A type-based analysis of causality loops in hybrid systems modelers

Zelus is a new programming language for modeling systems that mix discrete logical time and continuous time behaviors. From a user's perspective, its main originality is to extend an existing Lustre-like synchronous language with Ordinary Differential Equations (ODEs). The extension is conservative: any synchronous program expressed as data-flow equations and hierarchical automata can be composed arbitrarily with ODEs in the same source code. A dedicated type system and causality analysis ensure that all discrete changes are aligned with zero-crossing events so that no side effects or discontinuities occur during integration. Programs are statically scheduled and translated into sequential code that, by construction, runs in bounded time and space. Compilation is effected by source-to-source translation into a small synchronous subset which is processed by a standard synchronous compiler architecture. The resultant code is paired with an off-the-shelf numeric solver.We show that it is possible to build a modeler for explicit hybrid systems a la Simulink/Stateflow on top of an existing synchronous language, using it both as a semantic basis and as a target for code generation.

Hybrid systems modeling languages are widely used in the development of embedded systems. Two representatives are Simulink/Stateflow1 that combine Ordinary Differential Equations (ODEs), data-flow and difference equations, hierarchical automata a la StateCharts [14] together with imperative features; and the Modelica language [1]2 based on DAEs with features for modeling discrete components. Ptolemy II3 is another example in which several models of computation are combined [15].The formal verification of hybrid systems has been extensively studied [9]. Yet, we share the viewpoint of Lee and Zheng that hybrid modeling languages are best viewed as programming languages that happen to have a hybrid systems semantics [16, 17]. This raises important questions related to their design, semantics and implementation, to get efficient and reliable simulations as well as provably equivalent embedded target code. While sequential code generation in hybrid modeling tools is routinely used for efficient simulation, it is little used or not used at all to produce target embedded code in critical applications that are submitted to strong safety requirements. This results in a break in the development chain: parts of applications must be rewritten into sequential code and all properties verified on the source model cannot be trusted and have to be reverified on the target code.Sequential code generation from a synchronous language like Lustre [12] has been studied in detail [13]. It can be formalized as a series of source-to-source transformations that eliminate high level constructs like hierarchical automata [11] and the generation of a generic intermediate representation for transition functions, turned itself into C code [6]. This approach, initiated in Lucid Synchrone [18], is implemented in the Scade Suite KCG code generator of Scade 64, used for developing various critical applications.Yet, synchronous languages only manipulate discrete-time signals. Their expressiveness is limited to insure important safety properties like determinacy, execution in bounded time and space, and simple, traceable code generation. Their cyclic execution requires minimal run-time support and does not suffer the complications that accompany numerical solvers of ordinary differential equations. Conversely, a hybrid modeling language allows discrete and continuous time behaviors to interact. But this interaction is not constrained enough, nor specified with adequate precision in tools like Simulink/Stateflow and this occasion semantics pitfalls and bugs [10, 5, 2]. A precise description of all the compilation steps, that is, the actual implemented semantics, is mandatory in safety critical development processes where target code must be trustworthy. Our goal, in short, is to increase the expressiveness of synchronous languages without sacrificing any confidence in their compilers.In previous works, we introduced a novel approach for the design and implementation of a hybrid modeling language that reuses synchronous language principles and an existing compiler infrastructure. We introduced an ideal synchronous semantics based on non standard analysis [5] for a Lustre-like language with ODEs [4], and then extended the kernel language with hierarchical automata [3] and a modular causality analysis [2]. These results form the foundation of Zelus [8]5 and were validated inside the industrial Scade Suite KCG code generator (Release 6.4, 2014) developed at Esterel-Technologies/ANSYS [7].In this talk, I will summarize the ongoing work on Zelus and the way it has been applied to the Scade Suite KCG code generator. In the later, it was possible to reuse the existing infrastructure entirely with little modifications: static typing, the causality and initialization analysis, intermediate languages and the various compiler optimizations. The proposed language extension is conservative in that regular synchronous functions are compiled as before --- the same synchronous code is used both for simulation and for execution on target platforms. It also shows the versatility of the KCG infrastructure based on a successive rewriting. The precise definition of all compilation steps, built on the proven compiler infrastructure of a synchronous language avoids the rewriting of control software and may also increase the confidence in simulation results.This work results from a collaboration with Albert Benveniste, Benoit Caillaud (INRIA, Rennes), Timothy Bourke (INRIA, Paris-Rocquencourt), Jean-Louis Colaco, Bruno Pagano and Cedric Pasteur (Esterel-Technologies/ANSYS).

This paper proposes a method for three-phase state estimation (SE) in power distribution network including onload tap changers (OLTC) for voltage control. The OLTC tap positions are essentially discrete variables from the SE point of view. Estimation of these variables in SE presents a formidable challenge. The proposed methodology combines discrete and continuous state variables (voltage magnitudes, angles, and tap positions). A hybrid particle swarm optimization (HPSO) is applied to obtain the solution. The method is tested on standard IEEE 13- and 123-bus unbalanced test system models. The proposed algorithm accurately estimates the network bus voltage magnitudes and angles, and discrete tap values. The HPSO-based tap estimation provides a more accurate estimation of losses in the network, which helps in fair allocation of cost of losses in arriving at overall cost of electricity.

In this paper we describe a Bayesian approach to fault diagnosis based on Markov chain Monte Carlo algorithms. These approaches are largely applied to hybrid diagnosis problems in which the system being diagnosed is modelled with a mixture of discrete and continuous state variables. We describe the probabilistic hybrid automaton model typically used, and an algorithm based on particle filtering that can be applied to these models. Diagnosis provides some particular challenges for Monte Carlo approaches, including large dimensional state spaces, and low probability transitions in the Markov chain. We discuss these and some proposed solutions to them. Finally, we examine some open challenges for the Bayesian approach.

The switching system can be viewed as a kind of hybrid system because it has both continuous state variables and discrete state variables. Viewing the controller as hierarchical, then the switch strategy belongs to the higher hierarchy. It represents the intelligent factors and plays a key role in system performance. In this paper, the intelligent switching system methodology is researched, and the DESSC (Discrete event system supervisor and controller) is constructed with an intelligent method. A coke oven is used as the control object. Based on the analysis of the coke oven heating process and its state partition, the control strategy of intelligent switching systems is used which can effectively resolve process control problems of the complex system with large time-delay, realize coke oven automatic heating control, and good performance of control can be obtained.

We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by R.S. Ellis, Physica D 133:106 (1999), which uses large deviation techniques. We show how it can be adapted to obtain the solution of a large class of simple models, which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free Electron Laser) state variables. This latter extension gives access to the comparison with dynamics and to the study of non-equilibrium effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the α-Ising model in one-dimension with 0 ⩽ α < 1.

Structured demographic models offer powerful methods for addressing important questions in ecology and evolution. Integral Projection Models (IPMs) are related to classic matrix models, but are more appropriate for modelling structured populations when the variable describing individuals' demography is continuous (e.g. size, weight, etc.). We present IPMpack, a free open-source software (R) package for building IPMs. The package estimates key population characteristics from IPMs, such as population growth rate in both deterministic and stochastic environments, age-specific trajectories of survival and reproduction, and sensitivities and elasticities to changes in underlying vital rates. IPMpack can be used for species across a range of life cycle complexity and can include continuous and discrete (e.g. seed bank, hibernation) state variables, as well as environmental covariates of interest. Methods for diagnostics, sensitivity analyses, plotting, model comparison and many other features allow users to move from data input through analysis to inference using an array of internal functions. IPMpack fills a need for readily usable tools for constructing and analysing IPMs and is designed to facilitate their use for experts and open up their use for those researchers who have little experience in the details of population models. A standardized IPM modelling framework will also facilitate cross-study and cross-species comparative demography, encouraging the exploration of broader ecological and evolutionary questions that can be addressed by population models. © 2012 The Authors. Methods in Ecology and Evolution

Thrombocytosis associated with malignant ovarian lesions within a pediatric and adolescent population

Hybrid systems modelers like Simulink come with a rich collection of discrete-time and continuous-time blocks. Most blocks are not defined in terms of more elementary ones—and some cannot be—but are instead written in imperative code and explained informally in a reference manual. This raises the question of defining a minimal set of orthogonal programming constructs such that most blocks can be programmed directly and thereby given a specification that is mathematically precise, and whose compiled version performs comparably to handwritten code. In this paper, we show that a fairly large set of blocks of a standard library like the one provided by Simulink can be programmed in a precise, purely functional language using stream equations, hierarchical automata, Ordinary Differential Equations (ODEs), and deterministic synchronous parallel composition. Some blocks cannot be expressed in our setting as they mix discrete-time and continuous-time signals in unprincipled ways that are statically forbidden by the type checker. The experiment is conducted in Zélus, a synchronous language that conservatively extends L ustre with ODEs to program systems that mix discrete-time and continuous-time signals.

This paper discusses the integrated topology and sizing optimization of frame structures where beam elements are used in the structural analysis model. Based on the ground structure approach, discrete variables (0, 1) representing the absence or presence of beam members and continuous sizing variables for beam cross sections are involved in the problem. A two-level multipoint approximation strategy is introduced to address this mixed-variable problem. A first-level approximate problem is first constructed using the branched multipoint approximate function involving both discrete and continuous variables. For solving this problem, discrete variables are optimized through a genetic algorithm, and when calculating the fitness in the genetic algorithm, a second-level approximate problem solved by the dual method is established to optimize the cross sections for the retained beam members. Temporal deletion techniques are used for displacement and stress constraints. Meanwhile, by considering local vibration modes in frequency-constrained problems, material density is assigned with an extremely small value for the removed beams to avoid these local modes. Thence, the singularities encountered in stress, displacement, and frequency constraints are overcome. Typical examples and a satellite application are given to verify the feasibility and efficiency of this method in handling the integrated topology and sizing optimization for frame structures.

Engineering constraint solvers for automatic analysis of probabilistic hybrid automata

The Sustainable Development Goals, a set of ambitious targets embraced by United Nations member states, are designed to meet global challenges head‐on while shaping a sustainable future. Of these, Goal 7, in particular, focuses on the critical need for affordable, reliable, sustainable, and modern energy for all. Wind energy holds a significant potential in fulfilling Goal 7 of the sustainable development goals. In Norway, there exists a unique scenario, where nearly 98% of electricity is generated from renewable resources. However, without a subsequent increase in power production, a deficit in power is projected by 2027 according to a short‐term market analysis by Statnett. To prevent this, it is imperative to increase the production of electricity from wind. However, in recent years, there has been a significant rise in opposition towards wind power projects in Norway. Some of the wind power projects have even been put on hold because of the increase in protests. In light of this, we apply systems thinking methodologies to improve our understanding of this complex problem. Initially, we identify the stakeholders in our system of interest and categorize them through stakeholder salience analysis framework. Then, we developed a systemigram to graphically represent the system of interest. Finally, we carry out causal loop analysis to find causal loops in our system of interest. Our primary focus with this work is to better understand the factors shaping public perception of wind power projects in Norway. By gaining a deeper understanding about the factors influencing public perception of wind power projects in Norway, we aim to find better solutions to improve the social acceptance of these initiatives in Norway in future works.

Starting from a resilience assessment of Harare's water supply, the system interactions of the city’s water management arrangements are explored through a series of causal loop diagrams. These are based on economic, physical, commercial, environmental, and social subsystems and the reinforcing and balancing loops that influence key variables of interest in each are identified. The analysis identifies a series of shortcomings including a weak provider-customer relationship, limited governance capacity, inadequate coordination and integration between key players, shortfalls in physical supply and critical infrastructure, environmental degradation, and a lack of disaster response and recovery measures. A series of strategies are proposed as intervention actions that target the areas of potential leverage identified in the causal loop analysis, including improving customer-provider relationships; increasing coordination, collaboration, and integration; developing physical and informational infrastructure and enhancing environmental protection and rehabilitation. The impacts of these strategies are highlighted as strengthening key elements of the causal loop diagrams and addressing the resilience gaps identified. The systems mapping approach reveals that key issues are large-scale, cross-sectoral, and compounding. Remediation strategies must therefore also be multi-faceted and holistic in scope.

The mathematical foundations of physical systems modeling languages

This paper compares particle swarm optimization (PSO) techniques for a reactive power allocation planning problem in power systems. The problem can be formulated as a mixed-integer nonlinear optimization problem (MINLP). The PSO based methods determines a reactive power allocation strategy with continuous and discrete state variables such as automatic voltage regulator (AVR) operating values of electric power generators, tap positions of on-load tap changer (OLTC) of transformers, and the number of reactive power compensation equipment. Namely, this paper investigates applicability of PSO techniques to one of the practical MINLPs in power systems. Four variations of PSO: PSO with inertia weight approach (IWA), PSO with constriction factor approach (CFA), hybrid particle swarm optimization (HPSO) with IWA, and HPSO with CFA are compared. The four methods are applied to the standard IEEE14 bus system and a practical 112 bus system.