Process variable transmitter with diagnostics

Field of invention Process variable transmitters are used in industrial process control environments and are coupled to process fluids to provide measurements about the process. Process Variables Transmitters transmit one or more process variables related to fluids in a process plant, such as slurries, liquids, gases and gases in chemicals, pulp, oil, gas, chemicals, food, and other fluid processing plants. Configured to monitor. Process variables to be monitored can be pressure, temperature, flow, level, pH, conductivity, turbidity, density, concentration, chemical compensation, and other properties of the fluid. A process variable transmitter includes one or more sensors that can be inside the transmitter or outside the transmitter, depending on the needs of the process plant installation. A process variable transmitter produces one or more transmitter outputs that represent the sensed process variables. The transmitter output is configured for long-distance transmission to a control unit or indicator via the communication bus 242. In a typical fluid processing plant, the communication bus 242 should be a 4-20mA current loop that powers the transmitter, a fieldbus connection to a control, control system or reader, HART protocol communication or fiber optic connection. Can be done. Transmitters powered by a two-wire loop must be kept low in power to provide intrinsic safety in an explosive atmosphere.

Background of the invention One type of process variable transmitter is known as a pressure transmitter. Normally, the pressure transmitter is coupled to the process fluid through an impulse line. The operation of the pressure transmitter can easily deteriorate if one or both impulse lines are blocked.

Impulse line removal and inspection is one method used to detect and repair line blockages. Another known method for detecting clogging is to periodically add a "check pulse" to the measurement signal from the pressure transmitter. This check pulse causes the control system connected to the transmitter to block the flow. If the pressure transmitter fails to accurately detect the flow obstruction, a warning signal is generated to indicate a blockage in the line. Another known method for detecting clogging is to detect both static and differential pressures. If there is an improper correlation between static and differential pressure vibrations, a warning signal is subsequently generated to indicate line blockage. Yet another known method for detecting line clogging is to sense static pressure and pass it through a high-pass and low-pass filter. The noise signal obtained from the filter is compared to the threshold, and if the change in noise is less than the threshold, the warning signal then indicates that the line has been blocked.

These known methods use techniques that can increase device complexity and reduce reliability. Moreover, while these methods can sometimes detect clogged impulse lines, they generally begin to accumulate deposits inside the impulse lines, but cannot detect when the impulse lines are not yet clogged. .. Therefore, even if the pressure sensing ability of the pressure transmitter is impaired to some extent, the operation may continue. Therefore, in order to reduce costs or improve reliability, there is a need for better diagnostic techniques that provide predictive maintenance rather than post-maintenance.

Outline of the invention A process variable transmitter with diagnostics based on power spectral density (PSD) analysis of the process variable sensor signal is provided. In one embodiment, the process variable transmitter is a pressure transmitter and diagnostics are used to diagnose impulse line interruptions or near future interruptions. Other diagnoses are also useful, for example, in diagnosing deterioration of the primary element. The sensor signal is digitized and the digitized signal is converted into the frequency domain. The frequency power of the sensor signal is tested to provide enhanced diagnostics. In one embodiment, the diagnosis is directly generated with the sensor PSD data. In another aspect, PSD analysis is used to tune the filter to enhance traditional diagnostic algorithms.

Detailed explanation Embodiments of the invention generally perform spectral analysis to generate diagnostic information about process variable transmitters. This analysis is described as occurring inside the microprocessor system inside the process variable transmitter, but can be done by any suitable processing system. The processing system 88 can perform wavelet transforms, discrete wavelet transforms, Fourier transforms, or can use other techniques to determine the spectrum of the sensor signal. The power of the distributed frequencies is determined by monitoring such converted signals over an extended period of time. One example of this is power spectral density (PSD). Power spectral density can be defined as time series power (or change) and can be described as a way in which time series power (or change) is distributed by frequency. For example, this can be defined as the Fourier transform of a time series autocorrelation sequence. Another definition of power spectral density is the squared coefficient of the Fourier transform of the time series, which is standardized by the appropriate constant term.

FIG. 1 illustrates the general environment for flow or pressure diagnostic measurements at 220. Process variable transmitters such as flowmeter 230, level (pressure) transmitters 232, 234 on tank 236, and integrally molded orifice flowmeter 238 are shown connected to control system 240.

In FIG. 1, the integrally molded orifice flowmeter 238 is provided with a diagnostic output section that is further coupled along a communication bus 242 connected to the diagnostic output section. The control system 240 can be programmed to display a diagnostic output to a human operator or to change its behavior when a diagnostic warning is given by the flow meter 238. The control system 240 controls the operation of output devices such as control valves 244, pump motors or other control devices.

FIG. 2 shows an exploded view of the general diagnostic transmitter 82 of the present invention as a whole. The transmitter 82 includes a flange 83 for receiving differential pressure, a differential pressure sensor 31, an electronic device including an analog-to-digital converter 84, a microprocessor system 88, a digital-to-analog converter 96, and a digital communication circuit 100. The transmitter 82 is bolted to the flange adapter 87. In the embodiments shown herein, the sensor 31 can include sensors for absolute pressure, gauge pressure, differential pressure, or other types of pressure. Although embodiments of the present invention are useful in many applications, they are particularly advantageous when the process device is coupled to the process through impulse piping. The microprocessor 88 can be programmed by a diagnostic algorithm, which is described in more detail below. The flange adapter 87 connects to the impulse tubing, which in turn connects to the flow around the primary flow element (not shown in FIG. 2). The configuration of transmitter 82 in FIG. 2 is described in detail with reference to FIG.

FIG. 3 is a block diagram showing a fluid flow meter 60 adapted to sense the fluid flow 22 in the tube 24. The fluid flowmeter 60 includes a pressure generator 26 that includes a primary element 28 and an impulse line 30 that couples the pressure generated in the fluid flow around the primary element 28 to a differential pressure sensor 31 in the pressure transmitter 82. .. As used in this application, the term "pressure generator" refers to a primary element (eg, orifice plate, pitot) with an impulse tube or impulse path that couples to a pressure drop from a position near the primary element to a position outside the flow tube. Means pitot tubes, nozzles, venturis, branch bars, tube bends, or anything else that is adapted to cause a pressure drop in the flow and discontinues the flow) to average the pipe. At a position outside the flow tube, for the connected pressure transmitter 82, the spectral characteristics of this pressure, presented by this defined "pressure generator", are the state of the impulse tube in addition to the state of the primary element. May be affected by. The connected pressure transmitter 82 can be a built-in unit or, if desired, a remote seal, depending on the application. The flange 83 on the pressure transmitter 82 (or its remote seal) couples the flange adapter 87 on the impulse line 30 to complete the pressure connection. The pressure transmitter 82 couples to the primary flow element 28 via the impulse line 30 and senses the flow. The pressure transmitter 82 includes a differential pressure sensor 31 adapted to couple to the impulse line 30 via a flange configuration. The analog-to-digital converter 84 couples to the pressure sensor 31 to generate a series of digital representations of the sensed pressure. These digital representations are used by the flow circuit 34 to calculate the flow and provide a representation of the flow along line 36.

In one embodiment of the invention, the analog-to-digital converter is a known sigma-delta converter that provides 22 conversions per second. In this embodiment, each transformed digital representation of the process variable becomes a data point for power spectral density (PSD) analysis. Preferably, 32 points of Fast Fourier Transform (FFT) are applied to the data points of the digital process to generate PSD information. Since PSD analysis is performed using known analog-to-digital converters that operate in a known manner, this embodiment of the invention is performed entirely in software by adapting the behavior of the microprocessor system 88. be able to. Thus, embodiments of the present invention can be applied to process variable transmitters currently installed in the field or already manufactured without the need to modify their circuits. The algorithm for performing PSD analysis is described below.

Sigma-delta transducers are often used in the process measurement and control industry due to their fast conversion time and high accuracy. Sigma-delta transducers typically use an internal capacitor charge pumping scheme that produces a digital bitstream that is analyzed by counting positive ones over a set interval. For example, one sigma-delta transducer currently in use provides a bitstream signal consisting of a 50% 1 representing a minimum pressure measurement and a 75% 1 representing a maximum pressure measurement. Generally, the digital bitstream is filtered to remove or attenuate fluctuating components before determining the flow rate. The filtered data is then used with well-known formulas to calculate mass flow or volume flow.

In another embodiment of the invention, the digital bitstream inside the analog-to-digital converter is used directly for PSD analysis. Usually, this bitstream is an order of magnitude higher than the conversion frequency. For example, known sigma-delta transducers provide a digital bitstream with a frequency of approximately 57kHz. Those skilled in the art will recognize a number of methods that can perform PSD analysis on digital bitstreams, but the preferred methods are: Digital data from the bitstream is accumulated and stored for a predetermined interval, for example 10 seconds. The above example results in 570,000 bit storage of 57kHz data in 10 seconds. The DC component can be arbitrarily removed from the stored data by subtracting the average bit value (the number of 1s divided by the total number of bits) from each of the stored bits. Next, the power spectral density of the adjusted data is calculated. This is preferably done using 65536 FFTs and 65536 sized Hanning windows. The size of this FFT was chosen because it is the power of 2 closest to the sampling bit frequency, and assuming 10 seconds, it provides an acceptable average of the spectra. However, in embodiments of the present invention, other sizes may be used.

The power spectral density, Fi, can be calculated using the Welch method of averaged periodograms for a given data set. The method uses a measurement sequence x (n) sampled at f samples per second, where n = 1, 2, ... N. Prefix filters with filter frequencies less than f / 2 are used to reduce aliasing in spectral calculations. The dataset is F, as shown in Equation 1._{k, i}It is divided into.<maths num="1"><img file="JP5116675B2_D0001.tif" /></maths>F that overlaps the data segment_{k, i}If there is, and in each segment M is the number of points in the current segment, the periodogram is calculated. After all periodograms have been evaluated for all segments, they are all averaged to calculate the power spectrum.<maths num="2"><img file="JP5116675B2_D0002.tif" /></maths>Once the power spectrum in training mode is obtained, this sequence is stored in memory, preferably EEPROM, as a reference line power spectrum for comparison with the real-time power spectrum. Thus, Fi is a sequence of power spectra, and i varies from 1 to N, which is the total number of points in the original data sequence. N is usually a power of 2 and further sets the frequency resolution of the spectral estimation. Therefore, Fi is also known as the signal strength at the i-th frequency. In general, the power spectrum contains a number of points at predefined frequency intervals and defines the shape of the spectral power distribution as a function of frequency.

In performing a diagnosis using power spectral density, a sample with a relatively large spectral density in the history state of the reference line is compared with a sample having a relatively small spectral density in the monitoring state. The relatively small sample considers displaying the problem in real time in about 1 second. An increase in the associated frequency component of the power spectrum represents degradation of one or both impulse lines and / or primary elements. Figures 4-6 illustrate PSD data from a digital bitstream. These figures show the state of three different impulse lines: fully open, partial blockage with a 0.0135 inch diameter hole, and substantial blockage with a 0.005 inch hole. Integrating bitstream data from 1 to 10 hertz and / or 10 to 30 hertz, as seen in Figures 5 and 6, provides a valid indication of impulse line clogging.

The microprocessor system 88 receives a continuous digital representation (individual digital conversion, digital bitstream, or any combination thereof). The microprocessor system 88 has an algorithm stored therein that compares the PSD data in surveillance mode with the PSD data acquired during training mode. This comparison allows the process variable transmitter to detect failures that may affect process variable measurements. This failure can be a blockage in the impulse line in the pressure transmitter, deterioration of the primary element, or any other factor. System 88 generates diagnostic data 62 as a function of the current dataset for history. The digital-to-analog converter 96 coupled to the microprocessor system 88 represents the sensed flow rate.<u style="single">Analog transmitter output</u>To generate. The digital communication circuit 100 receives the diagnostic data 94 from the microprocessor system 88 and represents the diagnostic data.<u style="single">Transmitter output</u>To generate.<u style="single">Analog output (the analog transmitter output)</u>and<u style="single">Diagnostic data (transmitter output)</u>Can be coupled to an indicator or control unit, if desired.

FIG. 7 is a flow chart of a method of training a diagnostic process variable transmitter according to an embodiment of the present invention. Method 250 begins at start block 252. Block 252 can be performed at any time when the process variable transmitter is fully functional and is relatively certain to be coupled to a process operating within the specified range. Normally, block 252 is started by a technician, but in some situations block 252 can be started remotely. Method 250 continues to block 254, where process value data is received. This data can include multiple digital displays. These representations can be individually transformed process variable transformations, bits of the bitstream inside the analog-to-digital converter, or any combination thereof. At block 256, the digital data is FFTed. This FFT can be performed by any known method. In addition, an alternative method for analyzing the spectral components of the data can be done in block 256 in place of or in addition to the FFT. At block 258, the FFT power is calculated. This power information is then stored in the process variable transmitter. At step 260, the method determines if sufficient training has occurred. This can be done by making sure that sufficient time has passed, that sufficient training data has been obtained, or by any other suitable method. If not trained<u style="single">Method 250</u>Returns to block 254 and training continues. However, if it is determined in step 260 that training is complete, method 250 ends and the final set of power data Fi is stored in the non-volatile memory inside the process variable transmitter.

Many of the embodiments of the present invention use PSD analysis of process sensor data to provide diagnostics directly, but not in one embodiment. FIG. 8 illustrates a method of selecting digital filter parameters using PSD analysis. Method 270 begins by performing training method 272 and is preferably identical to method 250. At block 274, the power of the frequency is checked. At block 276, the digital filter frequency is selected based on the analysis of the power spectral density. Frequency selection involves selecting which "bin" of the FFT to use. Not only which bottle to use, but how many bottles to use also matters. This selection can be as simple or complicated as choosing a single bin. For example, you can select non-adjacent bins, you can select adjacent bins, you can select all bins that contribute to the whole, and you can weight them based on their respective size. , Or any combination thereof. The selection of bottles can be made using a number of criteria. For example, you can select the bin with the highest power, you can select the bin with the largest power variation, you can select the bin with the smallest power variation, and you can select the bin with the smallest scale. Can be selected, the bin with the highest standard deviation can be selected, the bin with the lowest standard deviation can be selected, or a group of adjacent bins with similar scales can be selected. it can. Once the bin is selected, the sensor data is digitally filtered using the corresponding filter characteristics, as shown in block 278. The data so filtered can then be used for more effective process measurements and / or diagnostics. In this way, the filter characteristics can be dynamically selected based on the PSD analysis of the sensor data. The filtered data is according to an embodiment of the present invention.

FIG. 9 is a flowchart of a method for performing PSD-based diagnosis according to an embodiment of the present invention. Many factors can affect digital bitstreams and thus process variables. Impulse lines can be clogged and / or primary elements can be corroded or contaminated. Method 280 begins at block 282, where training occurs. Block 282 is preferably identical to the training method 250 described for FIG. Once training is complete, method 280 moves to block 284, where process value data is calculated. On top of that, this data can be a set of individually analog-to-digital converted readings from the transducer 84, or this data is a digital bitstream generated inside the transducer 84. Including all or part of. At block 286, the data is transformed into the frequency domain, preferably using the FFT. At block 288, the power of the FFT is calculated and a set of power spectral data for the process variables<u style="single">Fi</u>Bring. Set with block 290<u style="single">Fi</u>Is compared to the stored training dataset Fi. This comparison can take many forms. For example, this comparison can include examining the sum of the magnitudes of the selected spectral range. This comparison was also compared to the standard deviation and mean of Fi.<u style="single">Fi</u>Can include a comparison of standard deviations and means of. Yet another comparison involves consistently comparing large or small frequency bands. With reference to FIG. 6 again, the fully open state will correspond to training set Fi using digital bitstream data. Comparing the integrals of the bitstream spectra from the selected frequency band in this way can show that the integrals of the spectra are substantially reduced when the impulse lines begin to clog. One frequency band that worked perfectly in the test was between 10-40Hz. However, the range between 10 and 30 Hz is also considered beneficial. In addition, there appears to be useful information provided at 30-40 Hz that may also be useful for detecting partial or complete blockages of the impulse line. With Fi as represented by the integral of the selected spectrum<u style="single">Fi</u>The difference between and can be compared to a preselected threshold to determine if a failure is present. In block 292, the failure determination is made based on the comparison in block 290. If the failure becomes apparent, control<u style="single">Block 284</u>The failure is indicated and the process variable transmitter can be stopped at will. This fault display can be a local display such as a device warning, or a display communicated to a remote object such as a control room or operator. The indication of failure can represent a serious failure now or a failure in the near future. If no failure is found, control returns to block 284 and the method continues to monitor process device activity.

Diagnosis of the primary elements and impulse lines that can be coupled to the pressure transmitter when any of the methods is performed on a computer readable medium by multiple instruction sequences, i.e., a microprocessor system within the pressure transmitter. It can be saved as a plurality of instruction sequences including a sequence that causes the method to be performed.

In one embodiment, the microprocessor system 88 passes through an analog-to-digital converter 84 that separates the signal components of the sensor signal, such as frequency, amplitude, or signal characteristics for a clogged impulse line 30 or degraded primary element 28. Includes a signal preprocessor coupled to sensor 31. The signal preprocessor provides a separate signal output to the signal evaluator within the microprocessor 88. The signal preprocessor separates parts of the signal by filtering, performing wavelet transforms, performing Fourier transforms, using neural networks, statistical analysis, or other signal evaluation techniques. Such preprocessing is preferably performed on the microprocessor 88, or on a specialized digital signal processor. The separated signal output relates to a clogged or clogged impulse line 30 or a degraded primary element 28 sensed by the sensor 31.

The signal components are separated through a signal processing technique that identifies the desired frequency, or other signal characteristic, such as amplitude, and provides a particular representation of them. Depending on the strength of the signal to be detected and their frequency, the signal preprocessor can include a filter, such as a bandpass filter, to produce a separate signal output. For more sensitive separation, advanced signal processing techniques such as the Fast Fourier Transform (FFT) are used to obtain the spectrum of the sensor signal. In one embodiment, the signal preprocessor includes a wavelet processor that uses discrete wavelet transforms to perform wavelet analysis of sensor signals as shown in FIGS. 10, 11 and 12. Wavelet analysis is perfectly suited for signal analysis with transient or other transient characteristics in the time domain. In contrast to the Fourier transform, wavelet analysis retains information in the time domain, i.e. when an event occurs.

Wavelet analysis is a method of converting a time domain signal into a frequency domain, which makes it possible to identify frequency components in the same manner as the Fourier transform. However, unlike the Fourier transform, in the wavelet transform, the output contains information about time. This can be expressed in the form of a three-dimensional graph with time on one axis, frequency on the second axis, and signal amplitude on the third axis. Consideration of wavelet analysis by L. Xiaoli et al. On-Line Tool Condition Moniterring System With Wavelet Fuzzy Neural Network, 8 JOURNAL OF INTELLIGENT MANUFACTURING, pp. 271-276 (1997). When performing continuous wavelet analysis, a part of the sensor signal is displayed in a window and convoluted by the wavelet function. This convolution is done by superimposing the wavelet function at the beginning of the sample, multiplying the wavelet function with a signal, and then integrating the results over the sample period. The result of the integration is standardized and provides the first value for the continuous wavelet transform at time = 0. Then, this point may be mapped on a three-dimensional plane. The wavelet function is then shifted to the right (forward in time) and the multiplication and integration steps are repeated to obtain another set of data points mapped in 3-D space. This process is repeated to move (fold) the wavelet throughout the signal. The wavelet function is then standardized, which modifies the frequency resolution of the transform and repeats the above steps.

The data from the wavelet transform of the sensor signal from the sensor 31 is shown in FIG. The data is graphed in three dimensions to form surface 300. As shown in the graph of FIG. 10, the sensor signal is time t₁With a small signal peak of about 1kHz and time t₂Includes another peak at about 100 Hz. Through subsequent processing by the signal evaluator, the surface 300 or part of the surface 300 is evaluated to determine the degradation of the impulse piping or primary element.

The continuous wavelet transform described above requires extensive computation. Therefore, in one embodiment, the microprocessor system 88 performs a discrete wavelet transform (DWT) that is perfectly suited for implementation in a microprocessor system. One valid discrete wavelet transform uses the Mallat algorithm, which is a two-channel subband coder. The Mallat algorithm provides a series of detached or decomposed signals that represent the individual frequency components of the original signal. FIG. 11 shows an example of such a system, where the original sensor signal S is decomposed using a subband coder of the Mallat algorithm. Signal S is 0 to maximum f_MAXHas a frequency band up to. The signal is 1 / 2f_MAX~ f_MAXThe first high-pass filter with frequency bands up to and 0 to 1 / 2f_MAXIt passes through a low-pass filter having a frequency band up to at the same time. This process is called decomposition. The output from the highpass filter provides the discrete wavelet transform coefficient "level 1". Level 1 coefficient is 1 / 2f_maxAnd f_maxRepresents the amplitude of that part of the input signal between and as a function of time. 0 ~ 1 / 2f_maxThe output from the low-pass filter of is followed by the high-pass filter (1 / 4f), if desired._max~ 1 / 2f_max) And low-pass filter (0 ~ 1 / 4f)_max) To provide an additional level of discrete wavelet transform coefficients (level 1 and above). If desired, the output from each lowpass filter can be further decomposed to provide additional levels of discrete wavelet transform coefficients. This process continues until the desired resolution is achieved or the number of data samples remaining after decomposition does not provide further information. The resolution of the wavelet transform is chosen to be about the same as the sensor or about the minimum signal resolution needed to monitor the signal. Each level of the DWT coefficient represents the signal amplitude as a time function for a given frequency band. By concatenating the coefficients of each frequency band, for example, a graph as shown in FIG. 10 is formed.

In some embodiments, padding is added to the signal by adding data to the sensor signal near the boundaries of the window used in wavelet analysis. This padding reduces the distortion of the frequency domain output. This technique can be used with continuous or discrete wavelet transforms. Padding is defined as adding additional data to both sides of the currently active data window, for example, adding additional data points that extend the current window by 25% beyond both ends of the window. In one embodiment, padding is generated by iterating over some of the data in the current window, so that the added data "padds" the existing signals on both sides. The entire dataset is then fitted to the quadratic equation used to extrapolate the signal beyond the active data window by 25%.

FIG. 12 is an example showing the signal S generated by the sensor 31 and the resulting approximate signals provided by the seven decomposition levels classified into levels 1-7. In this embodiment, the signal level 7 represents the lowest frequency DWT coefficient that can be generated. Any further decomposition results in noise. All levels, or only those related to impulse piping or primary element degradation, are provided.

The microprocessor 88 evaluates the isolated signal received from signal preprocessing, and in one embodiment monitors the amplitude of a predetermined frequency or the specified frequency band, and if the threshold is exceeded, a diagnostic output. I will provide a. Signal evaluators can also include more sophisticated decision-making algorithms such as fuzzy logic, neural networks, expert systems, rule-based systems, and the like. U.S. Pat. No. 6,017,143, assigned to the assignee of the present invention, describes various decision-making systems that can be implemented by the signal evaluator 154 and is incorporated herein by reference.

The microprocessor 88 uses the information extracted from the differential pressure sensor 31 to make a diagnosis about the impulse piping or the primary element. Below, many embodiments for realizing a diagnostic circuit are described. The diagnostic circuit can provide a calibration output used to estimate the remaining life, display the failure, display the failure in the near future, or repair the error of the detected process variable.

Although the present invention has been described with reference to preferred embodiments, it will be appreciated by those skilled in the art that modifications may be made in mode and detail without departing from the essence and scope of the invention. For example, the various functional blocks of the present invention are described with respect to circuits, but a large number of functional blocks may be implemented in other forms, such as digital / analog circuits, software and mixtures thereof. When implemented in software, the microprocessor performs a function and the signal contains the digital value at which the software operates. A general-purpose processor programmed with instructions that force the processor to perform the desired process element, a special-purpose hardware component with a built-in circuit wired to perform the desired element, and optional programming of the general-purpose processor and hardware component. Combinations of can be used. If desired, deterministic or fuzzy logic techniques can be used to make circuit or software decisions. Due to the inherent complexity of digital circuits, it is not necessary to divide the circuit elements into separate blocks as shown, but to mix and share the components used in the various functional blocks. be able to. As with software, within the scope of the invention, some instructions can be shared as part of multiple functions and mixed with irrelevant instructions. The diagnostic output can be a predictive indication of a future failure, eg, a future partial or complete blockage of the impulse line. Diagnosis can be applied to impulse piping and / or primary elements. In addition, various embodiments of the invention are described for pressure transmitters, but embodiments of the invention are practiced with any process device when the sensor is coupled to the process device through an analog-to-digital converter. can do.

<figref num="1">It is a figure of the normal fluid processing environment of a diagnostic pressure transmitter.</figref><figref num="2">FIG. 5 illustrates an embodiment of a differential pressure transmitter used in a fluid flow meter for diagnosing the condition of an impulse line and / or primary element.</figref><figref num="3">It is a block diagram of the fluid flow meter which provides the diagnosis of embodiment of this invention.</figref><figref num="4">It is a graph which illustrates the PSD analysis of the sensor data which shows the cutoff of an impulse pipe.</figref><figref num="5">It is a graph which illustrates the PSD analysis of the sensor data which shows the cutoff of an impulse pipe.</figref><figref num="6">It is a graph which illustrates the PSD analysis of the sensor data which shows the cutoff of an impulse pipe.</figref><figref num="7">FIG. 6 is a flow chart of a method of training a process variable transmitter for PSD-based diagnostics according to an embodiment of the present invention.</figref><figref num="8">It is a flowchart of the method of selecting the digital filter characteristic based on PSD analysis of the embodiment of this invention.</figref><figref num="9">It is a flowchart of the method of performing PSD-based diagnosis of embodiment of this invention.</figref><figref num="10">It is a graph of amplitude vs. frequency vs. time of a process variable signal.</figref><figref num="11">It is a block diagram of a discrete wavelet transform.</figref><figref num="12">It is a graph which shows the signal output from a discrete wavelet transform.</figref>