math_expression.md

MQTT Simulator - Data type math_expression

For general information on how to configure the MQTT Simulator see the README.md file.

For TYPE: "math_expression" we need five required configuration parameters: MATH_EXPRESSION, INTERVAL_START, INTERVAL_END, MIN_DELTA and MAX_DELTA. Each of these have some notes:

{
    ... 
    "TYPE": "math_expression",
    "MATH_EXPRESSION": "x**2",
    "INTERVAL_START": 30,
    "INTERVAL_END": 40,
    "MIN_DELTA": 0.1,
    "MAX_DELTA": 0.2,
    ...
}

• MATH_EXPRESSION:

  • The MATH_EXPRESSION's variable must be defined as x.
  • Any Pythonic expression is valid, so, for instance, if you declare it as x**2 or math.pow(x,2) the generated function will be the same.

• INTERVAL_START and INTERVAL_END:

  • These parameters will works as the function domain, restricting the value that x can reach.
  • When the variable x > INTERVAL_END, the function will be evaluated, and then the variable will be reset to x=INTERVAL_START. So keep in mind that the real interval is [INTERVAL_START,INTERVAL_END+MAX_DELTA).

• MIN_DELTA and MAX_DELTA:

  • It is possible to set both with the same value, in this case, it is expected that the curves are more similar between the "loops", and may be identical if RETAIN_PROBABILITY = 0.

Example 1 - Freezer Temperature

In the example below the MATH_EXPRESION = $2x²+1$, INTERVAL_START = 0, INTERVAL_END = 5, MIN_DELTA = 0 and MAX_DELTA = 0.5, so it is expected that the generated values are between 1 and 61.5, and the curves should be slightly different.

 {
    "TYPE": "single",
    "PREFIX": "freezer",
    "TIME_INTERVAL": 6,
    "DATA": [
        {
            "NAME": "temperature",
            "TYPE": "math_expression",
            "RETAIN_PROBABILITY": 0.1,
            "MATH_EXPRESSION": "2*math.pow(x,2)+1",
            "INTERVAL_START": 0,
            "INTERVAL_END": 5,
            "MIN_DELTA": 0.5,
            "MAX_DELTA": 0.5
        }
    ]
}

Example 2 - Car Velocity

In the example below the MATH_EXPRESION = $\sqrt{75x}$, INTERVAL_START = 0, INTERVAL_END = 100, MIN_DELTA = 10 and MAX_DELTA = 10, so it is expected that the generated values are between 0 and 87. As REATIN_PROBABILITY = 0 and the MIN_DELTA and MAX_DELTA are identicals, the curves must be identicals.

{
    "TYPE": "single",
    "PREFIX": "car",
    "TIME_INTERVAL": 6,
    "DATA": [
        {
            "NAME": "velocity",
            "TYPE": "math_expression",
            "RETAIN_PROBABILITY": 0,
            "MATH_EXPRESSION": "(75*x)**(1/2)",
            "INTERVAL_START": 0,
            "INTERVAL_END": 100,
            "MIN_DELTA": 10,
            "MAX_DELTA": 10
        }
    ]
}