Nonlinear Optimization Method Research Articles

Research and verification on parameter solution of mixed shock model for common cause failure based on particle swarm algorithm

AbstractMixed shock model is an explicit construction method of failure probability model based on component independent failure, system nonfatal shock, and fatal shock failure, which considers common cause failure (CCF) in redundant system. For aerospace systems, a modified mixed shock model is proposed, which considers several components may fail independently and simultaneously in operation. In order to solve the issue that the parameters of the mixed shock model cannot be solved directly based on the failure probability data, a parameter solving method based on particle swarm optimization (PSO) algorithm is proposed. Additionally, the relationship between the failure probability and the gradient of the parameter change is deduced, and the reduced‐order (RO) solution based on the gradient of the parameter change is proposed to improve the efficiency of the solution. A fitness function construction method based on the relative error of the solution probability and the true probability is proposed to improve the probability solution accuracy of multicomponent failure. The nonlinear inertia factor optimization method combined with fitness change is studied to improve the particle swarm dynamics. The accuracy of the results of different parameters solving sequence and different PSO methods are compared, and the effectiveness of the RO solution is verified. The results of the mixed shock model before and after modification are compared with the different CCF data, which verifies the effectiveness and wide applicability of the modified mixed shock model. The results show that the modified mixed shock model for CCF and its parameter solution method can significantly improve the probability solution accuracy of all components failure, and also provide a new theoretical basis and solution method for the quantitative analysis of multiredundant system failure.

High-order shape interpolation

We propose a simple yet effective method to interpolate high-order meshes. Given two manifold high-order triangular (or tetrahedral) meshes with identical connectivity, our goal is to generate a continuum of curved shapes with as little distortion as possible in the mapping from the source mesh to the interpolated mesh. Our algorithm contains two steps: (1) linearly blend the pullback metric of the identity mapping and the input mapping between two Bézier elements on a set of sampling points; (2) project the interpolated metric into the metric space between Bézier elements using the Newton method for nonlinear optimization. We demonstrate the feasibility and practicability of the method for high-order meshes through extensive experiments in both 2D and 3D.

Optimizing size and economic feasibility assessment of photovoltaic and energy storage setup in residential applications

Battery energy storage systems (BESSs) are essential in enhancing self-sufficiency, sustainability, and delivering flexibility services. However, adoption of this technology in residential applications is constrained, predominantly due to its suboptimal economic performance. A proper selection of design parameters and optimal resource utilization can significantly enhance performance and establish economic feasibility. This research introduces a photovoltaic (PV)-BESS optimization framework, formulated to ascertain optimal infrastructure sizing, and maximize economic performance. The proposed tool considers various elements, such as energy storage state of health status, renewable profiles, residential load profiles, and prevailing energy market conditions. A novel rule-based, non-linear optimization method is developed, with a focus on maximizing revenue while considering energy storage (ES) degradation to project more accurate and realistic scenarios and payback periods. Employing the Estonian energy market as an illustrative case study, the model probes the potential of integrating ES and PV technology in North European residences. The model achieved the shortest payback period of five years in our case study, underscoring the emerging potential of such technologies in behind-the-meter applications.

Accurate Temperature Reconstruction in Radiofrequency Ablation for Atherosclerotic Plaques Based on Inverse Heat Transfer Analysis.

Radio frequency ablation has emerged as a widely accepted treatment for atherosclerotic plaques. However, monitoring the temperature field distribution in the blood vessel wall during this procedure presents challenges. This limitation increases the risk of endothelial cell damage and inflammatory responses, potentially leading to lumen restenosis. The aim of this study is to accurately reconstruct the transient temperature distribution by solving a stochastic heat transfer model with uncertain parameters using an inverse heat transfer algorithm and temperature measurement data. The nonlinear least squares optimization method, Levenberg-Marquardt (LM), was employed to solve the inverse heat transfer problem for parameter estimation. Then, to improve the convergence of the algorithm and reduce the computational resources, a method of parameter sensitivity analysis was proposed to select parameters mainly affecting the temperature field. Furthermore, the robustness and accuracy of the algorithm were verified by introducing random noise to the temperature measurements. Despite the high level of temperature measurement noise (ξ = 5%) and larger initial guess deviation, the parameter estimation results remained closely aligned with the actual values, with an overall ERMS consistently below 0.05. The absolute errors between the reconstruction temperature at the measurement points TC1, TC2, and TC3, and the actual temperature, remained within 0.33 °C, 2.4 °C, and 1.17 °C, respectively. The Levenberg-Marquardt algorithm employed in this study proficiently tackled the ill-posed issue of inversion process and obtained a strong consistency between the reconstructed temperature the actual temperature.

Quadratic surface preserving parameterization of unorganized point data

Finding parameterizations of spatial point data is a fundamental step for surface reconstruction in Computer Aided Geometric Design. Especially the case of unstructured point clouds is challenging and not widely studied. In this work, we show how to parameterize a point cloud by using barycentric coordinates in the parameter domain, with the aim of reproducing the parameterizations provided by quadratic triangular Bézier surfaces. To this end, we train an artificial neural network that predicts suitable barycentric parameters for a fixed number of data points. In a subsequent step we improve the parameterization using non-linear optimization methods. We then use a number of local parameterizations to obtain a global parameterization using a new overdetermined barycentric parameterization approach. We study the behavior of our method numerically in the zero-residual case (i.e., data sampled from quadratic polynomial surfaces) and in the non-zero residual case and observe an improvement of the accuracy in comparison to standard methods. We also compare different approaches for non-linear surface fitting such as tangent distance minimization, squared distance minimization and the Levenberg Marquardt algorithm.

Multi-Parameter Inversion Optimization for Transverse Rib Profile Enhanced Convective Heat Transfer

The convective heat transfer performance of the rib-element approach in the channel is influenced by the transverse rib profile. In present work, a nonlinear multi-parameter optimization method based on inversion optimization is proposed and further used to obtain the optimal rib profile in a rectangular channel. Firstly, four conventional profiles as the original ribbed channel were selected to obtain the convective heat transfer performance of the channel by experiment and numerical solution; secondly, several control points were selected along the profile, and the polar radius was updated, and curve fitting was carried out. The results show that the inversion optimization can optimize the rib profile to improve the convective heat transfer performance. As the number of control points increases, the optimized profile changes hardly. The inversion optimization yields a similar optimized profile regardless of the original rib profile. With the increase of original rib height, the enhanced heat transfer performance of optimized profile is better. For the ribbed channel with original height 0.4 × channel height, as the Reynolds number increases from 6000 to 33,000, the performance evaluation criteria of the optimized profile increase by 14.94% to 21.2% compared with the original triangular profile.

A mobile prototype-based localization approach using inertial navigation and acoustic tracking for underwater

During underwater operations, divers must determine their own trajectories using the Inertial Navigation System (INS) they carry to improve operational efficiency. However, the INS contains a sensor bias that is also incorporated into the quadratic integration process to obtain the displacement, resulting in trajectory drift of the divers during prolonged self-guidance. To overcome the above problem, other aids are needed to correct the accumulated error of the INS. The single-beacon Assisted Inertial Navigation (AIN) method can improve the flexibility of inertial error correction while simplifying the localization equipment, which is suitable for the INS cumulative error correction scenario of divers. However, most of the traditional single-beacon assisted correction methods do not consider the effect of acoustic line bending on hydroacoustic ranging, and at the same time, they do not consider the problem of singular or pathological coefficient matrices introduced by inertial navigation neighbor localization deviations. Based on the above two shortcomings, this paper uses the acoustic velocity profile for acoustic line tracking, combines the localization idea of Mobile Primitives (MP), and proposes an MP-based acoustic line tracking-Assisted Inertial Navigation Localization (AINL) method, which constructs a sliding time window (STW) by taking the historical positioning of divers as a virtual primitive, and combines the nonlinear optimization method for iterative optimization search as a means to improve the accuracy and stability of self-navigation of the divers.

Role of nonlinear transmission term in stability of hand, foot and mouth disease dynamics

Aim: This study focuses on the nonlinear characteristics of two linearly stable equilibrium states within a theoretical hand, foot and mouth disease (HFMD) dynamics model. Methods: The conditional nonlinear optimal perturbation method, the Lyapunov method and the linear singular vector method are employed. Results: By utilizing the conditional nonlinear optimal perturbation method, it is determined that the two linearly stable equilibrium states (namely the free disease and disease HFMD states) also exhibit nonlinear stability. It is found that the stabilities of the free disease and disease HFMD equilibrium states differ in terms of returning to their original states. Conclusion: It is discovered that nonlinearity plays a crucial role in reinstating the original equilibrium states.

3-D LiDAR Localization Based on Novel Nonlinear Optimization Method for Autonomous Ground Robot

3D Light Detection and Ranging (LiDAR)-based localization for autonomous ground robot in unknown environment is a critical ability, which has been extensively studied. In this paper, we propose a novel nonlinear optimization method to promote the 3D LiDAR localization performance. Firstly, due to that the objective function is the summation of point correspondence matching error items, a novel item quality evaluation criterion is proposed. The quality of each item is directly proportional to the degree of its matching error distance descent during the optimization process. Then, an attention mechanism based on the criterion is proposed and the objective function is iteratively refined by putting different attention weights on the matching error items. Thirdly, in the Gauss-Newton optimization framework for LiDAR localization, we point out that the Hessian matrix is essentially the sum of the Hessian matrices of high-quality and low-quality point correspondence subsets. To increase the dominance of the Hessian matrix derived from the high-quality point correspondences, the Hessian matrix of the estimated high-quality point correspondence subset in the last updating step is added to the current Hessian matrix. The proposed LiDAR localization is extensively evaluated on public and custom datasets. The experimental results demonstrate that the proposed mechanisms can effectively promote the LiDAR localization performance. We will make our source code open to serve as a new baseline for the robotic community.

Local convergence of primal–dual interior point methods for nonlinear semidefinite optimization using the Monteiro–Tsuchiya family of search directions

Local convergence of primal–dual interior point methods for nonlinear semidefinite optimization using the Monteiro–Tsuchiya family of search directions

A nonlinear optimization method for calibration of large‐scale deep cement mixing in very soft clay deep excavation

AbstractThis work proposes a novel technique to conduct back‐analysis of lateral displacement of deep cement mixing (DCM) columns in deep excavation construction. For the first time, we propose a process to investigate both soil and underground structure end‐to‐end automatically. The novel technique is a complex combination of three crucial factors: (1) a nature‐inspired optimization algorithm (O), (2) a three‐dimensional PLAXIS Geotechnical Engineering software (P) and (3) a modern Python language programming (P), hereinafter called the a nature‐inspired optimization algorithm (O), a three‐dimensional PLAXIS Geotechnical Engineering software (P) and a modern Python language programming (P) (OPP) technique. The novel meta‐heuristic algorithm simulated the co‐evolved partnership behavior of shrimps and goby fishes, termed Shrimp and Goby Association (SGA), which plays an important role in complex analyses. A series of exams to determine the SGA's performance is conducted on 38 benchmark test functions (IEEE Congress on Evolutionary Computation 2017 and 2019) and three real‐world engineering design problems to showcase its applicability. The metaheuristic and PLAXIS 3D analysis work well together, which makes the back‐analysis technique powerfully to determinate stiffness parameters instead of the traditional approaches. Based on the optimized parameters, the lateral deflection of DCM and soil are well predicted for excavation. This study proposes a technique to estimate efficiently the stiffness parameter for very soft soil. As a consequence of the optimization process, an equation to determine the stiffness parameter of DCM columns from laboratory test is also proposed. Based on the obtained results, this research provides a comprehensive methodology for predicting risk, enhancing safety, saving time and money, and effectively designing and constructing underground structures.

Nonlinear Optimal Control for a PMLSG-VSC Wave Energy Conversion Unit

This article aims to treat the nonlinear control problem for the complex dynamics of a wave energy unit (WEC) that consists of a Permanent Magnet Linear Synchronous Generator (PMLSG) and a Voltage Source Converter (VSC). The article has developed a globally stable nonlinear optimal control method for this wave power generation unit. The new method avoids complicated state-space model transformations and minimizes the energy dispersion by the control loop. A novel nonlinear optimal control method is proposed for the dynamic model of a wave energy conversion system, which includes a Permanent Magnet Linear Synchronous Generator (PMLSG) serially connected with an AC/DC three-phase voltage source converter (VSC). The dynamic model of this renewable energy system is formulated and differential flatness properties are proven about it. To apply the proposed nonlinear optimal control, the state-space model of the PMLSG-VSC wave energy conversion unit undergoes an approximate linearization process at each sampling instance. The linearization procedure relies on a first-order Taylor-series expansion and involves the computation of the system’s Jacobian matrices. It takes place at each sampling interval around a temporary operating point, which is defined by the present value of the wave energy conversion unit’s state vector and by the last sampled value of the control inputs vector. An H-infinity feedback controller is designed for the linearized model of the wave energy conversion unit. To compute the feedback gains of this controller, an algebraic Riccati equation is repetitively solved at each time step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis.

A projected-search interior-point method for nonlinearly constrained optimization

AbstractThis paper concerns the formulation and analysis of a new interior-point method for constrained optimization that combines a shifted primal-dual interior-point method with a projected-search method for bound-constrained optimization. The method involves the computation of an approximate Newton direction for a primal-dual penalty-barrier function that incorporates shifts on both the primal and dual variables. Shifts on the dual variables allow the method to be safely “warm started” from a good approximate solution and avoids the possibility of very large solutions of the associated path-following equations. The approximate Newton direction is used in conjunction with a new projected-search line-search algorithm that employs a flexible non-monotone quasi-Armijo line search for the minimization of each penalty-barrier function. Numerical results are presented for a large set of constrained optimization problems. For comparison purposes, results are also given for two primal-dual interior-point methods that do not use projection. The first is a method that shifts both the primal and dual variables. The second is a method that involves shifts on the primal variables only. The results show that the use of both primal and dual shifts in conjunction with projection gives a method that is more robust and requires significantly fewer iterations. In particular, the number of times that the search direction must be computed is substantially reduced. Results from a set of quadratic programming test problems indicate that the method is particularly well-suited to solving the quadratic programming subproblem in a sequential quadratic programming method for nonlinear optimization.

Processing of nonlinear concrete creep curves using nonlinear optimization methods

The article proposes a method for determining the rheological parameters of concrete based on creep curves at various stress levels using the theory of V.M. Bondarenko. Using the proposed methodology, the experimental data presented in the work of A.V. Yashin is processed. The problem of searching for rheological parameters is posed as a nonlinear optimization problem. The sum of squared deviations of the experimental values of creep strains from the theoretical ones is minimized. The interior point method is used as a nonlinear optimization method. Four different expressions for the creep measure are considered, including the creep measure by N.Kh. Harutyunyan, creep measure by A.G. Tamrazyan, a creep measure in the form of a sum of two exponentials, and McHenry’s creep measure. It has been shown that the best agreement with experimental data is provided by the McHenry’s creep measure. An expression has been selected for the nonlinearity function, which describes the nonlinear relationship between stresses and creep strains. It is shown that the instantaneous nonlinearity of deformation and the nonlinearity that manifests itself over time cannot be described by a single function.

Application of Gradient Optimization Methods in Defining Neural Dynamics

Applications of gradient method for nonlinear optimization in development of Gradient Neural Network (GNN) and Zhang Neural Network (ZNN) are investigated. Particularly, the solution of the matrix equation AXB=D which changes over time is studied using the novel GNN model, termed as GGNN(A,B,D). The GGNN model is developed applying GNN dynamics on the gradient of the error matrix used in the development of the GNN model. The convergence analysis shows that the neural state matrix of the GGNN(A,B,D) design converges asymptotically to the solution of the matrix equation AXB=D, for any initial state matrix. It is also shown that the convergence result is the least square solution which is defined depending on the selected initial matrix. A hybridization of GGNN with analogous modification GZNN of the ZNN dynamics is considered. The Simulink implementation of presented GGNN models is carried out on the set of real matrices.

A Survey On Non – linear Optimization And Global Optimization Methods

Non-linear optimization and global optimization methods are crucial in solving complex real-world problems where the objective functions and constraints are not linear. Non-linear optimization involves finding the best solution in the presence of non-linear relationships among the variables. These problems arise in various fields such as engineering design, economics, machine learning, and operational research. The primary challenge in non-linear optimization is the potential existence of multiple local optima, which can make it difficult to identify the global optimum. Global optimization methods are designed to overcome this challenge by searching for the global optimum, which is the best possible solution among all local optima. These methods can be broadly categorized into deterministic and stochastic approaches. Deterministic methods, such as branch and bound, interval analysis, and cutting-plane methods, systematically explore the search space and provide guarantees of finding the global optimum or bounds on the global optimum. These methods are often rigorous but can be computationally expensive, especially for high-dimensional problems. On the other hand, stochastic methods, such as genetic algorithms, simulated annealing, and particle swarm optimization, use probabilistic rules to explore the search space. These methods are inspired by natural processes and heuristics, offering flexibility and often being more efficient for large-scale problems. While they do not guarantee finding the global optimum, they are widely used due to their ability to escape local optima and explore the search space effectively. Hybrid methods that combine deterministic and stochastic approaches have also gained popularity. These methods leverage the strengths of both approaches, enhancing the robustness and efficiency of the optimization process. For example, a hybrid algorithm might use a stochastic method to explore the search space broadly and then apply a deterministic method to refine the search around promising areas. Recent advancements in computational power and algorithmic development have significantly improved the efficiency and applicability of non-linear and global optimization methods. Techniques such as machine learning-based optimization and parallel computing have enabled the handling of more complex and larger-scale optimization problems. Moreover, these advancements have facilitated the integration of optimization methods into real-time and adaptive systems, further broadening their applications.

Thermometrical determination of the postmortem interval by non-linear optimization method

To develop and implement an online application for the numerical method of determination of the postmortem interval and its limiting faults, caused by errors of measurement processes, based on the Marshall-Hoare law of cooling and dual thermometry of the corpse's core. The numerical search for a minimum of two variables' target function, obtained from the system of non-linear Marshall-Hoare equations, reflecting the dual thermometry of the corpse's core was performed. The code of online program was written in Python 3 programming language. The method for determination of the postmortem interval, based on iterative algorithm of non-linear optimization, allowing by dual thermometry of the corpse to consider the uniqueness of its cooling conditions, as well as to calculate the degree of uncertainty of computational estimations, caused by the impact of measurement errors, has been developed. The method is implemented in the format of the Warm Bodies Z online application. The developed numerical method and its online application are recommended for determining of the postmortem interval.

A Survey On Non – linear Optimization And Global Optimization Methods

bjective functions and constraints are not linear. Non-linear optimization involves finding the best solution in the presence of non-linear relationships among the variables. These problems arise in various fields such as engineering design, economics, machine learning, and operational research. The primary challenge in non-linear optimization is the potential existence of multiple local optima, which can make it difficult to identify the global optimum. Global optimization methods are designed to overcome this challenge by searching for the global optimum, which is the best possible solution among all local optima. These methods can be broadly categorized into deterministic and stochastic approaches. Deterministic methods, such as branch and bound, interval analysis, and cutting-plane methods, systematically explore the search space and provide guarantees of finding the global optimum or bounds on the global optimum. These methods are often rigorous but can be computationally expensive, especially for high-dimensional problems. On the other hand, stochastic methods, such as genetic algorithms, simulated annealing, and particle swarm optimization, use probabilistic rules to explore the search space. These methods are inspired by natural processes and heuristics, offering flexibility and often being more efficient for large-scale problems. While they do not guarantee finding the global optimum, they are widely used due to their ability to escape local optima and explore the search space effectively. Hybrid methods that combine deterministic and stochastic approaches have also gained popularity. These methods leverage the strengths of both approaches, enhancing the robustness and efficiency of the optimization process. For example, a hybrid algorithm might use a stochastic method to explore the search space broadly and then apply a deterministic method to refine the search around promising areas. Recent advancements in computational power and algorithmic development have significantly improved the efficiency and applicability of non-linear and global optimization methods. Techniques such as machine learning-based optimization and parallel computing have enabled the handling of more complex and larger-scale optimization problems. Moreover, these advancements have facilitated the integration of optimization methods into real-time and adaptive systems, further broadening their applications.

An Improved Particle Swarm Optimization Method for Nonlinear Optimization

Nonlinear optimization is becoming more challenging in information sciences and various industrial applications, but nonlinear problems solved by the classical particle swarm‐based methods are usually characterized by low efficiency, accuracy, and convergence speed in specific issues. To solve these problems and enhance the nonlinear optimization performance, an improved metaheuristic particle swarm optimization (PSO) model is proposed here. First, the optimization principles and model of the new method are introduced, and algorithms of the improved PSO are presented by updating the displacement and velocity of the moving particle according to Euler–Maruyama (EM) principle rather than traditional standard normal distribution. Then, the influence of the model parameters, input dimensions, and different nonlinear problems on the PSO optimization characterizations are studied by Pareto set solving and optimization performance comparison. The analysis regarding diverse nonlinear problems and optimization methods manifests that the improved method is capable of solving various nonlinear problems especially for multiobjective models, while the robustness and reliability can always keep consistent regardless of the change of model parameters. Finally, the performance evaluation is exhibited by the case study of nonlinear parameter optimization, 3 groups of CEC benchmark problems, and rank‐sum test for 6 comparable optimization algorithms, which all verify its effectiveness and reliability, as well as the significance and great application promise. The results show that the new proposed PSO method has the fastest convergence speed and least iteration numbers in searching for the global best solution of 9 nonlinear problems among 8 different optimization models indicated by the p values smaller than 0.05. Additionally, the main conclusions showing the calculation efficiency, stability, robustness, and great application promise of the proposed method are summarized, and future work is discussed.

Multi-Objective Finned-Tube Heat Exchanger Optimization Using a Genetic Algorithm

Heat exchangers are a significant component in many industries, particularly in energy conversion systems. The design of heat exchangers itself is a complex process because it involves experience-based decisions, numerous variables and parameters, and some of them are competing with each other. Genetic Algorithms (GAs) are one of the first evolutionary algorithms which remains one of the most extensively used non-linear optimization methods today. This study explores the implementation of Non-Dominated Sorting Genetic Algorithm II (NSGA-II) for thermal design and optimization of a finned-tube heat exchanger. The chosen objective functions were minimizing the heat exchanger volume and minimizing the air side pressure drop. The decision variables for the design were tube outer diameter, number of tube rows, fin pitch, unit height, and unit width. The calculated parameters and estimated cost of both preliminary design and optimized design were also compared. The optimized design offered a bigger alternative design while meeting all the constraints according to standards and industrial needs. The optimization reduced annualized operational and maintenance costs by 228% and lowered air pressure drop by 413% with bigger heat exchanger volume of 12% compared to the preliminary design.