Series Approximation Method Research Articles

Accurate EVSI Estimation for Nonlinear Models Using the Gaussian Approximation Method.

The expected value of sample information (EVSI) measures the expected benefits that could be obtained by collecting additional data. Estimating EVSI using the traditional nested Monte Carlo method is computationally expensive, but the recently developed Gaussian approximation (GA) approach can efficiently estimate EVSI across different sample sizes. However, the conventional GA may result in biased EVSI estimates if the decision models are highly nonlinear. This bias may lead to suboptimal study designs when GA is used to optimize the value of different studies. Therefore, we extend the conventional GA approach to improve its performance for nonlinear decision models. Our method provides accurate EVSI estimates by approximating the conditional expectation of the benefit based on 2 steps. First, a Taylor series approximation is applied to estimate the conditional expectation of the benefit as a function of the conditional moments of the parameters of interest using a spline, which is fitted to the samples of the parameters and the corresponding benefits. Next, the conditional moments of parameters are approximated by the conventional GA and Fisher information. The proposed approach is applied to several data collection exercises involving non-Gaussian parameters and nonlinear decision models. Its performance is compared with the nested Monte Carlo method, the conventional GA approach, and the nonparametric regression-based method for EVSI calculation. The proposed approach provides accurate EVSI estimates across different sample sizes when the parameters of interest are non-Gaussian and the decision models are nonlinear. The computational cost of the proposed method is similar to that of other novel methods. The proposed approach can estimate EVSI across sample sizes accurately and efficiently, which may support researchers in determining an economically optimal study design using EVSI. The Gaussian approximation method efficiently estimates the expected value of sample information (EVSI) for clinical trials with varying sample sizes, but it may introduce bias when health economic models have a nonlinear structure.We introduce the spline-based Taylor series approximation method and combine it with the original Gaussian approximation to correct the nonlinearity-induced bias in EVSI estimation.Our approach can provide more precise EVSI estimates for complex decision models without sacrificing computational efficiency, which can enhance the resource allocation strategies from the cost-effective perspective.

Correlated Queues with Inter-Arrival Times Depending on Service Times

We consider a type of correlated queue in which the inter-arrival time between two consecutive customers linearly depends on the service time of the first customer. We first derive infinite systems of linear equations for the moments of the waiting time in two special cases, based on which we then develop several methods to calculate the moments of the waiting time by using MacLaurin series approximation, Padé approximation and truncation method. In addition, we show how the moments and covariances of the inter-departure times of the correlated queue can be calculated based on the moments of the waiting time. Finally, extensive numerical examples are provided to validate our methods.

Generalized linear‐constrained optimal power flow for distribution networks

AbstractOptimal power flow (OPF) plays an important role in the secure and economical operation of the distribution network. This paper proposes a novel generalized linear‐constrained optimal power flow (GLOPF) model for both radial and mesh distribution networks, which iteratively approaches the optimal solution to the original OPF problem. The first‐order Taylor series approximation method is applied to linearize the non‐linear and non‐convex power flow constraints for a given Taylor expansion point (TEP). In addition, the objective function of the GLOPF model is only added with an easy‐compute second‐order penalty on state variables, which is at least positive semi‐definite and guarantees the convexity of the quadratic optimization. Then a TEP‐based iterative (TEP‐I) method is proposed in the GLOPF model to construct a series of linear‐constrained convex quadratic optimizations, which avoids the complex calculation of quasi‐Hessian or Hessian matrices in traditional sequential programming methods. The converged solution to the GLOPF model is proved to satisfy the Karush–Kuhn–Tucker conditions of the original OPF problem. Furthermore, the GLOPF model at first and second iterations can be implemented as the ‘cold‐start’ and ‘warm‐start’ LOPF models, respectively. Case studies verify the super‐linear convergence and high accuracy of the proposed GLOPF model.

Nonlinearity and forecast performance of realized volatility

This study examines whether accounting for the nonlinearity of realized volatility leads to better forecast performance. We propose a new realized volatility forecasting model that considers nonlinearities without the assumption of a particular nonlinear model. The proposed model uses the Taylor series approximation method to account for nonlinearities. We applied it to the realized volatility of representative stock indices from the U.S., Japan, the U.K., and China and observed their in-sample nonlinearities. Additionally, we evaluate out-of-sample forecast performance. The empirical results show that realized volatility has nonlinearity, and the proposed models exhibit better forecast performance than standard models.

An Analytical Solution of the Total Strain Energy Release Rate and Mode Partitioning of a Beam Type Delamination Specimen under High Speed Mixed-Mode Loading

In this work an analytical solution for the calculation of the total Stain Energy Release Rate and mode partitioning of beam type delamination specimen, at crack initiation, under high speed, mixed-mode loading is obtained for the first time. The analytical model is based on the dynamic response of a Mixed-Mode End Load Split type specimen subjected to loading with a constant velocity. The Timoshenko beam theory is used to model the specimen's kinematics and the mode partitioning method used is based on the Virtual Crack Closure Technique. To model the bonded region a method based on Lagrangian multipliers is utilized. The specimen is considered as a waveguide and the waves that are allowed to propagate are analytically obtained. Due to the complexity of the analytical form of the wavenumbers for the bonded region of the specimen, which makes the calculation of eigenfrequencies intractable, a series approximation method is used. The results of the proposed analytical solution are verified using a 2D Finite Element Model. The results show the dependency of the Strain Energy Release Rate and the mode mixity on the eigenfrequencies and the eigenmodes of the specimen rendering the value of the mode mixity highly inconsistent through time.

Nonlinear technique of prestressing spatial structures

One of the crucial aspects of the design of structural space systems is the degree of prestressing since it is involved in the load transferring, deformability and charges. The prestress state can be reached via required member alteration. This paper presents an efficient nonlinear numerical approach based on the force method for prestressing the spatial nonlinear structures to the desired level through computing nonlinear actuation as a function of external nodal displacements. Two equations are derived for indicating the required amount of member alteration eo and prestressing level by using Taylor's series and Pade approximation methods. This technique can be applied to both rigid and flexible spatial structures. The present technique is validated based on three numerical examples, and the computational findings are in well agreement with the compared methods. The results show that the new approach requires less effort and makes greater economic sense. Moreover, the member forces with concern to nonlinear eo of double-layer space grid structure by imposing lack of fit of some members successfully obtained.

Soret Dissipation Effect On Heat And Mass Transmission Of Non-Newtonian Casson Radiative Nanofluid Flow With Lorentz Drag And Rosseland Radiation

The goal of the current study considers the impact of Lorentz force and radiation on the reactive Casson-Nanofluid flow over a flow over a stretched surface with Soret impact. However, its industrial and technological applications are numerous but not limited to solar power, glass spinning, nuclear reactors, processing and packaging of food, etc. The flow being considered is a function of the stretched surface along its direction in line with a linearly changing velocity with such distance from a given immovable point. The partial differential equations describing the momentum, energy (heat) and mass transfer equations were transformed into non-linear ordinary differential equations in non-dimensional forms through the use of the similarity variables approach. The solution which was carried out through the application of the series approximation method is presented analytically. However, the Mathematica software was used in obtaining the numerical solutions. Thus, the impacts of physical parameters of the fluid were studied. The results indicated that: the velocity of fluid flow lessens due to the combined intensification of values of the non-Newtonian Casson fluid and magnetic field parameters. An upsurge in Grashof heat and radiation factors yields a rise in the velocity. Influence of collective Casson and magnetic parameters leads to an appreciation of heat distribution. Also, the concentration field declines as both the Casson and Schmidt parameters improve. The diminishing distribution fields of both the wall energy and mass gradients are functions of the appreciating values of the non-Newtonian number.

Improved DFT Method for DOA Estimation with Extended Coprime Array:Based on Large Difference CoArray

In this paper, Direction of arrival estimation (DOA) in coprime array is investigated, and an advanced method for DOA estimation is presented with extended coprime array (ECA). Specifically, we use Discrete Fourier Transform (DFT) to obtain initial DOA estimation with large difference co-arrays generated by ECA, then perform Taylor series approximation and total least squares (TLS) method around the initial estimation to compensate the estimation offset. Compared to conventional DFT method, the proposed method enjoys better estimation accuracy with fewer computational burden since it avoids extra searches and benefits more from large difference co-array. Besides, in contrast to spatial smoothing based methods which halve array aperture, the proposed method avoids the process of spatial smoothing and fully utilizes uniform degrees of freedom (DOFs). In this case, the proposed method has advantages on estimation accuracy and computational efficiency with multiple impinging signals, especially under the condition of large difference co-array. Furthermore, the proposed method is applicable to other types of advanced coprime array. The superiority of the proposed method has been proved by numerical simulations.

ENDOGENEITY IN SEMIPARAMETRIC THRESHOLD REGRESSION

This paper estimates threshold regression models with an endogenous threshold variable using a nonparametric control function approach. Assuming diminishing threshold effects, we derive the consistency and limiting distribution of our proposed estimator constructed from the series approximation method for weakly dependent data. In addition, we propose a test for the endogeneity of the threshold variable, which is valid regardless of whether the threshold effects exist. We assess the performance of our methods using Monte Carlo simulations.

Application of power series approximation techniques to valuation of European style options

Fourier transforms provide versatile techniques for pricing financial derivative securities. In applying such techniques, a typical derivative valuation expression is often written as an inner product of the Fourier transform of payoff and the characteristic function of the underlying asset dynamics. Some modelling specifications imply that it might be challenging to find a closed-form expression for the characteristic function. In such situations, numerical approximations have to be employed. This paper utilises the power series approximation technique in finding explicit expressions of the characteristic function for the underlying stochastic variables. We analyse the convergence and accuracy of this technique in the context of valuing European style options written on underlying securities whose dynamics evolve under the influence of multiple Heston-type stochastic volatilities [Heston, S., A closed-form solution for options with Stochastic volatility with applications to Bond and currency options. Rev. Financ. Stud., 1993, 6, 327–343] and Cox–Ingersoll–Ross stochastic interest rates [Cox, J., Ingerson, J. and Ross, S., A theory of the term structure of interest rates. Econometrica, 1985, 53, 385–407]. This paper contributes to the existing literature four-fold by: (i) adapting the valuation technique to long-dated instruments; (ii) providing an adjustment to a series of points around which the power series expansion is performed; (iii) analysing the performance of different strategies for hedging European call options; (iv) applying the power series approach to the valuation of guaranteed minimum accumulation benefit riders embedded in variable annuity contracts. Our results demonstrate a high computational efficiency of the power series approximation method for evaluation of derivative prices and hedge ratios.

Complexity Reduction in Massive-MIMO-NOMA SIC Receiver in Presence of Imperfect CSI

One of the main reasons for switching to the next generation of communication systems is the demand of increasing capacity and network connections. This goal can be achieved using massive multiple input - multiple output (massive-MIMO) systems in combination with Non-orthogonal multiple access (NOMA) technique. NOMA technology uses the successive interference cancellation (SIC) receiver to detect user’s signals which imposes an additional complexity on the system. In this paper, we proposed two methods to reduce the system complexity. The proposed method despite imperfect channel state information (CSI) in the receiver, there is not significantly reduction in the system performance. Since the computation of matrices inverse has a high computational complexity, we used the Neumann series approximation method and the Gauss-Seidel decomposition method to compute matrices inverse in the SIC receiver. Simulation results are provided at the end of the paper in terms of bit error rate (BER) at the receiver which show, these methods have lower computational complexity in comparison with the traditional methods while they cause a slight performance reduction in the SIC receiver. Also, we examined the increasing and decreasing value of imperfect channel state information in the system performance which shows the increasing value of imperfect channel state information, cause a slight performance reduction in SIC receiver.

Series Estimation of Stochastic Processes: Recent Developments and Econometric Applications

This paper overviews recent developments in series estimation of stochastic processes and some of their applications in econometrics. Underlying this approach is the idea that a stochastic process may under certain conditions be represented in terms of a set of orthonormal basis functions, giving a series representation that involves deterministic functions. Several applications of this series approximation method are discussed. The first shows how a continuous function can be approximated by a linear combination of Brownian motions (BMs), which is useful in the study of the spurious regressions. The second application utilizes the series representation of BM to investigate the effect of the presence of deterministic trends in a regression on traditional unit-root tests. The third uses basis functions in the series approximation as instrumental variables (IVs) to perform efficient estimation of the parameters in cointegrated systems. The fourth application proposes alternative estimators of long-run variances in some econometric models with dependent data, thereby providing autocorrelation robust inference methods in these models. We review some work related to these applications and some ongoing research involving series approximation methods.

Stationary analysis of certain Markov-modulated reflected random walks in the quarter plane

In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with coupled queues. The transition rates of the two-dimensional process depend on the state of a finite state Markovian background process. Such a modulation is space homogeneous in the set of inner states of the two-dimensional lattice but may be different in the set of states at its boundaries. To obtain the stationary distribution, we apply the power series approximation method, and the theory of Riemann boundary value problems. We also obtain explicit expressions for the first moments of the stationary distribution under some symmetry assumptions. An application in the modelling of a priority retrial system with coupled orbit queues is also presented. Using a queueing network example, we numerically validated the theoretical findings.

Estimating Marginal Treatment Effects under Unobserved Group Heterogeneity

This paper studies endogenous treatment effect models in which individuals are classified into unobserved groups based on heterogeneous treatment choice rules. Such heterogeneity may arise, for example, when multiple treatment eligibility criteria and different preference patterns exist. Using a finite mixture approach, we propose a marginal treatment effect (MTE) framework in which the treatment choice and outcome equations can be heterogeneous across groups. Under the availability of valid instrumental variables specific to each group, we show that the MTE for each group can be separately identified using the local instrumental variable method. Based on our identification result, we propose a two-step semiparametric procedure for estimating the group-wise MTE parameters. We first estimate the finite-mixture treatment choice model by a maximum likelihood method and then estimate the MTEs using a series approximation method. We prove that the proposed MTE estimator is consistent and asymptotically normally distributed. We illustrate the usefulness of the proposed method with an application to economic returns to college education.

Minimum Energy Trajectory Optimization for Driving Systems of Palletizing Robot Joints

Palletizing robot is widely used in logistics operation. At present, people pay attention to not only the loading capacity and working efficiency of palletizing robots, but also the energy consumption in their working process. This paper takes MD1200-YJ palletizing robot as the research object and studies the problem of low energy consumption optimization of joint driving system from the perspective of trajectory optimization. Firstly, a multifactor dynamic model of palletizing robot is established based on the conventional inverse rigid body dynamic model of the robot, the Stribeck friction model and the spring balance torque model. And then based on joint torque, friction torque, motion parameter, and joule’s law, the useful work model, thermal loss model of joint motor, friction energy consumption model of joint system, and total energy consumption model of palletizing robot are established, and through simulation and experiment, the correctness of the multifactor dynamic model and energy consumption model is verified. Secondly, based on the Fourier series approximation method to construct the joint trajectory expression, the minimum total energy consumption as the optimization objective, with coefficients of Fourier series as optimization variables, the motion parameters of initial and final position, and running time constant as constraint conditions, the genetic algorithm is used to solve the optimization problem. Finally, through the simulation analysis the optimized Fourier series motion law and the 3-4-5 polynomial motion law are comprehensively evaluated to verify the effectiveness of the optimization method. Moreover, it provides the theoretical basis for the follow-up research and points out the direction of improvement.

Octave Error Reduction in Pitch Detection Algorithms Using Fourier Series Approximation Method

ABSTRACTPitch detection has been an area of research in the field on Music Information retrieval, which has always received great attention. Pitch is defined as the frequency of a pure tone signal which the brain perceives while listening to a signal. Pitch detection methods ideally identify the fundamental frequency (f0) or fundamental time period (T) of a signal and f0 is defined as the inverse of T. Several pitch detection algorithms have been proposed in the past and each one has its advantages and disadvantages. One of the prominent problems seen across all pitch detection algorithms is to identify the correct octave to which the pitch or f0 belongs to. Ideally, we are required to find the fundamental harmonic. Due to the structure of vocal tract and the acoustic nature of the instruments and due to various other factors like noise, the speech, and music signals are not perfectly periodic in nature and are termed as quasi-periodic signals. In this paper, we have proposed a method using Fourier series to approximate the quasi-periodic signals with a periodic signal, which analyses the strengths of various harmonics of the signal to arrive at a better estimate of the pitch for monophonic sounds. The brain perceives a periodic signal even while listening to a quasi-periodic signal. Hence, the idea is to approximate the quasi-periodic signal with a perfectly periodic signal and estimate the fundamental frequency of the signal which gives the best approximation. The method was tested on synthetic signals and real music signals and found to improve the pitch detection accuracy.

Quasi-Natural Humanoid Robot Walking Trajectory Generator Based on Five-Mass With Angular Momentum Model

This paper proposes to develop a quasi-natural humanoid robot walking trajectory generator based on five-mass with angular momentum model using feedback–feedforward controller. This approach aims to minimize modeling error and improve the frequency characteristics from nonminimum phase properties so that walking performance and tracking accuracy are enhanced. This proposed model focuses on the angular momentum effects from arm and leg rotation to reduce modeling error to enhance walking performance. Based on pole-zero cancelation using series approximation method, it can overcome the sudden change of the natural zero-moment point reference due to the frequency characteristics in the nonminimum phase control system. The humanoid walking pattern generator is verified and demonstrated using a humanoid robot developed in our laboratory based on the proposed model.

Finding a better shape: Morphological description of strain response envelopes using a Fourier series approximation method

This paper introduces a new method for quantifying the morphological evolution of the strain response envelope (SRE). The Fourier series approximation was used to trace the morphological characteristics of SREs. Two SREs computed via numerical simulations using the Modified Cam Clay (MCC) model and three SREs obtained from stress-probing experiments on Chicago clay were used to validate the proposed method of Fourier series approximation. The results show that using a harmonic number of 1 or 2, the target shape of the SRE can be approximated within a 10% error.

Orthogonal Series Estimation of Nonparametric Regression Measurement Error Models with Validation Data

In this article we study the estimation method of nonparametric regression measurement error model based on a validation data. The estimation procedures are based on orthogonal series estimation and truncated series approximation methods without specifying any structure equation and the distribution assumption. The convergence rates of the proposed estimator are derived. By example and through simulation, the method is robust against the misspecification of a measurement error model.

Estimation of Nonparametric Regression Models with Measurement Error Using Validation Data

We consider the problem of estimating a function g in nonparametric regression model when only some of covariates are measured with errors with the assistance of validation data. Without specifying any error model structure between the surrogate and true covariables, we propose an estimator which integrates orthogonal series estimation and truncated series approximation method. Under general regularity conditions, we get the convergence rate of this estimator. Simulations demonstrate the finite-sample properties of the new estimator.