Minimization Of Mean Square Error Research Articles

Development of statistical estimators for speech enhancement using multi-objective grey wolf optimizer

Statistical Estimation using the SNR uncertainty technique is one of the effective Speech Enhancement (SE) algorithms. In this method, the Gain function plays a crucial role and it depends on the proper selection of the smoothing and threshold constants. In the literature, the values of these constants have been optimized by considering a single objective function of maximization of speech quality for a specific noise condition. But in practice, the noise magnitude varies and one set of optimized parameters cannot always provide consistent performance. In this paper, this problem has been addressed and solved in three steps. The first step is multi-objective optimization to find the best set of values of smoothing and threshold constants at different noise levels by considering the objectives of maximization of speech quality, intelligibility, and minimization of mean square error. The second step is the classification of the noisy speech into four SNR levels such as 0 dB, 5 dB, 10 dB, and 15 dB by using appropriate audio features. The values obtained in steps one and two are stored and in the third step, when the unknown noisy speech signal is to be enhanced the best-chosen values of the smoothing and threshold constants are selected for this task. Finally, the performance of the proposed method is evaluated in two different speech datasets. Then, comparative performance and statistical analysis are carried out using six other standard SE algorithms and it is demonstrated that the proposed approach provides superior performance than others.

Challenges for Simulating Growth and Phenology of Silage Maize in a Nordic Climate with APSIM

APSIM Next Generation was used to simulate the phenological development and biomass production of silage maize for high latitudes (i.e., >55°). Weather and soil data were carefully specified, as they are important drivers of the development and growth of the crop. Phenology related parameters were calibrated using a factorial experiment of simulations and the minimization of the root mean square error of observed and predicted phenological scaling. Results showed that the model performed well in simulating the phenology of the maize, but largely underestimated the production of biomass. Several factors could explain the discrepancy between observations and predictions of above-ground dry matter yield, such as the current formalization of APSIM for simulating the amount of radiation absorbed by the crop at high latitudes, as the amount of diffuse light and intercepted light increases with latitude. Another factor that can affect the accuracy of the predicted biomass is the increased duration of the day length observed at high latitudes. Indeed, APSIM does not yet formalize the effects of extreme day length on the balance between photorespiration and photosynthesis on the final balance of biomass production. More field measurements are required to better understand the drivers of the underestimation of biomass production, with a particular focus on the light interception efficiency and the radiation use efficiency.

Cloud and Edge Multicast Beamforming for Cache-Enabled Ultra-Dense Networks

For the cache-enabled ultra-dense networks, edge caching is a promising technique for realizing low-latency transmission. In this paper, we study cache-enabled ultra-dense networks with the wireless fronthaul, in which edge nodes (ENs) have the capability of caching and signal processing. Under such a setup, by exploiting the feature that users requesting the same content form a multicast group and can be served by a cluster of ENs, we first formulate a problem to optimize the cloud and edge multicast beamforming design for maximizing the minimum rate among the user groups. Due to the coupling of transmit and receive beamforming and the non-convex constraints of delivery rate, the formulated problem is difficult to be directly solved. To this end, we propose to use the weighted sum mean-square error minimization approaches and certain transformation techniques to convert the original problem into a convex one. An optimal solution is then obtained by using bisection search and second order cone (SOC) transformation. The results indicate that the performance of the proposed precoding scheme with wireless frothauling will close to that of the wired fronthauling.

An optimal pointwise weighted ensemble of surrogates based on minimization of local mean square error

Surrogate models are often used as surrogates for computationally intensive simulations. And there are a variety of surrogate models which are widely used in aerospace engineering–related investigation and design. In general, there is an optimal individual surrogate for a certain research object. However, the behavior of an individual surrogate is unknown in advance. Building an ensemble of surrogates by combining different individual surrogates into a weighted-sum formulation is an efficient method to enhance the accuracy and robustness of the surrogate model. Motivated by the previous researches on the ensemble of surrogates, we propose an optimal pointwise weighted ensemble (OPWE) method, wherein the optimal pointwise weight factors are obtained based on the minimization of the local mean square error which is constructed by the global-local error (GLE). By using six well-known mathematical problems and four engineering problems, it is proved that the OPWE proposed in this paper is better than the other ensembles of surrogates in terms of both accuracy and robustness.

Evaluation of the Mass Diffusion Coefficient and Mass Biot Number Using a Nondominated Sorting Genetic Algorithm

A precise determination of the mass diffusion coefficient and the mass Biot number is indispensable for deeper mass transfer analysis that can enable finding optimum conditions for conducting a considered process. The aim of the article is to estimate the mass diffusion coefficient and the mass Biot number by applying nondominated sorting genetic algorithm (NSGA) II genetic algorithms. The method is used in drying. The maximization of coefficient of correlation (R) and simultaneous minimization of mean absolute error (MAE) and root mean square error (RMSE) between the model and experimental data were taken into account. The Biot number and moisture diffusion coefficient can be determined using the following equations: Bi = 0.7647141 + 10.1689977s − 0.003400086T + 948.715758s2 + 0.000024316T2 − 0.12478256sT, D = 1.27547936∙10−7 − 2.3808∙10−5s − 5.08365633∙10−9T + 0.0030005179s2 + 4.266495∙10−11T2 + 8.33633∙10−7sT or Bi = 0.764714 + 10.1689091s − 0.003400089T + 948.715738s2 + 0.000024316T2 − 0.12478252sT, D = 1.27547948∙10−7 − 2.3806∙10−5s − 5.08365753∙10−9T + 0.0030005175s2 + 4.266493∙10−11T2 + 8.336334∙10−7sT. The results of statistical analysis for the Biot number and moisture diffusion coefficient equations were as follows: R = 0.9905672, MAE = 0.0406375, RMSE = 0.050252 and R = 0.9905611, MAE = 0.0406403 and RMSE = 0.050273, respectively.

Pricing-Based Semi-Distributed Clustering and Beamforming for User-Centric MIMO Networks

User-centric dynamic base station (BS) clustering can efficiently avoid cell edge effect, which results in overlapped clusters and introduces tremendous complexity in beamforming optimizations. However, existing works mainly focus on addressing the problem in a centralized manner. In this letter, a semi-distributed user-centric clustering and beamforming scheme for sum-rate maximization is proposed, where the optimization problem is split by introducing interference pricing and solved subsequently at the anchor of each cluster. Specifically, based on interference pricing, the problem is decomposed into parallel subproblems by decoupling interference constraints and power constraints, where beamforming matrices are optimized at the anchor of each cluster through generalized iterative minimization of mean-square error; besides, cluster size is controlled by taking power spent as penalizing term and minimum rate constraints are taken into consideration to guarantee the throughput of edge users. Simulation results show about $3\times $ gains in sum-rate criteria and $2\times $ gains in proportional fair criteria of the proposed scheme in terms of 5%-tile user throughput compared to BS-centric and centralized schemes.

Estimation of the Biot Number Using Genetic Algorithms: Application for the Drying Process

The Biot number informs researchers about the controlling mechanisms employed for heat or mass transfer during the considered process. The mass transfer coefficients (and heat transfer coefficients) are usually determined experimentally based on direct measurements of mass (heat) fluxes or correlation equations. This paper presents the method of Biot number estimation. For estimation of the Biot number in the drying process, the multi-objective genetic algorithm (MOGA) was developed. The simultaneous minimization of mean absolute error (MAE) and root mean square error (RMSE) and the maximization of the coefficient of determination R2 between the drying model and experimental data were considered. The Biot number can be calculated from the following equations: Bi = 0.8193exp(−6.4951T−1) (and moisture diffusion coefficient from D/s2 = 0.00704exp(−2.54T−1)) (RMSE = 0.0672, MAE = 0.0535, R2 = 0.98) or Bi = 1/0.1746log(1193847T) (D/s2 = 0.0075exp(−6T−1)) (RMSE = 0.0757, MAE = 0.0604, R2 = 0.98). The conducted validation gave good results.

Testing Signals for Electronics: Criteria for Synthesis

Expressions for calculation of optimal criteria for highest information and sensitivity indices and lowest mean square error in test signals for radio-electronic systems (RES), working under influence of the additive Gaussian noise, are derived. In this framework, the technical state of a RES is determined via measurement of its dynamic characteristics. Because at negligible electromagnetic noise, all test signals are equivalently optimal, the test signal of the RES, which is optimal for a high-level noise, is considered to be optimal for the noise of lower level. It is proven, that at high levels of noise these three criteria (maximums of informative and sensitivity indices and minimum of mean square error) reduce into a single criterion. This universal criterion can be used to synthesize test signals with optimal parameters for determination of the technical state of any radio electronic device at any level of an additive Gaussian noise and can be applied in situ of RES operation.

MMSE Receiver Design and SINR Calculation in MU-MIMO Systems With Imperfect CSI

The performance of the uplink of multiuser multiple input multiple output systems depends critically on the receiver architecture and on the quality of the acquired channel state information. A popular approach is to design linear receivers that minimize the mean squared error (MSE) of the received data symbols. Unfortunately, most of the literature does not take into account the presence of channel state information errors in the MSE minimization. In this letter we develop a linear minimum MSE (MMSE) receiver that employs the noisy instantaneous channel estimates to minimize the MSE, and highlight the dependence of the receiver performance on the pilot-to-data power ratio. By invoking the theory of random matrices, we calculate the users' signal-to-interference-plus-noise ratio as a function of the number of antennas and the pilot-to-data power ratio of all users. Numerical results indicate that this new linear receiver outperforms the classical mismatched MMSE receiver.

Distributed Digital and Hybrid Beamforming Schemes With MMSE-SIC Receivers for the MIMO Interference Channel

This paper addresses the problem of weighted sum-rate maximization and mean squared error (MSE) minimization for the multiple-input multiple-output (MIMO) interference channel. Specifically, we consider a weighted minimum MSE architecture where each receiver employs successive interference cancellation (SIC) to separate the various received data streams and derive a hybrid beamforming scheme, where the transmitters operate with a number of radio frequency chains smaller than the number of antennas, particularly suited for millimeter-wave channels and 5G applications. To derive our proposed schemes, we first study the relationship between sum-rate maximization and weighted MSE minimization when using SIC receivers, assuming fully digital beamforming. Next, we consider the important-and, as it turns out, highly non-trivial-case where the transmitters employ hybrid digital/analog beamforming, developing a distributed joint hybrid precoding and SIC-based combining algorithm. Moreover, for practical implementation, we propose a signaling scheme that utilizes a common broadcast channel and facilitates the acquisition of channel state information, assuming minimal assistance from a central node such as a cellular base station. Numerical results show that both the proposed weighted MMSE-SIC schemes exhibit great advantages with respect to their linear counterparts in terms of complexity, feedback information, and performance.

A new method for designing multiplierless two-channel filterbank using shifted-Chebyshev polynomials

ABSTRACTThis paper presents an efficient design method for a digital multiplierless two-channel filterbank using the shifted-Chebyshev polynomials and common sub-expression elimination (CSE) algorithm for reducing hardware requirements such as adders and multipliers. For designing a two-channel filterbank, the design problem is constructed as minimization of integral mean square error between the desired and designed response of a prototype filter in the passband and stopband. For controlling the performance in passband and stopband, two parameters (KP, and KS) are used, whose optimum values are determined by swam optimization techniques such as differential evolution algorithm, artificial bee colony optimization, particle swarm optimizations, cuckoo search algorithm and hybrid method using a fitness function, constructed by perfect reconstruction condition of a filterbank. The number of polynomials used for approximation depends upon the order of a prototype filter. A new hybrid CSE is proposed for further reduction of hardware requirement. A comparative study of various CSE techniques such as horizontal, vertical and proposed hybrid CSE is also made. Numerical examples illustrate the effectiveness of the proposed algorithm in the reduction of adders with comparisons accomplished using existing methods. It has been found that almost 43% adder gain can be achieved when a filter is designed with N = 32 and wordlength (WL) as 12 using proposed methodology.

МЕТОД ПАКЕТНОГО ОБУЧЕНИЯ НЕЙРОСЕТИ С ЗАДЕРЖКОЙ ВО ВХОДНОМ СЛОЕ ДЛЯ КОМПЛЕКСНОЙ ДИАГНОСТИКИ СОСТОЯНИЯ ВЕНТИЛЯТОРНОЙ УСТАНОВКИ ГЛАВНОГО ПРОВЕТРИВАНИЯ

Currently, the increasing of operational safety is one of the major problems that exist in mining industry. The problem of mining equipment accident rate is caused by avalanche accumulating part of its physical resource exhaustion. Fan installation of the main airing, which ensures normal vital activitiesof mine personnel, is of the most importance among mining equipment. Therefore, an important task is to develop a software component, designed to diagnose the state of it and to be used in computer systems. The problem of building effective methods, providing high speed of diagnostics modeltraining, as well as a high probability, adequacy and speed of recognition of signals, which contain the vibrational information, lies at the heart of this objective. At present, as a tool for vibration diagnostics, such calculation methods as: kurtosis, crest factor, RMS value, envelope spectrum are mostcommonly used. However, when using these markers separately for diagnosis of fan installations of the main airing condition, the probability of error is no less than 0.05. On the other hand, the processing speed of vibrational information is poor. Therefore, the development of methods for intelligent integrated diagnostics of fan installations of the main airing is relevant. As the use of artificial neural networks in the diagnosis gives a tangible advantage, which is that: the interaction between the factors is studied on finished models; it does not require any assumptions regarding the distribution of factors; a priori information about the factors can be omitted; the initial data can be highly correlated, incomplete or noisy; it is possible to conduct the analysis of systems with a high degree of nonlinearity; fast model development; high adaptability; the analysis of systems with a large number of factors; it does not require a complete enumeration of all possible models; the analysis of systems withnonuniform factors, neural network method of diagnosis is used in the article. The aim of the study is to develop a method for analysis of the process of changing the condition of fan installations of the main airing. The model structure of an artificial neural network, which is a multilayer perceptron withtime delay in the input layer and provides a comprehensive analysis of diagnostic factors, is determined in the article. As a criterion for evaluation the efficiency of neural network model diagnostics the minimum of mean-square error is chosen. As a result of numerical study, it has been found that tenhidden neurons does not change the RMS error significantly, the proposed network provides the diagnostic results with minimum deviation. The use of the proposed batch training mode has made it possible to accelerate the forward stroke for approximately. The created algorithms can be used to solve problems associated with the diagnosis of electromechanical objects.

Equivalent linearization technique in nonlinear stochastic dynamics of a cable-mass system with time-varying length

In this paper the transverse vibrations of a vertical cable carrying a concentrated mass at its lower end and moving slowly vertically within the host structure are considered. It is assumed that longitudinal inertia of the cable can be neglected, with the longitudinal motion of the concentrated mass coupled with the lateral motion of the cable. An expansion of the lateral displacement of a cable in terms of approximating functions is used. The excitation acting upon the cable-mass system is a base-motion excitation due to the sway motion of a host tall structure. Such a motion of a structure often results due to action of the wind, hence it may be adequately idealized as a narrow-band random process. The narrow-band process is represented as the output of a system of two linear filters to the input in a form of a Gaussian white noise process. The non-linear problem is dealt with by an equivalent linearization technique, where the original non-linear system is replaced with an equivalent linear one, whose coefficients are determined from the condition of minimization of a mean-square error between the non-linear and the linear systems. The mean value and variance of the transverse displacement of the cable as well as those of the longitudinal motion of the lumped mass are determined with the aid of an equivalent linear system and compared with the response of the original non-linear system subjected to the deterministic harmonic excitation.

Joint Transmit Precoding and Receive Antenna Selection for Uplink Multiuser Massive MIMO Systems

This paper considers the uplink of multiuser multiple-input multiple-output systems, where several mobile stations (MSs) cooperatively transmit hybrid messages, including common messages and private messages, to a single base station (BS). We aim to jointly design transmit precoding at the MSs' side and antenna selection at the BS side to maximize the achievable system throughput while reducing implementation complexity. The problem at hand is nonconvex and difficult to solve due to the antenna selection constraint. By exploiting the problem structure and linear relaxation, we propose using the Frank-Wolfe method and the well-known weighted mean-square error minimization approach to tackle the problem, leading to an efficient iterative algorithm. Moreover, due to the large number of antennas, the sparsity of antenna selection is also taken into account by introducing an l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm penalty function into the objective function. To tackle this nonconvex and discontinuous problem, we resort to quadratic approximation with smooth optimization and extend our proposed algorithm to the sparse optimization problem. The convergence of the proposed algorithms is analyzed and its effectiveness is verified by numerical examples in terms of the achieved system throughput.

A New Method for Designing of Stable Digital IIR Filter Using Hybrid Method

In this paper, a new technique for designing of a stable digital infinite impulse response filter, with improved performance in passband and stopband regions using quantum particle swarm optimization (QPSO) and artificial bee colony (ABC) algorithm, is explored in frequency domain. In the proposed method, QPSO technique is modified with exploiting the novelty of search and replacement mechanism of scout bee from ABC algorithm. For this purpose, a new design problem is constructed as a nonlinear minimization of mean square error between the designed and desired filter responses in passband, stopband, and transition band simultaneously, allowing permissible ripples in passband and stopband. Efficiency of the proposed technique is measured by several attributes like passband error, stopband error, total squared error (SE), maximum stopband attenuation, maximum passband error $$ \left( {e_{pb}^{\hbox{max} } } \right) $$ , passband ripple, and maximum phase deviation in passband. Experimental results evidence that a significant reduction is achieved in sum of the SE in passband and stopband from 12 to 54%, and the performance is not degraded due to quantization and truncation process. However, computation time in term of CPU time is increased from 0.77 to 4.1%, along with 2.62–7.43% hike in number of function evaluation, when compared to QPSO. A comparative study reveals that the proposed method yields better fidelity parameter as compared other evolutionary algorithms such as gravitational search algorithm, genetic algorithm, and variants of PSO. The proposed technique is also suitable for higher filter taps.

Subchannel Allocation and Hybrid Precoding in Millimeter-Wave OFDMA Systems

Constrained by the number of transmitted data streams, this paper proposes sub-carrier allocation (SA) and hybrid precoding (HP) designs for sum-rate maximization in mm-wave OFDMA systems. The optimization is first formulated as a computation sparsity-constrained HP design problem, which is non-convex and challenging to solve. Two two-stage solution approaches are proposed. In the first approach, a fully digital precoder (FDP) is optimized considering the computation sparsity constraint in the first stage. In the second approach, the sparsity constraint is only imposed in the second stage. To find the FDP, we employ the minimization of the weighted mean-squared error and the $\ell 1$ -reweighted methods to tackle the non-convex objective function and sparsity constraints, respectively. In the second stage of each approach, we exploit an alternating weighted mean-squared error minimization algorithm to reconstruct HP’s based on the FDP found in the first stage. Two novel analog precoding designs, namely semi-definite-relaxation-based and projected-gradient-descent-based, are then proposed to optimize the analog part of the obtained HP’s. We also study the impacts of various system parameters on the system sum-rate and provide resource provisioning insights for HP systems. Numerical results show the superior performances of the proposed designs over joint SA and HP benchmark algorithms.

Noninvasive determination of the pulmonary artery input impedance

A reliable noninvasive method for the estimation of pulmonary function in healthy and diseased subjects should be of great importance in the prognosis, diagnosis, and treatment of pulmonary hypertension. Here we propose such a method, which is based on the parameter identification of the five-element Windkessel model of pulmonary circulation. The method requires the following input variables: the heart rate, the stroke volume, the Doppler echocardiographic measurements of the tricuspid regurgitation and the pulmonary valve velocity profiles, and estimations of the right atrium and the pulmonary vein pressure. The stroke volume is calculated as a product of the left ventricle outflow tract area and the velocity-time integral measured at the same place. The model parameter identification procedure is based on minimization of the root mean square error between the pulmonary artery root pressure calculated from the aforementioned Doppler velocity profiles (from the Bernoulli equation applied during the ejection phase) and the pressure from the Windkessel model during the same period. The output from the model contains the calculated pulmonary artery input impedance (i.e. the model parameters: pulmonary vascular resistance, pulmonary artery proximal and distal compliances, inertance, and characteristic impedance) and the pulmonary artery pressure profile during the whole heart period. Our method is applied to a subject with pulmonary hypertension. The right heart Swan-Ganz catheterization has been performed in this subject. The results obtained by using this method show that the five-element Windkessel model reconstructs the main features of the pulmonary artery input impedance very well: its modulus shows the minimum where the phase angle changes its sign. The pulmonary vascular resistance, the systolic, diastolic and mean pulmonary artery pressures obtained from the method are in good agreement with the values obtained invasively from the catheterization. Sensitivity analysis shows that the mean pulmonary pressure is fairly insensitive to slight overestimation/ underestimation of all input parameters, except for the right atrium pressure. The absolute error in the mean pulmonary artery pressure is nearly the same as the error in the right atrium pressure. Since the proposed method offers a deeper insight into the pulmonary circulation than the catheterization itself because it provides the proximal and distal compliance, the inertance and the characteristic impedance, it seems that it can serve in clinical practice as a good substitute for catheterization.

Joint Transceiver Designs for MSE Minimization in MIMO Wireless Powered Sensor Networks

In this paper, we study vector parameter estimation in multiple-input multiple-output wireless-powered sensor networks (WPSNs) where sensor nodes operate by harvesting the radio frequency signals transmitted from energy access points (E-APs). We investigate a joint design of sensor data precoders, a fusion rule, and energy covariance matrices to minimize the mean square error (MSE) of the parameter estimate based on a non-linear energy harvesting model. First, we propose a centralized algorithm to solve the MSE minimization problem. Next, to reduce the computational complexity at the fusion center (FC) and feedback overhead from the sensors to the FC, we present a distributed algorithm to locally compute the precoders and the energy covariance matrices. We employ the alternating direction method of multipliers technique to minimize the MSE in a distributed manner without any coordination from the FC. In the proposed distributed algorithm, each sensor node calculates its own precoders and determines the local information of the fusion rule, and then messages are broadcast to other sensor nodes and E-APs. Simulation results demonstrate that the distributed algorithm performs close to the centralized algorithm with reduced complexity. Moreover, the proposed methods exhibit superior estimation performance over conventional techniques in WPSNs.

Optimal Training Design for MIMO Systems With General Power Constraints

Training design for general multiple-input multiple-output (MIMO) systems is investigated in this paper. Unlike prior designs that are applicable only for centralized MIMO systems with total power constraints, general power constraints are considered here. They cover total power constraints, individual power constraints, and mixed individual and per-user sum-power constraints as special cases. By writing the MIMO received signals in matrix and vector forms, respectively, and using Kronecker structured channel and noise statistics, three channel estimation schemes, i.e., right estimation, left estimation, and right-left estimation, are discussed. Their corresponding training designs are considered individually with the general power constraints. Under each channel estimation scheme, optimal training sequences to maximize the mutual information between the true channel and its estimated counterpart, and to minimize the mean square error (MSE) of the channel estimate are, respectively, proposed in semiclosed forms. The relationship between the two design criteria, i.e., the mutual information maximization and the MSE minimization, is clearly revealed. The optimal training designs under the three estimation schemes are also compared in depth. It is demonstrated that right estimation exploits less statistical information about the channel and noise, and provides worse performance than the left estimation but with lower computational complexity. On the other hand, right-left estimation performs in between the other two and provides a good compromise between complexity and performance. Finally, the optimality and effectiveness of the proposed training designs are verified by extensive simulations.

Numerical solutions of nonlinear 3‐dimensional Volterra integral‐differential equations with 3D‐block‐pulse functions

This paper studies nonlinear 3‐dimensional Volterra integral‐differential equations, by implementing 3‐dimensional block‐pulse functions. First, we prove a theorem and corollary about sufficient condition for the minimum of mean square error under the block pulse coefficients and uniqueness of solution of the nonlinear Volterra integral‐differential equations. Then, we convert the main problem to a nonlinear system to the 3‐dimensional block‐pulse functions. In addition, illustrative examples are included to demonstrate the validity and applicability of the presented method.