An Uncertainty Toolbox

An Uncertainty Toolbox (AUT) is a software tool for MATLAB, developed to perform uncertainty calculations in Measurement Science. The aim is to provide a simple and intuitive tool that allows to write compact and well understandable code. Initially, it was intended to be used in education only but it has been used more and more also in practical applications.

AUT makes uncertainty propagation simple. Assume you already have some matlab code to compute a quantity of interest, e.g a resistor value based on measured voltage and current:

>> U=10;
>> I=0.12;
>> R=U/I

R =

83.3333

With AUT, all you have to do is to provide the uncertainty information (i.e. estimate and standard uncertainty) when you assign your inputs:

>> U=unc_t(10,0.1);
>> I=unc_t(0.12,0.001);
>> R=U/I

R =

83.3(1.1)

The results is reported in the GUM notation, i.e. the values in the bracket are the standard uncertainy expressed in terms of the last digits of the value; here the estimate of R is 83.3 Ohms with a standard uncertainty u(R)=1.1 Ohms, based on a voltage estimate of U=10 V with u(U)=0.1 V and a current estimate of I=0.12 A with a standard uncertainty u(I)=1 mA.

The toolbox keeps full track of correlations, e.g. the covariance matrix of U,I and R can be obtained as follows:

>> C=get_cov_mat([U,I,R])

C =

0.0098 -0.0000 0.0818
-0.0000 0.0000 -0.0007
0.0818 -0.0007 1.1664

The toolbox includes three different approaches: Linearization, Monte Carlo(MC) and Unscented Transformation(UT). AUT is also intended to be useful for system analysis and optimization, provinding a simple way to switch between the aforementioned methods.  Information about how to use AUT and some examples are available in the folders Documentation and Examples, respectively.

BTW: AAU offers a campus license for MATLAB.

Download:

An Uncertainty Toolbox(AUT)

Please refer to

Hubert Zangl, Klaus Hoermaier, Educational aspects of uncertainty calculation with software tools,
Measurement, Volume 101, 2017, Pages 257-264, ISSN 0263-2241,https://doi.org/10.1016/j.measurement.2015.11.005. (http://www.sciencedirect.com/science/article/pii/S0263224115005916)
Preprint: Educational aspects of uncertainty calculation with software tools

Dailys Arronde Pérez, Harald Gietler and Hubert Zangl,  Automatic Uncertainty Propagation Based on the Unscented Transform, IEEE International Conference on Instrumentation and Measurement (I2MTC) May 2020, Dubrovnik, Croatia
Preprint: Automatic Uncertainty Propagation Based on the Unscented Transform