Parameters Of Linear Function Research Articles

Effective optimization strategies for abrasive water jet machining of glass-carbon fiber reinforced composites: A comparative study of evolutionary optimization techniques

This study applied evolutionary optimization techniques and neural networks to predict optimum machining parameters of Abrasive Water Jet Machining (AWJM) for machining Glass-Carbon Fiber Reinforced Composite (GCFRC) materials. Several researchers have employed different optimization techniques; however, evolving computational capabilities further open avenues to optimize such parameters. Five evolutionary techniques, namely Artificial Neural Network (ANN), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Simulated Annealing (SA), and Nonlinear Least Square Error (LSE), were applied to minimize surface roughness (Ra) and maximize kerf width (Kw) and material removal rate (MRR). The output performance parameters (Ra, Kw, and MRR) were formulated as a linear mathematical function of machining parameters: tool feed rate (TFR), cutting speed rate (CSR), and stand-off distance (SOD). Though this study solves linear optimization problems, the proposed technique will be a strong tool for solving complex associations of machining and performance parameters in the future. A dataset of machining parameters and subsequent performance parameters was adopted from the available literature. The results indicated that the LSE method outperformed other techniques, yielding the lowest Root Mean Square Error (RMSE) in predicting Ra, Kw, and MRR, thus ensuring high machining accuracy. LSE technique reported relatively least RMSE values of 0.37 µm, 0.149Mm, and 237.23 mm3/min for Ra, Kw, and MRR, respectively. SA and PSO displayed identical and competitive RMSE values, slightly higher than LSE (up to 20 % higher). ANN and GA techniques were not effective relative to other considered techniques. LSE, SA, and PSO provide superior performance in optimizing AWJM parameters. The significant contribution of this research is the proposed optimization technique, offering a clear direction for solving complex associations between the performances and machining parameters of AWJM. This work also provides a foundation for future research to optimize such associations for other machining setups.

Conditions When the Problems of Linear Programming Are Algorithmically Unsolvable

We study the properties of the constructive linear programming problems. The parameters of linear functions in such problems are constructive real numbers. Solving such a problem involves finding the optimal plan with the constructive real number components. We show that it is impossible to have an algorithm that solves an arbitrary constructive real programming problem.

Approximate dynamic programming approach to efficient metro train timetabling and passenger flow control strategy with stop-skipping

Urban metro systems continuously face high travel demand during rush hours, which brings excessive energy waste and high risk to passengers. In order to alleviate passenger congestion, improve train service levels and reduce energy consumption, a nonlinear dynamic programming (DP) model of efficient metro train timetabling and passenger flow control strategy with stop-skipping is presented, which consists of state transition equations concerning train traffic and passenger load. To overcome the curse of dimensionality, the formulated nonlinear DP problem is transformed into a discrete Markov decision process, and a novel approximate dynamic programming (ADP) approach is designed based on the lookahead policy and linear parametric value function approximation. Finally, the effectiveness of this method is verified by three groups of numerical experiments. Compared with Particle Swarm Optimization (PSO) and Simulated Annealing (SA), the designed ADP approach could obtain high-quality solutions quickly, which makes it applicable to the practical implementation of metro operations.

Research and analysis on the preparation of C4 olefin by ethanol coupling method based on regression algorithm with computer technology

Computer technology has been used to study the different combination of catalyst and temperature on the ethanol conversion (one-way conversion rate of 100% per unit time ethanol (alcohol intake - ethanol residue)/ethanol intake) and C4 olefin selectivity (the proportion of all products of C4 olefin), it is necessary to decompose the catalyst composition into several indicators. The effects of several indexes on ethanol conversion and C4 olefins selectivity were analyzed by computer technology. Canonical correlation analysis was used to study them, and the coefficient before each component represented the degree of importance. The results showed that the higher the catalyst combination temperature, the higher the weight of hydroxyapatite, the higher the ethanol conversion and C4 olefins selectivity, and vice versa. When the C4 olefin yield (its value is the selectivity of C4 olefin to ethanol conversion) is as high as possible, the multiple linear stepwise regression function of catalyst parameters and temperature on C4 olefin yield is obtained. MATLAB software was used to calculate the function formula. The absolute value of coefficients determines the importance of each index to C4 olefin yield. Combined with chemical reaction, when the mass ratio is 200:200 and the temperature is 400℃, the yield of C4 olefins can be maximized, and the yield of C4 olefins is 44.728%. Through the establishment of decision tree regression model by computer technology, it can be intuitively concluded that when the temperature is lower than 350℃, the best experimental condition is the C4 olefins yield of 17.264%.

The Role of Auxiliary Stages in Gaussian Quantum Metrology

The optimization of the passive and linear networks employed in quantum metrology, the field that studies and devises quantum estimation strategies to overcome the levels of precision achievable via classical means, appears to be an essential step in certain metrological protocols achieving the ultimate Heisenberg-scaling sensitivity. This optimization is generally performed by adding degrees of freedom by means of auxiliary stages, to optimize the probe before or after the interferometric evolution, and the choice of these stages ultimately determines the possibility to achieve a quantum enhancement. In this work we review the role of the auxiliary stages and of the extra degrees of freedom in estimation schemes, achieving the ultimate Heisenberg limit, which employ a squeezed-vacuum state and homodyne detection. We see that, after the optimization for the quantum enhancement has been performed, the extra degrees of freedom have a minor impact on the precision achieved by the setup, which remains essentially unaffected for networks with a larger number of channels. These degrees of freedom can thus be employed to manipulate how the information about the structure of the network is encoded into the probe, allowing us to perform quantum-enhanced estimations of linear and non-linear functions of independent parameters.

Static behaviours and collision onset criterion of two adjacent vertical risers

ABSTRACT This study aims to investigate the static behaviours of two risers and establish the generalised dual-riser collision onset criterion (COC). The dual-riser model is developed based on the vector form intrinsic finite element method where the Blevins wake model is used to consider the wake effects. The governing equations including a virtual damping force are solved by the central difference method to obtain the static behaviours of risers. Then, the effects of initial spacing, top tension factor and current velocity on the static behaviours of two vertical risers arranged tandem are investigated. Further, the dual-riser COC is established with three non-dimensional parameters by linear-regression analysis. The results show that a larger top tension factor of the upstream riser and a smaller that of the downstream riser is a more effective combination to avoid collisions. The dual-riser COC can be described by a linear function of non-dimensional parameters.

Energy consumption prediction method of energy saving building based on deep reinforcement learning

In order to overcome the problems of low-prediction accuracy and long prediction time of traditional building energy consumption prediction methods, this paper proposes a new energy-saving building energy consumption prediction method based on deep reinforcement learning. Through the deep reinforcement learning algorithm, a number of energy consumption behaviour return information of specific value network and strategy network are calculated, respectively to build the energy consumption probability model of energy-saving building energy consumption equipment. The linear rectification function with leakage is used to update the probability model and parameters, and the linear relationship prediction function of energy consumption parameters is constructed by using the learning process and results to complete the dynamic prediction of energy consumption of energy-saving buildings. The experimental results show that the proposed method has fast prediction speed and high accuracy, which can provide reference for the implementation of energy-saving building.

Ordinary least squares estimation of parameters of linear model

This research article primarily focuses on the method of ordinary least squares estimation of parameters of linear model. Here an innovative proof of Gauss-Markoff theorem for linear estimation has been presented. An extensive discussion in evaluating Best Linear Unbiased Estimator (BLUE) of a linear parametric function of the classical linear model is made by using the Gauss-Markoff theorem. Furthermore the importance of mean vector and covariance matrix of BLUE is discussed. Moreover generalized Gauss-Markoff theorem for linear estimation, properties of OLS estimators and problems of linear model by violating the assumptions are extensively discussed.

Indentation Induced Mechanical Behavior of Spark Plasma Sintered WC-Co Cemented Carbides Alloyed with Cr3C2, TaC-NbC, TiC, and VC.

The focus of this paper is on examining the mechanical behavior of spark plasma sintered WC-Co based composites doped with Cr3C2, TaC-NbC, TiC, and VC, as well as defining some parameters characterizing deformation and fracture processes during hardness measurement. The calculated microhardness of WC-Co cemented carbides for all the studied compositions is found to be higher than the results obtained during hardness testing. Therefore, the ratio of the experimental and calculated values of microhardness is shown to be an approximate indication of WC-Co cemented carbide sensitivity to damage processes during indentation. Some parameters characterizing the microstructure–microhardness relationship are defined, and the nanomechanical properties of WC-Co cemented carbide phases are examined in order to separate the deformation and fracture processes during the indentation process. Strain gradient linear function parameters are calculated for 10-cycle nanoindentation. It was found that the nanoindentation curve after 10 cycles shows anomalous behavior of the WC grains, which indicates their fracture processes.

Ordinary least squares estimation of parameters of linear model

This research article primarily focuses on the method of ordinary least squares estimation of parameters of linear model. Here an innovative proof of Gauss-Markoff theorem for linear estimation has been presented. An extensive discussion in evaluating Best Linear Unbiased Estimator (BLUE) of a linear parametric function of the classical linear model is made by using the Gauss-Markoff theorem. Furthermore the importance of mean vector and covariance matrix of BLUE is discussed. Moreover generalized Gauss-Markoff theorem for linear estimation, properties of OLS estimators and problems of linear model by violating the assumptions are extensively discussed.

Robust D-Stabilization Analysis of Fractional-Order Control Systems With Complex and Linearly Dependent Coefficients

This article focuses on the robust D-stabilization analysis of fractional-order control systems where each of the system and the controller may be of fractional order. The coefficients of the system are considered as complex linear functions of interval uncertain parameters, so this article deals with fractional-order polytopic systems. First, a necessary and sufficient condition is introduced for the robust D-stabilization of the closed-loop control system based on the zero exclusion condition and the value set concept. Then, the geometric pattern of the value set of the characteristic polynomial is obtained analytically using the exposed vertices. Second, a function is presented to check the introduced condition. Third, the transition points, at which the exposed vertices of the value set may change, are derived to reduce the computational burthen. Fourth, a new function is provided to determine the D-stability robustness radius (margin) of these control systems, that is, determining bounds on the uncertain parameters such that the control system remains D-stable. The achieved results are applicable to systems of incommensurate order and consequently of commensurate order. Finally, numerical simulations and practical experiments based on a three-degrees-of-freedom flight simulator turn table are conducted to illustrate the achieved results.

Using Parameter Elimination to Solve Discrete Linear Chebyshev Approximation Problems

We consider discrete linear Chebyshev approximation problems in which the unknown parameters of linear function are fitted by minimizing the least maximum absolute deviation of errors. Such problems find application in the solution of overdetermined systems of linear equations that appear in many practical contexts. The least maximum absolute deviation estimator is used in regression analysis in statistics when the distribution of errors has bounded support. To derive a direct solution of the problem, we propose an algebraic approach based on a parameter elimination technique. As a key component of the approach, an elimination lemma is proved to handle the problem by reducing it to a problem with one parameter eliminated, together with a box constraint imposed on this parameter. We demonstrate the application of the lemma to the direct solution of linear regression problems with one and two parameters. We develop a procedure to solve multidimensional approximation (multiple linear regression) problems in a finite number of steps. The procedure follows a method that comprises two phases: backward elimination and forward substitution of parameters. We describe the main components of the procedure and estimate its computational complexity. We implement symbolic computations in MATLAB to obtain exact solutions for two numerical examples.

VROHI: Visibility Recovery for Outdoor Hazy Image in Scattering Media

Additive haze model (AHM), due to its high simplicity, has a potential to increase the efficiency of the restoration procedure of images degraded by scattering media. However, AHM is designed for hazy remote sensing data and is not suitable to be used on outdoor images. In this paper, according to the low-frequency feature (LFC) of haze, AHM is modified via gamma correction technique to make it suitable for modeling outdoor images. Benefitting from the modified AHM (MAHM), a simple yet effective method called VROHI is proposed to enhance the visibility of an outdoor hazy image. In specific, a low complexity LFC extraction method is designed by utilizing characteristic of the discrete cosine transform. Subsequently, by constructing the linear function of unknown parameters and imposing the saturation prior on MAHM, the image dehazing problem can be derived into a global optimization function. Experiments reveal that the proposed VROHI is superior to the other state-of-the-art techniques in terms of both the processing efficiency and recovery quality.

Ellipsoid Method for Linear Regression Parameters Determination

Introduction. Linear regression parameters determination can be formulated as a non-smooth function minimization problem, which is Lp-norm of residual of the linear equations system. To solve it non-smooth function minimization methods can be used, e.g. subgradient methods. The article [7] considers ellipsoid method application for finding Lp-solution of redefined linear equations system with 1≤p≤2. The purpose of the paper is to extend the algorithm based on the ellipsoid method for a linear regression parameters determination problem with an arbitrary value of parameter p≥2 so that under big values of p the solution of the problem equals minimax method solution, which corresponds to p=∞ case. To describe the formulation of observation approximation problem with quadratic function as linear regression parameters determination problem. To analyze algorithm work results for great number of observations and outliers. To compare the minimax method and the ellipsoid method algorithm work results for linear regression parameters determination problem with big values of parameter p. Results. The way of calculation of objective function and its subgradient values with large values of parameter p was developed and verified on example of observation approximation containing outliers with linear function. Algorithm based on ellipsoid method changes linear function parameters monotonically using parameter p adjusting, thereby permits to reject or consider these or those observations. It is shown in [3] that Least Absolute Deviations method (LAD) is advised to be used as far as it ignores outliers and reconstructs linear function accurately. Experiment results with big number of observations and outliers using p=1 confirmed that conclusion: LAD ignores outlier groups and approximates observations with linear function adequately. Least Square Method (LSM) deviates from optimal linear function if a group of outliers is present in particular area. In case of using big values of parameter p problem solution converges to minimax method solution. Conclusions. Algorithm based on ellipsoid method permits to determine linear regression parameters with arbitrary value of parameter p≥1. So, three known methods can be used – LAD, LSM and minimax method – as its special cases. Moreover, directing p to 1, intensity of outliers ignoring can be regulated, that gives a possibility to use external sources of information (expert opinions, measuring devices readings, statistical forecasts, etc.) for more correct and adequate approximation function reconstruction. Keywords: ellipsoid method, linear regression, outliers.

Modeling ringdown. II. Aligned-spin binary black holes, implications for data analysis and fundamental theory

The aftermath of binary black hole coalescence is a perturbed remnant whose gravitational radiation rings down, encoding information about the new black hole's recent history and current state.It is expected that this ringdown radiation will be composed primarily of Kerr quasinormal modes, and thereby enable tests of general relativity.Here, the first complete ringdown signal model for nonprecessing binary black hole systems is presented: multipole amplitudes and phases are modeled as functions of initial binary parameters. It is found that using the peak time of the dominant merger multipole as a reference results in the dominant mode's excitation being a remarkably simple linear function of system parameters, strongly suggesting that an analytic treatment may be within reach.In particular, for initially nonspinning black holes, the dominant quadrupole is excited as -4 times the system's symmetric mass ratio.Application of the model to parameter estimation allows general relativity predictions for mode amplitudes independently of signal strength.Treatment of GW150914 indicates some mode amplitudes and relative phases are intrinsically difficult to constrain.

A new model for sizing thermosiphon solar heating systems

The purpose of this work is to present a simple methodology which enables to size a thermosyphon system without always having to resort to a computational simulation. As a result of many system simulations using the TRNSYS software, whereby several project and equipment parameters were varied, a group of expressions were obtained which allow the determination of the system thermal daily efficiency (monthly average). The developed correlation includes geometric and thermal aspects related to the collector, the storage tank and the connecting pipes, as well as operational data such as thermal load, solar radiation and room temperature. This model is able to optimize several variables that comprise thermosyphon solar water-heating systems for the requirements of particular applications. The resulting correlation shows that the efficiency is a linear function of meteorological conditions, collector quality and parameters related to storage tank volume, volume load (consumption profile) and collector area. The correlation is very useful since it is a simple, fast alternative for the calculation of system efficiency without depending on experimental determination or numerical simulation results. The determination and sizing of the collector area and the volume storage tank that satisfy the required thermal load can be appropriately performed in a simple and fast way by using the proposed correlation.

Fast enclosing the solution set of the parametric Sylvester matrix equations

ABSTRACT In this work, we study the parametric Sylvester matrix equation whose elements are linear functions of uncertain parameters varying within some intervals. We first explore some properties of its solution set and then present some sufficient conditions for boundedness of the solution set. The main work is developing a modified variant of the parametric Krawczyk operator which reduces the computational complexity of enclosing the solution set significantly, compared to the parametric Krawczyk operator on the Kronecker product form. Some numerical experiments are given to illustrate the effectiveness of the proposed method.

Incentives for Model Calibration on Decentralized Derivatives Exchanges: Consensus in Continuum

We consider the problem of risk model calibration that is faced by all decentralized derivative exchanges. Financial model calibration is hard for two reasons: firstly it relies on data inputs that can be unreliable, incorrect and in general needing manual cleaning. Secondly, even if perfectly correct data is available the problem typically involves non-convex minimization resulting in local minima that are moreover highly dependent on small perturbations to input. Thus even honest parties won't necessarily produce the same parameters. On a decentralized exchange multiple parties need to agree on the correct calibration. Moreover, malicious actors may benefit in providing calibration parameters that benefit their trading, in case they can convince others that their calibration is the right one. Effectively we have a problem of trying to achieve consensus in continuum. We propose a phenomenological model for the problem. We analyse this in the framework of stochastic differential games and we show that a Nash equilibrium exists. We present empirical results for simple situations that arise when the risk model is assumed to be a linear function of calibration parameters.

Confidence Analysis of Linear Unbiased Estimates under Uncertain Unimodal Noise Distributions

The estimation problem for a linear parametric function in a linear regression model with uncertain symmetric unimodal noise distributions and given noise covariances is solved. The quality of estimation is determined by the probability that the error exceeds specified limits. For taking the uncertainty into account, a minimax optimization problem is formulated. The main result of this paper is that the Gauss inequality defines a tight upper bound of the error probability for any linear unbiased estimate. The worst-case distribution of the noise vector is constructed by using a linear transformation of a Gaussian random vector and a uniform random variable. The estimate that is minimax with respect to the probability criterion coincides with the least-squares estimate. The obtained solution is illustrated by the example of estimating motion parameters for several hypotheses about noise distributions.

Enclosing the solution set of the parametric generalised Sylvester matrix equation A(p)XB(p) + C(p)XD(p) = F(p)

In this paper, we investigate the parametric generalised Sylvester matrix equation , whose elements are linear functions of uncertain parameters varying within intervals. This model generalises both interval matrix equations and parametric interval linear systems, so it is a quite general model. First, we give some sufficient conditions under which the solution set of this parametric equation is bounded. We then propose several approaches for enclosing the solution set that acquire tighter enclosures than those obtained by relaxing the parametric system to an interval system. Some special cases of interval systems that inherently are parametric (have dependent structure) are considered, too. Finally, numerical experiments are given to illustrate the effectiveness of the proposed methods.