Symbolic simulation of hybrid systems

Number of software Reliability growth models has been proposed in the literature. A mathematical technique which describes the software testing phenomenon known as the software reliability growth model. Software reliability growth models are used to predict the number of faults and reliability of the software. In the view of this software reliability growth models are basically differentiated as the continuous and discrete models. There is a plenty of development in the continuous models but little towards the discrete models. In this paper we have presented a discrete reliability growth model with different discrete testing effort functions and the same time software release policy is discussed. A new imperfect debugging discrete software reliability growth model with testing effort is proposed. All calculations are done on real data. The results shows the proposed testing effort models are perfectly fit to the data.

In this paper, we introduce a novel parallelization technique for Discrete Event System Specification (DEVS) simulation of continuous and hybrid systems. Here, like in most parallel discrete event simulation methodologies, the models are first split into several sub-models which are then concurrently simulated on different processors. In order to avoid the cost of the global synchronization of all processes, the simulation time of each sub-model is locally synchronized in a real-time fashion with a scaled version of physical time, which implicitly synchronizes all sub-models. The new methodology, coined Scaled Real-Time Synchronization (SRTS), does not ensure a perfect synchronization in its implementation. However, under certain conditions, the synchronization error introduced only provokes bounded numerical errors in the simulation results. SRTS uses the same physical time-scaling parameter throughout the entire simulation. We also developed an adaptive version of the methodology (Adaptive-SRTS) where this parameter automatically evolves during the simulation according to the workload. We implemented the SRTS and Adaptive-SRTS techniques in PowerDEVS, a DEVS simulation tool, under a real-time operating system called the Real-Time Application Interface. We tested their performance by simulating three large-scale models, obtaining in all cases a considerable speedup.

The discrete Lotka power function describes the number of sources (e.g., authors) with n = 1, 2, 3, … items (e.g., publications). As in econometrics, informetrics theory requires functions of a continuous variable j, replacing the discrete variable n. Now j represents item densities instead of number of items. The continuous Lotka power function describes the density of sources with item density j. The discrete Lotka function one obtains from data, obtained empirically; the continuous Lotka function is the one needed when one wants to apply Lotkaian informetrics, i.e., to determine properties that can be derived from the (continuous) model. It is, hence, important to know the relations between the two models. We show that the exponents of the discrete Lotka function (if not too high, i.e., within limits encountered in practice) and of the continuous Lotka function are approximately the same. This is important to know in applying theoretical results (from the continuous model), derived from practical data.

One confusing question over a long period of time is how transfer the discrete function transfers into continuous function. Recently the issue has been resolved but some details of the transformation process will be introduced in the paper. The correlation coefficients of 100,000 values are established from the two groups of data with the range between -1 and 1, creating a histogram from these correlation coefficient values known as “the probability mass function.” The coefficient values are brought into the discrete distribution function, so that transfers into the discrete cumulative function, next converted into a continuous cumulative function, next which is differentiated to get the density function, so that it is easy to being research analysis. A model will be established during the process of the conversion what the medium is “the least squares algorithm.” Finally, when the integral of the area within the range of the density function equals to 1, this implies that the transformation complete succeeds from the discrete function to the continuous function.

Model based approaches to diagnosis for dynamic systems have been based on continuous and discrete event models. Systems that combine continuous and discrete behaviors, i.e., hybrid systems have been typically abstracted into discrete event models or approximated by continuous models with steep slopes so that existing algorithms can be applied for fault isolation tasks. This approach runs into problems when both discrete events and continuous behaviors provide vital diagnostic information. We propose a diagnostic methodology that uses hybrid models of the system to perform diagnosis.

In this paper, a novel intelligent modeling framework is introduced for modeling hybrid dynamical systems, which may contain both continuous-valued and discrete-valued dynamics and/or signals. The proposed modeling framework consists of a fuzzy relational hybrid model (FRHM) structure and an online identification algorithm. The FRHM structure has some useful properties, e.g., the ability of modeling both hard and soft switchings (even simultaneously), model transparency (in view of knowledge extraction and knowledge embedment), and possibility of connecting disjoint models through mathematical operations (to construct larger model structures). In addition, the proposed FRHM structure can be used to model a wide variety of hybrid dynamical systems, including nonlinear dynamical systems, dynamical systems with switchings or logical functions, dynamical systems with discrete-valued or qualitative inputs and/or outputs, etc. The fuzzy relational hybrid dynamical system is an important product of the proposed modeling structure, which, in this paper, has applied to modeling an asynchronous dc–dc buck converter as the case study.

COSMOS is a new simulation language for description of continuous, discrete or combined continuous/discrete models. For continuous models, the COSMOS language definition constitutes a superset of CSSL with many additional structuring elements being incorporated, e.g. for convenient modelling of piecewise continuous models and variable structure systems. Discrete models are coded according to the process interaction world view. The design of the language constructs makes it possible to write simulation programs in accordance with modem software engineering methodology. The model and experiment description, for example, are totally separated. In addition, models can be separated into submodels.

This paper summarizes models for software reliability demonstration testing (SRDT). The models are briefly classified into three types: (1) continuous models, (2) discrete models and (3) models considering damage sizes of software failures. Under the continuous models, the software product of interest is tested for time t and is accepted if the number of software failures in the test does not exceed a prespecified integer s. The values of design variables, t and s are determined based on (i) the concept of a statistical test (a statistical model) and (ii) the Kullback–Leibler information (a K–L model). The K–L model has less parameters to be prespecified than the statistical model. Under the discrete models for SRDT, the software of interest is tested with n input data sets and is accepted if the number of input data sets causing software failures in the test does not exceed a prespecified integer c. A statistical model as well as a K–L model is described for the discrete models. Neither continuous nor discrete models in the above take the damage size of software failures into consideration. The third type of models are continuous and discrete models which consider the cumulative damage size caused by software failures as well as the number of software failures in the test.

Interval-based Solving of Hybrid Constraint Systems

This paper deals with a model builder for Hybrid Dynamic Systems (HDS), where technological components including sensors in an iconic format can be automatically dragged from a database and interconnected to produce the overall HDS, following industrial technological schemes. Once the model has been created, its consistency can be checked, and a block diagram simulation can be performed. The theory behind the software is based on Hybrid Bond Graphs (HBG), whose structural and causal properties will be exploited for the automatic generation of the diagnosis algorithms, which will be implemented online. Compared with developed programs for automated modeling of HDS, the presented methodology is valid for continuous and hybrid systems, and the HBG is used not only for block diagram simulation builders but also for the generation of Fault Detection and Isolation algorithms. The theory is illustrated by an industrial application that consists of the pneumo-electrical control of metro rolling stock.

The numerical simulation of non-smooth hybrid systems exhibiting chattering behavior requires high computational costs. In the worst case, the simulation appears to come to a halt, since infinitely many discrete transitions would need to be simulated. In this paper we present an FMI-based framework and prototypical implementation for robust and reliable detection and elimination “On the Fly” of chattering behavior in run-time simulation of non-smooth hybrid systems. The main benefit of the developed framework is that it establishes solvability requirements and theorems for simulating hybrid systems while performing the chattering path avoidance internally in the master algorithm of the interface. This increases the efficiency of the chattering-free simulation as no enumeration of modes is required during the chattering detection and elimination process. The developed FMI-based framework can generate a chattering-free simulation for any generic chattering Functional Mockup Unit (FMU) conforming to the FMI standard v2.0 Specification for model exchange.

Solid oxide fuel cell (SOFC)/ gas turbine (GT) hybrid systems possess the capacity for unprecedented performances, such as electric efficiencies nearly twice that of conventional heat engines at variable scale power ratings inclusive of distributed generation. Additionally, these hybrids can have excellent operational flexibility with turndowns possibly as great as 85%. There are, however, developmental needs such as turbomachinery characterization and re-design. A leading example is that of greater propensity to have occurrences of stall-surge given the significantly different operating environment in contrast to conventional heat engines. Additionally, dynamic variation in power generation has to be done with significant a priori insight to avoid thermomechanical threats to cell stack and turbomachinery. State-of-the-art approaches involving hardware-in-the-loop simulation and, ultimately, additive manufacturing are being pursued to enable such characterization and re-design considerations given variable and dynamic operability requirements. Compressor performance in hybrid systems has been characterized at the United States National Energy Technology Laboratory (NETL), inclusive of a capability of feed forward hardware-in-the-loop simulation of hybrid systems under dynamic conditions and a capability of replacing turbine and compressor components at a relatively low cost. This paper highlights some of the simulation results, and the net result is an approach that addresses hybrid system developmental needs for accommodating generation transients.

This article focuses on production planning in the metallurgical sector. This study undertakes a detailed comparative study of mixed-integer linear programming models using different time representations: continuous and discrete. The analysis shows that the continuous model consistently outperforms its discrete counterpart in all evaluated scenarios. The key difference between the continuous and discrete models is the continuous model’s ability to deliver better makespan results, achieving an improvement of up to 15% compared to the discrete model. This advantage holds even in complex environments with a high number of tasks and machines, where the continuous model consistently outperforms the discrete model by over 6% in the scenario with the highest number of tasks and machines. This preference extends beyond makespan considerations. The continuous model also maintains an edge in terms of runtime efficiency, achieving better times with a 99% improvement over the discrete model in all scenarios except one. These findings provide concrete evidence for the use of continuous models, which promise more effective production planning in analogous manufacturing domains.

This mansscript studies analytically the consequences of changing the scale of measurement of a continuous independent variable in a multiple linear regression setting. Assuming the continuous outcome variable, a continuous exposure variable, and a continuous control variable follow a trivariate Gaussian distribution, we examine the effect upon the structure of the modei of dichotomizing the continuous control variable. It is shown that, after dichotomizaiion, the condirionai expected vaiiie of the response is a quotient of two non-hear functions and hence is no longer linear in the exposure variable. Thus, when an underlying continuous independent variable is dichotomized in multiple linear regression, and one fits a linear model using the dichotomous variable, this model's linear structure is misspecified. The estimates obtained from this model are incorrect and potentially misleading.

Random Cantor set models for the elastic-perfectly plastic contact of rough surfaces