Equivalent Linear Model Research Articles

Model-Free Tracking Control with Prescribed Performance for a Shape Memory Alloy-Based Robotic Hand

The shape memory alloy (SMA)-based robotic hand has been a new emerging technology with potential applications ranging from life service to surgical treatment, because of the characteristics of SMA, such as high power-to-weight ratio, small volume and low driving voltage. However, due to the complex dynamic model and nonlinear aspects of SMA, it is complicated to control an SMA-based robotic hand. This paper presents a novel model free adaptive control for the SMA-based robotic hand system. By applying the Taylor series expansion method and the differential mean value theorem, the SMA based robotic hand system can be transformed into an equivalent linearization model, which merely depends on measurement data without any information on the system. Combined with prescribed performance control, the novel control method can constrain the tracking error in a preassigned domain. Experiments are conducted on the SMA-based robotic hand system to verify the performance of the presented control method.

Evaluating the Accuracy of an Equivalent Linear Model in Predicting Peak Displacement of Seismic Isolation Systems using Single Friction Pendulum Bearings

This study evaluates the accuracy of an equivalent linear model in predicting peak nonlinear time-history displacement of seismic isolation systems with single friction pendulum bearings. To perform this evaluation, dynamic response of numerical models of 120 isolation systems subjected to 390 strong earthquake ground motions, including motions with pulse and motions without pulse, was analyzed and statistically processed. The results show that the equivalent linear model can partly predict the peak displacement of its counterpart nonlinear model. However, the equivalent model can also underestimate or overestimate the peak displacement. On average sense, the equivalent linear model underestimates small peak displacement and overestimates large peak displacement. It is also observed that the relationship between linear and nonlinear peak displacements depends on ground motion types. Based on the analysis data, equations representing relationship between linear and nonlinear peak displacements at different reliable levels for different ground motion types were proposed. These equations can be used in practice.

Measuring group performance based on metafrontier

Afsharian et al. proposed a metafrontier-based group performance evaluation model under centralised management scenario. Their model is a mixed integer linear programming model under constant returns to scale. Their model suffers from infeasibility when variable returns to scale is assumed. We convert their model into an equivalent linear programming model under constant returns to scale. We extend the linear programming model to variable returns to scale and resolve the infeasibility. Models for centralised and decentralised scenarios are proposed in current paper. An example of a maritime carrier is introduced to demonstrate how the models proposed can be used to investigate the influence of the decision on joining maritime alliance on the performance of a carrier. Another example of solar industry is introduced to illustrate the application of the decentralised model in measuring the technology gap ratio.

Seismic Response of Two Site Models and Their Effects on the Railway Cable-Stayed Bridge

In order to accurately analyze the seismic response of the site and their effects on a railway cable-stayed bridge, the site condition of the railway cable-stayed bridge was surveyed, and geotechnical exploration holes ZK1 and ZK2 were set near the left and right tower of the bridge to gain the detailed geological data, then 32 representative ground motions records were selected corresponding to the site characteristics, and the equivalent linear and nonlinear model were established to analyze the site seismic response of 32 representative ground motions based on the Deepsoil Software. Next, to investigate the influence of site seismic response on the long-span railway cable-stayed bridge, the seismic response of the cable-stayed bridge considering site effect are calculated and evaluated via time history analysis under one-dimensional and multi-point excitation based on the ANSYS platform. At last, several critical and meaningful conclusions are drawn.

Seismic analysis of underground structures employing extended response spectrum method

Response spectrum method (RSM) has been applied in seismic analysis of underground structures considering linear soil-structure interaction (SSI). However, the RSM has two main shortcomings: it does not account for soil nonlinearity and it is computationally inefficient for processing large soil domains. This paper addresses these shortcomings by extending the RSM to consider soil nonlinearity and by simplifying the modal analysis of SSI systems. The soil nonlinearity is considered by transforming the one-dimensional (1D) frequency-domain equivalent linearization model into a modal damping linear elastic model, in which two explicit formulations of the modal damping ratio are presented. The resulting degraded shear modulus and modal damping ratio are applied to the SSI model to consider soil nonlinearity. In addition, it was found that a small number of natural frequencies and mode shapes of the SSI system are already sufficient to evaluate vibration characteristics in a typical 2D SSI analysis. Accordingly, the first three natural vibration modes of the 1D soil site are used as the loading condition to determine the effective characteristics of the SSI system by iterative static analysis of the SSI system. The effectiveness of the proposed procedure in considering soil nonlinearity and avoiding modal analysis of the SSI system is verified by comparisons with numerical examples. Finally, the extended RSM is applied to the seismic design of three prototype underground structures.

Supply chain network design considering customer psychological behavior-a 4PL perspective

From the perspective of Fourth Party Logistics, a novel supply chain network design problem considering customer psychological behavior is proposed in this paper. First, we calculate the minimum cost of the supply chain network design in Fourth Party Logistics when the demand of customers is fully satisfied. In the shortage of investment in the process of supply chain network design, the demand of customers can be partially satisfied. Then, customer psychological behavior is considered to maximize the value function of customer satisfaction under cost constraint. After introducing the definitions of the psychological reference point and the service level for customers based on the prospect theory, we formulate a non-linear integer programming model for Fourth Party Logistics network design problem. Since the objective function of the proposed model is non-linear, an approximation linearization method is introduced to adjust the proposed model to be an equivalent linear model. Numerical experiments are designed to justify the effectiveness of the proposed method. Through a thorough analysis on customer psychological behavior, it can be seen that customers tend to be more risk-averse for gains than risk-seeking for losses in Fourth Party Logistics supply chain network design. Moreover, valuable investment insights are recapitulated. This proposed method provides an effective tool for a Fourth Party Logistics provider to give reasonable suggestions to an investor in Fourth Party Logistics supply chain network design. Furthermore, we extend the basic model of 4PL supply chain network design considering customer satisfaction with multiple commodities and provid a solution method based on greedy adding heuristic to further reduce the calculation time for large scale cases.

Dynamic Deformation Characteristics of Soil in the Tasks of Seismic Micro Zoning

The article discusses a technique for determining the nonlinear characteristics of the layers of computational models of the soil profile for the equivalent linear and nonlinear modeling of its response to seismic effects. The results of studying the factors influencing the curves of the strain-dependent shear modulus G (γ) and damping ratio D (γ) are analyzed. Based on the results of the analysis, the main parameters have identified that control the shape of the curves and allow you to quickly select the corresponding curves from the existing database with acceptable accuracy for each layer of the soil profile model. For clayey rocks: this is the plasticity index PL and the depth of occurrence; for sandy rocks: particle size, percentage, and depth. The paper presents the results of studying the effect of relative errors that arise when choosing the curves G (γ) and D (γ) for the soil layers of the computational seismic-geological model on the parameters of the frequency response of the soil, calculated using the equivalent linear modeling of ground vibrations during earthquakes. It was found that errors in determining the strain characteristics of soil layers in the calculation model lead to a shift in the maxima of the amplitude-frequency characteristic, to a change in the amplification factors of oscillations, as well as to the appearance of "false" maxima at high frequencies.
 The methodological approach to the formation of computational seismic-geological models of soil strata, by introducing the curves G (γ) and D (γ), which reflect the nonlinear properties of the soil, makes it possible to improve the computational methods for determining the resonance properties of soils under construction sites. The most accurate values of the frequency characteristics of the soil strata under construction sites are necessary for the development of effective measures to ensure the seismic resistance of the designed and existing facilities.
 As a result, the validity and accuracy of determining the quantitative parameters of seismic hazard at the construction and operational sites under study are increased.

Energy Efficiency Analysis of Light-Emitting Diodes With High Modulation Bandwidth

This letter proposes an analytical model on the energy efficiency for visible light communications (VLC) based on light-emitting diode (LED). We certify the variation pattern of energy efficiency of LEDs follows the second-order system rather than the first-order system like the LED’s frequency response. This pattern means considerable power loss in the VLC transmission, which should be taken care of when designing VLC systems. This letter demonstrates a series of simulations and experiments to prove this viewpoint’s accuracy. Moreover, by comparing the experimental results, we analyze the influence of LED’s parasitic parameters on energy efficiency. Furthermore, a linear LED equivalent circuit model is given for the high modulation bandwidth application. We test it by calculating its decisive coefficients according to different LEDs’ experimental results.

A Chance Constrained Programming Approach for No-Wait Flow Shop Scheduling Problem under the Interval-Valued Fuzzy Processing Time

This work focuses on the study of robust no-wait flow shop scheduling problem (R-NWFSP) under the interval-valued fuzzy processing time, which aims to minimize the makespan within an upper bound on total completion time. As the uncertainty of actual job processing times may cause significant differences in processing costs, a R-NWFSP model whose objective function involves interval-valued fuzzy sets (IVFSs) is proposed, and an improved SAA is designed for its efficient solution. Firstly, based on the credibility measure, chance constrained programming (CCP) is utilized to make the deterministic transformation of constraints. The uncertain NWFSP is transformed into an equivalent deterministic linear programming model. Then, in order to tackle the deterministic model efficiently, a simulated annealing algorithm (SAA) is specially designed. A powerful neighborhood search method and new acceptance criterion are applied to find better solutions. Numerical computations demonstrate the high efficiency of the SAA. In addition, a sensitivity analysis convincingly shows that the applicability of the proposed model and its solution strategy under interval-valued fuzzy sets.

Seismic response analysis and modal identification of a full-scale five-story base-isolated building tested on the NEES@UCSD shake table

This paper presents the analysis of the seismic response and the identification of the dynamic properties of an equivalent linear time-invariant model of a full-scale five-story base-isolated reinforced concrete building tested on the unidirectional NEES@UCSD shake table. A sequence of seven scaled historic earthquake records was applied by the shake table to the building, progressively increasing the seismic demand on the structure and its nonstructural components and systems. The effects of the isolation system on elongating the predominant period of the building, concentrating the displacement in the isolation layer, and augmenting the energy dissipation capacity of the building system are investigated. Low-amplitude white noise (WN) base excitation tests were conducted before and after each seismic test and ambient vibration (AV) data were recorded continuously for a period of approximately sixteen days containing the sequence of seven seismic tests performed. Because of the low intensity of the white noise base and ambient excitations, a quasi-linear response of the base-isolated building is assumed, allowing the modal parameters of an equivalent linear viscously damped time-invariant model to be estimated from vibration data recorded during the WN and AV tests. Different state-of-the-art system identification methods, including output-only and input-output methods, are used to estimate the modal properties of the base-isolated building. Results show that the identified modal parameters obtained from different methods are in good agreement and that the assumption of quasi-linear response for each low-amplitude test is appropriate. The effects of the amplitude of the excitation, earthquake input motions, and environmental conditions are clearly evidenced by the changes induced in the estimated modal parameters of the building.

The Importance of Phase in Complex Compressive Sensing

We consider the question of estimating a real low-complexity signal (such as a sparse vector or a low-rank matrix) from the phase of complex random measurements. We show that in this phase-only compressive sensing (PO-CS) scenario, we can perfectly recover such a signal with high probability and up to global unknown amplitude if the sensing matrix is a complex Gaussian random matrix and the number of measurements is large compared to the complexity level of the signal space. Our approach proceeds by recasting the (non-linear) PO-CS scheme as a linear compressive sensing model built from a signal normalization constraint, and a phase-consistency constraint imposing any signal estimate to match the observed phases in the measurement domain. Practically, stable and robust estimation of the signal direction is achieved from any instance optimal algorithm of the compressive sensing literature (such as basis pursuit denoising). This is ensured by proving that the matrix associated with this equivalent linear model satisfies with high probability the restricted isometry property under the above condition on the number of measurements. We finally observe experimentally that robust signal direction recovery is reached at about twice the number of measurements needed for signal recovery in compressive sensing.

Kinematic Analysis of SAVGS

The SAVGS as active low bandwidth retrofitted in the double-wishbone arrangement is studied. In this study, two configurations of arm linkages and variations of single-link are investigated. A linear equivalent model of the quarter car is presented based on energy conservation principles. The estimated results captured that the spring stiffness and damping coefficients of the equivalent model behave smaller when lengthening the lower arm geometry. On the other hand, the spring stiffness, damping coefficients, and linear actuator speed of the equivalent model increase when lengthening the single-link.

Identifying proactive ICU patient admission, transfer and diversion policies in a public-private hospital network

Management of hospital beds is a high-impact issue for two-tier healthcare systems, due principally to their critical importance and high costs. Bed capacity in the public sector is generally insufficient to provide immediate care to all critical patients and thus a significant proportion of public expenditure is assigned to the diversion of patients for treatment in the private sector. We formulate and approximately solve a discounted infinite-horizon Markov Decision Process (MDP) that seeks to identify cost-effective policies for transferring ICU patients between hospitals or diverting them to private clinics. The solution approach employs an affine architecture for approximating the value function of the MDP model and solves the equivalent linear programming model using column generation. The approach can handle a high level of dimensionality, enabling it to consider the arriving patients’ many different diagnostic groups and their corresponding lengths of stay. The decisions generated through this approach often differ from the intuitive ones produced in a typical day-by-day decision process, that does not consider the impact of the current day’s decisions on the future performance of the system. In particular, the resulting policies will in many cases proactively transfer patients to a different public facility or divert them to a private one even though the hospital they first arrived at had beds available. The performance of the proposed method was evaluated by simulating a case study based on data from a hospital network in Santiago, Chile, producing savings of almost 49% due mostly to reduced usage of private services.

On the implementation and validation of a three‐dimensional pressure‐dependent bounding surface plasticity model for soil nonlinear wave propagation and soil‐structure interaction analyses

AbstractNumerous experiments and prior analyses have confirmed that soil inelasticity, which is known to come into effect even at very low strain levels, can significantly affect site response and dynamic soil‐structure interaction (SSI) behavior. To date, only a few studies were able to consider multi‐axial wave propagation problems with appropriate models of soil nonlinearity. Most existing works are limited to either homogeneous soil configurations or equivalent linear soil models. The instances wherein soil nonlinearity is accurately considered have been confined to single element tests and one‐dimensional problems. In this study, an improved pressure‐dependent bounding surface plasticity soil model—with appropriate plastic strain rate direction definition and overshooting correction scheme—is implemented in Abaqus, and validated using recordings from both the Lotung borehole array and centrifuge test data on embedded flexible structures. The implemented model is capable of comprehensively reproducing complex soil behaviors, such as stiffness degradation, damping, dilatancy, and compaction while under a wide strain range, and under general loading conditions using only a few material parameters to be calibrated. Consequently, numerically predicted results are observed to be in better agreement with experimentally measured data, in comparison with linear and another plasticity model, which include accelerations, and bending and hoop strains along the walls of the specimen structures, for low‐ as well as high‐amplitude input motions.

Regression-based flexible models for photochemical air pollutants in the national capital territory of megacity Delhi

Modelling photochemical pollutants, such as ground level ozone (O3), nitric oxide (NO) and nitrogen dioxide (NO2), in urban terrain was proven to be cardinal, chronophagous and complex. We built linear regression and random forest regression models using 4-years (2015–2018; hourly-averaged) observations for forecasting O3, NO and NO2 levels for two scenarios (1-month prediction (for January 2019) and 1-year prediction (for 2019)) — with and without the impact of meteorology. These flexible models have been developed for, both, localised (site-specific models) and combined (indicative of city-level) cases. Both models were aided with machine learning, to reduce their time-intensity compared to models built over high-performance computing. O3 prediction performance of linear regression model at the city level, under both cases of meteorological consideration, was found to be significantly poor. However, the site-specific model with meteorology performed satisfactorily (r = 0.87; RK Puram site). Further, during testing, linear regression models (site-specific and combined) for NO and NO2 with meteorology, show a slight improvement in their prediction accuracies when compared to the corresponding equivalent linear models without meteorology. Random forest regression with meteorology performed satisfactorily for indicative city-level NO (r = 0.90), NO2 (r = 0.89) and O3 (r = 0.85). In both regression techniques, increased uncertainty in modelling O3 is attributed to it being a secondary pollutant, non-linear dependency on NOx, VOCs, CO, radicals, and micro-climatic meteorological parameters. Analysis of importance among various precursors and meteorology have also been computed. The study holistically concludes that site-specific models with meteorology perform satisfactorily for both linear regression and random forest regression.

A credibility-based fuzzy programming model for the hierarchical multimodal hub location problem with time uncertainty in cargo delivery systems

This paper studies the fuzzy hierarchical multimodal hub location problem for cargo delivery systems. It differs from traditional hub location problem in two ways. First, this paper constructs a hierarchical multimodal hub-and-spoke distribution network for the cargo delivery systems, which involves two transportation modes (road and air), two types of hubs (ground and airport) and three corresponding layers. Second, this paper develops a credibility-based fuzzy programming model capturing the uncertainty in travel time and handling time of the cargo delivery systems. This new model aims to minimize the latest arrival time (travel time plus handling time) for delivering cargoes from each pair of origin and destination nodes under diverse credibility of chance constraints. Under mild assumptions, the original model can be turned into an equivalent deterministic integer linear programming model. However, even for small instances of the problem, the equivalent model becomes too hard to be tackled by a general solver, e.g., CPLEX. This fact motivates the development of a two-stage heuristic procedure, wherein the first stage for the hub location subproblem is solved by a variable neighborhood search algorithm. These location solutions are then embedded into the second-stage process for the link assignment subproblem based on a shortest path method. To verify the proposed model and method, extensive numerical experiments are conducted on the well-known Turkish network data set.

Massive MIMO Channel Estimation With Low-Resolution Spatial Sigma-Delta ADCs

We consider channel estimation for an uplink massive multiple-input multiple-output (MIMO) system where the base station (BS) uses an array with low-resolution (1-2 bit) analog-to-digital converters and a spatial Sigma-Delta ( ΣΔ) architecture to shape the quantization noise away from users in some angular sector. We develop a linear minimum mean squared error (LMMSE) channel estimator based on the Bussgang decomposition that reformulates the nonlinear quantizer model using an equivalent linear model plus quantization noise. We also analyze the uplink achievable rate with maximal ratio combining (MRC), zero-forcing (ZF) and LMMSE receivers and provide a lower bound for the achievable rate with the MRC receiver. Numerical results show superior channel estimation and sum spectral efficiency performance using the ΣΔ architecture compared to conventional 1- or 2-bit quantized massive MIMO systems.

Linear Equivalent Model for VHF Class Φ2 Inverter Based on Spectrum Quantification Method to Reduce GaN Reverse Conduction Loss

Reverse conduction loss of GaN high electron mobility transistors (HEMTs) in very high frequency (VHF) converters is non-neglectable due to the absence of body diode. To reduce the reverse conduction time, this paper proposes a linear equivalent model for class <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi _{2}$ </tex-math></inline-formula> inverter to derive optimal duty cycles for different working conditions. The proposed model is derived from frequency-domain perspective, which simplifies the derivation process and provides an intuitive physical insight for class <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi _{2}$ </tex-math></inline-formula> inverter. Firstly, the power switch is modeled as a current source according to time-domain expressions of inductor current, which simplifies the circuit to a linear network. Based on quantitative analysis of the current source spectrum characteristics, the linear network response to the current excitation is derived, which forms the linear equivalent model. Then, drain voltage of the main switch under different working conditions is obtained. With the zero-crossing point of the drain voltage, numerical solutions of the optimal duty cycles are calculated. Finally, the optimal duty cycles are implemented with a high-resolution duty cycle generation circuit in a 27.12MHz prototype, which achieves not only a peak efficiency of 93.6% at full load, but also higher efficiency over the whole load and input voltage range compared to conventional fixed duty cycle.

Some Non-Linear Problems in Accounting and Finance: Can we Apply Regression?

Recent studies have indicated that many decision problems in accounting and finance can be better modeled by non-linear models in practice. However, existing literatures have also shown that managers and decision makers are not very conversant with non-linear models as compared to linear models because of the simplicity of linear models. In this paper, attempts are made to transform some non-linear models in accounting and finance which conform to exponential and power functions to their equivalent linear forms. The resulting equivalent linear models are subjected to regression analysis. The paper documents interesting practical non-linear problems in accounting and finance where it is possible to apply regression, and provides technical interpretations of coefficients of resulting regression equations. Some non-linear problems which have been documented in this analysis include; depreciation of non-current assets, the learning curve model, life cycle costing, compounding, discounting and exponential growth bias. Although logarithmic transformation of non- linear functions is not a novel idea in literature of accounting and finance, there is no evidence in literature that scholars have proposed particular cases in finance and accounting where these linear transformations and their resulting regression equations would yield meaningful results that can enhance management decision making. This paper fills this gap by documenting practical non-linear problems in finance and accounting where linearization and subsequent application of regression analysis generates useful results for management decision making purposes.

ГЕОДИНАМІКА

Purpose. The paper substantiates the need for building seismic zoning maps of Kyiv in the physical parameters of ground motions: peak ground accelerations (PGA), peak ground velocities (PGV) or peak ground displacements (PGD), which are the basis for the effective use of methods for calculating seismic loads on buildings, structures and individual responsible constructions. An intermediate stage in the creation of such maps is the development of a map of seismic zoning of the territory of Kyiv in terms of relative integral estimates of spectral increments in seismic soil oscillations, arising from the influence of the peculiarities of the distribution of physical parameters of soils. The intermediate map gives the distribution over the city territory of a quantitative assessment of the influence of the spectral characteristics of the soil on the seismic hazard, expressed in systemic physical quantities. Methodology. An analytical-empirical approach to mapping the seismic hazard of territories is applied. Within the territory of Kyiv, using the method of seismic-geological analogies, areas (taxonomic zones) were identified, where the seismic effect can differ significantly both in physical parameters: displacement, speed, acceleration – and the ability of soil strata to significantly affect the spectral characteristics of the soil. Results. For each taxonomic zone, a computational seismic-geological model with inelastic deformation parameters has been built, which makes it possible to take into account the occurrence of nonlinear effects under significant seismic influences. Equivalent linear modeling was used to calculate the frequency response of seismic-geological soil models for each taxonomic zone. The averaged frequency response for the ground conditions of the territory of Kyiv was calculated. A map of the distribution of the deviation of the integral amplification of seismic oscillations from the average value for the territory of Kyiv was built. The integral spectral amplification is the area of the subspectral function. A dynamic analysis of the propagation of seismic oscillations in seismic-geological models is carried out and the influence of the upper sedimentary layer on the value of the peak ground acceleration PGA on the free surface is illustrated. Originality. For the first time within the territory of Kyiv, areas (taxonomic zones) have been identified, where the response of the soil to the seismic effect will differ. A map of the distribution of the deviation of the integral amplification of seismic oscillations by soils from the average value for the territory of Kyiv was constructed. Practical significance. The map of seismic zoning of Kyiv in amplitude terms of soil oscillations is proposed to be used when applying the spectral method for calculating an emergency combination of loads, taking into account seismic effects, to determine the value of the calculated relative ground accelerations of the construction site under study.