Input-output Behavior Research Articles

Nonlinear Model Reduction in Power Systems by Balancing of Empirical Controllability and Observability Covariances

In this paper, nonlinear model reduction for power systems is performed by the balancing of empirical controllability and observability covariances that are calculated around the operating region. Unlike existing model reduction methods, the external system does not need to be linearized but is directly dealt with as a nonlinear system. A transformation is found to balance the controllability and observability covariances in order to determine which states have the greatest contribution to the input-output behavior. The original system model is then reduced by Galerkin projection based on this transformation. The proposed method is tested and validated on a system comprised of a 16-machine 68-bus system and an IEEE 50-machine 145-bus system. The results show that by using the proposed model reduction the calculation efficiency can be greatly improved; at the same time, the obtained state trajectories are close to those for directly simulating the whole system or partitioning the system while not performing reduction. Compared with the balanced truncation method based on a linearized model, the proposed nonlinear model reduction method can guarantee higher accuracy and similar calculation efficiency. It is shown that the proposed method is not sensitive to the choice of the matrices for calculating the empirical covariances.

RETRACTED ARTICLE: Evaluation of the Filtered Noise Turbulent Inflow Generation Method

Flows around buildings and in urban areas have the ability to exchange mass and momentum through mixing layers. The complex dynamical phenomena arising in mixing layers can be studied using Large Eddy Simulation (LES). As mixing layers depend on the turbulence conditions upstream of the buildings or urban areas, appropriate turbulent inlet conditions have to be provided to a simulation. Due to the high efficiency and level of control, the filtered noise inflow method was selected. The control over the Reynolds stresses as well as nine length scales make this method suitable to replicate conditions measured in experiments. In this paper, a formal method to obtain the filter coefficients is presented. This is achieved by relating the spatial filtering to a Finite Impulse Response (FIR) filter and the temporal filtering to an Autoregressive (AR) model. Three closed-form solutions for the spatial filter coefficients are presented having a Gaussian, double-exponential and exponential correlation function. By means of an LES simulation of a turbulent wall-bounded flow, the input-output behaviour is investigated. It was found that a combination of a Gaussian filter with length scales that increase with increasing wall distance result in the fastest downstream development of the artificial turbulence and the smallest loss of turbulent kinetic energy.

Self-Powered Random Number Generator Based on Coupled Triboelectric and Electrostatic Induction Effects at the Liquid-Dielectric Interface.

Modern cryptography increasingly employs random numbers generated from physical sources in lieu of conventional software-based pseudorandom numbers, primarily owing to the great demand of unpredictable, indecipherable cryptographic keys from true random numbers for information security. Thus, far, the sole demonstration of true random numbers has been generated through thermal noise and/or quantum effects, which suffers from expensive and complex equipment. In this paper, we demonstrate a method for self-powered creation of true random numbers by using triboelectric technology to collect random signals from nature. This random number generator based on coupled triboelectric and electrostatic induction effects at the liquid-dielectric interface includes an elaborately designed triboelectric generator (TENG) with an irregular grating structure, an electronic-optical device, and an optical-electronic device. The random characteristics of raindrops are harvested through TENG and consequently transformed and converted by electronic-optical device and an optical-electronic device with a nonlinear characteristic. The cooperation of the mechanical, electrical, and optical signals ensures that the generator possesses complex nonlinear input-output behavior and contributes to increased randomness. The random number sequences are deduced from final electrical signals received by an optical-electronic device using a familiar algorithm. These obtained random number sequences exhibit good statistical characteristics, unpredictability, and unrepeatability. Our study supplies a simple, practical, and effective method to generate true random numbers, which can be widely used in cryptographic protocols, digital signatures, authentication, identification, and other information security fields.

A gradient descent control for output tracking of a class of non-minimum phase nonlinear systems

In this paper we present a new approach to design the input control to track the output of a non-minimum phase nonlinear system. Therefore, a cascade control scheme that combines input–output feedback linearization and gradient descent control method is proposed. Therein, input–outputfeedback linearization forms the inner loop that compensates the nonlinearities in the input–output behavior, and gradient descent control forms the outer loop that is used to stabilize the internal dynamics. Exponential stability of the cascade-control scheme is provided using singular perturbation theory. Finally, numerical simulation results are presented to illustrate the effectiveness of the proposed cascade control scheme.

Caspo: a toolbox for automated reasoning on the response of logical signaling networks families.

SummaryWe introduce the caspo toolbox, a python package implementing a workflow for reasoning on logical networks families. Our software allows researchers to (i) learn a family of logical networks derived from a given topology and explaining the experimental response to various perturbations; (ii) classify all logical networks in a given family by their input-output behaviors; (iii) predict the response of the system to every possible perturbation based on the ensemble of predictions; (iv) design new experimental perturbations to discriminate among a family of logical networks; and (v) control a family of logical networks by finding all interventions strategies forcing a set of targets into a desired steady state.Availability and Implementationcaspo is open-source software distributed under the GPLv3 license. Source code is publicly hosted at http://github.com/bioasp/caspo.

Exploiting the dynamic properties of covalent modification cycle for the design of synthetic analog biomolecular circuitry.

BackgroundCycles of covalent modification are ubiquitous motifs in cellular signalling. Although such signalling cycles are implemented via a highly concise set of chemical reactions, they have been shown to be capable of producing multiple distinct input-output mapping behaviours – ultrasensitive, hyperbolic, signal-transducing and threshold-hyperbolic.ResultsIn this paper, we show how the set of chemical reactions underlying covalent modification cycles can be exploited for the design of synthetic analog biomolecular circuitry. We show that biomolecular circuits based on the dynamics of covalent modification cycles allow (a) the computation of nonlinear operators using far fewer chemical reactions than purely abstract designs based on chemical reaction network theory, and (b) the design of nonlinear feedback controllers with strong performance and robustness properties.ConclusionsOur designs provide a more efficient route for translation of complex circuits and systems from chemical reactions to DNA strand displacement-based chemistry, thus facilitating their experimental implementation in future Synthetic Biology applications.

Training a Network of Electronic Neurons for Control of a Mobile Robot

An adaptive training procedure is developed for a network of electronic neurons, which controls a mobile robot driving around in an unknown environment while avoiding obstacles. The neuronal network controls the angular velocity of the wheels of the robot based on the sensor readings. The nodes in the neuronal network controller are clusters of neurons rather than single neurons. The adaptive training procedure ensures that the input–output behavior of the clusters is identical, even though the constituting neurons are nonidentical and have, in isolation, nonidentical responses to the same input. In particular, we let the neurons interact via a diffusive coupling, and the proposed training procedure modifies the diffusion interaction weights such that the neurons behave synchronously with a predefined response. The working principle of the training procedure is experimentally validated and results of an experiment with a mobile robot that is completely autonomously driving in an unknown environment with obstacles are presented.

Model Reduction by Nice Selections for Linear Switched Systems

A moment-matching method for model reduction of linear switched systems (LSSs) is presented. The method can be seen as a non-trivial extension of the Krylov subspace methods for linear time-invariant (LTI) systems. The procedure is based on the so called “nice selections,” which represent a choice of basis in the reachability or observability space of the LSS. The framework can also be used for exact matching of the input-output behavior of an LSS with a reduced order LSS for a specific switching sequence. Conditions for applicability of the method for model reduction are stated and finally the results are illustrated on numerical examples.

Coordination of heterogeneous nonlinear multi-agent systems with prescribed behaviours

ABSTRACTIn this paper, we consider a coordination problem for a class of heterogeneous nonlinear multi-agent systems with a prescribed input–output behaviour which was represented by another input-driven system. In contrast to most existing multi-agent coordination results with an autonomous (virtual) leader, this formulation takes possible control inputs of the leader into consideration. First, the coordination was achieved by utilising a group of distributed observers based on conventional assumptions of model matching problem. Then, a fully distributed adaptive extension was proposed without using the input of this input–output behaviour. An example was given to verify their effectiveness.

Reachability and observability reduction for linear switched systems with constrained switching

We present an algorithm for reducing the number of continuous states of a discrete time linear switched system, such that the reduced system has the same input–output behavior as the original system for a subset of switching sequences. The procedure can be interpreted as reachability and observability reduction for a linear switched system with constrained switching. The proposed method is expected to be useful for abstraction based control synthesis methods for hybrid systems.

Implementation of a digital evaluation platform to analyze bifurcation based nonlinear amplifiers

Abstract. Recently, nonlinear amplifiers based on the supercritical Andronov–Hopf bifurcation have become a focus of attention, especially in the modeling of the mammalian hearing organ. In general, to gain deeper insights in the input-output behavior, the analysis of bifurcation based amplifiers requires a flexible framework to exchange equations and adjust certain parameters. A DSP implementation is presented which is capable to analyze various amplifier systems. Amplifiers based on the Andronov–Hopf and Neimark–Sacker bifurcations are implemented and compared exemplarily. It is shown that the Neimark–Sacker system remarkably outperforms the Andronov–Hopf amplifier regarding the CPU usage. Nevertheless, both show a similar input-output behavior over a wide parameter range. Combined with an USB-based control interface connected to a PC, the digital framework provides a powerful instrument to analyze bifurcation based amplifiers.

High dimensional model representation constructed by support vector regression. I. Independent variables with known probability distributions

High dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for capturing high dimensional input-output system behavior. In practice, the HDMR component functions are each approximated by an appropriate basis function expansion. This procedure often requires many input-output samples which can restrict the treatment of high dimensional systems. In order to address this problem we introduce svr-based HDMR to efficiently and effectively construct the HDMR expansion by support vector regression (SVR) for a function \(f(\mathbf{x})\). In this paper the results for independent variables sampled over known probability distributions are reported. The theoretical foundation of the new approach relies on the kernel used in SVR itself being an HDMR expansion (referred to as the HDMR kernel ), i.e., an ANOVA kernel whose component kernels are mutually orthogonal and all non-constant component kernels have zero expectation. Several HDMR kernels are constructed as illustrations. While preserving the characteristic properties of HDMR, the svr-based HDMR method enables efficient construction of high dimensional models with satisfactory prediction accuracy from a modest number of samples, which also permits accurate computation of the sensitivity indices. A genetic algorithm is employed to optimally determine all the parameters of the component HDMR kernels and in SVR. The svr-based HDMR introduces a new route to advance HDMR algorithms. Two examples are used to illustrate the capability of the method.

Analysis of fractional models physical consistency

Recently, for fractional order model, a distinction has emerged between real state and pseudo state. Pseudo state is a vector of finite dimension but does not have the property of a state (it does not allow to determine future behavior of the system for instance). The real state is of infinite dimension as it is distributed, but is distributed on an infinite domain. A fractional model can thus be viewed as a doubly infinite model (distributed model on an infinite domain). It is shown in the paper, that this last feature induces the real state ability to store an infinite amount of energy using an electrical interpretation of fractional models. Thus, fractional models do not reflect the reality of macroscopic physical systems in terms of energy storage ability. As a consequence, even if fractional models permit to capture accurately the input-output dynamical behavior of many physical systems, such a property highlights a physical inconsistence of fractional models. They do not reflect the internal behavior of the modelled system. This analysis is made for explicit and implicit differentiation based fractional order models.

Quantum Annealing with Markov Chain Monte Carlo Simulations and D-Wave Quantum Computers

Quantum computation performs calculations by using quantum devices instead of electronic devices following classical physics and used by classical computers. Although general purpose quantum computers of practical scale may be many years away, special purpose quantum computers are being built with capabilities exceeding classical computers. One prominent case is the so-called D-Wave quantum computer, which is a computing hardware device built to implement quantum annealing for solving combinatorial optimization problems. Whether D-Wave computing hardware devices display a quantum behavior or can be described by a classical model has attracted tremendous attention, and it remains controversial to determine whether quantum or classical effects play a crucial role in exhibiting the computational input–output behaviors of the D-Wave devices. This paper consists of two parts where the first part provides a review of quantum annealing and its implementations, and the second part proposes statistical methodologies to analyze data generated from annealing experiments. Specifically, we introduce quantum annealing to solve optimization problems and describe D-Wave computing devices to implement quantum annealing. We illustrate implementations of quantum annealing using Markov chain Monte Carlo (MCMC) simulations carried out by classical computers. Computing experiments have been conducted to generate data and compare quantum annealing with classical annealing. We propose statistical methodologies to analyze computing experimental data from a D-Wave device and simulated data from the MCMC based annealing methods, and establish asymptotic theory and check finite sample performances for the proposed statistical methodologies. Our findings confirm bimodal histogram patterns displayed in input–output data from the D-Wave device and both U-shape and unimodal histogram patterns exhibited in input–output data from the MCMC based annealing methods. Further statistical explorations reveal possible sources for the U-shape patterns. On the other hand, our statistical analysis produces statistical evidence to indicate that input–output data from the D-Wave device are not consistent with the stochastic behaviors of any MCMC based annealing models under the study. We present a list of statistical research topics for the future study on quantum annealing and MCMC simulations.

Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation

Abstract Since the so-called Hopf-type amplifier has become an established element in the modeling of the mammalian hearing organ, it also gets attention in the design of nonlinear amplifiers for technical applications. Due to its pure sinusoidal response to a sinusoidal input signal, the amplifier based on the normal form of the Andronov-Hopf bifurcation is a peculiar exception of nonlinear amplifiers. This feature allows an exact mathematical formulation of the input-output characteristic and thus deeper insights of the nonlinear behavior. Aside from the Hopf-type amplifier we investigate an extension of the Hopf system with focus on ambiguities, especially the separation of solution sets, and double hysteresis behavior in the input-output characteristic. Our results are validated by a DSP implementation.

Shift-Independent Model Reduction of Large-Scale Second-Order Mechanical Structures

Nonmodal model order reduction (MOR) techniques present accurate and efficient ways to approximate input–output behavior of large-scale mechanical structures. In this regard, Krylov-based model reduction techniques for second-order mechanical structures are typically known to require a priori knowledge of the original system parameters, such as expansion points (or eigenfrequencies). The calculation of the eigenfrequencies of the original finite-element (FE) model can be significantly time-consuming for large-scale structures. Existing iterative rational Krylov algorithm (IRKA) addresses this issue by iteratively updating the expansion points for first-order formulations until convergence criteria are achieved. Motivated by preserving the model properties of second-order systems, this paper extends the IRKA method to second-order formulations, typically encountered in mechanical structures. The proposed second-order IRKA method is implemented on a large-scale system as an example and compared with the standard Krylov and Craig-Bampton reduction techniques. The results show that the second-order IRKA method provides tangibly reduced error for a multi-input-multi-output (MIMO) mechanical structure compared to the Craig-Bampton. In addition, unlike the standard Krylov methods, the second-order IRKA does not require the information on expansion points, which eliminates the need to perform a modal analysis on the original structure. This can be especially advantageous for large-scale systems where calculations of the eigenfrequencies of the original structure can be computationally expensive. For such large-scale systems, the proposed MOR technique can lead to significant reductions of the computational time.

A methodology for equivalent modeling of distribution system based on nonlinear model reduction

This paper presents a new method to construct the low-order equivalent model for distribution system, which is very essential in large power system simulations. The distribution system connected to a substation is seen from the transmission power system as a nonlinear input–output system. In order to cope with the computation complexity, nonlinear model reduction technique based on covariance matrix is employed to obtain a new low-order dynamic system, which can closely represent the dynamic characteristics of the detailed system. The absence of drastic simplifications, direct consideration of the distribution network and the proper preservation of the input–output behavior of the detailed distribution system allow the equivalent model to attain good accuracy. Simulations and analysis are carried out on WSCC system to verify the validity of the proposed method. The simulation results show that this new method could attain high accuracy of simulation of distribution system under various operating conditions, thus improving the precision of power system stability analysis.

Cross‐gramian‐based dynamic equivalence of wind farms

This study presents dynamic equivalence of wind farms using the cross-gramian (CG)-based model order reduction method. For the purpose of wind fluctuation simulation, the dynamic model of wind farms can be described as a high-order linear input–output system, whose input is the wind speed and output is the active power injected from point of common coupling (PCC). The main input–output behaviours of the system can be measured by its CG. The right and left eigenspaces associated with large eigenvalues of CG are used to obtain a low-order model. Frequency-domain analysis of wind farms consisted of doubly-fed induction generators shows that the proposed method is rapid and numerically stable. The non-linear dynamic simulation also confirms that the reduced model is capable of retaining the dynamic relationship between the input and output of original wind farms. The proposed method offers a potential solution to dynamic simulation of the power system with large-scale wind farms.

Runtime enforcement of regular timed properties by suppressing and delaying events

Runtime enforcement is a verification/validation technique aiming at correcting possibly incorrect executions of a system of interest. In this paper, we consider enforcement monitoring for systems where the physical time elapsing between actions matters. Executions are thus modelled as timed words (i.e., sequences of actions with dates). We consider runtime enforcement for timed specifications modelled as timed automata. Our enforcement mechanisms have the power of both delaying events to match timing constraints, and suppressing events when no delaying is appropriate, thus possibly allowing for longer executions. To ease their design and their correctness-proof, enforcement mechanisms are described at several levels: enforcement functions that specify the input–output behaviour in terms of transformations of timed words, constraints that should be satisfied by such functions, enforcement monitors that describe the operational behaviour of enforcement functions, and enforcement algorithms that describe the implementation of enforcement monitors. The feasibility of enforcement monitoring for timed properties is validated by prototyping the synthesis of enforcement monitors from timed automata.

Hydroclimatic influences on non-stationary transit time distributions in a boreal headwater catchment

Understanding how water moves through catchments – from the time it enters as precipitation to when it exits via streamflow – is of fundamental importance to understanding hydrological and biogeochemical processes. A basic descriptor of this routing is the Transit Time Distribution (TTD) which is derived from the input–output behavior of conservative tracers, the mean of which represents the average time elapsed between water molecules entering and exiting a flow system. In recent decades, many transit time studies have been conducted, but few of these have focused on snow-dominated catchments. We assembled a 10-year time series of isotopic data (δ18O and δ2H) for precipitation and stream water to estimate the characteristics of the transit time distribution in a boreal catchment in northern Sweden. We applied lumped parameter models using a gamma distribution to calculate the Mean Transit Time (MTT) of water over the entire period of record and to evaluate how inter-annual differences in transit times relate to hydroclimatic variability. The best fit MTT for the complete 10-year period was 650 days (Nash–Sutcliff Efficiency = 0.65), while the best fit inter-annual MTT ranged from 300 days up to 1200 days. Whilst there was a weak negative correlation between mean annual total precipitation and the annual MTT, this relationship was stronger (r2 = 0.53, p = 0.02) for the annual rain water input. This strong connection between the MTT and annual rainfall, rather than snowmelt, has strong implications for understanding future hydrological and biogeochemical processes in boreal regions, given that predicted warmer winters would translate into a greater proportion of precipitation falling as rain and thus shorter MTT in catchments. Such a change could have direct implications for the export of solutes and pollutants.