Time Filtering Research Articles

A Numerical Study of a Stabilized Hyperbolic Equation Inspired by Models for Bio-Polymerization

Abstract This report investigates a stabilization method for first order hyperbolic differential equations applied to DNA transcription modeling. It is known that the usual unstabilized finite element method contains spurious oscillations for nonsmooth solutions. To stabilize the finite element method the authors consider adding to the first order hyperbolic differential system a stabilization term in space and time filtering. Numerical analysis of the stabilized finite element algorithms and computations describing a few biological settings are studied herein.

Rehabilitation Management of Intensive Care Unit-acquired Weakness (ICU-AW): A Narrative Review

Background: Intensive Care Unit-acquired weakness (ICU-AW) is one of the most common neuromuscular disorders affecting intensive care unit (ICU) patients' outcomes and clinical course. ICU-AW is found in 30-50% of patients and increases to 67% in sepsis-critically ill patients. Prolonged ICU stay, the difficulty of weaning from the ventilator, higher hospitalization costs, and an increase in mortality, as well as long-term morbidity, are associated with ICU-AW. ICU-AW causes skeletal muscle weakness, including respiratory muscles, which results in complications that continue even years after being discharged from the hospital. Aim: To describe the rehabilitation management of ICU-AW and provide the information needed clinically to manage these patients. Methods: The authors reviewed all types of articles without time filtering using PubMed and Google Scholar databases with “ICU-AW”, “ICU-related weakness”, “rehabilitation”, and “early mobilization” used as keywords. Results: Rehabilitation management can be done as early as possible, beginning while the patient is still in the ICU. Early mobilization programs require teamwork consisting of doctors, therapists, and nurses. Physical activity and early mobilization in the ICU must be carried out with consideration for safety. Monitoring patient safety before and during mobilization is an essential factor to be considered. Any mobilization program should be the decision of the ICU care team. Implementation of rehabilitation programs and early mobilization improves outcomes for patients with ICU-AW and should be continued until the follow-up period. Conclusion: The rehabilitation management aiming at preventing and treating ICU-AW should be done since the patient was still in the ICU and under careful consideration of safety aspects.

An efficient accuracy improvement method for cable defect location based on instantaneous filtering in time-frequency domain

Time-frequency domain reflectometry is a highly sensitive method to locate cable defect. However, locating a potential defect far from the cable head may be less accurate because of the signal amplitude attenuation and the interference parts. To solve the problem, this paper proposes an accuracy improvement method based on instantaneous filtering in time-frequency domain. The method extracts the frequency spectrum of the time-frequency signal, and then filters the spectrum and reconstructs the signal based on the difference between the signal and interference spectra, which can eliminate the interference and improve the location accuracy. In simulation, the location error of this method improves from 5.47 % to 0.57 %. In experiment, the proposed method reduces the location errors and magnifies the location peaks of the breakage defect, thermal aging defect, and ground faults. For the defects studied in this paper, the method improves the defect location accuracy and defect amplitude detectability of TFDR.

Lithium-ion battery-pumped storage control strategy for smoothing wind-photovoltaic power fluctuation

Abstract Wind, as well as photovoltaic (PV), is widely used. Like loads, its power cannot be predicted, which results in the grid having to bear the power imbalance between wind-PV and loads, and substantial power fluctuations are not tolerated. Hybrid energy storage systems (HESS) containing multiple storage methods are considered effective solutions. In this paper, pumped storage and lithium-ion battery storage are fully considered, as they are supposed to have excellent performance and are highly complementary. We categorize the power imbalance into low, medium, and high according to the magnitude of the power imbalance. When the power fluctuation is low, the battery dominates. In contrast, the pumped storage dominates when the power fluctuation is high. Most importantly, when the power fluctuation is medium, we utilize an optimized first-order low-pass filter to allocate the power between the pumped storage and the lithium-ion battery. We change the filtering time in real-time according to the battery’s state of charge (SOC) to reasonably allocate the power between the pumped storage and the lithium-ion battery and ensure the SOC fluctuates within a reasonable range. This paper confirms the feasibility of the proposed strategy, where the pumped storage power fluctuates very little, in contrast, the battery power fluctuates significantly, and the SOC is always within the set reasonable range. Most importantly, the strategy proposed in this paper is straightforward to implement, which is crucial for engineering applications.

Evaluation of firewall performance metrics with ranging the rules for Poisson incoming packet flow and exponential filtering time

The given article is a continuation of a number of works devoted to the development of models and methods for ranging the filtration rules to prevent a decrease in the firewall performance caused by the use of a sequential scheme for checking packet compliance with the rules, as well as by the heterogeneity and variability of network traffic. The article includes a description of a firewall mathematical model given in the form of a complex system and a queuing system with a phase-type discipline for request servicing, which formalizes the network traffic filtering process with the functionality of ranging the rules. The purpose of modeling is to obtain estimates for major firewall performance metrics for various network traffic behavior scenarios, as well as to evaluate an increase in the firewall performance due to ranging a filtration rule set. Calculation of estimates for the firewall (FW) performance metrics was made using the analytical method for a Poisson request flow. Based on the analysis of the modeling results, conclusions were drawn on the effectiveness of ranging the filtration rules in order to improve the firewall performance for traffic scenarios that are close to real ones.

Real-time correction of channel-bed roughness and water level in river network hydrodynamic modeling for accurate forecasting

The accuracy and reliability of hydrodynamic models are sensitive to both hydraulic state variables and model parameters, particularly the bed roughness, while their simultaneous real-time corrections and corresponding effects still need to be well-established and understood. This paper presents a real-time data assimilation model that corrects channel-bed roughness and water level in a river network hydrodynamic model, ensuring its accuracy and reliability. Experiments and parameter analysis evaluated the effect of initial roughness and observation noise level on model performance. Correcting both roughness and water level improved filtering time and forecasting accuracy by up to 63% and 80%, respectively, compared to methods only correcting water level. The filtering time was reduced by 44–63%, and the water level forecasting RMSE decreased by up to 80%. Both models experienced increased filtering time and forecasting error as observation noise increased, but the proposed model had a lower increase. With accurate hydraulic state measurement (e.g., 0.005 m error), the model achieved negligible water level forecasting error after 7 h of data assimilation. The model's accuracy depended on the initial channel-bed roughness, and the algorithm enables real-time roughness correction, making it useful for flood forecasting.

Comparing Loon Superpressure Balloon Observations of Gravity Waves in the Tropics With Global Storm‐Resolving Models

AbstractSuperpressure balloons, which drift approximately on isopycnal surfaces, get displaced by gravity waves and are thus capable of detecting gravity wave signatures. The project Loon provides superpressure balloon data in the upper troposphere and lower stratosphere from 2011 to 2021. We compare Loon data from the 6 years of best data coverage with output of global storm‐resolving models from the DYnamics of the Atmospheric general circulation Modeled On Non‐hydrostatic Domains winter initiative in the tropics. We study the variance of the vertical velocity and, for the models, the gravity wave momentum flux as function of distance to closest convection. The models show large differences in the variance of the vertical wind velocity, which is crucial for calculating vertical gravity wave momentum fluxes. We find large differences between the models with respect to simulated convection, lateral propagation, and the wave background away from sources. We then sample balloons as models by optimizing the match of vertical wind distributions using a temporal low pass filter. The average distance the balloons travel during the optimum low pass filtering time turns out to correspond approximately to four times the model grid spacing. The functional dependence of the vertical velocity variance on distance to closest convection is similar between the models and the observations sampled as models. The robustness of this result across all models suggests that storm‐resolving models provide a useful resource for machine learning some characteristics of convectively generated gravity waves.

A pansharpening method combining iterative filtering and NSST-NSML-PAPCNN to optimize spatial detail extraction and injection

ABSTRACT Spatial injection-based pansharpening methods are prone to spatial or spectral distortions in pansharpening images due to insufficient extraction of spatial details and a mismatch between the amount of spatial detail information injected and the required amount. To this end, this paper proposes a pansharpening method that optimizes spatial detail extraction and injection. Firstly, a method to optimize the amount of spatial detail injection is proposed, that is, to extract the high-frequency information of the image through iterative filtering and determine the optimal number of iterations based on the global analysis of the method. Then, to fully extract and combine the spatial detail information of the source image, the detailed high-frequency image extracted corresponding to the optimal iterative filtering times is decomposed by non-subsampled shearlet transform (NSST), and a new multi-scale sum-modified-Laplacian (NSML) as an external stimulus to a parameter-adaptive pulse-coupled neural network model (PAPCNN). A fusion rule based on multi-scale morphological gradients is designed to extract a small amount of detailed information for the low-frequency subband. The fused spatial detail image can be obtained by combining the fused low-frequency and high-frequency subbands and inverse NSST transformation. Finally, pansharpening can be realized by combining spatial detail image, injection coefficient, and MS image. In this paper, many experiments are carried out on the QuickBird, GeoEye-1, and WorldView-4 datasets, and quantitative and qualitative comparisons are made with eight advanced methods. Experimental results show that the method proposed in this paper can achieve better fusion results.

A Novel Adaptive Power Smoothing Approach for PV Power Plant with Hybrid Energy Storage System

Clouds passing over solar photovoltaic (PV) power system causes power fluctuations, which contributes to power quality issues. Power fluctuations are usually compensated by an energy storage system (ESS) integrated with a filtering or smoothing controller. However, there is a great burden to tune and determine the filtering time constant (TF) that leads to better alleviation of PV power fluctuations because the irradiance variability varies from day to day. Lack of cloud information leads to incorrect selection of TF values which leads to poor smoothing performance when setting low values on cloudy days, or to unnecessary ESS operation when setting high values on clear days. This paper introduces a novel power smoothing framework to avoid the arbitrary selection of TF values and reduce the stress on ESS based on predictive and adaptive smoothing mechanisms. The proposed controller contains two layers, the first layer predicts the next day's irradiance profile and uses a clear sky model to identify the cloud class. Next, the controller sets the initial values of the filter time constants for cloudy, moderate, and mild days, and disables smoothing on clear and overcast days. The second layer adaptively adjusts the initial filter time constant based on the current power ramp rate and shares power for a hybrid energy storage system (HESS). The performance of the proposed controller is tested against the forecasting errors and compared to fixed time constant-based smoothing techniques and ramp rate control in a range of scenarios, including smoothing, ramp rate reduction, and battery degradation assessment.

Analysis of a Filtered Time-Stepping Finite Element Method for Natural Convection Problems

In this paper, we present, analyze, and test a novel low-complexity time-stepping finite element method for natural convection problems utilizing a time filter (TF). First, via a TF to postprocess the solutions of backward Euler (BE) schemes, we make a minimally intrusive modification to the existing codes to improve the time accuracy by one order. This also provides, at no extra complexity, an estimate of the temporal error,which is easy to construct a novel adaptive algorithm. Additionally, the TF can remove the overdamping of the BE scheme while remaining unconditionally energy stable. Hence, this paper addresses the question, how can one improve the time accuracy without increasing computational and cognitive complexity? Then long time stability and error estimates of BE plus time filter (BETF) with constant time stepsize are proved. Moreover, we construct adaptive algorithms by extending the approach to variable time stepsize, and we extend the methods to higher order algorithms. Finally, numerical tests confirm the convergence rates of our method and validate the theoretical results.

Ringtail: A Python Tool for Efficient Management and Storage of Virtual Screening Results.

Virtual screening using molecular docking is now routinely used for the rapid evaluation of very large ligand libraries in early stage drug discovery. As the size of compound libraries which can feasibly be screened grows, so do the challenges in result management and storage. Here we introduce Ringtail, a new Python tool in the AutoDock Suite for efficient storage and analysis of virtual screening data based on portable SQLite databases. Ringtail is designed to work with AutoDock-GPU and AutoDock Vina out-of-the-box. Its modular design also allows for easy extension to support input file types from other docking software, different storage solutions, and incorporation into other applications. Ringtail's SQLite database output can dramatically reduce the required disk storage (36-46 fold) by selecting individual poses to store and by taking advantage of the relational database format. Filtering times are also dramatically reduced, requiring minutes to filter millions of ligands. Thus, Ringtail is a tool that can immediately integrate into existing virtual screening pipelines using AutoDock-GPU and Vina, and is scriptable and modifiable to fit specific user needs.

Water Level Simulation in River Network by Data Assimilation Using Ensemble Kalman Filter

Water level simulation for complex water river networks is complex, and existing forecasting models are mainly used for single-channel rivers. In this paper, we present a new data assimilation model based on the ensemble Kalman filter (EnKF) for accurate water level simulation in complex river networks. The EnKF-based data model was tested on simulated water level data from a river network hydrodynamic model and optimized through parameter analysis. It was then applied to a real mountainous single-channel river and plain river network and compared with a data assimilation model based on the extended Kalman filter (EKF). The results showed that the EnKF-based model, with a medium ensemble sample size of 100–150, normal observation noise of 0.0001–0.01 m, and a high standard deviation of 0.01–0.1 m, outperformed the EKF-based model, with a 49% reduction in simulation errors, a 45% reduction in calculation cost, and a 43% reduction in filtering time. Furthermore, the EnKF-based data assimilation model predicted the water level in the plain river network better than the mountainous single-channel river. Around 5 to 8 h were required for data assimilation; afterwards, the model could make accurate predictions covering 20 to 30 h. The EnKF-based data assimilation model offers a potential solution for water level predictions in river networks.

Filtering performance of ceramic filter with mullite whisker for non-exhaust particulate matter from transportation

Fabrication and filtering performance of ceramic filter were investigated to reduce non-exhaust particulate matter (PM) from vehicles. For this purpose, filter needs to be porous structure with high mechanical strength, thus it can be operated with low differential pressure. When the vehicle runs at a high speed, wheel temperature rises up to 700 °C. Therefore, filter material for non-exhaust PM filter also requires high temperature durability to be operated under such condition. Porous ceramic filter with mullite whiskers, which has advantages of high temperature durability and mechanical strength, was prepared using replica template method and MoO3 catalyst. The fabricated ceramic filter with mullite whiskers showed improved filtering performance for non-exhaust PM. Initially, the filtering performance was 56.3% for PM2.5 and 88.0% for PM10. The filtering performance gradually improved over filtering time to 86.4% for PM2.5 and 93.0% for PM10. The differential pressure was confirmed as 210 Pa, which was applicable for non-exhaust PM filter of vehicles.

多枝柽柳年轮生长速率测量及TRGR指标优势分析

PDF HTML阅读 XML下载 导出引用 引用提醒 多枝柽柳年轮生长速率测量及TRGR指标优势分析 DOI: 10.5846/stxb202202080312 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: 欧盟Erasmus+项目（598838-EPP-1-2018-EL-EPPKA2-CBHE-JP） Tree-ring growth rate measurement of Tamarix ramosissima and tree-ring growth rate index superiority analysis Author: Affiliation: Fund Project: This work was supported by the GIS and RS for Sustainable Forestry and Ecology（598838-EPP-1-2018-EL-EPPKA2-CBHE-JP） 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:灌木对生境和气候变化具有高度敏感性，其年轮资料在认识区域环境演变过程、全球气候变化和环境保护中具有重要作用。灌木植株在生长过程中受遗传和极端环境的影响，年轮常出现偏心和不规则生长，这使得专业年轮分析软件测量的年轮宽度数据难以准确反映其整体径向生长信息。为探讨适合于寒旱区灌木年轮学研究的年轮测量指标和测量方法，研究以该区域荒漠常见植物多枝柽柳（Tamarix ramosissima Ledeb.）为研究对象，通过U-net深度学习方法，获得年轮提取训练模型，自动获取扫描轮盘各年早材区域。轮盘扫描及语义分割后的图像经GIS配准赋坐标、ENVI图像处理后，借助GIS编辑和测量工具，完成多枝柽柳各年年轮生长速率（Tree-ring growth rate，TRGR）、年轮宽度（Tree-ring width，TRW）和树木基部断面积生长增量（Basal area increment，BAI）的测量；研究基于Timesat Savitzky-Golay （S-G）滤波时间序列拟合，获取点样尺度归一化植被指数（Normalized difference vegetation index，NDVI）季节曲线峰值、季节开始时的增长速率、大季节积分和季节结束时的值等7个关键参数。将多枝柽柳TRGR、TRW和BAI测量结果与NDVI季节曲线关键参数进行相关性分析，检验TRGR指标的合理性，分析指标优势。结果表明：测量的多枝柽柳TRGR指标与点样尺度NDVI关键参数间存在高度正相关，最高相关系数达0.98。TRGR指标不仅能够反映多枝柽柳年轮整体径向生长情况，而且可以有效去除年轮指标中的胸径趋势，突显指标环境趋势，有利于解决树木年轮学中指标去趋势难的问题。TRGR与TRW和BAI指标相比优势明显，可以作为灌木年轮学研究的新代用指标。研究结果为多枝柽柳年轮信息重构NDVI或反之提供了有利证据。研究构建的年轮测量方法相比于专业年轮分析系统具有更为多样的测量手段。研究结果可推动寒旱区灌木年轮学发展。 Abstract:Shrubs are highly sensitive to habitat and climate change, and its tree-ring data plays an important role in understanding regional environmental evolution, global climate change and environmental protection. Due to the influence of heredity and extreme environment during shrub growth, the growth rings often have serious eccentricity and irregular growth, which makes it difficult for the tree-ring width measurement by professional tree-ring analysis software to accurately reflect the overall radial growth information. In order to explore the measuring indexes and methods of tree-ring, which are suitable for study on shrub dendrochronology in cold and arid regions, this study takes Tamarix ramosissima Ledeb., a common desert plant in this region, as the study object. Based on U-net deep learning method, we created the training model of Tamarix ramosissima tree-ring extraction, which would automatically obtain each year tree-ring springwood area of scanning disc. After tree-ring scanning image and semantic segmentation image were processed by GIS assigning measurement coordinates and ENVI image processing, tree-ring growth rate (TRGR), tree-ring width (TRW), and basal area increment (BAI) of tamarix ramosissima were measured by using GIS editing and measurement tools. Based on Timesat Savitzky-Golay (S-G) filtering time series fitting, seven key parameters of seasonal curve of normalized difference vegetation index (NDVI) were obtained at point-scale, including peak value, rate of increase at the beginning of the season, large seasonal integral and value for the end of the season etc. The correlation between TRGR, TRW, BAI and the key parameters of NDVI seasonal curve were analyzed to test the rationality and to analyze the advantages of TRGR index. The results show that there are high positive correlations between TRGR index of Tamarix ramosissima and the key parameters of point-scale NDVI seasonal curve. The highest correlation coefficient is 0.98.TRGR index can not only reflect the overall radial growth of tree-ring, but also effectively remove trend of diameter at breast height (DBH) in tree-ring index and highlight the index's environmental trend, which is helpful to solve the problem of index detrending in dendrochronology. Compared with TRW and BAI, TRGR index has obvious advantages and it can be used as a new index for shrub dendrochronology. The results provide evidence for NDVI reconstruction from tree-ring information of tamarix ramosissima or vice versa. Research methods have more diverse means than the professional tree-ring analysis system measurement. The results can promote the development of shrub dendrochronology in cold and arid regions. 参考文献 相似文献 引证文献

Evaluasi Efektivitas Kinerja Filter Press Plate and Frame pada Proses Pemanenan Spirulina sp

Spirulina sp can be used as raw material for making masks and medicines. This research wasconducted to determine the effectiveness of the performance of using a Filter Press (plate and frame) in harvesting Spirulina sp. In this study, Spirulina was cultured in 60 L styrofoam containers with different photoperiods (light/T and dark/G), for 12 hours per day (12T-12G). Parameters observed include dry biomass. For 12 hours per day (12T-12G), Press Filters with 2 and 3 plates were used and pressure of procrsess are 1, 1.5, and 3 Psi. In this study, Spirulina sp can grow well with a concentration of 0.6636 gr mL-1. The filter press plate and frame can be used to harvest Spirulina Sp with the optimum conditions for the Spirulina filtration process by pressing two psi and the number of plates 3, where the highest amounts of filtered Spirulina are 39.653 g with a filtering time of 2 x 103 seconds.

Improving Actuator Wearing Using Noise Filtering.

Actuator, mostly valve, wearing is an important factor of the overall industrial control system operational cost. Actuator operational wear strongly depends on its operation. Highly utilized elements have a tendency to degrade faster. Therefore, the maintenance teams prefer to minimize their moves. In contrary, control engineers need the actuators to actively operate in their control loops to mitigate disturbances and follow the desired trajectories. Higher control performance is often achieved with an active use of actuators. Control loop quality depends on the controller setup and loop auxiliary functionality. Properly designed filtering not only facilitates controller action, but also impacts actuator operational wear. Industrial control templates are built using the blockware that is embedded in the existing control system. Distributed control system (DCS) and programmable logic controller (PLC) have a limited number of control algorithms. An engineer has to design the control structure and the associated sensor noise filtering using available functionality. This paper evaluates and measures the impact of noise filtering on the loop performance and on the actuator weariness. Relations between noise filtering time constant, loop performance and valve travel deliver recommendations for control engineers.

Improving seismograms’ resolution by using a phase-shrinkage filtering method

The improvement in the temporal resolution of seismograms is usually achieved by compressing, or deconvolving, the seismic pulse. In this paper, I present a new method of filtering time series that shrinks the positive or negative polarity band of a signal while expanding its opposite polarity. The filtering method uses the complex seismic trace to compute the instantaneous phase, which is shrunk around the positions of the local maxima (or minima) values corresponding to the reflections of the original signal. It calculates the real and imaginary components afterward, thus representing the filtered signal. The method is applied trace-by-trace and promotes a significant improvement in the temporal resolution of the seismograms, revealing in greater detail the reflections and structures of the subsurface. Numerical examples with stacked seismic - 2D from the Pelotas Basin, from the mouth of the Amazon river - and, 3D - from F3Demo, illustrate the performance of the new method proposed here. The average amplitude spectra of the filtered data reveal the presence of the high and low frequency contents in the filtered results.

Star angle/ double-differenced pulse time of arrival integrated navigation method for Jupiter exploration

Pulsar navigation is a promising autonomous navigation system for spacecraft, which is applicable to the entire solar system. However, the pulsar’s directional error and the onboard clock error are two types of systematic errors that seriously reduce navigation accuracy. To solve this problem, a star angle/double-differenced pulse time of arrival(SA/DDTOA) integrated navigation method is proposed. Since measurements obtained by observing different pulsars contain the same clock errors, the measurements can be differed to eliminate the common clock error. Then, the pulsar-differenced measurements at neighbor filtering time can be differed to suppress the effect of the pulsar’s directional error on navigation precision. Star angle is used to obtain absolute navigation information, which denotes the angles between the light of sight of Jupiter and that of its background stars. Simulation results demonstrate that the proposed method can eliminate the influence of the onboard clock error and greatly weaken the effects of the pulsar’s directional error. The navigation accuracy is better than the traditional star angle/pulse time of arrival integrated navigation method and star angle/pulse time difference of arrival integrated navigation method. In addition, the navigation accuracy of the SA/DDTOA integrated navigation method is less affected by Jupiter’s ephemeris error. This work greatly reduces the influence of common systematic errors in pulsar navigation on navigation accuracy.

Correcting Atmospheric Effects on the InSAR Measurements using GPS Data

The effect of the atmospheric error in the spaceborne synthetic aperture radar (SAR) signal is more prominent in Malaysia due to its hot and wet conditions. Because the atmospheric error is believed to happen constantly in space and randomly in time, low-pass filtering in space and high-pass filtering in time is employed to measure it. However, with few scenes, the filtering technique’s reliability in removing atmospheric error may be insufficient, leading to erroneous surface deformation. Therefore, an external atmospheric correction needs to be modelled to improve the accuracy of surface deformation. In this study, the atmospheric error correction was estimated from GPS and applied to the deformation analysis. The result shows that the atmospheric error level estimated from the filtering technique was –6.9 to 7.5 radians, while using GPS was -1.0 to 1.9 radians. After using the filtering process, the rate of deformation fell dramatically. However, compared to the reference deformation, the rate was too low, indicating that the filtering technique overstated the level of atmospheric error. At many data collections, the atmospheric correction calculated from GPS gave deformation values closer to the reference deformation. Hence, this study will help the researchers to model the atmospheric correction over the Malaysia region in future.

Use of surfactants for efficient removal of calcium phosphate particles from water

Today, softening of water in offices and private homes is mainly carried out by the ion exchange method, despite its significant negative impact on the hydrosphere. The development of alternative safe technologies in this field is extremely relevant today. Such an alternative can be considered the use of effective reagents that transfer hardness ions into the solid phase.
 The use of phosphates as such reagents allows, depending on the conditions, to reduce the residual hardness of water to the level of 0.1 mg-eq/dm3 or less. An important problem of this technology is the efficiency of separating the solid phase from the mother liquor. This step can be implemented by advocating or filtering. Using model calcium solutions treated with appropriate doses of sodium phosphate and flocculants, the most effective of them in settling processes were selected. As flocculants, polyacrylamide was used - as a nonionic flocculant, Magnofloc - 336 from Ciba - as an anionic flocculant, Zetag - 7692 from Ciba - as a cationic flocculant.
 The flocculant Magnofloc - 336 turned out to be the most effective in settling highly dispersed particles of calcium phosphate. At a flocculant concentration of 30 mg/dm3 for 10 min of settling, the apparent volume of the solid phase decreases to 30 % of the initial volume of the suspension and stabilizes at this value. Other types of flocculants and other doses were less effective.
 A somewhat different situation is observed when separating the solid phase by filtration. The greatest influence on the filtration rate is caused by the temperature, the hydrogen index and the ratio between the components. Only temperatures below 20 °C significantly affect the rate of filtration. This is especially noticeable at a temperature of 5 °C. At this temperature, the volume of filtrate is 8-20 minutes behind the volume of filtrate of distilled water. At 15 °C, this difference is smaller, and at temperatures above 20 °C, the curves generally overlap. In the pH range of 5-9, there is no significant effect on the filtration rate. Only in a strongly alkaline environment do the necessary filtering times increase significantly, which, in our opinion, is due to the formation of a significant number of amorphous particles of various composition, which can block the pores of the filters. With the stoichiometric ratio of the components, the curve of the change in the filtration rate practically coincides with the curve of the change in the filtration rate of distilled water under the same conditions. When the ratio changes both downward and upward, the conditions for filtering the suspension deteriorate. And the more the ratio differs from stoichiometry, the more developed the structure of the solid phase is and the worse its separation from the liquid phase is. As the ratio between the components changes, so does the pH of the zero charge of the solid particles. If the stoichiometric ratio of the components is at pH 8.15, then when the ratio decreases to 0.5, it decreases to pH 7.41, and when it increases to 2, it increases to pH 8.64. A change in the ratio of components affects not only the sign of the surface charge, but also its magnitude, which cannot help but affect the efficiency of solid phase separation. The type and dosage of flocculants determined to be most effective in settling do not always provide the same effect in filtration. Suspensions without the addition of flocculants have the highest filtration speed. The study of the effect of flocculants at their concentrations of 10 and 30 mg/dm3 showed that none of its different types and at their different concentrations contributes to an increase in the filtration rate. Obviously, significant doses of flocculants contribute to the rapid calming of the porous medium of the filters and cause a decrease in the rate of transport of the liquid phase.
 The obtained results make it possible to determine effective reagents for removing calcium ions from natural waters and the optimal conditions for their use and serve as a basis for the development of effective and environmentally safe technologies for softening natural waters.