Effective Use of Statistical Models to Establish and Update Vibration Alarm

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1 Knowledge Base Article Effective Use of Statistical Models to Establish and Update Vibration Alarm Article ID: NK Publish Date: 27 Feb 2015 Article Status: Article Type: Required Action: Approved General Product Technical Information Information Only Recent Article Revision History: Revision/Publish Description of Revision 27 Feb 2015 updated affected products (See end of article for a complete revision history listing.) Affected Products: Product Line Category Device Version Machinery Health AMS Machinery Manager Data Analysis Management Software Machinery Health AMS Machinery Manager Database Apps / System Management Software Machinery Health Management AMS Machinery Manager Software Reporting Effective Use of Statistical Models to Establish and Update Vibration Alarm Levels Mark Slemp Robert Skeirik Computational Systems, Inc. Knoxville, Tennessee Abstract This paper will discuss various statistical techniques for automatic determination of alarm limits in vibration analysis. The goal is to determine the method which yields the highest level of diagnostic accuracy in the most automated fashion while producing the minimum number of "false alarms". Several approaches can be taken to this task including: 1) statistical calculation of alarm limits for user-definable frequency bands, 2) statistical generation of external envelope alarm limits based on a single reference spectrum, 3) statistical generation of external envelope alarm limits based on a composite spectrum representing "normal" machine operation, and 4) variable state statistical analysis (for machines with variations in speed, load, etc.). This paper will contrast the performance for each type of alarm limit based on an actual machine study. It will also go beyond any single method to demonstrate how the various alarm limit types can be combined to achieve the stated goal of maintaining high diagnostic accuracy with minimal occurrence of false alarms. Introduction Defining effective vibration alarm limits is arguably the most difficult step in establishing an effective condition monitoring program. At the point of the program start-up, the level of experience and knowledge about machinery characteristics is typically insufficient to determine appropriate alarm levels. Due to the time commitment involved in running the program, alarm levels typically remain unchanged - regardless of validity - until an unexpected machinery failure occurs. The

2 approach presented in this paper outlines an innovative new technique that address both of these issues: first it provides a more effective way to automatically establish alarm levels at the onset of a new program; second it offers a way to painlessly update and refine these alarm levels as more information about individual machine performance becomes available. One general application of statistics to a condition monitoring program involves the establishment of effective alarm limits for user-defined frequency bands or "analysis parameter bands". Results can be enhanced by increasing the statistical sample size through intelligent grouping of machinery components that have similar vibration signatures. The second general application of statistics involves an alarm generation technique which calculates narrowband envelope alarm limits. On large data sets, it is possible to create highly specific alarm sets by generating different alarm values for each measurement point orientation (e.g. vibration in the horizontal direction may be substantially higher than vertical or axial measurements, and vice versa). Similarly, envelope alarm limits can also be created for different operational parameters, such as variations in machine speed or load. Despite the high level of customization, this entire process can be carried out automatically. Field tests have shown that this procedure can generate valid alarm for 80-95% of the machines being monitored. Note: In order to deal with undetected fault patterns as they occur, it is important for this type of alarm generation program to include an option to manually create or edit a constructed envelope. Once the alarm limits for analysis parameter bands and the narrowband envelope alarm limits have been calculated, they may be used to identify the presence of faults in rotating machinery. Perhaps the most common application of this technique would be for the analysis of the machines that are routinely monitored in a vibration-based predictive maintenance program. A truly automated approach to machinery diagnostics would involve the use of statistical alarm limits to feed suspect data points into an expert system for automated diagnostics. This assures that only spectra which are in alarm with respect to the statistically calculated alarm limits can trigger a diagnostic call. This approach has proven to increase diagnostic accuracy, while at the same time, reducing the percentage of "false alarms". To obtain optimum results, all machines belonging to a specific type or class should be grouped together for analysis. If a large enough data sample is available, it may also be interesting to identify different alarm levels for each sensor orientation (e.g. horizontal, vertical, and axial) on the same bearing point. Regardless of the method selected for the creation of alarm levels, a rigorous application of statistics will include multiple methods to identify bad data referred to as "statistical outliers". Statistical formulas can be useful for this function. In addition, the user may require the ability to establish an upper and/or lower validity limit based on accumulated experience with this type of equipment. These outlier limits can then be used to re-evaluate the spectra that were used to construct the envelope. This is an attempt to identify and eliminate individual spectral data values, or spectral peaks that are outside the bounds of what would seem normal. For example, consider ten spectra that are being included in the construction of a single envelope limit. If the overall values of the ten spectra are relatively consistent, they will each be allowed into the construction of an outlier limit on a peak-by-peak basis. The resulting outlier spectrum could then be used to reevaluate the individual spectral data values to identify peaks that are probably not representative of "normal operating condition". Such exceptional data values are excluded on a peak-by-peak basis from the construction of the final envelope limit. This means that if the constructed envelope was then applied to the spectrum which had the abnormal peak present, the peak should penetrate the envelope alarm, signaling an analyst or a diagnostic program that there is reason to analyze this machine. Statistical Calculation of Alarm Limits for Analysis Parameter Sets The first type of statistical alarm limit that we will examine is for user-definable frequency bands or analysis parameter bands. This method is appropriate whenever there is already some knowledge of the potential failure patterns that might develop on a specific type or class of machine. Statistical Generation of External Envelope Alarm Limits Overview of Envelope Alarm Limit Generation There are several types of envelope alarm limits that may be used to detect faults in rotating machinery. Up to this point, references have mainly been made to statistically created envelopes or envelope limits in general. However, there are in fact several types of envelope limits that will be discussed in this section. The shape of the envelope will be determined by the spectrum which is used as a baseline for the envelope and the number and variety of parameters used to calculate the envelope. The specific type of envelope that is most appropriate for a given machine depends mainly on the amount of spectral data that has been accumulated over time on that machine.

3 Variable Baseline Data Amplitude Calculation Criteria Frequency Criteria State Analysis Options Single Reference Spectrum Statistical Composite Spectrum Constant Percent Increase Constant Delta Increase Absolute Levels (Maximum or Minimum) Fixed Frequency Units (Hz, CPM) Order-based Constant percent bandwidth Variable Speed Variable Load This paper will provide an in-depth analysis of the impact of the baseline data choice (e.g. single reference spectrum or statistical composite spectrum). It will not, however, cover the individual impact of each of the other envelope construction options. Instead, it will simply be asserted that the construction of a composite envelope which uses all three ampl itude calculation criteria is superior to the envelope constructed when using only one of these criteria. Similarly, it will simply be asserted that the frequency criteria must be either order-based or constant percent bandwidth to minimize false alarms on variable speed equipment. In fact, the highest accuracy level can be obtained by coupling order-based frequency units with variable state analysis. This approach not only accommodates variable machine speeds but also provides a means to reduce false alarms caused by fixed frequency components in the spectrum (e.g. 120 Hz electrical frequency) as well as false alarms caused by load or speed induced increases in vibration level. For the purposes of this study, we will use an order-based composite envelope. Single Reference Spectrum Once a baseline reading has been collected and a valid reference spectrum has been established, an envelope may be generated from the tagged spectrum. This type of envelope limit provides more customized alarm levels around the frequencies at which peaks are present in the reference spectrum. The frequency range of the envelope that is to be constructed is first divided into separate envelope windows. A given envelope window is usually three to seven lines wide so that the appropriate limit will be applied to a given peak even if the location of that peak shifts a line or two due to slight variations in machine speed. Each of these windows is where a spectral peak is expected to occur. An alarm limit determination algorithm is then applied to each window individually. The envelope alarm limit is therefore composed of the individual alarm levels that are determined for each of the envelope windows. These envelope windows can be thought of as narrow parameter bands, and it is for this reason that this type of alarm limit is referred to by some as a narrowband envelope alarm limit. The alarm limit determination technique incorporates several heuristic envelope construction parameters. For each envelope window, a number of alarm limits are proposed by using these different alarm limit construction parameters, and the most appropriate limit is selected by the algorithm. The automated specification of the individual envelope window alarm limits, which results in the construction of useable envelope alarm limits, is the main reason why this technique is so powerful. Such a process would not be remotely practical if performed manually for even a handful of machines. Statistical Composite Spectrum For more established condition monitoring programs, historical data often gives a comprehensive view of how a machine's vibration signature varies over time. A machine's previously collected spectra give a more complete picture of its typical vibration characteristics, as opposed to a single reference spectrum, which often gives more of a snapshot of a machine's vibration signature. The statistical composite narrowband envelope construction technique that will be introduced considers the nominal vibration levels at which spectral peaks are expected to occur, as well as the variance of the amplitude of those peaks. Software then presents a narrowband envelope alarm limit that is a composite of the individual alarm levels that are calculated separately for the frequencies at which spectral peaks are expected to occur. The process for constructing these statistically-based envelopes is similar to the construction technique used for reference-based envelopes. It should be noted at this point that in order for this technique to be effective, the construction

4 spectra must be order-normalized. The first step in this process is to perform a line-by-line statistical examination of the spectra that are to be included in the construction of an envelope. This involves extracting a set of meaningful statistical values for each line of the raw spectral data. In the case of a composite spectrum, separate mean and standard deviation arrays are constructed on a line-by-line, order-normalized basis. This means that each line of a spectrum is used to update a separate set of statistical values. These values would then be used to construct an outlier limit. The statistical values that are calculated for each line of the envelope spectrum are then used in the envelope alarm limit determination algorithm that is applied to each envelope window, recalling that the frequency range of an envelope limit is divided into narrow bands or windows where spectral peaks are expected to occur. As in the construction of the referenced-based envelopes, several alarm limits are proposed for each envelope window. However, the calculated statistical values give additional information that is not available when using only a reference spectrum to construct an envelope limit. This allows more accurate alarm limits to be proposed for each envelope window. Once the envelope alarm limits are created, they are assigned to the points from which data was taken during the construction process. At this point, analysis-oriented applications may take advantage of the alarm levels that have been developed in an attempt to increase the accuracy and efficiency of routine machinery diagnostics. Case Study The following case study will illustrate the increased diagnostic accuracy and efficiency that can be attained by statistically calculating alarm levels. For this example, eight design equivalent motors are grouped together. Each unit is a verticallymounted, four-pole, induction motor connected to a forced draft fan blowing air through a heat exchanger mounted horizontally above it. The fan shaft is belt driven with a four-times reduction in speed. The fan bearings were inaccessible to the analyst, thus data was only collected at five measurement points on the motor. Vibration data was collected on each machine over the period from March, 1995 until June, During this period, a total of twelve faults were diagnosed by the analyst, including nine bearing faults, two cases of imbalance and one case of misalignment. The analyst was using the analysis parameter alarming method (e.g. user-selectable narrow band alarming) with the overall level plus 6 analysis parameters (see Figure 1). Figure 1: Original Analysis Parameter Set At this point, this original alarm limit set must be applied to the data associated with the eight machines included in the study. This will establish a baseline for the accuracy and efficiency to which the results from using a statistically calculated alarm set to analyze the data will be compared. First, consider that an exception which is indicated when the alarm limit set is applied to data collected on a machine during a measurement survey must be either a correct call, with respect to the analyst's diagnosis, or a false alarm. For the machines on which an exception is not indicated for a given measurement survey, this must be either a correct screen or a missed call. Thus, for each measurement survey, each machine can be either diagnosed correctly or incorrectly, or it can be screened correctly or incorrectly when the alarm limit set is applied to the collected data. Ideally, an alarm limit set would indicate each of the twelve instances where calls were made on a machine, and data from no other machines would be identified as needing further examination. It should be noted here that if an exception is identified on any of the spectra associated with the machine for a given measurement survey, then the whole machine is considered to be identified as requiring further examination. Since calls are made on a machine-by-machine basis, this means that if only one of the spectra collected on the five measurement points of this motor have an exception indicated, then the whole machine is considered to require a closer look. Figure 2 gives a summary of the results that are generated when the original alarm limit set is used to analyze the data collected over sixteen months for the eight machines included in the study.

5 Figure 2: Results using Original Parameters Figure 3: Performance Statistics for Original Parameters It can be seen from the high percentage of missed calls that the analyst did not rely heavily on the alarm limits originally assigned to these machines. His analysis was in fact performed manually, by examining each collected data set in an attempt to identify recognizable fault patterns. The high percentage of correct screens is ideal, but the low percentage of correct calls necessitates the examination of the spectra individually. Thus, a prerequisite for the screening efficiency to be taken advantage of by an analyst is that the diagnostic accuracy must be high. If an analyst cannot be certain that the machines screened by a diagnostic technique do not in fact require a closer look, then he will manually analyze all of the data anyway. No unexpected machinery failures occurred during the sixteen months that these machines were monitored, so the analyst's manual technique was inarguably effective. However, the efficiency of the technique could be improved considerably, and this will be illustrated in the next phase of this case study. Figure 4: Statistically Calculated Alarm Limits Figure 4 shows the alarm limit set that was statistically calculated for the group of eight motors that are included in this case study. These alert levels of this alarm limit set were calculated by taking the mean of each parameter and adding

6 two times its standard deviation. The fault levels were calculated by adding three standard deviations to each parameter's mean. Figure 5: Results using Statistical Parameters Figure 5 shows the results that were generated when this alarm limit set was applied to the data collected on the machines included in this study. Figure 6: Performance Statistics for Statistical Parameters It can be seen from these results that new alarm limits set significantly increased the percentage of correct calls. Of the remaining instances where a machine did not require further analysis, the statistically calculated alarm limit set effectivel y screened two out of three machines. Thus the time spent by the analyst in analyzing machines that did not in fact justify any manual examination could have been reduced by a factor of two-thirds, while maintaining the manual level of diagnostic accuracy. External Narrowband Envelope based on a single reference spectrum: Now the same analysis is repeated again, but this time we will use the other approach to statistical alarming by creating an envelope over the baseline spectrum. First we will determine the results when using a single reference spectrum as the baseline. This is the easiest form of statistical analysis to implement because it is fully automatic and only uses a single measurement as the baseline for analysis. As the results will show, however, there is a significant drop in efficiency and accuracy when using this type of simplistic approach.

7 Figure 7: External Envelope based on single Reference Spectrum As shown in Figure 7, this approach is also capable of correctly identifying the 11 real alarm cases. At the same time, however, it generates nearly twice as many false alarms as the analysis parameter method shown above resulting in 59% false alarms. Even worse, of the total 52 spectrum that will flagged by this approach, only 11 or about 20% will refer to a real problem. While this approach could conceivably help the analyst by correctly screening out 29 of the vibration spectra, however, due to the high percentage of false alarms, most individuals will quickly learn to question the validity of the report and revert back to manual analysis techniques. Figure 8: Results from Alarm Envelope using single reference baseline The high level of false alarms can be explained by the fact that this simplistic application of statistics will provide notification of ANY increase in the machine vibration regardless of the root cause of the increase. There are many other factors that can lead to increased machine vibration aside from developing mechanical faults, such as: changes in turning speed or load, process changes, environmental changes such as ambient temperature, humidity, or even cross -over vibration from other parts of the plant.

8 Figure 9: Performance Statistics for Alarm Envelope using single reference spectrum Even worse, false alarms generated by this type of simplistic statistical method can be particularly problematic because the analyst will typically be able to identify a clear increase in vibration when reviewing a spectrum in alarm. The burden then falls on the analyst to determine whether this increase is significant. As a result, it easy to spend hours examining spectra which contain no significant diagnostic information. External Narrowband Envelope based on statistical composite spectrum Now we will repeat the analysis, but try to improve the results by creating a more intelligent data set to serve as the baseline for the analysis. This achieved by expanding the scope of data that is used to construct the baseline spectrum. At a minimum, all available trend data on any given machine should be included in composite spectrum. Beyond this, if there are other design equivalent machines in the plant, the trend data collected on these machines could be included as well. Ideally, it should be possible to combine trend data from any design equivalent machines located anywhere. The implementation of this approach will be determined by the software program being used for the analysis and the measurement consistency between different plant sites. Figure 10: External Envelope based on Statistical Composite Spectrum To the extent that the user is able to combine trend data collected on equivalent machines, it will increase the data sample size and should improve the quality of the statistical model. The result will be greater accuracy of alarms with minimal false alarms. Figure 10 shows the composite spectrum that results from calculating a statistical baseline for the machines in our case history. The program used to create the composite spectrum included an algorithm to automatically identify statistical

9 "outliers" which did not properly belong in the data set. There are many reasons why data should be omitted. Some of the more common reasons include user error (e.g. grouping dissimilar machines), inclusion of data which already exhibits clear indication of a developing fault, and equivalent machines being operated under different environmental parameters. Figure 11: Results from External Envelope using Composite spectrum as baseline This analysis provides the best results yet with 100% accuracy and only around 25% indication of false alarms. This outperforms both the analysis parameter method (33% false alarms) and the external envelope based on a single reference spectrum (59% false alarms). It is notable that this result was achieved in an automated fashion that did not require the end user to have any knowledge of vibration analysis or machinery diagnostics. In a large plant, the time savings for the vibration analyst resulting from the increased reliability of the alarming technique can be substantial. Furthermore, since this approach is fully automated, the user may re-calculate his statistical baseline based on the most recently available data at any time. Despite the complexity of the data and the extensive mathematics required to determine the statistical model, it can literally be updated with the push of a button to include the expanding base of information on the machine's operation. Combined Approach Figure 12: Performance Statistics for External Envelope based on Composite Spectrum One further thought which has proven beneficial is the idea of combining these two techniques in the same analysis. This should provide a more effective filter between the analyst and the volumes of vibration data that he is confronted with on a daily basis. This concept was tested on our case history with some surprising results.

10 Figure 13: Results from Combined Approach Alarm limits were calculated for the eight machines as outlined in the paper according to both the analysis parameter method and the external envelope method (using a statistical composite spectrum for the baseline). A report was generated of all machines which were in alarm according to BOTH methods. Figure 13 shows that accuracy was maintained at 100%, while the number of false alarms was decreased down to 5 - only 7%. Figure 14: Performance Statistics for Combined Approach The suspected reason for this striking increase in reliability can be found in the focus of each of the respective alarming methods. Put into one simple statement, the analysis parameter method scans the data for significant changes in vibration, while the external envelope method scans the data for substantial changes in vibration. If a change in vibration is identified as both significant and substantial, then it is more likely to represent an actual indication of a developing machine fault. 4.0 Conclusion After testing several sets of statistical calculation methods for vibration alarms, it was determined t hat the external alarm envelope method, when based on a statistically derived composite spectrum, provides the single best results of any individual alarming method. It is fully automatic and provides high accuracy with very high reliability (e.g. low occ urrence of false alarms). The analysis parameter method offered similar results but did require the end users to have at least a basic understanding of the frequency ranges in which various types of mechanical faults may appear. The simplistic application of external envelopes based a single reference spectrum yielded the worst results with over the half of the machines triggering a false alarm. The idea of combining the two different alarm methods to provide a greater level of scrutiny of the vibration data provided the overall best results. This approach was able to correctly identify 100% of the machines in alarm and appropriately

11 exclude 93% of the machines not currently exhibiting a fault. It is believed that these exceptional results are achieved due to the fundamentally different focus of the two alarming methods: 1) Analysis Parameter Method - machine specific focus; utilizes knowledge about potential machine faults to divide the spectrum into discrete frequency bands; changes in vibration must correlate to one of these bands (analysis parameters) to be deemed significant and trigger an alarm. 2) External Alarm Method - data specific focus; utilizes statistics to identify any substantial changes in the data set without comment as to the significance of the change. Based the results obtained in the testing performed on this limited data set, this combined approach represents a significant advancement in the area of vibration-based condition monitoring. It removes one of the most difficult obstacles confronted in establishing a new vibration program, while providing an automated method to update alarm levels as new data and information becomes available. Complete Article Revision History: Revision/Publish Description of Revision 27 Feb 2015 updated affected products 06 Dec 2010 Original release of article Emerson Process Management All rights reserved. For Emerson Process Management trademarks and service marks, click this link to see trademarks. All other marks are properties of their respective owners. The contents of this publication are presented for informational p urposes only, and while every effort has been made to ensure their accuracy, they are not to be construed as warrantees or guarantees, express or implied, regarding the products or services described herein or their use or applicability. All sales are governed by our terms and co nditions, which are available on request. We reserve the right to modify or improve the design or specification of such products at any time without notice. View Emerson Products and Services: Click This Link