Iterative Form Research Articles

One-Step Prediction-Enhanced FIR Filter and its Application in INS/Vision-Integrated Mobile Robot Localization

In this paper, to address the problem that some inertial navigation system (INS) data are not used for data fusion, which affects the accuracy of the system with INS and vision, one-step prediction enhanced finite impulse response (FIR) filter will be introduced in this work. Firstly, the integrated scheme for fusing the INS technique with vision technology is present. Then, the FIR filter with iterative form will be derived based on the INS/vision integrated data fusion model. Thirdly, the one-step prediction will be employed by the FIR filter for improving the localization error. The validity of the method derived in this work has been verified by a practical experiment. Test results demonstrate that the FIR algorithm can enhance the localization accuracy when compared with the Kalman filter respectively by employing the one-step prediction. And the proposed method shows more robust when compared with the Kalman filter.

Role of technology learning in the decarbonization of the iron and steel sector: An energy system approach using a global-scale optimization model

The iron and steel sector, characterized by fossil fuel-driven processes is one of the most difficult to decarbonize and a significant source of greenhouse gas emissions. Various new technologies promise to change this, but their development is highly uncertain. This paper aims to analyze the prospects of key low-carbon technologies in the sector, focusing on the impact of technology learning, in the light of the uncertainty related to the learning rate. An optimization energy system model was used with an iterative learning formulation, adopting different learning assumptions. The results show that learning may have only a minor impact in the short and medium term, reducing global carbon emissions of the sector by 3% (at most) in 2050, compared to a non-learning scenario. In the long term, high learning potentials for novel processes are important, leading to a market share of up to the 80% by the end of the century. The learning potential for Carbon Capture and Storage processes, however, plays no role in the simulations. Early investments and research and development can help unlock the full potential of the technologies, while more detailed studies should be performed to better understand the retrofitting impact in the shorter term.

Robust state estimation for uncertain linear discrete systems with d‐step measurement delay and deterministic input signals

AbstractIn this study, the state estimation problems for linear discrete systems with uncertain parameters, deterministic input signals and d‐step measurement delay are investigated. A robust state estimator with a similar iterative form and comparable computational complexity to the Kalman filter is derived based on the state augmentation method and the sensitivity penalisation of the innovation process. It is discussed that the steady‐state properties such as boundedness and convergence of the robust state estimator under the assumptions that the system parameters are time invariant. Numerical simulation results show that compared with the Kalman filter, the obtained state estimator is more robust to modelling errors and has nice estimation accuracy.

Multi-channel transmission scheduling with hopping scheme under uncertain channel states

This paper investigates the multi-channel transmission scheduling problem for remote state estimation based on a hopping scheme in cyber-physical systems. The smart sensor sends multiple subpackets over different orthogonal channels to the remote end simultaneously. Owing to the randomness and vulnerability of transmission environments, the uncertain multi-channel states are considered in this paper, which relaxes the assumption of existing deterministic models. The objective is to find an appropriate hopping scheme that minimizes the remote estimation error covariance. First, the multi-channel selection problem is modeled as a multi-arm bandits (MAB) matrix via taking the packet receiving probability as the gain. From the perspective of strategy and channel, two exponential-weight online learning algorithms are designed with the assistance of transmission energy switching policy. Then, based on Bernstein’s inequality for martingales and mini-batching loop, the upper bounds of algorithms’ regret values are analyzed under stochastic and adversarial channel states, respectively. Further, the estimator expression in iterative form and a sufficient condition for the error covariance to be bounded are derived. Finally, an example of unmanned vehicle moving demonstrates all the theoretical results.

Tensor Principal Component Analysis in High Dimensional CP Models

The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence conditions on the basis vectors for the CP components. In this paper, we propose new computationally efficient composite PCA and concurrent orthogonalization algorithms for tensor CP decomposition with theoretical guarantees under mild incoherence conditions. The composite PCA applies the principal component or singular value decompositions twice, first to a matrix unfolding of the tensor data to obtain singular vectors and then to the matrix folding of the singular vectors obtained in the first step. It can be used as an initialization for any iterative optimization schemes for the tensor CP decomposition. The concurrent orthogonalization algorithm iteratively estimates the basis vector in each mode of the tensor by simultaneously applying projections to the orthogonal complements of the spaces generated by other CP components in other modes. It is designed to improve the alternating least squares estimator and other forms of the high order orthogonal iteration for tensors with low or moderately high CP ranks, and it is guaranteed to have second or higher order convergence when the error of any given initial estimator is bounded by a small constant. Our theoretical investigation provides estimation accuracy and convergence rates for the two proposed algorithms. Both proposed algorithms are applicable to deterministic tensor, its noisy version, and the order- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2K$ </tex-math></inline-formula> covariance tensor of order- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> tensor data in a factor model with uncorrelated factors. Simulation experiments demonstrate significant practical superiority of our approach over existing methods.

Editorial: Tensor numerical methods and their application in scientific computing and data science

Editorial: Tensor numerical methods and their application in scientific computing and data science

Weighted singular value decomposition basis of Szegő kernel and its applications to signal reconstruction and denoising

For any circular analytic signal f+(eit)∈H2(T), if the sequence {ak}k=0∞ in the unit disc D satisfies the hyperbolic non-separability condition ∑k=0∞(1−|ak|)=∞, it is known that the first N+1 term approximation function based on the Takenaka–Malmquist system (SN+1f+)(eit)=∑k=0N〈f+(eit),Bk(eit)〉Bk(eit),can approximate the analytic signal f+(eit) in the L2-norm sense, where Bk(eit)=1−|ak|21−ak¯eit∏l=0k−1eit−al1−al¯eit, k∈N is the Takenaka–Malmquist system which can be seen as a generalization of Fourier series. We find that (SN+1f+)(eit) can also be represented by the standard basis, Lagrange basis and weighted SVD basis. Different bases have different merits. The standard basis is simple. The Lagrange basis has a neat and compact form, which is very convenient for theoretical analysis. With the Takenaka–Malmquist system, the first N+1 term approximation function (SN+1f+)(eit) is able to write in an iterative form. The Takenaka–Malmquist system has the advantage of inheritance, and the point ak∈D can be easily selected step by step through the greedy principle. In this paper, we focus our attention on the weighted SVD basis. We give some orthogonal properties of the weighted SVD basis. It demonstrates that any real signal f(eit)∈L2(T) can be precisely reconstructed within the given error range by the weighted SVD basis decomposition. The experimental results reveal that the algorithm based on weighted SVD basis is more stable and accurate. Furthermore, compared with classical Fourier decomposition and adaptive Fourier decomposition algorithms, the experimental results show that the weighted SVD basis decomposition is more insensitive to noise. This will provide a new method for signal denoising.

An improved mayfly algorithm based on Kapur entropy for multilevel thresholding color image segmentation

Multilevel thresholding segmentation of color images plays an important role in many fields. The pivotal procedure of this technique is determining the specific threshold of the images. In this paper, an improved mayfly algorithm (IMA)-based color image segmentation method is proposed. Tent mapping initializes the female mayfly population to increase population diversity. Lévy flight is introduced in the wedding dance iterative formulation to make IMA jump from the local optimal solution quickly. Two nonlinear coefficients were designed to speed up the convergence of the algorithm. To better verify the effectiveness, eight benchmark functions are used to test the performance of IMA. The average fitness value, standard deviation, and Wilcoxon rank sum test are used as evaluation metrics. The results show that IMA outperforms the comparison algorithm in terms of search accuracy. Furthermore, Kapur entropy is used as the fitness function of IMA to determine the segmentation threshold. 10 Berkeley images are segmented. The best fitness value, peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and other indexes are used to evaluate the effect of segmented images. The results show that the IMA segmentation method improves the segmentation accuracy of color images and obtains higher quality segmented images.

An Antenna Pattern Correction Algorithm for Conical Scanning Spaceborne Radiometers: The CIMR Case

The rapid evolution of the effects observed in various areas of our planet related to climate change poses urgent questions about the knowledge of the state of the polar area and requires satellite acquisitions with fine spatial resolution and high accuracy to develop advanced products. The Copernicus Imaging Microwave Radiometer (CIMR) mission, based on a multifrequency microwave radiometer and designed to observe the ocean, sea ice, and Arctic environment, requires brightness temperature measurements with a total absolute uncertainty of 0.5 K and a spatial resolution of 5 km. This constraint demands very large reflectors with a gain value of tens of decibels. Mechanical constraints will be attained by using a mesh reflector, which guarantees the required resolution but with the drawback of a radiation pattern characterized by many grating lobes that contaminate the value of the brightness temperature associated with the boresight position. In this article, an antenna pattern correction (APC) is proposed to correct these effects. The algorithm takes advantage of an iterative formulation based on the Jacobi Method, providing a suitable correction that depends on the chosen spatial resolution. The APC algorithm was tested at both K- and Ka-bands with similar performance. Here, only the results from the latter are shown, as its antenna pattern is the most challenging among CIMR.

New Analytical Analysis-Oriented Stress-Strain Model for FRP-and-Steel Confined Concrete

Application of fiber-reinforced polymer (FRP) composites in the strengthening of reinforced concrete (RC) structures has become an increasingly accepted engineering practice. In particular, the use of externally bonded FRP wraps as a confining material for concrete can enhance both the compressive strength and the ultimate strain of concrete, making it suitable for strengthening and/or seismic retrofit of existing RC columns. This paper focuses on a recently developed analysis-oriented iterative FRP-and-steel confinement model for concrete and proposes a new optimization procedure to obtain an analytical expression for the corresponding monotonic envelope, reduce the associated computational cost, and increase the corresponding numerical robustness. Several analytical functions were evaluated in terms of their capability to fit the iteratively-generated stress-strain monotonic envelope for confined concrete. The newly proposed analytical formulation of the confined concrete stress-strain model was compared with the original iterative formulation in terms of computational cost for two examples of nonlinear seismic response analyses for: (1) an experimentally-tested concrete-filled FRP tube bridge column of a two-column bridge pier; and (2) a five-span bridge structure with FRP-retrofitted RC piers. It is found that the use of the newly proposed optimization-based analytical monotonic envelope can reduce by more than 30% the computational time associated with the original iteration-based monotonic envelope with negligible changes in the structural response prediction at both global and local levels.

2-D Modeling and Analysis of Time-Domain Electromagnetic Anomalous Diffusion With Space-Fractional Derivative

Recently, the electromagnetic (EM) anomalous diffusion phenomenon has been observed in time-domain EM (TDEM) surveys. Furthermore, the data interpretation accuracy has been reduced by adopting the traditional EM theory and methods. A number of models, such as random medium and roughness electrical conductivity theory, have been adopted to model the EM anomalous diffusion. However, problems such as modeling difficulty and massive discretization exist regarding characterizing the long-range correlation of EM anomalous diffusion. The space-fractional derivative has been proven to preferably describe the long-range correlation characteristic. Only a handful of studies on TDEM anomalous diffusion with space-fractional derivative have been conducted due to the difficulties in computational engineering problems. Therefore, we performed a series of studies about 2-D TDEM anomalous diffusion with space-fractional derivative. The 2-D TDEM space-fractional diffusion equation was constructed based on the space-fractional Ohm’s law model. Furthermore, the discretization and iteration forms of the control equation were derived based on the finite element method (FEM) by introducing the Riemann–Liouville (R–L)-type Riesz fractional derivatives. The 2-D mountain-shaped function and partial integration method (PIM) were combined to convert the fractional derivative into the primitive function form. Hence, the 2-D modeling of the space-fractional EM diffusion was realized. The effectiveness of our method was verified by the function construction method and wavenumber-domain analytical solution. The spatial and temporal characteristics of the space-fractional EM diffusion were analyzed by different geological models. Furthermore, we discuss the differences with the classical EM diffusion. Our method can effectively model the space-fractional EM diffusion in TDEM surveys and provide theoretical bases for improving the TDEM interpretation accuracy with complex geological conditions.

Research Acceleration in Self‐Driving Labs: Technological Roadmap toward Accelerated Materials and Molecular Discovery

The urgency of finding solutions to global energy, sustainability, and healthcare challenges has motivated rethinking of the conventional chemistry and material science workflows. Self‐driving labs, emerged through integration of disruptive physical and digital technologies, including robotics, additive manufacturing, reaction miniaturization, and artificial intelligence, have the potential to accelerate the pace of materials and molecular discovery by 10–100X. Using autonomous robotic experimentation workflows, self‐driving labs enable access to a larger part of the chemical universe and reduce the time‐to‐solution through an iterative hypothesis formulation, intelligent experiment selection, and automated testing. By providing a data‐centric abstraction to the accelerated discovery cycle, in this perspective article, the required hardware and software technological infrastructure to unlock the true potential of self‐driving labs is discussed. In particular, process intensification as an accelerator mechanism for reaction modules of self‐driving labs and digitalization strategies to further accelerate the discovery cycle in chemical and materials sciences are discussed.

SVR-TO-APMA: Hybrid efficient modelling and topology framework for stable topology optimization with accelerated performance measure approach

The topology design under uncertainties is an acceptable framework for providing a safe design and optimum configuration of structures. In this regard, the accuracy, efficiency, and robustness of the analytical topology optimization coupled with reliability analysis are the main efforts for reliability-based topology optimization (RBTO) of continuous structures. In the present investigation, a hybrid RBTO approach is developed for robust iterative formulation of reliability loop and an effective and simple optimization approach for topology loop. A multi-level set analytical framework is proposed based on the performance measure approach to seek the optimum results under multi uncertainties in size, mechanical properties, and loads of structures. The considered topology optimization procedure to derive the optimal layout of the structure which is called moving iso-surface threshold (MIST) is a powerful and enhanced topology optimization method in which, unlike other optimization methods, it has the capability of having no direct sensitivity analysis making it easier and simple. The accelerated first-order reliability method is introduced for searching the most probability points in the reliability loop of the RBTO model. The proposed reliability method is developed based on a stable iterative formulation. For reducing the computational burden of the topology optimization loop, the machine learning approach given from the support vector regression (SVR) is applied for estimating the probabilistic constraints in the RBTO model. Four examples of 2D, and 3D compliance, 2D complaint mechanism problem, and frequency maximization are presented for validation and highlighting the abilities in having the most accuracy and safety levels of the proposed hybrid framework named SVR-TO-APMA. The results indicate that the hyperparameters of SVR are directly affected by the accuracy of RBTO results. The stability of the RBTO model is shown by the accelerated PMA and the optimum layout is different from topology optimization in comparison with the RBTO results for 3D compliance and frequency maximization problems. The optimum design with uncertainties is increased by about 40%–90% with a reliability index of 3 compared to TO results for the studied example.

An operating condition information-guided iterative variational mode decomposition method based on Mahalanobis distance criterion for surge characteristic frequency extraction of the centrifugal compressor

As a significant high-speed rotating machinery being widely used in modern industry, the centrifugal compressor is subject to a potentially damaging phenomenon called surge, which may lead to property damage, casualties and even catastrophic accidents. Therefore, it is necessary to identify the early surge state of centrifugal compressors to prevent such accidents. In this paper, an operating condition information-guided iterative variational mode decomposition (OCIGIVMD) analysis method is proposed to extract the surge characteristic frequencies (SCFs) from the vibratory signals of centrifugal compressors under early surge state. The variational mode decomposition (VMD) is an effective methodology to decompose a multi-component signal into a series of amplitude-modulated-frequency-modulated (AM-FM) sub-signals with limited bandwidth, from which the characteristic frequencies can be extracted. However, when implementing VMD, the optimal determination of the decomposition mode number is still a challenging task, especially in face of complex signals containing a lot of noise and unknown interference components. Coping with the complex vibration signals of the centrifugal compressor, the VMD in an iterative form based on operating condition information is developed to extract the SCFs, while the decomposition process is controlled by Mahalanobis distance criterion to avoid under-decomposition or over-decomposition and it is needless to select the sensitive intrinsic mode function (IMF) from the multiple IMFs generated by OCIGIVMD. Finally, comparisons with the conventional VMD, empirical mode decomposition (EMD), spectral kurtosis (SK), local mean decomposition (LMD) and two improved VMD methods are conducted using both simulation and experimental data, which demonstrates that the proposed OCIGIVMD is a superior approach in extracting SCFs of the centrifugal compressor under different operating conditions.

Range Difference-Based Target Localization Under Stratification Effect and NLOS Bias in UWSNs

This letter proposes a robust target localization technique for acoustic underwater wireless sensor networks (UWSNs) that simultaneously experience the stratification effect and the non-line-of-sight (NLOS) bias. Specifically, we develop the range difference (RD)-based majorization minimization expression and its theoretical analysis, which leads to a surrogate function coupling with an iterative form. To figure out the initial estimate of the iteration, the proposed method converts the original localization problem into an RD-based generalized trust-region subproblem (RD-GTRS) after selecting a reference node. Eventually, an RD-based target localization approach (RD-TLA) is presented to iteratively estimate the final location. Simulation results show that the proposed RD-TLA method achieves better localization accuracy compared with other state-of-the-art methods in different scenarios.

Enhancing topological information of the Lyapunov‐based distributed model predictive control design for large‐scale nonlinear systems

SummaryIn this paper, a distributed model predictive control architecture based on graph theory for integrated large‐scale nonlinear process systems is proposed. This architecture is first agglomerated using popular community detection techniques and then organized on account of the relative master–slave relationship according to the ample information of interactions among separate subsystems. Both sequential and iterative distributed nonlinear model predictive coordination forms are considered for the reduction of the communication and computational burden within an acceptable loss of performance. Furthermore, the control performance of the large‐scale integrated system could be improved to some extent under the architecture and the communication strategy we propose, whereby a brave exploration is made on the relationship between the control structure and the control performance, ulteriorly obtaining some notable results towards the untapped territory. The effectiveness of the proposed coordination method is evaluated by a standard reactor‐separator process system.

Analysis on the Establishment and Management of Library Resource Base Based on Modern Information Technology

The current rapid development of modern network information technology, along with the arrival of this trend, has profoundly changed people’s living and learning methods. In the past, the management of book resources in the traditional period has gradually exposed many drawbacks, and it is difficult to meet the technological development of the information age. Combined with the complexity of book management parameters, high variable dimensions, and the characteristics of multiattribute data points including not only numerical attributes but also category attributes and mixed attributes, the fuzzy clustering algorithm is combined with attribute weighted optimization, and then, the optimization is derived. Iterative formula and form show a weighted clustering algorithm to perform cluster analysis on relevant influencing factors in book data management. Digital library is not a library entity: it corresponds to various real social activities of public information management and dissemination and is manifested in various new information resource organizations and information dissemination services. As a fuzzy association rule mining algorithm, FP-growth algorithm is obviously better than Apriori algorithm in execution efficiency. However, due to the lack of fuzzy attributes and the large space complexity, the FP-growth algorithm cannot achieve effective multilayer association rule mining when dealing with large transaction databases, such as library databases. First, the algorithm divides the large-scale book transaction database into several sub-databases according to the transaction of the first item and constructs the corresponding sub-FP-tree structure; then, the parent items that are not frequent items in the hierarchical tree are filtered out in real time to reduce the scanning space.

VINCENT

Exploratory search is a search paradigm that plays a vital role in databases, data mining, and information retrieval to assist users to get familiar with the underlying databases. It supports iterative query formulation to explore the data space. Despite its growing importance, exploratory search on graph-structured data has not received adequate attention in the literature. In this paper, we demonstrate a novel system called Vincent that facilitates an efficient exploratory subgraph search in a graph database containing a large collection of small or medium-sized graphs. By automatically generating the content for panels in GUI and diversified patterns from databases and providing a visual result explorer, Vincent supports data-driven visual query formulation, incremental subgraph processing, and efficient query result summarization.

Maximum Likelihood recursive state estimation using the Expectation Maximization algorithm

A Maximum Likelihood recursive state estimator is derived for non-linear state–space models. The estimator iteratively combines a particle filter to generate the predicted/filtered state densities and the Expectation Maximization algorithm to compute the maximum likelihood filtered state estimate. Algorithms for maximum likelihood state filtering, prediction and smoothing are derived. The convergence properties of these algorithms, which are inherited from the Expectation Maximization algorithm and the particle filter, are examined in two examples. For nonlinear state–space systems with linear measurements and additive Gaussian noises, it is shown that the filtering and prediction algorithms reduce to gradient-free optimization in a form of a fixed-point iteration. It is also shown that, with randomized reinitialization, which is feasible because of the simplicity of the algorithm, these methods are able to converge to the Maximum Likelihood Estimate (MLE) of multimodal, truncated and skewed densities, as well as those of disjoint support.

A variational framework for the inverse Henderson problem of statistical mechanics

The inverse Henderson problem refers to the determination of the pair potential which specifies the interactions in an ensemble of classical particles in continuous space, given the density and the equilibrium pair correlation function of these particles as data. For a canonical ensemble in a bounded domain, it has been observed that this pair potential minimizes a corresponding convex relative entropy functional, and that the Newton iteration for minimizing this functional coincides with the so-called inverse Monte Carlo (IMC) iterative scheme. In this paper, we show that in the thermodynamic limit analogous connections exist between the specific relative entropy introduced by Georgii and Zessin and a proper formulation of the IMC iteration in the full space. This provides a rigorous variational framework for the inverse Henderson problem, valid within a large class of pair potentials, including, for example, Lennard-Jones-type potentials. It is further shown that the pressure is strictly convex as a function of the pair potential and the chemical potential, and that the specific relative entropy at fixed density is a strictly convex function of the pair potential. At a given reference potential and a corresponding density in the gas phase, we determine the gradient and the Hessian of the specific relative entropy, and we prove that the Hessian extends to a symmetric positive semidefinite quadratic functional in the space of square integrable perturbations of this potential.