sensors with combinations of physical sensors and virtual sensors; and
a third sensor group containing virtual sensors.

5. The method according to claim 1, wherein the establishing includes:
obtaining data records associated with one or more input variables and the at least one sensing parameters;
selecting the plurality of measured parameters from the one or more input variables;
generating a computational model indicative of the interrelationships between the plurality of measured parameters and the at least one sensing parameters;
determining desired statistical distributions of the plurality of measured parameters of the computational model; and
recalibrating the plurality of measured parameters based on the desired statistical distributions to define a desired input space.

6. The method according to claim 5, wherein selecting further includes:
pre-processing the data records; and
using a genetic algorithm to select the plurality of measured parameters from the one or more input variables based on a mahalanobis distance between a normal data set and an abnormal data set of the data records.

7. The method according to claim 5, wherein generating further includes:
creating a neural network computational model;
training the neural network computational model using the data records; and
validating the neural network computation model using the data records.

8. The method according to claim 5, wherein determining further includes:
determining a candidate set of the measured parameters with a maximum zeta statistic using a genetic algorithm; and
determining the desired distributions of the measured parameters based on the candidate set,
wherein the zeta statistic ζ is represented by:





  
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            (
            
              
                
                  x
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provided that xi represents a mean of an ith input; xj represents a mean of a jth output; σi represents a standard deviation of the ith input; σj represents a standard deviation of the jth output; and |Sij| represents sensitivity of the jth output to the ith input of the computational model.

9. The method according to claim 1, wherein the providing includes:
separately obtaining values of the at least one sensing parameters from a physical sensor;
determining that the physical sensor has failed; and
providing the values of the at least one sensing parameters from the virtual sensor process model to the control system.

10. A method for retrofitting a first machine lacking a supporting physical sensor with a virtual sensor created based on a second machine with a supporting physical sensor, comprising:
obtaining data records including data from a plurality of sensors that are available on both of the first machine and the second machine, and from the supporting physical sensor on the second machine;
calculating correlation values between the supporting physical sensor and each of the plurality of sensors based on the data records;
selecting correlated sensors from the plurality of sensors based on the correlation values;
creating the virtual sensor for the supporting physical sensor based on the correlated sensors; and
using the virtual sensor in the first machine to provide functionalities that were provided by the supporting physical sensor on the second machine.

11. The method according to claim 10, wherein creating includes:
establishing the virtual sensor process model indicative of interrelationships between at least one sensing parameters provided by the plurality of sensors and a plurality of measured parameters of the supporting physical sensor based on the data records.

12. The method according to claim 11, wherein the establishing includes:
obtaining data records associated with one or more input variables and the at least one sensing parameters;
selecting the plurality of measured parameters from the one or more input variables;
generating a computational model indicative of the interrelationships between the plurality of measured parameters and the at least one sensing parameters;
determining desired statistical distributions of the plurality of measured parameters of the computational model; and
recalibrating the plurality of measured parameters based on the desired statistical distributions to define a desired input space.

13. The method according to claim 12, wherein selecting further includes:
pre-processing the data records; and
using a genetic algorithm to select the plurality of measured parameters from the one or more input variables based on a mahalanobis distance between a normal data set and an abnormal data set of the data records.

14. The method according to claim 12, wherein generating further includes:
creating a neural network computational model;
training the neural network computational model using the data records; and
validating the neural network computation model using the data records.

15. The method according to claim 12, wherein determining further includes:
determining a candidate set of the measured parameters with a maximum zeta statistic using a genetic algorithm; and
determining the desired distributions of the measured parameters based on the candidate set,
wherein the zeta statistic ζ is represented by:





  
    ζ
    =
    
      
        ∑
        1
        j
      
      ⁢
      
        
          ∑
          1
          i
        
        ⁢
        
          
            
            
              S
              ij
            
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          ⁢
          
            (
            
              
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            (
            
              
                
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            )
          
        
      
    
  
  ,



provided that xi represents a mean of an ith input; xj represents a mean of a jth output; σi represents a standard deviation of the ith input; σj represents a standard deviation of the jth output; and |Sij| represents sensitivity of the jth output to the ith input of the computational model.

16. The method according to claim 10, wherein using includes:
obtaining a set of values corresponding to the plurality of measured parameters;
calculating the values of the at least one sensing parameters simultaneously based upon the set of values corresponding to the plurality of measured parameters and the virtual sensor process model; and
providing the values of the at least one sensing parameters to a control system of the first machine.

17. The method according to claim 10, wherein selecting includes:
selecting the correlated sensors each with a correlation value beyond a predetermined threshold.

18. A computer system, comprising:
a database configured to store information relevant to a virtual sensor process model; and
a processor configured to:
obtain data records including data from a plurality of sensors for the machine;
determine a virtual sensor corresponding to one of the plurality of sensors;
establish the virtual sensor process model of the virtual sensor indicative of interrelationships between at least one sensing parameters and a plurality of measured parameters based on the data records;
obtain a set of values corresponding to the plurality of measured parameters;
calculate the values of the at least one sensing parameters substantially simultaneously based upon the set of values corresponding to the plurality of measured parameters and the virtual sensor process model; and
provide the values of the at least one sensing parameters to a control system.

19. The computer system according to claim 18, wherein, to determine the virtual sensor, the processor is further configured to:
calculate correlation values between any two sensors of the plurality of sensors;
separate the plurality of sensors into a plurality of sensor groups based on the correlation values; and
determine the virtual sensor corresponding to the one of the plurality of sensors from a desired sensor group.

20. The computer system according to claim 19, wherein, to separate the plurality sensors, the processor is further configured to:
create a correlation matrix with rows representing the respective plurality of sensors, columns representing the respective plurality of sensors, and each element representing a correlation value between the corresponding two sensors from a row and a column, respectively;
determine a score for each of the plurality of sensors based on the correlation matrix; and
separate the plurality of sensors into the plurality of sensor groups based on the score of each of the plurality of sensors.

21. A machine having a retrofitted virtual sensor to provide functionalities of a corresponding physical sensor without the supporting physical sensor being installed on the machine, comprising:
a power source configured to provide power to the machine;
a control system configured to control the power source; and
a virtual sensor system, corresponding to the supporting physical sensor, including a virtual sensor process model indicative of interrelationships between at least one sensing parameters provided by a plurality of sensors and a plurality of measured parameters of the supporting physical sensor, the virtual sensor system being configured to:
obtain a set of values corresponding to the plurality of measured parameters;
calculate the values of the at least one sensing parameters simultaneously based upon the set of values corresponding to the plurality of measured parameters and the virtual sensor process model; and
provide the values of the at least one sensing parameters to the control system to provide functionalities corresponding to the supporting physical sensor,

wherein the virtual sensor is created by:
obtaining data records including data from the plurality of sensors and the supporting physical sensor;
calculating correlation values between the supporting physical sensor and the plurality of sensors based on the data records;
selecting correlated sensors from the plurality of sensors based on the correlation values; and
creating the virtual sensor of the supporting physical sensor based on the correlated sensors.

22. The method according to claim 21, wherein selecting includes:
selecting the correlated sensors each with a correlation value beyond a predetermined threshold.

23. The method according to claim 21, wherein the creating includes:
obtaining data records associated with one or more input variables and the at least one sensing parameters;
selecting the plurality of measured parameters from the one or more input variables;
generating a computational model indicative of the interrelationships between the plurality of measured parameters and the at least one sensing parameters;
determining desired statistical distributions of the plurality of measured parameters of the computational model; and
recalibrating the plurality of measured parameters based on the desired statistical distributions to define a desired input space.