Small State Space Research Articles

A Reliability Assessment Method for Complex Systems Based on Non-Homogeneous Markov Processes.

The Markov method is a common reliability assessment method. It is often used to describe the dynamic characteristics of a system, such as its repairability, fault sequence and multiple degradation states. However, the "curse of dimensionality", which refers to the exponential growth of the system state space with the increase in system complexity, presents a challenge to reliability assessments for complex systems based on the Markov method. In response to this challenge, a novel reliability assessment method for complex systems based on non-homogeneous Markov processes is proposed. This method entails the decomposition of a complex system into multilevel subsystems, each with a relatively small state space, in accordance with the system function. The homogeneous Markov model or the non-homogeneous Markov model is established for each subsystem/system from bottom to top. In order to utilize the outcomes of the lower-level subsystem models as inputs to the upper-level subsystem model, an algorithm is proposed for converting the unavailability curve of a subsystem into its corresponding 2×2 dynamic state transition probability matrix (STPM). The STPM is then employed as an input to the upper-level system's non-homogeneous Markov model. A case study is presented using the reliability assessment of the Reactor Protection System (RPS) based on the proposed method, which is then compared with the models based on the other two contrast methods. This comparison verifies the effectiveness and accuracy of the proposed method.

SEPIC converter in discontinuous conduction mode: Small signal modeling and analysis

AbstractIn this article, a new approach is applied to solve the small signal state space average (SSA) model for pulse width modulated (PWM) single ended primary inductor converter (SEPIC) under discontinuous conduction mode (DCM) of operation. Authors proposed a novel approach to get duty ratio constrains that is based on variation of current in inductor. The approach used a unique correction matrix (M) in the modeling process and obtained better results for DCM. To demonstrate the whole technique, the SEPIC‐based power supply of 75 W is designed and system loop gain is derived with the help of this new technique. The frequency response of the proposed system is captured with the help of linearization technique using MATLAB Simulink platform. The frequency plot from the proposed techniques is much closer to simulation results as compared to conventional method. This claims high predictions for dc–dc converter operating in DCM with wide range of input supply. The proposed model is analyzed with previous SSA small signal modeling for comparative results on the basis of frequency analysis and stability. The experiment results of designed power supply have shown good power quality performance at 220‐V AC mains for light‐emitting diode (LED) lighting application.

Modeling and parameter analysis for consensus based secondary control of parallel Virtual Synchronous Generators

In recent years, the consensus control has become a research hotspot in microgrid cooperative control. However, when the VSG control is applied, the system has higher order, more parameters and more complex dynamic response. And there are few studies on the dynamic characteristics of parallel VSGs with the consensus control. Aiming at this problem, the small signal state space model of parallel VSG with consensus based secondary control is established in this paper firstly. Then the influences of damping, inertia, secondary control parameters on dynamic response are analyzed, and the design criterion of secondary control parameters is proposed. Finally, the simulation results verify the accuracy of model and correctness of conclusions.

Computing Dynamic Heterogeneous-Agent Economies: Tracking the Distribution

Theoretical formulations of dynamic heterogeneous-agent economies typically include a distribution as an aggregate state variable. This paper introduces a method for computing equilibrium of these models by including a distribution directly as a state variable if it is finite-dimensional or a fine approximation of it if it is infinite-dimensional. The method accurately computes equilibrium in an extreme calibration of Huffman's (1987) overlapping-generations economy where quasi-aggregation, the accurate forecasting of prices using a small state space, fails to obtain. The method also accurately solves for equilibrium in a version of Krusell and Smith's (1998) economy wherein quasi-aggregation obtains but households face occasionally binding constraints. The method is demonstrated to be not only accurate but also feasible with equilibria for both economies being computed in under ten minutes in Matlab. Feasibility is achieved by using Smolyak's (1963) sparse-grid interpolation algorithm to limit the necessary number of gridpoints by many orders of magnitude relative to linear interpolation. Accuracy is achieved by using Smolyak's algorithm, which relies on smoothness, only for representing the distribution and not for other state variables such as individual asset holdings.

A hybrid control strategy for Z-source inverter DG systems

A hybrid control system for Z-source inverter (ZSI) with LC filter which is used in distributed generation (DG) systems is presented in this study. The proposed system has two different controllers, dc-side and ac-side. While designing the ac-side controller, a proportional-resonant (PR) controller was used. Besides, to be able to adjust the voltage of the Z-source capacitor according to the reference value of it, a proportional–integral (PI) controller was employed on the dc-side of the ZSI. In the end, a dynamic ZSI model was obtained by the help of small signal analysis and state space averaging. After the mathematical model of the ZSI was derived, the dc-side and ac-side controllers were designed. Using both controllers, inverter reference tracking performance was enhanced. The proposed controller offers superior output voltage regulation regardless of the linear and nonlinear loads. Taking into account the abrupt variations in both the dc source and linear/nonlinear load level, the effectiveness of the proposed control system was tested and supported by Matlab®/Simulink simulations.

Small Signal Modeling of Inverter-based Grid-Connected Microgrid to Determine the Zero-Pole Drift Control with Dynamic Power Sharing Controller

This paper presents a small signal state space modeling of three-phase inverter-based microgrid (MG) system with consideration of improved droop control. The complete system matrices for one distribution source-grid connects to the local load have been elaborated by applying high, medium and low-frequency clusters to the system without considering the switching action on the inverter during power-sharing. Moreover, the final matrices will be used to determine the location of the eigenvalues for the control parameters gains due to dynamic effect of the MG, by observing the root locus graph on cluster identification. Sensitivity analysis of all types of frequency cluster showed that power-sharing control parameters such as load current, source current, and inverter voltage are influencing system stability and must be considered when designing the proportional-integral (PI) control when different load scenarios have been applied from the zero-pole drifting. Those eigenvalues of the system model are indicating the frequency and damping oscillatory components when there is sudden changed at the inverter-grid connection. The matrices’ eigenvalues are being plotted using MATLAB/Simulink to identify system stability region and find the PI controller parameters.

Simultaneous Design of a Small UAV (Unmanned Aerial Vehicle) Flight Control System and Lateral State Space Model

In this study, the design of a small unmanned aerial vehicle (UAV) and the real-time application of the flight control system and lateral state-space model were investigated. For this purpose, an UAV production was carried out, which was assembled from different locations at certain intervals to the wing and tail set body and moved back and forth before the flight. An autopilot was then used which allowed the change of P, I, D values ​​between 1 and 100. First of all, we obtained a lateral state space model of the UAV and obtained a simulation model of Unmanned Aerial Vehicle. At the same time, the block diagram of the autopilot system was extracted and modeled in MATLAB / Simulink environment. Afterwards, SPSA developed a cost function consisting of ascent, seating time and maximum overrun, and the Unmanned Aircraft and autopilot system were redesigned simultaneously to minimize this cost function. High performance is easily observed in simulation responses and real flights.

Multi-Agent Reinforcement Learning Using Linear Fuzzy Model Applied to Cooperative Mobile Robots

A multi-agent system (MAS) is suitable for addressing tasks in a variety of domains without any programmed behaviors, which makes it ideal for the problems associated with the mobile robots. Reinforcement learning (RL) is a successful approach used in the MASs to acquire new behaviors; most of these select exact Q-values in small discrete state space and action space. This article presents a joint Q-function linearly fuzzified for a MAS’ continuous state space, which overcomes the dimensionality problem. Also, this article gives a proof for the convergence and existence of the solution proposed by the algorithm presented. This article also discusses the numerical simulations and experimental results that were carried out to validate the proposed algorithm.

POMDP-Based Decision Making for Fast Event Handling in VANETs

Malicious vehicle agents broadcast fake information about traffic events and thereby undermine the benefits of vehicle-to-vehicle communication in vehicular ad-hoc networks (VANETs). Trust management schemes addressing this issue do not focus on effective/fast decision making in reacting to traffic events. We propose a Partially Observable Markov Decision Process (POMDP) based approach to balance the trade-off between information gathering and exploiting actions resulting in faster responses. Our model copes with malicious behavior by maintaining it as part of a small state space, thus is scalable for large VANETs. We also propose an algorithm to learn model parameters in a dynamic behavior setting. Experimental results demonstrate that our model can effectively balance the decision quality and response time while still being robust to sophisticated malicious attacks.

Symbolic analysis-based reduced order Markov modeling of time series data

This paper presents reduced-order modeling of time-series data for a special class of Markov models using symbolic dynamics. These models are constructed from the time-series signal by partitioning the data and then inferring a probabilistic finite state automaton (PFSA) from the resulting symbol sequence, capturing a finite history (or memory) of symbol strings. In the proposed approach, the size of the temporal memory of a symbol sequence is estimated from spectral properties of the resulting stochastic matrix corresponding to a first-order Markov model of the symbol sequence. Then, agglomerative hierarchical clustering is used to cluster states of the corresponding full-order Markov model to construct a reduced-order Markov model based on information-theoretic criteria with a non-deterministic algebraic structure; the parameters of the reduced-order model are identified from the original model by making use of a Bayesian inference rule. The model size is inferred using an information-theoretic inspired criteria; the Markov parameters of the reduced-order model are identified from the original model by making use of a Bayesian inference rule. The paper also identifies theoretical bounds on the error induced in the reduced-size model in terms of expected Hamming distance between the sequences generated by the original and final reduced-size models. The proposed concept is elucidated and validated by two examples on different data sets. The first example analyzes a set of time series of pressure oscillations in a swirl-stabilized combustor, where controlled protocols are used to induce flame instabilities. Variations in the complexity of the derived Markov model represent how the system operating condition changes from stable to an unstable combustion regime. The second example is built upon a public data set of NASA’s repository for prognosis of rolling-element bearings. It is shown that: (i) even with a small state-space, the reduced-order models are able to achieve comparable performance, and (ii) the proposed approach provides flexibility in the selection of a reduced-order model for data representation and learning.

Uniform Model and Analysis of PWM DC–DC Converter for Discontinuous Conduction Mode

ABSTRACTIn this paper, a modified small signal state space average model is proposed to analyze the pulse width modulated converter operating in discontinuous conduction mode (DCM). It is based on a unique correction matrix (Mc) and new duty ratio constrain which is derived on the basic properties of inductor current. A 12 volt, 5 watt power supply based on Cuk converter is designed to demonstrate this proposed methodology. Transfer functions (input-to-output and control-to-output) of this power supply are calculated theoretically with the help of proposed modelling procedure. Bode plots of those transfer function are achieved using MATLAB toolboxes. To validate the proposed model, a simulation is also performed in MATLAB and frequency response is captured at run time using linearization technique. Bode plots from proposed model are very much in line with simulation results and offer improved predictions for high frequency dynamics of converter operating in DCM. The validity of presented work is reconfirmed by experimental set-up. The presented work is also compared with conventional small signal modelling on the basis of frequency analysis.

Integrated simulation method for interaction between manufacturing process and machine tool

The interaction between the machining process and the machine tool (IMPMT) plays an important role on high precision components manufacturing. However, most researches are focused on the machining process or the machine tool separately, and the interaction between them has been always overlooked. In this paper, a novel simplified method is proposed to realize the simulation of IMPMT by combining use the finite element method and state space method. In this method, the transfer function of the machine tool is built as a small state space. The small state space is obtained from the complicated finite element model of the whole machine tool. Furthermore, the control system of the machine tool is integrated with the transfer function of the machine tool to generate the cutting trajectory. Then, the tool tip response under the cutting force is used to predict the machined surface. Finally, a case study is carried out for a fly-cutting machining process, the dynamic response analysis of an ultra-precision fly-cutting machine tool and the machined surface verifies the effectiveness of this method. This research proposes a simplified method to study the IMPMT, the relationships between the machining process and the machine tool are established and the surface generation is obtained.

Performance Analysis, Modeling and Control of Multi-Port DC-DC Boost Converter for an Integrated Power Generation System.

Objective: This paper presents a new DC-DC boost converter for renewable hybrid power generation scheme is designed using five controllable switches in its unified structure. Methods/ Statistical Analysis: In this research work, converter operation is discussed with four different operating modes based on the renewable resources availability. To rectify the difficulties associated with controller design of this converter, multi input - multi output controller design is obtained by deducing the small signal equations and state space modeling for all the operating modes. In this study, MATLAB/Simulink is used to design the model for DC-DC boost converter. A strategy to manage the power flow between the different energy sources is presented. Findings: Uncomplicated structure, centralized control, transformer-less operation, less weight, highly stable and increased output voltage is the best qualities of the designed converter. This study demonstrates that the overall power management is efficient and demand is balanced successfully. Applications/Improvement: This research helps to find the best power electronic converter structure for renewable based hybrid power generation system.

Clustered Simple Cell Mapping: An extension to the Simple Cell Mapping method

When a dynamical system has a complex structure of fixed points, periodic cycles or even chaotic attractors, Cell Mapping methods are excellent tools to discover and thoroughly analyse all features in the state space. These methods discretize a region of the state space into cells and examine the dynamics in the cell state space. By determining one or more image cells for each cell, the global behaviour within the region can be quickly determined. In the simplest case – Simple Cell Mapping (SCM) method – only one image corresponds to a cell and usually a rectangular grid of cells is used. In typical applications the grid of cells is refined at specific locations.This paper, however, introduces a different approach, which is useful to expand the analysed state space region to include all features which properly characterize the global dynamics of the system. Instead of refining the initial cell state space, we start with a small initial state space region, analyse other interesting regions of the state space and incorporate them into a cluster of cell mapping solutions. By this approach, trajectories escaping the original state space region can be followed automatically and additional objects in the state space can be discovered.To illustrate the benefits of the method, we present the exploration of the phase-space of the micro-chaos map – a simple model of digitally controlled systems.

Structure-preserving approach to multi-port dynamic compact models of nonlinear heat conduction

A novel approach for constructing multi-port dynamic compact thermal models of nonlinear heat diffusion in electronic components is presented, extending a technique previously conceived for the one-port case. The approach allows achieving high levels of accuracy even for small state–space dimensions of the model. It is also very efficient since it requires the solutions to a few linear heat diffusion problems in the frequency domain. The multi-port compact models exhibit structure similar to the one-port counterparts and can be used to accurately approximate not only the junction temperatures, but also the whole space–time temperature distribution within the electronic components.

Parallel Concatenated Convolutional Lattice Codes With Constrained States

Convolutional lattice codes, also known as signal codes, have been proposed as a technique to generate structured codes that have good performance. While in principle optimal decoding can be achieved using the Viterbi Algorithm, in practice due to Tomlinson-Harashima precoding, the size of the state space is too large, and one must resort to suboptimal techniques such as sequential decoding. In this paper, we take an alternate approach. By employing a judicious selection of tap coefficients and in combination with precoding, we show that the state space can be constrained to a relatively small set such that Viterbi decoding is practical. The performance of such codes still exhibits a large gap to capacity, and we further propose a parallel concatenation similar to that of turbo codes, resulting in a “turbo signal code.” Due to the relatively small state space, iterative decoding based on the BCJR algorithm is now possible. The gaps between the SNR for a frame error rate of 1% and the optimal performance theoretically achievable for a code of the same rate over an AWGN channel are found by simulation to be within 0.75-0.85 dB with a block length of 8192.

Parametric Reduction of FE Models with Variable Mesh Topology

AbstractDesigning whole machines or processes you may need both, an integrated dynamic simulation of all components on system level and a detailed analysis of how the macroscopic behavior of a component depends on geometry and material parameters. The former analysis is usually based on systems of differential algebraic equations representing a component by not more than a few hundred states and requires tools like Matlab‐Simulink® or Dymola®. The latter analysis solves discretized partial differential equations with several 100,000 degrees of freedom using finite element software like Ansys® or Comsol®. Model reduction bridges the gap between the two worlds providing small state space models with approximately the same input‐output behavior as the original large finite element models. Building systems from generic components, e.g. a gas transport network from pipeline models with variable length, or optimizing the design of a device with respect to mechanical or thermal properties, we need parametric reduced models. The idea is to reduce FE models offline for selected parameter sets and to generate models for new parameters by cheap interpolation rather than expensive reduction. The different approaches to parametric linear model reduction may be divided into three classes [1]. Interpolation of transfer functions is well suited for parabolic or highly damped hyperbolic problems. However, poles are duplicated rather than shifted, which is unacceptable for weakly damped hyperbolic problems like in mechanics. The second class of methods look for a basis of state space covering system behavior over the full range of parameters. They share the critical assumption that number and meaning of states do not change with the parameters. In terms of finite elements this means that the meshes for different design parameters are morphed variants of the same reference mesh.This may become a severe restriction in practice when automatic meshing is to be applied to complicated geometries. Therefore, we propose a method from the third class, which is based on interpolating reduced system matrices [2]. Only those parts of the mesh need to share a constant topology where nodal inputs are applied and outputs are collected. The inner mesh, however, may change for different parameters. The main challenges arise from the fact that state space representations of a system are unique only up to a change of basis and that interpolating matrices which refer to non‐fitting bases may cause arbitrary errors. In the article we will show how problems like leaving and entering modes or eigenvalue crossing can be overcome by using normal forms and eigenvalue tracking in parameter space. The method, which is implemented in the Fraunhofer Model Reduction Toolbox, is applied to a parametric model of a mechanical device the eigenfrequencies of which have to be kept away from some dominant excitation frequencies. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Compact thermal models for stochastic thermal analysis

An effective approach is proposed for constructing compact thermal models for the stochastic thermal analysis of electronics components and packages. This approach exhibits high levels of accuracy for small state space dimensions of the model. The achieved compact thermal models can be used to accurately approximate the stochastic properties not only of junction temperatures but also of the whole space–time temperature rise distribution within the electronics component or package.

Specification guidelines to avoid the state space explosion problem

During the last two decades, we modelled the behaviour of a large number of systems. We noted that different styles of modelling had quite an effect on the size of the state spaces of the modelled systems. The differences were so substantial that some specification styles led to far too many states to verify the correctness of the model, whereas with other styles, the number of states was so small that verification was a straightforward activity. In this article, we summarize our experience by providing seven specification guidelines to keep state spaces small. For each guideline, we provide an application, generally from the realm of traffic light controllers, for which we provide a 'bad' model with a large state space, and a 'good' model with a small state space. The good and bad models are both suitable for their purpose but are not behaviourally equivalent. For all guidelines, we discuss circumstances under which it is reasonable to apply the guidelines. Copyright © 2014 John Wiley & Sons, Ltd.

Pushing the Power of Stochastic Greedy Ordering Schemes for Inference in Graphical Models

We study iterative randomized greedy algorithms for generating (elimination) orderings with small induced width and state space size — two parameters known to bound the complexity of inference in graphical models. We propose and implement the Iterative Greedy Variable Ordering (IGVO) algorithm, a new variant within this algorithm class. An empirical evaluation using different ranking functions and conditions of randomness, demonstrates that IGVO finds significantly better orderings than standard greedy ordering implementations when evaluated within an anytime framework. Additional order of magnitude improvements are demonstrated on a multi-core system, thus further expanding the set of solvable graphical models. The experiments also confirm the superiority of the MinFill heuristic within the iterative scheme.