Expressing Measurement Uncertainty in OCL/UML Datatypes

Abstract

Uncertainty is an inherent property of any measure or estimation performed in any physical setting, and therefore it needs to be considered when modeling systems that manage real data. Although several modeling languages permit the representation of measurement uncertainty for describing certain system attributes, these aspects are not normally incorporated into their type systems. Thus, operating with uncertain values and propagating uncertainty are normally cumbersome processes, difficult to achieve at the model level. This paper proposes an extension of OCL and UML datatypes to incorporate data uncertainty coming from physical measurements or user estimations into the models, along with the set of operations defined for the values of these types.

Managing Uncertain Complex Events in Web of Things Applications

“…Comparison operators between UReal variables return UBoolean values. For example, if a = 2.0±0.3 and b = 2.5±0.25, we obtain that a < b with a confidence of 0.893 [2]. Assigning probabilities to complex events.…”

“…In a previous paper [2] we extended the basic UML and OCL datatypes so they incorporate the associated uncertainty. Thus, Real values with uncertainty are represented in terms of UReal values, composed of pairs (x, u), also noted as x ± u, where x is the value, and u represents its uncertainty as the standard deviation of its possible variations.…”

“…This has been implemented in Esper, using the Java implementation we have developed for the library of OCL types extended with uncertainty [2]. With this, the TempIncrease rule can be written to account for uncertainty as follows.…”

“…We depart from these approaches in two main ways. First, we use the extended type system for reals numbers and boolean values defined in [2]. This greatly simplifies the representation of the uncertainty and its propagation, as we have seen in Section 3.…”

“…More precisely, we address uncertainty in the occurrence of the events, on the values of their attributes (including their timestamps), and on the confidence of the derivation rules. We make use of an extension of UML and OCL basic datatypes [14,2] to represent uncertain values and to transparently deal with measurement uncertainty, greatly simplifying these tasks. A case study is used to describe the proposal, and an implementation on top of the Esper language [6] is also presented.…”