Nonlinear Response Model Research Articles

Investigating inconsistent uncertainty quantification encountered in neural network modelling of nonlinear response of a laminar flame

Neural network models, thanks to their flexibility and ability to approximate any function, are gaining popularity across all research fields. In thermoacoustics, one of their applications is modelling of a nonlinear flame response, learned from a single broadband forcing time series obtained through a computational fluid dynamics simulation. However, the investigations on this flame modelling approach conducted by Jaensch et al. [1] and Tathawadekar et al. [2] report contradictory results, concerning the performance and uncertainty of the derived multi-layer perceptron networks, despite using identical training data. This paper reevaluates their findings and aims to reconcile the opposing conclusions. This work demonstrates the reason for the different network performances, by reviewing the data split policies and identifying shuffling as a detrimental factor. Additionally, in this study different regularisation techniques such as L1 and L2 regularisation as well as network size reduction are considered. Those are compared against the previously tested implementation of dropout [2], which was believed to be responsible for the difference in the results between the two studies.

Fly Ash and Slag as Partial Replacement of Cement for the Synthesis of Low Carbon Cementitious Materials

Tailings known as solid waste are generated by the mining industry. The development of tailings as wet shotcrete aggregates has significant economic and environmental benefits. The fine particle size of the tailings results in a large consumption of traditional cement as a cementitious material and insignificant improvement in strength. Therefore, a composite cementitious system of cement and solid waste resources (fly ash and slag powder) is explored for this study. In this paper, the response surface methodology (RSM) is used to optimize the experimental design and a multivariate nonlinear response model with cement, fly ash and slag powder contents as variables are constructed, which can investigate the effect of the composite cementitious system on the strength of tailing wet shotcrete (TWSC). In addition, the information entropy (IE) is introduced and combined with the RSM to evaluate the composite cementitious system. Finally, the desirability function (DF) combined with RSM is used to optimize the composite cementitious system. The results show that the response model constructed in this paper has R2 = 0.96 and P-value < 0.01 (the test result of the model is P-value < 0.01), which indicates that the model has high reliability. The higher the content of slag powder and cement in the composite cementitious system, the higher the strength and comprehensive score of the TWSC. There is a critical value of fly ash content, which makes the maximum cementation of the composite cementing system. The optimal mix proportion of the composite cementitious system is obtained based on RSM-DF, which leads to the strength of TWSC at different curing time to achieve the expected index.

Fibonacci hyperbolic quantum wells: a model for two-level non-linear optical response

Fibonacci hyperbolic quantum wells: a model for two-level non-linear optical response

An amplitude-nested surrogate model for nonlinear response using double-layer Hilbert–Huang transform

Uncertainty parameters are ubiquitous in engineering and have a significant influence on the performance of mechanical systems. When evaluating the effect of uncertainty parameters on time-dependent response, a previous method is based on building surrogate models at each time instant for the amplitude, phase, and trend of the response, which can be obtained through signal decomposition techniques such as Hilbert–Huang transform. However, for a nonlinear oscillatory response, not only the response itself but also its amplitude might contain vibration components. Therefore, when modeling nonlinear responses, the previous method encounters an approximation error due to the increasingly complicated relationship between uncertainty parameters and the amplitude over time. To reduce this error, this paper proposes an amplitude-nested surrogate model using double-layer Hilbert–Huang transform through two steps. First, the response and its amplitude are successively decomposed through Hilbert–Huang transform to obtain the first- and second-layer decomposition results, respectively. Then, the polynomial surrogate models are built for the amplitude, phase, and trend in the first- and second-layer results at each time instant. The proposed method can improve the accuracy of the previous single-layer surrogate model without increasing the number of samples. Numerical examples have verified the effectiveness of the proposed method. This method can expand uncertainty analysis methods of dynamics.

Correction: Kathmandu Basin as a local modulator of seismic waves: 2-D modelling of non-linear site response under obliquely incident waves

Correction: Kathmandu Basin as a local modulator of seismic waves: 2-D modelling of non-linear site response under obliquely incident waves

Research on nonlinear characteristics for frequency domain dielectric response of transformer oil-paper insulation

Frequency domain dielectric response technology is widely used to detect the major insulation status of transformers. The influence of the test excitation amplitude on the nonlinear change of the dielectric characteristics of oil-paper insulation will interfere with the accuracy of the assessment results. In this paper, the electric field intensity distribution law of the oil gap in the oil-paper insulation model is obtained through test and simulation analysis. The influence of insulation aging, test temperature, and excitation frequency on the electric field distribution in the oil gap is clarified, it provides a reference for field strength for nonlinear loss calculation of oil-paper insulation. Meanwhile, based on the Garton’s ion motion nonlinear response model, considering the influence of the external electric field on the ion recombination in the oil gap, the nonlinear loss calculation model of transformer oil-paper insulation is corrected. Furthermore, the mechanism of positive and negative nonlinear loss variation for the oil-paper insulation model in a wide frequency range is revealed, and the calculation method of critical frequency and critical field strength of nonlinear loss variation in the oil-paper insulation model is proposed. Finally, according to the test results of the frequency domain dielectric response of oil-paper insulation with different aging and the apparent ion mobility in transformer oil, combined with the corrected calculation method proposed in this paper, the influence of the test excitation amplitude on the nonlinear change of the loss factor of oil-paper insulation is eliminated at different temperatures. The mean square error (MSE) of the corrected loss factor is reduced by 88.03% on average compared with that before.

Investigation of the strength of concrete-like material with waste rock and aeolian sand as aggregate by machine learning

Abstract Solid waste filling is an important development direction for filling mining technology. This paper proposes to use waste rock and aeolian sand as aggregates to fill the underground extraction area in order to reduce the environmental damage of related waste solid. The experiments are optimized by response surface methodology and multivariate nonlinear response models are constructed to investigate the effects of different factors on uniaxial compressive strength (UCS) of concrete-like material (CLM). The performance of different swarm intelligence optimization algorithms is analyzed and combined with support vector regression model (SVR) to construct an intelligent prediction model for UCS. The results show that the packing density has a maximum value of 0.74 when the proportion of waste rock is around 0.6. The response model constructed in this paper has a P-value &amp;lt; 0.01 and R2 &amp;gt; 0.8, which indicates its high significance and goodness of fit. The UCS of CLM increases with the increase of cement content and slurry mass fraction, while it also increases and then decreases with the increase of proportion of waste rock. The ratio of waste rock and aeolian sand will affect the compactness of cemented structure. The better the ratio, the higher the average grey value of the cemented structure, the more compactness the cemented structure. The whale optimization algorithm-SVR model constructed in this paper has a prediction accuracy of more than 99% for UCS of CLM, which achieves high accuracy and fast prediction of UCS under multifactor conditions.

Active-set algorithm-based statistical inference for shape-restricted generalized additive Cox regression models

Recently the shape-restricted inference has gained popularity in statistical and econometric literature to relax the linear or quadratic covariate effect in regression analyses. The typical shape-restricted covariate effect includes monotone increasing, decreasing, convexity or concavity. In this paper, we introduce the shape-restricted inference to the celebrated Cox regression model (SR-Cox), in which the covariate response is modelled as shape-restricted additive functions. The SR-Cox regression approximates the shape-restricted functions using a spline basis expansion with data-driven choice of knots. The underlying minimization of negative log-likelihood function is formulated as a convex optimization problem, which is solved with an active-set optimization algorithm. The highlight of this algorithm is that it eliminates the superfluous knots automatically. When covariate effects include combinations of convex or concave terms with unknown forms and linear terms, the most interesting finding is that SR-Cox produces accurate linear covariate effect estimates which are comparable to the maximum partial likelihood estimates if indeed the forms are known. We conclude that concave or convex SR-Cox models could significantly improve nonlinear covariate response recovery and model goodness of fit.

Trends and factors associated with thinness among late adolescent girls in Ethiopia: Multivariate decomposition and multilevel analysis.

Undernutrition among adolescent girls is still a major public health problem in low- and middle-income countries (LMICs). Even though the global prevalence of thinness among adolescent girls declined over time, it remains steady in LMICs including Ethiopia. Therefore, this study aimed to assess the trends and factors associated with thinness. A logit-based multivariate decomposition analysis for a non-linear response model was fitted to identify factors that contributed to the change in thinness over time. For the associated factors, a multilevel binary logistic regression model was employed. The intra-class correlation coefficient (ICC) and likelihood ratio (LR) test were used to assess the presence of the clustering effect, and deviance was used for model comparison. Statistical significance was declared at p < 0.05. Thinness among late adolescent girls declined significantly from 34.4% (95% CI: 32.8%, 36.0%) in 2000 to 24.9% (95% CI: 23.4%, 26.5%) in 2016 with an annual average reduction rate of 1.73%. About 84% of the decrement in thinness was attributed to the change in the effect of the characteristics. The place of residence and marital status were significantly associated with a change in thinness due to the change in coefficients. The compositional changes in the age of the adolescents, religion, and types of toilet facilities were also significantly associated with the change in thinness. From the multilevel binary logistic regression, higher age of adolescents (AOR = 0.83; 95% CI: 0.77, 0.90), improved toilet facility (AOR = 0.45; 95% CI: 0.31, 0.65), middle wealth index (AOR = 1.45; 95% CI: 1.10, 1.90), and female head of the household (AOR = 0.77; 95% CI: 0.61, 0.98) were significantly associated at an individual level, whereas being from Somali (AOR = 2.14; 95% CI:1.76, 3.10) and SNNP region (AOR = 0.35; 95% CI: 0.18, 0.68), they had a statistically significant association with thinness at community level. Thinness among late adolescent girls declined substantially, but it remains a major public health concern. Nutritional interventions targeting thinness reduction among late adolescent girls should base on the identified factors. Age, residence, marital status, type of toilet facility, religion, wealth index, sex of head of the household, and region were all associated with thinness in this study.

Kathmandu Basin as a local modulator of seismic waves: 2-D modelling of non-linear site response under obliquely incident waves

SUMMARYThe 2015 Mw 7.8 Gorkha, Nepal earthquake is the largest event to have struck the capital city of Kathmandu in recent times. One of its surprising features was the frequency content of the recorded ground motion, exhibiting a notable amplification at low frequencies (&amp;lt;2 Hz) and a contrasting depletion at higher frequencies. The latter has been partially attributed to the damper behaviour of the Kathmandu basin. While such weak high-frequency ground motion helped avoiding severe damage in the city, the catastrophic outcomes of earlier earthquakes in the region attest to a contrasting role of the Kathmandu basin as a broad-band amplifier, in addition to possible source effects. Given the possibility of future strong events in the region, our main objective is to elucidate the seismic behaviour of the Kathmandu basin by focusing on site effects. We numerically model 2-D P–SV wave propagation in a broad frequency band (up to 10 Hz), incorporating the most recent data for the Kathmandu basin geometry, soil stratigraphy and geotechnical soil properties, and accounting for the non-linear effect of multidimensional soil plasticity on wave propagation. We find that: (1) the Kathmandu basin generally amplifies low frequency ground motion (&amp;lt;2 Hz); (2) waves with large incidence angles relative to vertical can dramatically amplify the high frequency ground motion with respect to bedrock despite the damping effect of soil non-linearity and (3) the spatial distribution of peak ground motion amplitudes along the basin is highly sensitive to soil non-linearity and wave incidence (angle and direction), favouring larger values near the basin edges located closer to the source, as observed during the 2015 event. Our modelling approach and findings can support the ongoing resilience practices in Nepal and can guide future seismic hazard assessment studies for other sites that feature similar complexities in basin geometry, soil stratigraphy and dynamic soil behaviour.

The estimation of frequency response of nonlinear quarter car model and bilinear model of damper characteristics

The paper presents proposed and tested methods of estimation of frequency response of nonlinear quarter car suspension model and comparison with method for linear model used for research of vehicle vertical dynamics. Linear quarter car suspension model is widely used for estimation of comfort and safety performance of passive and semiactive suspensions. The real suspension - especially shock absorbers - are non-linear in three aspects: static characteristics, hysteresis and the presence of friction. Testing linear suspension model is possible with the use of analytical transfer function formulas but testing real suspension on a testing stand or even virtual but nonlinear suspension needs to use methods of transfer function estimation. It was necessary to design appropriate input signal allowing to get useful response signals. With the use of obtained frequency responses a method of linear estimation of nonlinear suspension for a given range of working condition was proposed. Also the bilinear model of damper characteristic estimation was proposed and tested proving to be good alternative to nonlinear characteristic.

A phenomenological framework for modeling of nonlinear mechanical responses in soft network materials with arbitrarily curved microstructures

Soft network materials (SNMs), consisting of rationally designed filamentary microstructures distributed periodically in lattice patterns, offer high air permeability, excellent defect insensitivity and highly tunable mechanical properties that could match precisely those of biological tissues. Owing to these excellent physical properties, SNMs have been widely used in stretchable electronics, biomedical engineering, soft robotics, and other areas. Although a few theoretical models were developed previously to predict nonlinear J-shaped stress–strain curves of SNMs with horseshoe microstructures, these models are not applicable to SNMs with arbitrarily curved microstructures. Herein, we establish a phenomenological framework capable of predicting nonlinear mechanical responses of SNMs with arbitrarily curved microstructures and various lattice topologies. The phenomenological framework incorporates a two-segment model that exploits simple, explicit expressions to capture the J-shaped stress–strain relationship, and a machine learning (ML) approach that enables the determination of the single phenomenological parameter in the model. Both finite element analysis (FEA) and experimental measurements on a diversity of SNMs have been conducted to validate the phenomenological model. The developed model enables a rapid inverse design of biomimetic SNMs for reproducing the target J-shaped stress–strain curves of soft biological tissues, and can be also extended to model anisotropic mechanical responses of SNMs with horseshoe microstructures. The versatile applicability of the phenomenological framework suggests that it can serve as a reliable design tool of SNMs for uses in tissue engineering and bioelectronics.

MatNERApor—A Matlab Package for Numerical Modeling of Nonlinear Response of Porous Saturated Soil Deposits to P- and SH-Waves Propagation

The paper is devoted to the problem of numerical modeling of earthquake response of porous saturated soil deposits to seismic waves propagation. Site-specific earthquake response analysis is a necessary and important component of seismic hazard assessment. Accounting for the complex structure of porous saturated soils, i.e., the content in them, in addition to the solid matrix, pore water, gas mixture and ice, is especially important for the water areas in the zones of continuous or sparse permafrost, as well as the massive release of bubble gas from bottom sediments. The purpose of this study is to introduce an algorithm and its Matlab implementation for numerical modeling of the nonlinear response of porous saturated soil deposits to vertical P- and SH-waves propagation. The presented MatNERApor package consists of a set of Matlab scripts and functions. The package was tested and verified using the records of vertical seismic arrays of the Kik-net network. In addition, the records of local earthquakes obtained by ocean bottom seismographs in the Laptev Sea in 2019–2020 were used to demonstrate the effect of the water layer above the seabed sites on the reduction of vertical motions spectra. The results of the calculations showed good agreement with the data obtained from real seismic records, which justifies the correctness of the theoretical basis of the presented algorithm and its software implementation.

Investigation of microstructural evolution and suitable potential barrier model for non-linear electrical response of Sr and Nb co-doped CaCu3Ti4O12 ceramics

This work reported about impact of co-doping on structural and non-linear electrical property of CaCu 3 Ti 4 O 12 (CCTO) ceramics with composition Ca 0·95 Sr 0·05 Cu 3 Ti 3·94 Nb 0·06 O 12 prepared by solid state reaction technique. Rietveld refinement of X-ray diffraction data was performed to analyse various parameters for its structure exploration. Microstructure and compositional information of prepared ceramic was determined by SEM, EDX and elemental mapping. The grain size was found 2.32 μm with the use of ImageJ software on SEM images. The identical Raman mode were observed in present doped CCTO ceramics comparative to that reported for pure CCTO in Raman spectroscopy. The resistivity of prepared sample reveals NTC behaviour of the ceramic. The parameters; non-linear coefficient (α = 1.86), breakdown electric field (E b = 191.56V/cm) and leakage current (I = 0.44 mA) were obtained by current voltage measurement at room temperature (RT∼303K). The detail comparative study of various barrier models was carried out and found Schottky barriers as most suited model for potential barrier at grain boundaries in the present system. • Ca0·95Sr0·05Cu3Ti3·94Nb0·06O12 ceramic was synthesized using Solid State Reaction method. • Structural Properties were investigated by XRD, SEM, Raman and FT-IR spectroscopy. • Schottky emission model was found most suitable for non-linear electrical response of prepared ceramics. • The value of nonlinear coefficient and Breakdown field suggest it was suitable for low voltage application. • The present sample exhibits good NTC behaviour at low DC voltage and found useful for varistor and thermistor application.

Rural and urban disparities in anemia among Peruvian children aged 6-59 months: a multivariate decomposition and spatial analysis.

Anemia is a global public health issue that affects mainly children aged less than 5 years. In Peru, despite the reduction in the prevalence of anemia between 2010 and 2018, anemia remains a major concern, especially in high-risk zones such as rural areas. Several sociodemographic factors have been associated with anemia in children; however, components contributing to the urban-rural gap have not been previously assessed. The purpose of this study was to evaluate the determinants of the difference in anemia prevalence between urban and rural areas, and its spatial distribution in Peruvian children aged 6-59 months. A secondary data analysis was conducted using the 2019 Peruvian Demographic Health Survey. The study population included 18 846 children aged 6-59 months. A multivariate decomposition analysis for non-linear response model was performed to identify the factors contributing to the gap in the prevalence of anemia across urban and rural areas. Global Moran&acute;s I autocorrelation, Ordinary Kriging interpolation and Bernoulli-based purely spatial scan statistics were employed to assess the spatial pattern of anemia. Nationwide, the prevalence of anemia in Peru was 29.47% (95%CI 28.63-30.33). In rural areas, it was 38.25%, and in urban areas 26.39%. The decomposition analysis revealed that 88.61% of the difference in the prevalence of anemia between urban and rural areas was attributed to the difference in the respondents' characteristics. Wealth index, mother&acute;s education, mother&acute;s employment status, number of living children and mother&acute;s age were key determinants contributing to the rural-urban gap. Spatial heterogeneity of anemia prevalence in childhood was observed at both inter- and intradepartmental level. The SaTScan spatial analysis identified six significant cluster areas with high prevalence of anemia in childhood. A considerable gap of anemia prevalence between urban and rural areas was found. Targeted interventions are necessary to reduce geographic disparities.

Real-time parameter identification of ship maneuvering response model based on nonlinear Gaussian Filter

In order to solve the problem of parameter identification of nonlinear ship motion model in ship autonomous navigation control, a real-time parameter identification method based on nonlinear Gaussian filtering algorithm and nonlinear ship response model is proposed. It is proved theoretically that the influence of parameter drift on parameter identification can be reduced by increasing the number of observers and filters, and the system identification accuracy can be improved. The validity of the proposed method is verified by parameter identification experiments based on Zig-zag motion simulation data of Mariner standard ship model. Simulation results show that compared with EKF, the nonlinear Gaussian filter algorithm can effectively improve the parameter identification accuracy and reduce the computational complexity. The application of parallel structure is helpful to improve the identification accuracy and convergence rate of nonlinear Gaussian filter algorithm.

A pharmacokinetic and pharmacodynamic analysis of drug forgiveness.

Nonadherence to medication is a major public health problem. To combat nonadherence, some clinicians have suggested using "forgiving" drugs, which maintain efficacy in spite of delayed or missed doses. What pharmacokinetic (PK) and pharmacodynamic (PD) factors make a drug forgiving? In this paper, we address this question by analyzing a linear PK/PD model for a patient with imperfect adherence. We assume that the drug effect is far from maximal and consider direct effect, effect compartment (biophase), and indirect response PD models. We prove that the average drug effect relative to the clinically desired effect is simply the fraction of prescribed doses actually taken by the patient. Hence, under these assumptions, drug forgiveness cannot be defined in terms of the average effect. We argue that forgiveness should instead be understood in terms of effect fluctuations. We prove that the rates of PK absorption, PK elimination, and PD elimination are exactly equivalent for determining effect fluctuations. We prove all the aforementioned results for any pattern of nonadherence, including late doses, missed doses, drug holidays, extra doses, etc. To obtain quantitative estimates of effect fluctuations, we consider a simple statistical pattern of nonadherence and analytically calculate the coefficient of variation of effect. We further show how effect fluctuations can be reduced by taking an extra "make up" dose following a missed dose if any one of the aforementioned PK/PD rates is sufficiently slow. We illustrate some of our results for a nonlinear indirect response model of metformin.

Better experimental design by hybridizing binary matching with imbalance optimization

AbstractWe present a new experimental design procedure that divides a set of experimental units into two groups in order to minimize error in estimating a treatment effect. One concern is the elimination of large covariate imbalance between the two groups before the experiment begins. Another concern is robustness of the design to misspecification in response models. We address both concerns in our proposed design: we first place subjects into pairs using optimal nonbipartite matching, making our estimator robust to complicated nonlinear response models. Our innovation is to keep the matched pairs extant, take differences of the covariate values within each matched pair, and then use the greedy switching heuristic of Krieger et al. (2019) or rerandomization on these differences. This latter step greatly reduces covariate imbalance. Furthermore, our resultant designs are shown to be nearly as random as matching, which is robust to unobserved covariates. When compared to previous designs, our approach exhibits significant improvement in the mean squared error of the treatment effect estimator when the response model is nonlinear and performs at least as well when the response model is linear. Our design procedure can be found as a method in the open source R package available on CRAN called GreedyExperimentalDesign.

Modeling of nonlinear viscous damper response for analysis and design of earthquake-resistant building structures

Modeling of nonlinear viscous damper response for analysis and design of earthquake-resistant building structures

An Improved On-Orbit Relative Radiometric Calibration Method for Agile High-Resolution Optical Remote-Sensing Satellites With Sensor Geometric Distortion

Noticeable striping artifacts in collected satellite imagery, caused by the inconsistency of pushbroom sensor detector responses, degrade the image quality. Relative radiometric calibration aims to calibrate inconsistencies in terms of detector responses, thereby eliminating detector-level striping artifacts. Yaw calibration has become the preferred imagery-based calibration method for satellites without on-board calibration equipment, owing to its high accuracy and convenience. However, it often relies on a large uniform field on the Earth’s surface and is a linear calibration method. This method does not consider acquisition-related geometric errors associated with the sensor, resulting in reduced calibration accuracy. In this study, we propose an improved method for yaw calibration, which accounts for the geometric distortion of sensor imaging and does not require a uniform field. A fast geometric-positioning algorithm was used to remove geometric distortion, followed by high-precision extraction of the calibration reference for each sensor’s detector. The dynamic range of the sensor calibration was extended, followed by the calibration of the sensor nonlinear response model. Our results based on Yaogan-25 images suggest the following: 1) the improved method effectively eliminates the “sawtooth” caused by the yaw calibration method without considering the geometric distortion and 2) it outperforms other imagery-based calibration methods with respect to visual destriping effects such that the root-mean-square deviations of the corrected imagery experienced a decrease of 0.65 percentage point, compared with that of the statistical method, and 0.17 percentage point for the yaw calibration. Such improvements will promote high-quality applications of remote-sensing images.