processNOCdata: Simulate NOC Observations from a Single-State or Multi-State...

In mvMonitoring: Multi-State Adaptive Dynamic Principal Component Analysis for Multivariate Process Monitoring

Simulate NOC Observations from a Single-State or Multi-State Process

Description

This function generates data under normal operating conditions from a single-state or multi-state process model.

Usage

processNOCdata(
  startTime = "2015-05-16 10:00:00 CST",
  period = 7 * 24 * 60,
  stateDuration = 60,
  increment = "min",
  multiState = TRUE,
  autocorellation = 0.75,
  tLower = 0.01,
  tUpper = 2,
  errVar = 0.01
)

Arguments

startTime	a POSIXct object specifying the day and time for the starting observation.
period	The observation cycle length. Defaults to one week's worth of minute-level observations (10,080 observations).
stateDuration	The number of observations generated during a stay in each state. Defaults to 60.
increment	The time-sequence base increment. See "Details" of the seq.POSIXt() function options. Defaults to "min" for minutes.
multiState	Should the observations be generated from a multi-state process? Defaults to TRUE.
autocorellation	The autocorrelation parameter. Must be less than 1 in absolute value, or the process generated will be nonstationary. Defaults to 0.75 in accordance to Kazor et al (2016).
tLower	Lower bound of the latent $t$ variable. Defaults to 0.01.
tUpper	Upper bound of the latent $t$ variable. Defaults to 2.
errVar	Error variance of the normal white noise process on the feature variables.

Details

This function randomly generates a non-stationary (sinusoidal) and autocorrelated latent variable t with lower and upper bounds given by the arguments "tLower" and "tUpper", respectively, with autocorrelation governed by the "autocorrelation" argument. Necessarily, this coefficient must be less than 1 in absolute value, otherwise the latent variable will be unbounded. Next, this function draws a realization of this random variable t and calculates three functions of it, then jitters these functions with a normal white noise variable (with variance set by "errVar"). These three functions are:

x :

x(t) = t + error

y :

y(t) = t ^ 2 - 3t + error

z :

z(t) = -t ^ 3 + 3t ^ 2 + error

This function is called by the mspProcessData() function. See ?mspProcessData for more details.

Value

An data frame with the following information:

dateTime –

A POSIXct column of times starting at the user-defined 'startTime' argument, length given by the 'period' argument, and spacing given by the 'increment' argument. For example, if the starting value is "2016-01-10", period is 10080, and the incrementation is in minutes, then this sequence will be one week's worth of observations recorded every minute from midnight on the tenth of January.

state –

An integer column of all 1's (when the 'multiState' argument is FALSE), or a column of the state values (1, 2 or 3).

x –

A double column of generated values for the first feature.

y –

A double column of generated values for the second feature.

z –

A double column of generated values for the third feature.

See Also

Called by: mspProcessData.

Examples

processNOCdata()

mvMonitoring documentation built on Nov. 22, 2023, 1:09 a.m.