Processor Time Research Articles

A Class of Seventh Order Hybrid Extended Block Adams Moulton Methods for Numerical Solutions of First Order Delay Differential Equations

This paper considers the computational solution of some first order delay differential equations (DDEs) using a class of seventh order Hybrid Extended Block Adams Moulton Methods (HEBAMM) without the application of interpolation techniques in evaluating the delay term. The delay term was evaluated by a valid expression of sequence. By matrix inversion techniques, the discrete schemes of the proposed method were obtained through its continuous derivations with the help of linear multistep collocation procedure. The convergence and stability analysis of the method were investigated. After the demonstration of the proposed method in solving some first order DDEs, it was observed that the higher step number k = 4 integrated with a hybrid extended future point performed better and faster in terms of efficiency, accuracy, consistency, convergence, region of absolute stability and Central Processing Unit Time (CPUT) than the lower step numbers k = 3 and 2 integrated with hybrid extended future points when compared with the exact solutions and other existing methods at fixed step size .

Effect of the duty cycle of the ultrasonic processor on the efficiency of extraction of phenolic compounds from Sorbus intermedia

This paper studies the effect of different ultrasonic parameters on the yield of extraction and antioxidant activity of selected phenolic compounds from Sorbus intermedia berries. The sonication was carried out in two modes: continuous and pulse. In the pulse mode, the samples were sonicated with the following processor settings: 1 s on–2 s off. The effective ultrasonic processor times were 5, 10, and 15 min, and the total extraction times were 15, 30, and 45 min. The results showed that the duty cycle significantly affected the antioxidant activity of the extracts and the yield of chlorogenic acid, rutin, and total flavonoids. Compared to the continuous mode, the pulse ultrasound increased the extraction yield of rutin by 5–27%, chlorogenic acid by 12–29%, and total flavonoids by 8–42%. The effect of the duty cycle on the extraction yield was dependent on the intensity and duration of the ultrasound treatment. The mechanism of the influence of the pulsed ultrasound field on the extraction process has been elucidated. This research clearly demonstrated the superiority of pulsed ultrasound-assisted extraction for production of antioxidants from Sorbus intermedia berries.

The bone conduction implant BONEBRIDGE increases quality of life and social life satisfaction

PurposeTranscutaneous active bone conduction hearing aids represent an alternative approach to middle ear surgery and conventional hearing aids for patients with conductive or mixed hearing loss. The aim of this study was to determine quality of life, subjective hearing experience and patients’ satisfaction after implantation of a bone conduction hearing aid.MethodsThis monocentric and retrospective study included twelve adult patients who received a bone conduction hearing aid (Bonebridge, MedEL) consisting of an extracorporeal audio processor and a bone conduction implant (BCI) between 2013 and 2017. On average 40 months after implantation, the patients were asked to answer three questionnaires regarding quality of life (AqoL-8D), self-reported auditory disability (SSQ-12-B) and user’s satisfaction (APSQ) after implantation of the Bonebridge (BB). A descriptive statistical analysis of the questionnaires followed.Results12 patients aged 26–85 years (sex: m = 7, w = 5) were recruited. The quality of life of all patients after implantation of the BB (AqoL 8D) averaged an overall utility score of 0.76 (SD ± 0.17). The mean for ‘speech hearing’ in the SSQ-12-B was + 2.43 (SD ± 2.03), + 1.94 (SD ± 1.48) for ‘spatial hearing’ and + 2.28 (SD ± 2.32) for ‘qualities of hearing’. 11 out of 12 patients reported an improvement in their overall hearing. The APSQ score for the subsection ‘wearing comfort’ was 3.50 (SD ± 0.87), ‘social life’ attained a mean of 4.17 (SD ± 1.06). The ‘device inconveniences’ reached 4.02 (SD ± 0.71) and ‘usability’ of the device was measured at 4.23 (SD ± 1.06). The average wearing time of the audio processor in the cohort was 11 h per day, with 8 of 12 patients reporting the maximum length of 12 h per day.ConclusionBB implantation results in a gain in the perceived quality of life (AqoL 8D). The SSQ-12-B shows an improvement in subjective hearing. According to the APSQ, it can be assumed that the BB audio processor, although in an extracorporeal position, is rated as a useful instrument with positive impact on social life. The majority stated that they had subjectively benefited from BB implantation and that there were no significant physical or sensory limitations after implantation.

A coarse-grained multicomputer parallel algorithm for the sequential substring constrained longest common subsequence problem

In this paper, we study the sequential substring constrained longest common subsequence (SSCLCS) problem. It is widely used in the bioinformatics field. Given two strings X and Y with respective lengths m and n, formed on an alphabet Σ and a constraint sequence C formed by ordered strings (c1,c2,…,cl) with total length r, the SSCLCS problem is to find the longest common subsequence D between X and Y such that D contains in an ordered way c1,c2,…,cl. To solve this problem, Tseng et al. proposed a dynamic-programming algorithm that runs in Omnr+(m+n)|Σ| time. We rely on this work to propose a parallel algorithm for the SSCLCS problem on the Coarse-Grained Multicomputer (CGM) model. We design a three-dimensional partitioning technique of the corresponding dependency graph to reduce the latency time of processors by ensuring that at each step, the size of the subproblems to be performed by processors is small. It also minimizes the number of communications between processors. Our solution requires Onmr+(m+n)|Σ|p execution time with O(p) communication rounds on p processors. The experimental results show that our solution speedups up to 59.7 on 64 processors. This is better than the CGM-based parallel techniques that have been used in solving similar problems.

Elastic net feature selected multivariate discriminant mapreduce classification

Analyzing the <span>big stream data and other valuable information is a significant task. Several conventional methods are designed to analyze the big stream data. But the scheduling accuracy and time complexity is a significant issue. To resolve, an elastic-net kernelized multivariate discriminant map reduce classification (EKMDMC) is introduced with the novelty of elastic-net regularization-based feature selection and kernelized multivariate fisher Discriminant MapReduce classifier. Initially, the EKMDMC technique executes the feature selection to improve the prediction accuracy using the Elastic-Net regularization method. Elastic-Net regularization method selects relevant features such as central processing unit (CPU) time, memory and bandwidth, energy based on regression function. After selecting relevant features, kernelized multivariate fisher discriminant mapr classifier is used to schedule the tasks to optimize the processing unit. Kernel function is used to find higher similarity of stream data tasks and mean of available classes. Experimental evaluation of proposed EKMDMC technique provides better performance in terms of resource aware predictive scheduling efficiency, false positive rate, scheduling time and memory consumption.</span>

A dynamic data encryption method based on addressing the data importance on the internet of things

The rapid growth of internet of things (IoT) in multiple areas brings research challenges closely linked to the nature of IoT technology. Therefore, there has been a need to secure the collected data from IoT sensors in an efficient and dynamic way taking into consideration the nature of collected data due to its importance. So, in this paper, a dynamic algorithm has been developed to distinguish the importance of data collected and apply the suitable security approach for each type of data collected. This was done by using hybrid system that combines block cipher and stream cipher systems. After data classification using machine learning classifiers the less important data are encrypted using stream cipher (SC) that use rivest cipher 4 algorithm, and more important data encrypted using block cipher (BC) that use advanced encryption standard algorithm. By applying a performance evaluation using simulation, the proposed method guarantees that it encrypts the data with less central processing unit (CPU) time with improvement in the security over the data by using the proposed hybrid system.

Iterative Dynamic Critical Path Scheduling: An Efficient Technique for Offloading Task Graphs in Mobile Edge Computing

Recent years have witnessed a paradigm shift from centralized cloud computing to decentralized edge computing. As a key enabler technique in edge computing, computation offloading migrates computation-intensive tasks from resource-limited devices to nearby devices, optimizing service latency and energy consumption. In this paper, we investigate the problem of offloading task graphs in edge computing scenarios. Previous work based on list-scheduling heuristics is likely to suffer from severe processor time wastage due to intricate task dependencies and data transfer requirements. To this end, we propose a novel offloading algorithm, referred to as Iterative Dynamic Critical Path Scheduling (IDCP). IDCP minimizes the makespan by iteratively migrating tasks to keep shortening the dynamic critical path. Through IDCP, what is managed are essentially the sequences among tasks, including task dependencies and scheduled sequences on processors. Since we only schedule sequences here, the actual start time of each task is not fixed during the scheduling process, which effectively helps to avoid unfavorable schedules. Such flexibilities also offer us much space for continuous scheduling optimizations. Our experimental results show that our algorithm significantly outperforms existing list-scheduling heuristics in various scenarios, which demonstrates the effectiveness and competitiveness of our algorithm.

Embedded PSO for Solving FJSP on Embedded Environment (Industry 4.0 Era)

Since of the advent of Industry 4.0, embedded systems have become an indispensable component of our life. However, one of the most significant disadvantages of these gadgets is their high power consumption. It was demonstrated that making efficient use of the device’s central processing unit (CPU) enhances its energy efficiency. The use of the particle swarm optimization (PSO) over an embedded environment achieves many resource problems. Difficulties of online implementation arise primarily from the unavoidable lengthy simulation time to evaluate a candidate solution. In this paper, an embedded two-level PSO (E2L-PSO) for intelligent real-time simulation is introduced. This algorithm is proposed to be executed online and adapted to embedded applications. An automatic adaptation of the asynchronous embedded two-level PSO algorithm to CPU is completed. The Flexible Job Shop Scheduling Problem (FJSP) is selected to solve, due to its importance in the Industry 4.0 era. An analysis of the run-time performance on handling E2L-PSO over an STM32F407VG-Discovery card and a Raspberry Pi B+ card is conducted. By the experimental study, such optimization decreases the CPU time consumption by 10% to 70%, according to the CPU reduction needed (soft, medium, or hard reduction).

СХЕМОТЕХНИЧЕСКОЕ И ЭЛЕКТРОДИНАМИЧЕСКОЕ МОДЕЛИРОВАНИЕ КОЛЕБАТЕЛЬНОГО ПРОЦЕССА ПЕРЕРАСПРЕДЕЛЕНИЯ ЭНЕРГИИ В БИПОЛЯРНОМ ТРАНЗИСТОРЕ

The advantage of the promising method of passive radiosensor technical diagnostics(PRTD) over the currently existing methods for determining the technical condition (vibrometry,thermal control, JTAG-testing, optical control) are: no inertia, no processor time, no galvaniccontact with the object of study. In modern scientific literature, almost no attention is paid to numericalmodels of electronic devices, including those based on bipolar transistors (BPT), whichdescribe the process of oscillatory redistribution of energy and radiation used in PRTD. Therefore,the purpose of this study is to develop the PRTD method through the development, analysisand comparison of circuit and electrodynamic models of oscillatory energy redistribution in theBPT. The paper presents and analyzes simplified circuit and electrodynamic models of oscillatoryredistribution of energy in the BPT. The parameters of the models are calculated signal radioprofiles (SRP) are obtained for the electrical component of electromagnetic radiation created bythe radio-electronic unit itself, built on the BPT. Methods for adjusting the reference parametersdepending on the actual conditions for switching on the BPT are shown. It has been establishedthat the cross-correlation function of the SRP obtained as a result of circuit and electrodynamicmodeling is not lower than 0.93, which indicates a high similarity of the presented models. Inpractice, the use of the developed models in the analysis of SRP obtained by recording the intrinsicemissions of radio engineering components of electronic devices will allow us to determine theoperating mode of the BPT and its speed with a sufficiently high accuracy. This analysis can beused in the PRTD, indicating a malfunction of the signal circuits, or degradation of the parametersof the element itself in the early stages

Novel feature selection method via kernel tensor decomposition for improved multi-omics data analysis

BackgroundFeature selection of multi-omics data analysis remains challenging owing to the size of omics datasets, comprising approximately 10^2–10^5 features. In particular, appropriate methods to weight individual omics datasets are unclear, and the approach adopted has substantial consequences for feature selection. In this study, we extended a recently proposed kernel tensor decomposition (KTD)-based unsupervised feature extraction (FE) method to integrate multi-omics datasets obtained from common samples in a weight-free manner.MethodKTD-based unsupervised FE was reformatted as the collection of kernelized tensors sharing common samples, which was applied to synthetic and real datasets.ResultsThe proposed advanced KTD-based unsupervised FE method showed comparative performance to that of the previously proposed KTD method, as well as tensor decomposition-based unsupervised FE, but required reduced memory and central processing unit time. Moreover, this advanced KTD method, specifically designed for multi-omics analysis, attributes P values to features, which is rare for existing multi-omics–oriented methods.ConclusionsThe sample R code is available at https://github.com/tagtag/MultiR/.

Advanced spatially hybrid fluid‐kinetic modelling of plasma‐edge neutrals and application to ITER case using SOLPS‐ITER

AbstractA spatially hybrid fluid‐kinetic approach for the efficient simulation of plasma‐edge neutrals is extended with a kinetic‐fluid condensation process and an automated approach to select a fluid or kinetic treatment at each point along the divertor targets. With the proposed hybrid fluid‐kinetic methods, the dominant charge–exchange reaction can be largely removed from the kinetic neutral simulation. The hybrid methods achieve quantitative agreement with the standard kinetic approach, with relative errors on the peak target plasma density and peak target ion flux density of 5–30%, while the Central Processing Unit (CPU) time for the kinetic neutral solver is reduced by a factor 3–6.

Solving the time-independent Schrödinger equation for chains of coupled excitons and phonons using tensor trains.

We demonstrate how to apply the tensor-train format to solve the time-independent Schrödinger equation for quasi-one-dimensional excitonic chain systems with and without periodic boundary conditions. The coupled excitons and phonons are modeled by Fröhlich-Holstein type Hamiltonians with on-site and nearest-neighbor interactions only. We reduce the memory consumption as well as the computational costs significantly by employing efficient decompositions to construct low-rank tensor-train representations, thus mitigating the curse of dimensionality. In order to compute also higher quantum states, we introduce an approach that directly incorporates the Wielandt deflation technique into the alternating linear scheme for the solution of eigenproblems. Besides systems with coupled excitons and phonons, we also investigate uncoupled problems for which (semi-)analytical results exist. There, we find that in the case of homogeneous systems, the tensor-train ranks of state vectors only marginally depend on the chain length, which results in a linear growth of the storage consumption. However, the central processing unit time increases slightly faster with the chain length than the storage consumption because the alternating linear scheme adopted in our work requires more iterations to achieve convergence for longer chains and a given rank. Finally, we demonstrate that the tensor-train approach to the quantum treatment of coupled excitons and phonons makes it possible to directly tackle the phenomenon of mutual self-trapping. We are able to confirm the main results of the Davydov theory, i.e., the dependence of the wave packet width and the corresponding stabilization energy on the exciton-phonon coupling strength, although only for a certain range of that parameter. In future work, our approach will allow calculations also beyond the validity regime of that theory and/or beyond the restrictions of the Fröhlich-Holstein type Hamiltonians.

A Reduced-Order Extrapolation (ROE) Method for Solution Coefficient Vectors in the Mixed Finite Element (MFE) Method for the Two-Dimensional (2D) Fourth-Order Hyperbolic Equation

This study focuses on a reduced-order extrapolation method for the coefficient vectors of the mixed finite element solution for two-dimensional fourth-order hyperbolic equation. We first establish the mixed finite element scheme for the equation and give the matrix model of the mixed finite element scheme and the existence, stability and error estimates of its solutions. Then, we derive a reduced-order extrapolation mixed finite element matrix model with a small number of unknowns, where the proper orthogonal decomposition method is used to save central processing unit time, and prove the existence, stability and error estimates of the reduced-order extrapolation mixed finite element solutions with the help of matrix knowledge. More importantly, the reduced-order extrapolation mixed finite element matrix model have the same basis functions and error accuracy as the mixed finite element matrix model. Finally, some numerical experiments confirm the effectiveness of the reduced-order extrapolation mixed finite element matrix model, where the central processing unit time is greatly reduced and the accuracy is maintained.

ACCURACY OF DETERMINATION OF LINEAR SPECTRAL FREQUENCIES

The article describes the basic idea of coding a speech signal by the method of linear prediction (Linear Predictive Coding – LPC), which consists in the fact that instead of the parameters of the speech signal, the encoded parameters of a certain filter are transmitted over the communication line, which is, in a sense, an equivalent of the human vocal tract, as well as parameters of the excitation signal of this filter: tone or noise. The essence of the parameters of the synthesizing filter – linear prediction coefficients (LP), calculated in the process of frame-by-frame adaptive filtering – is disclosed. The main advantages of these coefficients are stated, which consists in the ability to completely describe the state of the predictor filter, as well as the main disadvantages obtained as a result of numerous studies that prevent the direct transmission of LPCs over the communication channel due to their sensitivity to quantization errors. The necessity of searching for mathematically equivalent parameters f the reducing filter is substantiated. Alternative parameters of the LSP representation of the vocal tract model, called Linear Spectral Frequencies (LSP), are proposed, and are most often used in low-speed speech codecs at the present time. The main difficulty of the task of calculating the LSP directly from the LSP in real time is described, and it is also investigated that most of the analyzer’s processor time, as a rule, is spent on this task. It is proved that despite the high level of development of digital processors, the problem of calculating the parameters of the vocal tract model in real time remains one of the main difficulties in speech coding. That is why methods that reduce the complexity of this procedure are currently of significant interest. A new method for calculating the LSP and an algorithm based on it are proposed. Its main advantages over the existing ones are described. An assessment of the possible improvement in the quality of speech processing was made, due to the use of the developed method for calculating the LSP.

Twitter Attribute Classification With Q-Learning on Bitcoin Price Prediction

Bitcoin price prediction based on people’s opinions on Twitter usually requires millions of tweets, using different text mining techniques, and developing a machine learning model to perform the prediction. These attempts lead to the employment of a significant amount of computer power, central processing unit (CPU) utilization, random-access memory (RAM) usage, and time. To address this issue, in this paper, we consider a classification of tweet attributes that effects on price changes and computer resource usage levels while obtaining an accurate price prediction. To classify tweet attributes having a high effect on price movement, we collect all Bitcoin-related tweets posted in a certain period and divide them into four categories based on the following tweet attributes: <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(i)$ </tex-math></inline-formula> the number of followers of the tweet poster, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(ii)$ </tex-math></inline-formula> the number of comments on the tweet, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(iii)$ </tex-math></inline-formula> the number of likes, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(iv)$ </tex-math></inline-formula> the number of retweets. We separately train and test by using the Q-learning model with the above four categorized sets of tweets and find the best accurate prediction among them. We compare our approach with a classic approach where all Bitcoin-related tweets are used as input data for the model, by analyzing the CPU workloads, RAM usage, memory, time, and prediction accuracy. The results show that tweets posted by users with the most followers have the most influence on a future price, and their utilization leads to spending 80% less time, 88.8% less CPU consumption, and 12.5% more accurate predictions compared with the classic approach.

Fast hybrid explicit group methods for solving 2D fractional advection-diffusion equation

&lt;abstract&gt;&lt;p&gt;In recent years, fractional partial differential equations (FPDEs) have been viewed as powerful mathematical tools for describing ample phenomena in various scientific disciplines and have been extensively researched. In this article, the hybrid explicit group (HEG) method and the modified hybrid explicit group (MHEG) method are proposed to solve the 2D advection-diffusion problem involving fractional-order derivative of Caputo-type in the temporal direction. The considered problem models transport processes occurring in real-world complex systems. The hybrid grouping methods are developed based upon a Laplace transformation technique with a pair of explicit group finite difference approximations constructed on different grid spacings. The proposed methods are beneficial in reducing the computational burden resulting from the nonlocality of fractional-order differential operator. The theoretical investigation of stability and convergence properties is conducted by utilizing the matrix norm analysis. The improved performance of the proposed methods against a recent competitive method in terms of central processing unit (CPU) time, iterations number and computational cost is illustrated by several numerical experiments.&lt;/p&gt;&lt;/abstract&gt;

Радиосенсорная идентификация и аутентификация радиоэлектронных устройств

The presented work is devoted to the study of a new physically unclonable function (PUF) associated with the intrinsic electromagnetic radiation of a radio electronic device. This PUF arises as a result of the technological spread of the parameters of electronic components. The relevance of this study is explained by the fact that modern methods of protecting radio-electronic products from illegal cloning have a number of serious drawbacks associated with increased power consumption, the use of processor time, and the need for galvanic access to the object of study. Partially, these problems are eliminated by PUF, which allow authentication of a radio-electronic device. However, this kind of protection also has serious vulnerabilities in the case of illegal overproduction of products in excess of the ordered quantity. In addition, the PUF does not allow for the identification of radio-electronic products. The purpose of this work is to increase the protection of radio electronic devices from illegal cloning, by studying a new PUF. The work uses experimental research methods to record the electrical component of the electromagnetic field emitted by the product - the signal radio profile (SRP). Correlation analysis methods for product authentication, Pearson's statistical agreement method for identification. SRPs registered from specially designed experimental samples are presented, a correlation analysis of SRP data is carried out. To decompose and extract the parameters of the SRP, its time-frequency spectrum was constructed. A correspondence table was compiled and an analysis of Pearson's agreement was carried out. The results obtained showed the possibility of using the SRP as a new physically unclonable function that allows the identification of radio electronic devices with a probability specified by the researcher, which determines the novelty of the work. It has been established that with Pearson's coefficient of agreement between the parameters of the studied SRP and the benchmark of more than 0.95, a radio-electronic device can be reliably identified. The practical significance of the work lies in the possibility of using the SRP to identify a group of devices and radio-technical protection of a radio-electronic product from fakes and illegal copies.

Software Optimisation of Lightweight Klein Encryption in the Internet of Things

The Internet of Things (IoT) and Wireless Sensor Network (WSN) devices are prone to security vulnerabilities, especially when they are resource constrained. Lightweight cryptography is a promising encryption concept for IoT and WSN devices, that can mitigate these vulnerabilities. For example, Klein encryption is a lightweight block cipher, which has achieved popularity for the trade-off between performance and security. In this paper, we propose one novel method to enhance the efficiency of the Klein block cipher and the effects on the Central Processing Unit (CPU), memory usage, and processing time. Furthermore, we evaluated another approach on the performance of the Klein encryption iterations. These approaches were implemented in the Python language and ran on the Raspberry PI 3. We evaluated and analysed the results of two modified encryption algorithms and confirm that two enhancing techniques lead to significantly improved performance compared to the original algorithm.

Determination of Parameters of Electronic Devices by the Method of Passive Radio-Sensor Technical Diagnostics

Introduction. Technical diagnostics (TD) as a nascent discipline is rapidly developing in the field of both software and hardware. Modern TD methods, such as vibrometry, thermal control, JTAG testing and optical control, either exhibit high inertia, consume processor time, require suspension of the electronic device, or demand a galvanic contact with the study object, which is often unacceptable. These disadvantages can be eliminated by passive radio-sensor TD. To date, little information has been published on the parameters of electronic devices provided by this method.Aim. Determination of the parameters of electronic devices, the assessment of which can be provided by passive radio-sensor TD.Materials and methods. Signal radio profiles were obtained experimentally using metrological equipment and software-numerical methods for modeling radio wave processes. The parameters of the signal radio profile were calculated by a mathematical method for solving differential equations.Results. The main principles and results of radio-sensor TD, as well as the simplest toolkit, are shown. An equation is obtained for the signal radio profile emitted by the electronic unit of the device, as well as an expression for its free components. An approach for assessing the TD correctness based on the number of free components of the received signal radio profile and the reference is described. The possibility of obtaining information about temperature, voltage drop, speed of emitting nodes, as well as the state of its components and modes of operation of p–njunctions is demonstrated. It is shown that this information is carried by the parameters of the basic equation for the signal radio profile.Conclusion. The derived basic equation allows a non-contact, remote passive radio-sensor TD to be conducted by correlation analysis of the received signal, providing a detailed examination of malfunctions in each electronic unit. The described TD method based on the presented parameters is promising for assessing the technical state of electronic devices.

Extended moving horizon estimation for chemical processes under non‐Gaussian noises

AbstractStudies on moving horizon estimation (MHE) for applications featuring process uncertainties and measurement noises that follow time‐dependent non‐Gaussian distributions are absent from the literature. An extended version of MHE (EMHE) is proposed here to improve the estimation for a general class of non‐Gaussian process uncertainties and measurement noises at no significant additional computational costs. Gaussian mixture models are introduced to the proposed EMHE to approximate offline the non‐Gaussian densities of these random variables. Moreover, the proposed EMHE‐based estimation scheme can be updated online by re‐approximating the corresponding Gaussian mixture models when the distributions of noises/uncertainties change due to sudden or seasonal changes in the operating conditions. These updates are not expected to increase the central processing unit times considerably. Illustrative case studies featuring open‐loop operation and closed‐loop control using nonlinear model predictive control have shown that the practical features offered by EMHE resulted in significant improvements in state estimation and online control.