Two different metrics quantifying model and simulator predictive capability are formulated and evaluated; both metrics exploit results from conducted validation experiments where simulation results are compared to the corresponding measured quantities. The first metric is inspired by the modified nearest neighbor coverage metric and the second by the Kullback?Liebler divergence. The two different metrics are implemented in Python and in a here-developed general metamodel designed to be applicable for most physics-based simulation models. These two implementations together facilitate both offline and online metric evaluation. Additionally, a connection between the two, here separated, concepts of predictive capability and credibility is established and realized in the metamodel. The two implementations are, finally, evaluated in an aeronautical domain context.

Combining performance and numerical stability is a key issue in co-simulation. The Transmission Line Modeling method uses physically motivated communication delays to ensure numerical stability for stiff connections. However, using a fixed communication delay may limit performance for some models. This paper proposes Steady-State Identifcation for enabling variable communication delays. Three algorithms for online Steady-State Identification are evaluated in three different co-simulation models. All algorithms are able to identify steady-state and can thereby determine when communication delays can be allowed to increase without compromising accuracy and stability. The results show a reduction in number of the solver derivative evaluations by roughly 40-60% depending on the model. The proposed method additionally supports connections with asymmetric communication delays, which allows each sub-model to independently control the delay of its input variables. Models supporting delay-size control can thereby be connected to those that do not so that the step length of each individual sub-model is maximized. Controlling the delay-size in sub-models also makes the method independent of the master co-simulation algorithm. 

Modeling and simulation are important tools for efficient product development. There is a growing need for collaboration, interdisciplinary simulation, and re-usability of simulation models. This usually requires simulation tools to be coupled together for co-simulation. However, the usefulness of co-simulation is often limited by poor performance and numerical instability. Achieving stability is especially hard for stiff mechanical couplings. A suitable method is to use transmission line modeling (TLM), which separates submodels using physically motivated time delays. The most established standard for tool coupling today is the Functional Mock-up Interface (FMI). Two example models in one dimension and three dimensions are used to demonstrate how the next version of FMI for co-simulation can be used in conjunction with TLM. The stability properties of TLM are also proven by numerical analysis. Results show that numerical stability can be ensured without compromising on performance. With the current FMI standard, this requires tailor-made models and custom solutions for the interpolation of input variables. Without using custom solutions, variables must be exchanged using sampled communication and extrapolation. In this case, stability properties can be improved by reducing communication step size. However, it is shown that stability cannot be achieved even when using unacceptably small communication steps. This motivates the need for the next version of FMI to include an intermediate update mode, where variables can be interchanged in between communication points. It is suggested that the FMI standard should be extended with optional callback functions for providing intermediate output variables and requesting intermediate input variables.

Establishing interoperability is an essential aspect of the often-pursued shift towards Model-Based Systems Engineering (MBSE) in, for example, aircraft development. If models are to be the primary information carriers during development, the applied methods to enable interaction between engineering domains need to be modular, reusable, and scalable. Given the long life cycles and often large and heterogeneous development organizations in the aircraft industry, a piece to the overall solution could be to rely on open standards and tools. In this paper, the standards Functional Mock-up Interface (FMI) and System Structure and Parameterization (SSP) are exploited to exchange data between the disciplines of systems simulation and geometry modeling. A method to export data from the 3D Computer Aided Design (CAD) Software (SW) CATIA in the SSP format is developed and presented. Analogously, FMI support of the Modeling & Simulation (M&S) tools OMSimulator, OpenModelica, and Dymola is utilized along with the SSP support of OMSimulator. The developed technology is put into context by means of integration with the M&S methodology for aircraft vehicle system development deployed at Saab Aeronautics. Finally, the established interoperability is demonstrated on two different industrially relevant application examples addressing varying aspects of complexity. A primary goal of the research is to prototype and demonstrate functionality, enabled by the SSP and FMI standards, that could improve on MBSE methodology implemented in industry and academia.

Modeling and Simulation (M&S) is seen as a means to mitigate the difficulties associated with increased system complexity, integration, and cross-couplings effects encountered during development of aircraft subsystems. As a consequence, knowledge of model validity is necessary for taking robust and justified design decisions. This paper presents a method for using coverage metrics to formulate an optimal model validation strategy. Three fundamentally different and industrially relevant use-cases are presented. The first use-case entails the successive identification of validation settings, and the second considers the simultaneous identification of n validation settings. The latter of these two use-cases is finally expanded to incorporate a secondary model-based objective to the optimization problem in a third use-case. The approach presented is designed to be scalable and generic to models of industrially relevant complexity. As a result, selecting experiments for validation is done objectively with little required manual effort.

Hopsan is an open-source simulation package developed as a collaboration project between industry and academia. The simulation methodology is based on transmission line modelling, which provides several benefits such as linear model scalability, numerical robustness and parallel simulation. All sub-models are pre-compiled, so that no compilation is required prior to starting a simulation. Default component libraries are available for hydraulic, mechanic, pneumatic, electric and signal domains. Custom components can be written in C++ or generated from Modelica and Mathematica. Support for simulation-based optimization is provided using population-based, evolutionary or direct-search algorithms. Recent research has largely focused on co-simulation with other simulation tools. This is achieved either by using the Functional Mock-up Interface standard, or by tool-to-tool communications. This paper provides a description of the program and its features, the current status of the project, and an overview of recent and ongoing use cases from industry and academia.

OpenModelica is a unique large-scale integrated open-source Modelica- and FMI-based modeling, simulation, optimization, model-based analysis and development environment. Moreover, the OpenModelica environment provides a number of facilities such as debugging; optimization; visualization and 3D animation; web-based model editing and simulation; scripting from Modelica, Python, Julia, and Matlab; efficient simulation and co-simulation of FMI-based models; compilation for embedded systems; Modelica-UML integration; requirement verification; and generation of parallel code for multi-core architectures. The environment is based on the equation-based object-oriented Modelica language and currently uses the MetaModelica extended version of Modelica for its model compiler implementation. This overview paper gives an up-to-date description of the capabilities of the system, short overviews of used open source symbolic and numeric algorithms with pointers to published literature, tool integration aspects, some lessons learned, and the main vision behind its development.

Modern aircraft can be seen as heterogeneous systems, containing multiple embedded subsystems which are in today’s simulations split into different domain-specific models based on different modelling methods and tools. This paper addresses typical workflow-driven model integration problems with respect to model fidelity, accuracy in combination with the selected abstraction methods and the target system characteristics. A short overview of integration strategies with the help of co-simulation frameworks including an analysis of the inherent problems that emerge because of different domain-specific modelling methods is being given. It is shown that huge benefits can be reached with the help of a smart system break-up. In detail, the discrepancy between the cyber-physical system simulations and human-machine interaction (HMI) models are being analysed. Therefore, a close look at the typical shortcomings of behavioural models is being discussed, too. To enable an effort-less human-in-the-loop integration into a cyber-physical system simulation, the usage of flight simulation software, offering real-time capability and a graphical user interface is suggested. This approach is applied to overcome today’s complexity and shortcomings in human psychological models. An example implementation based on a commercial flight simulator software (X-Plane) together with a high-performance system simulation tool (Hopsan) via UDP communication is presented and analysed.

Modelling and Simulation is key in aircraft system development. This paper presents a novel, multi-purpose, desktop simulator that can be used for detailed studies of the overall performance of coupled sub-systems, preliminary control design, and multidisciplinary optimization. Here, interoperability between industrially relevant tools for model development and simulation is established via the Functional Mockup Interface (FMI) and System Structure and Parametrization (SSP) standards. Robust and distributed simulation is enabled via the Transmission Line element Method (TLM). The advantages of the presented simulator are demonstrated via an industrially relevant use-case where simulations of pilot thermal comfort are coupled to Environmental Control System (ECS) steadystate and transient performance.

Composite modelling and simulation is a solution to utilize investments in models and tools, use the right tool for the right task, increase the accuracy by means of more accurate modelled boundary conditions, switch between levels in model complexity for a specific sub-system, and facilitate co-operation in organizations. With the new Functional Mock-up Interface (FMI) standardization, efforts are increasing to make this happen. SKF BEAST is an advanced dynamic simulation tool for rolling bearings and other mechanical systems with contacts. The tool incorporates a framework for composite modelling and cosimulation, i.e., a Master Simulation Tool (MST). It uses Transmission Line Modelling (TLM) to ensure robust numerical behaviour of the complete composite system model and supports the Functional Mock-up Interface (FMI) for model import, including both model exchange and co-simulation. In this paper, the tools and the techniques for composite modelling are discussed in further detail and application examples are given.

Hydraulic elevators with conventional long -stroke hydraulic cylinders are limited for use in low-rise buildings, up to five floors, due to low hydraulic stiffness, low natural frequency, low hydraulic pressure and large oil volume. With a new hydraulic actuation technology jointly invented at Linkoping University and SAAB named the Hydraulic Infinite Linear Hydraulic Actuator (HILA), these short -comings for hydraulic actuators can be reduced and hydraulic elevators can be offered for mid rise buildings. The HILA technology provides long strokes, high system pressure, compactness and small chamber volumes. The actuator has a higher stiffness and a higher natural frequency compared to conventional hydraulic cylinders. The higher system pressure allows for an even more compact system design, with lower flow levels and a smaller reservoir. The HILA technology combines two short -stroke cylinders with two engaging and disengaging clamping mechanisms into one actuator with long stroke length. The motion of each single short stroke piston linked together by the clamping mechanisms creates the motion of the piston rod. In this way the two pistons are moving along the rod in a kind of rope climbing motion. The challenge is to implement a control system which can provide a smooth motion without unacceptable jerk at load shift as seen with ordinary directional valves. Earlier research work on HILA technology has shown that a control system with fast servo valves can fulfil these requirements. This study shows promising results from simulation analysis combined with optimization techniques, using slightly modified standard directional hydraulic valves.

Simulation of fluid power systems typically requires models from multiple disciplines.Achieving accurate load dynamics for a system with complex geometry, for example, mayrequire both a 1D model of the hydraulic circuit and a 3D multi-body model. However, mostsimulation tools are limited to a single discipline. A solution to these kinds of problems isco-simulation, where different tools are coupled and simulated together. Co-simulation canprovide increased accuracy, improved modularity and facilitated collaboration between dif-ferent organizations. Unfortunately, tool coupling typically requires tedious and error-pronemanual work. It may also introduce numerical problems. For these reasons, co-simulation isoften avoided as long as possible. These problems have been addressed by the developmentof an open-source framework for asynchronous co-simulation. Simulation tools can be inter-connected through a stand-alone master simulation tool. An extensive range of tools is alsosupported via the Functional Mockup Interface standard. A graphical user interface has beenimplemented in the OpenModelica Connection Editor. System models can be created andedited from both a schematic view and a 3D view. Numerical robustness is enforced by theuse of transmission line modelling. A minimalistic programming interface consisting of onlytwo functions is used. An example model consisting of a hydraulic crane with two arms, twoactuators and a hanging load is used to verify the framework. The composite model consistsof nine multi-body models, one hydraulic system model and a controller. It is shown thatmodels from various simulation tools can be replaced with a minimal amount of user input.

Modelling and Simulation is extensively used for aircraft vehicle system development at Saab Aeronautics in Linköping, Sweden. There is an increased desire to simulate interacting sub-systems together in order to reveal, and get an understanding of, the present cross-coupling effects early on in the development cycle of aircraft vehicle systems. The co-simulation methods implemented at Saab require a significant amount of manual effort, resulting in scarcely updated simulation models, and challenges associated with simulation model scalability, etc. The Functional Mock-up Interface (FMI) standard is identified as a possible enabler for efficient and standardized export and co-simulation of simulation models developed in a wide variety of tools. However, the ability to export industrially relevant models in a standardized way is merely the first step in simulating the targeted coupled sub-systems. Selecting a platform for efficient simulation of the system under investigation is the next step. Here, a strategy for adapting coupled Modelica models of aircraft vehicle systems to TLM-based simulation is presented. An industry-grade application example is developed, implementing this strategy, to be used for preliminary investigation and evaluation of a cosimulation framework supporting the Transmission Line element Method (TLM). This application example comprises a prototype of a small-scale aircraft vehicle systems simulator. Examples of aircraft vehicle systems are environmental control systems, fuel systems, and hydraulic systems. The tightly coupled models included in the application example are developed in Dymola, OpenModelica, and Matlab/Simulink. The application example is implemented in the commercial modelling tool Dymola to provide a reference for a TLM-based master simulation tool, supporting both FMI and TLM. The TLM-based master simulation tool TLMSimulator is investigated in terms of model import according to the FMI standard with respect to a specified set of industrial needs and requirements.

Even though direct-search optimization methods are more difficult to parallelize than population-based methods, there are many unexploited opportunities. Five methods for parallelizing the Complex-RF methods have been implemented and evaluated. Three methods are based on the unchanged original algorithm, while two require modifications. The methods have been tested on two test function and one real simulation model. An analysis of the algorithm has been performed. This provides a basis for parametrization of the parallel methods. Without changing the original algorithm, speed-up of 2.5-3 is achieved. With allowing modifications, a speed-up of up to 5 is obtained without significantly reducing the probability of finding the global minimum. Speed-up does not scale linear to the number of threads. When more threads are added, parallelization efficiency decreases. However, a comparison with a particle swarm method shows that Complex-RF performs better regardless of the number of threads, due to its fast convergence rate.

Numerical stability is a key aspect in co-simulation of physical systems. Decoupling a system into independent sub-models will introduce time delays on interface variables. By utilizing physical time delays for decoupling, affecting the numerical stability can be avoided. This requires interpolation, to allow solvers to request input variables for the time slot where they are needed. The FMI for co-simulation standard does not support fine-grained interpolation using interpolation tables. Here, various modifications to the FMI standard are suggested for improved handling of interpolation. Mechanical and thermodynamic models are used to demonstrate the need for interpolation, as well as to provide an industrial context. It is shown that the suggested improvements are able to stabilize the otherwise unstable connections.

A major concern in the forest industry is impact on the soil caused by forest machines during harvesting. A six-wheel pendulum arm forwarder is being developed. The new forwarder aims at reducing soil damage by an even pressure distribution and smooth torque control and thereby also improving the working environment. The suspension contains pendulum arms on each wheel controlled by a hydraulic load sensing system in combination with accumulator.

A natural approach is to model each part of a system in the bestsuited software. In this case, the hydraulic system is modelled in the Hopsan simulation tool, while the vehicle mechanics is modelled in Adams. To understand the whole system it is necessary to simulate all subsystems together. An open standard for this is the Functional Mock-up Interface. This makes it possible to investigate the interaction between the hydraulic system and the multi-body mechanic model.

This paper describes how different simulation tools can be combined to support the development process. The technique is applied to the forwarder’s pendulum suspension. Controllers for height and soil force are optimized to minimize soil damage and maximize comfort for the operator.

Model Validation and Verification (V&V) has historically often been considered a final step in the model development process. However, to justify model-based design decisions throughout the entire system development process, a methodology for continuous model V&V is essential. That is, model V&V activities should be fast and easy to reiterate as new information becomes available. Using a high fidelity simulation model of the Environmental Control System (ECS) in the Saab Gripen fighter aircraft as a guiding example, this paper further extends to an existing semiautomatic framework for model steady-state validation developed during ECS model validation efforts. Generic methods for identification of steady-state operation are a prerequisite for steady-state validation of industry grade physics based models against insitu measurements. Four different established methods for steady-state identification are investigated and compared: steady-state conditions on the standard deviation estimated from in-situ measurements, conditions on the variation coefficient, t-test on the slope of a simple regression line, and comparison of differently estimated variances. The methods’ applicability, on ECS measurements in particular, is evaluated utilizing steady-state identification needs defined during Gripen ECS model validation activities.

Model Validation and Verification (V&V) has historically often been considered a final step in the model development process. However, to justify model-based design decisions throughout the entire system development process, a methodology for continuous model V&V is essential. That is, model V&V activities should be fast and easy to reiterate as new information becomes available.

Using a high fidelity simulation model of the Environmental Control System (ECS) in the Saab Gripen fighter aircraft as a guiding example, this paper further extends to an existing semi-automatic framework for model steady-state validation developed during ECS model validation efforts. Generic methods for identification of steady-state operation are a prerequisite for steady-state validation of industry grade physics based models against in-situ measurements. Four different established methods for steady-state identification are investigated and compared: steady-state conditions on the standard deviation estimated from in-situ measurements, conditions on the variation coefficient, t-test on the slope of a simple regression line, and comparison of differently estimated variances. The methods’ applicability, on ECS measurements in particular, is evaluated utilizing steady-state identification needs defined during Gripen ECS model validation activities.

By introducing physically motivated time delays, simulation models can be partitioned into decoupled independent sub-models. This enables parallel simulations on multi-core processors. An automatic algorithm is used for partitioning and running distributed system simulations. Methods for sorting and distributing components for good load balancing have been developed. Mathematical correctness during simulation is maintained by a busy-waiting thread synchronization algorithm. Independence between sub-models is achieved by using the transmission line element method. In contrast to the more commonly used centralized solvers, this method uses distributed solvers with physically motivated time delays, making simulations inherently parallel. Results show that simulation speed increases almost proportionally to the number of processor cores in the case of large models. However, overhead time costs mean that models need to be over a certain size to benefit from parallelization.

Distributed system simulation can increase performance, re-usability and modularity in model-based product development. This thesis investigates four aspects of distributed simulation: multi-threaded simulations, simulation tool coupling, distributed equation solvers and parallel optimization algorithms.

Multi-threaded simulation makes it possible to split up the workload over several processing units. This reduces simulation time, which can save both time and money during the product development cycle. The transmission line element method (TLM) is used to decouple models to independent sub-models.

Different simulation tools are suitable for different problems. Tool coupling makes it possible to use the best suited tool for simulating each part of the whole product. Models from different tools can then be coupled into one aggregated simulation model. An emerging standard for tool coupling is the Functional Mock-up Interface (FMI). It is investigated how this can be used in conjunction with TLM.

Equation-based object-oriented languages (EOOs) are becoming increasing popular. A logical approach is to let the equation solvers maintain the same structure that was used in the modelling process. Methods for achieving this using TLM and FMI are implemented and evaluated.

In addition to parallel simulations, it is also possible to use parallel optimization algorithms. This introduces parallelism on several levels. For this reason, an algorithm for profile-based multi-level scheduling is proposed.

In many organizations, the utilization of available computer power is very low. If it could be harnessed for parallel simulation and optimization, valuable time could be saved. A framework monitoring available computer resources and running distributed simulations is proposed. Users build their models locally, and then let a job scheduler determine how the simulation work should be divided among remote computers providing simulation services. Typical applications include sensitivity analysis, co-simulation and design optimization. The latter is used to demonstrate the framework. Optimizations can be parallelized either across the algorithm or across the model. An algorithm for finding the optimal distribution of the different levels of parallelism is proposed. An initial implementation of the framework, using the Hopsan simulation tool, is presented. Three parallel optimization algorithms have been used to verify the method and a thorough examination of their parallel speed-up is included.

The Modelica language offers an intuitive way to create object-oriented models. This makes it natural also to use an object-oriented solver, where each sub-model solves its own equations. Doing so is possible only if sub-models can be made independent from the rest of the model. One way to achieve this is to use distributed solvers by separating sub-models with transmission line elements. This offers robust and predictable simulations, simplified model debugging and natural parallelism. It also makes it possible to use different time steps and solver algorithms in different parts of the model to achieve an optimal trade-off between performance and accuracy. The suggested method has been implemented in the Hopsan simulation environment. Different modelling techniques for taking advantage of the distributed solver approach are explained. Finally, three example models are used to demonstrate the method.

As the speed increase of single-core processors keeps declining, it is important to adapt simulation software to take advantage of multi-core technology. There is a great need for simulating large-scale systems with good performance. This makes it possible to investigate how different parts of a system work together, without the need for expensive physical prototypes. For this to be useful, however, the simulations cannot take too long, because this would delay the design process. Some uses of simulation also put very high demands on simulation performance, such as real-time simulations, design optimization or Monte Carlo-based sensitivity analysis. Being able to quickly simulate large-scale models can save much time and money.

The power required to cool a processor is proportional to the processor speed squared. It is therefore no longer profitable to keep increasing the speed. This is commonly referred to as the "power wall". Manufacturers of processors have instead begun to focus on building multi-core processors consisting of several cores working in parallel. Adapting program code to multi-core architectures constitutes a major challenge for software developers.

Traditional simulation software uses centralized equation-system solvers, which by nature are hard to make parallel. By instead using distributed solvers, equations from different parts of the model can be solved simultaneously. For this to be effective, it is important to minimize overheadcosts and to make sure that the workload is evenly distributed over the processor cores.

Dividing an equation system into several parts and solving them separately means that time delays will be introduced between the parts. If these occur in the right locations, this can be physically correct, since it also takes some time for information to propagate in physical systems. The transmission line  element method (TLM) constitutes an effective method for separating system models by introducing impedances between components, causing physically motivated time delays.

Contributions in this thesis include parts of the development of the new generation of the Hopsan simulation tool, with support for TLM and distributed solvers. An automatic algorithm for partitioning models has been developed. A multi-threaded simulation algorithm using barrier synchronization has also been implemented.

Measurements of simulation time confirm that the simulation time is decreased almost proportionally to the number of processor cores for large models. The decrease, however, is reduced if the cores are divided on different processors. This was expected, due to the communication delay for processors communicating over shared memory. Experiments on real-time systems with four cores show that a four times as large model can be simulated without losing real-time performance.

The division into distributed solvers constitutes a sort of natural cosimulation. A future project could be to use this as a platform for linking different simulation tools together and simulating them with high performance. This would make it possible to model each part of the system in the most suitable tool, and then connect all parts into one large model.

This paper describes how models from different simulation tools can be connected and simulated on different processors by using the Functional Mockup Interface (FMI) and the transmission line element method (TLM). Interconnectivity between programs makes it possible to model each part of a complex system with the best suited tool, which will shorten the modelling time and increase the accuracy of the results. Because the system will be naturally partitioned, it is possible to identify weak links and replace them with transmission line elements, thereby introducing a controlled time delay. This makes the different parts of the system naturally independent, making it possible to simulate large aggregated system models with good performance on multi-core processors. The proposed method is demonstrated on an example model. A suggestion of an XML extension to the FMI standard for describing TLM ports is also presented.

Developments in computational hardware and simulation software have come to a point where it is possible to use whole mission simulation in a framework for conceptual/preliminary design. This paper is about the implementation of full system simulation software for conceptual/preliminary aircraft design. It is based on the new Hopsan NG simulation package, developed at the Linköping University. The Hopsan NG software is implemented in C++. Hopsan NG is the first simulation software that has support for multi-core simulation for high speed simulation of multi domain systems.

In this paper this is demonstrated on a flight simulation model with subsystems, such as control surface actuators.

The demand for large-scale real-time simulations of fluid power systems is in-creasing, due to growing demands for added functionality. Real-time simulationscan be used in for example hardware-in-the-loop experiments and embeddedcontrol systems. In order to achieve real-time performance, it is often necessaryto use small or simplified models, reducing the usefulness and accuracy of theresults. This article proposes the use of transmission line modelling (TLM) forexploiting multi-core hardware in real-time and embedded systems. The charac-teristics of the TLM method are analysed to identify difficulties and possibilities.A method for how to parallelise TLM models is then presented. Subsequently, aprogramming interface for implementing the parallel models in the target systemsis introduced. Practical experiments show that the approach works and that themethod is applicable. So far, however, it has required great effort on the part ofthe engineer, both when it comes to programming, compiling and importing themodel into the target environments, although some attempts to automate the pro-cedure have been successful, reducing the level of complexity.

Distributed solvers provide several benefits, such as linear scalability and good numerical robustness. By separating components with transmission line elements, simulations can be run in parallel on multi-core processors. At the same time, equation-based modelling offers an intuitive way of writing models. This paper presents an algorithm for generating distributed models from Modelica code using bilinear transform. This also enables hard limitations on variables and their derivatives. The generated Jacobian is linearised and solved using LU-decomposition. The algorithm is implemented in the Hopsan simulation tool. Equations are transformed and differentiated by using the SymPy package for symbolic mathematics. An example model is created andverified against a reference model. Simulation results are similar, but the equation-based model is four to five times slower. Further optimisation of the algorithm is thus required. The future aim is to develop a distributed simulation environment with integrated support for equation-based modelling.

Future research and development will depend on high-speed simulations, especially for large and complex systems. Rapid prototyping, optimization and real-time simulations require  simulation tools that can take full advantage of  computer hardware.  Recent developments  in the computer market indicate  a change in focus from increasing the speed of processor cores towards increasing the number of cores in each processor. HOPSAN is a simulation tool for fluid power and mechatronics, developed at Linköping University. It  is based upon the transmission line  modeling  (TLM)  technique. This method is very suitable for taking advantage of multi-core  processors.  This paper presents  the  implementation  of multi-core support in the next generation of HOPSAN. The concept is to divide the  model  into equally sized  groups of  independent components,  to make it possible to  simulate  them  in separate threads. Reducing overhead costs and finding an effective sorting algorithm constitute  critical steps for maximizing the benefits.  Experimental results show  a significant reduction in simulation time. Improvement of algorithms in combination with a continuous increase in the number of processor cores can potentially  lead to further  increases  in simulation performance. 

A suitable method for simulating large complex dynamic systems is represented by distributed modelling using transmission line elements. The method is applicable to all physical systems, such as mechanical, electrical and pneumatics, but is particularly well suited to simulate systems where wave propagation is an important issue, for instance hydraulic systems. By using this method, components can be numerically isolated from each other, which provide highly robust numerical properties. It also enables the use of multi-core architecture since a system model can be composed by distributed simulations of subsystems on different processor cores.

Technologies based on transmission lines has successfully been implemented in the HOPSAN simulation package, develop at Linköping University. Currently, the next generation of HOPSAN is developed using an object-oriented approach. The work is focused on compatibility, execution speed and real-time simulation in order to facilitate hardware-in-the-loop applications. This paper presents the work progress and some possible features in the new version of the HOPSAN simulation package.

The current development towards multiple processor cores in personal computers is making distribution and parallelization of simulation software increasingly important. The possible speedups from parallelism are however often limited with the current centralized solver algorithms, which are commonly used in today’s simulation environments. An alternative method investigated in this work utilizes distributed solver algorithms using the transmission line modeling (TLM) method. Creation of models using TLM elements to separate model components makes them very suitable for computation in parallel because larger models can be partitioned into smaller independent submodels. The computation time can also be decreased by using small numerical solver step sizes only on those few submodels that need this for numerical stability. This is especially relevant for large and demanding models. In this paper we present work in how to combine TLM and solver inlining techniques in the Modelica equation-based language, giving the potential for efficient distributed simulation of model components over several processors.

Shortening simulation time is an important step towards efficient simulation-based product development. A long-used method is to exploit physically motivated time delays to split up the model into distributed solvers. In this way, the use of a centralized sequential solver can be circumvented. For maximum simulation performance, however, an efficient scheduling technique is also required. Four task scheduling methods for distributed-solver simulations has been implemented and evaluated. Experiments indicate that the best choice largely depend on model size, load distribution and granularity. Lock-based barrier synchronization provides the highest speed-up for small models. A fork-join implementation, with implicit synchronization and work-stealing scheduling, works better for models with a large total workload. It is common that workload and load distribution of a simulation model varies during execution depending on the current state of the simulation. Three of the implemented schedulers support dynamic load balancing during execution. Results show that task-stealing is the most efficient method for the specific test model. A possible continuation of this work is an automatic selection of the best scheduling technique based on knowledge about model properties and available computer resources.