Dynamic Particle Swarm Optimization Algorithm Research Articles

Bidirectional machine learning-assisted sensitivity-based stochastic searching approach for groundwater DNAPL source characterization.

In this study, we designed a machine learning-based parallel global searching method using the Bayesian inversion framework for efficient identification of dense non-aqueous phase liquid (DNAPL) source characteristics and contaminant transport parameters in groundwater. Swarm intelligence organized hybrid-kernel extreme learning machine (SIO-HKELM) was proposed to approximate the forward and inverse input-output correlation with a high accuracy using the DNAPL transport numerical simulation model. An adaptive inverse-HKELM was established for preliminary estimation of the source characteristics and contaminant transport parameters to correct prior information and generate high-quality initial starting points of parallel searching. A local accurate forward-HKELM surrogate of the numerical model was embedded in the searching system for avoiding repetitive CPU-demanding likelihood evaluations. A sensitivity-based Metropolis criterion (MC), incorporating the dynamic particle swarm optimization (SD-PSO) algorithm, was developed for improving the search ergodicity and realizing precise inversion of all the unknown variables with drastic variations in sensitivity to the likelihood function. Results showed that the generalization capability and robustness of SIO-HKELM were superior to those of the traditional machine learning methods, including KELM and support vector regression (SVR), and it sufficiently approximated the forward and inverse input-output mapping of the numerical model with testing determination coefficients of 0.9944 and 0.6440, respectively. With high-quality prior information and initial starting points generated by the adaptive inverse-HKELM feed approach, the uncertainty in the inversion outputs was reduced, and the searching process rapidly converged to reasonable posterior distributions in around 60 iterations. Compared with the widely used multichain Markov chain Monte Carlo (MCMC) approach, the parallel searching lines generated by SD-PSO-MC adequately covered the searching space, and the "equifinality" effect was more effectively restrained by reducing the relative errors of all the point estimations to less than 8%. Therefore, the real source information reflected by the statistical characteristics of the SD-PSO-MC inversion outputs was more precise than that obtained using the multichain MCMC approach.

Intelligent driving model considering vehicular dynamics and heterogeneous road environments

ABSTRACT Understanding vehicles’ movement in complex environments becomes cruical with the fast development of connected automated vehicles (CAVs). Current microscopic traffic flow models lack consideration for vehicle dynamics and complex road topologies. This study develops a model addressing these issues, retrieving vehicles’ maneuvers and predicting vehicles’ two-dimensional motion. It introduces a two-dimensional intelligent driving model utilizing steering angle and acceleration as control inputs. Intricate road topologies are represented with potential fields and a virtual boundary to capture the heterogeneous environment’s complexity. A driving potential field model is also developed for off-ramp areas. Model parameters are optimized with the dynamic time warping (DTW) and particle swarm optimization (PSO) algorithm. Furthermore, model predictive control (MPC) enhances the realism of the model’s output. Field validation results demonstrate that the proposed models can accurately describe vehicles’ two-dimensional movement in intricate environments, offering valuable support for research on heterogeneous traffic flows for CAVs and CVs.

Optimization of Installation Position for Complex Space Curve Weldments in Robotic Friction Stir Welding Based on Dynamic Dual Particle Swarm Optimization

Robotic friction stir welding (RFSW), with its wide application range, ample working space, and task flexibility, has emerged as a vital development in friction stir welding (FSW) technology. However, the low stiffness of serial industrial robots can lead to end-effector deviations and vibrations during FSW tasks, adversely affecting the weld quality. This paper proposes a dynamic dual particle swarm optimization (DDPSO) algorithm through a new comprehensive stability index that considers both the stiffness and vibration stability of the robot to optimize the installation position of complex space curve weldments, thereby enhancing the robot’s stability during the FSW process. The algorithm employs two independent particle swarms for exploration and exploitation tasks and dynamically adjusts task allocation and particle numbers based on current results to fully utilize computational resources and enhance search efficiency. Compared to the standard particle swarm optimization (PSO) algorithm, the DDPSO approach demonstrated superior search capabilities and stability of optimization results. The maximum fitness value improved by 4.2%, the average value increased by 12.74%, and the concentration level of optimization results rose by 72.91% on average. The new optimization method pioneers fresh perspectives for optimizing the stability of RFSW, providing significant grounds for the process optimization and offline programming of complex spatial curve weldments.

Optimal Configuration of Wind–Solar–Thermal-Storage Power Energy Based on Dynamic Inertia Weight Chaotic Particle Swarm

The proposed approach involves a method of joint optimization configuration for wind–solar–thermal-storage (WSTS) power energy bases utilizing a dynamic inertia weight chaotic particle swarm optimization (DIWCPSO) algorithm. The power generated from the combination of wind and solar energy is analyzed quantitatively by using the average complementarity index (ACI) to determine the optimal ratio of wind and solar installations. We constructed a multi-objective optimization configuration model for the WSTS power generation systems, considering the equivalent annual income and the optimal energy consumption level as objective functions of the system. We solved the model using the chaotic particle swarm optimization algorithm with linearly decreasing dynamic inertia weight. To validate the effectiveness of the proposed approach, we conducted a simulation using the 2030 power energy base planning data of a particular region in Inner Mongolia. The results demonstrate that the proposed method significantly improves the annual income, enhances the consumption of wind–solar energy, and boosts the power transmission capacity of the system.

Optimal Trajectory Planning for Robotic Arm Based on Improved Dynamic Multi-Population Particle Swarm Optimization Algorithm

Optimal Trajectory Planning for Robotic Arm Based on Improved Dynamic Multi-Population Particle Swarm Optimization Algorithm

A framework for dynamical distributed flocking control in dense environments

The bio-inspired flocking model has been widely utilized in self-organized swarms. However, existing potential field methods fail to guarantee safe and orderly swarm movement in dense environments featuring both static and dynamic obstacles. In this study, we propose an innovative, dynamically optimized flocking control framework that integrates an improved and tunable self-propelled flocking model with an enhanced dynamic particle swarm optimization (DPSO) algorithm. Our model incorporates pigeon-inspired obstacle gap selection based on a probability approach to optimize steering decisions. Moreover, we introduce the DPSO algorithm, which combines a collaboration-based particle swarm optimizer with fractional order velocity incorporated history-guided estimation. This hybrid algorithm dynamically determines the optimal set of control parameters to maintain the desired swarm state. Through numerical comparison experiments with state-of-the-art models, we demonstrate that our approach enhances the safety, synchronization, and efficiency of the swarm even within a limited visual field, without prior environmental information. These features bring the simulations closer to real-world experiments.

Dynamic Temperature Compensation of Pressure Sensors in Migratory Bird Biologging Applications

This article proposes an improved dynamic quantum particle swarm optimization (DQPSO) algorithm to optimize a radial basis function (RBF) neural network for temperature compensation of pressure sensors used in tracking and monitoring wild migratory birds. The algorithm incorporates a temperature-pressure fitting model that includes temperature rate of change and gradient reference terms. It also includes a loss function that considers fitting accuracy and complexity, thereby improving the robustness of the sensor for complex temperature variations. The calibration experiments revealed that after implementation, the average absolute error of the pressure sensor output during dynamic temperature changes was reduced from 145.3 Pa to 20.2 Pa. This reduction represents an 86% improvement over the commercial polynomial compensation method, and the DQPSO approach significantly outperformed traditional feedforward network models. Finally, the algorithm was deployed and verified in an embedded environment for low-power, high-precision, real-time pressure compensation during the tracking and monitoring of wild migratory birds.

A mathematical model and metaheuristic approach to solve the real-time feeder vehicle routing problem

Unlike classic vehicle routing problems, real-time vehicle routing problems (RTVRPs) are real-world dynamic vehicle routing problems (DVRPs) in which customer requests are identified over the time horizon of operations without previous knowledge. In this problem, received requests are answered as quickly as possible and then dispatched to a service vehicle. Considering the RTVRP’s timing constraints, a solution must provide the best trade-off between the computation time required to find the solution and the proposed solution’s costs. A feeder vehicle routing problem (FVRP) consists of a heterogeneous fleet of vehicles, including trucks and motorcycles. In this problem, motorcycles pass easily in crowded areas, and the traffic of urban logistics is distributed easily. The feeder approach also lowers the number of times the vehicle returns to the central depot for loading, resulting in cost and time savings. The present article proposes a real-time feeder vehicle routing problem (RTFVRP) in a situation where every truck and every motorcycle can join during the freight delivery process. After modeling the RTFVRP through mixed-integer linear programming, a dynamic inertia weight particle swarm optimization (DIWPSO) algorithm is offered to solve the problem. The results of the static version of the FVRP in the small and the last time slices show that the GAMS outputs outperform those of the DIWPSO and differential evolution (DE), both indicating a similar performance. The results of running these algorithms for 21 DVRP test instances revealed that the PSO outperforms the DE in quality and solution runtime in both static and dynamic versions. Overall, the PSO and DE algorithms generated 34.33% and 30.37% cost savings in implementing RTFVRP, respectively, compared to the case that all requests were available at the beginning of the working day.

Dynamic particle swarm optimization-radial function extremum neural network method of HCF probability analysis for compressor blade

The high cycle fatigue (HCF) of compressor rotor seriously affects the performance and reliability of gas turbine. Probabilistic HCF evaluation is an effective measure to quantify the uncertain traits of vibration stresses and assess the reliable HCF life for compressor rotor. To improve modeling accuracy and computational efficiency in transient probability analysis of HCF life of gas turbine compressor, radial basis function neural network (RBFNN) and dynamic particle swarm optimization (DPSO) algorithm were introduced into extreme response surface method (ERSM). In this paper, we propose a HCF life probability evaluation method for compressor blades based on the dynamic particle swarm optimization-radial basis function extremum neural network (DPSO-RBFENN) model. By selecting random input variables such as aerodynamic load, centrifugal load and material parameters, a prediction model was established based on DPSO-RBFENN sample learning, and the reliability evaluation of compressor blade HCF life was carried out. Distribution characteristics, reliability and sensitivity to fatigue life were obtained, which provided a basis for the structural design of compressor blades. The Monte Carlo method, ERSM, RBFNN and DPSO-RBFENN are compared.

Wavelet-ARMA-Based Short-Term Drift Calibration of IMU Position on Human Lower Limbs

Position calibration in the inertial motion capture (Mocap) system is a crux to guarantee the correct calculation of human posture. Due to muscle movement and clothes slippage during motion, the position of inertial measurement units (IMUs) installed on the human body generates displacements. Aiming at the drift error caused by IMUs’ position shift in the short term, this paper proposes a wavelet-ARMA prediction model. Three different wavelet bases, Haar, Daubechies, and Coiflet, are selected to combine with the ARMA model to predict angle sequences, among which the Db4 wavelet-ARMA model with the best prediction performance, choosing the angle sequence predicted by the model and the measurement sequence to set up an error model, and using the Gauss-Newton (GN) and the dynamic weight particle swarm optimization (DWPSO) algorithms to realize IMUs’ position calibration. The experimental results show that the wavelet-ARMA model has better prediction performance than the ARMA, BP, and LSTM models with the value of the calibrated RMSE decreasing. The results confirm that the model proposed in this paper can accurately predict the changing trend of joint angle sequences on human lower limbs during gait motion and automatically calibrate the short-term drift error formed in the process of gait motion.

Research on stability control strategy of adjustable pressure wall-climbing robot based on adsorption identification

In order to solve the problem that it is difficult to accurately model the complex fluid domain in the negative pressure chamber of the robot in the process of wall climbing, and thus cannot quickly and steadily adsorb, a double closed-loop control strategy based on parameter identification and particle swarm optimization is proposed in this paper to improve the speed and stability of the adsorption response of the robot in the process of wall climbing. Firstly, a vacuum negative pressure wall climbing robot with a spring pressure regulating structure is developed, and the critical conditions of the robot’s instability are solved by mechanical analysis. Then, the rigid-flexible coupling model of the whole machine was established based on mass, spring and Maxwell viscoelastic elements. The model parameters of the adsorption system were identified by vacuum adsorption test. Compared with the experimental data, the accuracy of the model was more than 80%. On this basis, PID controller is used to adjust the adsorption response speed of the robot, a double closed-loop stable adsorption control strategy is designed, and the control parameters of the adsorption system are adjusted by using the dynamic weight standard particle swarm optimization algorithm. Finally, simulation and prototype tests show that, the proposed control strategy can shorten the static and dynamic response time of the adsorption system by about 3.5 s and 1.4 s, the flow response time by about 1.15s, the maneuvering performance of the whole system is improved by about 26%, and the parameter overshoot and steady-state error are lower, which provides a theoretical reference for the stability control and engineering application of the wall-climbing robot.

Dynamic Optimal Control for Wastewater Treatment Process Under Multiple Operating Conditions

Wastewater treatment process (WWTP) is operated with multiple conditions. Accurately identify these conditions and satisfy the different requirements are the keys to guarantee the optimal operation of WWTP. To solve this problem, a dynamic optimal control (DOC) strategy is designed in this paper. First, with the aid of the predicting models by adaptive fuzzy neural network for effluent nitrate and total nitrogen, different operating conditions can be identified. Corresponding to each condition, changing number of operating objectives are formulated to match the different requirements. Second, due to the changeable operating objectives can cause the expanded/contracted dimension of Pareto-optimal set, a dynamic multi-objective particle swarm optimization algorithm is developed. In this algorithm, self-adjusting mechanism of population size and global optimal solution are designed to derive the optimal solutions of control variables. Third, fuzzy controllers, matched with the different conditions, are designed to trace these optimal solutions. Finally, the effectiveness of DOC strategy is tested on a real WWTP. The results demonstrate that this proposed DOC strategy enables to achieve promising operating performance. <i>Note to Practitioners</i>&#x2014;This article aims to develop an optimal control strategy to match the multiple conditions and improve the operating performance. To achieve this goal, a dynamic optimal control (DOC) strategy, with the consideration of different operating conditions, is designed. Two key points are contained, the identification of multiple operating conditions and the satisfaction of different requirements. Due to each condition confronts with different requirements, it is important to accurately identify the conditions and construct the corresponding operating objectives. Based on the obtained operating data, changeable operating objectives are established to describe the different conditions. In addition, to satisfy the operating requirements, it is necessary to optimize the changeable objectives, but the changes in the number of objectives can cause the expanded/ contracted of Pareto-optimal set. A dynamic multi-objective particle swarm optimization algorithm, with self-adjusting mechanism of population size and global optimal solution, is designed to deal with this kind of optimization problem. The effectiveness and applicability of the proposed DOC strategy are evaluated on a pilot platform of a real WWTP, showing the improvement on the operating performance. These advantages can be valuable for transplanting this strategy to other real wastewater treatment plants to realize the optimal operation.

Dynamic Robust Particle Swarm Optimization Algorithm Based on Hybrid Strategy

Robust optimization over time can effectively solve the problem of frequent solution switching in dynamic environments. In order to improve the search performance of dynamic robust optimization algorithm, a dynamic robust particle swarm optimization algorithm based on hybrid strategy (HS-DRPSO) is proposed in this paper. Based on the particle swarm optimization, the HS-DRPSO combines differential evolution algorithm and brainstorms an optimization algorithm to improve the search ability. Moreover, a dynamic selection strategy is employed to realize the selection of different search methods in the proposed algorithm. Compared with the other two dynamic robust optimization algorithms on five dynamic standard test functions, the results show that the overall performance of the proposed algorithm is better than other comparison algorithms.

Research on the optimization of the path of the agricultural logistics industry under the innovative mode of “blockchain + supply chain finance”

Abstract To promote the development and application of “blockchain+supply chain finance” in the agricultural logistics industry, this paper uses the ECC algorithm in the blockchain model as the basis and implements an asymmetric encryption algorithm based on elliptic curve mathematical theory to optimize the ECC algorithm. Based on the ECC algorithm in the blockchain model, this paper implements an asymmetric encryption algorithm based on elliptic curve mathematical theory to optimize the ECC algorithm. Combining the dynamic variational particle swarm optimization algorithm and the AdaBoost integration algorithm, the DPSO-SVM algorithm is weighted and combined into a strong classifier, and an evaluation model based on AdaBoost-DPSO-SVM is established, and the model is compared with other models. The experimental results show that the data platform based on “blockchain + supply chain finance” can well solve the problem of loss of confidentiality in the process of identifying agricultural products in the agricultural logistics industry. This also shows that through the way of “blockchain + supply chain finance”, it can provide a better development path for the agricultural logistics industry and can truly achieve low-cost commercial communication, i.e. multi-functional integration development.

MCI Conversion Prediction Using 3D Zernike Moments and the Improved Dynamic Particle Swarm Optimization Algorithm

Mild cognitive impairment (MCI) conversion prediction is a vital challenge in the area of Alzheimer’s disease (AD) as it could determine possible treatment pathways for AD patients. In this work, we presented a robust MCI conversion prediction framework based on the 3D-Zernike Moment (3D-ZM) method that generates statistical features (e.g., shape, texture, and symmetry information) from 3D-MRI scans and improved dynamic particle swarm optimization (IDPSO) that finds an informative sub-set of Zernike features for MCI conversion prediction. We quantified the efficiency of the proposed prediction framework on a large sample of MCI patients including 105 progressive-MCI (pMCI) and 121 stable-MCI (sMCI) at the baseline from the ADNI dataset. Using the proposed MCI conversion prediction framework, pMCI patients were distinguished from sMCI patients with an accuracy exceeding 75% (sensitivity, 83%, and specificity, 68%), which is well comparable with the state-of-the-art MCI conversion prediction approaches. Experimental results indicate that the 3D-ZM method can represent informative statistical patterns from 3D-MRI scans and IDPSO has a great capability to find meaningful statistical features for identifying MCI patients who are at risk of conversion to the AD stage.

A Data-Driven Intelligent Prediction Approach for Collision Responses of Honeycomb Reinforced Pipe Pile of the Offshore Platform

The potential collision between the ship and the pipe piles of the jacket structure brings huge risks to the safety of an offshore platform. Due to their high energy-absorbing capacity, honeycomb structures have been widely used as impact protectors in various engineering applications. This paper proposes a data-driven intelligent approach for the prediction of the collision response of honeycomb-reinforced structures under ship collision. In the proposed model, the artificial neural network (ANN) is combined with the dynamic particle swarm optimization (DPSO) algorithm to predict the collision responses of honeycomb reinforced pipe piles, including the maximum collision depth (δmax) and maximum absorption energy (Emax). Furthermore, a data-driven evaluation method, known as grey relational analysis (GRA), is proposed to evaluate the collision responses of the honeycomb-reinforced pipe piles of offshore platforms. Results of the case study demonstrate the accuracy of the DPSO-BP-ANN model, with measured mean-square-error (MSE) of 5.06 × 10−4 and 4.35 × 10−3 and R2 of 0.9906 and 0.9963 for δmax and Emax, respectively. It is shown that the GRA method can provide a comprehensive evaluation of the performance of a honeycomb structure under impact loads. The proposed model provides a robust and efficient assessment tool for the safe design of offshore platforms under ship collisions.

Optimal control of sewage treatment process using a dynamic multi-objective particle swarm optimization based on crowding distance

A variety of multi-objective optimization algorithms has been extensively investigated in the past decades to tackle the optimal decision of sewage treatment process. However, achieving the ideal solutions is challenging in the multi-criteria decision-making process from Pareto optimal sets due to the complicated relationships among influencing factors, especially in the case of large decision variables involved in the wastewater treatment process. We thus proposed an improved dynamic multi-objective particle swarm optimization algorithm based on crowding distance (DMOPSO-CD) to obtain global optimal solutions for the balance between energy consumption (EC) and effluent quality (EQ) in sewage treatment processes. The algorithm consists of optimization modules and a self-organizing fuzzy neural network, improving the global searching ability of particles, maintaining the diversity of non-inferior solutions, and solving the multi-objective vital issues in the optimization of sewage treatment process. The proposed optimization algorithm was applied to benchmark simulation model No.1, and the optimization results showed that the EC for wastewater treatment in dry, rainy, and storm weather was reduced by 7.87%, 6.28%, and 7.30%, respectively. This methodology outperformed several widely applied algorithms, including the multi-objective cuckoo search, non-dominated sorting genetic algorithm-II, and improving Pareto evolutionary algorithm in terms of EQ and EC, which opens a new window for the optimal decision of sewage treatment.

Kinematic parameters calibration of industrial robot based on RWS-PSO algorithm

The positioning accuracy of an industrial robot has a significant impact on its application in precision manufacturing, and it is necessary to calibrate robot kinematic parameters. Previous studies have established numerous nonlinear equations to solve the kinematic parameters, which are complicated and time consuming. A standard particle swarm optimization (PSO) algorithm is limited by long running time and low solution efficiency. Therefore, in this study, a dynamic particle swarm optimization algorithm based on roulette wheel selection (RWS-PSO) is proposed to realize the kinematic parameters calibration. First, a kinematics model is constructed using the standard Denavit-Hartenberg (D-H) method, and the theoretical and actual values of the spatial position of the robot endpoint are obtained via forward kinematics and a Laser Tracker, respectively. Next, the kinematic parameters calibration problem is transformed into a solution of a high-dimensional nonlinear equation using the proposed RWS-PSO algorithm. In the proposed RWS-PSO algorithm, the inertia factor is considered as linearly decreasing and the number of particles is selected by the roulette wheel selection (RWS) to improve its computational efficiency. The proposed RWS-PSO and standard PSO algorithms are compared based on various indices by simulation. The results reveal that the time cost of the RWS-PSO algorithm is much lower than that of the standard PSO algorithm on the basis of high precision and a reduced running time of approximately 53%. Finally, the kinematic parameter errors obtained by the two algorithms are compensated. According to the experimental results, the positioning accuracy of the robot in three ( x-, y-, and z-) directions is improved by 78%, 46%, and 67%, respectively, compared to that of before compensation, which proves that the RWS-PSO algorithm is effective and practical for kinematic parameters calibration.

An improved algorithm for resolving overlapping peaks in ion mobility spectrometry and its application to the separation of glycan isomers.

Despite the popularity of ion mobility spectrometry (IMS) for glycan analysis, its limited structural resolution hinders the effective separation of many glycan isomers. This leads to the overlap of IMS peaks, consequently impacting the accurate identification of glycan compositions. To this end, an improved algorithm, namely second-order differentiation combined with a simulated annealing particle swarm optimization algorithm based on sine adaptive weights (DWSA-PSO), was proposed for the separation of overlapping IMS peaks formed by glycan isomers. DWSA-PSO first performed second-order differentiation to automatically determine the number of components in overlapping peaks and exclude impossible single-peak combinations. It then introduced sinusoidal adaptive weights and a simulated annealing mechanism to improve the algorithm's search capability and global optimization performance, thereby enabling accurate and efficient separation of individual peaks. To evaluate the performance of DWSA-PSO and its application to the separation of glycan isomers, multiple sets of overlapping peaks with different degrees of overlap were simulated, and various types of multi-component overlapping peaks were formed using six disaccharide and four trisaccharide isomers. The experimental results consistently demonstrated that the DWSA-PSO algorithm outperformed both the improved particle swarm optimization (IPSO) algorithm and the dynamic inertia weight particle swarm optimization (DIWPSO) algorithm in terms of separation accuracy, running time, and fitness values. In addition, the DWSA-PSO algorithm was successfully applied to the separation of glycan isomers in malt milk beverage. All these results reveal the capability of the DWSA-PSO algorithm to facilitate the accurate identification of glycan isomers.

Two-step particle swarm optimization algorithm for effective deconvolution and resolution enhancement of various overlapping peaks.

The existing particle swarm optimization (PSO) algorithms are only effective in deconvoluting the overlapping peaks in ion mobility spectra with fewer than four component peaks, which limits the applicability of these algorithms. A high-performance two-step particle swarm optimization (TSPSO) algorithm was developed. Compared to the existing PSO algorithms, TSPSO can narrow the search ranges of all coefficients for the overlapping peaks through Gaussian model calculation, and thus can deconvolute various overlapping peaks with high accuracy, even for 30-component overlapping peaks. In addition, the TSPSO could be further applied to enhance the resolution of the spectra by narrowing the peak widths after the peak deconvolution. Simulated overlapping peaks were first used to evaluate the performance of TSPSO as compared to the dynamic inertia weight particle swarm optimization (DIWPSO) algorithm. The results showed that the profiles of the peaks deconvoluted by using TSPSO were more consistent with the original ones. The fitness values and the standard deviations of the fitness values from TSPSO were also at least an order of magnitude less than those from DIWPSO. By applying TSPSO, the overlapping peaks from both mass spectrometry (MS) and field asymmetric waveform ion mobility spectrometry (FAIMS) spectra can also be well deconvoluted. In addition, the resolutions of the MS and FAIMS spectra can be effectively enhanced after peak deconvolution. The enhanced spectra matched excellently with the experimental ones acquired at high-resolution modes. The experiment results convincingly demonstrate that the TSPSO algorithm is capable of both deconvoluting complex overlapping peaks and enhancing the spectrum resolution with high accuracy.