Analyse-Plus allows you to perform a week of importing and analysis in an hour and provides definitive results as opposed to subjective visual interpretations. Spend your time and resources on making conclusions and solving problems instead of spending them importing data, trying to make useful graphs using software meant for simple business problems and making uncertain subjective conclusions. Then implement your solutions and save money by implementing them much sooner. Make captures of simple yet convincing graphs, frequency spectra or cross-correlations to share with others to move the team to the correct conclusions and solutions as quickly as possible.

Analyse-Plus is the best data analysis tool for industrial process and process control because:

• It has the most powerful and complete analysis and graphing tools.
• Its tools are unique. For example, the optional Profile Analysis False Colour Display or the optional PID Simulator. They are unique because they were designed for process and process control analysis and have been steadily improved over 25 years. They are not business or scientific tools repurposed. Analyse-Plus is not suitable for correlating Sales and Profit with 5 data points but rather for determining correlations between many variables with thousands or millions of data points with different sample periods and with time lags between variables.
• Its tools are complete. Analyse-Plus lets you zoom, overlay, pan and cursor your Time Series, Fourier, Integrated Fourier, Auto Correlation and Cross-Correlation plots, manipulate and filter data, correlate variables, simulate and work with 2-dimensional profile data.
• It is designed to handle hundreds of files at once, not just a few. Your process has hundreds of measurements, not just a few.
• We are process control experts. We use our own products every day. We receive continuous feedback leading to the next phase of improvement. If we can imagine a tool that could be useful, we don’t wish we had it. We build it.
• We have the experience. With almost 40 years in process control and 32 years building software tools, we know what we’re doing and what is required.

Graph Types

• Overlay - can show up to 10 traces in a single graph on the same x-axis even if they don’t all have the same sample period, all with independent Y-scales and a different colour for each trace.
  • Overlay Time: All graphs must have its Plot Type as Time Series. The traces can have no vertical overlap (overlay) if desired, but there is a setting for the percent overlay so typically a setting of about 50 % is used which usually provides a good view of all traces. It allows a great deal of control over the automatic y-axis scaling and position of each trace. For example, you may have two pressure measurements so you want the y-axis scaling to be automatic (minimum to maximum) but you want these particular two traces to have the same scale span to compare the magnitude of variation automatically but not necessarily the same scale minimum. Or two of your variables are a setpoint and a PV of the same control so you want those two traces to have identical y-axis scales AND to have only those two overlaid on one another.
  • Overlay Frequency: All graphs must have its Plot Type set to Fourier or Integrated Fourier. This is used to compare frequency spectra or to see the contribution of individual cycles or ranges of cycles.
• Separate - can show up to 4 traces stacked vertically, all in separate independent graphs with different x-axes and y-axes. Each can have a different sample period. There is a check-box on the graph to force all graphs to the same x-axis scale and lock the cursors to the same time if you wish. Any of the 5 Plot Types can be be displayed on each of the 4 independent graphs. Available plot (graph) types are:

Plot Types

• Time Series - shows the sampled data plotted against time.
• Fourier - shows the frequency spectrum with amplitude or power plotted against frequency or period with linear or log scale.
• Integrated Fourier - same as Fourier except that data is plotted cumulatively and scaled to 100 %.
• Auto Correlation - shows how the data is correlated to itself.
• Cross Correlation - shows how 2 data sets are correlated to each other (or are not correlated) at every possible delay.

Overlay Time Graph

• Every trace has its own y-axis scale yet all 10 traces can be clearly distinguished in properly spaced regions of the graph.
• The first (top) 2 variables are a Headbox Level setpoint and PV of the same controller so they are graphed in the same space and with identical scales. You can zoom in the x or y direction and this will be maintained. You can manually change the scale and there is a button to reset it for the viewed area. The third and fourth variables are alternate measurements of the second variable but with a different zero so they are graphed with the same y-axis span but not identical values. The fifth and sixth variables are related valves and have the same span as each other. The eighth and ninth variables are the Total Head Setpoint and PV and so overlaid (graphed in the same space) with identical y-axis scales. The seventh variable is related to the eighth and ninth traces and so has the same y-axis span but does not occupy the same space. This powerful feature allows making the correct conclusions quickly and often visually.
• All 10 variable have the same x-axis scale even if they have different sample periods. You can browse the cursor from sample to sample even if the sample period is different. The time units automatically adjusts (once) from msec to days.
• The colours of the legend, stats, cursor and y-axis labels agree to make it easy to compare.
• Three statistics (from 16 choices) are displayed per variable and all can be changed at any time. They can apply to the entire data set or to the viewed region and will update as you zoom or pan.
• The sample reading at the cursor position is shown. The cursor can be dragged with the mouse or keyboard and can be moved to any sample and any variable (but all 10 are shown).
• There is a whole toolbox in the lower right with many types of zooming and scaling options.
• There are 6 different ways to zoom in addition to simply typing in the desired time scale.
• For all Graph and Plot Types, the X and Y axes can have a linear or log scale (useful for Fourier and Integrated Fourier plot types. You can also change this while viewing the plot.
• You can change the colour setup right on the graph.

For Overlay plots, a legend at the bottom of the display matches the colours of the traces and y-axes labels. The plot area is maximized and the legend area minimized if you have less than 10 traces. The y-axis labels are stacked to prevent them from reducing the plot area. The legend grows in width appropriately to show long file names.


Graphs are setup using the Setup display. This one at left shows how the above graph was configured. The variables (one per data file) is chosen from the Quick List, a list of the last 500 files opened or created. The tag is automatically pulled from the file. You choose the Span/Zero/Overlay settings if you need them. There are 5 sets of these. They only mean something if at least 2 files are selected for the same Span, Zero or Overlay. In the above example, the first 2 traces (red and green) are the setpoint and PV of the same control loop “Bottom Headbox Level” so we set the Span, Zero and Overlay check boxes for those 2 files. This means that their y-axis scale will have the same zero and span and will be overlaid one on top of the other (they occupy the same graphing space). This was also done for the 8th and 9th files because they are the setpoint and PV of the same control loop “Bottom HB Total Head”. The 3rd and 4th files are alternate measurements for the second file so they may have a different measurement offset so we set these to have the same Span as the first 2 files. The 5th and 6th files are control outputs to valves used in the Headbox Level control and so should also have the same Span. Finally, the 6th file is a variable that should have similar variation to the 8th and 9th files. In this way, we can configure the graph so that we can immediately make a visual comparison of variation and draw conclusions quickly, saving a great deal of time.











This is a simpler example of the same thing where 3 pairs of setpoints and their PV’s are present, followed by 3 related flow setpoints, each different in magnitude but whose variation should be compared to evaluate the control.



















Also to facilitate evaluation, you can display up to 3 of these 16 available statistics on the graph. You can change the specific chosen statistic while setting up the plot or while viewing it and you can set it to calculate the stats for the entire data set or only the portion being viewed (it updates automatically as you pan and zoom). The Statistics and Cursor data are placed optimally on the plot depending on your video resolution.

Overlay Frequency Graph

It is often difficult to determine the relative contribution of a particular cycle. Knowing the relative contribution is useful because some cycles will not cause a great deal of variation and may not be worth the cost to correct them. The Integrated Fourier graph provides this contribution information by cumulatively adding the magnitude of all cycles and normalizing to an easy 0 to 100 % scale. If the Fourier and Integrated Fourier graphs can be overlaid, one on top of the other, the size and frequency of each cycle and relative contribution to the total variation can be easily seen.

In the example at left, there are no y-axis labels on the right side because there are only 4 traces displayed: 2 Fourier and 2 Integrated Fourier, the same 2 tags in both cases. This is a typical use case of an Overlay-Frequency plot where the frequency spectra of 2 or more variables must be compared and the Fourier and relative contribution of various frequency ranges must be shown in the Integrated Fourier. It shows that the frequency spectra of the 2 variables shown (Bottom HB Total Head and Bottom Headbox Level) are not very similar, the Total Head having a greater contribution of the low frequencies (16.7 to about 500 sec in period) than does the Headbox Level. Note also how the x-axis is displayed with a log scale. This is optional and there are many ways you can choose to display it.






















Different people, depending in their specific field and the tools they have used in the past, are accustomed to seeing frequency data presented in a certain way and are most comfortable interpreting the graphs this way. Only Analyse-Plus allows virtually any presentation possible:

• Fourier Scale: The y-axis can be displayed as Power (akin to variance) or Amplitude (akin to Standard Deviation).
• Presentation: The data points can be displayed conventionally where a line connects the dots or can be displayed as vertical lines. The latter option avoids the visual deception that points that are spread apart more, indicate greater area and therefore greater significance.
• X-Axis Linearity: The x-axis can be built in terms of Frequency (Hz) or Period (time units automatically scaled such as seconds, minutes etc). Generally, in Process Control, cycles are in fractions of Hz so units of Period are easier. If you choose Frequency, you can switch the units to Period and back to Frequency right in the graph as shown at the base of the graph above. In addition, the X and Y axes can be scaled linearly or logarithmically and this can be switched back and forth within the graph as well.
• Windows For Fourier: This is actually a pre-processing option that is not visual in nature. When a frequency spectrum is calculated, the amplitude (or power) at a finite number of specific frequencies results. The purpose of Windows is to prevent the spreading of amplitude (or power) data over many frequencies. This makes the plot easier to interpret. These are often selected based on personal preference. There are 9 choices. Hamming and Blackman are the two most widely used.

Separate Graph

In the example at left, 2 Time Series (zoomed) are shown followed by 1 Fourier and 1 Cross-Correlation. The Fourier graph shows the dominant Total Head cycles are in the 190 to 290 min range. For cross-correlation, you select the independent variable on the left side of the Setup and the dependent one on the right. The setup is shown below at left. In this example, the graph shows how Total Head is correlated to Headbox Level at various lags. These 2 variables are similar (Total Head means “Pressure” and is Headbox Level plus the unmeasured air pressure) and in the same location (not subject to transport delay), so you would think they would be fairly well correlated at a time lag of 0. But the graph shows this correlation is near 0 and well below the 95 % Confidence Limits (horizontal lines near 0 on the y-axis). The best correlation is at about -190 minutes and in the negative direction. Practically speaking, knowing this process, we know that these variables are more likely to be positively correlated and this should not occur at -190 min (level affecting pressure 190 min earlier) but rather would occur immediately. We can conclude that there is some numerical correlation (0.20 to 0.30) and likely some similarity in variation but there isn’t a good correlation that makes good physical sense. This likely means that both controls are fairly well-tuned and Total Head is not causing a lot of Level variation because, in this case, it is well-controlled.

Note that the Sample Periods of the 2 files used for cross-correlation don‘t even need to be the same. Analyse-Plus will notify you and resample one of the files to match the other before performing the cross-correlation.

















This is the Setup display for the above graph example. Cross-Correlation requires 2 files so the right-side pane of the window is now available for file selection.







It’s easy to customize your printout or screen captures of Overlay and Separate graphs. This feature allows printing or a direct copy and file-save to common graphics formats such as PNG, JPEG, BMP and copying to the clipboard. If you choose Colour Clean Print or B&W Clean Print, a "clean-screen" or simplified plot window will be displayed that is more suitable for plotting or capturing. This will be virtually an exact copy of the display including colour setup, scaling etc. (subject to the printer driver and printer's colour matching ability) but without buttons and the cursor and its size does not vary with your monitor resolution. Choose As-Is to print or capture the display you are viewing, without the buttons and optionally the cursor. Of course, if you want an identical copy to the clipboard, use Windows Alt-Print-Screen.

Practical Case Study 1

An additional cycle of 0.00167 min (0.1 sec) exists in the Total Head Back signal only. This is the aliased 60 Hz cycle.

























Upstream pressures were then simultaneously measured, namely the Primary Screen Feed and Accepts Pressures. The graph at left shows the frequency spectra of these variable plus those of the Headbox Pressures (also called “Heads”). Each graph represents 514,000 samples (171 min). The Headbox Head Front and Back clearly have a cycle of 0.17 min period or 10.1 sec and another of 0.056 min (3.38 sec). The 10.1 sec is present but quite small in the Primary Feed and Accepts Pressures. We concluded that the source of the cycle was somewhere near the Headbox itself because it was strongest there and that it occurred at a lower magnitude in the upstream pressures because the Headbox Head is controlled and it would react somewhat to the 10.1 sec by adjusting the speed of the pump (its controller output) which would affect any pressures between the pump and the Headbox.

Given this clear result, the Headbox itself was examined. The 10.1 sec cycle was isolated to the Headbox rotating shower whose rotational period was measured at 10.1 sec. The 3.38 sec matched perfectly the rotational period of the rectifier rolls. This is not propagated upstream because it is too fast for the Headbox Head control.

Interesting, by subtracting the Headbox Head Front and Back Pressures and noting that the 3.38 sec period remained, and zooming in on the previous graph, we could see that the 10.1 sec cycle is synchronized in both the Front and Back Heads but the 3.38 sec is not. This cycle affects the Front in the opposite direction as the back and vice-versa. These rectifier rolls (there are 2) spin in opposite directions. By changing the rotational speed of each (we could not safely stop them), we found that variation was increased if the speeds were not the same. Each roll partially cancelled out the pressure variation caused by the other.















Finally, Analyse-Plus has the Math Tools and Filtering Functions to calculate what the Time Series would look like if the 10.1 sec cycle could be removed. This would justify further work in this area. In fact, we can edit and manipulate any frequency spectra, increasing or decreasing the amplitude of any cycles, shifting them etc. The graph at left shows the frequency spectra of the as-measured Headbox Head Front followed by the same data with the 10.1 and 3.4 sec cycles removed. Their corresponding Time Series is below that. The 2-sigmas are displayed and the removal of these 2 cycles cuts the 2-sigma in half. This justified reduction in the shower water pressure which resulted in a reduction in Headbox Head variation and in Basis Weight variation.

Practical Case Study 2

For any consistency where dilution is present, an increase in stock flow would normally cause an increase in consistency (because it increases the ratio of stock to water). If the flow is the root cause, then a cross-correlation should be positive (in direction) and with very little lag (delay).

Another possibility is that the dilution pressure is changing. An increase in pressure might increase the Flow and would definitely reduce the Consistency and this would occur with very little lag (delay).

Some Consistency transmitters are flow sensitive and if so, usually an increase in Flow causes an increase in Consistency.

Another possibility is that the consistency measurement is read by the Weight (of the paper) Control and that it then adjusts the Thick Stock Flow [setpoint] to compensate. In that case, an increase in Consistency would cause the control to reduce the flow so we should see a negative correlation. Because the Weight control adjusts the flow setpoint, which takes some time to complete the adjustment, there should be some lag (delay).

The bottom graph is the Cross-Correlation from the Thick Stock Flow to the Consistency. The horizontal Confidence Lines are clearly visible. The x-axis is in minutes. There is a clear correlation of -0.52 at 15 sec lag that is well outside the Confidence Limits, meaning that it is likely statistically significant. This means that the Consistency changes first and then the flow changes in the opposite direction 15 sec later. Therefore we determined that Consistency variation was the root cause and was causing the flow variation because the Weight control was compensating for the consistency variation. We recommended a comparison to upstream consistency and also the installation of a Dilution Pressure transmitter.

Practical Case Study 3

Generally, flat profiles are desired and cycles in the profiles usually indicate a problem. We normally look for similarities in profiles because one profile’s variation can cause a similar variation in another profile. Most importantly, Dry Weight (Weight after calculation to remove the known Moisture) is well-known to affect both Moisture and Caliper.

The question frequently comes up: What are the causes of cycles (spatial cycles with a certain wavelength measurable in cm or inches) and do other profiles have the same wavelengths or what are their root cause?

The graph at left shows, at the top, the average Dry Weight profile over 11.5 hours. Obviously, the cycles are very stable in the cross direction (spatially). The x-axis are the profile cells or data boxes which are usually 1 cm wide. When importing spatial data, the usual technique is to assign the sample period to a convenient multiple of the profile cells. In this case, we used 1 msec for each cell (data box). This means that the x-axis is essentially in cells or cm. If the cells were 13 mm wide, for example, you might set the sample period at 13msec to have an x-axis in mm, or 1.3msec or just stay with 1 msec. In any case, it shows there is a definite stable spatial cycle.

The middle graph shows the frequency spectrum (Fourier). Clearly, there is a dominant period of about 7 cells with some variation from 6 to 9 cells. The x-axis is a log scale in msec which is also cells.

The bottom graph is our first example of an Auto-Correlation. This is a correlation of the Dry Weight Profile to itself at various lags (shifts of 1 sample). This normally shows what the dominant period is, if there is one. If it does not exceed the Confidence Limits (horizontal lines), then there may not really be a dominant period meaning that the cycles vary in period or the data is not really cyclic. In this case, the maximum correlation is at about 7 msec and well exceeds the Confidence Limit, confirming that the dominant period is 7 cells. Interestingly, 7 cells corresponded to about 1.0 slice screws at the Headbox (and a larger non-integer number of Dilution Actuators but both can greatly affect the profile).

The graph at right is the corresponding average Moisture profile over 11.5 hours, also with its Fourier and Auto-Correlation. These show there are significant wavelengths at 10 cells but the dominant one is at 12-13 cells. This machine had both a steambox and a rewet for CD Moisture control but the 13 cells corresponded to 2.0 rewet actuators. When there are control issues, often wavelengths of 2.0 X the actuator spacing are present in both the actuator profile and the measured (moisture) profile.




























Certainly the Dry Weight and Moisture profiles have streaks and cycles but visually, the Dry Weight streaks appear narrower than those of Moisture. Their Fourier’s and Auto-Correlation confirm this. But to be 100 % certain, we should perform a cross-correlation. The graph at left shows the 2 profiles plus the Cross-Correlation from Dry Weight to Moisture. It shows that the correlation is low (must be at a zero lag to make physical sense) at just ~ 0.15 but this is only slightly above the Confidence Limits. Therefore we can conclude definitively that the Weight profile streaks did not cause the Moisture streaks, that the Moisture profile streaks are likely caused by CD Moisture control problems at the Rewet and that the cause of the Dry Weight streaks are unknown but could be caused by the CD Weight control.
See also Case Study 5 for a similar but more difficult case.

Practical Case Study 4

The graph at left shows cross-correlations of:
Liner Stock Pressure to Liner Flow A
Liner Stock Pressure to Liner Flow B
Filler Stock Pressure Filler Flow C
Filler Stock Pressure to Filler Flow D
when all 4 flows and both pressures were in manual.

Since, in general, flow occurs due to a pressure drop, a flow and a pressure measurement on the same line should read a very similar pattern. In other words, their cross-correlation plots should show a high correlation and the peak should not be far from 0 lag. The measurements were taken with the Data Logger (analog-to-digital conversion) directly from the transmitters, bypassing all DCS processing but a peak that occurs anywhere from about -0.5 to +0.5 sec would be normal. In the graph at left, a high correlation near 0 lag is true for all cases except the bottom one (note that the y-axis scale is different so the correlation at 0 lag is low and the peak is just 0.16). This suggests that some of Filler Flow D’s variability may not be real and would also account for the fact that its flow variability is roughly double that of the other 3 Flows. We concluded that this flow measurement was suspect and we recommended that the flow meter be checked for proper operation and installation, especially grounding or other problems that could affect the noise level. We also recommended that the damping of all 4 flow transmitters also be checked and noted in case it explains the difference in correlation.

Practical Case Study 5

In this case, the mill management knew they had had some problems with “mapping” of the CD Caliper control which is known to cause streaks in the profile at a specific wavelength, specifically at twice the actuator spacing. However, since Dry Weight and its actuators are known to affect Caliper and since the Dry Weight profile also had streaks (but Caliper and its actuators do not affect Dry Weight), there was some confusion on whether the CD Caliper mapping problems were corrected and to what extent the remaining streaks were simply caused by Dry Weight streaks.

In the graph at left are 3 caliper profiles averaged over specific periods using Analyse-Plus in chronological order, followed by the Dry Weight profile averaged over the entire time frame covered by the 3 caliper profiles. The mapping of the CD Caliper control was known to be incorrect during the period covered by the red trace and was corrected just before the period covered by the green trace so this supposedly represents the period of lowest variation and virtually free of mapping error. The mapping became incorrect again between the periods covered by the green and black traces.

But to the eye, all 4 profiles are streaky with similar wavelengths and the green trace appears to simply have a lower amplitude of these wavelengths. The 2-Sigma stats in the lower right of the graph confirms that the green profile has the lowest variation of the 3 Caliper profiles and the black one is the worst.











The graph at left shows the frequency spectra (Fourier) of the 4 profiles above. The x-axis is the wavelength in cells (1 cell==1.0 cm). The dominant wavelength of 20 cells is present in all 4 profiles. When the CD Caliper mapping error was at its lowest (2nd from top), the 20 cm cycles are smaller than during the initial (top) case. When the mapping error is at its greatest (3rd from top), cycles appear at a wavelength of 15 to 16 cells. As expected, this is equal to double the spacing of the CD Caliper actuators (known as “picket fencing”). An auto-correlation plot shows that the dominant wavelength of each profile is respectively 18, 17, 15.5 and 20 cells. We concluded that the Dry Weight had its own problems resulting in a constant 20-cell wavelength which varied in amplitude over the 3 periods and which does indeed appear in CD Caliper but that the CD Caliper had its own mapping problems causing a 16 cm wavelength. The latter is most apparent in the frequency spectra when the CD Caliper mapping is poor (third profile) and the Dry Weight dominant wavelength is always present in Caliper but appears smaller when CD Caliper mapping problems are severe, such as in the third Caliper profile.

The cross-correlations from Dry Weight to the 3 Caliper profiles were 0.71, 0.59, and 0.38 respectively. This means that the amplitude of the Dry Weight wavelengths vary over time but also that they have a significant impact on the Caliper profile but when the CD Caliper mapping is incorrect (Caliper profile is worse), the impact is less because the picket-fencing is dominant. Ultimately, we recommended that the CD Caliper mapping correction be restored and that efforts should be made to determine why the Dry Weight profile has such stable streaks (although its 2-sigma is quite low) as they affect both the Dry Weight and the Caliper.

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