Nonlinear Macromodel Research Articles

A nonlinear macromodel for simulating the in-plane behavior of unreinforced masonry (URM) infilled frames

A nonlinear macromodel for simulating the in-plane behavior of unreinforced masonry (URM) infilled frames

A Nonlinear Macro-Model for the Analysis of Monotonic and Cyclic Behaviour of Exterior RC Beam-Column Joints

The study presents a numerical investigation on exterior reinforced concrete (RC) beam-column joints under seismic actions based on a macro-modelling approach proposed by the authors in a recent paper. The followed approach makes use of the well-known “scissors model” where two nonlinear rotational springs arranged in series were introduced to schematize the shear behavior of the joint panel and, moreover, the possible occurrence of the debonding of longitudinal steel rebars at the beam-joint interface. In this paper, the scissor model is employed in the context of a novel predictive approach with the twofold objective to: 1) develop a new model for the estimate of the maximum shear strength of RC joints by performing a multivariate linear regression analysis on a set of experimental tests and, 2) define a new multilinear backbone joint shear stress-strain law to be assigned to one of the mentioned springs. In particular, the identification of the shear strain parameters is obtained by performing a sensitivity analysis in which a number of monotonic load-drift numerical curves are derived by varying the strain values in ranges opportunely a-priori defined and compared with the experimental ones to investigate their accuracy. Finally, cyclic analyses on RC joints collected in the experimental database are carried out by considering the backbone joint shear stress-strain law identified in the calibration process. The analyses are performed by using the nonlinear open-source finite element platform, OpenSees, in which the “pinching4” uniaxial material model, available in the software library, is implemented to set the parameters governing the hysteresis rules and pinching effect. To this purpose, five literature proposals suggesting the values to use for such parameters are taken into account and their assessment is presented in the paper. The obtained outcomes have allowed, on the one hand, to identify the proposal providing the best numerical simulations of the experimental results and, on the other end, to draw useful indications on how to further improve the cyclic modelling by opportunely modifying the setting of the “pinching4” material model parameters.

Quantitative assessment of nonlinear macro-models for global behavior and design of planar RC walls

Performance-Based Seismic Design (PBSD) procedures require adequate estimation of the global cyclic force–displacement (F-D) behaviors of the primary lateral load-resisting elements. As reinforced concrete (RC) walls constitute one of the most widely used lateral load elements in building construction, several nonlinear analytical modeling approaches have been developed over the past several decades to numerically simulate the hysteretic behavior of these structures. However, comparisons between these models have often provided few details on the model input parameters, have not used consistent model discretization, and have assessed hysteretic predictions more qualitatively than quantitatively. Accordingly, the objectives of this paper are to: 1) provide detailed information on the modeling parameters used to simulate the cyclic lateral F-D behavior of a set of planar RC walls with flexure-dominant as well as shear-dominant behaviors, 2) evaluate the sensitivity of the F-D curves to different wall model discretizations applied consistently between different models, and 3) propose and use a new quantitative approach to assess the hysteretic behaviors predicted by the numerical models. The considered models are PERFORM 3D, MVLEM, SFI-MVLEM, and BTM. To represent the information that is typically known during the design of a structure, the nonlinear modeling parameters were limited to the wall geometry, reinforcing layout, concrete compression strength, and reinforcing steel yield strength, with no calibration of the material behaviors to the reported test results. A total of 2,300 analyses were performed to simulate four slender and four squat previously-tested RC walls. Results of the cyclic lateral F-D predictions were evaluated based on commonly used measures of effective stiffness, maximum strength, and ultimate displacement. Additionally, the hysteretic response of the numerical simulations was assessed by proposing, validating, and using the Modified Nash-Sutcliffe Efficiency (NSEm) metric. Comparisons between the computing times for the models were also made, as well as comparisons of the local nonlinear behavior of a slender wall. Results show that the discretization used in the PERFORM 3D, MVLEM, and SFI-MVLEM simulations did not significantly affect the predicted global response, whereas the discretization did affect the F-D curves from the BTM model. The values of NSEm agreed with qualitative evaluations of the F-D curves and were able to properly evaluate complex cyclic behaviors of RC walls including pinching and stiffness deterioration. The results of this investigation are expected to be used as modeling guidelines of RC walls when conducting PBSD.

Financial Fragility, Regime Switching and Monetary Policy - With Application to Emerging Markets

The experience of the Asian currency and financial crisis in the years 1997-8 encouraged economists to develop some open economy nonlinear macro models. Such models allow for nonlinearities – studying the effects of contractionary currency devaluation in contrast to the standard model of expansionary currency devaluation. One in particular can distinguish here between slow and fast moving risk premia and exchange rates. As shown currency depreciation and slow moving exchange rates and risk premia may render the economy expansionary whereas fast moving exchange rates (fast depreciation) and fast increase in risk premia may generate macroeconomic instability and contractions. This is of course impacted by monetary policy that recently has moved from conventional (interest setting) to unconventional (asset purchasing) policies. The latter was in particular aiming at asset prices and risk premia, namely to bring risk premia of private assets (stocks and bonds) down and reduce credit spread for private and public bond yields. By doing this central banks are de-risking assets to stimulate aggregate demand (Caballero et al. 2020). But the latter policy has produced also international tensions due to spillover and volatility effects to other countries. In a generic nonlinear dynamic model of the finance-macro link we include the dynamics of the inflation rates, output gap and financial variable such as credit flows, risk premia and exchange rates. In the empirical part of the paper we examine then the interaction between the real and financial sectors of emerging market economies in particular post the financial crisis 2008-9. Though the dynamic model is operating with both the output gap and credit gap in our empirical analysis we work with the output gap only, since credit flows are hard to obtain for the large number of EM countries we study. Looking at a two-regime output gap and some financial indicators – such as risk premia, banking beta, and exchange rates – we then adopt the non-linear logistic vector smooth transition autoregressive (LVSTAR) approach of Schleer and Semmler (2015) with a logistic type transition function governing the LVSTAR system. Our study reveals that financial indicators of emerging economies show different responses to external shocks. With a positive shock in risk premia, the exchange rate depreciations occur in most emerging economies, and more so if the country faces a negative output gap.

Non-linear macro modelling of cyclic response of non-seismically detailed reinforced-concrete connections

Past earthquakes show that a large number of existing reinforced-concrete (RC) buildings sustain relatively substantial damage especially at the beam­­–column connections where it is mostly caused by either diagonal shear cracks due to the absence of transverse reinforcement or by bar slippage due to the insufficient bond length of the beam bottom bars. Slip of the beam longitudinal reinforcement in the joint and shear deformation of the joint panel significantly decrease the rigidity of the joint and make a significant contribution to the lateral response of RC buildings. In the current study an efficient non-linear macro model in the OpenSees software platform was used to simulate the non-linear behaviour of joints which fail under joint shear cracking and bar slippage mode. The proposed method is validated by experimental results for both seismically and non-seismically detailed external RC beam­–column connections. The non-linear macro modelling results of seismic joints were compared with those of specimens with non-seismic joints. The analytical results confirmed that the proposed joint element successfully predicted the experimental cyclic behaviour of beam–column connections, and it was also found that the rigid joint assumption was not appropriate when assessing the behaviour of existing non-seismically detailed structures.

A Nonlinear Macro-model for Numerical Simulation of Perforated Steel Beams

Perforated steel beams are being used widely in moment resisting frames. Given the computational expense of detailed numerical simulations, it seems necessary to introduce a simplified macro-model to be used in nonlinear analyses. This paper presents a nonlinear macro-model for numerical simulation of perforated steel I-beams. Results of finite element analysis on eighty perforated beams are used to calibrate the parameters of proposed macro-model. Then, results from proposed macro-model are verified against eight experiments gathered from other references and nine FE models analyzed by authors. The comparison shows that, the proposed macro-model has acceptable accuracy and can be utilized for further studies on the perforated steel I-beams.

Does Inflation Explain Equity Risk Premia?

I derive a simple linear macro asset pricing model that contains inflation as a risk factor in addition to the standard consumption growth and market return factors. This model nests the baseline CCAPM and Epstein--Zin models as special cases. Inflation arises endogenously in the pricing kernel by assuming an intra-temporal utility that depends on both real and nominal consumption, which suits an investor with partial money illusion. However, the model can not explain the cross-sectional dispersion in risk premia associated with 60 equity portfolios (related to six major CAPM anomalies). Moreover, the inflation risk price estimates, and implied preference parameter estimates, are statistically insignificant and/or economically implausible in most cases. To a large degree, these results hold when one estimates the Euler equations associated with the non-linear macro model. The evidence from this paper largely suggests that inflation does not help explaining the cross-section of stock returns.

Efficient Simulation of Nonlinear Transmission Lines via Model-Order Reduction

A new method is introduced for simulation of nonlinear transmission lines based on model-order reduction using the proper-orthogonal decomposition technique. An algorithm is presented for estimating the optimum order of the resulting reduced nonlinear macromodel ensuring its efficiency and accuracy. In contrast to previous publications, the order-estimation algorithm is integrated with the reduction technique leading to significant reduction in the computational cost associated with the generation of the reduced model.

A nonlinear macromodel for current-feedback operational amplifiers

This paper proposes a macromodel to emulate the nonlinear behavior of current-feedback operational amplifiers (CFOAs) at low-frequency. The main difference between this macromodel and those reported previously in the literature is that herein, real physical active device performance parameters along with parasitic elements associated to the input–output terminals of the amplifier are considered. To validate the deduced behavioral model, a saturated nonlinear function series (SNFS) based on CFOAs is built and numerical simulations are generated. In this point, the modeling problem is cast in terms of an augmented set of equations but that, unlike a piece-wise linear (PWL) approach, the dynamic behavior of each CFOA is considered. Afterwards, the SNFS is experimentally tested by using commercially available active devices, confirming good agreement among theoretical simulations and experimental tests at two operating frequencies and showing a better accuracy compared with a PWL approach and a linear model for CFOAs. Because the derived nonlinear macromodel for CFOAs is used for generating the behavioral model of the SNFS, one concludes that the latter is also both accurate and efficient with respect to traditional techniques, such as PWL approaches.

A practice-oriented model for pushover analysis of a class of timber-framed masonry buildings

Timber-Framed (TF) masonry is a structural system characterised by high complexity and diversity. Limited experimental and analytical research has been carried out so far to explore their earthquake response, partly due to the complexity of the problem and partly due to the scarcity of TF buildings across the world. Here, a new practice-oriented non-linear (NL) macro-model is presented for TF masonry structures, based on the familiar diagonal strut approach with NL axial hinges in the struts. The constitutive law for the hinges (axial force vs. axial deformation) is derived on the basis of an extensive parametric analysis of the main factors affecting the response of TF masonry panels subjected to horizontal loading. The parameters studied are related to the geometric features of the panel and the strength of wood as well as the connections of the timber elements. The parametric analysis is performed using a micro-model based on Hill-type plasticity and it is shown that in the studied X-braced walls the masonry infills do not make a significant contribution to the lateral load resistance. Empirical expressions are proposed for the yield and maximum displacement and shear of a horizontally loaded TF panel. The model is verified against available experimental data, and is found to capture well the envelopes of the experimental loops. The model is readily applicable to NL static analysis (pushover) analysis for the assessment of the lateral load capacity of TF masonry buildings, as the number of input parameters for deriving the constitutive law has been limited to only five.

Accounting of nonlinearity in OTA macromodel, applicable for syn-thesis of high-order active filters

The article discusses the development of the nonlinearity model of operational transconductance amplifier. The analysis of existing approaches using Taylor polynomial is described accounting the method’s shortcomings. The main part presents the orthogonal Chebyshev approximation method. The author gives the balanced OTA calculation results, focusing on the reduction of the maximum approximation error, reduced sensitivity to calculation rounding errors, as well as the possibility of application of high-degree polynomials using the proposed approach. The paper also raised the model’s integration into CAD systems issue. In conclusion, the results of nonlinear macromodel verification are given, showing the high accuracy of imitating the characteristics of a low-level transistor model. The possibility of application of macromodel for the synthesis of high-order active filters was highlighted, as well as high precision evaluation of filter performance and harmonic distortion.Reference 11, figures 11.

Operational transconductance amplifier macromodel optimization for active piezoelectric filter design

This work addresses the problem of optimal operational transconductance amplifier (OTA) macromodel creation in terms of its application in active FBAR filters. Existing macromodels of active elements are reviewed from their structure and application point of view. A nonlinear macromodel of OTA was developed on the basis of single-pole three-stage macromodel, which takes into account the necessary effects of real devices: the finite input and output impedances, the frequency dependence of transconductance coefficient and its nonlinearity behavior, noise characteristics. The features of presented solution include versatility of application in most of nowadays CAD systems, the ability to estimate with sufficient accuracy the frequency response of the filter and its performance, dynamic range, harmonic and noise analysis. Simple structure allows the speed-up of calculation and direct digital optimization techniques can be adopted to optimize the characteristics of the filter. The verification of macromodel was demonstrated on the example of FBAR connected to gyrator circuit, which showed high precision imitation of transistor-level circuit. The analysis of transient response and harmonic balance proved the acceptance of power series approximation of operation range. The use of two diodes outside this range allowed for modeling in wide input voltages range. The developed macromodel can be successfully used for the synthesis of active FBAR filters.

Nonlinear Phase-Domain Macromodeling of Injection-Locked Frequency Dividers

This paper describes an original nonlinear phase-domain macromodel of Injection-Locked Frequency Dividers which are driven by a nonlinear input device that produces heavy harmonic distortion. These non-harmonic frequency dividers can provide wide lock ranges, however their analysis is complicated by the strong nonlinear behavior for which the hypothesis of weak injection does not apply. The proposed approach consists in adopting a nonlinear model for the input section of the divider and in combining it with a Perturbation-Projection-Vector-based macromodel for the linear-time-varying section of the oscillator. The proposed macromodel is employed to predict the synchronization regions of an ILFD driven by several types of injected waveforms. In addition, closed-form expressions for the output phase-noise spectrum are also provided.

Yield curve in an estimated nonlinear macro model

This paper estimates a sticky price macro model with US macro and term structure data using Bayesian methods. The model is solved by a nonlinear method. The posterior distribution of the parameters in the model is found to be bi-modal. The degree of nominal rigidity is high at one mode (“sticky price mode”) but is low at the other mode (“flexible price mode”). I find that the degree of nominal rigidity is important for identifying macro shocks that affect the yield curve. When prices are more flexible, a slowly varying inflation target of the central bank is the main driver of the overall level of the yield curve by changing long-run inflation expectations. In contrast, when prices are more sticky, a highly persistent markup shock is the main driver. The posterior probability of each mode is sensitive to the use of observed proxies for inflation expectations. Ignoring additional information from survey data on inflation expectations significantly reduces the posterior probability of the flexible price mode. Incorporating this additional information suggests that yield curve fluctuations can be better understood by focusing on the flexible price mode. Considering nonlinearities of the model solution also increases the posterior probability of the flexible price mode, although to a lesser degree than using survey data information.

Multiple attractors and business fluctuations in a nonlinear macro-model with equity rationing

A stylized model of business fluctuations is developed, where investment and debt accumulation are responsible for the endogenous dynamics of income. Despite the simplicity of the model, the resulting nonlinear, two-dimensional discrete-time dynamical system displays a wide range of possible dynamic outcomes. If a key parameter, representing the propensity to invest, shifts exogenously from low to high values, a transition across qualitatively different long-run scenarios is observed, associated to different levels of economic activity. Moreover, coexistence of attractors and path-dependence characterize the dynamics for an intermediate range of such a parameter. The impact of exogenous disturbances on such situations results in aperiodic time series subject to unpredictable booms and slumps.

Linearization and Higher-Order Approximations: How Good are They?

The standard procedure for analyzing transitional dynamics in non-linear macro models has been to employ linear approximations. Recently quadratic approximations have been explored. This paper examines the accuracy of these and higher-order approximations in an endogenous growth model with public capital, thereby extending the work done in the current literature on the neoclassical growth model. We find that significant errors may persist in computed transition paths and welfare even after resorting to approximations as high as fourth order. Moreover, the accuracy of approximations may not increase monotonically with the increase in the order of approximation. Also, as in the previous literature, we find that achieving acceptable levels of accuracy when computing the welfare consequences of a policy change typically requires a higher order approximation than attaining similar levels of accuracy in the computation of the transition path: typically an increase in order of approximation by one is sufficient.

How Misleading is Linearization? Evaluating the Dynamics of the Neoclassical Growth Model

The standard procedure for analyzing transitional dynamics in non-linear macro models has been to employ linear approximations. This paper investigates the reliability of this procedure in evaluating the dynamic adjustments to policy changes or structural shocks. We analyze this issue using the example of a Ramsey growth model, with two alternative specifications of productive government spending. If government expenditure is introduced as a flow and the dynamic adjustment is fast, linearization may be a reasonably good approximation of the true dynamics even for fairly large policy shocks. If government expenditure assumes the form of a stock, leading to more sluggish adjustment, linearization is more problematic. It may yield misleading predictions, both qualitatively and quantitatively. These errors occur at the beginning of the transition and weigh heavily in welfare calculations. The implications for these errors for temporary shocks and the speed of convergence are also considered.

Yield Curve in an Estimated Nonlinear Macro Model

What moves the yield curve? This paper specifies and estimates a dynamic stochastic general equilibrium (DSGE) model solved using a second order approximation to equilibrium conditions to answer this question. From the empirical analysis of U.S. data from 1983:Q1 to 2007:Q4, I find that the monetary policy response to the inflation gap defined by the difference between expected inflation and the inflation target of the central bank is a key channel transmitting macro shocks to the yield curve and that the degree of nominal rigidity determines which macro shocks are more important determinants of the yield curve. With the low degree of nominal rigidity, the inflation target of the central bank drives persistent movements of inflation and the yield curve while fluctuations of markups do so with the high degree of nominal rigidity. Although the estimated linear model puts nearly zero probability on the low degree of nominal rigidity, there is a positive probability mass in the nonlinear model. The analysis in this paper suggests caution on interpreting estimation results in which nonlinear terms of the DSGE model solution are ignored.

Compact Modelling of Electrical, Mechanical and Thermal Behaviour for MEMS with SPICE

ABSTRACTIn this paper we present a novel method of nonlinear macro model of a cantilever for mixed domain simulation only with SPICE. Based on lumped elements of equivalent circuits a model is developed, which realizes a coupled electro-thermal-mechanical simulation including crosstalk effects. The model is verified with measurement and helps to class and solve crosstalk. With SPICE as electrical circuit simulator the cantilever array could be simulate in conjunction with the excitations and analysis electronics more detailed like the system level models and faster like FEM-simulation.

Hierarchical Modeling, Optimization, and Synthesis for System-Level Analog and RF Designs

The paper describes the recent state of the art in hierarchical analog synthesis, with a strong emphasis on associated techniques for computer-aided model generation and optimization. Over the past decade, analog design automation has progressed to the point where there are industrially useful and commercially available tools at the cell level-tools for analog components with 10-100 devices. Automated techniques for device sizing, for layout, and for basic statistical centering have been successfully deployed. However, successful component-level tools do not scale trivially to system-level applications. While a typical analog circuit may require only 100 devices, a typical system such as a phase-locked loop, data converter, or RF front-end might assemble a few hundred such circuits, and comprise 10 000 devices or more. And unlike purely digital systems, mixed-signal designs typically need to optimize dozens of competing continuous-valued performance specifications, which depend on the circuit designer's abilities to successfully exploit a range of nonlinear behaviors across levels of abstraction from devices to circuits to systems. For purposes of synthesis or verification, these designs are not tractable when considered "flat." These designs must be approached with hierarchical tools that deal with the system's intrinsic design hierarchy. This paper surveys recent advances in analog design tools that specifically deal with the hierarchical nature of practical analog and RF systems. We begin with a detailed survey of algorithmic techniques for automatically extracting a suitable nonlinear macromodel from a device-level circuit. Such techniques are critical to both verification and synthesis activities for complex systems. We then survey recent ideas in hierarchical synthesis for analog systems and focus in particular on numerical techniques for handling the large number of degrees of freedom in these designs and for exploring the space of performance tradeoffs early in the design process. Finally, we briefly touch on recent ideas for accommodating models of statistical manufacturing variations in these tools and flows