Simple Nonlinear Model Research Articles

Advantages of q-logarithm representation over q-exponential representation from the sense of scale and shift on nonlinear systems

Addition and subtraction of observed values can be computed under the obvious and implicit assumption that the scale unit of measurement should be the same for all arguments, which is valid even for any nonlinear systems. This paper starts with the distinction between exponential and non-exponential family in the sense of the scale unit of measurement. In the simplest nonlinear model ${dy}/{dx}=y^{q}$, it is shown how typical effects such as rescaling and shift emerge in the nonlinear systems and affect observed data. Based on the present results, the two representations, namely the $q$-exponential and the $q$-logarithm ones, are proposed. The former is for rescaling, the latter for unified understanding with a fixed scale unit. As applications of these representations, the corresponding entropy and the general probability expression for unified understanding with a fixed scale unit are presented. For the theoretical study of nonlinear systems, $q$-logarithm representation is shown to have significant advantages over $q$-exponential representation.

Mixed-effects generalized height–diameter model for young silver birch stands on post-agricultural lands

The purpose of creating regression equations is often to predict unmeasured features based upon more easily obtainable ones. Species-specific height–diameter (H–D) models of trees are an example of this situation and can be defined as either simple or generalized. Simple H–D models express height as a function of tree diameter at the breast height. They are easily applicable without additional measurement but do not take properly into account the variability in H-D relationship between stands. Meanwhile, generalized models also include stand-level predictors. The H-D data sets are often characterized by a grouped structure. The mixed-effects modeling approach is a mainstream method employed for these types of forestry data. In this study, we created a mixed-effects generalized H–D model for young silver birch stands on post-agricultural lands in central Poland. This model was chosen from among 11 simple nonlinear models based on the goodness of fit and residual behavior. We accounted for two stand-level predictors that did not require additional measurements beyond tree diameter at the breast height: quadratic mean diameter at the breast height and basal area. Fixed- and random-effect predictions were then calculated to illustrate that increases in the number of measured trees improves height predictions. Moreover, the gain in predictive power is the largest if extreme trees (i.e., from the extrema of the diameter range) are used for random-effect prediction.

Simplified Nonlinear Model of Straight-Sheathed Wood Diaphragms in Unreinforced Masonry Buildings

AbstractA simplified nonlinear numerical model is proposed to predict the full dynamic response of straight-sheathed wood diaphragms in unreinforced masonry buildings. The straight-sheathing system...

On the Illumination Influence for Object Learning on Robot Companions.

Most collaborative tasks require interaction with everyday objects (e.g., utensils while cooking). Thus, robots must perceive everyday objects in an effective and efficient way. This highlights the necessity of understanding environmental factors and their impact on visual perception, such as illumination changes throughout the day on robotic systems in the real world. In object recognition, two of these factors are changes due to illumination of the scene and differences in the sensors capturing it. In this paper, we will present data augmentations for object recognition that enhance a deep learning architecture. We will show how simple linear and non-linear illumination models and feature concatenation can be used to improve deep learning-based approaches. The aim of this work is to allow for more realistic Human-Robot Interaction scenarios with a small amount of training data in combination with incremental interactive object learning. This will benefit the interaction with the robot to maximize object learning for long-term and location-independent learning in unshaped environments. With our model-based analysis, we showed that changes in illumination affect recognition approaches that use Deep Convolutional Neural Network to encode features for object recognition. Using data augmentation, we were able to show that such a system can be modified toward a more robust recognition without retraining the network. Additionally, we have shown that using simple brightness change models can help to improve the recognition across all training set sizes.

Analytical solution of linearized equations for transient gas flows in gas pipelines

We consider the new class of high precision simplified linear models of transient high-pressure gas flows along linear sections of pipelines. Representatives of this class are obtained from different initial models defined by partial differential equations. The new models are based on the exact solution of the Klein-Gordon equation, which appears as a result of piecewise linear approximation of nonlinear models in the form of Charny’s equations [1–4] or piecewise constant approximation in models that describe deviations of pressure and mass flow rates from their values in the basic stationary mode [10–13, 16–17]. The new class of models has significant advantages over nonlinear simplified models in optimization problems of large-scale networks, reducing the calculation time by more than two orders of magnitude. They are also free from errors of the approximate inverse Laplace transform or dimensionality reduction techniques traditionally applied in such situations.

Working Distance-Based Feedforward Control of the Weld Bead Height in Directed Energy Deposition

Due to large temperature gradients and high thermal conductivities, additive manufacturing processes for metals have challenging dynamics. A high process reliability and repeatability hinges upon the base layer control of the melt pool and the resulting weld bead geometry. The material feed rate has proven to be an appropriate manipulated variable for weld bead height control, but it can only be varied slowly and is subject to deadtimes. We propose to use the distance of the process head to the build surface (the working distance) as an alternative manipulated variable. We derive a simple nonlinear dynamic model that captures the effect of the working distance on the weld bead height. We show scanning velocity fluctuations, which can be treated as known disturbances, can be compensated with working distance feedforward control. We apply the proposed controller to a real DED process and demonstrate working distance control is an alternative to material feed rate control.

Precise Control of Small Satellites in Close Clusters using Simplified Nonlinear Model Predictive Control

Precise Control of Small Satellites in Close Clusters using Simplified Nonlinear Model Predictive Control

Constructing a control-ready model of EEG signal during general anesthesia in humans

Significant effort toward the automation of general anesthesia has been made in the past decade. One open challenge is in the development of control-ready patient models for closed-loop anesthesia delivery. Standard depth-of-anesthesia tracking does not readily capture inter-individual differences in response to anesthetics, especially those due to age, and does not aim to predict a relationship between a control input (infused anesthetic dose) and system state (commonly, a function of electroencephalography (EEG) signal). In this work, we developed a control-ready patient model for closed-loop propofol-induced anesthesia using data recorded during a clinical study of EEG during general anesthesia in ten healthy volunteers. We used principal component analysis to identify the low-dimensional state-space in which EEG signal evolves during anesthesia delivery. We parameterized the response of the EEG signal to changes in propofol target-site concentration using logistic models. We note that inter-individual differences in anesthetic sensitivity may be captured by varying a constant cofactor of the predicted effect-site concentration. We linked the EEG dose-response with the control input using a pharmacokinetic model. Finally, we present a simple nonlinear model predictive control in silico demonstration of how such a closed-loop system would work.

Control of the Deformation of a Circular Cylindrical Shell

Within the framework of simplified nonlinear models, the initial nonlinear-elastic stage of obtaining hollow gear parts from the circular shells by the method of hydrostatic compression from circular circles is studied by analytical and numerical methods. It is shown that a suitable choice of a rigid rod inside the shell allows one to control the corrugation of the cross section of the pipe billet, to prevent the formation of unwanted folds and ribs on the surfaces of gear products.

Seismic performance of prefabricated sheathed cold-formed thin-walled steel buildings: Shake table test and numerical analyses

Cold-formed thin-walled steel (CFS) building systems are widely used in residential construction due to their good seismic behaviour, rapid construction efficiency and high material properties. Although significant work has been conducted on CFS members and subsystems, including studs, beams, shear walls and floors, few researches exist on the seismic performance of full-scale building systems. In order to investigate the seismic response of the CFS building system, shake table tests on a prefabricated full-scale one-story complete building were carried out. The fundamental frequency, damping ratio, displacement response and acceleration response were summarized in this paper. Then a simplified nonlinear finite element model was established with commercial software ABAQUS and validated against the test results. It was found that the developed model was suitable to accurately simulate the dynamic responses of the tested building. Hereafter, parametric studies were preformed based on the validated model to investigate the influence of key parameters on the seismic behaviour of the CFS systems, including sheathing of shear walls, diagonal brace, numbers of stories, aspect ratio as well as plan layout. Finally, based on the test data and numerical analysis results, improved seismic construction measures were proposed to provide more applicable objectives for CFS structures.

Pre-seismic Electromagnetic Perturbations in Two Earthquakes in Northern Greece

Two medium-magnitude earthquakes separated by a distance of 230 km occurred within 34 days from each other in Northern Greece. A few hours before the manifestation of seismic activity, significant extra-low-frequency (ELF) perturbations were detected in a nearby Schumann resonance observation site. The typical spectrum of ELF measurements was deformed with the appearance of an enhanced spectral feature in the frequency range 20–25 Hz. A logit regression model was applied to the data to examine whether ELF perturbations could be considered as precursors of seismic activity. In general, two earthquakes so close to each other (in space, time, and magnitude) form a unique opportunity for the study of characteristic features of pre-seismic ultra-low-frequency (ULF)/ELF perturbations. Quantitative results from a simple nonlinear statistical model support the idea that there is some kind of physical interaction between seismic and atmospheric ELF activities, and that ELF measurements could potentially be used as a useful tool in the forecasting of seismic activity.

A novel anti-swing and position control method for overhead crane.

Based on Takagi-Sugeno fuzzy modeling and linear matrix inequality with decay rate, this article presents a novel anti-swing and position control scheme for overhead cranes. First, the simplified nonlinear dynamic model is proposed by adopting a virtual control variable method to reduce the number of nonlinear terms. Then, the Takagi-Sugeno fuzzy model is constructed using sector nonlinear technique, and the anti-swing and position controller of overhead crane is designed based on a linear matrix inequality with decay rate. Finally, the proposed control method is compared with the traditional Takagi-Sugeno fuzzy control method, and robustness of the system is discussed. The simulation results demonstrate that the proposed method is feasible and effective.

Estimation of Wind Conditions Utilizing RC Helicopter Dynamics

This paper investigates the applicability of a remote-controlled (RC) helicopter as a sensing platform for measuring local wind conditions. A simplified nonlinear multibody helicopter dynamics model has been proposed in this paper, which models local wind conditions in addition to capturing essential helicopter states such as fuselage dynamics, rotor inflow, blade flapping, and lead lagging. The critical aerodynamic parameters for the model were extracted using indoor calibration flights. This paper also presents the performance of particle swarm optimization in optimizing and validating the helicopter's dynamic model parameters. An in-house developed multisensor instrumentation system was used to track the helicopter dynamics and extract wind model parameters through anomalies in the helicopter dynamics estimates. A three-dimensional (3-D) map of local wind conditions was generated for a controlled turbulent wind environment created in an indoor test facility. To validate the system's performance, wind parameters estimated from the proposed system were quantitatively compared against the experimentally generated 3-D wind map.

Entner-Doudoroff glycolysis pathway as quadratic-cubic mixed autocatalytic network: A kinetic assay

Concentration oscillations are ubiquitous phenomenon in biochemical systems.The present paper considers the simple nonlinear chemical feedback model for standard glycolytic route with prototype autocatalytic steps.Quadratic S + P ⇄ 2P.Cubic S + 2P ⇄ 3P.We couple these steps to get the mixed quadratic-cubic model but remarkable array of complex behavior and oscillatory patterns as expected on coupling is surprisingly missing. The observation is in conformity with natural glycolytic alternatives like the Entner-Doudoroff (ED), and phosphoketolase pathways found in Archaea – Thermoproteustenax and other prokaryotes. The fundamental and the practical implications of our findings are thoroughly discussed with pilot calculations and numerical simulations supported via non-linear dynamic analysis. A basic kinetic scheme is suggested for natural glycolytic alternative, ED pathway with its comparison and contrast to other standard routes for glucose metabolism. A key outcome of the study is the phenomenon of oscillator death for the coupled network. A discussion on the thermodynamic aspect of entropy production rate for the model networks are also presented for a comparison.

A hybrid paradigm combining model-based and data-driven methods for fuel cell stack cooling control

The cooling of the open-cathode proton exchange membrane fuel cell (PEMFC) is critical for the operational safety and overall efficiency. However, its control is challenging because of the model uncertainties and frequent disturbances caused by the power adjustment. To this end, this paper proposes a hybrid cooling control strategy by combining the merits of the model-based and data-driven methods. Firstly, a simplified nonlinear mechanistic model is used to exhibit the dynamic perturbations in terms of the different fan speeds and power conditions. Secondly, a modified active disturbance rejection control (ADRC) is developed by incorporating an identified nominal linear model into extended state observer. The external disturbances and the internal uncertainties beyond the nominal model are lumped as a total term, which will be estimated and mitigated in a real-time data-driven manner. The simulation results show that the proposed hybrid method is able to give a faster response with stronger robustness and less noise sensitivity against the uncertainties than the conventional PI and ADRC methods. The experimental test on a 500W open-cathode PEMFC verifies the simulation merits in both set-point tracking and disturbance rejection, depicting a promising prospect of the proposed hybrid method in the open-cathode PEMFC cooling control practice.

Simulation of cyclic response of precast concrete beam-column joints

Experience of previous earthquakes shows that a considerable portion of concrete precast buildings sustain relatively large damages especially at the beam-column joints where the damages are mostly caused by bar slippage. Precast concrete buildings have a kind of discontinuity in their beam-column joints, so reinforcement details in this area is too important and have a significant effect on the seismic behavior of these structures. In this study, a relatively simple and efficient nonlinear model is proposed to simulate pre- and post-elastic behavior of the joints in usual practice of precast concrete building. In this model, beam and column components are represented by linear elastic elements, dimensions of the joint panel are defined by rigid elements, and effect of slip is taken into account by a nonlinear rotational spring at the end of the beam. The proposed method is validated by experimental results for both internal and external joints. In addition, the seismic behavior of the precast building damaged during Bojnord earthquake 13 May 2017, is investigated by using the proposed model for the beam-column joints. Damage unexpectedly inducing the precast building in the moderate Bojnord earthquake may confirm that bearing capacity of the precast building was underestimated without consideration of joint behavior effect.

Numerical validation of a simplified inverse analysis method to characterize the tensile properties in strain-softening UHPFRC

In previous research a simplified closed-form non-linear hinge model based on the Third Point Bending Test (TPBT) developed by the authors to derive the tensile material properties of Ultra-High-Performance Fiber-Reinforced Concrete (UHPFRC) was numerically validated. This simplified non-linear hinge model was calibrated for UHPFRC that exhibits strain-hardening constitutive behavior. The aim of this work is the numerical validation of the simplified inverse analysis method to characterize the tensile properties of UHPFRC even with those UHPFRCs which exhibit strain-softening behavior. To get this objective a Finite Element Model (FEM) is carried out. The parameters to characterize the concrete properties from the simplified inverse analysis method by means of TPBT are used in the numerical modelling. The constitutive model for UHPFRC is modelled using a discrete crack approach for the macrocrack position. Different parameters are analysed to quantify the accuracy of the FEM. As a result, the model shows conservative load-deflection response when it is compared to the experimental curves.

A new efficient parameter estimation algorithm for high-dimensional complex nonlinear turbulent dynamical systems with partial observations

Parameter estimation for high-dimensional complex nonlinear turbulent dynamical systems with only partial observations is an important and practical issue. However, most of the existing parameter estimation algorithms are computationally expensive in the presence of a large number of state variables or parameters. In this article, a parameter estimation algorithm is developed for high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures. This algorithm exploits the closed analytical form of the conditional statistics to recover the unobserved trajectories in an optimal and deterministic way, which facilitates the calculation of the likelihood function and circumvents the computationally expensive data augmentation approach in sampling the unobserved trajectories as widely used in the literature. Such an efficient method of recovering the unobserved trajectories is then incorporated into a standard Markov chain Monte Carlo (MCMC) algorithm to estimate parameters in complex dynamical system using only a short period of training data. Next, in light of the dynamical features, two effective strategies are developed and incorporated into the algorithm that facilitates the parameter estimation of many high-dimensional systems. The first strategy involves a judicious block decomposition of the state variables such that the original problem is divided into several subproblems coupled in a specific way that allows an extremely cheap parallel computation for the parameter estimation. The second strategy exploits statistical symmetry for a further reduction of the computational cost when the system is statistically homogeneous. The new parameter estimation algorithm is applied to a two-layer Lorenz 96 model with 80 state variables and 162 parameters and the model mimics the realistic features of atmosphere wave propagations and excitable media. The efficient algorithm results in an accurate estimation of the parameters, which further allows a skillful prediction by the model with estimated parameters. Other simple nonlinear models are also used to illustrate the features of the new algorithm.

Reservoir Computing Using Laser Networks

Reservoir computing is a neuromorphic computing scheme inspired by the human brain. It has found great success as a versatile hardware-compatible application of machine learning concepts. In this paper, we highlight the fundamental working principles and important characteristics of reservoir computing with a particular focus on photonic systems and networks. These systems can further be enhanced by the inclusion of delayed variables to produce complex spatiotemporally mixed “time-multiplexed” networks. We use a simple nonlinear oscillator model, that is not only applicable to lasers, but can also describe a variety of other oscillating systems.

Pile groups under axial loading: an appraisal of simplified non-linear prediction models

The settlement behaviour of vertically loaded pile groups has been the subject of an extensive body of research over the past two decades. In particular, this work has identified the over-conservatism associated with predictions of pile interaction derived from elastic theory and the corresponding amplification of group settlement relative to single pile values. Researchers have since redoubled efforts to refine settlement predictions for pile groups towards more economical design, largely through more rigorous treatment of soil stiffness non-linearity. Although foundation design engineers are increasingly employing three-dimensional continuum analyses to quantify pile interaction on a site-specific basis, simplified design approaches remain an integral part of preliminary foundation design. The purpose of this paper is to undertake a critical examination of these methods with a view to increasing their potential for take-up by foundation engineering practitioners. A database of simplified models has been collated for the prediction of non-linear pile interaction that exists within vertically loaded pile groups. These models are categorised as either analytical or empirical. The development, limitations and range of applicability of these models are explored in detail in the context of some published case histories.