Multilinear Model Research Articles

Numerical Modeling of Lyapunov Exponents for Structural Damage Identification

The main purpose of this article is to discuss the use of the Lyapunov exponents to evaluate the integrity of structures. The use of such coefficients is examined in an analysis that considers the geometric and physical nonlinearities, aiming to ensure the applicability of the method in robust simulations. The material nonlinearity is modeled using the multilinear isotropic elastoplastic model together with a recently developed damage model. The nonlinear equilibrium equations solution is obtained using the positional finite element method. The Newmark time-marching procedure is implemented to evaluate the Lyapunov coefficients and a nonlinear predictor technique that needs a single data series is employed. A numerical example of a frame structure is presented to illustrate the methodology applicability. Its results show that the Lyapunov exponents can be used as indicative parameters of structural integrity, since its analysis was able to detect the occurrence of the destabilization of the structure with the dynamic jump and the presence of material failures. The non-linear predictor proved to be an efficient technique for obtaining the Lyapunov exponents, with a low computational cost. The methodology presented to monitor structural integrity was shown to be a promising alternative.

Reduced alpha2 power is associated with slowed information processing speed in multiple sclerosis.

Cognitive impairment is common in multiple sclerosis (MS), significantly impacts daily functioning, is time-consuming to assess, and is prone to practice effects. We examined whether the alpha band power measured with magnetoencephalography (MEG) is associated with the different cognitive domains affected by MS. Sixty-eight MS patients and 47 healthy controls underwent MEG, T1- and FLAIR-weighted magnetic resonance imaging (MRI), and neuropsychological testing. Alpha power in the occipital cortex was quantified in the alpha1 (8-10 Hz) and alpha2 (10-12 Hz) bands. Next, we performed best subset regression to assess the added value of neurophysiological measures to commonly available MRI measures. Alpha2 power significantly correlated with information processing speed (p < 0.001) and was always retained in all multilinear models, whereas thalamic volume was retained in 80% of all models. Alpha1 power was correlated with visual memory (p < 0.001) but only retained in 38% of all models. Alpha2 (10-12 Hz) power in rest is associated with IPS, independent of standard MRI parameters. This study stresses that a multimodal assessment, including structural and functional biomarkers, is likely required to characterize cognitive impairment in MS. Resting-state neurophysiology is thus a promising tool to understand and follow up changes in IPS.

Relationships of in vivo brain norepinephrine transporter and age, BMI, and gender.

Previous research reported an age-related decline in brain norepinephrine transporter (NET) using (S, S)-[11C]O-methylreboxetine ([11C]MRB) as a radiotracer. Studies with the same tracer have been mixed in regard to differences related to body mass index (BMI). Here, we investigated potential age-, BMI-, and gender-related differences in brain NET availability using [11C]MRB, the most selective available radiotracer. Forty-three healthy participants (20 females, 23 males; age range 18-49 years), including 12 individuals with normal/lean weight, 15 with overweight, and 16 with obesity were scanned with [11C]MRB using a positron emission tomography (PET) high-resolution research tomograph (HRRT). We evaluated binding potential (BPND ) in brain regions with high NET availability using multilinear reference tissue model 2 (MRTM2) with the occipital cortex as a reference region. Brain regions were delineated with a defined anatomic template applied to subjects' structural MR scans. We found a negative association between age and NET availability in the locus coeruleus, raphe nucleus, and hypothalamus, with a 17%, 19%, and 14% decrease per decade, respectively, in each region. No gender or BMI relationships with NET availability were observed. Our findings suggest an age-related decline, but no BMI- or gender-related differences, in NET availability in healthy adults.

Two-dimensional integrated mixed-mode smeared crack model for simulating FRC structures

This paper describes the implementation and assessment of the predictive performance of a two dimensional mixed-mode fracture smeared crack model (MMFSCM) in a finite element method (FEM) based software. The referred constitutive model is based on the integration of the aggregate interlock and fibre pullout resisting mechanisms to simulate the behaviour of Fibre Reinforced Concrete (FRC) in both fracture mode I and II. The models used to simulate the contribution of each resisting mechanism predict the normal and shear stresses at the crack level based on the crack opening and sliding displacements. For this purpose, two aggregate interlock models and three fibre pullout models are used. The appraisal of this approach is conducted by simulating two numerical case studies consisting of a three-point notched beam bending test (3PNBBT) for assessing the structural behaviour in mode I, and shear panel tests to appraise the predictive performance of the model in mode II. In addition, modifications to the original formulation of the fibre pullout models are proposed, and a multi-linear branch model is also developed and implemented in order to facilitate the use of inverse analysis tools for defining the mode I behaviour. The numerical simulations have predicted with good accuracy the experimental responses, both in mode I and mode II, capturing not only the peak loads but also the evolution trend of the post-peak responses of the analysed scenarios. The modifications proposed to the fibre pullout models enhanced the overall predictive performance of the MMFSCM. The multi-linear branch model exhibited excellent performance, capturing the experimental response with very good accuracy in all 3PNBBT simulations.

Road Traffic Noise Predictions by means of L10 Modelling with a Multilinear Regression Calibrated on Simulated Data

Estimation of road traffic noise is fundamental for the health of people living in urban areas, and it is usually assessed based on field-measured data. Real data may not always be available, anyway, and for this reason, predictive models play an important role in the evaluation and controlling of the noise impact. In this contribution, the authors present a multilinear regressive model calibrated on simulated noise levels instead that on real measured ones, correlating percentile noise levels to independent traffic variables. The model efficiency is then evaluated on two field measurement datasets by analyzing data statistics and error metrics. Results show that the model provides good results in terms of mean error (less than 1 dBA on average) even if slight underestimations and overestimations are present. The presented model, then, can be used to assess the impact of road traffic noise anytime field measurements are not available, or even predict it when designing new road infrastructures.

Slenderness limit for inner tubes with internal stiffeners in DSSTCC columns

In recent years, composite columns have gained much attention in offshore and marine engineering. This paper, with the motivation of a better design for circular straight double skin steel tubes confined concrete (DSSTCC) columns, theoretically explores the local buckling of the internally stiffened inner skin in this column. Firstly, the force analysis of a DSSTCC stub column was conducted, and its common failure modes were outlined. Based on the similar structural performance of the inner tube and the fixed circular arch, a concise buckling analysis model was built up. Then different buckling modes of clamped circular arches under the uniform radial load were presented. The ultimate load-carrying capacity of internally stiffened inner tubes under different buckling modes was also discussed, which shows relatively high dependence on the structural stability. Next, the calculation method of the expected ultimate hoop compressive stress was given, and the main computational procedure of the cross-sectional slenderness limit for internally stiffened inner skins was illustrated. In addition, a very simple prescriptive equation that considers the elastic modulus, the yield stress, and the formed arch's central angle value was fitted to estimate the cross-sectional slenderness limit for inner tubes with internal stiffeners, with which a slender cross-section can be delineated from an effective one. Meanwhile, the elastic buckling stress of the inner tube was also given. Finally, the applicability of the proposed methodology to materials with the bilinear model, the bilinear plus nonlinear hardening model, the idealized multilinear model, or the Ramberg-Osgood model was investigated, thereby demonstrating its good adaptability to these four common nonlinear constitutive models.

The role of responsive heterogeneity in sub-Saharan smallholder farming sustainability: socio-economic and biophysical determinants of mineral and organic fertilizers used in South Western Burkina Faso

ABSTRACTSustainable soil nutrient management (SNM) is important for improving soil resources and food security in sub-Saharan African countries. Inherent livelihood diversity may lead to differences in household behavior in the adoption of SNM practices, thus challenging policy interventions uniformly implemented. This study aims at exploring the responsive heterogeneity in household behavior in the adoption of fertilizer use by farmers. Determinants of fertilizer uses were analyzed across different farm types. These farm types were identified from farm-household data collected in six villages in the South Western of Burkina Faso using the Sustainable Livelihood Framework. Using multilinear and binary logistic models, determinants of mineral, organic and combined mineral-organic fertilizer uses were analyzed. The results revealed that the determinants of SMN adoption include not only common determinants to whole sampled population (income, household size, access to roads and cereal areas), but also specific determinants to farm types (small ruminants, animal power, educational level and access to agro-training). This finding suggests that policy interventions will not be effective if the responsive heterogeneity in SNM adoption behavior is not taken into account. The study recommends the use of the presented framework, as an approach, to identify functional farm types to be considered in SNM policies.

Technical note: Improving the European air quality forecast of the Copernicus Atmosphere Monitoring Service using machine learning techniques

Abstract. Model output statistics (MOS) approaches relying on machine learning algorithms were applied to downscale regional air quality forecasts produced by CAMS (Copernicus Atmosphere Monitoring Service) at hundreds of monitoring sites across Europe. Besides the CAMS forecast, the predictors in the MOS typically include meteorological variables but also ancillary data. We explored first a “local” approach where specific models are trained at each site. An alternative “global” approach where a single model is trained with data from the whole geographical domain was also investigated. In both cases, local predictors are used for a given station in predictive mode. Because of its global nature, the latter approach can capture a variety of meteorological situations within a very short training period and is thereby more suited to cope with operational constraints in relation to the training of the MOS (frequent upgrades of the modelling system, addition of new monitoring sites). Both approaches have been implemented using a variety of machine learning algorithms: random forest, gradient boosting, and standard and regularized multi-linear models. The quality of the MOS predictions is evaluated in this work for four key pollutants, namely particulate matter (PM10 and PM2.5), ozone (O3) and nitrogen dioxide (NO2), according to scores based on the predictive errors and on the detection of pollution peaks (exceedances of the regulatory thresholds). Both the local and the global approaches significantly improve the performances of the raw ensemble forecast. The most important result of this study is that the global approach competes with and can even outperform the local approach in some cases. This global approach gives the best RMSE scores when relying on a random forest model for the prediction of daily mean, daily max and hourly concentrations. By contrast, it is the gradient boosting model which is better suited for the detection of exceedances of the European Union regulated threshold values for O3 and PM10.

Seismic performance assessment of eccentrically braced steel frame using demountable-metallic-corrugated-shear-panel dampers

In this study, the demountable-metallic-corrugated-shear-panel damper (DCSPD) were investigated experimentally and numerically. Based on the quasi-static cyclic loading experiment of the DCSPD, the influences of different corrugation directions, shear panel thickness, and flange plate thickness on the seismic performance of the damper were discussed in detail. It is found that the variation of the shear panel thickness has a significant effect on the performance of the damper, the high stiffness of the corrugated shear panel causes the oblique buckling deformation to deflect along the direction of the principal stress and to develop at an acute angle to the crest line, which makes the failure modes of the horizontal corrugated shear panel damper (DCSPD-H) and the vertical corrugated shear panel damper (DCSPD-V) significantly different. Then, the multilinear hysteretic model of the DCSPD was established based on the peak-oriented modified Ibarra-Medina-Krawinkler model. In addition, a five story eccentrically braced steel frame with a vertical shear link was used to verify the application effect of the DCSPD on structural vibration control. The dynamic analysis results show that the DCSPD could significantly improve the seismic resilience performance of the structure, compared to the reference steel frame, the performance levels of the improved steel frame with damper showed significant improvements.

Correlated stabilizing selection shapes the topology of gene regulatory networks.

The evolution of gene expression is constrained by the topology of gene regulatory networks, as co-expressed genes are likely to have their expressions affected together by mutations. Conversely, co-expression can also be an advantage when genes are under joint selection. Here, we assessed theoretically whether correlated selection (selection for a combination of traits) was able to affect the pattern of correlated gene expressions and the underlying gene regulatory networks. We ran individual-based simulations, applying a stabilizing correlated fitness function to three genetic architectures: a quantitative genetics (multilinear) model featuring epistasis and pleiotropy, a quantitative genetics model where each genes has an independent mutational structure, and a gene regulatory network model, mimicking the mechanisms of gene expression regulation. Simulations showed that correlated mutational effects evolved in the three genetic architectures as a response to correlated selection, but the response in gene networks was specific. The intensity of gene co-expression was mostly explained by the regulatory distance between genes (largest correlations being associated to genes directly interacting with each other), and the sign of co-expression was associated with the nature of the regulation (transcription activation or inhibition). These results concur to the idea that gene network topologies could partly reflect past selection patterns on gene expression.

Mixed exposure effect of seminal metals on semen quality, mediation of total antioxidant capacity, and moderation of GSTM1/GSTT1 gene deletion in Chinese reproductive-aged men

BackgroundThe effects of metal exposure on semen quality and the role of oxidative damage in this process remain unclear. MethodsWe recruited 825 Chinese male volunteers, and 12 seminal metals (Mn, Cu, Zn, Se, Ni, Cd, Pb, Co, Ag, Ba, Tl, and Fe), the total antioxidant capacity (TAC), and reduced glutathione were measured. Semen parameters and GSTM1/GSTT1-null genotypes were also detected. Bayesian kernel machine regression (BKMR) was applied to evaluate the effect of the mixed exposure to metals on semen parameters. The mediation of TAC and moderation of GSTM1/GSTT1 deletion were analyzed. ResultsMost seminal metal concentrations were correlated with each other. The BKMR models revealed a negative association between the semen volume and metal mixture, with Cd (cPIP = 0.60) and Mn (cPIP = 0.10) as the major contributors. Compared to fixing all scaled metals at their median value (50th percentiles), fixing the scaled metals at their 75th percentiles decreased the TAC by 2.17 units (95%CI: −2.60, −1.75). Mediation analysis indicated that Mn decreased the semen volume, with 27.82% of this association mediated by TAC. Both the BKMR and multi-linear models showed that seminal Ni was negatively correlated with sperm concentration, total sperm count, and progressive motility, which was modified by GSTM1/GSTT1. Furthermore, Ni and the total sperm count showed a negative association in GSTT1 and GSTM1 null males (β[95%CI]: 0.328 [-0.521, −0.136]) but not in males with GSTT1 and/or GSTM1. Although Fe and the sperm concentration and total sperm count were positively correlated, they showed inverse “U” shapes in univariate analysis. ConclusionExposure to the 12 metals was negatively associated with semen volume, with Cd and Mn as the major contributors. TAC may mediate this process. GSTT1 and GSTM1 can modify the reduction in the total sperm count caused by seminal Ni exposure.

Reducing procrastination on introductory physics online homework for college students using a planning prompt intervention

We examine the effectiveness of a planning prompt intervention to reduce procrastination on online homework for college students. The intervention asked students to indicate their intention to earn small amounts of extra credit for completing assignments earlier and form a plan to realize their intentions. Students’ learning behavior is measured by five data metrics collected from gradebook and student interaction logs from four sections of the same college level physics course, including three metrics that capture how students space their work on assignments and two that measure the level of student engagement when completing assignments. To separate the impact of extraneous factors from the treatment effect, we employ a “difference in differences” method—initially developed in economics—and construct multilinear models for each of the five metrics. Our models show that by simply asking students to form a plan prior to the assignment, students on average earned 5% more extra credit, completed homework significantly earlier, and spread out their work significantly more. However, the intervention did not significantly change students’ level of engagement with the learning materials, nor did it change students’ work distribution on the next assignment.Received 15 December 2022Accepted 9 February 2023DOI:https://doi.org/10.1103/PhysRevPhysEducRes.19.010123Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasInstructional materials developmentResearch methodologyProfessional TopicsLower undergraduate studentsPhysics Education Research

Hydrologic responses of single land use urban and forested watersheds and their implications to improving urban drainage design

The need for resilient stormwater infrastructure is increasingly critical as urbanization and climate change continue to threaten water resources. Engineers and practitioners require reliable methodologies to estimate rainfall-runoff responses to adequately size and design sewer pipes and inlets, flood controls, and stormwater control measures (SCMs). The National Resource Conservation Service Technical Release 55 (often referred to as curve number [CN] method), Simple, and Rational methods are methodologies commonly implemented for such designs by regulatory agencies due to the limited inputs needed to estimate runoff; however, uncertainty is present in each model since they simplify actual hydrological processes. In this study, 13 urban and two forested watersheds were monitored, and their observed hydrologic responses were compared to modeled hydrologic responses utilizing the aforementioned methods. Significant differences in observed normalized runoff volumes (i.e., runoff coefficients) and normalized peak flow rates were found between watersheds with similar watershed characteristics and rainfall patterns, demonstrating the meticulous model inputs required to differentiate hydrologic responses between similar watersheds. A suite of alternative predictive models, informed by feature selection algorithms, were formulated and compared to the performance of standard methods. Results suggested that composite CN methods were the best predictors of event runoff volume across all watersheds (Nash Sutcliffe [NSE] and Kling Gupta Efficiencies [KGE] of 0.74 and 0.52, respectively), but were outperformed by the Simple method for watersheds with more than 45% impervious cover (NSE and KGE scores of 0.85 and 0.76, respectively). However, composite CN methods underestimated runoff volume from every watershed, a limitation that was intended to be addressed through the creation of the distributed CN method. In the distributed approach, runoff volume estimations were improved compared to the composite CN approach only when directly connected impervious area in the watershed was extremely high or extremely low. The multi-linear regression runoff volume model created herein did not outperform traditional runoff models except when rainfall depth was less than 12.5 mm (i.e., the storms for which traditional runoff volume estimation methods performed the worst). Uncertainty in modeled peak flow rate was substantially greater than for runoff volume (NSE and KGE scores between 0.48 – 0.55 and 0.39 – 0.67, respectively) across all methodologies. There is a continued need to develop more dependable estimates of peak flow which are critical to the design of pipes, flood routing, and hydrograph prediction. Overall, these results suggest one model is not optimal in all scenarios. Municipalities, regulatory agencies, and stormwater engineers should consider the adoption of multiple methodologies and use guidance from the results herein to provide recommendations as to when each model is most applicable.

Low Temperature Effect on the Mechanical Properties of EH36 with Strain Rates

With the expansion of the Arctic route, the safety of ship crossing the area in light of the low temperature and ice has become of focus, especially with regards to the ship’s structure. The mechanical properties of the material making up the ship’s structure may not be suitable for the Arctic environment. A series of quasi-static and dynamic tests were performed to investigate the behaviour of EH36 steel, which is used to build Arctic ships, at temperatures ranging from 20 °C to −60 °C. The yield and ultimate tensile stress increased more than 10% as the temperature decreased from 20 °C to −60 °C, whereas the toughness decreased as the temperature decreased. A formula was derived to illustrate the relationship between the temperature reduction and the yield strength by fitting the experimental data. Four common constitutive rigid-perfectly plastic, elastic-perfectly plastic, bilinear elastic-plastic, and multi-linear elastic plastic models were fitted to simulate the hull structure under static loading and low temperature. Additionally, the strain rate effect of EH36 steel at low temperatures was illustrated by quasi-static and high-speed impact tests. A constitutive model including the low temperature and strain rate was introduced based on a modified Cowper-Symonds model, in which the coefficients of the constitutive model are fitted by the test results. It is improved by an iterative numerical method used to obtain more accurate coefficients using a series of numerical analyses. Detailed finite element simulations of the experiment conditions revealed that the constitutive model accurately predicts the dynamic response at low temperatures.

Impact of dataset size and long-term ECoG-based BCI usage on deep learning decoders performance.

In brain-computer interfaces (BCI) research, recording data is time-consuming and expensive, which limits access to big datasets. This may influence the BCI system performance as machine learning methods depend strongly on the training dataset size. Important questions arise: taking into account neuronal signal characteristics (e.g., non-stationarity), can we achieve higher decoding performance with more data to train decoders? What is the perspective for further improvement with time in the case of long-term BCI studies? In this study, we investigated the impact of long-term recordings on motor imagery decoding from two main perspectives: model requirements regarding dataset size and potential for patient adaptation. We evaluated the multilinear model and two deep learning (DL) models on a long-term BCI & Tetraplegia (ClinicalTrials.gov identifier: NCT02550522) clinical trial dataset containing 43 sessions of ECoG recordings performed with a tetraplegic patient. In the experiment, a participant executed 3D virtual hand translation using motor imagery patterns. We designed multiple computational experiments in which training datasets were increased or translated to investigate the relationship between models' performance and different factors influencing recordings. Our results showed that DL decoders showed similar requirements regarding the dataset size compared to the multilinear model while demonstrating higher decoding performance. Moreover, high decoding performance was obtained with relatively small datasets recorded later in the experiment, suggesting motor imagery patterns improvement and patient adaptation during the long-term experiment. Finally, we proposed UMAP embeddings and local intrinsic dimensionality as a way to visualize the data and potentially evaluate data quality. DL-based decoding is a prospective approach in BCI which may be efficiently applied with real-life dataset size. Patient-decoder co-adaptation is an important factor to consider in long-term clinical BCI.

Buckling Analysis of Thin-Walled Circular Shells under Local Axial Compression using Vector Form Intrinsic Finite Element Method

The buckling failure of thin-walled circular shells under local axial compression is common in engineering. This study uses the vector form intrinsic finite element (VFIFE) method to investigate the buckling behavior of thin-walled circular shells under local axial compression by introducing a multilinear hardening model, taking into account geometric and material nonlinearity. A buckling analysis program based on the VFIFE method was developed and verified by comparison with experimental results. The buckling mode and postbuckling behavior of thin-walled circular shells were studied by using the verified program. The results show that the VFIFE method with a multilinear hardening model can accurately calculate the buckling load of local axially compressed thin-walled circular shells, and effectively simulate the buckling development process, which offers great advantages in predicting the postbuckling of structures.

Non-carcinogenic health risk assessment and predicting of pollution indexing of groundwater around Osisioma, Nigeria, using artificial neural networks and multi-linear modeling principles

Non-carcinogenic health risk assessment and predicting of pollution indexing of groundwater around Osisioma, Nigeria, using artificial neural networks and multi-linear modeling principles

Constitutive model for superelastic shape memory alloys considering strength and stiffness degradation and residual strain: An empirical approach for engineering applications

In this work, a novel uniaxial multilinear model for superelastic shape memory alloys that considers stiffness and strength degradation, and residual strain is proposed. To develop it, the results of several tensile cyclic tests at both constant and incremental strain amplitudes on 1.4 mm-diameter CuAlBe wires were used. Thus, degradation models were constructed from statistical correlation between the cycle maximum strain and the deterioration of the mechanical properties: strength, stiffness, and residual strain. Results show that the properties degrade exponentially as the cycle maximum strain increases. The model is validated with experimental data from the literature, showing high accuracy in predicting the evolution of residual strain, modulus of elasticity, transformation stresses, dissipated energy, and damping ratio. Furthermore, the proposed methodology shows a good fit when applied to experimental tests with NiTi bars performed by other authors, demonstrating that it can be extended to other alloys with flag-shaped hysteresis. The engineering-oriented model presented, stands out for its simplicity and accuracy in estimating the complex phenomena associated to superelasticity in SMA, even if random loading paths are imposed.

Low-dimensional encoding of decisions in parietal cortex reflects long-term training history

Neurons in parietal cortex exhibit task-related activity during decision-making tasks. However, it remains unclear how long-term training to perform different tasks over months or even years shapes neural computations and representations. We examine lateral intraparietal area (LIP) responses during a visual motion delayed-match-to-category task. We consider two pairs of male macaque monkeys with different training histories: one trained only on the categorization task, and another first trained to perform fine motion-direction discrimination (i.e., pretrained). We introduce a novel analytical approach—generalized multilinear models—to quantify low-dimensional, task-relevant components in population activity. During the categorization task, we found stronger cosine-like motion-direction tuning in the pretrained monkeys than in the category-only monkeys, and that the pretrained monkeys’ performance depended more heavily on fine discrimination between sample and test stimuli. These results suggest that sensory representations in LIP depend on the sequence of tasks that the animals have learned, underscoring the importance of considering training history in studies with complex behavioral tasks.

Development of hysteretic model for LEM-filled CFS shear walls under cyclic loading

Lightweight EPS materials (LEM)-filled cold-formed steel (CFS) shear wall, as a novel-type CFS shear wall, is extensively used in low- and multi-storey rural residences. The previous experiments have revealed that this type of wall appeared significant load-bearing properties and elastic stiffness, and the hysteresis loop appeared obvious stiffness degeneration, slipping and pinching effect. This paper developed a hysteretic model for seismic analysis of these shear walls. Four feature points including elastic, yield, peak and ultimate point are put forward to determine the skeleton curve. Besides, the feature points are determined by considering the stress type of bending and shearing respectively. Through analyzing the typical hysteresis loop, four characteristic points were obtained to express the characteristic of the hysteretic loop. Through the combination of the skeleton curve and hysteretic rule, a multi-linear hysteretic model was established to represent the hysteretic curves. The representative characteristic points of the hysteretic loop were obtained based on test data and the existing literature. The generated skeleton and hysteretic curves were compared with test results and the comparison results showed great agreements in terms of feature points and hysteretic loops. The method would provide a meaningful theoretical basis to assessing the seismic response of the LEM-filled CFS shear wall.