Testing Thermostatic Bath End-Scale Stability for Calibration Performance with a Multiple-Sensor Ensemble Using ARIMA, Temporal Stochastics and a Quantum Walker Algorithm

Abstract

Thermostatic bath calibration performance is usually checked for uniformity and stability to serve a wide range of industrial applications. Particularly challenging is the assessment at the limiting specification ends where the sensor system may be less effective in achieving consistency. An ensemble of eight sensors is used to test temperature measurement stability at various topological locations in a thermostatic bath (antifreeze) fluid at -20 °C. Eight streaks of temperature data were collected, and the resulting time-series were processed for normality, stationarity, and independence and identical distribution by employing regular statistical inference methods. Moreover, they were evaluated for autoregressive patterns and other underlying trends using classical Auto-Regressive Integrated Moving Average (ARIMA) modeling. In contrast, a continuous-time quantum walker algorithm was implemented, using an available R-package, in order to test the behavior of the fitted coefficients on the probabilistic node transitions of the temperature time series dataset. Tracking the network sequence for persistence and hierarchical mode strength was the objective. The quantum walker approach favoring a network probabilistic framework was posited as a faster way to arrive at simultaneous instability quantifications for all the examined time-series. The quantum walker algorithm may furnish expedient modal information in comparison to the classical ARIMA modeling and in conjunction with several popular stochastic analyzers of time-series stationarity, normality, and data sequence independence of temperature end-of-scale calibration datasets, which are investigated for temporal consistency.

Keywords: ARIMA; normality; quantum walker; sensor ensemble; stability; stationarity; temperature calibration; thermostatic bath; uniformity.

Scheme 1

Detailed flowchart of the methodological steps.

Figure 1

Line graphs with data points for the eight temperature time series with increasing sensor identification numbers: (A–H) temperature plots.

Figure 1

Line graphs with data points for the eight temperature time series with increasing sensor identification numbers: (A–H) temperature plots.

Figure 1

Line graphs with data points for the eight temperature time series with increasing sensor identification numbers: (A–H) temperature plots.

Figure 2

Boxplot (A) and violin plot (B) screenings of the temperature data (in °C) from all eight sensors.

Figure 3

Correlograms for the eight time series: (A–H) temperature ACF plots.

Figure 3

Correlograms for the eight time series: (A–H) temperature ACF plots.

Figure 3

Correlograms for the eight time series: (A–H) temperature ACF plots.

Figure 3

Correlograms for the eight time series: (A–H) temperature ACF plots.

Figure 4

Partial autoregression correlograms for the eight time series: (A–H) temperature PACF plots.

Figure 4

Partial autoregression correlograms for the eight time series: (A–H) temperature PACF plots.

Figure 4

Partial autoregression correlograms for the eight time series: (A–H) temperature PACF plots.

Figure 5

ARIMA modeling diagnostics for the eight temperature time series: (A–H) residuals plots.

Figure 5

ARIMA modeling diagnostics for the eight temperature time series: (A–H) residuals plots.

Figure 5

ARIMA modeling diagnostics for the eight temperature time series: (A–H) residuals plots.

Figure 5

ARIMA modeling diagnostics for the eight temperature time series: (A–H) residuals plots.

Figure 5

ARIMA modeling diagnostics for the eight temperature time series: (A–H) residuals plots.

Figure 6

Scree-type plots (the quantum walker index value) for the eight temperature time series with increasing sensor identification numbers: (A–H) temperature plots.

Figure 6

Scree-type plots (the quantum walker index value) for the eight temperature time series with increasing sensor identification numbers: (A–H) temperature plots.

Figure 6

Scree-type plots (the quantum walker index value) for the eight temperature time series with increasing sensor identification numbers: (A–H) temperature plots.

Figure 7

Q-Q plots (the quantum walker regression coefficients) for the eight temperature time series with increasing sensor identification numbers: (A–H) temperature plots.

Figure 7

Q-Q plots (the quantum walker regression coefficients) for the eight temperature time series with increasing sensor identification numbers: (A–H) temperature plots.

Figure 7

Q-Q plots (the quantum walker regression coefficients) for the eight temperature time series with increasing sensor identification numbers: (A–H) temperature plots.