General Nonlinear Model Research Articles

Sensor fault–tolerant control of a quadrotor unmanned aerial vehicle

This article handles the issue of fault-tolerant control of a quadrotor unmanned aerial vehicle (UAV) in the existence of sensor faults. A general non-linear model of the quadrotor is presented. Several non-linear Kalman filters namely, the extended Kalman filter, the unscented Kalman filter and the cubature Kalman filter (CKF) are utilized to estimate the states of the quadrotor and to compare the estimation performances. Some flight scenarios are simulated, and the simulation results show that the CKF has the smallest estimation error as expected in theory. Control of the quadrotor heavily depends on the measured values received from sensors. Therefore, the control system requires fault-free sensors. However, small quadrotors and UAVs are mostly equipped with low-cost and low-quality sensors, and hence, they may fail to indicate correct measurement values. If the sensors are faulty, then the control system itself should be actively tolerant to sensor faults. Measurements of these kinds of sensors suffer from bias and external noise due to temperature variations, vibration and other external conditions. Since the bias is one of the very common faults in these sensors, a sensor bias is taken into consideration as a fault and occurs abruptly at a certain time and continues throughout the considered scenarios. By using the residual signals generated by the non-linear filters, sensor faults are detected and isolated. Then, two different methods are proposed for removing the effects of faults and achieving active fault–tolerant control. The effectiveness of the presented two techniques is shown in the simulations.

Thermodynamically consistent nonlinear viscoplastic formulation with exact solution for the linear case and well-conditioned recovery of the inviscid one

In this work, a consistent viscoplasticity formulation is derived from thermodynamical principles and employing the concept of continuum elastic corrector rate. The proposed model is developed based on the principle of maximum viscoplastic dissipation for determining the flow direction. The model uses both the equivalent viscoplastic strain and its rate as state variables. Power balance and energy balance give, respectively, separate evolution equations for the equivalent viscoplastic strain rate and the viscoplastic strain, the former written in terms of inviscid rates. Several key points distinguish our formulation from other proposals. First, the viscoplastic strain rate (instead of a yield function) consistently distinguishes conservative from dissipative behaviours during reverse loading; and the discrete implicit integration algorithm is an immediate discretization of the continuum theory based on the mentioned principles considered as separate equations. Second, the inviscid solution is recovered in a well-conditioned manner by simply setting the viscosity to zero. Indeed, inviscid plasticity, viscoelasticity and viscoplasticity are particular cases of our formulation and integration algorithm, and are recovered just by setting the corresponding parameters to zero (viscosity or yield stress). Third, the linear viscoplasticity solution is obtained in an exact manner for proportional loading cases, independently of the time step employed. Four, general nonlinear models (Perzyna, Norton, etc) may be immediately incorporated as particular cases both in the theory and the computational implementation.

Method for reducing waveform distortion by increasing damping strength for electromagnetic vibrators

Voice coil motors are frequently used as force drivers in electromagnetic vibrators. As a constant current is applied, the generated driving force is not constant but varies with displacement due to the inhomogeneous magnetic field within the stroke range. When a sinusoidal current is applied to the voice coil motors, the above effect can lead to a severe waveform distortion on the output acceleration. In order to find an effective method to reduce it, a general nonlinear dynamic model has been established and analyzed with a focus on the effect of the damping strength of the vibrator on the waveform distortion. The numerical calculations show that the waveform distortion can be efficiently reduced by increasing the damping strength under various working conditions. Based on these results, an eddy current damper (ECD) was designed with a maximized damping coefficient and applied to our home-made vibrator. Once the ECD is incorporated, the waveform distortion of the output acceleration is significantly reduced, which validates our modeling.

Global robust output regulation of a class of MIMO nonlinear systems by nonlinear internal model control

AbstractRecently, the global robust output regulation problem for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems which may not have well‐defined relative degree and are subject to a nonlinear exosystem has been studied based on a constructive nonlinear internal model. However, the proposed nonlinear internal model‐based control law is applicable to the case where the exogenous signals are reference input and/or measurable disturbance rather than unmeasurable disturbance. For this reason, this paper further studies the same control problem based on a general nonlinear internal model independent of the exogenous signal. It is shown that this control problem can be converted into a global robust stabilization problem of a more complicated MIMO nonlinear system with various uncertainties and well solved by a recursive state feedback controller design. Thus our approach applies to a broader class of output regulation problem of MIMO nonlinear systems.

Stochastic quasi-Newton with line-search regularisation

In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally attractive algorithms. In essence, this is achieved by learning the second-order (Hessian) information based on observing first-order gradients. We extend these ideas to the stochastic setting by employing a highly flexible model for the Hessian and infer its value based on observing noisy gradients. In addition, we propose a stochastic counterpart to standard line-search procedures and demonstrate the utility of this combination on maximum likelihood identification for general nonlinear state space models.

Modelling short-term monotonic response of timber–concrete composite structures

Timber–concrete composite is an efficient hybrid construction material that exploits the advantageous properties of timber and concrete. The use of shear connectors enables the two dissimilar materials to act together, resulting in an increase in global stiffness as well as load-carrying capacity. As this composite material is becoming increasingly more popular in the construction industry, there is a need to develop analysis tools that have general applicability to timber–concrete composite systems with variations in loading schemes, specimen configurations, materials, and types of shear connectors. One such tool, a generic two-dimensional nonlinear finite element model, is proposed in this paper; it is verified through numerical simulations of six experiment series carried out by other researchers. Good agreement between experimentally observed behaviour and numerical simulations was generally obtained.

Mechanics of soft polymeric materials using a fractal viscoelastic model

Soft materials are known for their plethora of biomedical applications, intricate structure–property correlation and nonlinear mechanical response. Multiple length–time scale phenomena and hierarchical structure results in their nonlinearity. Phenomenological and continuum mechanical models have been developed to predict their mechanics, which have mostly been very material-specific with inability to predict the mechanics of different types of soft materials simultaneously. This shortcoming has been addressed in the present work, wherein a generic nonlinear viscoelastic model has been proposed to predict the mechanical response of hydrogels, sponges, and xerogels. A fractal derivative viscoelastic model is proposed considering a fractal Maxwell model in parallel with a nonlinear spring. In particular, this model is chosen to qualitatively mimic the material nonlinearity inherent in soft materials. The fractal dashpot in combination with the nonlinear spring accounts for the power law time-dependent rheology of generic soft materials. These two different aspects in the form of nonlinear stiffness and non-Newtonian rheology account for mechanics of most soft materials. The present model is shown to fit well the existing literature results for mechanical response of a multitude of soft material classes with different test conditions and loading rates, which is one of the salient features of the model, apart from its simplistic mathematical framework. Further, a parametric study is reported on the mechanics of nanocellulose loaded poly(vinyl alcohol) xerogel. The model predictions are observed to be in conjunction with the experimental observations.

Synthesis analysis for multi-UAVs formation anomaly detection

PurposeThe purpose of this paper is to deal with the anomaly detection problem in multi-unmanned aerial vehicles (UAVs) formation that can be transformed to identify some unknown parameters; a more general nonlinear dynamical model for each UAV is considered to include two terms. Due to an unknown parameter corresponding to the normal or abnormal state for each UAV, the bias-compensated approach is proposed to obtain the unbiased parameter estimation. Meanwhile, the biased error and accuracy analysis are also given in case of strict statistical description of the uncertainty or white noise. To relax this strict statistical description on external noise, an analytic center approach is proposed to identify the unknown parameters in presence of bounded noise, such that two inner and outer ellipsoidal approximations are constructed to include the membership set. To be precise, this paper is regarded as one extension and summary for the author’s previous research on the anomaly detection in multi-UAV formation. Finally, one simulation example is given to confirm the theoretical results.Design/methodology/approachFirstly, one extended nonlinear relation is constructed to embody the mutual relationship of UAVs. Secondly, to obtain the unbiased parameter estimations, the bias-compensated approach is applied to achieve it under the condition of white noise. Thirdly, in case of unknown but bounded noise, an analytic center approach is proposed to deal with this special case. Without loss of generality, the author thinks this paper can be used as one extension and summary for research on multi-UAVs formation anomaly detection.FindingsAn anomaly detection problem in multi-UAVs formation can be transformed into a problem of nonlinear system identification, and in modeling the nonlinear dynamical model for each UAV, two terms are considered simultaneously to embody the mutual relationships with other nearest UAV.Originality/valueTo the best knowledge of the authors, this problem of the anomaly detection problem in multi-UAVs formation is proposed by the authors’ previous work, and the problem of multi-UAVs formation anomaly detection can be transferred into one problem of parameter identification. In case of unknown but bounded noise, an analytic center approach is proposed to identify the unknown parameters, which correspond to achieve the goal of the anomaly detection.

Quantum corrections to generic branes: DBI, NLSM, and more

We study quantum corrections to hypersurfaces of dimension d + 1 > 2 embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and arbitrary bulk metric. A variety of theories which are prominent in the modern amplitude literature arise as special limits: the scalar sector of Dirac-Born-Infeld theories and their multi-field variants, as well as generic non-linear sigma models and extensions thereof. Our explicit one-loop results unite the leading corrections of all such models under a single umbrella. In contrast to naive computations which generate effective actions that appear to violate the non-linear symmetries of their classical counterparts, our efficient methods maintain manifest covariance at all stages and make the symmetry properties of the quantum action clear. We provide an explicit comparison between our compact construction and other approaches and demonstrate the ultimate physical equivalence between the superficially different results.

A Multi-Region Nonlinear Size-Structured Population Model with Coagulation and Vertical Effects

A general nonlinear model describing the evolution of size-structured populations influenced by coagulation and vertical effects is presented. The nonlinear population dynamics occur in a multi-region setting in which the transfer, coagulation, and vital rates of an individual depend on a vector describing conditions in the environment. The model for these dynamics consists of a system of two-dimensional nonlinear-nonlocal hyperbolic partial differential equations coupled with a system of one-dimensional nonlocal differential equations parametrized by a vertical location coordinate $$${z}$$$ describing the environmental time-dynamics. A finite difference approximation approach is employed to study the wellposedness of the model and convergence of the scheme to the unique weak solution is established. Several examples are presented to illustrate the generality of the model and to motivate applications.

Deep Learning for Robotics

The application of deep learning to robotics over the past decade has led to a wave of research into deep artificial neural networks and to a very specific problems and questions that are not usually addressed by the computer vision and machine learning communities. Robots have always faced many unique challenges as the robotic platforms move from the lab to the real world. Minutely, the sheer amount of diversity we encounter in real-world environments is a huge challenge to deal with today’s robotic control algorithms and this necessitates the use of machine learning algorithms that are able to learn the controls of a given data. However, deep learning algorithms are general non-linear models capable of learning features directly from data making them an excellent choice for such robotic applications. Indeed, robotics and artificial intelligence (AI) are increasing and amplifying human potential, enhancing productivity and moving from simple thinking towards human-like cognitive abilities. In this paper, lots of learning, thinking and incarnation challenges of deep learning robots were discussed. The problem addressed was robotic grasping and tracking motion planning for robots which was the most fundamental and formidable challenge of designing autonomous robots. This paper hope to provide the reader an overview of DL and robotic grasping, also the problem of tracking and motion planning. The system is tested on simulated data and real experiments with success.

Method to Determine the Constitutive Permeability Parameters of Non-Linear Consolidation Models by Means of the Oedometer Test

This paper presents an easy-to-apply methodology that allows obtaining the permeability index and the initial hydraulic conductivity of clayey soils, basic constitutive parameters in non-linear models of consolidation, based on the laboratory oedometer test. For this, the data of the void ratio, compressibility index and characteristic consolidation time are taken from the test and, as an inverse problem, the constitutive permeability parameters sought are determined by applying the universal solutions of the characteristic time for a general non-linear consolidation model with constitutive relations void ratio-effective soil stress and hydraulic conductivity-void ratio of logarithmic type. The application protocol of the inverse problem is described in detail and illustrated by a series of applications carried out on real laboratory data belonging to two different soils. The influence that errors in laboratory parameter measurements can have on the final values of the permeability index and initial hydraulic conductivity is studied, showing the maximum deviations that may appear and, by last, the precision of the results obtained.

A General Linear Framework for Analysis of Islanded Inverter-Based Microgrids

Simulation and stability analysis of power systems are challenging topics due to nonlinear models. Fortunately, most power components are weakly nonlinear and by taking the advantages of this characteristic and also using the first-order term of the Taylor expansion, a general linear time-variant model for such systems is derived. Specifically, this article analyzes islanded inverter-based microgrids (IBMGs) using the proposed linear model driven directly from a general nonlinear model of IBMGs, and it is just as comprehensive as the reference one. Two methods to linearize the weakly and severely nonlinear state-space models are presented. A new time-step simulation is developed to modify the model dynamically and to calculate time-domain response as well as eigenvalues directly, which are much faster and more efficient than numerical methods and small-signal stability analyses. The capabilities of the proposed models make it possible to easily develop a time-saving eigenvalue calculator as well as a fast- and low computational direct power flow analysis. Different time-domain simulations in MATLAB/Simulink and other tests are investigated to verify the performance of the proposed simulations and their applications.

Atmospheric water vapor radiative effects on shortwave radiation under clear skies: A global spatiotemporal analysis

This global study analyzes how the total column water vapor (in terms of precipitable water, PW) is related to the attenuation of shortwave solar radiation (SWR) using data from the MERRA-2 reanalysis during 2000–2014 and SWR simulations obtained with the REST2 clear-sky radiation model. The water vapor radiative effect (WVRE) on SWR attenuation is investigated by comparing the clear-sky SWR predictions under humid and ideally dry atmospheres, whereas the quantitative effect of PW on WVRE is determined using the concept of precipitable water efficiency (PWE).At global scale, WVRE exhibits a distinct seasonal pattern ranging from –80.2 to 0 W m‐2, with lower values in humid regions where PW is typically high (>4 cm), making the water vapor contribution relatively small. This is attributed to the saturation effect in water vapor absorption. Over arid regions, the solar irradiance attenuation is mainly controlled by the high aerosol loads, and less negative WVRE values are found. Over high-altitude regions, the low PW reduces the atmospheric absorption, resulting in low absolute WVRE magnitudes.PWE is found to extend globally between –133.7 and 0 W m‐2 cm‐1 on a monthly scale. This range is smaller on a long-term mean monthly or annual basis. On a long-term basis, the monthly PWE results are mainly concentrated between −20 and 0 W m−2 cm−1, generating leptokurtic and left-skewed distributions peaking between −10 and −8 W m−2 cm−1, depending on month. PWE is inversely related to PW on a long-term annual scale, indicating that PWE tends to zero under very humid conditions. A general nonlinear model is proposed to evaluate the hourly PWE at global scale on a monthly basis, separately for the two hemispheres.A PW trend analysis reveals that the Middle East, equatorial regions, central Europe, and Australia exhibit significant temporal trends, further inducing significant trends in WVRE. For those areas, WVRE trends are calculated between −3.3 and 1.5 W m−2 over the entire 15-year period.In addition, the global WVRE over landmasses is classified in terms of the Köppen-Geiger (KG) climate classification system. The most pronounced radiative effects are found over the equatorial regions, with an average WVRE of −63 W m−2. The Arid KG class provides a complex WVRE pattern ranging from −66 to −24 W m−2. Further segregation of this class shows strongly variable WVRE, induced by local climate differentiation. Over Warm Temperate climates, WVRE is found to vary widely according to the various KG subclasses. For the Cold climate class, PW is mainly concentrated around 1 cm and WVRE is low. The Polar regions include high mountains where WVRE is low, with a median close to −28 W m−2.

On the generalized Chikungunya virus dynamics model with distributed time delays

In this paper, a stability analysis of a general nonlinear Chikungunya virus dynamics model is presented. Two kinds of infected cells, namely latently infected and actively infected are incorporated into the model. It is assumed that, the incidence rate of infection as well as the production, removal and proliferation rates of all compartments are modeled by general nonlinear functions that satisfy sufficient conditions. The model contains two distributed time delays. The nonnegativity and boundedness of the solutions of the model are investigated. Constructions of suitable Lyapunov functionals are established to prove the global stability of the steady states of the model. Numerical simulations are performed to confirm the validity of the established theoretical results.

Inventory policies for seasonal items with logistic-growth demand rate under fully permissible delay in payment: a neutrosophic optimization approach

The present study investigates an inventory system for seasonal products under variable demand rate and partial backordering in a competitive market. Among various demand rate functions used in the existing literature of economic order quantity (EOQ) models, the logistic-growth function is best known to estimate market already captured and fraction of market remaining to be captured by new seasonal and technology driven items. Weibull distribution well represents the seasonality and versatility of these products. Due to retailers’ reluctance to purchase and store these perishable products, supplier offers the delay in payment. In view of the above, the proposed EOQ model suitable for those items considers the logistic-growth demand rate, Weibull distribution deterioration rate and partial backordering along with fully permissible delay in payment. Since the neutrosophic set quantifies the imprecise information in real-life scenarios, the proposed EOQ model is optimized in neutrosophic environment. A general unconstrained nonlinear mathematical model with neutrosophic coefficients is optimized using the weighted arithmetic mean function, subject to specified neutrosophic norm. A special case with the neutrosophic conjunction norm along with four lemmata is considered to minimize the cost functions with neutrosophic coefficients to proposed EOQ model across various trade-credit intervals. Here, the managerial insights identified through sensitivity analysis advocate to reduce the expenses on early promotions for foreshortening the demand at the beginning of cycle. Also, the present study demonstrates the optimal inventory depletion time to depend on the demand during the shortages in neutrosophic environment.

An MI-SDP Model for Optimal Location and Sizing of Distributed Generators in DC Grids That Guarantees the Global Optimum

This paper deals with a classical problem in power system analysis regarding the optimal location and sizing of distributed generators (DGs) in direct current (DC) distribution networks using the mathematical optimization. This optimization problem is divided into two sub-problems as follows: the optimal location of DGs is a problem, with those with a binary structure being the first sub-problem; and the optimal sizing of DGs with a nonlinear programming (NLP) structure is the second sub-problem. These problems originate from a general mixed-integer nonlinear programming model (MINLP), which corresponds to an NP-hard optimization problem. It is not possible to provide the global optimum with conventional programming methods. A mixed-integer semidefinite programming (MI-SDP) model is proposed to address this problem, where the binary part is solved via the branch and bound (B&B) methods and the NLP part is solved via convex optimization (i.e., SDP). The main advantage of the proposed MI-SDP model is the possibility of guaranteeing a global optimum solution if each of the nodes in the B&B search is convex, as is ensured by the SDP method. Numerical validations in two test feeders composed of 21 and 69 nodes demonstrate that in all of these problems, the optimal global solution is reached by the MI-SDP approach, compared to the classical metaheuristic and hybrid programming models reported in the literature. All the simulations have been carried out using the MATLAB software with the CVX tool and the Mosek solver.

Heterogeneous Variable Selection in Nonlinear Panel Data Models: A Semi-Parametric Bayesian Approach

In this paper, we develop a general method for heterogeneous variable selection in Bayesian nonlinear panel data models. Heterogeneous variable selection refers to the possibility that subsets of units are unaffected by certain variables. It may be present in applications as diverse as health treatments, consumer choice-making, macroeconomics, and operations research. Our method additionally allows for other forms of cross-sectional heterogeneity. We consider a two-group approach for the model's unit-specific parameters: each unit-specific parameter is either equal to zero (heterogeneous variable selection) or comes from a Dirichlet process (DP) mixture of multivariate normals (other cross-sectional heterogeneity). We develop our approach for general nonlinear panel data models, encompassing multinomial logit and probit models, poisson and negative binomial count models, exponential models, among many others. For inference, we develop an efficient Bayesian MCMC sampler. In a Monte Carlo study, we find that our approach is able to capture heterogeneous variable selection whereas a standard'' DP mixture is not. In an empirical application, we find that accounting for heterogeneous variable selection and non-normality of the continuous heterogeneity leads to an improved in-sample and out-of-sample performance and interesting insights. These findings illustrate the usefulness of our approach.

Assessing the Robustness of Pan Evaporation Models for Estimating Reference Crop Evapotranspiration during Recalibration at Local Conditions

A classic method for assessing the reference crop evapotranspiration (ETo) is the pan evaporation (Epan) method that uses Epan measurements and pan coefficient (kp) models, which can be functions of relative humidity (RH), wind speed (u2), and temperature (T). The aim of this study is to present a methodology for evaluating the robustness of regression coefficients associated to climate parameters (RH, u2, and T) in pan method models during recalibration at local conditions. Two years of daily data from April to October (warm season) of meteorological parameters, Epan measurements from class A pan evaporimeter and ETo estimated by ASCE-standardized method for the climatic conditions of Thessaloniki (Greece, semi-arid environment), were used. The regression coefficients of six general nonlinear (NLR) regression Epan models were analyzed through recalibration using a technique called “random cross-validation nonlinear regression RCV-NLR” that produced 1000 random splits of the initial dataset into calibration and validation sets using a constant proportion (70% and 30%, respectively). The variance of the regression coefficients was analyzed based on the 95% interval of the highest posterior density distribution. NLR models that included coefficients with a 95% HPD interval that fluctuates in both positive and negative values were considered nonrobust. The machine-learning technique of random forests (RF) was also used to build a RF model that includes Epan, u2, RH, and T parameters. This model was used as a benchmark for evaluating the predictive accuracy of NLR models but, also, for assessing the relative importance of the predictor climate variables if they were all included in one NLR model. The findings of this study indicated that locally calibrated NLR functions that use only the Epan parameter presented better results, while the inclusion of additional climate parameters was redundant and led to underfitting.

Global stability analysis of a general nonlinear scabies dynamics model

Abstract In this work we present a general nonlinear model of scabies infection dynamics. The dynamics is described by a five-dimensional system of ordinary differential equations that expresses the transmissions between susceptible, infectious/infective individuals and adult scabiei mites. The intrinsic growth rate for susceptible individuals, the infection rates as well as the removal and transmission rates of infected individuals and adult mites are modeled by general nonlinear functions. Based on a set of conditions on these general functions we investigate and analyze our model. Nonnegativity and boundedness of solutions of the model are conducted. A basic reproduction number, ℜ 0 M , is calculated for the model which ensures the existence and stability of all corresponding equilibria. Using candidate Lyapunov functions, it is shown that whenever the basic reproduction number is less than or equal unity, the model has an associated disease-free equilibrium, Q 0 M , that is globally asymptotically stable. In addition, when the threshold exceeds unity the model has a globally asthmatically stable endemic equilibrium, Q ¯ M . Finally, using some parameter values related to the scabies infection dynamics, numerical simulation results are demonstrated to clarify the strength of our main theoretical results. Sensitivity analysis of the endemic equilibrium has been performed.