Non-affine Model Research Articles

Multiscale experimental characterization and physical-based constitutive modeling of silicone adhesive

Silicone adhesive has been widely used in assembly glass curtain walls which leads to its mechanical behaviors under heavy investigation. Due to its complexity, the microstructure of silicone adhesive stays unclear. A detailed description of microstructures of silicone adhesive is the basis to obtain an in-depth understanding of its mechanical behavior and the related mechanisms. In this work, series of multiscale experiments, uniaxial tension, uniaxial compression, simple shear and scanning electron microscopy (SEM) observation, were conducted to characterize mechanical behaviors and microstructure features of silicone adhesive. Stress-strain curves obtained through macroscale experiments were presented. Morphology and dispersion of filler clusters in silicone adhesive were analyzed using Gaussian mixed models. A modification of molecular chain spatial distribution was made to non-affine network model to consider anisotropic damage evolution of polymer matrix. A simplified term was further introduced to account for load-bearing capacity of filler clusters based on fractal theory where fractal dimensions of clusters work as a connection between microscale and macroscale. The modified model was further extended to describe Mullins effect combined with network alteration theory. The results of model validation and comparison demonstrated that due to the consideration of polymer chain anisotropic evolution and filler cluster microscopic features, the proposed model can predict the mechanical behavior of silicone adhesive under different loading conditions as well as the stress softening and permanent set of Mullins effect more accurately.

Adaptive neural trajectory tracking non-affine control for a hovercraft subject to multiple safety constraints

ABSTRACT Considering the internal, external uncertainties and robustness decreases, this paper addresses an adaptive neural trajectory tracking non-affine control method for a hovercraft under multiple safety constraints. Firstly, hovercraft’s non-affine model has been built and aim to approximate non-affine formulations, a neural network (NN) is utilized. Secondly, to stabilize the position errors, virtual surge velocity control law is obtained via a log-type barrier Lyapunov function (LBLF). Thirdly, a new asymmetric integral barrier Lyapunov function (AIBLF) is presented to address asymmetric safety constraint problems of hovercraft. Aim to guarantee heading control, the yaw angular velocity is obtained consequently. The proposed adaptive method can guarantee the surge velocity and yaw angular velocity to the inside of asymmetric boundaries with the requirements of safe performance during motion. The total system states are ultimately uniformly bounded (UUB) via Lyapunov stability theories. Finally, obtained simulations results demonstrate the effectiveness of the proposed control scheme.

A unified barrier function-based trajectory tracking control for hovercraft with asymmetric dynamic safety constraints

This paper addresses a trajectory tracking control scheme based on a unified barrier function for hovercraft subject to asymmetric dynamic safety constraints. Firstly, a non-affine model of hovercraft has been built and aims to estimate the lumped disturbance, an extended state observer is utilized. Secondly, for the sake of position constraints, virtual velocity control law is obtained by utilizing a unified barrier function (UBF). Thirdly, a constraint control scheme according to UBF is presented to address asymmetric safety constraint problems of hovercraft. The proposed method can transform the original constrained hovercraft control into an equivalent “non-constrained” one and guarantee the three velocities of hovercraft within asymmetric boundaries with requirements of safe performance during motion respectively. In addition, aims to handle the issue of the virtual control law's differential explosion, and considering that the output torque of the controller should be limited to a certain range, a bioinspired neurodynamic model (BNDM) is adopted. The total system is ultimately uniformly bounded (UUB) via Lyapunov stability theories and the stability lemma of the cascade system. Finally, obtained simulation results prove the effectiveness of the proposed control scheme.

Combined control algorithm based on synchronous reinforcement learning for a self-balancing bicycle robot

In this paper, balance control of a bicycle robot is studied without either a trail or a mechanical regulator when the robot moves in an approximately rectilinear motion. Based on the principle of moment balance, an input nonaffine nonlinear dynamics model of the bicycle robot is established. A driving velocity condition is proposed to maintain the robot balance. The nonaffine nonlinear system is transformed into an affine nonlinear system by defining the equivalent control. Subsequently, a feedback linearization controller is designed for the equivalent control. We design a combined control algorithm of synchronous policy iteration based on the actor–critic architecture. The actor neural network (NN) is designed based on the feedback linearization control law. Weight tuning laws for the critic and actor NNs are proposed. The system closed-loop stability and convergence of the NN weights are guaranteed based on the Lyapunov analysis. The optimality of the equivalent control policy is guaranteed. To satisfy the driving velocity condition, the values of the steering angle and driving velocity are determined based on the optimal equivalent control. The effectiveness of the proposed algorithm is verified through simulations and real experiments.

Dynamic modeling of hard-magnetic soft actuators: Unraveling the role of polymer chain entanglements, crosslinks, and finite extensibility

In recent years, there has been increasing interest in hard-magnetic soft materials (HMSMs) due to their ability to retain high residual magnetization and undergo large deformations under external magnetic loading. The performance of these materials in the dynamic mode of actuation is significantly influenced by internal properties, such as entanglements, crosslinks, and the finite extensibility of polymer chains. This article presents a theoretical framework for modeling the dynamic behavior of a hard-magnetic soft material-based planar actuator. A physics-based nonaffine material model is utilized to consider the inherent properties of polymer chain networks. The governing equation for dynamic motion is derived using Euler–Lagrange’s equation of motion for conservative systems. The devised dynamic model is utilized to examine the dynamic response, stability, periodicity, and resonance properties of a planar hard-magnetic soft actuator for different values of polymer chain entanglements, crosslinks, and finite extensibility parameters. The Poincaré maps and phase-plane plots are presented to analyze the stability and periodicity of the nonlinear vibrations of the actuator. The results reveal that transitions between aperiodic and quasi-periodic oscillations occur when the density of polymer chain entanglements and cross-linking changes. The findings from the present investigation can serve as an initial step towards the design and manufacturing of remotely controlled actuators for various futuristic applications.

A multiscale phase field fracture approach based on the non-affine microsphere model for rubber-like materials

Rubber-like materials have a broad scope of applications due to their unique properties like high stretchability and increased toughness. Hence, computational models for simulating their fracture behavior are paramount for designing them against failures. In this study, the phase field fracture approach is integrated with a multiscale polymer model for predicting the fracture behavior in elastomers. At the microscale, damaged polymer chains are modeled to be made up of a number of elastic chain segments pinned together. Using the phase field approach, the damage in the chains is represented using a continuous variable. Both the bond stretch internal energy and the entropic free energy of the chain are assumed to drive the damage, and the advantages of this assumption are expounded. A framework for utilizing the non-affine microsphere model for damaged systems is proposed by considering the minimization of a hypothetical undamaged free energy, ultimately connecting the chain stretch to the macroscale deformation gradient. At the macroscale, a thermodynamically consistent formulation is derived in which the total dissipation is assumed to be mainly due to the rupture of molecular bonds. Using a monolithic scheme, the proposed model is numerically implemented and the resulting three-dimensional simulation predictions are compared with existing experimental data. The capability of the model to qualitatively predict the propagation of complex crack paths and quantitatively estimate the overall fracture behavior is verified. Additionally, the effect of the length scale parameter on the predicted fracture behavior is studied for an inhomogeneous system.

Dual policy iteration-reinforcement learning to optimize the detection quality of passive remote sensing device

This paper presents the basic content of a Dual policy iteration algorithm (DPIA) based on reinforcement learning and proves the local convergence, global convergence, and optimality of “r – iteration” and “k – iteration”. The process of capturing information by remote sensing device is reversely transformed into the absorption of the captured information to the electric energy carried by the device, and the equivalent electric energy flow model is obtained accordingly. Based on this model, it is further transformed into a nonlinear non-affine model. A discrete-time index-cost function is also proposed based on the quality of information captured by various sensors. Finally, a kind of passive remote sensing device considered a virtual self-powered device, which can detect 16 kinds of information, has been simulated, and the effectiveness of the algorithm can be proved.

A model for rubber-like materials with three parameters obtained from a tensile test

Based on our recent findings on the chains orientational distribution in deformed rubber-like materials, we present a novel, accurate and simple non-affine model for isotropic, incompressible polymers. The model has only three material parameters that are easily calibrated from the characteristic behaviour of a tensile test: the initial slope, the slope of the mid-range, and the locking stretch. Once calibrated, the proposal reproduces accurately the behaviour of the material under the general deformation states for moderately large stretches measured by Kawabata (rubber) and Kawamura (silicone), and at least for three deformation states approaching the locking behaviour (Treloar’s tests on rubber).

Extremum Options Pricing of Two Assets under a Double Nonaffine Stochastic Volatility Model

In this paper, we consider the pricing problem for the extremum options by constructing a double nonaffine stochastic volatility model. The joint characteristic function of the logarithm of two asset prices is derived by using the Feynman–Kac theorem and one‐order Taylor approximation expansion. The semiclosed analytical pricing formulas of the European extremum options including option on maximum and option on minimum of two underlying assets are derived by using measure change technique and Fourier transform approach. Some numerical examples are provided to analyze the pricing results of extremum options under affine model, nonaffine model, Black–Scholes model, and the influences of some model parameters on the option. Numerical results show that the analytical pricing formulas have higher computational efficiency and accuracy than those of Monte Carlo simulation method. Also, results of sensitivity analysis report that the nonaffine models are more effective than other existing models in capturing the effect of volatility on option pricing.

Analytical approximation of European option prices under a new two-factor non-affine stochastic volatility model

<abstract><p>In this paper, the pricing of European options under a new two-factor non-affine stochastic volatility model is studied. In order to reduce the computational complexity, we use the Taylor expansion and Fourier-cosine method to derive an analytical approximation formula for European option prices. Numerical experiments prove that the proposed formula is fast and efficient for pricing European options compared with Monte Carlo simulations. The sensitivity of the parameters is analyzed to explain the rationality of the model. Finally, we present some preliminary empirical analysis revealing that the pricing performance of our proposed model is superior to that of the single-factor model.</p></abstract>

Non-fragile tracking control of constrained Waverider Vehicles with readjusting prescribed performance

The purpose of this article is to solve the fragile problem of prescribed performance control (PPC) with application to Waverider Vehicles (WVs). By fragile problem, it denotes that tracking errors may break away from prescribed funnels if actuators are saturated. Firstly, we propose a new type of readjusting prescribed performance which adaptively readjusts its prescribed funnels such that the spurred transient performance and steady-state performance are still guaranteed for tracking errors in the presence of actuator saturation. Then, we extend the finite-time PPC into the non-affine model of WVs, ensuring that tracking errors always evolve within prescribed funnels. Furthermore, the improved back-stepping procedure without the derivation of virtual control law is utilized to develop non-fragile tracking controllers, and specially, there is no need of any fuzzy/neural approximation, avoiding the computational burden problem. Finally, compared simulation results are presented to verify the effectiveness and advantage.

Berry–Esseen inequalities for the fractional Black–Karasinski model of term structure of interest rates

Abstract The Black–Karasinski model is a one-factor non-affine interest rate model as it describes interest rate movements driven by a single source of randomness and the drift function is a nonlinear function of the interest rate. The drift parameters represent the level and the speed of mean reversion of the interest rate. It belongs to the class of no-arbitrage models. The paper introduces some new approximate minimum contrast estimators of the mean reversion speed parameter in the model based on discretely sampled data which are efficient and studies their asymptotic distributional properties with precise rates of convergence.

A novel neural prescribed performance control design for constrained flexible hypersonic vehicles with compensation system

In this study, a novel prescribed performance function and auxiliary system are investigated for the constrained flexible hypersonic vehicles. The non-affine model of hypersonic vehicles is decomposed into velocity and altitude dynamic systems. For the velocity one, the adaptive neural prescribed controller is devised to guarantee that the tracking error converges to an arbitrary small compact. Then, the altitude dynamics subsystem is delivered as a pure feedback non-affine pattern, which gets the controller out of the dependence on precise affine model. On this premise, the exploited prescribed performance mechanism can not only avoid obtaining the initial sign of tracking error in advance but also can be employed in solving the problem that the conventional prescribed performance function could not cover the tracking error when the altitude subsystem is input constraint. And a Nussbaum-type function is employed to handle the control direction. Meanwhile, the controller utilizes a new auxiliary compensation algorithm to pursue the stable situation for the input restricted system. In order to cut down the computational burden, neural networks employ the min-learning parameter theory to approximate uncertainties in the subsystems. Finally, the simulation results convey that the presented approach has a superior dynamic and steady-state performance.

Fuzzy model-based disturbance rejection control for atomic force microscopy with input constraint

Accurate representation of the atomic force microscopy (AFM) system is not only necessary to achieve control objectives, but it is also beneficial for detecting the nanomechanical properties of the samples. To this end, this paper addresses the issue of controller design for the AFM system based on an accurate nonaffine nonlinear distributed-parameters model in which flexibility and distributed mass effects of the microcantilever beam are considered properly. First, a T-S fuzzy model is derived for this dynamical model of the AFM system in order to simplify the procedure of controller design. Then, a fuzzy model-based controller is designed to suppress the chaos and attenuate the disturbance in the AFM system through the linear matrix inequality (LMI) formulation. Moreover, by considering some criteria for disturbance rejection and transient performance, and some constraints on control input and states, new stabilization conditions are proposed based on a fuzzy Lyapunov function. Finally, simulation results are represented to demonstrate the effectiveness of the proposed method.

Optimal controller design for non-affine nonlinear power systems with static var compensators for hybrid UAVs

A generalized non-affine nonlinear power system model is presented for a single machine bus power system with a Static Var Compensator (SVC) or State Var System (SVS) for hybrid Unmanned Aerial Vehicles (UAVs). The model is constructed by differential algebraic equations on the MATLAB-Simulink platform with the programming technique of its S-Function. Combining the inverse system method and the Linear Quadratic Regulation (LQR), an optimized SVC controller is designed. The simulations under three fault conditions show that the proposed controller can effectively improve the power system transient performance.

An analytical approximation formula for European option prices under a liquidity-adjusted non-affine stochastic volatility model

<abstract><p>In this paper, we investigate the pricing of European options under a liquidity-adjusted non-affine stochastic volatility model. An analytical European option pricing formula is successfully derived with the COS method, based on an approximation for the characteristic function of the underlying log-asset price. Numerical analysis reveals that our results are very efficient and of reasonable accuracy, and we also present some sensitivity analysis to demonstrate the effects of different parameters on option prices.</p></abstract>

Effect of Concentration of Ion in the Solution on the Deformation Behavior of Gel under Simple Tension

Elastomeric gels are soft-elastic materials consisting of a three-dimensional cross-linked polymer network and liquid filling the space among such network. To take advantage of the swelling-deformation behavior of elastomeric gel and explore its possibility for applications in engineering as a structural member, the effect of concentration of ion in the solution on the deformation behavior of gel should be clarified, especially when the gel is loaded inside the solution. In this study, we at first proposed a nonaffine model for the elastomeric gel to account for the change of the entangling structure of polymer chains during the swelling-deformation process, in which the change of the number of polymer chains per unit volume N is depending on the first invariant of right Cauchy-Green deformation tensor I1. And then, the simple tensional deformation behavior of gel is calculated when the gel is loaded inside the solution with different concentration of ion. The results show that the nonaffine model can reproduce the experimental results very well. Moreover, the high concentration of ion leads to the high deformation resistance.

On a convergent power series method to price defaultable bonds in a Vasicek-CIR model

In this paper, we prove that the price of a defaultable bond, under a Vasicek short rate dynamics coupled with a Cox-Ingersoll-Ross default intensity model, is a real analytic function, in a neighborhood of the origin, of the correlation parameter between the Brownian motions driving the processes, used to express the dependence between the short rate and the default intensity of the bond issuer. Employing conditioning and a change of numéraire technique, we obtain a manageable representation of the bond price in this non-affine model which allows us to control its derivatives and assess the convergence of the series. By truncating the expansion at the second order, a quadratic approximation formula for the price is then provided. Finally, practical applications of the result are highlighted by performing a numerical comparison with alternative pricing methodologies.

Deformation of Molecular Chain's Network Structure of Spherical Gel under Quasi-static Compressive Loading Condition

Elastomeric gels are soft-elastic materials consisting of a three-dimensional crosslinked polymer network and liquid filling the space among such network. To take advantage of the swelling-deformation behavior of elastomeric gel and explore its possibility for applications in engineering as a structural member, investigations on the swelling-deformation behavior under various loading conditions are indispensable. Therefore, in this study, we at first proposed a nonaffine model for the elastomeric gel to account for the change of the entangling structure of polymer chains during the swelling-deformation process, in which the change of the number of polymer chains per unit volume N is depending on the first invariant of right Cauchy-Green deformation tensor I1. And then, to investigate the effect of the nonaffine movement of the polymer chain on the mechanical behavior of the elastomeric gel, we performed a FEM simulation for a spherical gel under quasi-static compressive loading condition. The results show that the swelling-deformation behavior of the spherical gel is quite different at the positions such as the polar, the equator or the center of the sphere.

Static and dynamic instability modeling of electro-magneto-active polymers with various entanglements and crosslinks

Electro-magneto-active (EMA) polymers-based smart actuators suffer from electro-magneto-mechanical instability (EMMI) phenomena arising due to the positive feedback between the applied electric and magnetic fields and reduction in the polymer thickness. This work presents a theoretical investigation of EMMI phenomena of an EMA polymeric actuator in both static and DC dynamic modes of operation. A physics-based non-affine material model is adopted here for capturing the effect of the polymer chain entanglements and crosslinks on the instability phenomena. Simultaneously, a computationally efficient energy approach for obtaining the DC dynamic instability parameters is constructed, which depends on the energy balance at the position of maximal overshoot in an oscillation cycle. The findings from the current study illustrate the trends of variation in the deformation, electric field, and magnetic field at the onset of static and dynamic EMMI with the polymeric entanglements and crosslinks parameters. It is observed that large entanglements and crosslinks in polymer chains improve the stable operation travel range, which positively impacts the actuator performance.