A coverage metric to evaluate tests for continuous-time dynamic systems

AbstractWe present a test quality measure that allows for quantifying the completeness of black-box tests for continuous-time dynamic systems. The measure is based on a state space model of the system under test. The metric has been called the state space coverage. The classical coverage metrics, such as statement, branch, and path coverage, are not appropriate for dynamic systems because such systems are defined by differential equations and usually have an infinite number of states. The objective of the paper is to develop a necessary foundation for the metric as well as to present guidance on its application to software systems that incorporate dynamic behavior. The purpose of the proposed solution is to better assure the test engineer that a given test set is sufficient and to indicate where additional testing is required. An application example is presented to illustrate theoretical analysis and mathematical formulation.

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Modelling of Continuous-Time Dynamic Systems

Modelling and Simulation ◽

10.1007/978-1-84628-622-3_7 ◽

2007 ◽

pp. 249-273

Author(s):

Louis G. Birta ◽

Gilbert Arbez

Keyword(s):

Dynamic Systems ◽

Continuous Time ◽

Time Dynamic

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Event-Based Impulsive Control of Continuous-Time Dynamic Systems and Its Application to Synchronization of Memristive Neural Networks

IEEE Transactions on Neural Networks and Learning Systems ◽

10.1109/tnnls.2017.2731865 ◽

2018 ◽

Vol 29 (8) ◽

pp. 3599-3609 ◽

Cited By ~ 27

Keyword(s):

Neural Networks ◽

Dynamic Systems ◽

Continuous Time ◽

Impulsive Control ◽

Memristive Neural Networks ◽

Time Dynamic ◽

Event Based

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Using approximate Bayesian inference for a “steps and turns” continuous-time random walk observed at regular time intervals

PeerJ ◽

10.7717/peerj.8452 ◽

2020 ◽

Vol 8 ◽

pp. e8452

Author(s):

Sofia Ruiz-Suarez ◽

Vianey Leos-Barajas ◽

Ignacio Alvarez-Castro ◽

Juan Manuel Morales

Keyword(s):

State Space ◽

Continuous Time ◽

Time Scale ◽

Animal Movement ◽

State Space Model ◽

Movement Direction ◽

Time Intervals ◽

Space Model ◽

Regular Time ◽

Approximate Bayesian

The study of animal movement is challenging because movement is a process modulated by many factors acting at different spatial and temporal scales. In order to describe and analyse animal movement, several models have been proposed which differ primarily in the temporal conceptualization, namely continuous and discrete time formulations. Naturally, animal movement occurs in continuous time but we tend to observe it at fixed time intervals. To account for the temporal mismatch between observations and movement decisions, we used a state-space model where movement decisions (steps and turns) are made in continuous time. That is, at any time there is a non-zero probability of making a change in movement direction. The movement process is then observed at regular time intervals. As the likelihood function of this state-space model turned out to be intractable yet simulating data is straightforward, we conduct inference using different variations of Approximate Bayesian Computation (ABC). We explore the applicability of this approach as a function of the discrepancy between the temporal scale of the observations and that of the movement process in a simulation study. Simulation results suggest that the model parameters can be recovered if the observation time scale is moderately close to the average time between changes in movement direction. Good estimates were obtained when the scale of observation was up to five times that of the scale of changes in direction. We demonstrate the application of this model to a trajectory of a sheep that was reconstructed in high resolution using information from magnetometer and GPS devices. The state-space model used here allowed us to connect the scales of the observations and movement decisions in an intuitive and easy to interpret way. Our findings underscore the idea that the time scale at which animal movement decisions are made needs to be considered when designing data collection protocols. In principle, ABC methods allow to make inferences about movement processes defined in continuous time but in terms of easily interpreted steps and turns.

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Integrated System for Soft Tissue Dynamic Simulation

Volume 2: Biomedical and Biotechnology Engineering ◽

10.1115/imece2010-40680 ◽

2010 ◽

Author(s):

Xiaodong Zhao ◽

Baoxiang Shan ◽

Assimina A. Pelegri

Keyword(s):

Finite Element ◽

Soft Tissue ◽

State Space ◽

Soft Tissues ◽

Mathematical Formulation ◽

State Space Model ◽

Order Reduction ◽

Integrated System ◽

Space Model ◽

Tissue Models

An integrated system is built to model and simulate the dynamic response of soft tissues. The mathematical formulation employs finite element and model order reduction approaches to develop a state space model for soft tissues that allows for time-efficient numerical analysis. The stimulus device and signal processing routines are built in Matlab/Simulink and then integrated with the finite element state space model. This integrated system facilitates expeditious numerical evaluation of different soft tissue models subjected to dynamic excitation. It further elucidates the effect of different stimulus sources, as well as relative influences of different sources of uncertainty.

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