Nonlinear Optimization Algorithm Research Articles

Unbiased Identification of Fractional Order System with Unknown Time-Delay Using Bias Compensation Method

In the field of engineering, time-delay is a typical occurrence. In reality, the inner dynamics of many industrial processes are impacted by delay or after-effect events. This paper discusses the identification of continuous-time fractional order system with unknown time-delay using the bias compensated least squares algorithm. The basic concept is to remove the imposed bias by including a correction term into the least squares estimations. The suggested approach makes a significant contribution by the estimation, iteratively, of fractional order system coefficients as well as the orders and the time-delay using a nonlinear optimization algorithm. The main advantage of this method is to provide a simple and powerful algorithm with good accuracy. The suggest method performances are assessed through two numerical examples.

A Fast and Simple Method for Absolute Orientation Estimation Using a Single Vanishing Point

Absolute orientation estimation is one of the key steps in computer vision, and n 2D–3D point correspondences can be used to obtain the absolute orientation, which is known as the perspective-n-point problem (PnP). The lowest number of point correspondences is three if there is no other information, and the corresponding algorithm is called the P3P solver. In practice, the real scene may consist of some geometric information, e.g., the vanishing point. When scenes contain parallel lines, they intersect at vanishing points. Hence, to reduce the number of point correspondences and increase the computational speed, we proposed a fast and simple method for absolute orientation estimation using a single vanishing point. First, the inertial measurement unit (IMU) was used to obtain the rotation of the camera around the Y-axis (i.e., roll angle), which could simplify the orientation estimation. Then, one vanishing point was used to estimate the coarse orientation because it contained direction information in both the camera frame and world frame. Finally, our proposed method used a non-linear optimization algorithm for solution refining. The experimental results show that compared with several state-of-the-art orientation estimation solvers, our proposed method had a better performance regarding numerical stability, noise sensitivity, and computational speed in synthetic data and real images.

A novel adaptive fault diagnosis algorithm for multi-machine equipment: application in bearing and diesel engine

This paper proposes an adaptive fault diagnosis algorithm based on vibration signals for fault diagnosis of bearings and diesel engines. First, the improved nonlinear gray wolf optimization algorithm (NGWO) is adopted to optimize the key parameter for variational mode decomposition (VMD) with the power spectral entropy as the fitness value. Meanwhile, adaptive noise reduction of the signal is realized. Then, sensitive fault features of bearings and diesel engines are selected through a feature sensitivity analysis on the vibration signals. Also, a single-layer sparse autoencoder is used to align the feature dimensions of each type of data to construct feature matrix samples. Subsequently, a deep neural network (DNN) consisting of a two-layer stacked sparse autoencoder (SSAE) and a Softmax classification layer is constructed to realize failure mode recognition. During the training process of DNN, a surrogate model formed by NGWO and a back propagation neural network is employed to optimize the hyperparameters of SSAE. Finally, to verify the effectiveness of the proposed fault diagnosis algorithm, fault diagnosis experiments are conducted on the fault data set of bearings and diesel engines. The diagnosis results show that the proposed method achieves high-precision fault diagnosis for bearings and diesel engines and performs stably for small samples.

Application of Boiler Optimization Monitoring System Based on Embedded Internet of Things

In order to study the deficiency of tuning PID controller in traditional boiler combustion air system, this paper proposes an embedded Internet of things monitoring system and puts forward a method of fuzzy PID controller with the help of nonlinear optimization algorithm to reasonably set the initial value of control parameters. Through the simulation comparison with the traditional engineering tuning PID controller, it is found that when the simulation process is t = 2000 s, the step disturbance with amplitude of 0.1 is added to the system input, and there will be slight disturbance in the combustion process. Through fuzzy PID and strong robustness support, the modeling error of the monitoring system model can be controlled between 10%∼25%, which proves that the nonlinear optimized PID has strong anti-interference and can meet the process requirements of the system.

Nondestructive EIS Testing to Estimate a Subset of Physics-based-model Parameter Values for Lithium-ion Cells

This paper is the final installment in a series of articles that collectively shows how to estimate parameter values for lumped-parameter physics-based models of lithium-ion cells without requiring cell teardown. In this paper, we leverage electrochemical impedance spectroscopy (EIS) to find estimates of all as-yet-unresolved parameter values. The characterization process regresses the measured cell impedance spectrum to exact analytic closed-form expressions of the frequency response of an extended Doyle–Fuller–Newman model to identify thirteen lumped parameters plus multiple reaction-rate constants. A nonlinear optimization algorithm performs the regression, and so it is important to provide reasonable initial parameter estimates and constraints, which we also discuss. As part of this process, the generalized distribution of realization times technique is used to isolate time constants from the two electrodes as well as to calibrate the laboratory EIS-test data. The overall methodology is studied on a virtual cell and on a laboratory cell (both having graphite//NMC chemistries). Parameter estimates found in the simulation study are highly accurate, leading us to have confidence in the values estimated for the physical cell as well.

Design and fabrication of a terahertz dual-plane hologram and extended-depth-of-focus diffractive lens

This work discusses the design and fabrication of a dual-plane terahertz (THz) hologram and an extended-depth-of-focus THz diffractive lens. The dual-plane THz hologram consists of 50 × 50 diffractive optical elements with identical element pixel size 1×1 mm, and the extended-depth-of-focus THz diffractive lens is designed with 25 concentric rings with identical ring width of 1 mm, resulting in same device dimension 50 mm × 50 mm. The height of the hologram pixels and concentric rings of the diffractive lens are optimized by nonlinear optimization algorithms with scalar diffraction theory based on Ray-Sommerfeld diffraction equation. Finite-Difference Time-Domain (FDTD) simulation results agree with optimization results obtained from the scalar diffraction theory for both the THz hologram and the THz diffractive lens. The demonstrated experimental results show that the proposed THz hologram and THz diffractive lens can generate the desired diffraction patterns. These diffractive structures have the potential to be applied in areas such as THz imaging, data storage, and displays.

Reaction Kinetics of Cinnamaldehyde Hydrogenation over Pt/SiO2: Comparison between Bulk and Intraparticle Diffusion Models

The liquid-phase hydrogenation of cinnamaldehyde over a Pt/SiO2 catalyst was investigated experimentally and theoretically. The experiments were conducted in a 300 cm3 stainless steel stirred batch reactor supplied with hydrogen gas and ethanol as a solvent. Five Langmuir–Hinshelwood kinetic models were investigated to fit the experimental data. The predictions from the bulk model were compared with predictions from the intraparticle diffusion model. Competitive and non-competitive mechanisms were applied to produce the main intermediate compound, cinnamyl alcohol. Reaction rate parameters for the different reaction steps were calculated by comparing between the experimental and mathematical models. All rate data utilized in the present study were obtained in the kinetic regime. The kinetic parameters were obtained by applying a nonlinear dynamic optimization algorithm. Nevertheless, the comparison between the methodology of the present model and these five models indicated that the non-competitive mechanism is more acceptable and identical with the single-site Langmuir–Hinshelwood kinetic model including mass transfer effects and it mimicked the reactant behavior better than the other models. In addition, the observed mean absolute error (MAE) for the non-competitive mechanism of the present model was 2.3022 mol/m3; however, the MAE for the competitive mechanism was 2.8233 mol/m3, which is an increase of approximately 18%. The prediction of the intraparticle diffusion model was found to be very close to that of the bulk model owing to the use of a catalyst with a very small particle size (<40 microns). Employing a commercial 5% Pt/SiO2 catalyst showed a result consistent with previous research using different catalysts, with an activation energy of ≈24 kJ/mol.

Research on gear decision method of commercial vehicle based on predictive road information

As an essential part of the transportation industry, it is necessary to reduce the fuel consumption of commercial vehicles from the perspective of the environment and economy. Previous studies have shown that optimizing the gear sequence can reduce vehicle fuel consumption. This paper presents a gear decision method based on predictive road information. Under the model predictive control framework, the dynamic programming algorithm is used to solve the multi-objective optimization problem of gear decision. To solve the problem of the long calculation time of the dynamic programming algorithm, the nonlinear optimization algorithm is used to optimize the dynamic programming sub-problem, and the optimal gear sequence of fuel consumption is obtained. The final optimized gear sequence is obtained through the dynamic programming algorithm. The simulation analysis of the proposed gear shift decision method shows that the gear shift decision method can effectively reduce fuel consumption under fixed working conditions. Compared with the economic shift schedule, the fuel consumption is reduced by 5%, and the computing speed is improved compared with the dynamic programming algorithm.

Nonlinear homotopy interior-point algorithm for 6-DoF powered landing guidance

The six-degree-of-freedom (6-DoF) powered landing guidance problem usually is difficult to solve for several reasons. First, this problem coupled with low-frequency translational and high-frequency rotational equations of motion is naturally large-scale. Second, the constraints enforced into the problem are highly coupled, nonlinear and non-convex, which makes the problem quite sensitive to the initial value guesses. Third, the initial position, velocity and attitude of the landing vehicle is quite difficult to forecast due to the complex endo-atmospheric environment, thus the traditional guidance methods are difficult to obtain a predetermined trajectory. In this paper, for the first time we proposed a nonlinear homotopy interior-point optimization algorithm (NHOPT) for solving the 6-DoF powered landing guidance problem. Different from general external homotopy strategies, we embed the concept of homotopy methods into the barrier line-search interior-point method. Using vertical landing without position and velocity offset, it is easy to provide initial guesses, which we define as the initial homotopy subproblem. Then a class of related homotopy subproblems is solved along a homotopy path using the algorithm until the original problem is converged. Numerical results demonstrate that the algorithm has high performance in terms of convergence and computational efficiency.

Data-driven design of thin-film optical systems using deep active learning.

A deep learning aided optimization algorithm for the design of flat thin-film multilayer optical systems is developed. The authors introduce a deep generative neural network, based on a variational autoencoder, to perform the optimization of photonic devices. This algorithm allows one to find a near-optimal solution to the inverse design problem of creating an anti-reflective grating, a fundamental problem in material science. As a proof of concept, the authors demonstrate the method's capabilities for designing an anti-reflective flat thin-film stack consisting of multiple material types. We designed and constructed a dielectric stack on silicon that exhibits an average reflection of 1.52 %, which is lower than other recently published experiments in the engineering and physics literature. In addition to its superior performance, the computational cost of our algorithm based on the deep generative model is much lower than traditional nonlinear optimization algorithms. These results demonstrate that advanced concepts in deep learning can drive the capabilities of inverse design algorithms for photonics. In addition, the authors develop an accurate regression model using deep active learning to predict the total reflectivity for a given optical system. The surrogate model of the governing partial differential equations can then be broadly used in the design of optical systems and to rapidly evaluate their behavior.

Fast nonlinear model predictive controller using parallel PSO based on divide and conquer approach

The high computationally expensive nature of nonlinear optimisation algorithms leads to limitations of its use in a real-time era. So, this is the main challenge against researchers to develop a fast algorithm that is used in real-time computations. This paper proposes a fast nonlinear model predictive control algorithm that utilises a parallel particle swarm optimisation with synchronous and asynchronous methods inclusion, that handles nonlinear optimisation problems with constraints. The additional divide and conquer approach of the proposed algorithm improves the speed of computation and disturbance rejection capability which proves its efficacy in real-time applications. A highly nonlinear fast dynamic real-time inverted pendulum system with hybrid embedded hardware platform (ARM + FPGA) is used to validate the performance of this algorithm under constraints. The solution presented in the paper is computationally feasible for smaller sampling times i.e. in miliseconds and it gives promising results with synchronous and asynchonous parallel PSO compared to the state-of-art PSO algorithm.

Calibration of a Finite Element Forward Model in Eddy Current Inspection

We report on the use of a novel constrained optimisation algorithm for calibrating the finite element model in an eddy current inspection application. An accurate finite element forward model is often important in such eddy current applications for training neural networks or as part of an iterative solver. However, the subject of calibration of the model has not received much attention in the literature to date. We consider a multi-frequency, eddy current depth profiling application, which is important for non-destructive testing in the nuclear industry. In the optimisation algorithm, we use a Levenberg-Marquardt algorithm and a bisection search to ensure constraints are satisfied, coupled with a truncated Gradient and Hessian method. We calibrate two types of finite element models, one using a filament representation for the coils and the other using a full 3D approach. The results show the feasibility of using the constrained non-linear optimisation algorithm for tuning the finite element model parameters. The mean signal-noise ratio after tuning on a truncated spectrum was 29.47 dB for the 3D model and 28.96 dB for the filament; in contrast the mean SNR using the measured coil parameters was 1.48 dB and 4.98 dB for the two uncalibrated models, respectively. The results show that a filament model is competitive with a 3D model of the coils (within the nuclear graphite application); therefore, a computationally faster filament model can be used with minimal effect on accuracy.

COMPARING FUEL-OPTIMAL AND SHORTEST PATHS WITH OBSTACLE AVOIDANCE

This paper presents a comparison of fuel-optimal and shortest paths of an unmanned combat aerial vehicle (UCAV) with obstacle avoidance. A nonlinear constrained optimization algorithm is applied to obtain the optimal paths. An initial value problem (IVP) and an inverse-dynamics approach are used separately to determine optimal paths for various scenarios and in order to reduce computation time. While inputs of the optimization algorithm are discrete control variables in the IVP method, discrete state variables are used as inputs in the inverse-dynamics method. The minimized path segments of the geometrical model provide an initial estimation of the heading angle for the aircraft flight mechanics model. The number of variables used by the optimization algorithm has a direct effect upon the optimal accuracy; however, the computation time is inversely proportional to the number of the variables. Simulation results demonstrate that the proposed IVP method effectively converges to optimal solutions.

Nonlinear optimization algorithm using monotonically increasing quantization resolution

AbstractWe propose a quantized gradient search algorithm that can achieve global optimization by monotonically reducing the quantization step with respect to time when quantization is composed of integer or fixed‐point fractional values applied to an optimization algorithm. According to the white noise hypothesis states, a quantization step is sufficiently small and the quantization is well defined, the round‐off error caused by quantization can be regarded as a random variable with identically independent distribution. Thus, we rewrite the searching equation based on a gradient descent as a stochastic differential equation and obtain the monotonically decreasing rate of the quantization step, enabling the global optimization by stochastic analysis for deriving an objective function. Consequently, when the search equation is quantized by a monotonically decreasing quantization step, which suitably reduces the round‐off error, we can derive the searching algorithm evolving from an optimization algorithm. Numerical simulations indicate that due to the property of quantization‐based global optimization, the proposed algorithm shows better optimization performance on a search space to each iteration than the conventional algorithm with a higher success rate and fewer iterations.

A survey of HPC algorithms and frameworks for large-scale gradient-based nonlinear optimization

Large-scale numerical optimization problems arise from many fields and have applications in both industrial and academic contexts. Finding solutions to such optimization problems efficiently requires algorithms that are able to leverage the increasing parallelism available in modern computing hardware. In this paper, we review previous work on parallelizing algorithms for nonlinear optimization. To introduce the topic, the paper starts by giving an accessible introduction to nonlinear optimization and high-performance computing. This is followed by a survey of previous work on parallelization and utilization of high-performance computing hardware for nonlinear optimization algorithms. Finally, we present a number of optimization software libraries and how they are able to utilize parallel computing today. This study can serve as an introduction point for researchers interested in nonlinear optimization or high-performance computing, as well as provide ideas and inspiration for future work combining these topics.

PARAMETRIC OPTIMIZATION OF INFORMATION SYSTEMS FOR PROACTIVE PROTECTION OF DATA TRANSMISSION SERVICE FROM NETWORK RECONNAISSANCE

The analysis of the FTP protocol revealed a number of vulnerabilities in it, which can be used by an adversary to uncover the IDs of data transfer service clients and compromise the used network security features. On the one hand, it is due to the possibility of repeated authorization attempts to unauthorized clients, allowing to implement a data transfer service username and password. On the other hand, the implementation of reactive measures of protection, which consists in breaking the control connection to the adversary after a number of unsuccessful authorization attempts, forcing him to change the strategy of exposure. In this regard, the use of proactive protection measures, allowing to increase the time of dialog interaction with the intruder and imposing restrictions on computing and temporal resources used by the intruder, is proposed as a countermeasure to the network reconnaissance tools. The essence of proactive protection measures consists in splitting the response of FTP server to unauthorized client commands into fragments and sending those fragments to the intruder after a specified delay time. Application of proactive protection gives the security system of information system a number of advantages over the intruder in using the time resource, allowing to implement additional protection measures. The problematic issues when implementing proactive protection measures for data transmission service of information systems are, firstly, the need to send fragments of response to the intruder at intervals shorter than the timeout time of waiting for these responses, set by the intruder. Secondly, the possibility of sending to the violator the limited number of fragments of response, that is caused by FTP protocol capabilities, regulating the size of response, as well as the excessive saturation of the communication channel by fragments of messages, that can lead to exhaustion of the resource opportunities of data transmission medium. Therefore, there is a need to find the optimal parameters of the information system in the configuration of data transmission parameters in the interaction with the network reconnaissance tools. The process of information system՚s data transmission service functioning under the influence of network reconnaissance tools is formalized in the form of a Markov random process with discrete states and continuous time. Intensities of streams of events, under which the system passes from state to state, are the input data for solving the task of finding the optimal parameters of the information system for the situation under consideration. The qualitative formulation of the task of determining the optimal parameters of the information system is formulated as follows: using a given mathematical model of the information system՚s data transmission service under conditions of network reconnaissance we should find such a set of parameters of information system՚s functioning, in which the maximum efficiency of its protection while ensuring a given level of availability is provided. The problem under consideration is a vector (multi-criteria) parametric optimization problem, which will be reduced to single-criteria (scalar) optimization by constraint method (main criterion). Main criterion method implies selection of one scalar target function and transfer of other target functions into additional restriction functions. As the constraints for solving the optimization problem set resource constraints, characterized by the coefficient of the transmission medium, as well as the condition of a given level of robustness of the information system, characterized by the number of conditionality of the matrix of the intensity of the flow of events. The research applies a nonlinear optimization algorithm, an annealing simulation algorithm that provides the ability to approximate the search for a global extremum. The results obtained during the study are presented in the form of an assortment of graphic dependences of changes in the optimal parameters of the information system on the intensity of the impact of network reconnaissance means and the imposed constraints.

A novel belief rule base expert system with interval-valued references

As an essential parameter in the belief rule base (BRB), referential values refer to evaluation criteria for describing attributes using quantitative data or linguistic terms, the rationality and preciseness of which are important to the modeling accuracy. At present, the studies on referential values of BRB are mainly related to single-valued data. However, due to the inherent uncertainty, ambiguity, and vagueness of expert knowledge, the single-valued references provided by experts cannot represent qualitative information adequately. In this paper, a novel BRB with interval-valued references (BRB-IR) is proposed, in which qualitative knowledge and quantitative data can be integrated to construct models. First, the interval-valued referential values provided by experts are optimized by a nonlinear optimization algorithm to obtain the optimal referential values. Furthermore, other model parameters are optimized by the projection covariance matrix adaptation evolutionary strategy (P-CMA-ES) algorithm. Finally, a case study for pipeline leak detection is constructed to verify the model's effectiveness, and the results show that the proposed BRB-IR is more effective and characterizes expert knowledge better than the classical BRB using single-valued references.

Parameter Identification of Lithium-Ion Batteries by Coupling Electrochemical Impedance Spectroscopy with a Physics-Based Model

Nondestructive, quick, and accurate diagnosis of Lithium-ion batteries are critical tools to extend battery lifetime and ensure safe operation under complicated real-time power demand conditions. In this study, an electrochemical characterization approach coupling impedance spectroscopy with a physics-based model (EIS-Physical) has been demonstrated to accurately identify key transport and kinetic parameters for an in-house assembled Li(Ni0.5Mn0.3Co0.2)O2/Li-metal half-cell. The parameter identification process has been realized by a nonlinear optimization algorithm, along with proper sensitivity and dependence analyses on initial guesses. The parameters obtained using this approach have been compared with those determined from the benchmark Galvanostatic Intermittent Titration Technique (GITT). Equivalent circuit method as an important state-of-the-art modeling approach to interpret EIS has also been compared against the proposed method. The results show that: i) cathode Li-ion diffusivity and cathode/electrolyte exchange current density are quadratic functions of x Li, which indicates cathode is the capacity limiting electrode and operates in a wide SOC range. Therefore, cathode must be simulated using the concentrated solution theory. ii) EIS-Physical method can provide consistent and unique parameters with clear physical meanings compared to its equivalent circuit counterpart. iii) EIS-Physical method is as precise as GITT but less time consuming (i.e., <2.5 h vs > 200 h). Consequently, the proposed method is found to be more practical to implement as a Lithium-ion battery diagnostic tool.

A Novel Multi-Objective Nonlinear Discrete Binary Gaining-Sharing Knowledge-Based Optimization Algorithm

GSK algorithm is based on the concept of how humans acquire and share knowledge through their lifespan. Discrete Binary version of GSK named novel binary Gaining Sharing knowledge-based optimization algorithm (DBGSK) depends on mainly two binary stages: binary junior gaining sharing stage and binary senior gaining sharing stage with knowledge factor 1. These two stages enable BGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space. Besides, one of these practical applications is to optimally schedule the flights for residual stranded citizens due to COVID-19. The problem is defined for a decision maker who wants to schedule a multiple stepped trip for a subset of candidate airports to return the maximum number of residuals of stranded citizens remaining in listed airports while comprising the minimization of the total travelled distances for a carrying airplane. A nonlinear binary mathematical programming model for the problem is introduced with a real application case study, the case study is solved using (DBGSK).

An Indoor Wi-Fi Localization Algorithm Using Ranging Model Constructed With Transformed RSSI and BP Neural Network

This paper focuses on improving indoor Wi-Fi localization by mitigating the effect of fluctuation of received signal strength indication (RSSI). The RSSI data collected at each reference point is first transformed through translation and scaling. The BP (Back Propagation) neural network is then used to construct the ranging model using the transformed RSSI to determine the distances between the target point and each reference point. A genetic algorithm (GA) is developed to optimize the initial values of weights and biases of the BP neural network. For convenience, our proposed ranging model is denoted as GTBPD. A new localization algorithm is then proposed, which uses the GTBPD model and the sequential quadratic programming (SQP, an iterative nonlinear optimization algorithm), and the algorithm is denoted as GTBPD-LSQP for simplicity. Experiments were conducted in three areas of two different teaching buildings with complex environments. The performance of the proposed GTBPD-LSQP algorithm is evaluated and compared with four existing algorithms. The experimental results show that our proposed GTBPD-LSQP algorithm achieves significantly higher location accuracy than the four existing algorithms.