Two-objective Optimization Research Articles

The evaluation of hydraulic reliability indices in water distribution networks under pipe failure conditions

Abstract. In this research, reliability indicators of water distribution networks were evaluated under pipe failure conditions. The case studies included two benchmark networks and one real-life water distribution network in Iran with more hydraulic constraints. Some important reliability indicators were presented, such as resilience index, network resilience, modified resilience index, and minimum surplus head index. GANetXL was used to do the one-objective and two-objective optimization of the previously mentioned water distribution networks in order to not only minimize the cost but also maximize the reliability indicators. Moreover, the results of a statistical analysis for each pipe were used to determine the sensitive pipes that were of the most failure probability. GANetXL is an optimization tool in the Microsoft Excel environment and works based on a genetic algorithm. GANetXL has the capability of being linked to EPANET (hydraulic simulation software). The results obtained clearly showed that network resilience index was poor performance when compared with the other indexes under pipe failure conditions, especially in real-life networks that include small pipe diameters. It was also showed that if a water distribution network was optimized only in terms of cost, then there would be an unacceptable pressure drop at some nodes in case of pipe failure.

Energy and exergy analysis and multi-objective optimization of using combined vortex tube-photovoltaic/thermal system in city gate stations

The goal of this study is to investigate the possibility of replacing the water bath heater and pressure relief valve with a hybrid vortex tube-photovoltaic/thermal system in pressure reduction stations like city gate stations. By using this system, both the natural gas pressure can be reduced to the desired level (from 5-7 MPa to 1.5–2 MPa) and electricity can be generated. The effect of cold mass fraction of vortex tube (0.01–0.1), air mass flow rate (0.569–5.69 kg/s) as well as the length (1–10 m), width (0.5–5 m) and depth (0.1–0.5 m) of the photovoltaic/thermal system on the energy and exergy performance of the hybrid vortex tube-photovoltaic/thermal system is investigated. Then, the genetic algorithm based two-objective optimization is used to find the appropriate value of these parameters to maximize the annual average first-law efficiency (ηI) and second-law efficiency (ηII) of the hybrid system. It was found that the ηI and ηII of the optimal system are respectively 74.05% and 19.46%. Moreover, it was observed that the use of optimal system causes a reduction in the CO2 emission by 27.7-tons per year.

A Surrogate Model Based Multi-Objective Optimization Method for Optical Imaging System

An optimization model for the optical imaging system was established in this paper. It combined the modern design of experiments (DOE) method known as Latin hypercube sampling (LHS), Kriging surrogate model training, and the multi-objective optimization algorithm NSGA-III into the optimization of a triplet optical system. Compared with the methods that rely mainly on optical system simulation, this surrogate model-based multi-objective optimization method can achieve a high-accuracy result with significantly improved optimization efficiency. Using this model, case studies were carried out for two-objective optimizations of a Cooke triplet optical system. The results showed that the weighted geometric spot diagram and the maximum field curvature were reduced 5.32% and 11.59%, respectively, in the first case. In the second case, where the initial parameters were already optimized by Code-V, this model further reduced the weighted geometric spot diagram and the maximum field curvature by another 3.53% and 4.33%, respectively. The imaging quality in both cases was considerably improved compared with the initial design, indicating that the model is suitable for the optimal design of an optical system.

Power density characteristic analysis and multi-objective optimization of an irreversible porous medium engine cycle

Based on irreversible Porous Medium cycle model established in the previous literature, this paper investigates cycle optimal performance by taking cycle power density as optimization objective and applying finite time thermodynamics. Various parameters are used to examine relationships among power density and thermal efficiency versus compression ratio. The cycle performance is compared under maximum power density circumstance and maximum power output circumstance. Compared with condition of maximum power output, the Porous Medium cycle engine gets higher thermal efficiency and smaller size under the maximum power density condition. One-, two-, three- and four-objective optimizations of the cycle are performed by using NSGA-II algorithm, choosing compression ratio as design variable, and choosing dimensionless power density, dimensionless power output, thermal efficiency, and dimensionless ecological function as optimization objectives. Using three decision schemes, LINMAP, TOPSIS and Shannon entropy, deviation indices under different optimization objective combinations are compared. For six two-objective optimizations, power output and thermal efficiency optimization has the smallest deviation index, 0.1215. For four three-objective optimizations, power output, ecological function and power density optimization has the smallest deviation index, 0.1235. For four-objective optimization, the deviation index is 0.1419. The appropriate solution should be selected according to the actual application.

Systematic analysis and multi-objective optimization of an integrated power and freshwater production cycle

This study represents the results of the analysis and optimization of an integrated system for cogenerating electricity and freshwater. This setup consists of a Solid Oxide Fuel cell (SOFC) for producing electricity. Unburned fuel of the SOFC is burned in the afterburner to increase the temperature of the SOFC's outlet gasses and operate a Gas turbine (GT) to produce additional power and operate the air compressor. At the bottom of this cycle, a combined setup of a Multi-Effect Desalination (MED) and Reverse Osmosis (RO) is considered to produce freshwater from the unused heat capacity of the GT's exhaust gasses. Also, a Stirling engine is used in the fuel supply line to increase the fuel's temperature. Using LNG and the Stirling engine will replace the fuel compressor with a pump which increases the system performance and eliminates the need for the expansion valve. To study the system performance a mathematical model is developed in Engineering Equation Solver (EES) program. Then, the system's simulated data from the EES has been sent to MATLAB to promote the best operating condition based on the optimization criteria. An energetic, exergetic, economic, and environmental analysis has been performed and a Non-dominated Sorting Genetic Algorithm (NSGA-II) is used to achieve the goal. The two-objective optimization is performed to maximize the exergetic efficiency of the proposed system while minimizing the system's total cost of production. This cost is a weighted distribution of the Levelized Cost of Electricity (LCOE) and Levelized Cost of freshwater (LCOW). The results showed that the exergetic and energetic efficiencies of the system can reach 73.5% and 69.06% at the optimum point. The total electricity production of the system is 99 MW. The production cost is 11.71 Cents/kWh, of which 1.04 Cents/kWh is emission-related and environmental taxes. The freshwater production rate is 42.44 kg/s which costs 4.38 USD/m3.

Utilizing coke oven gases as a fuel for a cogeneration system based on high temperature proton exchange membrane fuel cell; energy, exergy and economic assessment

Based on a high temperature proton exchange membrane fuel cell (HT-PEMFC), a cogeneration system is proposed to produce heat and power. The system includes a coke oven gas steam reformer, a water gas shift reactor, and an afterburner. The system is analyzed in detail considering the energy, exergy and economic viewpoints. The analyses reveal the importance of HT-PEMFC in the system and according to the results, 9.03 kW power is generated with energy and exergy efficiencies of 88.2% and 26.2%, respectively and the total product unit cost is calculated as 91.8 $/GJ. Through a parametric study the effects on system performance are studied of such variables as the current density, fuel cell and reformer operating temperatures, and cathode stoichiometric ratio. It is found that an increase in the fuel cell temperature and/or a decrease in the reformer temperature enhance the exergy efficiency. The exergy efficiency is also maximized at the cathode stoichiometric ratio of 2.4. By performing a two-objective optimization using genetic algorithm, the best operating point is determined at which the exergy efficiency is (32.86%) and the total product unit cost is (78.68 $/GJ).

A novel two-objective optimization computational framework for a two-body heaving wave energy converter

The present research introduces a novel two-objective optimization computational framework, named H∞ optimization criterion-constrained Two-Objective Optimization Genetic Algorithm (H∞ − cTOOGA). Within this optimization framework, the objectives considered are: (i) the sprung mass isolation, and (ii) the wave energy extraction of a heaving buoy coupled with a sprung (overlying) mass. In such a two-body heaving wave energy converter (WEC), the satisfaction of both objectives is pursued by proper selection of the buoy geometry (i.e., radius r and draft Dr) and the characteristics of the power take-off (PTO). The interrelation among potential buoy geometries and PTO characteristics is performed on the basis of a critical condition. The critical condition refers to the formation of equal double peaks in the sprung mass acceleration response curve and is imposed as the sprung mass acceleration limit that is not allowed to be exceeded throughout the entire frequency range of interest. The two-objective optimization is realized with r, Dr and the tuning ratio δOPT being the decision variables. The value of δOPT is constrained by the value of the critical tuning ratio δcrit, that is, δOPT <δcrit. This ensures the minimization of the maximum sprung mass acceleration response. Then, the Pareto-optimal solutions result to optimal wave energy extraction.

Multi-objective optimizations and exergoeconomic analyses of a high-efficient bi-evaporator multigeneration system with freshwater unit

Due to the ubiquitous, cost-effective, and environmentally friendly characteristics of renewable energies, employing renewable energy sources has become an inevitable part of new-designed energy systems. In this regard, the present study proposes a multi-generation system with the potential of power, cooling, and freshwater production by utilizing geothermal and solar energies at the same time. The proposed system consists of two evaporators operating at above and below zero temperatures and a humidification and dehumidification desalination system for freshwater production. Along with the parametric evaluations based on thermodynamic and exergoeconomic perspectives, two-objective optimizations are conducted by employing the NSGA-II method. The results show that cooling capacity and energy efficiency increase by an increment of the temperature of the flashing separator, evaporator 1 and 2. Besides, increasing the temperature of evaporator 2 leads to lower hydrogen and net electricity production. The results indicate that the exergy-cost case of optimization correspondingly leads to exergy efficiency and overall unit cost of products of 20.82% and 0.144 $/kWh. Also, the maximum value of cooling is produced in the energy-cost optimization, when the objective function is the energy efficiency, which is equal to 848.9 kW with a 48.16% improvement compared to the base state.

A sustainable framework for multi-microgrids energy management in automated distribution network by considering smart homes and high penetration of renewable energy resources

This paper presents a new framework for the scheduling of microgrids and distribution feeder reconfiguration (DFR), taking into consideration the uncertainties due to the load demand, market price, and renewable power generation. The model is implemented on the modified IEEE 118-bus test system, including microgrids and smart homes. The problem has been formulated as a two-stage model, which at the first stage, the day-ahead self-scheduling of each microgrid is carried out as a two-objective optimization problem. The two objectives include the minimization of the total operating cost and maximization of the consumer's comfort index. Then, the solution, obtained from the first stage is delivered to the distribution system operator (DSO). Then, at the second stage, the DSO determines the optimal configuration of the system with the aim of minimizing operating costs of the main grid and the penalty of deviating from microgrid scheduling. Note that the penalty is due to the difference in power exchange requested by the microgrids from the power exchange finalized by the DSO. The presented two-stage optimization problem is modeled in a mixed-integer linear programing (MILP) framework with four case studies, and solved in GAMS by using the GURUBI solver. The simulation results show that in the cases the DSO is able to reconfigure the system, the deviation from the optimal scheduling of microgrids would be considerably lower than the cases with fixed system configuration. • Proposing a two-stage optimization framework for scheduling of microgrids and DFR. • Considering smart homes and traditional loads in the model. • Two-objective modeling of microgrids' scheduling problem by the fuzzy method. • Solving the DFR problem with regard to the optimal scheduling of microgrids. • Investigating the impact of different objective functions on smart homes' scheduling.

Multi-criteria thermodynamic analysis of pumped-thermal electricity storage with thermal integration and application in electric peak shaving of coal-fired power plant

The development of efficient energy storage systems to compensate for the intermittency of renewable energy sources has become a key step in the widespread use of renewable energies. Pumped-thermal electricity storage, which has drawn wide attention in recent years, has the advantages of being unlimited by geographical conditions, high energy storage density and low costs. In this paper, a heat pump – organic Rankine cycle (HP-ORC) based storage system integrated with waste heat has been developed and analyzed to find the suitable operation parameters for the existing coal-fired power plant. The systematic exergy loss is calculated and the trade-off optimization between roundtrip efficiency and exergy efficiency is also performed to find the Pareto Front. It is concluded that the exergy losses of the sensible and latent heat stores account for 35% and 31% of the total exergy loss, respectively; when the heat source temperature is 110 °C, the roundtrip efficiency can reach 1.26. Furthermore, the two-objective optimization results show that when heat source temperature and maximum storage pressure are designed to be 87.1 °C and 3.6 MPa, roundtrip efficiency and exergy efficiency can reach 0.97 and 0.64, respectively. Under the optimization results, the maximum peak shaving capacity of the coal-fired power plant integrating Carnot battery can reach 94.4%.

Hydrodynamic design of a circulating water channel based on a fractional-step multi-objective optimization

In this study, a multi-objective optimization of a circulating water channel (CWC) circuit was conducted to reduce the circuit's total pressure loss and limit the construction costs. The numerical optimization system was composed of an optimal Latin hypercube design (Opt LHD), a fast flexible space-filling design (FFF design), the Design Program for Wind Tunnels and Circulating Water Channels (DPWC), a support vector machine (SVM), a support vector regression (SVR), and a particle swarm optimization (PSO). To save simulation time, a simplified CWC model was proposed and verified to replace the complete CWC model. The optimization process was divided into two steps. In the first step, four design variables, including the casing's diameter, the diffuser's width ratio, the diffuser's height ratio, and the nozzle's area ratio, were selected to reshape the circuit, and an initial sample set for classification was constructed through CFD simulation. Then, a design subspace was extracted by an SVM to avoid flow separation in derivative CWCs. In the second step, a new sample set was constructed in the design subspace, and an SVR-based surrogate model was constructed based on it. Finally, the multi-objective optimization was performed within the design subspace. Optimization results showed that the CWC's total pressure loss was negatively correlated with the CWC's surface area. The optimal CWC circuit was selected from the Pareto front of two-objective optimization. Numerical results of the optimal CWC circuit showed that the total surface area increased by 7.5% while the total pressure loss significantly decreased by 19.3%, and that the residual hydrodynamic performance met the design requirements.

Techno-economical aspects of electrocoagulation optimization in three acid azo dyes’ removal comparison

This study compares the optimization models for three acid azo dyes removal by electrocoagulation (EC). First, Response Surface Methodology (RSM) models were evaluated and compared via four independent parameters, including initial pH (4–10), initial dye concentration (0–600 mg/L), current density (41.67–291.66 A/m2), and reaction time (3–15 min). Then, second-order polynomial equations of dye removal and operating cost models were separately applied as benefit and cost functions in the two-objective Imperialist Competitive Algorithm (ICA), respectively. According to the statistical analysis, not all the parameters are essential in removal efficiency for the three selected dyes. For example, the initial dye concentration and current density were the effective independent parameters in the Acid Red 18 removal model. According to the Pareto solutions, by changing the operating cost function from US$/m3 to US$/Kg removed dye, the difference between the Pareto curve points of Acid Brown 14 and Acid Orange 7 decreased significantly. Therefore, the unit of operating cost and dye type can affect the treatment policy in practice. The two-objective optimization showed an RSM deficit in predicting some corner points as previously depicted in RSM main effect plots.

A framework for calibration of self-piercing riveting process simulation model

This paper presents a framework that integrates machine learning and global sensitivity analysis to calibrate process simulation model of self-piercing rivet (SPR). In the present framework, surrogate models are trained to represent the intrinsic numerical relationship between selected model parameters (e.g., material properties, interface frictions, and clamping force) and cross-section dimensions of SPR joint obtained from simulation. Under the assistance of surrogate models, a global sensitivity analysis is performed to identify critical parameters that have significant effects on SPR joining process. Then, new surrogate models are trained to present the sensitive parameters and the cross- section dimensions obtained from process simulation. The parameter calibration of the simulation model is described as a two-objective optimization problem to minimize errors of key cross-section dimensions between simulation and experiment. Combined the newly trained surrogate models with genetic algorithm, the model parameters are calibrated efficiently. A case study of simultaneous calibration of four SPR process simulation models is used to illustrate the proposed framework and examine the effectiveness of the proposed framework. A good consistency is achieved between calibrated models and experiments.

Improvement on the cyclic thermal shock resistance of the electronics heat sinks using two-objective optimization

Phase change materials (PCMs) can isothermally absorb heat in electronic devices, and optimizing PCM heat sink designs to improve heat dissipation is therefore important to improve the performance of a system, including its ability to withstand cyclic thermal shocks. In this study, a low melting point alloy (LMPA)-based heat sink with crossed copper fins is developed and optimized to cope with cyclic ultra-high thermal shocks (100 W/cm²). Gallium is selected as an LMPA candidate due to its high thermal conductivity. The numerical model is validated against available experimental results where the transient temperature is predicted with a maximum discrepancy of 4.9%. The main goal of the study is to determine the design configurations that minimize the heat sink peak temperature after thermal shock and with minimal cooling time. An approach that couples the Response Surface Methodology (RSM) with numerical simulations is applied for this purpose. The height and thickness of fins and the PCM thickness, are treated as design variables in the two-objective optimization. Two correlations are presented to estimate the peak temperature and cooling period of the system in presence of thermal shock. The effect of the three parameters is thoroughly analysed following the optimization process. The optimum values for fin height, fin thickness and PCM thickness are found to be 8.77 mm, 0.55 mm, and 1.51 mm, respectively, where the PCM volumetric percentage is found to be 53.73%. Single-objective optimizations are also conducted to design a system satisfying a minimum peak temperature or minimum cooling period separately. Overall, the cyclic evaluation shows that the two-objective optimized heat sink delivers peak temperature up to 8.63% and 36.26% lower than that of single-objective optimized systems after five cycles of thermal shocks within periods of 30–60 s. This study shows how LMPA-based heat sink may be optimized and demonstrates a potential approach in the design of novel thermal management systems to prevent overheating from thermal shocks.

Parameter optimisation of sliding window algorithm based on ensemble multi-objective evolutionary computation

The parameters of sliding window algorithm are difficult to determine. Therefore, a sliding window-based method for parameter optimisation of data stream trend anomaly detection algorithm is proposed in this study. This method regards the data stream anomaly detection as a two-objective optimisation problem. Three optimisation algorithms and ensemble strategies were used to obtain the optimal parameter settings of the algorithm. With this strategy, it is no longer difficult to determine the parameters of the data stream trend anomaly detection algorithm based on the sliding window. Through verification of multiple real parameter data in Tarim Oilfield, it could be known that this method could realise the optimal parameter settings, which provides a reference for the parameter setting of the data stream trend anomaly detection algorithm based on sliding window.

An Integration Method for Regional PM2.5 Pollution Control Optimization Based on Meta-Analysis and Systematic Review.

PM2.5 pollution in China is becoming increasingly severe, threatening public health. The major goal of this study is to evaluate the mortality rate attributed to PM2.5 pollution and design pollution mitigation schemes in a southern district of China through a two-objective optimization model. The mortality rate is estimated by health effect evaluation model. Subjected to limited data information, it is assumed that the meta-analysis method, through summarizing and combining the research results on the same subject, was suitable to estimate the percentage of deaths caused by PM2.5 pollution. The critical parameters, such as the total number of deaths and the background concentration of PM2.5, were obtained through on-site survey, data collection, literature search, policy analysis, and expert consultation. The equations for estimating the number of deaths caused by PM2.5 pollution were established by incorporating the relationship coefficient of exposure to reaction, calculated residual PM2.5 concentration of affected region, and statistical total base number of deaths into a general framework. To balance the cost from air quality improvement and human health risks, a two-objective optimization model was developed. The first objective is to minimize the mortality rate attributable to PM2.5 pollution, and the second objective is to minimize the total system cost over three periods. The optimization results demonstrated that the combination of weights assigned to the two objectives significantly influenced the model output. For example, a high weight value assigned to minimizing the number of deaths results in the increased use of treatment techniques with higher efficiencies and a dramatic decrease in pollutant concentrations. In contrast, a model weighted more toward minimizing economic loss may lead to an increase in the death toll due to exposure to higher air pollution levels. The effective application of this model in the Nanshan District of Shenzhen City, China, is expected to serve as a basis for similar work in other parts of the world in the future.

Multi-objective optimization of acetone droplet impingement on phase change material in direct-contact discharge method

Improving the discharge process of phase change materials (PCMs) is of great importance and can be effective for thermal energy storage (TES) systems. In this research, the direct-contact method for acetone droplet on molten paraffin is optimized to enhance the efficiency of the discharge process of PCMs and TES systems working with intermediate boiling fluid (IBF). In order to improve the storage rate and increase the freezing rate in the system, the NSGA-II algorithm is used. When the acetone droplet hits, owing to its low boiling point relative to the temperature of molten paraffin, the acetone evaporates, causing the creation of solidified paraffin area. The main goal of the current investigation is to maximize the solid volume, which depends on two parameters: the Weber acetone droplet and the temperature of the molten paraffin. Furthermore, maximizing this volume is equivalent to increasing the freezing rate and decreasing the melting rate. For better discernibility, the relative sensitivities of solidified paraffin area and maximum crater depth to the variations in the dimensionless parameters of paraffin surface temperature and Weber number are obtained. In this regard, the experimental results are fitted by exponential functions. Two-objective optimization with the solidified paraffin area and maximum crater depth as cost functions are performed to be maximized. Moreover, uncertainties and tolerances are considered through performing a robust triple optimization. By using final decision makings (FDMs), the results are achieved from Pareto front through two methods, LINMAP (We = 1699.428, θ = 1.188) and TOPSIS (We = 1699.325, θ = 1.202). Based on the results, the solidified paraffin areas obtained by LINMAP and TOPSIS methods are 168.616 mm2 and 155.101 mm2, respectively.

Multiobjective optimal design of reinforced concrete frames using two metaheuristic algorithms

Genetic algorithm (GA) and differential evolution (DE) are metaheuristic algorithms that have shown a favorable performance in the optimization of complex problems. In recent years, only GA has been widely used for single-objective optimal design of reinforced concrete (RC) structures; however, it has been applied for multiobjective optimization of steel structures. In this article, the total structural cost and the roof displacement are considered as objective functions for the optimal design of the RC frames. Using the weighted sum method (WSM) approach, the two-objective optimization problem is converted to a single-objective optimization problem. The size of the beams and columns are considered as design variables, and the design requirements of the ACI-318 are employed as constraints. Five numerical models are studied to test the efficiency of the GA and DE algorithms. Pareto front curves are obtained for the building models using both algorithms. The detailed results show the accuracy and convergence speed of the algorithms.

Thermodynamic Analysis, Advanced Non-Linear Dynamic Simulation and Multi-Criteria Optimization of a 100 MW Parabolic Trough Solar Steam Power Plant

Thermodynamic analyses of concentrating solar power plants and optimizing these cycles relying on the energetic and exergetic optimal efficiencies are quite common. However, it is found that just considering the efficiency of the system for performance optimization and neglecting the adverse effects of the plant's wrong operation timings, which is a function of the solar working fluid flow rate, can easily give misleading optimization results. This study's primary goal is to find the optimal operating point of the cycle in terms of the thermodynamic efficiencies considering the system's operating time. Thus, the Sliding Mode Control (SMC) approach is employed to provide a proper mass flow rate for the working fluid from the solar collector field to achieve a precise output temperature from the collectors in different operating conditions. Multi-objective optimization is performed using the Particle Swarm Optimization (PSO) algorithm. The results of power block sensitivity analysis indicate that a 70℃ increase in the solar collector outlet temperature remarkably enhances electricity generation and exergetic efficiency by 67 and 48%. The two-objective optimization shows 22.01%, 2.10%, and 5.46% enhancement in response time, thermal efficiency, and exergetic efficiency, and the three-objective optimization reveals 3.68% and 3.74% improvement in efficiency (thermal and exergetic), respectively.

A novel noise reduction method for natural gas pipeline defect detection signals

Since pipeline defect detection signals are often contaminated by noise, the accuracy of defect identification is reduced if inappropriate noise reduction methods are used. Therefore, the noise reduction of pipeline detection signals is critical for pipeline defect detection preprocessing technology. A denoising method based on differential-based empirical mode decomposition (DEMD) and extremum field mean mode decomposition (EMMD) is proposed in this paper and named derivative extremum field mean mode decomposition (DEMMD). The idea of DEMMD is to replace the EMD part of DEMD with EMMD. To simultaneously reduce the interference of noise and retain useful signal features, intrinsic mode function (IMF) reconstruction is viewed as a two-objective optimization problem. The objective function is constructed by a similarity measure based on a probability density function and a complexity measure based on fuzzy entropy. Monte Carlo simulations are performed to simulate the possible IMF component combinations. Then, based on the idea of a Pareto optimal solution, the IMF components that satisfy the optimization objective are selected to construct the denoised signal. Synthetic signal and field test data are used to verify the proposed method. The denoising results of the synthetic signal show that the method can decompose the main characteristic modes of defect signals and effectively recover the original signal. The results of a case study show that the denoised signal obtained by this method can not only suppress noise but also retain the defect details during reconstruction. The signal-to-noise ratio (SNR) and root mean square error (RMSE) are used to measure and compare the performance of the proposed method. The results show that the SNR of the proposed method is the highest, which is 29.1207, and the RSME is the lowest, which is 0.0045. Compared with other traditional denoised methods, it outperforms and suits pipeline detection signal denoising.