Equivalent Linear Model Research Articles

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.

Collaborative real-time optimization strategy for train rescheduling and track emergency maintenance of high-speed railway: A Lagrangian relaxation-based decomposition algorithm

To ensure the efficient operation and low maintenance costs of high-speed railway lines, a collaborative real-time optimization strategy for train rescheduling and track emergency maintenance is proposed in this paper. This strategy not only makes online decisions on the track emergency maintenance, but simultaneously deals with the delays caused by the track emergency and disturbances. Based on a bi-directional railway line, a mixed-integer nonlinear optimization model is established, in which the decision variables mainly include the track maintenance intervention type, the end time of track maintenance, arrival/departure time, arrival/departure orders, stopping plans, and train cancellations. The proposed nonlinear model is converted to an equivalent linear model by a linearization method to reduce the computational burden. Moreover, a Lagrangian relaxation-based decomposition algorithm under a rolling horizon framework is designed to satisfy the real-time performance further. Particularly, the rolling horizon framework divides the whole time horizon into three stages according to the status of the maintenance work, i.e., the maintenance decision-making stage, the maintenance stage, and the maintenance completion stage. Furthermore, the Lagrangian relaxation-based algorithm decomposes the original large-scale optimization problem into several smaller sub-problems, which can be computed in parallel to improve the solution procedure. This designed algorithm not only reduces the computation effort for the real-time implementation, but also realizes online feedback correction and improves the robustness of the control strategy. Several numerical experiments are carried out based on the data of Beijing-Shanghai high-speed railway to demonstrate the feasibility and effectiveness of the proposed strategy.

Equivalent linear pseudostatic and dynamic modelling of vertically vibrating monopile

To optimize offshore wind turbine (OWT) design, an engineering tool has been developed allowing for a detailed investigation of the effects of nonlinear soil stiffness and damping on foundation dynamics. We have studied the response of a vertically oscillating offshore wind monopile foundation in a realistic soil profile subjected to loads between 1 and 200 MN in the frequency range 0–10 Hz with pseudo-static and equivalent linear dynamic model. The non-linear soil behaviour is modelled with an equivalent linear method with shear modulus reduction and damping curves as input. The tool is verified and validated by comparison with elasto-dynamic model and experiments. With increasing load amplitudes foundation stiffness increases and damping decreases. For large load amplitudes the lower part of the pile foundation contributes more to foundation damping. The results indicate the nonlinear foundation stiffness and damping can be modelled rationally by combining stiffness and hysteretic damping from nonlinear static tools with apparent mass and radiation damping from elasto-dynamic analysis. The tool can be used to compute soil springs and dampers based on laboratory-based soil stiffness and damping.

Influence of Dose/Volume Parameters, Equivalent Uniform Dose and Linear Quadratic Model on Prediction Power of NTCP Model for IMRT: Based on the Analysis of Brain Injury

Influence of Dose/Volume Parameters, Equivalent Uniform Dose and Linear Quadratic Model on Prediction Power of NTCP Model for IMRT: Based on the Analysis of Brain Injury

Multicarrier Energy System Management as Mixed Integer Linear Programming

This paper presents the problem model of multicarrier energy system management. The proposed problem includes three types of energy that is as electrical, natural and heating. Electrical and gas energies are as hub input, and hub output is as electrical and heating. The electricity energy provides using (1) renewable energy sources (RESs), electrical energy storage system, combined heat and power (CHP) system that are managed by hub operator and are not to play at market and (2) electricity market with PoolCo and bilateral contracts models. Therefore, the proposed problem is as optimization problem that its objective function is minimizing energy cost of hub. The constraints are electrical, natural and district heating networks power flow, RES, storage system, CHP and market constraints, and limitation of all networks indexes. This problem is modeled as mixed integer nonlinear programming. But, this paper uses the equivalent mixed integer linear programming model for accessing to optimal solution with low calculation time and error. Finally, this problem applied to standard test network with GAMS software, and thus, the capability of proposed problem investigates.

A Winkler-based model for inelastic response of soil–structure systems with embedded foundation considering kinematic and inertial interaction effects

In this paper, a parametric study is carried out on the ductility and displacement demands of structures with embedded foundation considering nonlinear soil–structure interaction (SSI). The soil–embedded foundation interaction is simulated using the beam on Winkler foundation concept. The bilinear behavior is also assumed for the equivalent single-degree-of-freedom (SDOF) structure. Effect of key parameters including fundamental period, level of inelasticity, soil flexibility, embedment ratio, and slenderness ratio on the seismic demands is examined. A family of soil–structure systems are analyzed subjected to a group of 33 ground motions recorded on alluvium deposits. Both sway and rocking components of foundation input motion are applied to the system. Results reveal that foundation embedment generally increases the ductility demand of the SDOF system. Moreover, the kinematic interaction (KI) effect on ductility demands is more prominent for structures with deep embedment ratios. As the aspect ratio increases, the role of rocking input motion on ductility and displacement demands becomes more noticeable. It is also concluded that the nonlinear SSI can increase the displacement demand of interacting systems as compared to the equivalent linear soil model. Based on the obtained results, a simplified expression is proposed to estimate the displacement ratio for soil–structure systems with embedded foundation considering KI effects.

Equivalent linear model for the lateral dynamic analysis of pile foundations considering pile-soil interface degradation

An equivalent linear BEM-FEM model for the approximate analysis of the time harmonic lateral response of piles considering soil degradation along the soil-pile interface is proposed. The non-degraded soil around the foundation is modelled with boundary elements as a continuum, semi-infinite, isotropic, homogeneous or zoned homogeneous, linear, viscoelastic medium. Piles are modelled with finite elements as beams according to the Bernoulli hypothesis. Differently from what is considered in other BEM-FEM coupled numerical schemes, welded contact conditions are not assumed herein between piles and soil. On the contrary, displacements along FEM piles and within BEM soil are related through distributed springs and dashpots whose properties vary along the pile and that represent the varying stiffness and energy dissipation properties of a pile-soil interface with different levels of degradation at different depths. The developed numerical model is verified by comparison against a more rigorous but much more costly multi-domain boundary element model in which the same degraded soil regions around the pile are modelled as three-dimensional regions.

IGDT-Based Robust Optimization for Multicarrier Energy System Management

In this paper, the information-gap decision theory (IGDT)-based robust problem model for multicarrier energy system (MES) management is presented. It is noted that in the proposed problem, electrical and gas energies are inputs of MES or energy hub, and electrical and heating energies are outputs of MES. The output electrical energy of hub provided by renewable energy sources (RESs), storage system, combined heat and power (CHP) system is managed by hub manager, and they do not participate in the market and input electrical energy. Also, it is considered that input electrical energy is bought from the PoolCo and bilateral contract markets. Moreover, the CHP is only connecting element for different energies. Therefore, the deterministic problem model expresses in the first step, where its objective function is minimized of hubs energy cost. Also, the constraints of problem are power flow equations and indexes limit in electrical, natural gas and district heating networks, PoolCo and bilateral contract market models, RES, storage system and CHP equations. This problem is as mixed integer nonlinear programming, where in the next step, the equivalent mixed integer linear programming model is presented because this new model can obtain the global optimal solution with low calculation error and time. In addition, the different loads, energy price in PoolCo market and RESs output power are uncertain parameters. Hence, this paper for considering uncertainty parameters presents the IGDT-based robust optimization for proposed problem. Finally, this problem is applied to standard test network with GAMS software, and thus the capability of the proposed problem investigates.

Observer-Based Controllers for Two-Wheeled Inverted Robots with Unknown Input Disturbance and Model Uncertainty

In this paper, two controllers with a compound disturbance observer are proposed for a two-wheeled inverted robot (TWIR) with model uncertainty and unknown input disturbance. First, an equivalent linear model of the TWIR with uncertainty and input disturbance is proposed using the Taylor series expansion for the nonlinear model of the TWIR at an equilibrium point, in which the nonlinear part of the Taylor series and the model uncertainty are combined with unknown input disturbance as compound input disturbance. Then, the compound input disturbance is estimated by using the Newton method and reference model. As the estimated compound disturbance is used to compensate for the compound disturbance, the equivalent linear system becomes closely definite without compound input disturbance. Finally, two controllers are proposed using the equivalent linear system. Stability analysis of the proposed control methods is also given. To illustrate the proposed methods, some simulations for the TWIR are performed and compared with the existing methods. The main contribution of this work includes the following: (i) simple controllers based on compound input disturbance observer for trajectory tracking and balancing of TWIRs with unknown input disturbance and model uncertainty are proposed; (ii) the stability of proposed closed-loop control systems is proved; (iii) our proposed methods are simulated and compared with the existing methods.

Performance of multi-scenario equivalent hydropower models

Simulations and analysis of large hydro-thermal power systems easily become computationally heavy without simplifications of the system at hand. Hydropower, in particular, presents a challenge as complex river systems add a large amount of variables and linked constraints to the analysis. A possible simplification is to use aggregated Equivalent models for different parts of the hydrosystem which give similar results, with respect to e.g. power production, as a more detailed description of the Original system. In this paper, novel linear multi-scenario Equivalent models for hourly simulations of nonlinear hydropower systems are developed and their performance investigated. The new models consider multiple scenarios for inflow, price and start resp. end content in the reservoirs as well as reserves for balancing capacity. The performance analysis is based on case studies over Swedish hydropower systems located in the electricity trading area SE1. The average relative error in power production is 9–15% and the computation time is reduced from 9 hours to between 0.4 and 36 seconds.

Direct identification of nonlinear damping: application to a magnetic damped system

In the identification of mechanical systems through inverse receptance methods, a linear model is usually assumed, at least on a first approximation. However, most of the systems have a degree of nonlinearity in their elastic or dissipative properties. Usually, stiffness nonlinearities are identified, while damping nonlinearities are neglected or even not detected. Indeed, an equivalent linear damping model, correctly representing the nonlinear dissipation of the system under testing condition, can always be found, but it is test-specific and not generally valid.This paper addresses the identification of dissipative models for multi degrees of freedom mechanical systems with a single damping nonlinearity. Based on the direct damping matrix identification through inverse receptance methods, this research proposes an extension of the Stabilised Layers Method, valid for linear systems, to damping nonlinearities, resulting in the identification of the test-independent linear and nonlinear damping matrices of the system. The proposed method is theoretically derived for the identification of nonlinear damping forces depending on powers of displacement and velocity. The sinusoidal input describing function approximation of the nonlinear damping is exploited to identify the coefficients of the nonlinear damping force from the system receptances, measured under sinusoidal sweeps at constant amplitudes of oscillation across the nonlinearity.The presented method is applied to identify the linear and nonlinear damping matrices of a multi degrees of freedom system with a localised nonlinear magnetic damper. The coefficients of the nonlinear magnetic damping force are identified for two configurations of the magnetic damper.The proposed approach is a parametric method to identify the nonlinear damping models of mechanical systems using standard experimental techniques usually adopted for linear systems. The identified model is valid under general excitation forces, predicting the system behaviour in a broader range of operation than the test-specific linear equivalent model.

A study of the effects of foundation uplift on the seismic loading of wind turbine tower and shallow foundation using a new dynamic Winkler model

In this study, the effects of foundation uplift on the seismic loading of wind turbine tower and shallow foundation are investigated. A dynamic Winkler model is proposed for the dynamic response analysis of shallow foundation supported structures and is named as QzSimple4, in which PySimple3 is applied to replace the elastoplastic component in QzSimple2 for the compression under the foundation and the gap model in QzSimple1 is assembled to capture the foundation uplift. The proposed model agrees well with the q-z experimental backbone curves and reasonably captures the acceleration responses of the bridge deck and the settlement-rotation responses of the shallow foundation under various excitation levels. However, QzSimple2 model strongly overestimates the q-z backbone curves in terms of linear range and ultimate bearing capacity, which leads to obviously overestimate some acceleration responses of the bridge deck and significantly underestimate the settlement responses of the shallow foundation. Finally, a systematical study is performed to investigate the effects of foundation uplift on the seismic loading by using the proposed Winkler model and the equivalent linear sway-rocking model. The foundation uplift occurs under severe earthquakes. Without considering the foundation uplift, the moment on the wind turbine tower is slightly overestimated, while that on the shallow foundation is significantly underestimated for the large soil stiffness. This is one reason why the shallow foundations at Aso-Nishihara wind farm were damaged during the Kumamoto earthquake.

Nonlinear Model Predictive Control of Steam-Assisted-Gravity-Drainage Well Operations for Real-Time Production Optimization

Summary In deep oil-sands deposits using the steam-assisted-gravity-drainage (SAGD) recovery process, real-time optimization (RTO) involves controlling optimum subcool to ensure steam conformance. Contemporary workflows use linear model predictive control (MPC) with oversimplified models that are inadequate to represent highly complex, spatially distributed, and nonlinear reservoir dynamics. In this research, two novel workflows using nonlinear MPC (NMPC) are proposed. The first workflow reduces an NMPC problem to linear MPC by estimating an equivalent linear model of a nonlinear black-box model in a mean-square-error sense. Another approach is to use nonlinear dynamic models explicitly for accurate prediction of the plant states and/or outputs. The resulting nonconvex, nonlinear cost optimization problem is solved using an interior-point algorithm at each control interval. Proposed workflows are tested using the history-matched, field-scale model of a SAGD reservoir located in northern Alberta, Canada. Qualitative and quantitative analysis of the results reveals that nonlinear black-box models based on system identification theory can successfully capture the nonlinearity of the SAGD process. Also, both workflows can control the subcool above the desired set-point while ensuring stable well operations. More than a 24% increment is achieved in net present value (NPV) using proposed NMPC workflows compared with the field operations with no closed-loop control. Overall, NMPC can successfully be used for improved RTO, energy efficiency, and greenhouse gas emissions while considering available surface facilities and well configurations.

From residential electric load profiles to flexibility profiles – A stochastic bottom-up approach

This paper presents a stochastic bottom-up model for flexibility in the residential electric load profile. The model accounts for user-behaviour and all relevant technologies, characterising their diversity in sizing and controller settings. The flexibility of technology is mapped into a linear electrical storage equivalent model, which is parameterised on-the-fly during simulation of the load profiles. Using a linear storage representation makes it suitable for optimisation methods that are commonly used in optimal controls.The model is used to study the flexibility of individual technologies as well as of a residential area in Germany taking into account technology penetration rates. The results indicate that EV and PV battery systems offer the largest values of switchable power and storage capacity. However when technology penetration rates are taken into account, heat pumps emerge as a major provider of flexibility.

A new multiaxial fatigue life prediction model considering additional hardening effect

The established linear fatigue life prediction model based on the Miner rule has been widely applied to fatigue life prediction under constant amplitude uniaxial and multiaxial loading. Considering the physical significance of crack formation and propagation, a multiaxial equivalent linear fatigue life prediction model is put forward based on Miner rule and critical plane method under constant amplitude loading. The essence of this approach is that the equivalent strain, which consists of the shear strain and normal strain on the critical plane, replaces the relevant parameter of uniaxial nonlinear fatigue damage model. The principal axes of stress/strain rotate under non-proportional loading. Meanwhile, the microstructure of material and slip systems change, which lead to additional hardening effect. The ratio of cyclic yield stress to static yield stress is used to represent the cyclic hardening capacity of material, and the influence of phase difference and loading condition on the non-proportional hardening effect is considered. The multiaxial fatigue life is predicted using equivalent stain approach, maximum shear stain amplitude model, CXH model, and equivalent multiaxial liner model under proportional and/or non-proportional loading. The smooth and notched fatigue specimens of four kinds of materials (Q235B steel, titanium alloy TC4, Haynes 188, and Mod.9Cr-1Mo steel) are used in the multiaxial fatigue experiments to verify the proposed model. The predicted results of these materials are compared with the test results, and the results show that these four models can achieve good effect under proportional loading, but the proposed model performs better than the other three models under non-proportional loading. Meanwhile, it also verifies that the proposed enhancement factor can reflect the influence of phase difference and material properties on additional hardening.

Approximate Analysis for Shear Force Amplification Effect in Ordinary RC Shear Walls

An approximate analysis method is proposed to predict the dynamic amplification of shear forces in ordinary reinforced concrete shear walls as a preliminary study. First, a seismic design for three groups of ordinary reinforced concrete shear walls higher than 60 m was created on the basis of nonlinear dynamic analysis. Causes for the dynamic amplification effect of shear forces were investigated through a detailed evaluation of the nonlinear dynamic analysis result. A new modal combination rule was proposed on the basis of that observation, in which fundamental mode response and combined higher mode response were summed directly. The fundamental mode response was approximated by nonlinear static analysis result, while higher mode response was computed using response spectrum analysis for equivalent linear structural models with the effective stiffness based on the nonlinear dynamic analysis result. The proposed approximate analysis generally predicted vertical distribution of story shear and shear forces of individual walls from the nonlinear dynamic analysis with comparable accuracy.

Spectral Efficiency of One-Bit Sigma-Delta Massive MIMO

We examine the uplink spectral efficiency of a massive MIMO base station employing a one-bit Sigma-Delta sampling scheme implemented in the spatial rather than the temporal domain. Using spatial rather than temporal oversampling, and feedback of the quantization error between adjacent antennas, the method shapes the spatial spectrum of the quantization noise away from an angular sector where the signals of interest are assumed to lie. It is shown that, while a direct Bussgang analysis of the Sigma-Delta approach is not suitable, an alternative equivalent linear model can be formulated to facilitate an analysis of the system performance. The theoretical properties of the spatial quantization noise power spectrum are derived for the Sigma-Delta array, as well as an expression for the spectral efficiency of maximum ratio combining (MRC). Simulations verify the theoretical results and illustrate the significant performance gains offered by the Sigma-Delta approach for both MRC and zero-forcing receivers.

A location model for capacitated alternative-fuel stations with uncertain traffic flows

To maximize the total amount of alternative fuel consumption in a traffic network and satisfy the travel demands to the greatest extent possible, this paper addresses the problem of finding the optimal locations in a transportation network in which to construct capacitated alternative-fuel stations with a limited construction budget. Different from most existing studies that treat traffic flows in each origin-destination pair as a constant, a stochastic chance-constrained programming model (SCCPM) is proposed to characterize the problem of interest in this paper, where random variables are employed to capture the uncertainty of traffic flows. Moreover, for solution convenience, a linear equivalent model of the proposed one is deduced. Finally, two sets of numerical experiments are implemented by the Cplex solver to test the performance of the model. Firstly, a series of experiments are conducted on the small scale network to analyze the sensitivities of the parameters in the proposed model. Then we find the optimal locations for alternative-fuel stations in the large-scale network and draw the conclusion that most of the alternative-fuel vehicles are located in demands cluster districts according to the thermodynamic diagram.

Composite equivalent mechanical models for large-amplitude liquid sloshing in axisymmetrical tanks

Equivalent mechanical models are widely used to describe the dynamics of liquid sloshing in aerospace engineering, but the traditional equivalent mechanical models based on linear theory have poor applicability and accuracy in large-amplitude sloshing. The composite equivalent modeling method suitable for large-amplitude sloshing in normal and low-gravity is proposed in this paper. By considering the change of liquid equilibrium position in sloshing, the large-amplitude motion of the liquid relative to the tank is decomposed into bulk motion following the equivalent gravity and additional small-amplitude sloshing, thus greatly expands the application scope of the linear equivalent mechanical model. Taking the axisymmetrical tanks as examples, the liquid dynamic equilibrium position following the equivalent gravity under large-amplitude sloshing is determined, and the composite equivalent mechanical model in the form of a spherical pendulum is established. For spherical tanks, all liquid is assumed to be involved in bulk motion and the model parameters are found constant during sloshing. For non-spherical tanks such as cylindrical and Cassini tanks, liquid near the tank wall is assumed motionless relative to the tank, and the time-dependent model parameters are approximated by linear interpolation based on equivalent gravity and inclination of the liquid surface. Based on the spherical pendulum model, the dynamic equation of the equivalent system is derived, thus the slosh forces, moments and positions of the liquid center of mass under large translational and rotational excitations are calculated in 3D axisymmetrical tanks. To verify the validity of the modeling method and the accuracy of the composite model, the results of the composite equivalent mechanical model, the traditional equivalent mechanical model as well as the computational fluid dynamics (CFD) software are compared and analyzed. As shown by the results, the composite equivalent mechanical model proposed can accurately predict the dynamic responses of large-amplitude liquid sloshing in axisymmetrical tanks.