Output Error Research Articles

Fuzzy-SIRD model: Forecasting COVID-19 death tolls considering governments intervention

Modeling the trend of contagious diseases has particular importance for managing them and reducing the side effects on society. In this regard, researchers have proposed compartmental models for modeling the spread of diseases. However, these models suffer from a lack of adaptability to variations of parameters over time. This paper introduces a new Fuzzy Susceptible–Infectious–Recovered–Deceased (Fuzzy-SIRD) model for covering the weaknesses of the simple compartmental models. Due to the uncertainty in forecasting diseases, the proposed Fuzzy-SIRD model represents the government intervention as an interval type 2 Mamdani fuzzy logic system. Also, since society’s response to government intervention is not a static reaction, the proposed model uses a first-order linear system to model its dynamics. In addition, this paper uses the Particle Swarm Optimization (PSO) algorithm for optimally selecting system parameters. The objective function of this optimization problem is the Root Mean Square Error (RMSE) of the system output for the deceased population in a specific time interval. This paper provides many simulations for modeling and predicting the death tolls caused by COVID-19 disease in seven countries and compares the results with the simple SIRD model. Based on the reported results, the proposed Fuzzy-SIRD model can reduce the root mean square error of predictions by more than 80% in the long-term scenarios, compared with the conventional SIRD model. The average reduction of RMSE for the short-term and long-term predictions are 45.83% and 72.56%, respectively. The results also show that the principle goal of the proposed modeling, i.e., creating a semantic relation between the basic reproduction number, government intervention, and society’s response to interventions, has been well achieved. As the results approve, the proposed model is a suitable and adaptable alternative for conventional compartmental models.

Computation of Time of Concentration Based on Two-Dimensional Hydraulic Simulation

Time of concentration (TC) is a parameter in runoff estimation, used to study and design different types of projects in watersheds. Any error in TC calculation leads to an inaccurate estimation of the design flow, which can lead to over-sizing or under-sizing of designed facilities that can have great economic and environmental consequences. Therefore, choosing the correct method to estimate TC is of great importance. Due to the diversity of estimation methods in the literature, the obtained TC values are different. This study aims to present a new method to calculate TC, based on its main concept, i.e., the time required for a water parcel to reach its outlet from the farthest hydrological point of a watershed. A two-dimensional hydraulic simulation was used to model the water parcel travel. A watershed was selected as a case study, and its time of concentration was determined by salt solution tracing. The field measurement results were used for calibration of the numerical simulation model. Meanwhile, 31 empirical relations in the literature were reviewed to determine the most accurate ones. Estimated TC values were compared with the measured ones, and the relative error percentage was used to evaluate the accuracy of the result. In the empirical TC methods, the maximum error was above 300%, and the minimum error was 6.7% for the field studied area. The relative errors of hydraulic simulation outputs were between 3 and 27%. The results showed that only three empirical methods, namely Simas and Hawkins, SCSlag, and Yen and Chow, had the least errors respectively equal to 6.7%, 8.660%, and 13.5%, which can be recommended for the studied area and those with similar hydrological characteristics. On the other hand, hydraulic simulation is also introduced as an efficient method to determine TC which can be used in any desired watershed.

Identification of Nonlinear State-Space Systems via Sparse Bayesian and Stein Approximation Approach

This paper is concerned with the parameter estimation of non-linear discrete-time systems from noisy state measurements in the state-space form. A novel sparse Bayesian convex optimisation algorithm is proposed for the parameter estimation and prediction. The method fully considers the approximation method, parameter prior and posterior, and adds Bayesian sparse learning and optimization for explicit modeling. Different from the previous identification methods, the main identification challenge resides in two aspects: first, a new objective function is obtained by our improved Stein approximation method in the convex optimization problem, so as to capture more information of particle approximation and convergence; second, another objective function is developed with L1-regularization, which is sparse method based on recursive least squares estimation. Compared with the previous study, the new objective function contains more information and can easily mine more important information from the raw data. Three simulation examples are given to demonstrate the proposed algorithm’s effectiveness. Furthermore, the performances of these approaches are analyzed, including parameter estimation of root mean squared error (RMSE), parameter sparsity and prediction of state and output result.

Takagi–Sugeno Fuzzy Realization of Stability Performance-Based Fault-Tolerant Control for Nonlinear Systems

This article is dedicated to studying realization issues of the stability performance-based nonlinear fault-tolerant control framework via Takagi–Sugeno (T–S)fuzzy models. To this end, the nonlinear fault-tolerant control strategy with an online fault detection system monitoring the system stability performance degradation induced by faults is first introduced by means of the stable image and kernel representations. On this basis, the T–S fuzzy models are applied to approximate the nonlinear system, and a design approach of the fuzzy observer-based controller is proposed for the system stabilization via the iterative linear matrix inequality method. With the controller gains, the fuzzy-model-based nominal stable image representation of the system is formulated, which leads to the generation of the input and output error signals. Then, with the reference signal and system input and output error signal data, a data-driven algorithm is given to online estimate the evaluation function defined in terms of system uncertainties and faults. By virtue of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> input–output stability of the controller stable kernel representation, a threshold calculation method is presented and, thus, the stability performance-based fault detection system based on fuzzy models is realized. Furthermore, for fault-tolerant purpose, the fault-tolerant controller design is discussed, which aims to retain the system stability. Two examples are provided in the end to illustrate the proposed results.

Event-Based Distributed Fuzzy Load Frequency Control for Multiarea Nonlinear Power Systems With Switching Topology

This article investigates the event-based distributed fuzzy load frequency control approach for nonlinear interconnected power systems under a switching topology. Specifically, nonlinear factors and uncertain parameters existing in turbine and governor dynamics are modeled and analyzed under the interval type-2 fuzzy method. New memory-based adaptive event-triggered mechanisms, whose directions and threshold parameters are dynamically updated based on the output change trend and relative output error of multiple memories, are proposed to further save network energy. Aiming at communication topology changes in multiarea power systems, a novel switched control system is established by introducing a time-varying communication matrix. Then, the system’s asymptotic stability is ensured by the piecewise Lyapunov–Krasovskii method. Furthermore, to further relax stability conditions, slack matrices are considered with the boundary information of membership functions. Finally, three-area power systems are shown to demonstrate the effectiveness of proposed distributed load frequency control strategies.

Output error behavior for discretizations of ergodic, chaotic systems of ordinary differential equations

The use of numerical simulation for prediction of characteristics of chaotic dynamical systems inherently involves unpredictable processes. In this work, we develop a model for the expected error in the simulation of ergodic, chaotic ordinary differential equation (ODE) systems, which allows for discretization and statistical effects due to unpredictability. Using this model, we then generate a framework for understanding the relationship between the sampling cost of a simulation and the expected error in the result and explore the implications of the various parameters of simulations. Finally, we generalize the framework to consider the total cost—including unsampled spin-up timesteps—of simulations and consider the implications of parallel computational environments to give a realistic model of the relationship between wall-clock time and the expected error in simulation of a chaotic ODE system.

Day-ahead joint clearing model of electric energy and reserve auxiliary service considering flexible load

With the increasing of renewable energy penetration, adequate reserve capacity is more important to modern power system facing with various uncertain factors. Mobilizing the enthusiasm of units and demand response to participate in reserve auxiliary service can reduce the reserve providing pressure of conventional power supplies, which is conducive to the reliable and economical operation of system. The uncertain factors such as system random failure, prediction error of both load and renewable energy output are considered, and taking unit reserve, demand response such as flexible loads as system reserve resources, this paper establishes the risk cost models to optimize system up and down reserve requirement and make optimal allocation among units and flexible loads. A joint market clearing model of day-ahead electric energy and reserve auxiliary service is established in which both the units and flexible loads participate, and is solved by the robust optimization theory. The joint market clearing model takes the reliability and the economy of the system operation into account, and optimizes the clearing scheme for market decision makers, which can provide a decision reference for the market to resist the risk of uncertainty. Finally, the effectiveness of the model and method proposed in this paper is verified by a modified 10-machine 39-bus simulation example system.

Guaranteed-performance resilient consensus for multi-agent systems subject to actuator attacks

This article is concerned with achieving resilient consensus for multi-agent systems under cyber attacks. Without loss of generality, we consider a leader-following multi-agent system where each agent is modeled with a Lipschitz nonlinear model, and the actuator attacks are imposed on agents’ states. To begin with, an adaptive observer is constructed to estimate the attacks for each follower based on relative output errors with respect to its neighbors and the leader. The global error system is proved to be asymptotically stable. Moreover, a resilient consensus control protocol is proposed for each follower where the guaranteed-performance is considered. Under this control protocol, the impact of the attack is compensated and the state of each agent is consistent. Different from the existing secure control scheme, the new one can simultaneously resist multiple types of attacks. Finally, simulation results are given to verify the effectiveness of attack estimation and resilient consensus control protocol for multi–unmanned aerial vehicle systems.

Terminal constrained robust hybrid iterative learning model predictive control for complex time-delayed batch processes

This work mainly addresses terminal constrained robust hybrid iterative learning model predictive control against time delay and uncertainties in a class of complex batch processes with input and output constraints. In this work, an equivalently novel extended two-dimensional switched system is first constructed to represent the process model by introducing state difference, output error and new relaxation variable information. Then, a hybrid predictive updating controller is proposed and an optimal performance index function including terminal constraints is designed. Under the condition that the switching signal meets certain conditions, the solvable problem of model predictive control is realized by Lyapunov stability theory. Meanwhile, the design scheme of controller parameters is also given. In addition, the robust constraint set is adopted to overcome the disadvantage that the traditional asymptotic stability cannot converge to the origin when it involves disturbances, such that the system state converges to the constraint set and meets its expected value. Finally, the effectiveness of the proposed algorithm is verified by controlling the speed and pressure parameters of the injection molding process.

Toward reliability in the NISQ era: Robust interval guarantee for quantum measurements on approximate states

Near-term quantum computation holds potential across multiple application domains. However, imperfect preparation and evolution of states due to algorithmic and experimental shortcomings, characteristic in the near-term implementation, would typically result in measurement outcomes deviating from the ideal setting. It is thus crucial for any near-term application to quantify and bound these output errors. We address this need by deriving robustness intervals which are guaranteed to contain the output in the ideal setting. The first type of interval is based on formulating robustness bounds as semi-definite programs, and uses only the first moment and the fidelity to the ideal state. Furthermore, we consider higher statistical moments of the observable and generalize bounds for pure states based on the non-negativity of Gram matrices to mixed states, thus enabling their applicability in the NISQ era where noisy scenarios are prevalent. Finally, we demonstrate our results in the context of the variational quantum eigensolver (VQE) on noisy and noiseless simulations.

Attractivity of unstable equilibria for a controlled Chen system via small output feedback

We present an output feedback controller for a single-input single-output variant of the Chen dynamical system that renders an unstable equilibrium point of the unforced system attractive using small control signals. The controller first exploits ergodicity of the unforced dynamics to asymptotically estimate the system’s state vector. Then, based on the proximity of the estimate to the desired equilibrium and a computable minimum wait time, a second stage begins applying static output error feedback. Attractivity is proven using interconnected system theory and Lyapunov analysis.

Genetically Optimized Pitch Angle Controller of a Wind Turbine with Fuzzy Logic Design Approach

An important engineering challenge is the design of a wind turbine’s pitch angle controller. The dependability, safety, and power output maximization of a wind turbine are all impacted by this controller. In this study, a 2 MW doubly fed induction generator wind turbine’s blade angle controller design with a novel fuzzy logic controller is tested in a simulated environment. The evolutionary algorithm technique is used to optimize the fuzzy logic controller with three inputs. A genetic algorithm is used to optimize the specified pitch angle controller for a number of coefficients. After the optimization process, the controller’s performance is assessed in terms of power output, overshoot, and steady-state error characteristics.

Parameter estimation for a controlled autoregressive autoregressive moving average system based on a recursive framework

In this paper, an adaptive recursive estimation scheme based on a novel recursive framework is proposed for a controlled autoregressive autoregressive moving average (CARARMA) system. A common loss function is established using the prediction error scheme, which has two shortcomings in case of interference, namely, biased estimation and minima problems. To overcome the two shortcomings, a recursive estimation scheme is proposed by using output error data with a discount factor and initial error data with a penalty operator. The former data do not involve the noise information of system data, so the biased estimation issue can be improved. The latter data include initial value information, such that the minima problem can be resolved. To achieve the target, polynomial transformation is applied to transform the CARARMA system into a particular model, then the loss function is introduced. Based on the loss function and recursive structure, a recursive estimator is developed. Moreover, the convergence of the proposed identification scheme is strictly analyzed. The advantage and practicality of the proposed estimator are evaluated by using a numerical example and real-world process.

Vertical ground heat exchanger parameter characterization through a compound design of experiments

Vertical ground heat exchangers (VGHE) are the most extended elements in geothermal utilization systems. For design and optimization purposes, the precise determination of several thermal properties is of utmost importance. While soil properties can be accurately obtained from simple mathematical models and short identification procedures, the grout characterization and additional uncertainties are usually identified from time-consuming and complex models. In order to optimize and simplify this process, without loss of accuracy, the present work proposes the use of design of experiments (DoEs) for that estimation. Thus, a multi-physic 3D model that replicates the geothermal heat exchanger (GHE) environment has been employed to develop a fractional factorial design of experiments, obtaining a set of output errors by comparison with experimental data. A response surface methodology (RSM) has been used to conduct second-order linear regression fittings, that approximate the error functions to obtain the parameter values through the minima of such surfaces. Overall mean errors lower than 0.01 °C are obtained, which provide excellent agreement in modelling the experimental test. Finally, an additional full-scale experiment has been simulated in order to validate the numerical DoE approach. Consequently, the proposed methodology has been demonstrated to accurately predict the grout thermal parameters.

Distributed fault-tolerant secondary control for DC microgrids against false data injection attacks

This paper focuses on the issue of unknown false data injection attacks (FDIA) of controllers in DC microgrid, and proposes a distributed fault-tolerant secondary controller for DC microgrid to ensure that the control objectives of voltage regulation and current sharing can be achieved when the system is subject to FDIA. Firstly, the secondary control problem in DC microgrid with FDIA is transformed into a first-order leader-following multi-agent system fault-tolerant consensus problem, and the impact of FDIA signals on the microgrid system is analyzed. Then, a distributed extended state observer (DESO) is designed based on the derived multi-agent system, which observes the injected FDIA signals using the relative output error of each distributed generators and its neighbours. Further, based on the observed FDIA signals, a fault-tolerant secondary controller is designed to eliminate the adverse effects of the attack signals on the system. Particularly, the stability analyses for the designed DESO and secondary controller prove that the control system is global asymptotically stable. Finally, the effectiveness and superiority of the proposed fault-tolerant secondary control method are verified by simulation analyses of five cases.

Adaptive neural fault‐tolerant control of an uncertain 2‐DOF helicopter system with actuator faults and output error constrains

AbstractThis paper develops an adaptive neural fault‐tolerant control for an unknown two‐degree of freedom helicopter nonlinear system with output error constraints, actuator fault, and unknown external disturbances. A neural network disturbance observer is used to estimate system uncertainties and actuator gain failures. The tan‐type barrier Lyapunov equation is used to solve the system's output error constraint. To compensate for actuator bias failures and unknown external disturbances in the system, an adaptive auxiliary parameter is established. Furthermore, rigorously analyzing the chosen Lyapunov function, the system's stability is ensured. Finally, the numerical simulation results prove the rationality and effectiveness of the proposed control strategy.

Folk Music Audio Enhancement Method Combining Internet of Things and GA

The current methods of music sound enhancement mainly use the way of enhancing the intensity of the sound source, which ignores the spatial noise cancellation of the human ear, resulting in poor sound enhancement effect. Therefore, this paper proposes an audio enhancement method for folk music combining Internet of Things and GA. After acquiring folk music audio by Internet of Things technology, the postprocessing algorithm of wavelet packet decomposition combined with Wiener filter is used to suppress the noise in music. On the basis of HRTF, genetic algorithm is used to reduce the output error of left and right sound channels and realize the enhancement of music sound effect. The simulation experiment verifies the method of application research. The reverberation is established at 65 ms and lasts for a long time, which has good effect of sound enhancement.

Application of stochastic time dependent parameters to improve the characterization of uncertainty in conceptual hydrological models

• We test stochastic processes to improve modeling of uncertainty in a real case study. • Bayesian inference and cross-validation are used to calibrate and assess performances. • Results highlight clear benefits for appropriate modeling choices. • We make recommendations to uncover/avoid issues due to overparameterization. • We test a novel parallel framework that simplifies access to HPC resources. The traditional description of a hydrological system with a deterministic, conceptual model and a lumped output error term does not explicitly consider the main mechanisms of uncertainty generation due to approximate process representation, unobserved variability in processes and influence factors, and input uncertainty. In this study, we test the description of such intrinsic uncertainty in conceptual models by making process rates stochastic through stochastic, time-dependent rate parameters. We analyze the advantages and challenges of this approach by using Bayesian inference to jointly estimate model parameters, parameters of the stochastic processes, and the time series of the stochastic parameters. Numerically, we use a particle filter to infer the stochastic time series and to approximate the marginal likelihood for Markov chain sampling of the constant parameters. Compared to the lumped error formulation, we achieve a more realistic description of uncertainty, as we obtain larger errors in intrinsic states, larger uncertainty during prediction than calibration periods (a feature missing for simple lumped error models), and autocorrelated model outputs. However, the additional degrees of freedom introduced with stochastic parameters can lead to an unintentional compensation for model deficits or input errors. This problem is symptomatic of model structure inadequacy or poor selection of the parameters that are made stochastic, and can be diagnosed through cross-validation and careful posterior analysis. The proposed approach is computationally more demanding and its implementation more challenging than the traditional description of hydrological systems using a deterministic model with a lumped error term. However, its advantages both in providing a more realistic representation of uncertainties and in diagnosing model deficiencies suggest its adoption and further development in future studies.

Emulation and modelling of semiconductor optical amplifier-based all-optical photonic integrated deep neural network with arbitrary depth

We experimentally demonstrate the emulation of scaling of the semiconductor optical amplifier (SOA) based integrated all-optical neural network in terms of number of input channels and layer cascade, with chromatic input at the neuron and monochromatic output conversion, obtained by exploiting cross-gain-modulation effect. We propose a noise model for investigating the signal degradation on the signal processing after cascades of SOAs, and we validate it via experimental results. Both experiments and simulations claim that the all-optical neuron (AON), with wavelength conversion as non-linear function, is able to compress noise for noisy optical inputs. This suggests that the use of SOA-based AON with wavelength conversion may allow for building neural networks with arbitrary depth. In fact, an arbitrarily deep neural network, built out of seven-channel input AONs, is shown to guarantee an error minor than 0.1 when operating at input power levels of −20 dBm/channel and with a 6 dB input dynamic range. Then the simulations results, extended to an arbitrary number of input channels and layers, suggest that by cascading and interconnecting multiple of these monolithically integrated AONs, it is possible to build a neural network with 12-inputs/neuron 12 neurons/layer and arbitrary depth scaling, or an 18-inputs/neuron 18-neurons/layer for single layer implementation, to maintain an output error <0.1. Further improvement in height scalability can be obtained by optimizing the input power.

Second-Order-Optimal Filter on Lie Groups for Planar Rigid Bodies

Attitude estimation is a core problem in many mobile robotic systems, such as unmanned aerial and ground vehicles. The configuration space of these systems is properly modeled by exploiting the theory of Lie groups. In this article, we propose a second-order-optimal minimum-energy filter on the matrix Lie group TSE(2), the tangent bundle of the special Euclidean group SE(2), where the optimality is with respect to a cost function in the unknown input and output error measurements. In this article, the measurement equation consists of a global positioning system-like device with two antennas attached to the planar rigid body and an inertial measurement unit-like device. Even though the mathematics is quite complicated, the accuracy of the filter justifies this approach. Simulations show the effectiveness of the proposed filter.