Detect low voltage by comparing measured Tach vs expected given PWM

This section will go through how you can use the local database to get calculate expected Tachometer readings given a PWM. We can then use this to compare with the measured PWM and Tachometer. If the difference is to high then we might expect the voltage to be too low.

create function tach(Integer pwm) -> Number;


create function get_tach(Integer pwm) -> Number
   as select x
        from Number x, Integer i, Integer diff
       where x = tach(i)
         and diff = abs(pwm - i)
         order by diff asc
         limit 1;

Note

ice how get_tach will find the entry in the tach function with the closest pwm reading.

We can fill the tach function with the following query:

select addfunction("tach", [p],[ta])
  from Integer p, Number ta
 where (p,ta) in (
     select pwm, mean(tach)
       from Integer pwm, Integer tach, Vector of Number v
      where v in class_stream(2)
        and tach = Number(v[4])
        and pwm = round(Number(v[5]))
      group by pwm
);

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Looking at difference

{'sa_plot': 'Scatter plot',
 'labels':['pwm','tach', 'rati',"class","i"],
 "y_axis": "rati", "color_axis": "class", "size_axis": "off"};
select vector of [pwm,tach,tach/get_tach(pwm),c,i]
  from Integer i, Number tach, Number pwm,
       Vector of vector v, Integer c
 where v = windowed_stats_1024(i,c)
   and c in([1,2,4])
   and tach = v[4,1]
   and pwm = v[5,1]

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Now lets predict of the test set and see the result:

Testing the fit.

The following query will classify each point in a stream of 1024 stats over the whole training set. Remember that we are only trying to identify Low Voltage. That's why we set the label for every other dataset to -1).

set :v = (select Vector of [
              v[1],
              is_low_voltage(pwm,tach),
              tach,
              pwm
            ]
            from Vector v, Number tach, Number pwm
           where v in merge([widowed_stats_test_stream(1,1),
                             widowed_stats_test_stream(2,-1),
                             widowed_stats_test_stream(3,-1),
                             widowed_stats_test_stream(4,-1)])
             and tach = v[2,4,1]
             and pwm = v[2,5,1]);

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Then we can use cluster_stats which takes a bag of vector where each vector contains [actual, predicted] and calculates Precision, Recall, F-measure, Rand-index:

pp(label_vector(["Precision","Recall","F-measure","Rand-index"],
             cluster_stats(in(:v),1)));

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If you use the same training values as defined here you will see that you get a precision around 0.76 which is not terrible, but not very good either. Let's take a look at the predictions in a scatter plot.

{
  'sa_plot': 'Scatter plot',
  'labels':['label','predict',"tach","pwm"],
  'x_axis': 'tach', 'y_axis': 'pwm', 'color_axis': 'predict',
  'size_axis': 'off'
};
:v

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With some further investigation it was found that the Tachometer was much higher in the test set for class 4 (obstructed) than the rest. That is what you see with the two separate groupings to the right in the graph above.