Nonlinear Optimization Method Research Articles

Operational stability study of lactate biosensors: modeling, parameter identification, and stability analysis

IntroductionThis paper investigates the operational stability of lactate biosensors, crucial devices in various biomedical and biotechnological applications. We detail the construction of an amperometric transducer tailored for lactate measurement and outline the experimental setup used for empirical validation.MethodsThe modeling framework incorporates Brown and Michaelis–Menten kinetics, integrating both distributed and discrete delays to capture the intricate dynamics of lactate sensing. To ascertain model parameters, we propose a nonlinear optimization method, leveraging initial approximations from the Brown model’s delay values for the subsequent model with discrete delays.ResultsStability analysis forms a cornerstone of our investigation, centering on linearization around equilibrium states and scrutinizing the real parts of quasi-polynomials. Notably, our findings reveal that the discrete delay model manifests marginal stability, occupying a delicate balance between asymptotic stability and instability. We introduce criteria for verifying marginal stability based on characteristic quasi-polynomial roots, offering practical insights into system behavior.DiscussionQalitative examination of the model elucidates the influence of delay on dynamic behavior. We observe a transition from stable focus to limit cycle and period-doubling phenomena with increasing delay values, as evidenced by phase plots and bifurcation diagrams employing Poincaré sections. Additionally, we identify limitations in model applicability, notably the loss of solution positivity with growing delays, underscoring the necessity for cautious interpretation when employing delayed exponential function formulations. This comprehensive study provides valuable insights into the design and operational characteristics of lactate biosensors, offering a robust framework for understanding and optimizing their performance in diverse settings.

Review of Machine Learning Techniques in Soft Tissue Biomechanics and Biomaterials.

Advanced material models and material characterization of soft biological tissues play an essential role in pre-surgical planning for vascular surgeries and transcatheter interventions. Recent advances in heart valve engineering, medical device and patch design are built upon these models. Furthermore, understanding vascular growth and remodeling in native and tissue-engineered vascular biomaterials, as well as designing and testing drugs on soft tissue, are crucial aspects of predictive regenerative medicine. Traditional nonlinear optimization methods and finite element (FE) simulations have served as biomaterial characterization tools combined with soft tissue mechanics and tensile testing for decades. However, results obtained through nonlinear optimization methods are reliable only to a certain extent due to mathematical limitations, and FE simulations may require substantial computing time and resources, which might not be justified for patient-specific simulations. To a significant extent, machine learning (ML) techniques have gained increasing prominence in the field of soft tissue mechanics in recent years, offering notable advantages over conventional methods. This review article presents an in-depth examination of emerging ML algorithms utilized for estimating the mechanical characteristics of soft biological tissues and biomaterials. These algorithms are employed to analyze crucial properties such as stress-strain curves and pressure-volume loops. The focus of the review is on applications in cardiovascular engineering, and the fundamental mathematical basis of each approach is also discussed. The review effort employed two strategies. First, the recent studies of major research groups actively engaged in cardiovascular soft tissue mechanics are compiled, and research papers utilizing ML and deep learning (DL) techniques were included in our review. The second strategy involved a standard keyword search across major databases. This approach provided 11 relevant ML articles, meticulously selected from reputable sources including ScienceDirect, Springer, PubMed, and Google Scholar. The selection process involved using specific keywords such as "machine learning" or "deep learning" in conjunction with "soft biological tissues", "cardiovascular", "patient-specific," "strain energy", "vascular" or "biomaterials". Initially, a total of 25 articles were selected. However, 14 of these articles were excluded as they did not align with the criteria of focusing on biomaterials specifically employed for soft tissue repair and regeneration. As a result, the remaining 11 articles were categorized based on the ML techniques employed and the training data utilized. ML techniques utilized for assessing the mechanical characteristics of soft biological tissues and biomaterials are broadly classified into two categories: standard ML algorithms and physics-informed ML algorithms. The standard ML models are then organized based on their tasks, being grouped into Regression and Classification subcategories. Within these categories, studies employ various supervised learning models, including support vector machines (SVMs), bagged decision trees (BDTs), artificial neural networks (ANNs) or deep neural networks (DNNs), and convolutional neural networks (CNNs). Additionally, the utilization of unsupervised learning approaches, such as autoencoders incorporating principal component analysis (PCA) and/or low-rank approximation (LRA), is based on the specific characteristics of the training data. The training data predominantly consists of three types: experimental mechanical data, including uniaxial or biaxial stress-strain data; synthetic mechanical data generated through non-linear fitting and/or FE simulations; and image data such as 3D second harmonic generation (SHG) images or computed tomography (CT) images. The evaluation of performance for physics-informed ML models primarily relies on the coefficient of determination . In contrast, various metrics and error measures are utilized to assess the performance of standard ML models. Furthermore, our review includes an extensive examination of prevalent biomaterial models that can serve as physical laws for physics-informed ML models. ML models offer an accurate, fast, and reliable approach for evaluating the mechanical characteristics of diseased soft tissue segments and selecting optimal biomaterials for time-critical soft tissue surgeries. Among the various ML models examined in this review, physics-informed neural network models exhibit the capability to forecast the mechanical response of soft biological tissues accurately, even with limited training samples. These models achieve high values ranging from 0.90 to 1.00. This is particularly significant considering the challenges associated with obtaining a large number of living tissue samples for experimental purposes, which can be time-consuming and impractical. Additionally, the review not only discusses the advantages identified in the current literature but also sheds light on the limitations and offers insights into future perspectives.

Optimizing the Location of Supports under a Monolithic Floor Slab

Monolithic reinforced concrete floor slabs are one of the most common types of building structures, and their optimization is an urgent task. The article presents the methodology for finding the optimal position of point supports under a reinforced concrete floor slab of arbitrary configuration at arbitrary load. The slab is considered thin, elastic and isotropic, with constant over-the-area stiffness, that is, the reinforcement is not taken into account or is constant. The solution is performed using the finite element method in combination with the nonlinear optimization methods. Finite element analysis is implemented by authors in MATLAB (R2024a) environment in such a way that the location of the columns may not coincide with the nodes of the finite element mesh of the slab. This allows to significantly increase the efficiency of solving the optimization problem compared to previously used algorithms, including the Monte Carlo method. Boundary conditions are taken into account using the Lagrange multiplier method. As an optimization criterion, the maximum deflection value is used, as well as the value of the potential strain energy. The effectiveness of six nonlinear optimization methods is compared in the example of a square slab under the action of a uniformly distributed load. For solutions obtained using the pattern search, simulated annealing and internal point methods, the maximum deflections are at least 1.2 times higher than for solutions obtained using the particle swarm method and genetic algorithm. An example of real object optimization is also presented. By changing the position of seven columns, it was possible to reduce the maximum deflection of the floor slab by 1.6 times.

Development of a New Method to Optimize Operations of an Existing Crude Unit

A nonlinear optimization method working with the Simplex Method was developed to find optimum operating conditions of a crude oil distillation unit subject to defined process constraints, product specifications and prevailing market conditions. Then the method was applied to a commercial crude unit. This crude unit was modeled using Aspen Hysys V12.1 process simulation software. Two sets of market scenarios designated as the maximum gasoline scenario and minimum gasoline scenario were applied to the simulation model. It was found that the model minimized naphtha production and maximized kerosene production for minimum gasoline scenarios where the price of kerosene and diesel products were higher than naphtha products. Similarly, the model maximized the naphtha product yield for the maximum gasoline scenario where the naphtha price exceeds the mid-distillate product price. The iterative procedure developed for the study monotonically converged to optimum operating conditions for both market scenarios. It was observed that the optimization scheme developed in this study could generate a significant profit increase in the conventional crude unit investigated in this study without and capital investment.

A two-phase nonlinear optimization method for routing and sizing district heating systems

This paper presents a method to find the optimal topology, pipe sizing, and operational parameters of a district heating system under consideration of one design point. The current high costs of district heating systems set limits regarding the minimum heat demand density required for economic network expansions. Optimized routing with ideal pipe sizing and optimal operating parameters offers a potential for cost reduction. Therefore, this paper introduces a new two-phase method for district heating network expansion planning. This method consists of consecutive optimizations, starting with a mixed-integer linear programming followed by a nonlinear optimization. During the mixed-integer linear programming, the district heating system is optimized with continuous diameters, and the nonlinear pressure and temperature dependencies must be linearized. The resulting topology and the continuous diameters are afterward handed over to a nonlinear sparse sequential quadratic programming. The continuous diameters are discretized using a numerical continuation strategy that gradually forces the continuous diameter variables into discrete diameter choices. As a proof of concept, the district heating system for a small town with 400 consumers is optimized and analyzed. The two-phase optimization is performed in 251.68sec, and in most cases, discrete or near discrete diameters are achieved in a nonlinear continuous optimization.

Design and optimization of air-cooled heat dissipation structure of an on-board supercapacitor box

An effective nonlinear optimization method is proposed for heat dissipation structure of the supercapacitor box in this paper. Supercapacitor has been widely used in modern tramcar for its fast charging and discharging, long cycle life and environmental protection. However, the large amount of heat generated during operation is difficult to be emitted, which hinders its further application. The existing studies mainly focus on the simulation of heat dissipation structure of lithium-ion battery pack, and there is relatively few literatures on simulation of supercapacitor module. This paper takes supercapacitor box of a tramcar as the research object. Firstly, a finite element model for heat dissipation is established. Then the heat dissipation characteristics are simulated. The spacings of the supercapacitor modules along x and y directions are optimized. The results show that the cooling effect is the best when the x-direction spacing is 120 mm, and y-direction spacing is 30 mm. The peak temperature is 312.22 K with a reduction of 1.5 %, and the temperature difference is only 3.24 K with a reduction of 12.4 %. Because the heat generation of supercapacitor modules is highly nonlinear, the mutation theory is used to optimize the heat dissipation structure. The results show that the best cooling effect is achieved when the air inlet is asymmetric and the out inlet is symmetric. The peak temperature is 310.15 K with a reduction of 2.2 %, and the temperature difference is 1.73 K with a reduction of 53.2 %. The results of this study could provide a scientific basis for the design of heat dissipation structure for the supercapacitor box.

Multi-objective design of parametric equivalent-input-disturbance approaches with application to vehicle suspension systems

A multi-objective parametric design method is developed for an equivalent-input-disturbance-based control system with mismatched disturbances. Different from the existing design methods that calculated control parameters by stability conditions, multiple performance objectives including unmeasurable output estimation, disturbance rejection, noise suppression, input refinement, and robustness, are simultaneously optimized in the developed design. First, for the sake of low computation complexity, the closed-loop system is represented. Then, the parameterization of the design conditions for multiple performance objectives is given. Further, a nonlinear optimization method is used to perform the performance-oriented system design. Lastly, the efficacy and benefits of the developed methods are demonstrated through simulations of a quarter-vehicle suspension system and comparisons with other alternative methods.

Nonlinear electromechanical topology optimization method for stretchable electronic interconnect structures

Nonlinear electromechanical topology optimization method for stretchable electronic interconnect structures

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

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.

Nonlinear optimal control for triangular tethered multi-satellite formations

Triangular satellite constellations are created by three satellites which are linked through tethers. Such formations serve distributed observation space missions or the creation of high-density satellite communication networks over high-frequency bands. In a tethered multi-satellite system consisting of three-satellites in triangular formation the associated dynamic model exhibits strong nonlinearities. Stabilization and precise positioning of the multi-satellite constellation is a nontrivial task and the solution of the associated nonlinear control problem is an elaborated procedure. In this article a novel nonlinear optimal control method is applied to the above-noted model the tethered multi-satellite system in triangular formation. First, the state-space model of the triangular tethered multi-satellite formation undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the tethered satellites a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution of the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of setpoints under moderate variations of the control inputs and a minimum dispersion of energy when changing the position of the satellites in their triangular tethered formation.

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.

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.

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