Nonlinear Modeling Techniques Research Articles

Parametric reduced-order modeling enhancement for a geometrically imperfect component via hyper-reduction

In this paper, an improved nonlinear reduced-order modeling technique capable of describing the parameterized shape defect is presented. In the proposed framework, a set of defect-shapes are pre-determined based on a nominal configuration. Then, the reduced-order representation is created in a polynomial form comprising a set of reduced-tensor coefficients of defect and physical displacement fields. However, constructing reduced tensors using a large number of discretized elements usually requires enormous amounts of computational resources. Therefore, to reduce the computational expense, a quadratic-manifold-based energy-conserving sampling and weighting approach was employed to obtain the reduced tensors concerning only a few optimally selected elements. This approach can be used to conduct both time-transient and frequency response analyses on rotating mechanical components. It was found that the proposed approach can accurately estimate the broad defect-parametric variation. In particular, its computational efficiency demonstrated a significant improvement over that of existing approaches.

Prediction of mechanical properties of In1-x GaxAsyP1-y lattice-matched to different substrates using artificial neural network (ANN)

ABSTRACT The mechanical properties, namely the elastic constants (C11, C12, and C44), bulk B, shear Cs, and Young’s modulus Y0, of the In1-xGaxAsyP1-y lattice-matched GaAs and InP substrates, were estimated using an artificial neural network (ANN method). This study aimed to create ANN networks that facilitate the estimation of the mechanical properties of alloys subjected to different temperatures and hydrostatic pressures. We aimed to predict the mechanical properties of InGaAsP alloys matched to InP and GaAs substrates as a function of temperature and hydrostatic pressure. ANN learning was performed based on the results validated by the empirical pseudopotential method data within the virtual crystal approximation, including the actual disorder potential. An ANN is a nonlinear process modeling technique frequently encountered in materials science. The predictive curves show high reliability, and underline the importance of using this approach to replace the time-consuming and costly experimental test, as well as to predict the mechanical response of the material where conventional modeling approaches have failed. Our method can consolidate the theoretical references found in the literature, it can also serve the field of engineering the mechanical properties of semiconductors, facilitate the successful design of optoelectronic devices, and serve future experimental works.

THREE-DIMENSIONAL DISPLACEMENT COMPATIBLE STRUT AND TIE METHOD FOR THREE-PILE CAPS SUBJECTED TO CONCENTRIC AXIAL LOADS

Pile caps are large structural elements that act as an interface between the superstructure and the pile foundation. The displacement Compatible Strut and Tie Method (C–STM) is an effective nonlinear modelling technique that is mainly used to simulate the behavior of structural reinforced concrete elements having considerable disturbed (D-) regions. Unlike STM, which considers only force equilibrium, C–STM considers displacement compatibility and constitutive material relationships as well. Recently, a three-dimensional (3D) C–STM was formulated and validated for the analysis of four-pile cap specimens of various shapes. In this study, the 3D C–STM is used to predict the complete load-deformation response of three-pile caps under concentric axial loads. The constitutive material relations for concrete and steel used in this study accounts for both concrete softening and tension stiffening. The overall load-deformation behavior simulated using the 3D C–STM agrees well with the experimental data. Moreover, the 3D C–STM also envisages the progression of nonlinear events leading up to the failure of three-pile cap specimen quite well.

Effect of pneumatic rubber fenders on the prevention of structural damage during collisions between a ship-shaped offshore installation and a shuttle tanker working side-by-side

ABSTRACT This study investigated the effects of pneumatic fenders on the prevention of structural damage from collisions between a ship-shaped offshore installation and a shuttle tanker during side-by-side offloading operations. A nonlinear finite element modelling technique was developed to simulate the kinetic energy absorption behaviour of pneumatic fenders during collisions. Full-scale pneumatic fenders were physically tested to validate the computational model at various collision speeds. The developed pneumatic fender model was integrated with a conventional finite element model of a hull structure to simulate the crashworthiness of the hull structure in collisions with a shuttle tanker during side-by-side offloading. This integrated computational model was then applied to examine case studies involving a VLCC class ship-shaped offshore installation hull with and without pneumatic rubber fenders colliding with a Suezmax class shuttle tanker. The key findings and insights of these investigations, particularly the collision energy absorption characteristics are summarised.

A review of effect of higher-order nonlinear theories on analysis of piezoelectric laminates

The paper aims at reviewing the modeling of piezoelectric laminated structures for stress distribution, vibration and noise control, shape control, health monitoring, and energy harvesting. Accurate modeling of piezoelectric laminates using linear and non-linear modeling techniques is essential at the high and low electric fields. The review is done in the field application of (1) different deformation theories (2) geometric non-linear theories (3) material non-linear models for the analysis of piezoelectric laminates. The literature review emphasizes using a higher-order non-linear model to analyze piezoelectric laminates and their effect on the composite structure.

THREE-DIMENSIONAL DISPLACEMENT COMPATIBLE STRUT AND TIE METHOD FOR THREE-PILE CAPS SUBJECTED TO CONCENTRIC AXIAL LOADS

Pile caps are large structural elements that act as an interface between the superstructure and the pile foundation. The displacement Compatible Strut and Tie Method (C–STM) is an effective nonlinear modelling technique that is mainly used to simulate the behavior of structural reinforced concrete elements having considerable disturbed (D-) regions. Unlike STM, which considers only force equilibrium, C–STM considers displacement compatibility and constitutive material relationships as well. Recently, a three-dimensional (3D) C–STM was formulated and validated for the analysis of four-pile cap specimens of various shapes. In this study, the 3D C–STM is used to predict the complete load-deformation response of three-pile caps under concentric axial loads. The constitutive material relations for concrete and steel used in this study accounts for both concrete softening and tension stiffening. The overall load-deformation behavior simulated using the 3D C–STM agrees well with the experimental data. Moreover, the 3D C–STM also envisages the progression of nonlinear events leading up to the failure of three-pile cap specimen quite well.

Contrasting patterns of richness, abundance, and turnover in mountain bumble bees and their floral hosts.

Environmental gradients generate and maintain biodiversity on Earth. Mountain slopes are among the most pronounced terrestrial environmental gradients, and the elevational structure of species and their interactions can provide unique insight into the processes that govern community assembly and function in mountain ecosystems. We recorded bumble bee-flower interactions over 3 years along a 1400-m elevational gradient in the German Alps. Using nonlinear modeling techniques, we analyzed elevational patterns at the levels of abundance, species richness, species β-diversity, and interaction β-diversity. Though floral richness exhibited a midelevation peak, bumble bee richness increased with elevation before leveling off at the highest sites, demonstrating the exceptional adaptation of these bees to cold temperatures and short growing seasons. In terms of abundance, though, bumble bees exhibited divergent species-level responses to elevation, with a clear separation between species preferring low versus high elevations. Overall interaction β-diversity was mainly caused by strong turnover in the floral community, which exhibited a well-defined threshold of β-diversity rate at the tree line ecotone. Interaction β-diversity increased sharply at the upper extreme of the elevation gradient (1800-2000 m), an interval over which we also saw steep decline in floral richness and abundance. Turnover of bumble bees along the elevation gradient was modest, with the highest rate of β-diversity occurring over the interval from low- to mid-elevation sites. The contrast between the relative robustness bumble bee communities and sensitivity of plant communities to the elevational gradient in our study suggests that the strongest effects of climate change on mountain bumble bees may be indirect effects mediated by the responses of their floral hosts, though bumble bee species that specialize in high-elevation habitats may also experience significant direct effects of warming.

Cetane index prediction based on biodiesel distillation curve

Cetane number (CN) is one of the most important parameters affecting diesel fuel behavior. It is related to the time that elapses between fuel injection and beginning of combustion. To determine it, a combustion standardized test, under ASTM D613 regulation, needs to be carried out. As this process is limiting, since it requires a specific engine, CN can be approximated from the distillation temperatures of diesel fuels, providing another dimensionless parameter, named calculated cetane index (CCI). It also provides an approach to the explosion delay. ASTM D4737 standard is the regulation that allows its calculation. It is based on a four-term equation that may be applied to oil-derived products. Chemical composition of diesel fuel is composed exclusively of hydrocarbons of different nature. However, biodiesel is mainly composed of alkyl esters and, to a lesser extent, glycerides and glycerol impurities. This difference makes convenient to adapt the equation to biodiesel distillation curve. The aim of this work is to provide an alternative to CN calculation for biodiesel, based on CCI prediction. This manuscript presents distillation curves and density values of 14 different biodiesel types, from both animal and vegetable origin. This data, together with data from literature, have been used with non-linear equation modeling techniques. As a result, a modification of ASTM D4737 regulation with experimental data from biodiesel sources has been proposed. The proposed equation exhibits an error with respect to experimental data below 3.5% for most evaluated cases. Subsequently, it may be concluded that the proposed methodology may be applied to accurately calculate biodiesel CCI, as a substitute of CN.

A new strategy for butanol extraction from COVID-19 mask using catalytic pyrolysis process over ZSM-5 zeolite catalyst and its kinetic behavior

This research aims to develop a new thermochemical strategy to extract butane from the billions of wasted COVID-19 masks that are generated every month. The experiments were conducted with 3-ply face masks (3PFM) over ZSM-5 zeolite with different ratios of ZSM-5 to 3PFM (w/w: 6, 12, 25, and 50 wt.%) using thermogravimetry (TGA) at different heating conditions. Also, the effect of ZSM-5 concentration and heating rates was examined using TG-FTIR and GC–MS measurements. Besides, the kinetics behavior of the developed strategy was modelled using linear and nonlinear isoconversional modeling techniques, thus calculating the activation energy (Ea) for each conversion region. Finally, all required parameters to fit TGA and differential scanning calorimetry (DTG) experimental curves were estimated using the distributed activation energy (DAEM) and the independent parallel reactions (IPR) techniques, respectively. The results showed that the decomposed samples are very rich in aromatic and aliphatic (-C-H) compounds. Meanwhile, and based on GC–MS results, butanol compound was the basic component in the generated compounds with abundance of 31% at 25 wt.% of ZSM-5 at lowest heating rate (5 °C/min), whereas the average Ea at 25% of ZSM-5 (sample enriched with butanol) was estimated in the ranges 158–187 kJ mol−1 (linear methods with R2 > 0.96) and 167–169 kJ/mol (nonlinear methods with R2 > 0.98). Finally, DAEM and IPR succeeded to simulate TGA and DTG curves of ZSM-5/3PFM samples with very small deviation. Based on that, the catalytic pyrolysis strategy over ZSM-5 zeolite can be used effectively to dispose of COVID-19 masks and to convert them into butanol compound that can be used as a liquid fuel and lubricant.

Population pharmacokinetics of methotrexate in paediatric patients with acute lymphoblastic leukaemia and malignant lymphoma

This study aimed to identify physiological and pharmacogenomic covariates and develop a population pharmacokinetic model of high-dose methotrexate (HD-MTX) in Chinese paediatric patients with acute lymphoblastic leukaemia (ALL) and malignant lymphoma. A total of 731 MTX courses and 1658 MTX plasm concentrations from 205 paediatric patients with ALL and malignant lymphoma were analysing using a non-linear mixed-effects model technique. 47 SNPs in 16 MTX-related genes were genotyped and screened as covariates. A PPK model was established to determine the influence of covariates, such as body surface area (BSA), age, laboratory test value, and SNPs on the pharmacokinetic process of HD-MTX. Two-compartmental model with allometric scaling using BSA could nicely characterise the in vivo behaviour of HD-MTX. After accounting for body size, rs17004785 and rs4148416 were the covariates that influence MTX clearance (CL). The PPK model obtained was: CL = 9.33 * (BSA/1.73)0.75 * e0.13*rs17004785 * e0.39*rs4148416 * eηCL, Vc = 24.98 * (BSA/1.73) * eηvc, Q = 0.18 * (BSA/1.73)0.75 * eηQ and Vp = 4.70 * (BSA/1.73) * eηvp. The established model combined with the Bayesian approach could estimate individual pharmacokinetic parameters and optimise personalised HD-MTX therapy for paediatric patients with ALL and malignant lymphoma.

RC-INSANE – an interactive environment for nonlinear analysis of reinforced concrete structures

Abstract The development of numerical and computational resources that can present reliable models for the analysis of reinforced concrete structures is mainly driven by its widespread use. Considering that reinforced concrete is a composite material and bond is the load-carrying mechanism, these models must consider that the structural behavior is affected by the interaction between concrete and reinforcement. On this basis, the Finite Element Method (FEM) is a well-established method able to provide consistent results for reinforced concrete modeling through reinforcement and bond models. Nevertheless, to simplify the analysis, the hypothesis of strain compatibility between concrete and reinforcement is usually considered. Under certain loads and specific geometries, this hypothesis is not valid, and the bond-slip phenomenon must be considered to fully characterize the structural behavior. To fulfill this need, this paper presents a graphic interface that enables the modeling of reinforced concrete structures through discrete and embedded reinforcement models, with the possibility to include the bond-slip phenomenon based on several constitutive laws proposed in the literature. The computational implementations were held in the INSANE (INteractive Structural ANalysis Environment), an open-source software based on the Object-Oriented Programming paradigm, which enclosures several constitutive models for nonlinear concrete modeling and different numerical techniques, and a post-processing application able to represent the results by way of a friendly-user graphic interface.

Nonlinear Modeling of a Plate Heat Exchanger of a District Heating System

The integration of renewable and residual energy sources requires a detailed level of knowledge of district heating components such as thermal pipes, pipes, pumps, and heat exchanger of a substation. The thermal energy stored in these components can be utilized to match the heat demand and heat generation in time for next generation district heating networks. The goal of this paper is to provide accurate substation models that can be utilized for controlled energy exchange between primary and secondary networks. The proposed method introduces an efficient, user-friendly, combined parametric and nonparametric nonlinear data-driven modeling technique illustrated on a plate heat exchanger which is installed in the district heating network of the Vrije Universiteit Brussel. A fair comparison between a physics-based white-box and a data-driven black-box modeling techniques is provided. The white-box model is developed on the first principle modeling approach of the heat balance equations, which allows calculating the temperature evolution and heat transfer in the plate heat exchanger. As for the data-driven modeling approach, there are four interrelated consecutive steps. First, the measurement is processed to obtain a frequency response function model. Second, a linear parametric (state-space) model is estimated. Third, a polynomial nonlinear model is built. Last, a decoupled model structure is obtained based on the previously obtained PNLSS model. The proposed black-box method outperforms the white-box techniques in terms of prediction capabilities and computational needs.

Relationships of climate, human activity, and fire history to spatiotemporal variation in annual fire probability across California.

In the face of recent wildfires across the Western United States, it is essential that we understand both the dynamics that drive the spatial distribution of wildfire, and the major obstacles to modeling the probability of wildfire over space and time. However, it is well documented that the precise relationships of local vegetation, climate, and ignitions, and how they influence fire dynamics, may vary over space and among local climate, vegetation, and land use regimes. This raises questions not only as to the nature of the potentially nonlinear relationships between local conditions and the fire, but also the possibility that the scale at which such models are developed may be critical to their predictive power and to the apparent relationship of local conditions to wildfire. In this study we demonstrate that both local climate–through limitations posed by fuel dryness (CWD) and availability (AET)–and human activity–through housing density, roads, electrical infrastructure, and agriculture, play important roles in determining the annual probabilities of fire throughout California. We also document the importance of previous burn events as potential barriers to fire in some environments, until enough time has passed for vegetation to regenerate sufficiently to sustain subsequent wildfires. We also demonstrate that long-term and short-term climate variations exhibit different effects on annual fire probability, with short-term climate variations primarily impacting fire probability during periods of extreme climate anomaly. Further, we show that, when using nonlinear modeling techniques, broad-scale fire probability models can outperform localized models at predicting annual fire probability. Finally, this study represents a powerful tool for mapping local fire probability across the state of California under a variety of historical climate regimes, which is essential to avoided emissions modeling, carbon accounting, and hazard severity mapping for the application of fire-resistant building codes across the state of California.

A Machine Learning-Based QSAR Model for Quinolines Tested As Corrosion Inhibitors of Mild Steel in HCl Solution

The investigation of organic compounds as potential inhibitors of metal corrosion using several experimental and/or computational techniques has been well established in literature. Recent advances in the development of corrosion inhibitors has led to the exploration of quantitative structure activity relationship (QSAR) as a worthy alternative to the rigorous, sometimes expensive and time-consuming experimental/computational procedures. QSAR is a robust computational method that generates mathematical models that maps the structural features of organic compounds with their inhibition performances. The obtained mathematical models can then be further used to predict the chemical activity of new and untested organic molecules. Although linear and non-linear methods have been reported in developing QSAR models, only few works have explored the use of state-of-the-art artificial neural network (ANN). This study reports the development of QSAR models for sixty quinolines investigated as corrosion inhibitors for mild steel corrosion in 1 M HCl using both linear and non-linear modelling techniques. Density functional theory (DFT) and Dragon 7 software were used to generate molecular descriptors for model development and were reduced to a significant few using feature selection tools. The significant molecular descriptors were employed in model building using conventional multiple linear regression (MLR) and ANN modelling techniques. The developed models were evaluated using several statistical performance metrics and the ANN-based model was found to produce the best correlation between the predicted and experimental inhibition efficiencies. Furthermore, nine new quinoline molecules were theoretically designed and their inhibition efficiencies were predicted using the best developed ANN model.

Exploratory Data Analysis Based Short-Term Electrical Load Forecasting: A Comprehensive Analysis

Power system planning in numerous electric utilities merely relies on the conventional statistical methodologies, such as ARIMA for short-term electrical load forecasting, which is incapable of determining the non-linearities induced by the non-linear seasonal data, which affect the electrical load. This research work presents a comprehensive overview of modern linear and non-linear parametric modeling techniques for short-term electrical load forecasting to ensure stable and reliable power system operations by mitigating non-linearities in electrical load data. Based on the findings of exploratory data analysis, the temporal and climatic factors are identified as the potential input features in these modeling techniques. The real-time electrical load and meteorological data of the city of Lahore in Pakistan are considered to analyze the reliability of different state-of-the-art linear and non-linear parametric methodologies. Based on performance indices, such as Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE) and Mean Absolute Error (MAE), the qualitative and quantitative comparisons have been conferred among these scientific rationales. The experimental results reveal that the ANN–LM with a single hidden layer performs relatively better in terms of performance indices compared to OE, ARX, ARMAX, SVM, ANN–PSO, KNN, ANN–LM with two hidden layers and bootstrap aggregation models.

A comprehensive nonlinear finite element modelling and parametric analysis of reinforced concrete beams

PurposeThis study aims to present comprehensive nonlinear material modelling techniques and simulations of reinforced concrete (RC) beams subjected to short-term monotonic static load using the robust and reliable general-purpose finite element (FE) software ANSYS. A parametric study is carried out to analyse the flexural and ductility behaviour of RC beams under various influencing parameters.Design/methodology/approachTo develop and validate the numerical FE models, a total of four experimentally tested simply supported RC beams are taken from the available literature and two beams are selected from each author. The concrete, steel reinforcements, bond-slip mechanism, loading and supporting plates are modelled using SOLID65, LINK180, COMBIN39 and SOLID185 elements, respectively. The validated models are then used to conduct parametric FE analysis to investigate the effect of concrete compressive strength, percentage of tensile reinforcement, compression reinforcement ratio, transverse shear reinforcement, bond-slip mechanism, concrete compressive stress-strain constitutive models, beam symmetry and varying overall depth of beam on the ultimate load-carrying capacity and ductility behaviour of RC beams.FindingsThe developed three-dimensional FE models can able to capture the load and midspan deflections at critical points, the accurate yield point of steel reinforcements, the formation of initial and progressive concrete crack patterns and the complete load-deflection curves of RC beams up to ultimate failure. From the numerical results, it can be concluded that the FE model considering the bond-slip effect with Thorenfeldt’s concrete compressive stress-strain model exhibits a better correlation with the experimental data.Originality/valueThe ultimate load and deflection results of validated FE models show a maximum deviation of less than 10% and 15%, respectively, as compared to the experimental results. The developed model is also capable of capturing concrete failure modes accurately. Overall, the FE analysis results were found quite acceptable and compared well with the experimental data at all loading stages. It is suggested that the proposed FE model is a practical and reliable tool for analyzing the flexural behaviour of RC members and can be used for performing parametric studies.

Efficient cross-validatory algorithm for identifying dynamic nonlinear process models

Kernel partial least squares (KPLS) is an effective nonlinear modeling technique for control engineering applications, including model predictive control, process monitoring or general system diagnosis. It can deal with small sample sizes and variable sets that are noisy and highly correlated. Kernel partial least squares maps the input (or cause) variables to a feature space and carries out the task of producing an optimal prediction model for the process output (or effect) variables using the standard linear partial least squares (PLS) approach. Resulting from the typically large size of the feature space, the kernel partial least squares procedure can be computational intensive. In particular, if the optimal model structure is estimated using cross-validation, KPLS is not efficient in handling large data sets. This paper first modifies the conventional kernel partial least squares procedure in order to embed it within a leave-one-out cross-validation (LOOCV) framework. The proposed efficient kernel partial least squares (EKPLS) is able to reduce the computational complexity by an order of magnitude compared to the conventional approach, which is proven both analytically and through modeling applications to three industrial data sets.

Comparing responses of special and intermediate moment frames under repeated earthquakes

Steel moment-resisting frames (MRFs) are designed to resist a design-level single seismic event. However, every earthquake may be accompanied by several foreshocks or aftershocks. The cyclic deterioration of structural elements during early earthquakes may cause the lateral-load-resisting system to collapse under the mainshock or aftershocks. The differences in the seismic performance of special and intermediate MRFs (here called SMFs and IMFs, respectively) subjected to single and multiple earthquake events were investigated. For this purpose, four perimeter steel MRFs with four and eight storeys were designed and subjected to 22 synthesised multi-record earthquake events. The non-linear modelling technique adopted accounts for the cyclic deterioration of structural elements, which is a key parameter in the evaluation of seismic performance under sequential earthquakes. The results showed that structural collapse capacity may be reduced considerably if the structure is subjected to foreshock and aftershock events in addition to the mainshock. In addition, it was found that, for the IMF models, the switch from the life safety (LS) limit state to the collapse prevention limit state was immediate. Therefore, the design of IMFs for the LS performance level may result in a substantial risk of collapse when the structure is exposed to repeated earthquakes.

Combining Deep Learning and Multiresolution Analysis for Stock Market Forecasting

Due to its complexity, financial time-series forecasting is regarded as one of the most challenging problems. During the past two decades, nonlinear modeling techniques, such as artificial neural networks, were commonly employed to solve a variety of time-series problems. Recently, however, deep neural network has been found to be more efficient than those in many application domains. In this article, we propose a model based on deep neural networks that improves the forecasting of stock prices. We investigate the impact of combining deep learning techniques with multiresolution analysis to improve the forecasting accuracy. Our proposed model is based on an empirical wavelet transform which is shown to outperform traditional stationary wavelet transform in capturing price fluctuations at different time scales. The proposed model is demonstrated to be substantially more effective than other models when evaluated on the S&P500 stock index and Mackey-Glass time series.

Energy Absorption Enhancement for Multiple Impact Angles of a Rear Crash Attenuator

This research aims at developing a reliable finite element framework to investigate the specific energy absorption of a rear crash attenuator of an open-wheel-type IndyCar vehicle. The failure behavior was learnt based on various nonlinear finite element modeling techniques to simulate a crash as per regulations from the governing body of IndyCar, utilizing the continuum damage mechanics model. The sandwich structure material characterization for the tuning of the material model was done by the means of a correlation with experimental data and adjusting the non-physical input parameters in the software. Post-calibration, the development of the rear impact attenuator was performed with a finite element model. The failure modes were investigated for head-on and oblique impact angles. The specific energy absorption was determined for these configurations of impact by evaluating the force over the crushed displacement. The insights from the simulation were utilized to improve the overall specific energy absorption by 41.8% with a gradual deceleration value to that of the prescribed. Finally, the results were compared to the previous IndyCar structure and a new prototype was suggested with highlights of the refreshed results.