Optimized parameters of downhole all-metal PDM based on genetic algorithm

Currently,deep drilling operates under extreme conditions of high temperature and high pressure,demanding more from subterranean power motors.The all-metal positive displacement motor,known for its robust performance,is a critical choice for such drilling.The dimensions of the PDM are crucial for its performance output.To enhance this,optimization of the motor's profile using a genetic algorithm has been undertaken.The design process begins with the computation of the initial stator and rotor curves based on the equations for a screw cycloid.These curves are then refined using the least squares method for a precise fit.Following this,the PDM's mathematical model is optimized,and motor friction is assessed.The genetic algorithm process involves encoding variations and managing crossovers to optimize objective functions,including the isometric radius coefficient,eccentricity distance parameter,overflow area,and maximum slip speed.This optimization yields the ideal profile parameters that enhance the motor's output.Comparative analyses of the initial and optimized output characteristics were conducted,focusing on the effects of the isometric radius coefficient and overflow area on the motor's performance.Results indicate that the optimized motor's overflow area increased by 6.9%,while its rotational speed reduced by 6.58%.The torque,as tested by Infocus,saw substantial improvements of38.8%.This optimization provides a theoretical foundation for improving the output characteristics of allmetal PDMs and supports the ongoing development and research of PDM technology.

Maximum Power Point Tracking Based on Improved Kepler Optimization Algorithm and Optimized Perturb&Observe under Partial Shading Conditions

Under the partial shading conditions(PSC)of Photovoltaic(PV)modules in a PV hybrid system,the power output curve exhibits multiple peaks.This often causes traditional maximum power point tracking(MPPT)methods to fall into local optima and fail to find the global optimum.To address this issue,a composite MPPT algorithm is proposed.It combines the improved kepler optimization algorithm(IKOA)with the optimized variable-step perturb and observe(OIP&O).The update probabilities,planetary velocity and position step coefficients of IKOA are nonlinearly and adaptively optimized.This adaptation meets the varying needs of the initial and later stages of the iterative process and accelerates convergence.During stochastic exploration,the refined position update formulas enhance diversity and global search capability.The improvements in the algorithmreduces the likelihood of falling into local optima.In the later stages,the OIP&O algorithm decreases oscillation and increases accuracy.compared with cuckoo search(CS)and gray wolf optimization(GWO),simulation tests of the PV hybrid inverter demonstrate that the proposed IKOA-OIP&O algorithm achieves faster convergence and greater stability under static,local and dynamic shading conditions.These results can confirm the feasibility and effectiveness of the proposed PV MPPT algorithm for PV hybrid systems.

Optimized scheduling of integrated energy systems for low carbon economy considering carbon transaction costs

With the introduction of the“dual carbon”goal and the continuous promotion of low-carbon development,the integrated energy system(IES)has gradually become an effective way to save energy and reduce emissions.This study proposes a low-carbon economic optimization scheduling model for an IES that considers carbon trading costs.With the goal of minimizing the total operating cost of the IES and considering the transferable and curtailable characteristics of the electric and thermal flexible loads,an optimal scheduling model of the IES that considers the cost of carbon trading and flexible loads on the user side was established.The role of flexible loads in improving the economy of an energy system was investigated using examples,and the rationality and effectiveness of the study were verified through a comparative analysis of different scenarios.The results showed that the total cost of the system in different scenarios was reduced by 18.04%,9.1%,3.35%,and 7.03%,respectively,whereas the total carbon emissions of the system were reduced by 65.28%,20.63%,3.85%,and 18.03%,respectively,when the carbon trading cost and demand-side flexible electric and thermal load responses were considered simultaneously.Flexible electrical and thermal loads did not have the same impact on the system performance.In the analyzed case,the total cost and carbon emissions of the system when only the flexible electrical load response was considered were lower than those when only the flexible thermal load response was taken into account.Photovoltaics have an excess of carbon trading credits and can profit from selling them,whereas other devices have an excess of carbon trading and need to buy carbon credits.

Phase-Based Optical Flow Method with Optimized Parameter Settings for Enhancing Displacement Measurement Adaptability

To enhance the applicability and measurement accuracy of phase-based optical flow method using complex steerable pyramids in structural displacement measurement engineering applications, an improved method of optimizing parameter settings is proposed. The optimized parameters include the best measurement points of the Region of Interest (ROI) and the levels of pyramid filters. Additionally, to address the issue of updating reference frames in practical applications due to the difficulty in estimating the maximum effective measurement value, a mechanism for dynamically updating reference frames is introduced. Experimental results demonstrate that compared to representative image gradient-based displacement measurement methods, the proposed method exhibits higher measurement accuracy in engineering applications. This provides reliable data support for structural damage identification research based on vibration signals and is expected to broaden the engineering application prospects for structural health monitoring.

An Optimized System of Random Forest Model by Global Harmony Search with Generalized Opposition-Based Learning for Forecasting TBM Advance Rate

As massive underground projects have become popular in dense urban cities,a problem has arisen:which model predicts the best for Tunnel Boring Machine(TBM)performance in these tunneling projects?However,performance level of TBMs in complex geological conditions is still a great challenge for practitioners and researchers.On the other hand,a reliable and accurate prediction of TBM performance is essential to planning an applicable tunnel construction schedule.The performance of TBM is very difficult to estimate due to various geotechnical and geological factors and machine specifications.The previously-proposed intelligent techniques in this field are mostly based on a single or base model with a low level of accuracy.Hence,this study aims to introduce a hybrid randomforest(RF)technique optimized by global harmony search with generalized oppositionbased learning(GOGHS)for forecasting TBM advance rate(AR).Optimizing the RF hyper-parameters in terms of,e.g.,tree number and maximum tree depth is the main objective of using the GOGHS-RF model.In the modelling of this study,a comprehensive databasewith themost influential parameters onTBMtogetherwithTBM AR were used as input and output variables,respectively.To examine the capability and power of the GOGHSRF model,three more hybrid models of particle swarm optimization-RF,genetic algorithm-RF and artificial bee colony-RF were also constructed to forecast TBM AR.Evaluation of the developed models was performed by calculating several performance indices,including determination coefficient(R2),root-mean-square-error(RMSE),and mean-absolute-percentage-error(MAPE).The results showed that theGOGHS-RF is a more accurate technique for estimatingTBMAR compared to the other applied models.The newly-developedGOGHS-RFmodel enjoyed R2=0.9937 and 0.9844,respectively,for train and test stages,which are higher than a pre-developed RF.Also,the importance of the input parameters was interpreted through the SHapley Additive exPlanations(SHAP)method,and it was found that thrust force per cutter is the most important variable on TBMAR.The GOGHS-RF model can be used in mechanized tunnel projects for predicting and checking performance.

Towards the performance limit of catenary meta-optics via field-driven optimization

Catenary optics enables metasurfaces with higher efficiency and wider bandwidth,and is highly anticipated in the imaging system,super-resolution lithography,and broadband absorbers.However,the periodic boundary approximation without considering aperiodic electromagnetic crosstalk poses challenges for catenary optical devices to reach their performance limits.Here,perfect control of both local geometric and propagation phases is realized through field-driven optimization,in which the field distribution is calculated under real boundary conditions.Different from other optimization methods requiring a mass of iterations,the proposed design method requires less than ten iterations to get the efficiency close to the optimal value.Based on the library of shape-optimized catenary structures,centimeter-scale devices can be designed in ten seconds,with the performance improved by ~15%.Furthermore,this method has the ability to extend catenary-like continuous structures to arbitrary polarization,including both linear and elliptical polarizations,which is difficult to achieve with traditional design methods.It provides a way for the development of catenary optics and serves as a potent tool for constructing high-performance optical devices.

Optimized sequential therapy vs 10- and 14-d concomitant therapy for eradicating Helicobacter pylori: A randomized clinical trial

BACKGROUND A cure for Helicobacter pylori(H.pylori)remains a problem of global concern.The prevalence of antimicrobial resistance is widely rising and becoming a challenging issue worldwide.Optimizing sequential therapy seems to be one of the most attractive strategies in terms of efficacy,tolerability and cost.The most common sequential therapy consists of a dual therapy[proton-pump inhibitors(PPIs)and amoxicillin]for the first period(5 to 7 d),followed by a triple therapy for the second period(PPI,clarithromycin and metronidazole).PPIs play a key role in maintaining a gastric pH at a level that allows an optimal efficacy of antibiotics,hence the idea of using new generation molecules.This open-label prospective study randomized 328 patients with confirmed H.pylori infection into three groups(1:1:1):The first group received quadruple therapy consisting of twice-daily(bid)omeprazole 20 mg,amoxicillin 1 g,clarith-romycin 500 mg and metronidazole 500 mg for 10 d(QT-10),the second group received a 14 d quadruple therapy following the same regimen(QT-14),and the third group received an optimized sequential therapy consisting of bid rabe-prazole 20 mg plus amoxicillin 1 g for 7 d,followed by bid rabeprazole 20 mg,clarithromycin 500 mg and metronidazole 500 mg for the next 7 d(OST-14).AEs were recorded throughout the study,and the H.pylori eradication rate was determined 4 to 6 wk after the end of treatment,using the 13C urea breath test.RESULTS In the intention-to-treat and per-protocol analysis,the eradication rate was higher in the OST-14 group compared to the QT-10 group:(93.5%,85.5%P=0.04)and(96.2%,89.5%P=0.03)respectively.However,there was no statist-ically significant difference in eradication rates between the OST-14 and QT-14 groups:(93.5%,91.8%P=0.34)and(96.2%,94.4%P=0.35),respectively.The overall incidence of AEs was significantly lower in the OST-14 group(P=0.01).Furthermore,OST-14 was the most cost-effective among the three groups.CONCLUSION The optimized 14-d sequential therapy is a safe and effective alternative.Its eradication rate is comparable to that of the 14-d concomitant therapy while causing fewer AEs and allowing a gain in terms of cost.

Advanced Optimized Anomaly Detection System for IoT Cyberattacks Using Artificial Intelligence

While emerging technologies such as the Internet of Things(IoT)have many benefits,they also pose considerable security challenges that require innovative solutions,including those based on artificial intelligence(AI),given that these techniques are increasingly being used by malicious actors to compromise IoT systems.Although an ample body of research focusing on conventional AI methods exists,there is a paucity of studies related to advanced statistical and optimization approaches aimed at enhancing security measures.To contribute to this nascent research stream,a novel AI-driven security system denoted as“AI2AI”is presented in this work.AI2AI employs AI techniques to enhance the performance and optimize security mechanisms within the IoT framework.We also introduce the Genetic Algorithm Anomaly Detection and Prevention Deep Neural Networks(GAADPSDNN)sys-tem that can be implemented to effectively identify,detect,and prevent cyberattacks targeting IoT devices.Notably,this system demonstrates adaptability to both federated and centralized learning environments,accommodating a wide array of IoT devices.Our evaluation of the GAADPSDNN system using the recently complied WUSTL-IIoT and Edge-IIoT datasets underscores its efficacy.Achieving an impressive overall accuracy of 98.18%on the Edge-IIoT dataset,the GAADPSDNN outperforms the standard deep neural network(DNN)classifier with 94.11%accuracy.Furthermore,with the proposed enhancements,the accuracy of the unoptimized random forest classifier(80.89%)is improved to 93.51%,while the overall accuracy(98.18%)surpasses the results(93.91%,94.67%,94.94%,and 94.96%)achieved when alternative systems based on diverse optimization techniques and the same dataset are employed.The proposed optimization techniques increase the effectiveness of the anomaly detection system by efficiently achieving high accuracy and reducing the computational load on IoT devices through the adaptive selection of active features.

Product quality prediction based on RBF optimized by firefly algorithm

With the development of information technology,a large number of product quality data in the entire manufacturing process is accumulated,but it is not explored and used effectively.The traditional product quality prediction models have many disadvantages,such as high complexity and low accuracy.To overcome the above problems,we propose an optimized data equalization method to pre-process dataset and design a simple but effective product quality prediction model:radial basis function model optimized by the firefly algorithm with Levy flight mechanism(RBFFALM).First,the new data equalization method is introduced to pre-process the dataset,which reduces the dimension of the data,removes redundant features,and improves the data distribution.Then the RBFFALFM is used to predict product quality.Comprehensive expe riments conducted on real-world product quality datasets validate that the new model RBFFALFM combining with the new data pre-processing method outperforms other previous me thods on predicting product quality.

Multi-objective optimization and evaluation of supercritical CO_(2) Brayton cycle for nuclear power generation

The supercritical CO_(2) Brayton cycle is considered a promising energy conversion system for Generation IV reactors for its simple layout,compact structure,and high cycle efficiency.Mathematical models of four Brayton cycle layouts are developed in this study for different reactors to reduce the cost and increase the thermohydraulic performance of nuclear power generation to promote the commercialization of nuclear energy.Parametric analysis,multi-objective optimizations,and four decision-making methods are applied to obtain each Brayton scheme’s optimal thermohydraulic and economic indexes.Results show that for the same design thermal power scale of reactors,the higher the core’s exit temperature,the better the Brayton cycle’s thermo-economic performance.Among the four-cycle layouts,the recompression cycle(RC)has the best overall performance,followed by the simple recuperation cycle(SR)and the intercooling cycle(IC),and the worst is the reheating cycle(RH).However,RH has the lowest total cost of investment(C_(tot))of$1619.85 million,and IC has the lowest levelized cost of energy(LCOE)of 0.012$/(kWh).The nuclear Brayton cycle system’s overall performance has been improved due to optimization.The performance of the molten salt reactor combined with the intercooling cycle(MSR-IC)scheme has the greatest improvement,with the net output power(W_(net)),thermal efficiencyη_(t),and exergy efficiency(η_(e))improved by 8.58%,8.58%,and 11.21%,respectively.The performance of the lead-cooled fast reactor combined with the simple recuperation cycle scheme was optimized to increase C_(tot) by 27.78%.In comparison,the internal rate of return(IRR)increased by only 7.8%,which is not friendly to investors with limited funds.For the nuclear Brayton cycle,the molten salt reactor combined with the recompression cycle scheme should receive priority,and the gas-cooled fast reactor combined with the reheating cycle scheme should be considered carefully.

Enhancing Renewable Energy Integration:A Gaussian-Bare-Bones Levy Cheetah Optimization Approach to Optimal Power Flow in Electrical Networks

In the contemporary era,the global expansion of electrical grids is propelled by various renewable energy sources(RESs).Efficient integration of stochastic RESs and optimal power flow(OPF)management are critical for network optimization.This study introduces an innovative solution,the Gaussian Bare-Bones Levy Cheetah Optimizer(GBBLCO),addressing OPF challenges in power generation systems with stochastic RESs.The primary objective is to minimize the total operating costs of RESs,considering four functions:overall operating costs,voltage deviation management,emissions reduction,voltage stability index(VSI)and power loss mitigation.Additionally,a carbon tax is included in the objective function to reduce carbon emissions.Thorough scrutiny,using modified IEEE 30-bus and IEEE 118-bus systems,validates GBBLCO’s superior performance in achieving optimal solutions.Simulation results demonstrate GBBLCO’s efficacy in six optimization scenarios:total cost with valve point effects,total cost with emission and carbon tax,total cost with prohibited operating zones,active power loss optimization,voltage deviation optimization and enhancing voltage stability index(VSI).GBBLCO outperforms conventional techniques in each scenario,showcasing rapid convergence and superior solution quality.Notably,GBBLCO navigates complexities introduced by valve point effects,adapts to environmental constraints,optimizes costs while considering prohibited operating zones,minimizes active power losses,and optimizes voltage deviation by enhancing the voltage stability index(VSI)effectively.This research significantly contributes to advancing OPF,emphasizing GBBLCO’s improved global search capabilities and ability to address challenges related to local minima.GBBLCO emerges as a versatile and robust optimization tool for diverse challenges in power systems,offering a promising solution for the evolving needs of renewable energy-integrated power grids.

Determination of the Pile Drivability Using Random Forest Optimized by Particle Swarm Optimization and Bayesian Optimizer

Driven piles are used in many geological environments as a practical and convenient structural component.Hence,the determination of the drivability of piles is actually of great importance in complex geotechnical applications.Conventional methods of predicting pile drivability often rely on simplified physicalmodels or empirical formulas,whichmay lack accuracy or applicability in complex geological conditions.Therefore,this study presents a practical machine learning approach,namely a Random Forest(RF)optimized by Bayesian Optimization(BO)and Particle Swarm Optimization(PSO),which not only enhances prediction accuracy but also better adapts to varying geological environments to predict the drivability parameters of piles(i.e.,maximumcompressive stress,maximum tensile stress,and blow per foot).In addition,support vector regression,extreme gradient boosting,k nearest neighbor,and decision tree are also used and applied for comparison purposes.In order to train and test these models,among the 4072 datasets collected with 17model inputs,3258 datasets were randomly selected for training,and the remaining 814 datasets were used for model testing.Lastly,the results of these models were compared and evaluated using two performance indices,i.e.,the root mean square error(RMSE)and the coefficient of determination(R2).The results indicate that the optimized RF model achieved lower RMSE than other prediction models in predicting the three parameters,specifically 0.044,0.438,and 0.146;and higher R^(2) values than other implemented techniques,specifically 0.966,0.884,and 0.977.In addition,the sensitivity and uncertainty of the optimized RF model were analyzed using Sobol sensitivity analysis and Monte Carlo(MC)simulation.It can be concluded that the optimized RF model could be used to predict the performance of the pile,and it may provide a useful reference for solving some problems under similar engineering conditions.

Fixed-Time Cluster Optimization for Multi-Agent Systems Based on Piecewise Power-Law Design

Dear Editor,This letter focuses on the fixed-time(FXT)cluster optimization problem of first-order multi-agent systems(FOMASs)in an undirected network,in which the optimization objective is the sum of the objective functions of all clusters.A novel piecewise power-law control protocol with cooperative-competition relations is proposed.Furthermore,a sufficient condition is obtained to ensure that the FOMASs achieve the cluster consensus within an FXT.

A Special Issue“Planning and Optimal Operation of New-Type Power System”of Global Energy Interconnection

The power system,as an energy hub,plays a crucial role in the transformation of energy production and consumption.On July 19,2023,the International Energy Agency(IEA)released a Global Electricity Market Report for 2023-2024.This report indicates that the development of the world’s energy production is rapidly moving towards the critical point where the proportion of electricity generated from renewable sources surpasses that from non-renewable sources.

Retraction:Optimized Design of Bio-inspired Wind Turbine Blades

The published article titled“Optimized Design of Bio-inspired Wind Turbine Blades”has been retracted from Fluid Dynamics&Materials Processing.

Wellbore-heat-transfer-model-based optimization and control for cooling downhole drilling fluid

To address the two critical issues of evaluating the necessity of implementing cooling techniques and achieving real-time temperature control of drilling fluids underground in the current drilling fluid cooling technology,we first established a temperature and pressure coupled downhole heat transfer model,which can be used in both water-based and oil-based drilling fluid.Then,fourteen factors,which could affect wellbore temperature,were analyzed.Based on the standard deviation of the downhole temperature corresponding to each influencing factor,the influence of each factor was quantified.The influencing factors that can be used to guide the drilling fluid's cooling technology were drilling fluid thermal conductivity,drilling fluid heat capacity,drilling fluid density,drill strings rotation speed,pump rate,viscosity,ROP,and injection temperature.The nondominated sorting genetic algorithm was used to optimize these six parameters,but the optimization process took 182 min.Combining these eight parameters'influence rules with the nondominated sorting genetic algorithm can reduce the optimization time to 108 s.Theoretically,the downhole temperature has been demonstrated to increase with the inlet temperature increasing linearly under quasi-steady states.Combining this law and PID,the downhole temperature can be controlled,which can reduce the energy for cooling the surface drilling fluid and can ensure the downhole temperature reaches the set value as soon as possible.

Optimized Phishing Detection with Recurrent Neural Network and Whale Optimizer Algorithm

Phishing attacks present a persistent and evolving threat in the cybersecurity land-scape,necessitating the development of more sophisticated detection methods.Traditional machine learning approaches to phishing detection have relied heavily on feature engineering and have often fallen short in adapting to the dynamically changing patterns of phishingUniformResource Locator(URLs).Addressing these challenge,we introduce a framework that integrates the sequential data processing strengths of a Recurrent Neural Network(RNN)with the hyperparameter optimization prowess of theWhale Optimization Algorithm(WOA).Ourmodel capitalizes on an extensive Kaggle dataset,featuring over 11,000 URLs,each delineated by 30 attributes.The WOA’s hyperparameter optimization enhances the RNN’s performance,evidenced by a meticulous validation process.The results,encapsulated in precision,recall,and F1-score metrics,surpass baseline models,achieving an overall accuracy of 92%.This study not only demonstrates the RNN’s proficiency in learning complex patterns but also underscores the WOA’s effectiveness in refining machine learning models for the critical task of phishing detection.

A reduced combustion mechanism of ammonia/diesel optimized with multi-objective genetic algorithm

For the deep understanding on combustion of ammonia/diesel,this study develops a reduced mechanism of ammonia/diesel with 227 species and 937 reactions.The sub-mechanism on ammonia/interactions of N-based and C-based species(N—C)/NOx is optimized using the Non-dominated Sorting Genetic Algorithm II(NSGA-II)with 200 generations.The optimized mechanism(named as 937b)is validated against combustion characteristics of ammonia/methane(which is used to examine the accuracy of N—C interactions)and ammonia/diesel blends.The ignition delay times(IDTs),the laminar flame speeds and most of key intermediate species during the combustion of ammonia/methane blends can be accurately simulated by 937b under a wide range of conditions.As for ammonia/diesel blends with various diesel energy fractions,reasonable predictions on the IDTs under pressures from 1.0 MPa to5.0 MPa as well as the laminar flame speeds are also achieved by 937b.In particular,with regard to the IDT simulations of ammonia/diesel blends,937b makes progress in both aspects of overall accuracy and computational efficiency,compared to a detailed ammonia/diesel mechanism.Further kinetic analysis reveals that the reaction pathway of ammonia during the combustion of ammonia/diesel blend mainly differs in the tendencies of oxygen additions to NH_2 and NH with different equivalence ratios.

Enhancing photovoltaic power prediction using a CNN-LSTM-attention hybrid model with Bayesian hyperparameter optimization

Improving the accuracy of solar power forecasting is crucial to ensure grid stability,optimize solar power plant operations,and enhance grid dispatch efficiency.Although hybrid neural network models can effectively address the complexities of environmental data and power prediction uncertainties,challenges such as labor-intensive parameter adjustments and complex optimization processes persist.Thus,this study proposed a novel approach for solar power prediction using a hybrid model(CNN-LSTM-attention)that combines a convolutional neural network(CNN),long short-term memory(LSTM),and attention mechanisms.The model incorporates Bayesian optimization to refine the parameters and enhance the prediction accuracy.To prepare high-quality training data,the solar power data were first preprocessed,including feature selection,data cleaning,imputation,and smoothing.The processed data were then used to train a hybrid model based on the CNN-LSTM-attention architecture,followed by hyperparameter optimization employing Bayesian methods.The experimental results indicated that within acceptable model training times,the CNN-LSTM-attention model outperformed the LSTM,GRU,CNN-LSTM,CNN-LSTM with autoencoders,and parallel CNN-LSTM attention models.Furthermore,following Bayesian optimization,the optimized model demonstrated significantly reduced prediction errors during periods of data volatility compared to the original model,as evidenced by MRE evaluations.This highlights the clear advantage of the optimized model in forecasting fluctuating data.

Thiourea crystal growth kinetics,mechanism and process optimization during cooling crystallization

In the cooling crystallization process of thiourea,a significant issue is the excessively wide crystal size distribution(CSD)and the abundance of fine crystals.This investigation delves into the growth kinetics and mechanisms governing thiourea crystals during the cooling crystallization process.The fitting results indicate that the crystal growth rate coefficient,falls within the range of 10^(-7)to 10^(-8)m·s^(-1).Moreover,with decreasing crystallization temperature,the growth process undergoes a transition from diffusion-controlled to surface reaction-controlled,with temperature primarily influencing the surface reaction process and having a limited impact on the diffusion process.Comparing the crystal growth rate,and the diffusion-limited growth rate,at different temperatures,it is observed that the crystal growth process can be broadly divided into two stages.At temperatures above 25℃,1/qd(qd is diffusion control index)approaches 1,indicating the predominance of diffusion control.Conversely,at temperatures below 25℃,1/qd increases rapidly,signifying the dominance of surface reaction control.To address these findings,process optimization was conducted.During the high-temperature phase(35-25℃),agitation was increased to reduce the limitations posed by bulk-phase diffusion in the crystallization process.In the low-temperature phase(25-15℃),agitation was reduced to minimize crystal breakage.The optimized process resulted in a thiourea crystal product with a particle size distribution predominantly ranging from 0.7 to 0.9 mm,accounting for 84%of the total.This study provides valuable insights into resolving the issue of excessive fine crystals in the thiourea crystallization process.