Nonlinear Path Research Articles

Titanium alloy microstructure fingerprint plots from in-process machining

Titanium alloy components require several machining stages of forged billets which are supplied in a range of annealing conditions. Generally, the machining performance is influenced by the heat treatment and changes in billet microstructures are often overlooked by tool manufacturers and machinists. Due to the non-linear strain path during primary forging, titanium alloy billets are anisotropic in nature and require ex-situ non-destructive evaluation (NDE) during the manufacturing stages to ensure excellent service performance, particularly in safety-critical aerospace components. In this study, the local analysis of the fluctuations presented in the force response during face-turning operations is directly linked to the billet heat treatment condition and presented as microstructure fingerprint plots. The evolution of cutting forces in four different billet conditions of the alpha + beta titanium alloy Ti–6Al–2Sn–4Zr–6Mo (Ti-6246) was measured. The magnitude and fluctuations in force were directly correlated to microstructural features derived from the heat treatments. In addition, local spatial high-resolution synchronization of the cutting forces was used to determine the effects of microstructure from the heterogeneous upstream forging process and subsequent heat treatment. These rapidly produced microstructure fingerprint plots are an important development step for providing manufacturers with an in-process machining NDE method: this will help to qualify material upstream prior to expensive secondary forging or finish machining stages.

A novel acoustic feedback compensation filter for nonlinear active noise control system

The acoustic feedback is widely seen in the active noise control (ANC) system for short acoustic duct such as the intake system of an automobile engine, which severely destabilizes the stability of the original ANC system. The conventional acoustic feedback compensation methods based on IIR filter can only be applied to the linear acoustic path and is not suitable for a nonlinear ANC (NANC) system. To solve this problem, this paper proposes a Volterra recursive even mirror Fourier nonlinear (VREMFN) filter, which can effectively suppress both linear acoustic feedback and nonlinear acoustic feedback in the NANC system. In this paper, we show the solutions for the linear acoustic feedback and nonlinear acoustic feedback of VREMFN and discuss its stability condition. Moreover, a new leaky normalized LMS algorithm is also developed to further improve the performance of NANC system based on VREMFN. Simulated results comparing IIR, Volterra and VREMFN based on parameter adaptive algorithm (PAA), FXLMS and FULMS show that the proposed VREMFN dramatically improves the noise reduction performance of NANC system both in linear acoustic feedback path and nonlinear acoustic feedback path. Furthermore, two experiments with different acoustic feedback paths also demonstrate the effectiveness of the proposed VREMFN.

Social and Economic Convergence Across Brazilian States Between 1990 and 2010

The present paper analyzes the convergence in economic and social terms across Brazilian states from 1990 to 2010. We argue that a more ample perspective is enlightening because income convergence does not necessarily go hand in hand with social convergence and income is not the only relevant aspect of well-being. Social convergence is captured by selected indicators, such as years of study, life expectancy at birth and the absence of crime. Using OLS, fixed effects and spatial dependence models, we find that GDP per capita has the highest dispersion across states and its absolute convergence is relatively slow. Social conditions, in contrast, have become considerably more equal and seem to converge towards a unique steady state at half-lives between 8 and 12 years. Absence of crime shows a peculiar behavior and a non-linear inconclusive convergence path.

Internal contact modeling for finite strain topology optimization

The present work proposes an extension of the third medium contact method for solving structural topology optimization problems that involve and exploit self-contact. A new regularization of the void region, which acts as the contact medium, makes the method suitable for cases with very large deformations. The proposed contact method is implemented in a second order topology optimization framework, which employs a coupled simultaneous solution of the mechanical, design update, and adjoint problems. All three problems are derived and presented in weak form, and discretized with finite elements of suitable order. The capabilities and accuracy of the developed method are demonstrated in a topology optimization problem for achieving a desired non-linear force-displacement path.

Disentangling the Drivers of Obesity: An Analytical Framework Based on Socioeconomic and Intrapersonal Factors.

Obesity is increasing at exponential rates in developed economies despite the numerous policy interventions being implemented. The causes of obesity are multifactorial demanding a holistic review for targeted intervention. This study, therefore, provides a holistic overview of multiple factors affecting body weights i.e., socioeconomic and intrapersonal factors. We used data from a household and experimental survey carried out in Spain (Barcelona) in 2014. A non-linear path analysis was used considering the non-linear relationships that might exist between these factors and body weight. Results confirm non-linear relationships between some socioeconomic, intrapersonal factors and body weight. Among the intrapersonal factors, obesity is directly influenced by volitional control of obesity, attitude toward obese persons, holding a correct body image and body image dissatisfaction. Socioeconomic factors that have significant influence on obesity were age, education and gender. Risk attitudes do not correlate with obesity.

Urban ecological risk transmission model based on Bayesian network

Simulating this ecological risk transmission process helps to judge the key path and propose the accurate urban risk control measures. This paper develops an urban ecological risk transmission conceptual framework based on Bayesian Network to quantify the non-linear transmission paths via HA (human activity) — ES (ecosystem service) — ER (ecological risk). Ecosystem services are used as ecological risk measurement endpoints to quantify service provision and possible adverse effects from human activities. Direct and indirect impacts of urban human activities that threaten ecosystem services were considered. Nine cities in the Pearl River Delta (China) are selected as a case to simulate the ecological risk transmission process. Results show that: (1) Zhongshan and Guangzhou tied for the city most at ecological risk and Foshan jumped to the city with the highest ecological risk after considering the impact of pollution; (2) After analyzing the sensitive of human activities to ecological risks, the key risk transmission path of each city can be judged. There are three types of key paths: pollution dominant path (including Guangzhou, Foshan, Dongguan and Zhuhai), ES dominant path (including Shenzhen, Zhongshan and Jiangmen) and dual dominant path (including Zhaoqing and Huizhou); (3) Buildup area, afforestation area and wetland protection & restoration investment are the top three key human activities that impact the urban ecological risk. Adjusting these key variables can be simulated to effectively reduce the urban ecological risk. The model can be used as a useful tool to guide policy and risk management decisions, and to engage and negotiate with stakeholders with different views.

Investigation on the forming limit diagram of AA5754-O alloy by considering strain hardening model, strain path, and through-thickness normal stress

This study clarified the effects of the chosen hardening model, through-thickness normal stress, and non-linear strain path on the precision of forming limit diagram (FLD). The Marciniak-Kuczynski (M-K) instability theory was employed to calculate the FLD of AA5754-O based on the different hardening models. Swift, Voce, modified Voce, Kim-Tuan, and modified Kim-Tuan hardening models were adopted to predict the forming limits, and their constant parameters were presented. Predicted FLDs indicate that modified Kim-Tuan has a better agreement with experimental data than other models. After that the influences of through-thickness normal stress on the forming limit diagram were examined. The three-dimensional stress state was converted to plane-stress condition according to the assumption that hydrostatic stress is ineffective on the plastic deformation. The results show that formability improves when normal stress increases. However, the effect of the normal stress on FLD for various hardening models is different. Due to the complexity of sheet metal forming, the strain path of the material may change during the deformation process. The results indicated that strain path has a significant effect on the FLD, and the path dependence of the forming limit stress diagram (FLSD) will be examined in detail. Finally, the forming limits were computed to analyze the effect of the normal stress on the non-linear loading path deformation. It was observed that by increasing the amount of pre-strain, the effect of the normal stress on the formability will diminish. Moreover, results showed that normal stress will affect the path dependence of the FLSD.

Anneal-path correction in flux qubits

Quantum annealers require accurate control and optimized operation schemes to reduce noise levels, in order to eventually demonstrate a computational advantage over classical algorithms. We study a high coherence four-junction capacitively shunted flux qubit (CSFQ), using dispersive measurements to extract system parameters and model the device. Josephson junction asymmetry inherent to the device causes a deleterious nonlinear cross-talk when annealing the qubit. We implement a nonlinear annealing path to correct the asymmetry in situ, resulting in a substantial increase in the probability of the qubit being in the correct state given an applied flux bias. We also confirm the multi-level structure of our CSFQ circuit model by annealing it through small spectral gaps and observing quantum signatures of energy level crossings. Our results demonstrate an anneal-path correction scheme designed and implemented to improve control accuracy for high-coherence and high-control quantum annealers, which leads to an enhancement of success probability in annealing protocols.

Large deformation behavior of functionally graded porous curved beams in thermal environment

The in-plane thermoelastic response of curved beams made of porous materials with different types of functionally graded (FG) porosity is studied in this research contribution. Nonlinear governing equations are derived based on the first-order shear deformation theory along with the nonlinear Green strains. The nonlinear governing equations are solved by the aid of the Rayleigh–Ritz method along with the Newton–Raphson method. The modified rule-of-mixture is employed to derive the material properties of imperfect FG porous curved beams. Comprehensive parametric studies are conducted to explore the effects of volume fraction and various dispersion patterns of porosities, temperature field, and arch geometry as well as boundary conditions on the nonlinear equilibrium path and stability behavior of the FG porous curved beams. Results reveal that dispersion and volume fraction of porosities have a significant effect on the thermal stability path, maximum stress, and bending moment at the crown of the curved beams. Moreover, the influence of porosity dispersion and structural geometry on the central radial and in-plane displacement of the curved beams is evaluated. Results show that various boundary conditions make a considerable difference in the central radial displacements of the curved beams with the same porosity dispersion. Due to the absence of similar results in the specialized literature, this paper is likely to provide pertinent results that are instrumental toward a reliable design of FG porous curved beams in thermal environment.

A computational framework for multi-stability analysis of laminated shells

The multi-stability of composite shells often exhibits complex mechanical behaviors, accompanied by large deformation, strong nonlinearity and multiple equilibrium branches. We present a numerical framework for stability analysis of laminated composite shells, which is capable of efficiently computing nonlinear equilibrium paths and critical points, and effectively assessing the stability of the structure’s equilibrium. The computational framework is applied to investigate several multi-stability problems in cylindrical laminated shells. Good agreement is observed even in an “extreme” experimental case where the multi-stability is highly sensitive, and it is found that the precise approximation of the strain energy is crucial for accurate prediction of shell stability. This study is believed to provide a powerful alternative to other methods for the stability analysis and the design of advanced composite shell structures.

Formability enhancement of 5052 aluminium alloy sheet in electromagnetic impaction forming

Electromagnetic impaction forming of 5052 aluminium alloy sheets using a V-shaped die and a conical die was performed. The conventional quasi-static forming limit curve (QS-FLC) is obtained according to the linear loading condition, which can only describe linear strain paths. However, it cannot accurately evaluate the formability of electromagnetic impaction forming, especially strain paths that have become highly non-linear. In this study, the formability of electromagnetic impaction forming, which considers a bilinear strain path and a continuous highly non-linear strain path, was investigated. The conventional QS-FLC is no longer suitable to evaluate the formability of electromagnetic impaction forming. Therefore, modified FLCs were established in strain space that follow bilinear strain paths and continuous non-linear strain paths. The actual formability improvement was compared with the modified FLC. The maximum safe strain of bilinear strain paths near the sidewall of V-shaped specimens increased in formability by approximately 30% at the discharge voltage of 20 kV compared with conventional QS forming. The maximum safe strains near the apex of the conical specimens increased in formability by approximately 100% at the same discharge energy. It should be noted that the increase in formability above the modified FLC is a conservative estimate, because the limit strains at the necking location were not known in the electromagnetic impaction forming. The influencing factors of the formability improvement of 5052 aluminium alloy sheet in electromagnetic impaction forming were also discussed.

Nonlinear output path following control using a two-loop robust model predictive control approach

In this paper, output tracking of a geometric path for a nonlinear uncertain system with input and state constraints is considered. We propose an enhanced two-loop model predictive control approach for output tracking of a nonlinear uncertain system. Additionally, we propose an optimal version of output path following control problem to improve the controller synthesis. Satisfaction of the dynamical constraints of a system such as velocity, acceleration and jerk limitations is added to the problem introducing a new augmented system. The recursive feasibility of the proposed method is demonstrated, and its robust stability is guaranteed such that relaxation on the terminal constraint and penalty are achieved. To validate the theoretical benefits of the proposed controller, it is simulated on a SCARA robot manipulator and the results are compared with a two-loop model predictive controller successfully.

Nonlinear Feedback-Based Path Following Control for Underactuated Ships via an Improved Compound Line-of-Sight Guidance

To promise the high fidelity of path following control for the underactuated ship from the aspect of the nautical practice, this paper develops a nonlinear feedback-based control scheme with an improved compound line-of-sight (ICLOS) guidance law, which has the energy-saving and efficient performance. Based on the methodology of the nonlinear disturbance observer and method of reduced-order extended state observer (ESO), a reduced-order state nonlinear sideslip angle observer is developed for online estimation of the time-varying sideslip angel caused by external disturbances, and a sideslip angle controller is incorporated to avert the sharp acting of actuators. Meanwhile, unlike the traditional line-of-sight (LOS) guidance law, a time-varying lookahead distance is designed as a function that relates to the ship' cruising speed and the cross track error, while the advance steering distance is also variable responding to the ship's length and turning angle, both of them make the turning process smoother. In the control scheme, the second-order closed-loop gain shaping algorithm (CGSA) is employed to design a concise robust controller, where the fuzzy logic system (FLS) is introduced to adjust the integral coefficient online to improve the transient performance. In addition, to further reduce the steering frequency and energy consumption of the system, nonlinear feedback technology (NFT) is adopted. Numerical simulation and comprehensive comparisons are conducted to demonstrate the remarkable performance and superiority of the proposed path following control system.

Fused Deposition Modeling of an Aircraft Wing using Industrial Robot with Non-linear Tool Path Generation

Fused Deposition Modelling (FDM) is an additive manufacturing process to build 3D objects on a horizontal plane from bottom to top. In the conventional FDM process, the printing of curved objects causes the staircase effect and results in poor surface finish. In this work, the FDM process integrated with a 6-DOF Industrial robot is used to print the curved objects by generating non-linear tool paths to avoid the staircase effect. A standard NACA 0015 aircraft wing having curved surfaces is printed without staircase effect at a uniform deposition rate using an industrial robot. The wing is sliced into concentric curved layers either in the form of convex or a concave shape. A new methodology is developed by combining the non-linear toolpaths with the change in extruder orientation to print curved objects at a uniform deposition without any staircase effect. ABB Robotstudio simulation software is used for simulating the printing process and simulation results are validated by printing the portion of the wing using the Industrial robot with an FDM extruder as an end effector. The experimental results showed that the aircraft wing is printed successfully with uniform deposition at constant velocity without any staircase effect.

Training nonlinear elastic functions: nonmonotonic, sequence dependent and bifurcating.

The elastic behavior of materials operating in the linear regime is constrained, by definition, to operations that are linear in the imposed deformation. Although the nonlinear regime holds promise for new functionality, the design in this regime is challenging. In this paper, we demonstrate that a recent approach based on training [Hexner et al., PNAS 2020, 201922847] allows responses that are inherently non-linear. By applying designer strains, a disordered solid evolves through plastic deformations that alter its response. We show examples of elaborate nonlinear training paths that lead to the following functions: (1) frequency conversion, (2) logic gate and (3) expansion or contraction along one axis, depending on the sequence of imposed transverse compressions. We study the convergence rate and find that it depends on the trained function.

Optimal Output-Constrained Active Noise Control Based on Inverse Adaptive Modeling Leak Factor Estimate

Output saturation, mainly caused by the power amplifier, is a critical issue influencing the performance and stability of an adaptive system, such as in active noise control. In this paper, a quadratically constrained quadratic program (QCQP) is defined to achieve optimal control under the averaging-output-power constraint, which ensures the output of the system operates linearly and hence, avoids the output saturation. To solve this QCQP problem recursively in practice, this paper utilizes one of the leaky-based filtered-x least mean square algorithm with an optimal leak factor. However, this method only can be applied when the statistical feature of the control signal with maximum output-power is known, which is difficult to obtain in practice. Hence, by incorporating the adaptive inverse modeling technique, we can derive a practical estimation of the optimal leaky factor, which is applicable to different noise types. Furthermore, as the optimal output-constraint control forces the output to operate linearly, the nonlinear amplifier model is not required for the leak factor estimate. The simulation of the proposed algorithm is carried out on measured nonlinear paths to validate its efficacy.

Horizontal Nonlinear Path Following Guidance Law for a Small UAV With Parameter Optimized by NMPC

In this study, the problem of guiding a small fixed-wing unmanned aerial vehicle (UAV) toward a predefined horizontal path is studied. A stable nonlinear guidance law, which is a function of the inertial positions and velocities of the UAV and the predefined path, is designed using Lyapunov stability arguments. The concept of the nonlinear model predictive control (NMPC) technique was applied to optimize a key parameter of the guidance law to improve the performance of the controller (PFC_NMPC), where the stability of the relative nonlinear system is maintained. The proposed method was verified in the MATLAB/Simulink environment to realize following the straight-line, square and circular paths. The path- following performance of the proposed method is compared with those of the guidance laws with parameter fixed (PFC) or tuned by fuzzy logic (PFC_FL). With the predictive ability, the proposed method can make the UAV fly more on the desired square and circular paths than the other two methods, PFC and PFC_FL. The error overshoot by using PFC_NMPC is much smaller than those by using the PFC and PFC_FL methods in the presence of wind at 8m/s.

Strategic Investment in an International Infrastructure Capital: Nonlinear Equilibrium Paths in a Dynamic Game between Two Symmetric Countries

This paper develops a two-country model of intra-industry trade with trade costs that can be reduced by public investment in an international infrastructure capital, the stock of which accumulates over time. Depending on the trade costs and international distribution of manufacturing firms, equilibrium patterns of trade are determined, and national welfare in each country is affected by these trade patterns. Taking into account the relationship between trade costs and national welfare, the governments carry out a dynamic game of public investment. We show that the dynamic equilibrium of the policy game may exhibit history dependency; if the initial stock of international infrastructure is smaller (larger) than a threshold level, the infrastructure stock decreases (increases) over time, and the world economy will end up in autarky (two way free trade) in the long run. We also show that international cooperation is beneficial in the sense that it may enable the world economy to escape from a “low development trap”.

Thermal Postbuckling of Temperature-Dependent Functionally Graded Nanocomposite Annular Sector Plates Reinforced by Carbon Nanotubes

In this study, the thermal buckling and postbuckling of functionally graded (FG) nanocomposite annular sector plates reinforced by carbon nanotubes (CNTs) are numerically analyzed. The effective material properties of FG nanocomposite are temperature-dependent (TD) and evaluated via the modified micromechanical method and rule of mixture. Based on the higher-order shear deformation theory (HSDT) and using the principle of virtual work and variational differential quadrature (VDQ) approach, the unified weak form of discretized nonlinear governing equilibrium equations is derived. Then, by using the linear part of equations and solving the derived eigenvalue problem, the critical temperature rise and associated mode shapes are obtained, which are used as the initial guess in solving the nonlinear thermal postbuckling problem. The pseudo-arc-length method and an iterative solver are employed to obtain the nonlinear thermal postbuckling equilibrium path of the FG nanocomposite annular sector plates. The influences of geometrical parameters, boundary conditions (BCs), CNT volume fraction, and CNT distribution pattern on the critical temperature rise and thermal postbuckling behavior of the FG nanocomposite annular sector plates are evaluated and discussed. Also, comparisons are made between the results considering the TD and temperature-independent (TID) properties. It is demonstrated that for higher values of sector angle, the effect of sector angle on the critical temperature rise and thermal postbuckling path is negligible. Moreover, by increasing the sector angle, the effect of BCs of straight edges vanishes, and the critical temperature rise and thermal postbuckling curves of for BCs of CSCS and SCSC approach those for CCCC and SSSS ones.

Isogeometric nonlinear bending and instability analysis of cylindrical composite shells reinforced with graphene platelets

In the present study, by using IGA (isogeometric analysis) method, the nonlinear bending and instability behavior of cylindrical composite shells embedded with GPLs (graphene platelets) having functional gradation is investigated. In IGA, NURBS functions are employed both to construct the geometry and to approximate the field variables. Advantages of adopting IGA include: the exact geometrical description, high accuracy and efficacy, higher-order smoothness. The nonlinear equations of equilibrium are derived via the virtual work principle on the basis of a higher-order shell theory with the large deflection. A solution procedure in which the arc length method is modified and exploited in combination with the modified Newton-Raphson method for the highly nonlinear problem is designed to trace accurately the nonlinear equilibrium path that encompasses the snap-through and snap-back phenomena. Four patterns of the GPL dispersions are prepared: uniform, O-type, X-type and A-type, and evenly distributed and central point loadings are considered. The proposed IGA approach is evidenced to successfully capture the complete nonlinear equilibrium path of the composite shell under flexure. The further parametric examinations that follow to highlight the impacts of the loading and constraint conditions, GPL weight fraction, reinforcement schemes and shell geometric parameter on the nonlinear bending and instability responses.