Patent Publication Number: US-2021164826-A1

Title: Detecting a change in a vibratory meter based on two baseline meter verifications

Description:
TECHNICAL FIELD 
     The embodiments described below relate to changes in a vibratory meter and, more particularly, to detecting a change in the vibratory meter based on two or more baseline meter verifications. 
     BACKGROUND 
     Vibratory meters, such as for example, Coriolis mass flowmeters, liquid density meters, gas density meters, liquid viscosity meters, gas/liquid specific gravity meters, gas/liquid relative density meters, and gas molecular weight meters, are generally known and are used for measuring characteristics of fluids. Generally, vibratory meters comprise a meter assembly and an electronics portion. The material within the meter assembly may be flowing or stationary. Each type of sensor may have unique characteristics, which a meter must account for in order to achieve optimum performance. For example, some sensors may require a tube apparatus to vibrate at particular displacement levels. Other meter assembly types may require special compensation algorithms. 
     The meter electronics, among performing other functions, typically include stored sensor calibration values for the particular sensor being used. For example, the meter electronics may include a stiffness measurement. The reference sensor stiffness represents a fundamental measurement related to the sensor geometry for a specific meter assembly, for example, as measured in the factory under reference conditions or when it was last calibrated. A change between a stiffness measured after a vibratory meter is installed at a customer site and a reference sensor stiffness may represent physical change in the meter assembly due to coating, erosion, corrosion, or damage to conduits in the meter assembly, in addition to other causes. A meter verification or health check test can detect these changes. 
     The meter verification may determine if a difference between the measured stiffness and the reference stiffness is within a range. For example, the comparison may determine if the measured stiffness is within a range of the reference stiffness. If the comparison indicates a change of greater than or outside the range, the vibratory meter can send an alarm to notify the user to investigate the fault. This simple comparison of a single stiffness value may not, however, be able to indicate the underlying cause of the fault. That is, the user will not know if the fault is due to erosion/corrosion, damage (e.g., freezing, over-pressurization, etc.), or a coating. This is due to the range being set to include all of the possible underlying causes or changes to the conduits and to prevent false alarms—causes that are not due to changes in the conduits. Examples of false alarms are increased variation in stiffness measurements caused by high velocity or high noise gas flows. 
     If the changes can be correctly detected, then the changes can be detected early in their formation. Additionally, correctly detecting the changes can minimize false alarms. If the changes to the conduits can be identified, the user can be notified with an indication of the nature of the change. This can prevent downtime of the vibratory meter due to false alarms and ensure that the post-alarm procedures are more suited to the condition in the vibratory meter. The above benefits may be improved by using two or more baseline measurements to identify the change. Accordingly, there is a need for detecting and identifying a change in a vibratory meter based on two or more baseline measurements. 
     SUMMARY 
     A meter electronics for detecting a change in a vibratory meter based on two or more baseline meter verifications is provided. According to an embodiment, the meter electronics comprises an interface configured to receive sensor signals from a meter assembly and provide information based on the sensor signals, and a processing system communicatively coupled to the interface. The processing system is configured to use the information to determine a first baseline meter verification value at a first set of process conditions, determine a second baseline meter verification value at a second set of process conditions, and determine a baseline meter verification value based on the first baseline meter verification value and the second baseline meter verification value. 
     A method of detecting a change in a vibratory meter based on two or more baseline meter verifications is provided. According to an embodiment, the method comprises receiving with an interface sensor signals from a meter assembly and providing information based on the sensor signals, determining a first baseline meter verification value at a first set of process conditions, determining a second baseline meter verification value at a second set of process conditions, and determining a baseline meter verification value based on the first baseline meter verification value and the second baseline meter verification value. 
     Aspects 
     According to an aspect, a meter electronics ( 20 ) for detecting a change in a vibratory meter ( 5 ) based on two or more baseline meter verifications comprises an interface ( 201 ) configured to receive sensor signals ( 100 ) from a meter assembly ( 10 ) and provide information based on the sensor signals ( 100 ), and a processing system ( 202 ) communicatively coupled to the interface ( 201 ). The processing system ( 202 ) is configured to use the information to determine a first baseline meter verification value at a first set of process conditions, determine a second baseline meter verification value at a second set of process conditions, and determine a baseline meter verification value based on the first baseline meter verification value and the second baseline meter verification value. 
     Preferably, the processing system ( 202 ) being configured to determine the first baseline meter verification value and the second baseline meter verification value comprises the processing system ( 202 ) being configured to determine one of a first baseline stiffness value and a second baseline stiffness value, and a first baseline mass value and a second baseline mass value. 
     Preferably, the processing system ( 202 ) being configured to determine the baseline meter verification value based on the first baseline meter verification value and the second baseline meter verification value comprises the processing system ( 202 ) being configured to interpolate the baseline meter verification value from the first baseline meter verification value and the second baseline meter verification value. 
     Preferably, the processing system ( 202 ) is configured to interpolate the baseline meter verification value relative to a common parameter of the first set of process conditions and the second set of process conditions. 
     Preferably, the processing system ( 202 ) being configured to interpolate the baseline meter verification value comprises the processing system ( 202 ) being configured to linearly interpolate the baseline meter verification value. 
     Preferably, the processing system ( 202 ) is further configured to determine a condition of a conduit ( 130 ,  130 ′) in the vibratory meter ( 5 ), wherein the condition of the conduit ( 130 ,  130 ′) comprises at least one of an erosion, a corrosion, a damage, and a coating of the conduit ( 130 ,  130 ′). 
     Preferably, the processing system ( 202 ) is further configured to obtain a central tendency value and a dispersion value and determine a probability based on the central tendency value and the dispersion value to detect if the central tendency value is different than the baseline meter verification value. 
     Preferably, the processing system ( 202 ) being configured to determine a probability based on the central tendency value and the dispersion value comprises the processing system ( 202 ) being configured to calculate a t-value and calculate the probability using the t-value. 
     A method of detecting a change in a vibratory meter based on two or more baseline meter verifications comprises receiving with an interface sensor signals from a meter assembly and providing information based on the sensor signals, determining a first baseline meter verification value at a first set of process conditions, determining a second baseline meter verification value at a second set of process conditions, and determining a baseline meter verification value based on the first baseline meter verification value and the second baseline meter verification value. 
     Preferably, determining the first baseline meter verification value and the second baseline meter verification value comprises determining one of a first baseline stiffness value and a second baseline stiffness value, and a first baseline mass value and a second baseline mass value. 
     Preferably, determining the baseline meter verification value based on the first baseline meter verification value and the second baseline meter verification value comprises interpolating the baseline meter verification value from the first baseline meter verification value and the second baseline meter verification value. 
     Preferably interpolating the baseline meter verification value comprises the processing system being configured to linearly interpolate the baseline meter verification value. 
     Preferably, the method further comprises determining a condition of a conduit of the vibratory meter based on the baseline meter verification value, the condition comprising at least one of an erosion, a corrosion, a damage, and a coating of the conduit of the vibratory meter. 
     Preferably, the method further comprises obtaining a central tendency value and a dispersion value and determining a probability based on the central tendency value and the dispersion value to detect if the central tendency value is different than the baseline meter verification value. 
     Preferably, determining a probability based on the central tendency value and the dispersion value comprises the processing system being configured to calculate a t-value and calculate the probability using the t-value. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The same reference number represents the same element on all drawings. It should be understood that the drawings are not necessarily to scale. 
         FIG. 1  shows a vibratory meter  5 . 
         FIG. 2  shows the meter electronics  20  for detecting and identifying a change in a vibratory meter according to an embodiment. 
         FIGS. 3 a  and 3 b    show graphs  300   a ,  300   b  that illustrate stiffness change and stiffness symmetry variations determined during multiple meter verification runs. 
         FIGS. 4 a  and 4 b    show graphs  400   a ,  400   b  that illustrate stiffness change and stiffness symmetry variation data points determined during multiple meter verification runs, where a probability distribution is assigned to each data point. 
         FIGS. 5 a  and 5 b    show graphs  500   a ,  500   b  that illustrate stiffness change and stiffness symmetry variation data points determined during multiple meter verification runs, where a probability is assigned to each data point. 
         FIG. 6  shows a method  600  for detecting and identifying a change in a vibratory meter according to an embodiment. 
         FIG. 7  shows a method  700  for detecting and identifying a change in a vibratory meter according to an embodiment. 
         FIG. 8  shows a graph  800  illustrating two baseline measurements that can be used to detect a change in a vibratory meter. 
         FIG. 9  shows a method  900  for detecting a change in a vibratory meter based on two or more baseline meter verifications. 
     
    
    
     DETAILED DESCRIPTION 
       FIGS. 1-9  and the following description depict specific examples to teach those skilled in the art how to make and use the best mode of embodiments of detecting a change in a vibratory meter based on two or more meter verifications. For the purpose of teaching inventive principles, some conventional aspects have been simplified or omitted. Those skilled in the art will appreciate variations from these examples that fall within the scope of the present description. Those skilled in the art will appreciate that the features described below can be combined in various ways to form multiple variations of detecting the change in the vibratory meter based on two or more meter verifications. As a result, the embodiments described below are not limited to the specific examples described below, but only by the claims and their equivalents. 
     A baseline meter verification value may be determined based on the first baseline meter verification value and the second baseline meter verification value. The first and second baseline meter verification values may respectively be determined at a first and second set of process conditions. For example, the first baseline meter verification value may be determined at a resonant frequency that is different than a resonant frequency of the second baseline meter verification value. By using, for example interpolation between these two frequencies, the baseline meter verification value may correspond to, for example, a resonant frequency that is the same as a resonant frequency of an online or process meter verification. As a result, therefore, the baseline stiffness meter verification value is a more accurate reference value for the stiffness at the process conditions of the online or process meter verification, yielding a more accurate detection of the change in the vibratory meter. 
     The change in the vibratory meter can be accurately detected by using the baseline meter verification value determined based on a first and a second baseline meter verification values determined at different process conditions and by using statistics. Statistics previously was not used in a meter electronics due to the meter electronics having limited computing abilities compared to, for example, a computer workstation running statistical software. The statistical methods employed herein exploits data available in registers of a processing system in the meter electronics to enable embedded code to calculate a probability that a change is not present in the vibratory meter. By calculating this probability, a null hypothesis that changes have not occurred can be rejected, thereby indicating that the probability a change has occurred in the vibratory meter is high. Because the probability is calculated by the meter electronics, even with limited computing resources, this probability may be updated as the meter verifications are performed. Accordingly, changes that would not be detected by comparing a stiffness change to, for example, a predetermined limit, can be detected. In addition, the accurate detection of the change can prevent false alarms. 
     The change in the vibratory meter can be identified by determining a condition, such as erosion, corrosion, damage, or the like, of a conduit of the vibratory meter based on a first stiffness change associated with a first location of the conduit and a second stiffness change associated with a second location of the conduit. For example, the condition may be determined based on whether the first and second stiffness changes indicate an increase or decrease in stiffness. Additionally, the symmetry of the first and second stiffness changes may be used to determine the condition. In one example, if the first stiffness change indicates a decrease, the second stiffness change indicates an increase, and the stiffness symmetry is considered “right low”, then the determined condition may be erosion or corrosion of the conduits in the vibratory meter. 
       FIG. 1  shows a vibratory meter  5 . As shown in  FIG. 1 , the vibratory meter  5  comprises a meter assembly  10  and meter electronics  20 . The meter assembly  10  responds to mass flow rate and density of a process material. The meter electronics  20  is connected to the meter assembly  10  via sensor signals  100  to provide density, mass flow rate, and temperature information over path  26 , as well as other information. 
     The meter assembly  10  includes a pair of manifolds  150  and  150 ′, flanges  103  and  103 ′ having flange necks  110  and  110 ′, a pair of parallel conduits  130  and  130 ′, driver  180 , resistive temperature detector (RTD)  190 , and a pair of pick-off sensors  1701  and  170   r . Conduits  130  and  130 ′ have two essentially straight inlet legs  131 ,  131 ′ and outlet legs  134 ,  134 ′, which converge towards each other at conduit mounting blocks  120  and  120 ′. The conduits  130 ,  130 ′ bend at two symmetrical locations along their length and are essentially parallel throughout their length. Brace bars  140  and  140 ′ serve to define the axis W and W′ about which each conduit  130 ,  130 ′ oscillates. The legs  131 ,  131 ′ and  134 ,  134 ′ of the conduits  130 ,  130 ′ are fixedly attached to conduit mounting blocks  120  and  120 ′ and these blocks, in turn, are fixedly attached to manifolds  150  and  150 ′. This provides a continuous closed material path through meter assembly  10 . 
     When flanges  103  and  103 ′, having holes  102  and  102 ′ are connected, via inlet end  104  and outlet end  104 ′ into a process line (not shown) which carries the process material that is being measured, material enters inlet end  104  of the meter through an orifice  101  in the flange  103  and is conducted through the manifold  150  to the conduit mounting block  120  having a surface  121 . Within the manifold  150  the material is divided and routed through the conduits  130 ,  130 ′. Upon exiting the conduits  130 ,  130 ′, the process material is recombined in a single stream within the block  120 ′ having a surface  121 ′ and the manifold  150 ′ and is thereafter routed to outlet end  104 ′ connected by the flange  103 ′ having holes  102 ′ to the process line (not shown). 
     The conduits  130 ,  130 ′ are selected and appropriately mounted to the conduit mounting blocks  120 ,  120 ′ so as to have substantially the same mass distribution, moments of inertia and Young&#39;s modulus about bending axes W—W and W′—W′, respectively. These bending axes go through the brace bars  140 ,  140 ′. Inasmuch as the Young&#39;s modulus of the conduits change with temperature, and this change affects the calculation of flow and density, RTD  190  is mounted to conduit  130 ′ to continuously measure the temperature of the conduit  130 ′. The temperature of the conduit  130 ′ and hence the voltage appearing across the RTD  190  for a given current passing therethrough is governed by the temperature of the material passing through the conduit  130 ′. The temperature dependent voltage appearing across the RTD  190  is used in a well-known method by the meter electronics  20  to compensate for the change in elastic modulus of the conduits  130 ,  130 ′ due to any changes in conduit temperature. The RTD  190  is connected to the meter electronics  20  by lead  195 . 
     Both of the conduits  130 ,  130 ′ are driven by driver  180  in opposite directions about their respective bending axes W and W′ and at what is termed the first out-of-phase bending mode of the flow meter. This driver  180  may comprise any one of many well-known arrangements, such as a magnet mounted to the conduit  130 ′ and an opposing coil mounted to the conduit  130  and through which an alternating current is passed for vibrating both conduits  130 ,  130 ′. A suitable drive signal is applied by the meter electronics  20 , via lead  185 , to the driver  180 . 
     The meter electronics  20  receives the RTD temperature signal on lead  195 , and the left and right sensor signals appearing on sensor signals  100  carrying the left and right sensor signals  1651 ,  165   r , respectively. The meter electronics  20  produces the drive signal appearing on lead  185  to driver  180  and vibrate conduits  130 ,  130 ′. The meter electronics  20  processes the left and right sensor signals and the RTD signal to compute the mass flow rate and the density of the material passing through meter assembly  10 . This information, along with other information, is applied by meter electronics  20  over path  26  as a signal. 
     A mass flow rate measurement {dot over (m)} can be generated according to the equation: 
         {dot over (m)}=FCF [Δ t−Δt   0 ]  [1]
 
     The Δt term comprises an operationally-derived (i.e., measured) time delay value comprising the time delay existing between the pick-off sensor signals, such as where the time delay is due to Coriolis effects related to mass flow rate through the vibratory meter  5 . The measured Δt term ultimately determines the mass flow rate of the flow material as it flows through the vibratory meter  5 . The Δt 0  term comprises a time delay at zero flow calibration constant. The Δt 0  term is typically determined at the factory and programmed into the vibratory meter  5 . The time delay at zero flow Δt 0  term will not change, even where flow conditions are changing. The flow calibration factor FCF is proportional to the stiffness of the flow meter. 
     It is a problem that the conduits may change with time, wherein an initial factory calibration may change over time as the conduits  130 ,  130 ′ are corroded, eroded, or otherwise changed. As a consequence, the conduits&#39;  130 ,  130 ′ stiffness may change from an initial representative stiffness value (or original measured stiffness value) over the life of the vibratory meter  5 . Meter verification can detect such changes in the conduits&#39;  130 ,  130 ′ stiffness, as is explained below. 
       FIG. 2  shows the meter electronics  20  for detecting and identifying a change in a vibratory meter according to an embodiment. The meter electronics  20  can include an interface  201  and a processing system  202 . The meter electronics  20  receives a vibrational response, such as from the meter assembly  10 , for example. The meter electronics  20  processes the vibrational response in order to obtain flow characteristics of the flow material flowing through the meter assembly  10 . 
     As previously discussed, the flow calibration factor FCF reflects the material properties and cross-sectional properties of the flow tube. A mass flow rate of flow material flowing through the flow meter is determined by multiplying a measured time delay (or phase difference/frequency) by the flow calibration factor FCF. The flow calibration factor FCF can be related to a stiffness characteristic of the meter assembly. If the stiffness characteristic of the meter assembly changes, then the flow calibration factor FCF will also change. Changes in the stiffness of the flow meter therefore will affect the accuracy of the flow measurements generated by the flow meter. 
     The interface  201  receives the vibrational response from one of the pick-off sensors  1701 ,  170   r  via the sensor signals  100  of  FIG. 1 . The interface  201  can perform any necessary or desired signal conditioning, such as any manner of formatting, amplification, buffering, etc. Alternatively, some or all of the signal conditioning can be performed in the processing system  202 . In addition, the interface  201  can enable communications between the meter electronics  20  and external devices. The interface  201  can be capable of any manner of electronic, optical, or wireless communication. The interface  201  can provide information based on the vibrational response. 
     The interface  201  in one embodiment is coupled with a digitizer (not shown), wherein the sensor signal comprises an analog sensor signal. The digitizer samples and digitizes an analog vibrational response and produces the digital vibrational response. 
     The processing system  202  conducts operations of the meter electronics  20  and processes flow measurements from the meter assembly  10 . The processing system  202  executes one or more processing routines and thereby processes the flow measurements in order to produce one or more flow characteristics. The processing system  202  is communicatively coupled to and is configured to receive the information from the interface  201 . 
     The processing system  202  can comprise a general purpose computer, a micro-processing system, a logic circuit, or some other general purpose or customized processing device. Additionally or alternatively, the processing system  202  can be distributed among multiple processing devices. The processing system  202  can also include any manner of integral or independent electronic storage medium, such as the storage system  204 . 
     The storage system  204  can store flow meter parameters and data, software routines, constant values, and variable values. In one embodiment, the storage system  204  includes routines that are executed by the processing system  202 , such as the operational routine  210  and verification  220  of the vibratory meter  5 . The storage system can also store statistical values, such as, a standard deviation, confidence intervals or the like. 
     The storage system  204  can store a baseline meter stiffness  230 . The baseline meter stiffness  230  may be determined during manufacturing or calibration of the vibratory meter  5 , or during a prior recalibration. For example, the baseline meter stiffness  230  can be determined by the verification  220  before the vibratory meter  5  is installed in the field. The baseline meter stiffness  230  is representative of the stiffness of the conduits  130 ,  130 ′ before any changes have occurred, such as erosion/corrosion, damage (e.g., freezing, over-pressurization, etc.), coatings, etc. The baseline meter stiffness  230  may be a mean of a plurality of baseline meter stiffness measurements. As such, the baseline meter stiffness  230  may have an associated dispersion characteristic, as will be discussed in more detail below, where the baseline meter stiffness measurements may vary. The more the baseline meter stiffness measurements vary, the greater the dispersion. 
     The storage system  204  can store a meter stiffness  232 . The meter stiffness  232  comprises a stiffness value that is determined from vibrational responses generated during operation of the vibratory meter  5 . The meter stiffness  232  may be generated in order to verify proper operation of the vibratory meter  5 . The meter stiffness  232  may be generated for a verification process, wherein the meter stiffness  232  serves the purpose of verifying proper and accurate operation of the vibratory meter  5 . Similar to the baseline meter stiffness  230 , the meter stiffness  232  may be a mean of a plurality of meter stiffness measurements. As such, the meter stiffness  232  may have an associated dispersion characteristic, as will be discussed in more detail below, where the meter stiffness measurements may vary. The more the meter stiffness measurements vary, the greater the dispersion characteristic. 
     The storage system  204  can store a stiffness change  234 . The stiffness change  234  can be a value that is determined by comparing the baseline meter stiffness  230  and the meter stiffness  232 . For example, the stiffness change  234  can be a difference between the baseline meter stiffness  230  and the meter stiffness  232 . In this example, a negative number may indicate that the stiffness of the conduits  130 ,  130 ′ increased since being installed in the field. A positive number may indicate that the physical stiffness of the conduits  130 ,  130 ′ decreased since the baseline meter stiffness  230  was determined. 
     As can be appreciated, the comparison may be performed in various ways. For example, the stiffness change  234  may be a difference between the meter stiffness  232  and the baseline meter stiffness  230 . Accordingly, an increase in stiffness will result in a positive number and a decrease in stiffness will result in a negative number. Additionally or alternatively, values derived from or related to the baseline meter stiffness  230  and/or the meter stiffness  232  can be employed, such as ratios that employ other values, such as conduit geometry, dimensions, or the like. 
     If the meter stiffness  232  is substantially the same as the baseline meter stiffness  230 , then it can be determined that the vibratory meter  5 , or more specifically, the conduits  130 ,  130 ′, may be relatively unchanged from when it was manufactured, calibrated, or when the vibratory meter  5  was last re-calibrated. Alternatively, where the meter stiffness  232  significantly differs from the baseline meter stiffness  230 , then it can be determined that the conduits  130 ,  130 ′ have degraded and may not be operating accurately and reliably, such as where the conduits  130 ,  130 ′ have changed due to erosion, corrosion, damage (e.g., freezing, over-pressurization, etc.), coating, or other condition. 
     As discussed above, the baseline meter stiffness  230  and the meter stiffness  232  are determined for both the left and right pick-off sensors  1701 ,  170   r . That is, the baseline meter stiffness  230  and the meter stiffness  232  are proportional to the stiffness of the conduits  130 ,  130 ′ between the left and right pick-off sensors  1701 ,  170   r . As a result, different conditions of the conduits  130 ,  130 ′ can cause similar stiffness changes  234 . For example, erosion, corrosion, and/or damage to the conduits  130 ,  130 ′ can result in similar decreases in physical stiffness, which may be indicated by a negative or “low” stiffness change  234 . Accordingly, when only relying on the stiffness change  234 , the specific condition of the conduits  130 ,  130 ′ may not be ascertainable. 
     However, the left pick-off sensor  1701  and the right pick-off sensor  170   r  can each have their own associated stiffness value. More specifically, as discussed above, the driver  180  applies a force to the conduits  130 ,  130 ′ and the pick-off sensors  1701 ,  170   r  measure a resulting deflection. The amount of deflection of the conduits  130 ,  130 ′ at the location of the pick-off sensors  1701 ,  170   r  is proportional to the stiffness of the conduits  130 ,  130 ′ between the driver  180  and the pick-off sensors  1701 ,  170   r.    
     Accordingly, the stiffness associated with the left pick-off sensor  1701  is proportional to the physical stiffness of the conduits  130 ,  130 ′ between the driver  180  and the left pick-off sensor  1701  and the stiffness associated with the right pick-off sensor  170   r  is proportional to the physical stiffness of the conduits  130 ,  130 ′ between the driver  180  and the right pick-off sensor  170   r . Therefore, if there is erosion, corrosion, damage, coating, or the like, between the driver  180  and, for example, the right pick-off sensor  170   r , then the stiffness associated with the right pick-off sensor  170   r  may decrease whereas the stiffness associated with the left pick-off sensor  1701  may not change. To track the changes, the storage system  204  may also include stiffness values associated with the left and right pick-off sensors  1701 ,  170   r.    
     For example, as shown in  FIG. 2 , the storage system  204  includes a baseline LPO stiffness  240 , which is proportional to the physical stiffness of the conduits  130 ,  130 ′ between the driver  180  and the location of the left pick-off sensor  1701  on the conduits  130 ,  130 ′. Similarly, the storage system  204  also includes a baseline RPO stiffness  250 , which is proportional to the physical stiffness of the conduits  130 ,  130 ′ between the driver  180  and the location of the right pick-off sensor  170   r  on the conduits  130 ,  130 ′. The baseline LPO and RPO stiffness  240 ,  250  may be determined by the verification  220  before the vibratory meter  5  is installed in the field, such as, for example, during manufacture or calibration of the vibratory meter  5 , or during a prior recalibration. 
     The storage system  204  also includes an LPO stiffness  242  and an RPO stiffness  252 . The LPO stiffness  242  is proportional to the physical stiffness of the conduits  130 ,  130 ′ between the driver  180  and the location of the left pick-off sensor  1701 , but after the baseline LPO stiffness  240  is determined. Similarly, the RPO stiffness  252  is proportional to the physical stiffness of the conduits  130 ,  130 ′ between the driver  180  and the location of the right pick-off sensor  170   r , but after the baseline RPO stiffness  250  is determined. 
     Also as shown in  FIG. 2 , the storage system  204  further includes an LPO stiffness change  244  and an RPO stiffness change  254 . The LPO and RPO stiffness change  244 ,  254  are proportional to a difference between the baseline LPO, RPO stiffness  240 ,  250  and the LPO, RPO stiffness  242 ,  252 . For example, a negative LPO stiffness change  244  may indicate that the physical stiffness of the conduits  130 ,  130 ′ between the driver  180  and the left pick-off sensor  1701  has increased. A positive LPO stiffness change  244  may indicate that the physical stiffness of the conduits  130 ,  130 ′ between the driver  180  and the left pick-off sensor  1701  decreased since the baseline LPO stiffness  240  was determined. Alternatively, the LPO and RPO stiffness change  244 ,  254  may be a difference between the LPO and RPO stiffness  242 ,  252  and the baseline LPO and RPO stiffness  240 ,  250 . Accordingly, for example, a positive LPO stiffness change  244  can indicate that the physical stiffness of the conduits  130 ,  130 ′ between the driver  180  and the left pick-off sensor  1701  increased since the baseline LPO stiffness  240  was determined. Although the LPO and RPO stiffness change  244 ,  254  are described as being determined from a difference, any values derived from or related to the baseline LPO and RPO stiffness  240 ,  250  and the LPO and RPO stiffness  242 ,  252  can be employed, such as a ratio of a stiffness value and other values, such as a conduit geometry, dimensions, or the like. The LPO and RPO stiffness change  244 ,  254  can be expressed in any suitable units, such as whole numbers, ratios, percentages etc. 
     An increase or decrease in the physical stiffness associated with the left and right pick-off sensors  1701 ,  170   r  can indicate an underlying condition of the conduit  130 ,  130 ′ that is causing the physical stiffness change. For example, erosion of an inner wall of the conduits  130 ,  130 ′ may reduce the physical stiffness of the conduits  130 ,  130 ′. In particular, erosion, for example, of the inner wall of the conduits  130 ,  130 ′ between the left pick-off sensor  1701  and the driver  180  may cause the physical stiffness of the conduits  130 ,  130 ′ between the left pick-off sensor  1701  and the driver  180  to decrease. Conversely, an increase in stiffness may indicate that, for example, coatings have formed on the inner wall. 
     Additionally, the relative increase or decrease of the physical stiffness of the conduits  130 ,  130 ′ between the driver  180  and the left pick-off sensor  1701  and the physical stiffness of the conduits  130 ,  130 ′ between the driver  180  and the right pick-off sensor  170   r  can further indicate the underlying condition of the conduits  130 ,  130 ′ causing the physical stiffness change. This relative increase or decrease in the physical stiffness may be indicated by a stiffness symmetry  260  in the storage system  204 . 
     The stiffness symmetry  260  can be any suitable value or values that indicate the relative values of, for example, the LPO stiffness change  244  and the RPO stiffness change  254 . For example, the LPO stiffness change  244  and the RPO stiffness change  254  may indicate that the physical stiffness of the conduits  130 ,  130 ′ associated with the left and right pick-off sensors  1701 ,  170   r  both increased, but that, for example, the physical stiffness associated with the left pick-off sensor  1701  increased more than the physical stiffness associated with the right pick-off sensor  170   r . In one example, the stiffness symmetry  260  can be expressed in percentages and be determined by: 
       SMV Symmetry %=SMV stiffness,LPO %−SMV Stiffness,RPO %;
 
     where:
         SMV stiffness,LPO % is, in this example, the LPO stiffness change  244  expressed in percentage change; and   SMV Stiffness,RPO % is, in this example, the RPO stiffness change  254  expressed in percentage change.       

     The stiffness change  234 , LPO stiffness change  244 , RPO stiffness change  254 , and stiffness symmetry  260  may be any suitable value, such as, for example, a value that is directly proportional to the property being measured, an intermediate value that represents the physical stiffness, a value that indicates whether there was an increase or decrease in the physical stiffness, etc. For example, the LPO stiffness change  244  may be a positive or negative value proportional to the stiffness change. The processing system  202  can further process these values to generate a toggle indicator where only an increase or decrease in the physical stiffness of the conduits  130 ,  130 ′ between the driver  180  and the left pick-off sensor  1701  is indicated. These values and/or toggle indicators can be utilized to determine the underlying change in the conduits  130 ,  130 ′, as is shown in the following truth table. 
                                                                                     Condition of                                   conduits 130,                                   130′           LPO   LPO   RPO   RPO   Stiffness   Stiffness   UN = unchanged           Stiffness   Stiffness   Stiffness   Stiffness   Symmetry   Symmetry   CT = coating           Change   Change   Change   Change   260   260   E = erosion           244   244   254   254   (High   (Low   C = corrosion       Case   (High)   (Low)   (High)   (Low)   Right)   Right)   D = damage                  A   0   0   0   0   0   0   UN       B   0   0   0   0   0   1   CT or E/C       C   0   0   0   0   1   0   CT or E/C       D   0   1   0   1   0   0   C       E   1   0   1   0   0   0   D       F   0   0   1   0   1   0   CT or D       G   0   0   0   1   0   1   CT or E/C       H   1   0   0   0   0   1   CT or D       I   0   1   0   0   1   0   CT or E/C       J   0   1   0   1   0   1   E/C       K   0   1   0   1   1   0   E/C       L   1   0   1   0   0   1   D       M   1   0   1   0   1   0   D       N   1   0   0   1   0   1   CT       O   0   1   1   0   1   0   CT                    
As can be seen, the combinations of the LPO stiffness change  244 , RPO stiffness change  254 , and stiffness symmetry  260  can be used to distinguish between the different possible changes in the conduits  130 ,  130 ′. For example, both case J and N have stiffness symmetry  260  values that are “low right” and RPO stiffness change  254  that are “low.” However, case J has a LPO stiffness change  244  of “low” whereas case N has a LPO stiffness change  244  of “high.” Case J is indicated as a possible erosion/corrosion of the conduits  130 ,  130 ′, whereas case N is indicated as a possible coating of the conduits  130 ,  130 ′.
 
     Although the above table utilizes the LPO stiffness change  244 , RPO stiffness change  254 , and stiffness symmetry  260  to determine the condition of the conduits  130 ,  130 ′, any suitable means, such as, alternative tables, logic, objects, relationships, circuits, processors, routines, or the like, can be employed to determine the condition in the conduit. For example, referring to the meter electronics  20  described with reference to  FIG. 2 , only the LPO stiffness change  244  and RPO stiffness change  254  may be utilized to determine the condition of the conduits  130 ,  130 ′. However, as can be appreciated, utilizing the stiffness symmetry  260  may allow for more specific determinations of the condition of the conduits  130 ,  130 ′. 
     Additionally or alternatively, the actual values of the LPO stiffness change  244 , RPO stiffness change  254 , and stiffness symmetry  260  may be employed instead of the toggle indicator to determine the condition of the conduit. For example, the conditions determined by the above table may be supplemented by further steps that determine, for example, that case J is more likely to be corrosion, rather than erosion, if the stiffness symmetry  260  is a relatively small “right low.” That is, the relatively small “right low” stiffness symmetry  260  may be due to the more uniform nature of corrosion compared to erosion, which may be more prevalent at an inlet of a conduit. 
     Although the above discussion pertained to meter stiffness, other meter verification parameters may be employed, additionally or alternatively. For example, a residual flexibility may be compared to a baseline residual flexibility. Residual flexibility can be defined as a portion of a frequency response associated with one vibration mode that is at a resonant frequency of another vibration mode. For example, a frequency response of various vibration modes (e.g., bend, twist, etc.) may be characterized as a frequency response function (e.g., magnitude response relative to frequency). The frequency response function is typically centered at a resonant frequency of a given vibration mode with a sloping decrease in magnitude in proportion to the distance from the resonant frequency. For example, a first order bend mode (e.g., main out-of-phase bend mode) with two-nodes located at brace bars, may have a first order bend mode resonant frequency ω 1 . A second order bend mode with four nodes may have a second order bend mode resonant frequency ω 2  that is greater than the first order bend mode resonant frequency ω 1 . The frequency response function of the second order bend mode can overlap the first order bend mode resonant frequency ω 1 . Accordingly, the residual flexibility of the first order bend mode caused by the second order bend mode is the portion of the frequency response function of the second order bend mode that lies at the first order bend mode resonant frequency ω 1 . As can be appreciated, when erosion, corrosion, damage, coating, or the like occurs, this residual flexibility value of a given mode may change because the frequency response of each vibration mode will change. Accordingly, the residual flexibility can also be used to identify a change in the vibratory meter. 
     Damping can also be employed. For example, the meter verification can compare a measured damping value to a baseline damping value. Damping can be useful in detecting coating because damping may not be affected by erosion or corrosion. 
     Similarly, a mass associated with the left or right pick-off sensors  1701 ,  170   r  can be compared to a baseline mass associated with the left or right pick-off sensors  1701 ,  170   r . In one example, an expected mass may be employed. In an example, an expected mass based on the calibrated air and water mass values and the measured or known density of the process fluid may be calculated using the below equation: 
     
       
         
           
             
               
                 
                   
                     
                       m 
                       expected 
                     
                     = 
                     
                       
                         m 
                         
                           factory 
                           , 
                           air 
                         
                       
                       + 
                       
                         
                           
                             ( 
                             
                               
                                 m 
                                 
                                   factory 
                                   , 
                                   water 
                                 
                               
                               - 
                               
                                 m 
                                 
                                   factory 
                                   , 
                                   air 
                                 
                               
                             
                             ) 
                           
                           
                             ( 
                             
                               
                                 ρ 
                                 water 
                               
                               - 
                               
                                 ρ 
                                 air 
                               
                             
                             ) 
                           
                         
                          
                         
                           ( 
                           
                             
                               ρ 
                               
                                 k 
                                  
                                 n 
                                  
                                 o 
                                  
                                 w 
                                  
                                 n 
                               
                             
                             - 
                             
                               ρ 
                               
                                 a 
                                  
                                 i 
                                  
                                 r 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   ; 
                 
               
               
                 
                   [ 
                   2 
                   ] 
                 
               
             
           
         
       
     
     where:
         m expected  is the expected mass—the mass that should be measured if change did not occur in the vibratory meter;   m factory,air  is a mass measured where the vibratory meter is filled with air;   ρ air  is a density of air;   ρ water  is a density value of water; and   ρ known  is a density of the material being measured.
 
The expected mass m expected  can be used to calculate a normalized mass deviation expressed as a percent via the following equation:
       

     
       
         
           
             
               
                 
                   
                     
                       m 
                       Deviation 
                     
                     = 
                     
                       
                         
                           
                             m 
                             
                               m 
                                
                               e 
                                
                               a 
                                
                               s 
                                
                               u 
                                
                               r 
                                
                               e 
                                
                               d 
                             
                           
                           - 
                           
                             m 
                             
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                                
                               x 
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                               p 
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                               e 
                                
                               c 
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                               t 
                                
                               e 
                                
                               d 
                             
                           
                         
                         
                           m 
                           
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                              
                             x 
                              
                             p 
                              
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                             d 
                           
                         
                       
                       * 
                       1 
                        
                       0 
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                       0 
                     
                   
                   ; 
                 
               
               
                 
                   [ 
                   3 
                   ] 
                 
               
             
           
         
       
     
     where:
         m measured  is a mass measured during meter verification; and   m Deviation  is a mass deviation of the measured mass m measured  from the expected mass m expected .
 
As can be appreciated, erosion, corrosion, damage, coating, or the like, can affect the mass of the conduits in the vibratory meter. Accordingly, the expected mass can be used to detect a change in the vibratory meter by comparing a measured mass to the expected mass.
       

     As discussed above, conduit geometries may also be considered when determining the condition of the conduit. For example, U-shaped tubes may be more prone to erosion than corrosion at certain locations in the conduit compared to, for example, a straight tube. Additionally or alternatively, some process/conduit combinations may be more prone to certain conditions. For example, the conduits  130 ,  130 ′ may be more prone to damage in cryogenic processes that employ nitrogen compared to high temperature processes that employ a corrosive material. Accordingly, the LPO stiffness change  244 , RPO stiffness change  254 , and stiffness symmetry  260 , or the methods that use these values, can include, for example, other values, such as factors related to conduit geometry, construction, dimensions, process variables, etc. 
     As can also be seen in  FIG. 2 , the storage system  204  can also store a stiffness standard deviation  236 , an LPO stiffness standard deviation  246 , and an RPO stiffness standard deviation  256 . These values can be determined from the meter stiffness measurements that, for example, comprise the baseline meter stiffness  230  and the meter stiffness  232 . For example, the stiffness standard deviation  236  may be a pooled standard deviation. Accordingly, the stiffness standard deviation  236  is a measure of how much the meter stiffness  232  varied, including the meter stiffness measurements that comprise the baseline meter stiffness  230 . The LPO stiffness standard deviation  246  and the RPO stiffness standard deviation  256  may also be pooled standard deviations. 
     Although the example shown in  FIG. 2  utilizes stiffness standard deviation, other measures of variation and dispersion in a meter verification parameter data may be employed. For example, a variance may be employed instead of a standard deviation. That is, the stiffness standard deviation  236 , LPO stiffness standard deviation  246 , and RPO stiffness standard deviation  256  are dispersion values of an exemplary meter verification parameter. Additionally or alternatively, other measures of central tendency can be employed instead of a mean value that may be employed for the baseline meter stiffness  230  and the meter stiffness  232 . Accordingly, the baseline meter stiffness  230  and meter stiffness  232  are central tendency values of an exemplary meter verification parameter. 
     The storage can also store other statistical values, such as a confidence interval  270 . As will be explained in more detail below, the confidence interval  270  can be calculated based on a t-value  272 , a significance level  274 , and a degree-of-freedom  276 . The significance level  274  may be a scalar value that is set, for example, by the verification  220 . The significance level  274  can be defined as the probability of rejecting a null hypothesis when the hypothesis is actually true (e.g., detecting a change when a change has not occurred in the vibratory meter) and is typically a small value, such as 1% or 0.01. The degree-of-freedom  276  is calculated from the number of samples used to determine, for example, the stiffness standard deviation  236 . Also shown is a bias dead band  278 , which is a scalar value that may also be set by the verification  220  to ensure that biases in the vibratory meter do not induce false flags. 
     The confidence interval  270  can detect small changes in the physical stiffness of the vibratory meter  5  while also reducing the number of false alarms compared to, for example, the predetermined limits previously used in meter verification. Additionally, the confidence interval  270  can be calculated using relatively simple mathematical operations, thereby allowing the processing system  202  to employ robust statistical techniques using a verification  220  that employs relatively simple embedded code. 
     Predetermined Alarm Limits 
       FIGS. 3 a  and 3 b    show graphs  300   a ,  300   b  that illustrate stiffness change and stiffness symmetry variations determined during multiple meter verification runs. As shown, the graphs  300   a ,  300   b  include run number axes  310   a ,  310   b . The run number axes  310   a ,  310   b  range from 0 to 600 and indicate a run number for a meter verification. For example, run number “100” indicates a 100 th  meter verification run out of 600 meter verification runs. The graph  300   a  also includes a percent change in stiffness axis  320   a , which is a percentage representation of, for example, the LPO stiffness change  244  and the RPO stiffness change  254 . The graph  300   b  includes a percent stiffness difference axis  320   b , which is a percentage representation of, for example, the stiffness symmetry  260 . For example, a 0 percent stiffness difference means, for example, that the LPO stiffness change  244  is equal to the RPO stiffness change  254 . The graphs  300   a ,  300   b  also respectively show stiffness change data  330   a  and stiffness difference data  330   b.    
     The stiffness change data  330   a  and the stiffness difference data  330   b  are comprised of data points determined in groups of runs for various flow material/flow rate configurations where coating is present in conduits. More specifically, there are four groups of data, which are discernable from the stiffness difference data  330   b . The first two groups may be based on high and low water flow. The latter two groups may be based on high and low air flow. 
     The graph  300   a  shown in  FIG. 3 a    includes stiffness change data  330   a  that is comprised of data points representing a stiffness change for a given meter verification run. As can be seen, the stiffness change data  330   a  ranges from about −0.3% to about 2.0%. As can be appreciated, this seems to indicate that the stiffness is changing. However, an alarm may not be provided if an alarm limit is set at, for example, 4%. 
     The graph  300   b  shown in  FIG. 3 b    includes stiffness difference data  330   b  that is comprised of data points representing a stiffness difference, for example, the LPO stiffness change  244  and the RPO stiffness change  254 . As can be seen, the stiffness difference data  330   b  ranges from about −0.4% to about 0.6%. As can also be seen, the stiffness difference data  330  includes sporadic data points that do not follow any discernable trend. In addition, the stiffness difference data  330   b  suggests that stiffness symmetry values may be affected by the material in the conduit. 
     The graphs  300   a ,  300   b  illustrate that an alarm may not be raised if the alarm limit or range is greater than the stiffness change associated with a change in the vibratory meter. Additionally, if the alarm limit is less than sporadic data points, a false alarm may be raised. The following addresses this issue by eliminating limits and employing statistics that are able to execute on an embedded system. 
     Statistics for Embedded Code 
     Statistical methods that calculate the probability of an outcome can be used to detect a change in the vibratory meter but, due to their complexity, could not be performed by the meter electronics  20 . For example, P and T statistics may be employed to test whether a null hypothesis is met for a given set of data. Rejecting the null hypothesis does not determine if a condition exists in the vibratory meter, but that if it is false there is a lack of the condition. In the case of meter verification, the null hypothesis may be defined as: “the current meter verification result has the same mean as the baseline meter verification result.” If this null hypothesis is disproven, then it can be assumed that the mean of the current result is not the same as the baseline meter verification result due to a change in the vibratory meter. 
     By way of illustration, in a t-test, a t-value may be calculated using the following equation: 
     
       
         
           
             
               
                 
                   
                     t 
                     = 
                     
                       
                         
                           x 
                           _ 
                         
                         - 
                         
                           μ 
                           0 
                         
                       
                       
                         s 
                         / 
                         
                           n 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   [ 
                   4 
                   ] 
                 
               
             
           
         
       
     
     where:
         μ 0  is some specified value;     x  is a sample mean;   s is a sample standard deviation; and   n is the sample size.
 
In the context of meter verification, μ 0  is a reference meter verification value, such as a baseline stiffness value. Meter verification measurements are used to calculate the sample mean  x  and the sample standard deviation s for comparison with the reference meter verification value. The number of meter verification measurements is the sample size n. The t-test also typically includes a degree-of-freedom, which, for the above equation [2], is defined as n−1.
       

     As discussed above, the t-test can be used to test a null hypothesis, which, for meter verification, may be defined as whether the sample mean  x  is equal to the reference meter verification value. To test the null hypothesis, a P-value may be calculated using a known distribution of the t-value. To test the null hypothesis, the P-value is compared to a significance level a. The significance level a is typically set to a small value, such as, for example, 0.01, 0.05, or 0.10. If the P-value is less than or equal to the significance level a, then the null hypothesis is rejected for an alternative hypothesis. Since the null hypothesis is defined as “the current meter verification result has the same mean as the baseline meter verification results”, the alternative hypothesis is that the current meter verification does not have the same mean and, therefore, a change has occurred in the meter. 
     However, the P-value is difficult to calculate with limited computing resources. For example, the P-value may be calculated on a computer workstation with an operating system and a statistical software but may not be easily calculated in an embedded system. The meter electronics  20  described above may be an embedded system with limited computational resources. In addition, the ability to reject the null hypothesis in situ or in real time on the meter electronics could prevent the meter electronics  20  from sending false alarms while also correctly detecting a change in the conduits  130 ,  130 ′, which is a significant improvement over using predetermined alarm limits. 
     To this end, a confidence interval that exploits the meter electronics&#39;  20  limited computing resources is used instead of the P-value. As a result, the confidence interval can be calculated using the embedded code on the meter electronics  20 . For example, the meter electronics  20  can have a current stiffness value and a stiffness standard deviation value stored in two registers. As can be appreciated, the t-value described above can be calculated using the current stiffness value by using a significance level a and a degree-of-freedom. By way of example, the significance level a may be set at 0.01, which is a 99% confidence level. The number of meter verification tests may be set as 5. Accordingly, a pooled degree-of-freedom is determined to be 2·(5−1)=8. A two-tailed student t-value can be calculated from the significance level a and the pooled degree-of-freedom using a student t-value function as follows: 
         t   Student,99.8 =tinv(1−0.01/2,8)=3.36.  [5]
 
     A pooled standard deviation of stiffness values associated with the left and right pick-off sensors  170   l ,  170   r  may also be used. In a general case, calculating the pooled standard deviation can be complicated. However, due to the meter electronics  20  storing the measured stiffness standard deviation in the registers, the pooled standard deviation can simply be the stored standard deviation, such as the stiffness standard deviation  236  described above. A pooled standard error may also be calculated, which is defined as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           s 
                            
                           t 
                            
                           d 
                            
                           e 
                            
                           r 
                            
                           r 
                            
                           o 
                            
                           
                             r 
                             pooled 
                           
                         
                         = 
                         
                           
                             
                               ( 
                               
                                 2 
                                 · 
                                 
                                   
                                     ( 
                                     
                                       stddev 
                                       pooled 
                                     
                                     ) 
                                   
                                   2 
                                 
                               
                               ) 
                             
                             
                               n 
                               
                                 D 
                                  
                                 O 
                                  
                                 F 
                               
                             
                           
                         
                       
                        
                       
                         
 
                       
                        
                       
                         s 
                          
                         t 
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                         e 
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                         r 
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                         r 
                          
                         o 
                          
                         
                           r 
                           pooled 
                         
                       
                     
                     = 
                     
                       
                         
                           2 
                           / 
                           8 
                         
                       
                       · 
                       
                         
                           stddev 
                           pooled 
                           2 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       s 
                        
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                        
                       d 
                        
                       e 
                        
                       r 
                        
                       r 
                        
                       o 
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                         r 
                         pooled 
                       
                     
                     = 
                     
                       0.5 
                       · 
                       
                         
                           stddev 
                           pooled 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   [ 
                   6 
                   ] 
                 
               
             
           
         
       
     
     A confidence interval range can be calculated using the above determined standard error and the t-value as follows: 
       CI range =stderror pooled   ·t   student,99.8,   [7]
 
       CI range =stderror pooled ·3.36.
 
     Finally, the confidence interval can be calculated using the stiffness mean and the confidence interval range, which is shown in the following: 
       CI=Stiffness mean ±CI range  
 
     The confidence interval can be used to test the null hypothesis by determining if the confidence interval includes 0.0. If the confidence interval does include 0.0, then the null hypothesis is not rejected and the meter verification passes. If the confidence interval does not include 0.0, then the null hypothesis may be rejected and a meter verification fault may be sent. 
     As can be appreciated, by using a confidence interval instead of a P-value where the meter electronics  20  stores the stiffness value and the stiffness standard deviation value, the computations are relatively simple and can be performed using embedded code. For example, the meter electronics  20 , which may not have sufficient computing resources to calculate the P-value, can calculate the confidence interval to perform in-situ or real time statistical analysis. As can also be appreciated, the confidence interval can be used to test the null hypothesis with a desired confidence level. 
     In addition to the confidence interval, a bias dead band may be defined around zero to account for a bias in the meter stiffness measurements. The bias in the meter stiffness measurements may be due to the mounting, density, temperature gradients, or other conditions of the vibratory meter that can affect the meter verification measurements. This bias dead band in the t-test is a value around zero for which a small bias with a small variation, that would otherwise cause the confidence interval check to reject the hypothesis, does not reject the hypothesis. Accordingly, this bias dead band can be set to a value that reduces the number of false alarms sent by the meter electronics  20 . 
     In the example of a confidence interval that is compared to a zero, the bias dead band is a range around zero where, if the zero is not within the confidence interval but a portion of the bias dead band is within the confidence interval, then the null hypothesis will not be rejected. Mathematically, this test can be expressed as whether the mean meter stiffness value is less than the bias dead band. Or using the above discussed nomenclature: if  x &lt;db bias , where db bias  is the bias dead band, then the null hypothesis cannot be rejected. 
     The bias dead band can be implemented alone or in conjunction with other dead bands. For example, the bias dead band can be implemented in conjunction with a variation dead band. In one example, the variation dead band can be determined from db variation =db bias /t student,99.8 , where the db variation  is the variation dead band. The variation dead band may be compared with a meter stiffness standard deviation to determine if the null hypothesis should be rejected. In an example, the bias dead band may be compared as discussed above and the variation dead band can be compared to the meter stiffness standard deviation as follows: if  x &lt;db bias  and if s&lt;db variation , then the null hypothesis cannot be rejected. The foregoing test can be utilized after the null hypothesis has been rejected by the confidence interval check. Alternatively, if  x &lt;db bias  and if s&lt;db variation , then the mean meter stiffness  x  is set to zero and a meter stiffness variation is to be equal to the variation dead band. Accordingly, when the confidence interval check is performed, the null hypothesis may not be rejected due to bias in the meter stiffness measurements. 
       FIGS. 4 a  and 4 b    show graphs  400   a ,  400   b  that illustrate stiffness change and stiffness symmetry variation data points determined during multiple meter verification runs, where a probability distribution is assigned to each data point. As shown, the graphs  400   a ,  400   b  include run number axes  410   a ,  410   b . The run number axes  410   a ,  410   b  range from 0 to 600 and indicate a run number for a meter verification. The graph  400   a  also includes a percent change in stiffness axis  420   a , which is a percentage representation of, for example, the LPO stiffness change  244  and the RPO stiffness change  254 . The graph  400   b  includes a percent stiffness difference axis  420   b , which is a percentage representation of, for example, the stiffness symmetry  260 . 
       FIGS. 5 a  and 5 b    show graphs  500   a ,  500   b  that illustrate stiffness change and stiffness symmetry variation data points determined during multiple meter verification runs, where a probability is assigned to each data point. As shown, the graphs  500   a ,  500   b  include run number axes  510   a ,  510   b . The run number axes  510   a ,  510   b  range from 0 to 140 and indicate a run number for a meter verification. The graph  500   a  also includes a percent change in stiffness axis  520   a , which is a percentage representation of, for example, the LPO stiffness change  244  and the RPO stiffness change  254 . The graph  500   b  includes a percent stiffness difference axis  520   b , which is a percentage representation of, for example, the stiffness symmetry  260 . 
     The graphs  400   a ,  500   a  include stiffness deviation plots  430   a ,  530   a  comprised of a plurality of data points representing a stiffness deviation, which may be the stiffness change  234  stored in the storage system  204 , of a meter stiffness. The graphs  400   b ,  500   b  include stiffness symmetry plots  430   b ,  530   b  comprised of data points representing stiffness symmetry change. Also shown are change indication plots  440   a - 540   b  illustrated as exclamation points, which indicate that a confidence interval does not include a zero. 
     In  FIGS. 4 a -5 b   , the change indication plots  440   a - 540   b  are used to indicate that a rejection of the null hypothesis has occurred for a given data point. As discussed above, the null hypothesis may be when the measured value equals the baseline value, but that this test is performed with a probability. As shown in  FIGS. 4 a -5 b   , the probability is a confidence interval, although any suitable probability may be employed. The confidence interval is represented by bars associated with each data point. In the examples shown in  FIGS. 4 a -5 b   , the bars represent a 99% confidence interval. 
     As can be appreciated, the exclamation points are associated with data points where the confidence interval does not include the zero axis. In  FIG. 5 b   , the zero axis of the stiffness symmetry represents the null hypothesis that the measured stiffness symmetry equals a baseline stiffness symmetry value. That is, the zero axis represents no change in the stiffness symmetry of the vibratory meter. Accordingly, when the confidence interval does not include the zero axis, the null hypothesis is rejected. This indicates, for example, with at least a 99% confidence, where the significance level is set at 0.01, that the null hypothesis has been rejected and a change has occurred in the vibratory meter. 
     As can be appreciated, various systems and methods can use the above described LPO stiffness change  244 , RPO stiffness change  254 , and stiffness symmetry  260  to indicate the change in the conduits  130 ,  130 ′. Exemplary methods are described in more detail in the following with reference to  FIG. 6 . 
       FIG. 6  shows a method  600  for detecting and identifying a change in a vibratory meter according to an embodiment. As shown in  FIG. 6 , the method  600  begins by determining a first stiffness change associated with a first location of a conduit of a vibratory meter in step  610 . The vibratory meter and conduit may be the vibratory meter  5  and one of the conduits  130 ,  130 ′ described with reference to  FIG. 1 . In accordance with this example, the first location of the conduit can, for example, be the location of the left pick-off sensor  1701  on the conduit  130 , although any suitable location may be employed. The first stiffness change associated with the first location may therefore be the LPO stiffness change  244 , which, as discussed above, may represent a physical stiffness change of the conduit  130  between the driver  180  and the location of the left pick-off sensor  1701 . 
     The method  600 , in step  620 , can determine a second stiffness change associated with a second location of the conduit in the vibratory meter. Continuing with the example described above with reference to step  610 , the second location of the conduit can be a location of the right pick-off sensor  170   r  on the conduit  130 , although any suitable location can be employed. The second stiffness change associated with the second location may therefore be the RPO stiffness change  254  associated with the location of the right pick-off sensor  170   r  on the conduit  130 , which, as discussed above, may represent a physical stiffness change of the conduit  130  between the driver  180  and the location of the right pick-off sensor  170   r.    
     In step  630 , the method  600  determines a condition in the conduit based on the first stiffness change and the second stiffness change. In the above discussed example, the condition may be determined based on the LPO stiffness change  244  and the RPO stiffness change  254 . The condition may be anything that affects the stiffness of the conduit, such as erosion, corrosion, damage (e.g., freezing, over-pressurization, etc.), coating, or the like. By way of example, the first and second stiffness change may be the LPO stiffness change  244  and RPO stiffness change  254  indicated as “low.” Additionally, the stiffness symmetry  260 , which may also be based on the LPO stiffness change  244  and the RPO stiffness change  254 , may be “low right”. The method  600  can, for example, employ a table similar to the table described above to determine that the condition of the conduit  130  is corrosion/erosion. 
     The method  600  can further identify, suggest, or allow procedures suited for each of the determined conditions of the conduit. For example, the alarm may be provided with the determined condition of the conduit and the user can proceed with further diagnostics, maintenance, servicing, etc., that are specific to that condition. The procedure for damaged conduits may include removing the vibratory meter  5  from operation and repairing/replacing the meter assembly  10 . In the case of coatings, procedures that reduce or eliminate the coating without removing the vibratory meter  5  from operation may be more appropriate. 
       FIG. 7  shows a method  700  for detecting and identifying a change in a vibratory meter. As shown in  FIG. 7 , the method  700  begins by obtaining a central tendency value of a meter verification parameter and a dispersion value of the meter verification parameter from a storage in a meter electronics of the vibratory meter in step  710 . In step  720 , the method  700  determines a probability based on the meter verification parameter and the dispersion value to determine if the central tendency value is different than a baseline value. 
     In step  710 , the central tendency value and the dispersion value may be obtained from, for example, the storage system  204  described above with reference to  FIG. 2 . The storage system  204  may be registers of the processing system  202 . Accordingly, the processing system  202  may obtain the central tendency value and the dispersion value from the registers and perform simple mathematical operations to determine the probability. In one example, the central tendency value may be a meter stiffness and the dispersion value may be a meter stiffness standard deviation. 
     In the example using the meter stiffness and the dispersion value, in step  720 , the processing system  202  can calculate a t-value based on the number of meter stiffness measurements comprising the meter stiffness and calculate the probability using the t-value. In one example, the t-value can be determined from a significance level a and a degree-of-freedom, as discussed above. The meter stiffness may, for example, be a mean meter stiffness determined from meter stiffness measurements taken after the baseline value, such as a baseline meter stiffness, was determined. The baseline value may be a baseline central tendency value. Accordingly, the baseline meter stiffness may be a mean of baseline meter stiffness measurements. 
     The method  700  may include additional steps, such as, for example, setting a bias dead band. As discussed above, if a meter stiffness, which may be the central tendency value, is less than the bias dead band, then the method  700  may determine that the meter stiffness and the baseline meter stiffness are not different. For example, before the meter stiffness is compared with the bias dead band, a confidence interval may not include a zero and, therefore, a flag may be set indicating that the null hypothesis has been rejected. However, if the meter stiffness is less than the bias dead band, then the flag may be reset to indicate that the null hypothesis has not been rejected. Accordingly, the method  700  may not send an alarm. 
       FIG. 8  shows a graph  800  illustrating two baseline measurements that can be used to detect a change in a vibratory meter. As shown in  FIG. 8 , the graph  800  includes a frequency axis  810  and a stiffness axis  820 . The frequency axis  810  is in units of Hertz and the stiffness axis  820  are unit-less. The graph  800  also includes a meter stiffness plot  830 . The meter stiffness plot  830  includes a first baseline stiffness value  830   a  and a second baseline stiffness value  830   b . The first and second baseline stiffness values  830   a ,  830   b  are baseline meter verification values. Other baseline meter verification values may be employed, such as a baseline mass meter verification value, for example. 
     The first baseline stiffness value  830   a  may be a stiffness meter verification value that is determined during a first set of process conditions. For example, the first baseline stiffness value  830   a  can be measured when a conduit, such as one of the conduits  130 ,  130 ′ described above, is filled with air and the environmental conditions. The nominal conditions may be conditions at a factory when a vibratory meter and the conduit are in calibration. However, the first set of process conditions may be at other temperatures and pressures, including non-nominal conditions. 
     The second baseline stiffness value  830   b  may be a stiffness meter verification value that is determined during a second set of process conditions. For example, the second baseline stiffness value  830   b  can be measured when the conduit is filled with water and the environmental conditions are at non-nominal conditions. The non-nominal conditions may include a non-calibration temperature or pressure. The second set of process conditions may include a resonant frequency that is different than a resonant frequency during calibration. For example during calibration, the conduit may be filled with air. As a result, the resonant frequency at calibration may be different than a resonant frequency of the conduit filled with water. 
     Parameters in the first and second sets of process conditions may include, for example, a resonant frequency of the conduit, the type, density, total mass, and/or composition of a material in the conduit, the temperature of the conduit and/or a meter assembly including the conduit, and a pressure of the atmosphere of the vibratory meter. More or fewer parameters may be employed. The first and second sets of process conditions may or may not have the same set of parameters. 
     As shown in  FIG. 8 , the stiffness plot  830  includes the first and second baseline stiffness values  830   a ,  830   b . The stiffness plot  830  may be an interpolation, such as a linear interpolation, based on the first and second baseline stiffness values  830   a ,  830   b . The interpolation may yield an equation, such as a linear equation: 
         y=mx+b;   [8]
 
     where:
         x is a resonant frequency of a conduit during a meter verification; and   y is an interpolated baseline meter verification value that, for example, can be used in a confidence interval testing.
 
The stiffness plot  830  of  FIG. 8  may be represented by:
       

         y= 40.00 x+ 20,000.00.  [9]
 
     Accordingly, a baseline meter stiffness value may be determined based on the first baseline meter verification value and the second baseline meter verification value. For equation [9], the baseline meter verification value may be determined by inputting a frequency value of a meter verification. 
     For example a customer may perform an online or process meter verification at a set of process conditions that are not the same as the first and second set of process conditions. As a result, a resonant frequency of the process conditions may be between 225 Hz and 250 Hz. For example, the resonant frequency during the online or process meter verification may be at 240 Hz. Equation [9] above can be used to determine a corresponding baseline stiffness meter verification value that is 29,600. 
     As shown in  FIG. 8 , the interpolation is performed relative to the resonant frequencies of the conduit at the first and second sets of process conditions. Accordingly, the frequency can be a common parameter of the first and second sets of process conditions. Also, although the stiffness plot  830  may be relative to a frequency, other parameters of the first and second set of process conditions may be employed. For example, an interpolation may be performed for stiffness meter verification values relative to temperature. Accordingly, an alternative stiffness plot may be relative to a temperature of the conduit. 
     As can be appreciated, the processing system  202  can perform methods to detect a change in a vibratory meter based on the two or more baseline meter verifications. An exemplary method is described below. 
       FIG. 9  shows a method  900  for detecting a change in a vibratory meter based on two or more baseline meter verifications. The method  900  begins by determining a first baseline meter verification value at a first set of process conditions in step  910 . In step  920 , the method  900  determines a second baseline meter verification value at a second set of process conditions. In step  930 , the method  900  determines a baseline meter verification value based on the first baseline meter verification value and the second baseline meter verification value. The method  900  may be used in a meter electronics, such as the meter electronics  20  described above, to detect a change in a vibratory meter based on two or more baseline meter verification values. 
     In step  910 , the method may determine a first baseline meter verification value at a first set of process conditions. Accordingly, a processing system, such as the processing system  202  in the meter electronics  20 , for example, may be configured to determine a first baseline meter verification value at a first set of process conditions. The first set of process conditions may be at a factory with temperatures, pressures, or the like, that are at nominal values. 
     In step  920 , the method  900  may determine a second baseline meter verification value at a second set of process conditions. Accordingly, the processing system may also be configured to determine a second baseline meter verification value at a second set of process conditions. The second set of process conditions may be at a process site (e.g., customer site, field use, etc.). The second set of process conditions may or may not be the same as the first set of process conditions. The processing system  202  may also be configured to determine a baseline meter verification value based on the first baseline meter verification value and the second baseline meter verification value. 
     As discussed above, the baseline meter verification value may be a baseline mass meter verification value. Accordingly, a processing system, such as the processing system  202  described above, may be configured to determine one of a first baseline stiffness value and a second baseline stiffness value, and a first baseline mass value and a second baseline mass value. The processing system may also be configured to interpolate the baseline meter verification value from the first baseline meter verification value and the second baseline meter verification value. The interpolation may be linear, although any suitable interpolation may be employed, such as non-linear interpolations. Alternatively, the interpolation may be performed offline or in a different electronics and then stored in the processing system. 
     As described above with reference to  FIGS. 6 and 7 , a baseline meter verification value may be used to detect and determine a process condition. For example, first and second baseline meter verification values that are respectively associated with a first location and a second location on a conduit may be determined according to  FIG. 9 . The first and second baseline meter verification values may, for example, be baseline stiffness meter verification values that can be used to determine a first and second meter stiffness change in the conduit. For example, the first and second meter stiffness change can be determined by comparing first and second process stiffness meter verification values to the first and second baseline meter verification values. Accordingly, a condition of the conduit may be determined according to step  630  described above by using the first and second baseline stiffness meter verification values. 
     Similarly, the method  900  may further comprise the method  700  described above. Accordingly, the method  700  described above can be employed in a meter electronics having a processing system, such as the meter electronics  20  having the processing system  202  described above, configured to obtain a central tendency value and a dispersion value and determine a probability based on the central tendency value and the dispersion value to detect if the central tendency value is different than the baseline meter verification value. The processing system  202  may also be configured to determine a probability based on the central tendency value and the dispersion value comprises the processing system  202  being configured to calculate a t-value and calculate the probability using the t-value. 
     The meter electronics  20  described with reference to  FIG. 1 , or other electronics, devices, or the like, can perform the methods  600 ,  700 ,  900  or other methods that detect and/or identify a change in a vibratory meter. The change in the vibratory meter may be detected by using the baseline meter verification value determined based on the first baseline meter verification value and the second baseline meter verification value. Accordingly, the meter electronics  20 , and the processing system  202 , may be configured to receive information from the interface  201 , use the baseline meter verification value determined from above described method  900  to determine a first stiffness change associated with a first location of a conduit  130 ,  130 ′ of the vibratory meter  5  and determine a second stiffness change associated with a second location of the conduit  130 ,  130 ′ of the vibratory meter  5 . With reference to the vibratory meter  5  of  FIG. 1 , the first location may be a location of a left pick-off sensor  1701  on the conduit  130 ,  130 ′ of the vibratory meter  5 . Similarly, the second location may be a location of a right pick-off sensor  170   r  on the conduit  130 ,  130 ′ of the vibratory meter  5 . 
     The meter electronics  20  can also be configured to determine a condition of the conduit  130 ,  130 ′ based on the first stiffness change and the second stiffness change. The meter electronics  20  may also be configured to determine a stiffness symmetry, such as the stiffness symmetry  260  shown in  FIG. 2 , of the conduit  130 ,  130 ′. The meter electronics  20  may also be configured to provide an alarm based on the determination of the condition of the conduit. The alarm may be provided by, for example, sending a signal, message, packet, etc., over path  26 . 
     The meter electronics  20  and, in particular, the processing system  202 , can also obtain a meter stiffness and a meter stiffness standard deviation from the storage in the meter electronics  20 . The meter electronics  20  or processing system  202  can determine a probability based on the meter stiffness and the meter stiffness standard deviation to determine if the meter stiffness is different than a baseline meter stiffness determined using the method  900  described above. 
     The above description provides a meter electronics  20  and methods  600 ,  700 ,  900  that can detect and identify a change in the vibratory meter  5 . The change can be identified by detecting a condition of the conduits  130 ,  130 ′ in the vibratory meter  5  based on a first stiffness change associated with a first location of a conduit and a second stiffness change associated with a second location of a conduit. These and other steps can be performed by the meter electronics  20 , processing system  202  in the meter electronics  20 , and/or method  600 , or other electronics, systems, and/or methods. 
     The baseline meter verification value determined from above described method  900  may correspond to, for example, a resonant frequency that is the same as a resonant frequency of an online or process meter verification. As a result, therefore, the baseline stiffness meter verification value is a more accurate reference value for the stiffness at the process conditions of the online or process meter verification. Accordingly, the methods  600 ,  700 ,  900  and meter electronics  20  can more accurately detect the change in the vibratory meter. 
     The change can be detected by employing statistics in a specific way such that a probability can be determined with limited computational resources. For example, the probability may be a confidence interval around a meter stiffness where if a zero is within the confidence interval, then a null hypothesis is rejected. In addition, to ensure that biases in the meter stiffness measurements do not induce false alarms, the meter electronics  20  can compare the meter stiffness to a bias dead band. Accordingly, in contrast to limits that do not change, the probability, which may be continually updated, can accurately detect the change in the vibratory meter  5  without causing false alarms. 
     Although the above discussion refers to the vibratory meter  5  shown in  FIG. 1 , any suitable vibratory meter may be employed. For example, vibratory meters with more than one driver and more than two pick-off sensors may be employed. Accordingly, in an exemplary vibratory meter having two pick-off sensors and two drivers, more than two stiffness changes may be determined. In this example, stiffness changes between each of the drivers and each of the pick-off sensors may be determined. Similarly, symmetry between the stiffness changes between the two drivers and two sensors may also be determined. 
     The detailed descriptions of the above embodiments are not exhaustive descriptions of all embodiments contemplated by the inventors to be within the scope of the present description. Indeed, persons skilled in the art will recognize that certain elements of the above-described embodiments may variously be combined or eliminated to create further embodiments, and such further embodiments fall within the scope and teachings of the present description. It will also be apparent to those of ordinary skill in the art that the above-described embodiments may be combined in whole or in part to create additional embodiments within the scope and teachings of the present description. 
     Thus, although specific embodiments are described herein for illustrative purposes, various equivalent modifications are possible within the scope of the present description, as those skilled in the relevant art will recognize. The teachings provided herein can be applied to other ways of detecting a change in a vibratory meter based on two or more baseline meter verifications and not just to the embodiments described above and shown in the accompanying figures. Accordingly, the scope of the embodiments described above should be determined from the following claims.