Prediction-correction Method Research Articles

The Prediction and Dynamic Correction of Drifting Trajectory for Unmanned Maritime Equipment Based on Fully Connected Neural Network (FCNN) Embedding Model

At present, unmanned maritime equipment has become the main force in the implementation of marine exploration tasks. However, due to the complexity of the marine environment, equipment is susceptible to damage and loss. This is why achieving more effective search and rescue (SAR) of unmanned maritime equipment plays an extremely important role. The drifting trajectory and range predicted by the traditional methods are normally no longer corrected dynamically, which results in a low SAR efficiency. In this work, we propose a trajectory prediction and dynamic correction method based on a fully connected neural network (FCNN). It can dynamically correct the original predicted trajectory using the SAR target’s feedback of its own position information. This method can significantly improve the accuracy of SAR drifting trajectory and region prediction. In addition, the introduction of the dynamic correction model can also improve the adaptive capability and efficiency of the model. During the actual sea experiments, the average deviation distance between predicted and actual trajectories was reduced from 5.75 km to 4.11 × 10−1 km by the proposed method.

Chaotic dynamics and optimal therapeutic strategies for Caputo fractional tumor immune model in combination therapy.

In this paper, a Caputo fractional tumor immune model of combination therapy is established. First, the stability and biological significance of each equilibrium point are analyzed, and it is demonstrated that chaos may arise under specific conditions. Combined with the mathematical definition of Caputo fractional differentiation (CFD), it is found that there is a high correlation between the chaotic phenomenon of the patient's condition and the sensitivity of the patient to the change in the state of the day. The bifurcation threshold of each parameter is determined through numerical simulation, and the Hopf bifurcation of direct competition coefficient and inhibition coefficient between tumor cells and host healthy cells is elaborated upon in detail. Subsequently, a novel method combining optimal control theory with the particle swarm optimization (PSO) algorithm is proposed for the optimal control of the tumor immune model in combination therapy. Finally, the Adams-Bashforth-Moulton (ABM) prediction correction method is utilized in numerical simulations which demonstrate that the introduction of the CFD alters the model dynamics. Furthermore, these results indicate that fractional calculus can effectively be applied to tumor immune models better to elucidate complex chaotic dynamics of tumor cell evolution. Concurrently, the PSO can be successfully integrated with optimal control theory to address optimization challenges in cancer treatment.

An equilibrium analysis of blockchain integration strategies in the livestock meat supply chain considering consumers’ preference for quality trust

PurposeThis paper aims to explore blockchain integration strategies within a three-level livestock meat supply chain in which consumers have a preference for quality trust in livestock meat products. The paper investigates three questions: First, how does consumers’ preference for quality trust affect blockchain integration and transaction decisions among supply chain participants? Second, under what circumstances will retailers choose to participate in the blockchain? Finally, how can other factors such as blockchain costs and supplier–retailer partnership value affect integration decisions?Design/methodology/approachThis paper formulates a supply chain network equilibrium model and employs the logarithmic-quadratic proximal prediction-correction method to obtain equilibrium decisions. Extensive numerical studies are conducted using a pork supply chain network to analyze the implications of blockchain integration for different supply chain participants.FindingsThe results reveal several key insights: First, suppliers’ increased blockchain integration, driven by higher quality trust preference, can negatively affect their profits, particularly, with excessive trust preferences and high blockchain costs. Second, an increase in consumers’ preference for quality trust expands the range of unit operating costs for retailers engaging in blockchain. Finally, the supplier–retailer partnership drives retailer blockchain participation, facilitating enhanced information sharing to benefit the entire supply chain.Originality/valueThis study provides original insights into blockchain integration strategies in an agricultural supply chain through the application of the supply chain network equilibrium model. The investigation of several key factors on equilibrium decisions provides important managerial implications for different supply chain participants to address consumers’ preference for quality trust and enhance overall supply chain performance.

A Novel Path-Following Method for Time-Varying Optimizations with Optimal Parametric Functions

We address a broad category of nonlinear constrained optimization problems. We then reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system to track the respective optimal solution. We then re-parameterize the dynamical system according to a linear combination of parametric functions. By applying the calculus of variations, we optimize these parametric functions to minimize the optimality distance. Consequently, we develop an iterative dynamic algorithm, termed as OP-TVO, to achieve efficient convergence to the solution. We compare the performance of the proposed algorithm with the prediction correction method (PCM) in terms of optimality and computational complexity. The results demonstrate that OP-TVO effectively competes with PCM for the given class of optimization problems, suggesting a promising alternative to PCM. This work also introduces a novel paradigm for solving parametric dynamic systems.

Cross-Scale Modeling of Shallow Water Flows in Coastal Areas with an Improved Local Time-Stepping Method

A shallow water equations-based model with an improved local time-stepping (LTS) scheme is developed for modeling coastal hydrodynamics across multiple scales, from large areas to detailed local regions. To enhance the stability of the shallow water model for long-duration simulations and at larger LTS gradings, a prediction-correction method using a single-layer interface that couples coarse and fine time discretizations is adopted. The proposed scheme improves computational efficiency with an acceptable additional computational burden and ensures accurate conservation of time truncation errors in a discrete sense. The model performance is verified with respect to conservation and computational efficiency through two idealized tests: the spreading of a drop of shallow water and a tidal flat/channel system. The results of both tests demonstrate that the improved LTS scheme maintains precision as the LTS grading increases, preserves conservation properties, and significantly improves computational efficiency with a speedup ratio of up to 2.615. Furthermore, we applied the LTS scheme to simulate tides at grid scales of 40,000 m to 200 m for a portion of the Northwest Pacific. The proposed model shows promise for modeling cross-scale hydrodynamics in complex coastal and ocean engineering problems.

Clinical outcomes of a modified ophthalmic viscosurgical device-free implantable collamer lens implantation.

To investigate the efficacy and safety of a modified dual-incision ophthalmic viscosurgical device-free (OVD-free) method for implantable collamer lens (ICL) implantation in high myopic eyes. A total of 68 participants were enrolled in this prospective randomized clinical trial, including 33 in the OVD-free group and 35 in the standard group. Operation time and intraocular pressure (IOP) at 2 hours postoperatively were recorded. Visual acuity, refractive power, IOP, corneal endothelium parameters, and anterior segment parameters were assessed at 1 day, 1 week, 1 month, 3 months, and 6 months postoperatively. Postoperative subjective visual quality at 3 months was recorded through a Quality of Vision (QoV) questionnaire. No significant differences in visual acuity, refractive outcomes, and corneal endothelial parameters were found, while the operation time was significantly shorter in the OVD-free group. Both groups showed a significant increase in IOP at 2 hours after surgery, but the increase in the OVD-free group was significantly smaller than that in the standard group. In addition, the frequency of ring-shaped dysphotopsia in the OVD-free group (15.15%) was significantly lower than that in the standard group (40%), and the severity and annoyance of this symptom were also significantly lower in the OVD-free group. The modified OVD-free ICL implantation is a safe, effective, and predictable method for myopia correction, which could be a better choice for short surgery time, better subjective visual perception, and low occurrence of IOP elevation.

Discrete-time Euler-smoothing methods for time-varying convex constrained optimization

In this paper, we propose two kinds of prediction–correction methods, discrete-time Euler-smoothing methods, for solving the general time-varying convex constrained optimization problem. By using the complementarity function and smoothing technique, the Karush–Kuhn–Tucker (KKT) trajectory of the problem can be reformulated as a system of smooth equations and considering the dynamics of the system of smooth equations in a discrete constant time-sampling periods scheme. The proposed methods mainly consist of the prediction step derived by Euler approximation and the correction step generated by one or multiple Newton iterations. Under some reasonable conditions, the approximate solution trajectories produced by the methods achieve the asymptotic error bound behaving as O(h4) with respect to optimal trajectory both in the primal and dual space as the smoothing parameter approaches to zero, where h is the sampling period. Finally, the experimental results show that our methods are efficient, and the steady-state tracking errors are much smaller than the other prediction–correction methods under the same conditions.

Wetting boundary condition for three-dimensional curved geometries in lattice Boltzmann color-gradient model

A wetting boundary condition for handling contact line dynamics on three-dimensional curved geometries is developed in the lattice Boltzmann color-gradient framework. By combining the geometrical formation and the prediction-correction wetting scheme, the present wetting boundary condition is able to avoid the necessity to select an appropriate interface normal vector from its multiple solutions in the previous prediction-correction method. The effectiveness and accuracy of the wetting boundary condition are first validated by several benchmark cases, namely a droplet resting on a flat surface and on a solid sphere, and the spontaneous imbibition into a cylindrical tube. We then use the color-gradient model equipped with the developed wetting boundary condition to study the trapping behavior of a confined droplet in a microchannel with a cylindrical hole on the top surface, in which the effects of the hole radius and the droplet radius are identified for varying capillary numbers. Results show that the simulated critical capillary numbers, below which the droplet would be anchored by the hole, and the steady-state shapes of the anchored droplet generally match well with their theoretical solutions. The critical capillary number is found to decrease by either decreasing the hole radius or increasing the droplet radius, which is attributed to the weakened anchoring surface energy gradient and the enhanced driving force from outer flow, respectively. In addition, we show that the previous theoretical solutions are valid only when the initial droplet radius is greater than twice the height of the channel.

Cross-dimensional isothermal model for the transient restart of weakly compressible laminar/turbulent flow of time-dependent non-Newtonian fluid in a long pipeline

Based on reasonable simplifications of three-dimensional governing equations, a cross-dimensional isothermal model for the transient flow restart of time-dependent non-Newtonian fluid in a long pipeline is established, in which conservation equations are in one-dimensional (1D) form and two key variables (average velocity and wall shear stress) in the 1D conservation equations are related to some two-dimensional (2D) equations. This model considers fluid compressibility, complex non-Newtonian rheological behavior, and flow pattern transition. A prediction-correction method and a trial calculation method are combined to solve the cross-dimensional model. The presented cross-dimensional simulation is validated from different perspectives using a theoretical formula, a mature empirical formula, and numerical results from 2D and 1.5-dimensional (1.5D) simulations. The presented cross-dimensional simulation is considered to have strong universality for predicting flow processes in long pipelines. Moreover, the complex flow restart in a long waxy crude oil pipeline is numerically simulated. The results indicate that the flow restart can be divided into three stages according to differences in various influence factors and flow features. These three stages include the laminar/turbulent flow in the yield front movement, the laminar/turbulent flow in the fluid structure breakdown and flow pattern transition, and the turbulent flow in the pure fluid structure breakdown. Analysis of flow processes in these three stages reveals the complex characteristics of the flow restart in a long pipeline.

Statistical analysis and suppression of vibration frequency bifurcation in diamond turning of Al 6061 mirror

In diamond turning of metal mirrors, the reflectivity heavily relies on the mirror surface roughness, and the vibration of machine tool is one of the crucial factors affecting the mirror surface roughness. Previous articles mostly focused on the vibration of the spindle, but in the process of spherical surface machining, the influence of Z-direction moving parts can not be ignored. In this work, by using the transfer matrix and prediction-correction method, a dynamics model is developed to determine the different order vibration frequencies for Z-direction moving parts. The vibration patterns are further revealed in terms of the state vector of each order component with consideration of the external forces, e.g. dynamic cutting forces and linear motor thrust harmonics. As the machining parameters increase, the vibration tends to become instability, and the bifurcation of vibration frequency appears. The sensitivity analysis results firstly show that the cutting depth and workpiece surface slope are the most important factors influencing the vibration frequency bifurcation phenomenon. The probability density distribution of the vibration frequency bifurcation is firstly established as a function of the workpiece shape by stochastic big data simulations, and an adaptive optimization algorithm of interpolation point position is established. Finally, the correctness of the model is verified by experiments, and the relative error is kept below 10%. Through the new interpolation point planning algorithm, the vibration is reduced by more than 50%. Our findings are of significant importance for improving the spherical/aspherical surface reflectivity of metal mirrors.

Extrapolation-Based Prediction-Correction Methods for Time-varying Convex Optimization

In this paper, we focus on the solution of online optimization problems that arise often in signal processing and machine learning, in which we have access to streaming sources of data. We discuss algorithms for online optimization based on the prediction-correction paradigm, both in the primal and dual space. In particular, we leverage the typical regularized least-squares structure appearing in many signal processing problems to propose a novel and tailored prediction strategy, which we call extrapolation-based. By using tools from operator theory, we then analyze the convergence of the proposed methods as applied both to primal and dual problems, deriving an explicit bound for the tracking error, that is, the distance from the time-varying optimal solution. We further discuss the empirical performance of the algorithm when applied to signal processing, machine learning, and robotics problems.

Analysis of wind power output characteristics and output prediction

A fuzzy clustering method and a prediction correction method based on the Copula function are used to establish an analytical model of wind power generation output characteristics. It also predicts the expected and corrected values of its power generation to alleviate the pressure on the grid caused by the high proportion of random new energy sources connected to the grid. Based on the natural properties of wind, a new characteristic index based on the traditional load characteristic index and the new energy output curve is proposed to quantify and evaluate the characteristics of new energy power generation. The results show that the method proposed in this paper can effectively reduce the influence of climate change on output prediction; in comparison to the traditional index, the new index is more refined and instructive.

Algorithmic Spatial Form-Finding of Four-Fold Origami Structures Based on Mountain-Valley Assignments

AbstractOrigami has attracted tremendous attention in recent years owing to its capability of inspiring and enabling the design and development of reconfigurable structures and mechanisms for applications in various fields such as robotics and biomedical engineering. The vast majority of origami structures are folded starting from an initial two-dimensional crease pattern. However, in general, the planar configuration of such a crease pattern is in a singular state when the origami starts to fold. Such a singular state results in different motion possibilities of rigid or non-rigid folding. Thus, planar origami patterns cannot act as reliable initial configurations for further kinematic or structural analyses. To avoid the singularities of planar states and achieve reliable structural configurations during folding, we introduce a nonlinear prediction–correction method and present a spatial form-finding algorithm for four-fold origami. In this approach, first, initial nodal displacements are predicted based on the mountain-valley assignments of the given origami pattern, which are applied to vertices to form an initial spatial and defective origami model. Subsequently, corrections of nodal displacements are iteratively performed on the defective model until a satisfactory nonplanar configuration is obtained. Numerical experiments demonstrate the performance of the proposed algorithm in the form-finding of both trivial and non-trivial four-fold origami tessellations. The obtained configurations can be effectively utilized for further kinematic and structural analyses. Additionally, it has been verified that corrected and nonplanar configurations are superior to initial configurations in terms of matrix distribution and structural stiffness.

Improved Lagrangian-PPA based prediction correction method for linearly constrained convex optimization

<p style='text-indent:20px;'>This paper presents an improved Lagrangian-PPA based prediction correction method to solve linearly constrained convex optimization problem. At each iteration, the predictor is achieved by minimizing the proximal Lagrangian function with respect to the primal and dual variables. These optimization subproblems involved either admit analytical solutions or can be solved by a fast algorithm. The new update is generated by using the information of the current iterate and the predictor, as well as an appropriately chosen stepsize. Compared with the existing PPA based method, the parameters are relaxed. We also establish the convergence and convergence rate of the proposed method. Finally, numerical experiments are conducted to show the efficiency of our Lagrangian-PPA based prediction correction method.</p>

A prediction-correction based proximal method for monotone variational inequalities with linear constraints

<abstract><p>The monotone variational inequalities are being widely used as mathematical tools for studying optimal control problems and convex programming. In this paper, we propose a new prediction-correction method for monotone variational inequalities with linear constraints. The method consists of two procedures. The first procedure (prediction) utilizes projections to generate a predictor. The second procedure (correction) produces the new iteration via some minor computations. The main advantage of the method is that its main computational effort only depends on evaluating the resolvent mapping of the monotone operator, and its primal and dual step sizes can be enlarged. We prove the global convergence of the method. Numerical results are provided to demonstrate the efficiency of the method.</p></abstract>

Fractional dynamic analysis and optimal control problem for an SEIQR model on complex networks.

A fractional order susceptible-exposed-infected-quarantined-recovered model is established on the complex networks. We calculate a specific expression for the basic reproduction number R0, prove the existence and uniqueness with respect to the solution, and prove the Ulam-Hyers stability of the model. Using the Latin hypercube sampling-partial rank correlation coefficient method, the influence of parameters on the R0 is analyzed. Based on the results of the analysis, the optimal control of the model is investigated as the control variables with vaccination rate and quarantine rate applying Pontryagin's minimum principle. The effects of α, degree of nodes, and network size on the model dynamics are simulated separately by the prediction correction method.

Distributed Time-Varying Economic Dispatch via a Prediction-Correction Method

The time-varying economic dispatch over a network is considered where both the cost function and the equality constraint are time-varying. A distributed algorithm is first designed combing the prediction-correction framework and the consensus + innovations approach. In the prediction steps, the sensitivity analysis method is introduced to calculate the shift between the estimated and the exact optimization solution of the correction steps. Afterwards, the overall optimal errors in two steps are calculated by the sub-optimal analysis method. The convergence analysis shows that the dispatch errors are bounded and the convergence process is Q-linear. A dynamic prediction-correction algorithm is then presented to improve the accuracy at every time instant. Finally, numerical examples using the IEEE 118-bus system are presented to illustrate the validity of the algorithms.

Рефракционная хирургическая коррекция зрения у пациентки с клинически тонкой роговицей на фоне миопии высокой степени

The article evaluates the clinical effectiveness of implantation of a phakic intraocular lens model (IOL) Visian ICL in a patient with a combination of high myopia and clinically thin cornea on the example of a clinical case. Implantation of a personalized posterior chamber phakic IOL is a clinically effective, safe and predictable method for the surgical correction of high myopia, including in patients with clinically thin corneas, when keratorefractive intervention is contraindicated. Keywords: myopia, phakic IOL ICL, intraoperative difficulties.

Learning-accelerated asynchronous decentralized optimization for integrated transmission and distribution systems over lossy networks

With the rapid growth of distributed renewable energy in distribution networks, the synergistic operation between transmission and distribution networks is increasingly important. Decentralized optimization is employed in the coordination of integrated transmission and distribution networks to reduce the communication burden and protect regional information privacy. Existing works on decentralized optimization algorithms for integrated transmission and distribution networks have seldom addressed packet losses. Moreover, the synchronous operation requirement is difficult to achieve for many decentralized optimization algorithms to solve problems with computationally heterogeneous subproblems and during the occurrence of communication failure. In order to tackle these problems, this paper proposes a decentralized scheme based on the relaxed alternating direction method of multipliers for coordinating the operation of integrated transmission and distribution networks considering communication failures and asynchronous updates. A momentum–extrapolation prediction–correction method is designed to allow operators to forecast their neighbors’ missing boundary variable values and to be solved continuously. Simulation results show that compared with the classical alternating direction method of multipliers, the relaxed alternating direction method of multipliers can obtain the nearly same operation costs with fewer iterations. In addition, the proposed algorithm shows robustness against packet losses and asynchronous computations. It is also found that the prediction–correction technique makes the proposed algorithm converge faster compared with no prediction. • Step size can change the performance of proposed algorithms. • Packet losses are represented by a binary probabilistic distribution model. • Convergence rates are affected by packet losses and asynchronous updates. • A prediction-correction approach is used to forecast the missing information.

A prediction–correction method for fast and accurate initial displacement field estimation in digital image correlation

Initial displacement estimation is one of the most critical issues in digital image correlation. A better initial value can greatly improve the convergence rate and accuracy of the algorithms with subpixel accuracy. This paper developed an efficient estimation method to yield high-quality initial displacement fields. This method finds the initial displacement of each subset in a prediction–correction way, in which the displacement of the seed point is found by exhaustive search, but the other subsets are first predicted by an extrapolation scheme and then corrected by a monotonous search strategy. This method was tested by extensive experiments and validated by comparing with the well-known exhaustive search and adaptive rood pattern search methods, and then it was combined with the inverse compositional Gauss–Newton algorithm to perform subpixel-optimization experiments. The results demonstrated excellent features of accuracy, effectiveness, and convergence. Finally, we presented a three-dimensional surface reconstruction experiment using the proposed method, obtaining a geometric accuracy with a relative error of 0.016%.