I have some data that I'm using to plot a curve in excel. It uses a non-linear calculation.
The calculation is called the rule of twelfths - it is used to calculate changes in tidal height between a high and low tide. The rule states that in the first sixth (often approximated to an hour) of the time period, the tide will move 1/12th of the overall range. In the second sixth, the tide will move 2/12th's of the overall range. In the 3rd and 4th sixth, the tide will move 3/12ths (in each), and then it will move 2/12ths again in the fifth sixth, and 1/12th in the final sixth.
The maths for this is relatively straightforward - if I know the High Water Time and Low Water time, and their respective heights, I can calculate a data point for each sixth. That then plots to a nice even curve (and some fun pie chart shenanigans shows it on a clock face too).
This produces the following sheet:
What I am now after is the ability to overlay onto that the height for a given time of day. This would be used in a 'live' sense to display the height 'now', or perhaps where the user dragged their finger on the curve if it was in an app. I'm only using this for screenshot/flat file purposes, so I just need it to base the overlay one the data in one cell.
So, in the attached screenshot, if we had a time of day of 1128, (based on Cell J3), excel would take the time in J3, and wherever it intersected the curve, draw both a vertical and a horizontal line, so that the height of tide data (HOT) could be measured off that axis.
This would look something like this (I've circled cell J3 too):
Is that something that's possible? It might be that it needs to do a lookup in the table of calculated data points and then interpolate just between those two - that would probably get close enough.
A two stage question I guess - firstly calculating the intercept, secondly getting it to draw on (complete with the vertical and horizontal lines if possible!).
There's a widget on planetcalc which does almost the same thing - it only gives the calculated data points (and it uses hours rather than the range), but it gives a nice visual idea.
PlanetCalc Tide Calculator
Any thoughts? Is it possible?
I created a solution to this myself in the end.
Given that the two values were easily calculated, I produced a pair of values for the desired time/height, and plotted each as an additional line graph on top of the existing (styled correctly).
This gave the appearance of what I wanted, and intersected my curve perfectly.
Related
I'm trying to create a scatter straight line chart to visually show how a retaining wall looks in elevation view. I have a top of wall dimension and bottom of wall dimension and the length of each wall section. I am able to use the top and bottom of wall dimension but having trouble showing the length of the run. I have tried to add the wall length as another data point, but doesn't work, it just skews the other two points. Tried to use a cumulative run length, helper column, but couldn't get that value to populate the x axis properly. I added some notes in red in the image below. Spent a few hours and appreciate any help.
I perhaps wouldn't use excel for diagramming this, but I think you would need to add more points and interpolate the values. If your minimum wall length is 25, then you could use 25 as your base. Wall 1 is 100, so you need 4 points (100 / 25). Wall 3 is 150 so you need 6 points. Plus 1 point for each wall to accommodate start/stop.
For missing values in wall 1 top, you would take (230-224.3)/4 = 1.425. Then add 1.425 to the value above it.
It would look something like this:
And this would need to be a line chart, where column A can represent the X-axis for labeling.
Below is an Excel Chart for the data shown in column A (x-coordinates--dates) and column B (y-coordinates--test results). There's no problem with the column B data. But note that the horizontal axis shows quite a few more dates than are contained in column A.
Is there any way to have only the actual x-coordinates shown on the horizontal axis with a scale that matches those values?
I kind of get it. Excel deliberately scales the horizontal axis to match as best it can the data in column A. But I don't want that. Beneath each "corner" point of the graph, I'd like to see the date that is associated with the test result in column B.
In other words, there is clearly a point with y-coordinate 154.5. I'd like to see 2/13/2018 directly below that point since that is the data in row 5. Note that the x-axis contains the "correct" date for the first plotted point: (2/9/2017, 70). But for the point with y-coordinate 80, it looks as if that test result occurred on 6/9/2017 rather than 6/16/2018.
So I'd like the graph to appear as shown in the second image, which likely would be impossible because of the "crowding" of x-coordinate values at the right-hand end, but just displaying whichever of the three dates would fit would be good enough, as would just showing one of the two dates in other "crowded" areas. That is to say that something like the third image would be fine.
I suppose I could write VBA code to make it happen, but I'd prefer that Excel do it.
(What crosses my mind is, "Are exact dates really this important?" And the jury is still out on this point. There are arguments both ways. I guess a hung jury goes to the judge, Excel.)
By inserting the points to be plotted into two arrays, datesArr and scaledArr, and putting those values into columns A and B (see worksheet) and in code saying ...
Set ch = ActiveChart
Set s = ch.SeriesCollection
s(1).Values = scaledArray
s(1).XValues = datesArr
... I got exactly what I wanted. Now granted that's not exactly built-in, but we're programmers, yes? And this was downright easy. Well, once I learned a few tricks, especially being able to set angle of dates to 45 degrees.
You need to plot two sets of data, the actual values, and a set of zeros, then smoke and mirrors make it work.
Data below left, make a line chart (top left chart). Add data labels to the second series; I colored the labels orange to match the points, for clarity in this description. Default labels show Y values, which are all zero (top right). Format the data labels to show category values (i.e., dates), below the points, rotated upwards (bottom left). Format format format (bottom right). Axis labels: none. Format second series with medium gray lines and medium gray cross markers. Drag bottom of plot area upwards to make room for the date labels. Hide legend.
I'm trying to determine where, in a set of measurement data, the data takes a dive...
... so I can plot a vertical line and
... plot a horizontal line in the graph.
I have no problem doing the 2nd and 3rd bullet points above on my own, so that's taken care of.
The problem I need help with is the first bullet point - determining WHERE the data takes a dive - WHERE the data crosses a threshold that basically says, "Whatever-it-is you're measuring, is no longer performing as it is expected to.".
Here's what I'm doing:
I am taking measurements using a measuring device and that device is logging the measurements in its internal memory and allowing me to download that measurement data to my computer into a csv when the test session is complete.
I pull that csv into an xls and plot the data on a graph. (see attached image)
Here's what I want to do:
If you look at the attached image I would like to find the value where the data DEFINITELY crosses BELOW the horizontal line so I can say, "Here is where the device being tested 'gave up the ghost' and was no longer able to perform as desired."
What the data roughly looks like:
Each measurement set will have the rough look and feel of the attached image but slightly different each time. (because each object I am testing will have roughly the same performance characteristics but they all have their own manufacturing defects and variations.)
The data set for the attached image is a data set of 7000 measurements.
I never really know where the horizontal line will be.
Examples of the data sets I have gotten in the past several tests look like this:
(394 to 0)
(390000 to 0)
(3.88 to 0)
(375000 to 0)
(39.55 to 0)
(59200 to 0)
and each data set will have about 1,000 to 7,000 measurements each.
Here's how I was trying to solve this issue:
I was using SLOPE() and trying to latch onto where the slop of the line took a dive / started to work its way to a zero slope (which is a vertical line) so when it starts approaching a really small slope then it MUST be taking a dive. That didn't really work.
I was looking at using STDEV.P() in Excel and feeding it the entire data set. Then I was looking at doing the same thing but feeding it only the first 10, 30, 60 measurements but then I thought - we never really know just how many measurements will come through. Then I thought I would use the first 10% of the measurements and feed that to STDEV.P().
Please let me know what you think of this and please let me know of any ideas you may have.
Thanks.
H
Something like this should work to flag when the decay rate increases.
To find what 'direction' your data is going in you need the derivative.
Excel doesn't have a derivative formula but you can set it up pretty easily by using the (change in y)/(change in x) as demonstrated here:
http://faculty.educ.ubc.ca/sanderson/lab/CLFbiom/demo/diff.htm
I would then check a formula which counts how many datarows you have (=COUNTA(A:A) or similar)
Then uses that to get a step of 10% of your data
Then check the value of the derivative in a cell against a cell 10% further down. If it's still a negative (to account for the slight downhill at first) then you'll know
The right way to go about this is to model the data with an unknown discontinuity, something like "if time < break_time then (some constant plus noise) else (decaying exponential)". A maximum likelihood estimation for that model might require iteration or other operations which are clumsy in Excel -- maybe you should consider VB or Python or some other programming language. I.e. choose the tool to fit the problem and not the other way around.
See Seber and Wild, "Nonlinear Regression", for an extensive discussion of models with discontinuities.
If your data can be generally characterized as having:
(A) a more or less flat plateau region, followed by
(B) a downward trending region
then a basic strategy could be to start at then end of the data and march towards the beginning one point at a time, checking to see that the values are increasing. Once they stop increasing, you've found the break point.
The strategy assumes (unwisely?) that the downward trending region is smooth/noiseless. To make the solution more robust to noise, you could compare values that are 5 apart, or 10 apart, or whatever interval works to filter out the noise. Or you could use a moving average.
This strategy could potentially be made more efficient by starting the search somewhere in the middle of the data but still in downward trending portion. If you know (based on experience) that any value that is (say) 0.5X the maximum is in the downward trending portion, you could start the search there.
Hope that helps.
It appears as though you want to detect when the slope changes from something near zero to something negative. One way to detect this is to calculate the 2nd derivative of the values (calculate the slope of the slope). The 2nd derivative should be near zero in the flat portion of the data AND in the downward trending portion of the data. It should go negative at the break point. So finding the minimum (most negative) value of the 2nd should locate the break point.
To implement this, you probably will need to filter noise. So calculate the first derivative (slope) over some suitable window of data:
=SLOPE(moving window of say 25 raw values)
Then calculate the second derivative (slope of slope):
=SLOPE(moving window of say 25 slope values)
Then look for the minimum.
Hope that helps.
I have a data set that has height values every so often, like topography data in a straight line with GPS coordinates. I used the GPS coordinates and trigonometry to make a cumulative distance column. However, the distance between points varies. Sometimes its 10 cm sometimes its 13, sometimes its 40.
I would like to take the average height every 0.5 meters, but sometimes the distance column doesnt even land on a multiple of 0.5! This would mean my output column would be significantly shorter than my raw data column.
I think my main problem is I do not know what this process is called in order to Google it. Another problem is that the distances are irregular as mentioned above. Things I think may have something to do with it:
averageif?
binning? I do not want a histrogram though, just the data.
Thanks for the help and if you do not know the answer but at least know what I should be writing in the search bars that would be helpful as well. Thanks!
Perhaps this will work for you. I made up a series of distance vs height measurements and determined that a third order polynomial curve fit pretty well. (A different curve might best fit your real data, so you would have to alter the formula accordingly). I then used that formula to derive a set of new heights for the desired ditances at, in my example five unit differences.
The formula under Extrapolated heights is an ARRAY formula entered into all the cells at once. You select D2:D12, enter the formula in D2 and, hold down CTRL-SHIFT while hitting ENTER. If you did this correctly, you will have the same formula in each cell surrounded by curly braces {...}
Then you can decide how you want to "Average" the heights.
I have stress strain data from tensile test. I have drawn a stress vs strain graph in excel.I need to find the yield point.For that, I need to draw a line parallel to the linear(straight) portion of the curve with 0.2% offset in x axis and see where it intersects with the original curve.
So, I tried to keep only the linear portion data and drew a trendline, which gives me straight line equation y=mx. Now, if I want 0.2% offset, equation of line is y=mx +c.
I have the equation, how to draw this line in excel with the equation? And how to get the intersection point? Is my approach right? Please help.
A Stress-strain curve with data courtesy of YouTube:
It can be observed that this is linear (elastic deformation) for about the first nine data points. Hide the other data points and add a liner trend line to the chart, with Display Equation on chart. This shows y=4232.x + 0.701.
In say N1 =4232*D2+.701 and copied down to N10 provides the data for an additional data series. Copy N2:N10, select the chart, Paste and format the added series to see the match:
For a 0.2% offset x is .002 when y=0. For a parallel line the slope (determined by 4232 in the formula) cannot be changed so the constant must be, from +0.701 to -7.763. A further data set can be created with the altered constant and added to the chart as before:
By observation the offset yield strength (0.2% proof strength) can be seen to be around 80 MPa in this example (where the green line intersects the blue curve).