Nonlinear Modeling Techniques Research Articles

Multi-level nonlinear modeling verification scheme of RC high-rise wall buildings

Earthquake-resistant reinforced concrete (RC) high-rise wall buildings are designed and detailed to respond well beyond the elastic range under the expected earthquake ground motions. However, despite their considerable section depth, in terms of analysis, RC walls are still often treated as linear elements, ignoring the effect of deformation compatibility. Due to the limited number of available comprehensive experimental studies on RC structural wall systems subjected to cycling loading, few in-depth analytical verification studies have been conducted. Motivated by the increasing need for more accurate seismic risk assessment of high-rise buildings in multi-scenario seismic regions, a multi-level nonlinear modeling verification scheme is presented in this paper to investigate two different nonlinear modeling techniques for shear walls (2- and 4-noded fiber-based elements). The investigated modeling approaches and their key parameters are verified against the results of Phase I of uniaxial shaking table specimen tests (performed at the University of California, San Diego) on a seven-story full-scale RC shear wall structure under base excitations representing four earthquake records of increasing intensities. Three numerical models are created using two different tools (ZEUS-NL and PERFORM-3D). The results obtained from the numerical models are compared with the experimental results both on global and local response levels (top displacement, interstory drift, story shear force, story bending moment, period elongation and rebar tensile strain). The study reveals the superior performance of 4-noded fiber-based wall/shell element modeling approach in accounting for the 3D effects of deformation compatibility between lateral and gravity-force-resisting systems. The study also highlights the sensitivity of attained results to the stiffnesses assigned to the rigid links and 3D joints required to connect the shear walls to neighboring elements when a 2-noded element is used.

Seismic performance of three-storey full-scale sub-standard reinforced concrete buildings

Two three-story full-scale sub-standard reinforced concrete buildings were tested under self-weight and reversed cyclic lateral displacements to examine their behavior during earthquakes. While one of these buildings was a part of an actual existing building (TB1) built in the beginning of 1990’s in Istanbul, the other was constructed by the authors as a representative building (TB2) that reflects the most common structural deficiencies of existing building stock in Turkey. Both buildings were constructed with plain bars, low strength concrete and inadequate lateral reinforcement. The differences between these buildings were axial load levels of first story columns, expected location of major structural damages (weak beam–strong column for TB1 and strong beam–weak column for TB2) and connection details of longitudinal bars in columns at the foundation–column interface (continuous for TB1 and lap-spliced with 180° hooks for TB2). Both buildings were pushed and pulled at increasing displacement amplitudes up to near collapse well beyond the life safety performance level. While TB1 was damaged significantly at 1.5 % inter-story drift ratio, TB2 reached near collapse damage at 4.0 % inter-story drift ratio. In this paper, details and test results of these two sub-standard buildings are presented. In addition, the available nonlinear modeling techniques and performance predictions of the Turkish Seismic Design Code (Specification for the buildings to be constructed in disaster areas. Ministry of Public Works and Settlement, Ankara, 2007), ASCE 41-13 (Seismic rehabilitation of existing buildings, ASCE/SEI 41-13. ASCE, Reston, 2014) and Eurocode 8-3 (Eurocode 8: Design of structures for earthquake resistance. Part 3: Assessment and retrofitting of buildings. Comite Europeen de Normalisation, Bruxelles, 2005) are compared with the experimental results.

Effect of linear and non-linear blade modelling techniques on simulated fatigue and extreme loads using Bladed

There is a trend in the wind industry towards ever larger and more flexible turbine blades. Blade tip deflections in modern blades now commonly exceed 10% of blade length. Historically, the dynamic response of wind turbine blades has been analysed using linear models of blade deflection which include the assumption of small deflections. For modern flexible blades, this assumption is becoming less valid. In order to continue to simulate dynamic turbine performance accurately, routine use of non-linear models of blade deflection may be required. This can be achieved by representing the blade as a connected series of individual flexible linear bodies - referred to in this paper as the multi-part approach. In this paper, Bladed is used to compare load predictions using single-part and multi-part blade models for several turbines. The study examines the impact on fatigue and extreme loads and blade deflection through reduced sets of load calculations based on IEC 61400-1 ed. 3. Damage equivalent load changes of up to 16% and extreme load changes of up to 29% are observed at some turbine load locations. It is found that there is no general pattern in the loading differences observed between single-part and multi-part blade models. Rather, changes in fatigue and extreme loads with a multi-part blade model depend on the characteristics of the individual turbine and blade. Key underlying causes of damage equivalent load change are identified as differences in edgewise- torsional coupling between the multi-part and single-part models, and increased edgewise rotor mode damping in the multi-part model. Similarly, a causal link is identified between torsional blade dynamics and changes in ultimate load results.

Criminal Careers: Discrete or Continuous?

Numerous empirical studies of criminal careers have made use of finite mixture modeling to analyze sequences of events such as crimes or arrests. This paper aims to demonstrate that the analysis of criminal careers can benefit from the use of alternative methods, including multilevel methods, and individual time series. We use multilevel nonlinear modeling and individual time series techniques to analyze artificial data as well as arrest histories for 3432 males released from the California Youth Authority in 1981 and 1986, and followed for several decades after release. Multilevel methods are capable of identifying discrete groups in longitudinal data. In the California Youth data set, we find little clear evidence of sharply discrete arrest trajectories. We recommend that researchers explore alternatives to finite mixture modeling when analyzing criminal career data.

Application Of Fuzzy Regression Model For Real Estate Price Prediction

Many studies have been conducted for modeling the underlying non-linear relationship between pricing attributes and price of property to forecast the housing sales prices. In recent years, more advanced non-linear modeling techniques such as Artificial Neural Networks (ANN) and Fuzzy Inference Systems (FIS) have emerged as effective techniques to predict the house prices. In this paper, we propose a fuzzy least-squares regression-based (FLSR) model to predict the prices of real estates. A comprehensive comparison studies in terms of prediction accuracy and computational complexity of ANN, Adaptive Neuro Fuzzy Inference System (ANFIS) and FLSR has been carried out. ANN has been widely used to forecast the price of real estates for many years while ANFIS has been introduced recently. On the other hand, FLSR is comparatively new. To the best of our knowledge, no property prices prediction using FLSR was developed until recently. Besides, a detailed comparative evaluation on the performance of FLSR with other modeling approaches on property price prediction could not be found in the existing literature. Simulation results show that FLSR provides a superior prediction function as compared to ANN and FIS in capturing the functional relationship between dependent and independent real estate variables and has the lowest computational complexity.

Real-Time Onboard Global Nonlinear Aerodynamic Modeling from Flight Data

Flight test and modeling techniques were developed to accurately identify global nonlinear aerodynamic models onboard an aircraft. The techniques were developed and demonstrated during piloted flight testing of an Aermacchi MB-326M Impala jet aircraft. Advanced piloting techniques and nonlinear modeling techniques based on fuzzy logic and multivariate orthogonal function methods were implemented with efficient onboard calculations and flight operations to achieve real-time maneuver monitoring, near-real-time global nonlinear aerodynamic modeling, and prediction validation testing in flight. Results demonstrated that global nonlinear aerodynamic models for a large portion of the flight envelope were identified rapidly and accurately using piloted flight test maneuvers during a single flight, with the final identified and validated models available before the aircraft landed.

Nonlinear mixed-effects branch diameter and length models for natural Dahurian larch (Larix gmelini) forest in northeast China

We developed the generalized branch diameter and length models using the multi-level nonlinear mixed-effects techniques for the natural Dahurian larch ( Larix gmelini ) forest in northeast China. Dahurian larch (Larix gmelini) is the most commercially cultivated timber species in northeastern China due to its ecological prevalence and its superior wood attribute. However, its timber quality was largely driven by the crown architecture, i.e., the number, size and distribution of branches. The majority of branch-level models in the literature are focused on planted forests, which have substantially different crown architecture than that grown in natural mixed forests. Therefore, the goal of this investigation was to develop branch diameter and length models for Dahurian larch that are grown in natural mixed forests. A multi-level nonlinear mixed-effects model technique, including the fixed-effects, random-effects, variance functions and correlation structures, was employed to develop the branch growth models. The results suggested that the cumulative branch diameter and length were both increased with the increases of branch depth into the crown. Diameter at breast height (DBH) had significant positive influences on the branch size; however, tree height (HT) produced negative influences on the branch size, i.e., larger DBH and smaller HT could lead to larger branch size. Model fitting and validation results confirmed that we should avoid developing over-complex models from the perspective of application. As for the branch diameter and length models in our study, addressing the stand and tree level effects as random component were quite reliable and accurate for predicting the branch growth process of Dahurian larch in northeastern China.

Memristor-based Lorenz hyper-chaotic system and its circuit implementation

To study the application of memristor in chaotic system, we employ the smooth continuous nonlinear flux-controlled memristor model and feedback control technique to design a hyperchaotic system based on the simplified Lorenz system. By using memristor as a positive feedback of the simplified Lorenz system, the dimensionless mathematical model is derived. The differences between the memristor-based chaotic system and ordinary chaotic system are then further studied. Firstly, the stable equilibrium and unstable equilibrium point sets of the system are analyzed theoretically, and it is found that the system has infinite equilibrium points including stable and unstable equilibrium points. The stable and unstable ranges of the system with different parameters are also determined. Theoretical analysis shows that the system has the same symmetry as the simplified Lorenz system. Thus the system has rich dynamical behaviors, such as limit cycle, chaotic attractor, and hyper-chaotic attractor. Secondly, by the methods of bifurcation diagram, Lyapunov exponent spectrum, Poincar section, and Spectral Entropy algorithm, the dynamical behaviors of the system are analyzed in detail. By calculating the Lyapunov exponent spectrum, the dynamical behaviors are studied and they change with system parameters and the initial conditions of memristor respectively. The maximum positive Lyapunov exponent of the memristor-based Lorenz hyperchaotic system is higher than that of the simplified Lorenz system, which indicates the memristor-based Lorenz hyperchaotic system is more complex. Further, we find all the complex dynamical behaviors to be coexisting with the infinite equilibrium sets, which is quite different from those of many ordinary hyper-chaotic systems. Meanwhile, we observe the attractors coexisting and state transition phenomenon in this system, caused by changing the initial conditions of the memristor. State transition phenomenon is then further studied by means of phase portraits and spectral entropy algorithm for the first time. Finally, by using operational amplifiers, diodes and other discrete components, we design an equivalent circuit of the smooth continuous nonlinear flux-controlled memristor model, and the equivalent circuit is used to design and realize the analog electronic circuit of the memristor-based Lorenz hyper-chaotic system. By using an analog oscilloscope, the phase portraits of hyper-chaotic attractor are observed clearly. The state transition phenomenon can also be seen using the oscilloscope. It is found that the circuit experimental results are in agreement with those of the theoretical analysis and numerical simulation. It verifies that the system is physically realizable, and lays a strong foundation for its applications in engineering. Next, we will try to investigate the chaotic secure communication based on this hyper-chaotic system.

Application of Chaos Theory in the Prediction of Motorised Traffic Flows on Urban Networks

In recent times, urban road networks are faced with severe congestion problems as a result of the accelerating demand for mobility. One of the ways to mitigate the congestion problems on urban traffic road network is by predicting the traffic flow pattern. Accurate prediction of the dynamics of a highly complex system such as traffic flow requires a robust methodology. An approach for predicting Motorised Traffic Flow on Urban Road Networks based on Chaos Theory is presented in this paper. Nonlinear time series modeling techniques were used for the analysis of the traffic flow prediction with emphasis on the technique of computation of the Largest Lyapunov Exponent to aid in the prediction of traffic flow. The study concludes that algorithms based on the computation of the Lyapunov time seem promising as regards facilitating the control of congestion because of the technique’s effectiveness in predicting the dynamics of complex systems especially traffic flow.

Nonlinear Finite Element Modeling of Composite Bridge Girders Strengthened with HM-CFRP Laminates

Steel composite beams with reinforced concrete deck which are generally used in bridges can be strengthened by high modulus of carbon fiber-reinforced polymer materials due to cross-sectional losses and increased traffic loads. Experimental studies on strengthened beams composed of concrete, epoxy and fiber-reinforced materials are not economical with respect to time and cost. Parametric studies over experimentally verified numerical models can be a solution for research studies when time and cost are at concern. Numerical modeling of four different materials to behave in composite manner as one structural element can be achieved by employing nonlinear finite element modeling techniques. This paper discusses the steps of creating a nonlinear finite element model with explicit dynamic methods to achieve the bending behavior of composite steel beams strengthened by high modulus of carbon fiber-reinforced polymers. The finite element model is verified with the results of three real tests conducted by the authors.

Tracking progress towards global drinking water and sanitation targets: A within and among country analysis

Global access to safe drinking water and sanitation has improved dramatically during the Millennium Development Goal (MDG) period. However, there is substantial heterogeneity in progress between countries and inequality within countries. We assessed countries' temporal patterns in access to drinking water and sanitation using publicly available data. We then classified countries using non-linear modeling techniques as having one of the following trajectories: 100% coverage, linear growth, linear decline, no change, saturation, acceleration, deceleration, negative acceleration, or negative deceleration. We further assessed the degree to which temporal profiles follow a sigmoidal pattern and how these patterns might vary within a given country between rural and urban settings. Among countries with more than 10 data points, between 15% and 38% showed a non-linear trajectory, depending on the indicator. Overall, countries' progress followed a sigmoidal trend, but some countries are making better progress and some worse progress than would be expected. We highlight several countries that are not on track to meet the MDG for water or sanitation, but whose access is accelerating, suggesting better performance during the coming years. Conversely, we also highlight several countries that have made sufficient progress to meet the MDG target, but in which access is decelerating. Patterns were heterogeneous and non-linearity was common. Characterization of these heterogeneous patterns will help policy makers allocate resources more effectively. For example, policy makers can identify countries that could make use of additional resources or might be in need of additional institutional capacity development to properly manage resources; this will be essential to meet the forthcoming Sustainable Development Goals.

RF Power Amplifier Behavioral Modeling [Book\/Software Reviews

This book describes the behavioral, or system-level, modeling of RF power amplifiers (PAs) for linearization. It provides a basic background and framework for the nonlinear, dynamical modeling of a PA. These nonlinear modeling techniques can be used to design the digital predistortion linearization algorithm. The author focuses on Volterra series methods to provide a good foundation for understanding how to handle the nonlinear behaviors and dynamic, or time-dependent, effects in the transmitter.

Finite element analysis of lidded flip-chip packages: A study on the impact of thermal interface material compressibility and stress-free conditions on modeling predictions

In this paper, we present the effects of assumptions made about the constitutive behavior of a cured, silicone gel type thermal interface material (TIM) and the package stress-free conditions on FEA modeling predictions. The focus will be on the deformations (or warpage) predicted by the models for lidded flip-chip packages. It is critical for such warpage predictions to be close to experimental measurements for accurate projection of mechanical stresses and strains in a package. Digital Image Correlation (DIC) warpage measurements on flip-chip modules are compared against the predicted values and the impact of above-mentioned assumptions will be discussed. It will be shown that the TIM mechanical and thereby, thermal degradation is a strong function of the TIM compressibility and stress-free condition assumptions. Bounds of non-linear elastic modeling technique for the TIM and guidelines for conducting numerical analysis for lidded flip-chip packages will be provided.

Flexure Hinge Mechanisms Modeled by Nonlinear Euler‐Bernoulli‐Beams

AbstractA flexure hinge is an innovative engineering solution for providing relative motion between two adjacent stiff members by the elastic deformation of an arbitrary shaped flexible connector. In the literature, modeling of compliant mechanisms incorporating flexure hinges is mainly focused on linear methods. However, geometrically nonlinear effects cannot be ignored generally. This study presents a nonlinear modeling technique for flexure hinges based on the Euler‐Bernoulli beam theory, in contrast to the predominant linear modeling approaches. Higher order beam elements of variable cross‐section are employed to model the flexure hinge region. A Newton‐Raphson scheme is applied to solve the resulting nonlinear system equations. The proposed approach reduces the overall degrees of freedom and is computationally efficient compared to commonly applied 3D finite element methods. A compliant displacement amplification mechanism is studied by means of the proposed method, where an excellent agreement with results of a reference solution is achieved. The modeling approach is suitable for the structural optimization of compliant mechanisms towards a less intuitive design process. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Analytical simulation of seismic collapse of RC frame buildings

Application of a fibre-element nonlinear modelling technique for seismic collapse capacity assessment of RC frame buildings in comparison with conventional lumped plasticity models is investigated in this paper. Constitutive material models of concrete and steel for fibre elements are adopted to enable simulation of the loss in vertical load carrying capacity of structural columns. Inclusion of the nonlinear second order P−Δ effects accelerated by degrading behaviour of steel and concrete materials in the fibre model allows prediction of the sidesway mode of collapse. The model is compared with nonlinear lumped plasticity models in which stiffness and strength degradation is replicated through degrading parameters in structural components. Static cyclic analyses of an example cantilever column and a portal frame indicate that the variation of axial loads in columns may result in accelerated degradation and failure of structural components which is not taken into account by lumped plasticity models. Moreover, incremental dynamic analysis of a ten-storey RC frame shows that the lumped plasticity model may overestimate building collapse capacity when vertical failure of structural components occurs prior to sidesway instability.

Fuzzy Logic Application for House Price Prediction

Various methods have been used previously to estimate housing sales prices to model the underlying non-linearity relation between housing attributes and the price of property. More advanced non-linear modelling techniques such as Artificial Neural Networks (ANN), Fuzzy Inference System (FIS) and Fuzzy Logic (FL) emerged recently to model the nonlinear relation between the independent variables and the price function. A new structured model for house prices prediction based on Fuzzy Logic is proposed. A fuzzy logic based regression model has proved to be effective to address many prediction problems used in business forecasting, marketing and insurance. This paper highlights the development of a theoretical formulation for sales price prediction through the utilisation of a fuzzy regression model by applying fuzzy logic and fuzzy inference system techniques. The results show favourable outputs which indicate superior prediction function when compared with ANN and FIS as well as indicate the fuzzy functional relationship between dependent and independent variables.

Example-based statistical framework for parametric modeling of human body shapes

This paper proposes a new example-based statistical modeling framework to conduct the parametric modeling of 3D human body shapes from linear anthropometric parameters. The modeling framework consists of the following three phases: construction of a training database of human body shapes, statistical analysis of human body shapes and human body shape modeling. In the training database construction phase, a consistent parameterization was carried out on 3D whole-body scan data of 80 males and 80 females with a wide variety of body shapes as the examples for this study. The surface-fitting process, which was improved relative to existing methods, was used to guarantee the high-quality parameterization in this phase and to generate an articulated body shape model in the modeling phase. To characterize the range of body shape variation, the training database was analyzed statistically. Additionally, a correlation between the body shapes and the anthropometric parameters was learned in the statistical analysis phase to estimate body shapes from intuitive and semantic parameters. A new technique to generate an optimal body shape model that precisely satisfies user input body dimensions was developed in the model generation phase. This technique enables the estimation of body shape variation, not only within the body shape space that was learned statistically, but also outside of the body shape space, while maintaining body shapes that stay in the human shape space. Our approach produced reasonable results having a high modeling accuracy satisfying user-specified anthropometric parameters, and high visual quality in expressing realistic body shapes. The resultant models were then segmented into 16 key regions of the human body, and had information on 15 key joints, and thus they could be a useful tool in various industries. Compared with other statistical modeling approaches, the proposed method contributes to related areas by introducing an improved surface-fitting process and a non-linear optimization-based optimal body shape modeling technique.

Predicting adsorption of aromatic compounds by carbon nanotubes based on quantitative structure property relationship principles

Quantitative structure property relationship (QSPR) models were developed to predict the adsorption of aromatic compounds by carbon nanotubes (CNTs). Five descriptors chosen by combining self-organizing map and stepwise multiple linear regression (MLR) techniques were used to connect the structure of the studied chemicals with their adsorption descriptor (K∞) using linear and nonlinear modeling techniques. Correlation coefficient (R2) of 0.99 and root-mean square error (RMSE) of 0.29 for multilayered perceptron neural network (MLP-NN) model are signs of the superiority of the developed nonlinear model over MLR model with R2 of 0.93 and RMSE of 0.36. The results of cross-validation test showed the reliability of MLP-NN to predict the K∞ values for the aromatic contaminants. Molar volume and hydrogen bond accepting ability were found to be the factors much influencing the adsorption of the compounds. The developed QSPR, as a neural network based model, could be used to predict the adsorption of organic compounds by CNTs.

Lithospheric structure of the Texas‐Gulf of Mexico passive margin from surface wave dispersion and migrated Ps receiver functions

AbstractThe seismic velocity structure beneath Texas Gulf Coastal Plain (GCP) is imaged by migrating Ps receiver functions with a seismic velocity model found by fitting surface wave dispersion. We use seismic data from a linear array of 22 broadband stations, spaced 16–20 km apart. A Common Conversion Point (CCP) stacking technique is applied to earthquake data to improve the S/N ratios of receiver functions. Using an incorrect velocity model for depth migration of a stacked CCP image may produce an inaccurate image of the subsurface. To find sufficiently accurate P and S‐velocity models, we first apply a nonlinear modeling technique to fit Rayleigh wave group velocity dispersion via Very Fast Simulated Annealing. Vs ranges from 1.5 km/s in shallow layers of the GCP to 4.5 km/s beneath the Llano uplift and just outboard of the Balcones Fault Zone (BFZ). The BFZ is characterized by slow velocities that persist to nearly 100 km depth. In the stacked image, the largest amplitude positive‐polarity event ranges from the surface, at the Llano uplift, to a maximum depth of ∼16 km beneath Matagorda Island. We attribute this event to the sediment‐basement contact, which is expected to produce a large impedance contrast. Another large‐amplitude and positive‐polarity event at ∼35 km depth, which likely marks the Moho, disappears outboard of the Luling Fault Zone. The disappearance of the Moho beneath the GCP may be due to serpentinization of the upper mantle, which would reduce the impedance contrast between the lower crust and upper mantle dramatically.

3D nonlinear transient field‐circuit modeling of inductive fault current limiters

SummaryDue to increasing levels of fault currents, fault current limiters (FCLs) are expected to play an important role in the protection of future power grids. Inductive saturable FCLs are particularly interesting due to their inherent reaction on the fault. Many different configurations have been proposed in literature. Being difficult or impossible to create accurate analytical models of some FCL configurations, the development of finite element (FE) models for inductive FCLs is required. This paper presents a 3D nonlinear transient FE modeling technique applied to two inductive FCLs, namely the so‐called open‐core and three‐leg single‐core FCLs. The models have been validated by comparing simulation results with lab measurements. Results show excellent agreement. The models constitute a valuable tool for design, optimization, and verification of inductive FCLs. Copyright © 2015 John Wiley & Sons, Ltd.