Mathematical Experimental Design Research Articles

Features of risk analysis, assessment and control methods in pharmaceutical development

Quality Risk Management (QRM) is an important aspect of pharmaceutical development in the Quality-by-Design paradigm, since it determines the Design Space, critical quality attributes and critical process attributes.The purpose of this review is to systematize and analyze the main aspects of the QRM system in relation to each element of pharmaceutical development. This review article discusses the following key elements of QRM such as: risk analysis, risk control, risk communication, risk verification. For risk analysis, the advantages and disadvantages of QRM tools such as Preliminary Hazard Analysis, Failure Mode Effects Analysis, Fault Tree Analysis are presented and analyzed, Hazard Operability Analysis and Hazard Analysis and Critical Control Points. In addition, a description of the methods of mathematical planning and design of experiments for pharmaceutical development and QRM is given and their significance for these systems is determined. Elements of QRM such as root cause analysis, brainstorming, and a corrective and preventive action procedure are given as risk control and mitigation tools.In this paper, the main stages of QRM are considered and conclusions are formulated regarding the main advantages and disadvantages of the methods of identification, analysis, control, risk reporting, and the main ways for further improvement of the presented system are proposed.

The economic essence of electro-pulse extraction technology in the production of extracts from sprouted grains of cereal crops

In this article, we present an economic analysis and optimization of the production process of functional beverages based on extracts from sprouted grains of cereal crops. When approaching process optimization in production, one of the key tools is mathematical experimental design. In particular, second-order rotational planning provides the opportunity to determine the optimal combination of input factors, which in turn leads to maximum economic efficiency of the extract extraction process. In this study, we applied this methodology to the process of ultrasonic extraction of sprouted grains of cereal crops. A series of experimental studies was conducted to minimize costs and maximize revenue from the production of functional beverages based at currently available economic information. As a result of the analysis, optimal process parameters were determined which ensure maximum economic efficiency. The study also included an assessment of the quality of the obtained extracts in terms of their content of biochemical compounds. The example economic forecast for Nestlé Corporation if introducing the proposed improvements has been given. The results of this study provide valuable data for functional beverage manufacturers and can serve as a basis for making informed strategic decisions regarding the use of ultrasonic extraction in their production processes for production costs reduction and maximization of revenue.

Optimization of coal tar gas chromatography conditions using probabilistic-deterministic design of experiment

The development of physicochemical methods for the analysis of objects of complex composition requires the application of methods of mathematical experiment design. This article investigates the possibility of using probabilistic-deterministic design of experiment (PDDoE) for obtaining a mathematical model of the chromatographic separation process of coal tar hydrogenation products on an Agilent 7890A device with an Rxi-5ms column. It is shown that the relationship between the column heating rate and the carrier gas pressure with the values averaged for the entire chromatogram can be established with a high accuracy. It is noted that the accuracy of modeling the individual characteristics of the mixture components’ peaks is less, but remains sufficient for many practical needs. Nonlinear multiple correlation coefficients (NMC) for the dependence of the average retention time and average intensity on the considered factors are more than 0.99; they are more than 0.98 for the average peak width. NMC for the dependence of the resolution with the relation to the peaks of naphthalene and 2-ethylphenol is more than 0.8 at a significant level that sufficient for practice. The quality of the mathematical model was checked by triple registration of the chromatogram at the values of the column heating rate and carrier gas pressure that were not used in the training experiment. The measurement results are excellent squared with those calculated using the obtained generalized equations. The PDDoE method can be recommended as a method for mathematical design of an optimization experiment in gas chromatography.

SELECTION AND JUSTIFICATION OF THE MATHEMATICAL 6 FACTORS EXPERIMENT PLAN IN THE STUDY OF ICE STARTING QUALITIES

The practical significance of the application of multivariate regression analysis in engineering practice as a necessary step towards improving and optimizing complex systems and processes is presented. The goal and investigation tasks have been actualized to optimize the start-up process of a high-speed subcompact diesel engine. Preparation of the plural factors experiment features of diesel start-up process based on regression analysis and the theory of mathematical design of experiment are presented. Qualitative optimizing parameters of the diesel engine cold start are determined: instantaneous acceleration of the crankshaft dn / dτ at the time of crankshaft cranking by an external energy source close to the time spent on starting the engine with optimal parameters of the starting system and starting energy consumed during the crankshaft cranking by an external energy source. Six main factors influence on certain parameters of the diesel engine start quality have been investigated. The regression equation for assessing the quality of the start-up process is substantiated. The form of regression equation is a full quadratic polynomial for the reproduction of the investigated functions, based on the previous study of some used in the study individual factors influence. The analysis of proposals for rational plan selection of a six-factor experiment to find the coefficients of the second-degree regression polynomial is carried out. The substantiation of the decision regarding the choice of the plan is given. Selection was based on the requirements of the investigation test bench and the conditions for study organizing. Main impact had the predecessors experience of similar investigation and the statistical criteria for different plans of experiment comparison used in mathematical theory of design of experiments. The points of the plan have been defined on a multidimensional cube due to the need to vary on three levels with a uniform step of all 6 factors that were identified as influential. Under the conditions of the available laboratory test bench, the current values of the factors of equivalent cold start temperature, crankshaft-cranking speed and maximum temperature of the glow plugs have a variance of the installation at different points of the plan, and the nature of the factors on energy consumption is unknown in advance. As a rational experimental design for organizing the current study, the Box-Wilson orthogonal central compositional plan was chosen, built by adding plan points on the axes of the factorial space to the full-factorial plan of the lowest order, while maintaining the requirement of orthogonality and symmetry of the plan.

Investigation into the Regularities of Hydrogen Fluoride Collection by the Developed Fibrous Ion-Exchange Material Under Dynamic and Static Conditions

Tests of respirators made of the developed material were conducted under dynamic and static conditions. Based on the methods of mathematical statistics and design of experiments, the authors determined the following dependences: of the dynamic activity of ion-exchanger on the sorbent layer height, of the sorption rate of hydrogen fluoride on the sorption time, of the effective protection time on the height of the layer of the material under investigation. The analysis of the results showed that the given fibrous ion-exchange material can be used as a sorption-filtering element of a respirator to ensure the required efficiency of protection against hydrogen fluoride.

Nitric acid leaching of the copper-bearing arsenic sulphide concentrate of Akzhal

This paper examines the possibility of using the hydrometallurgical process of nitric acid leaching to process the refractory sulphide concentrate of Akzhal. The study that looked at the structure and composition of this material confirmed that the studied material has a complex mineralogy due to dissemination of gold-bearing sulphides (mainly pyrite and arsenopyrite) in the gangue and their interpenetration, as well as the presence of finely dispersed gold (10 μm) in tight assemblage with the host minerals. A series of laboratory tests, as well as mathematical experimental design techniques, helped identify the most critical parameters governing the leaching efficiency. The following process parameters are recommended: nitric acid concentration — 5 mol/dm3, L/S = 5:1,  = 1 h. A high recovery into solution can be achieved in the above conditions, %: >98 Fe; >96 As; >90 S. The authors propose to use atmospheric deposition of scorodite to dispose of leach liquors. This is achieved by means of staged neutralization until the concentration of arsenic in the liquor reaches 20 mg/dm3. Sorption techniques are applied to recover copper and zinc from leach liquors. Leach cakes are subjected to sorption cyanidation with the total recoveries of gold and silver of >94 and >64%, correspondingly. The nitrous gas recovery stage proved highly efficient — >90%. A series of pilot tests was carried out to verify the findings. Thus, the developed hydrometallurgical process was applied to the copper-bearing arsenic sulphide concentrate of Akzhal at the testing facility of KazGidroMed, a research centre for innovative technology. The tests enabled to conduct a feasibility study, which proved the proposed processing techniques to be efficient and feasible.This research study was funded by the Russian Science Foundation (Project no. 18-19-00186).The study of arsenic precipitation from leach liquor was funded by the Russian Foundation for Basic Research under the Research Project no. 18-38-00914\18.

Development of Optimum Mixture for Multicomponent Inhibiting Composition by Methods of Mathematical Modeling of Experiment

Great loss of metals, numerous economic losses take place due to accidents in pipelines, industrial chemical and technological installations, etc. because of acceleration of corrosion processes. Therefore, actually all the developed countries of the world pay much attention to protection against corrosion in all manifestations thereof. Highly efficient multicomponent inhibiting composition to be obtained by modification of 4,4-dimethyl-1,3-dioxane wastes is developed and proposed to be industrially implemented by methods of mathematical design of experiment. Component mixture of each composition to be tested was optimized by maximum protective efficiency. Concentration of components in the mixture analyzed was considered as the major factor. Regression equation analysis enabled to find best component ratio. Synthesis of inhibitor obtained under 4,4-dimethyl-1,3-dioxane wastes enables to solve the problem of rational utilization thereof.

An integrated way to improve the properties of soil-cement pile foundations

The scientific article presents the results of the development of a method for improving the properties of soil-cement pile foundations by the drilling-mixing method using mechanical activation of soil-cement mixture in filler soils. Two methods for improving filler soils are considered. The choice of the mathematical methods for the research is justified. The feasibility of a complex combination of mathematical modeling methods and experimental design to achieve the goal set in this scientific article is substantiated. The physicomechanical characteristics of soil-cement are considered: a measure of brittleness, brittleness coefficient, compressive strength, splitting strength, strength variation coefficient. Based on the research, practical recommendations are given for improving soil-cement pile foundations.

Application of numerical methods in research of deformation anisotropy soil

The article provides a methodology for conducting studies of the effect of the deformation anisotropy on the stress and strain state of foundation soil provided. The investigation of the stress-strain state of a wide range of soil bases was performed by a finite element analysis with the application of method of mathematical experiment design techniques. The character of the stress change component depending on the variation for each factor considered characteristic zones subgrade as well, estimated effect on each component of the stress properties of the medium degree of meandering from the isotropic state. The efficiency of taking into account the deformation anisotropy of the soil in the calculations of the bases is estimated.

SUBSTANTIATION OF THE NESESSITY OF THE NEXT STEP OF THE EXPERIMENTAL DESIGN METHOD IN THE RESEARCH OF ICE

The role of the branch of mathematical experimental design, as well as the advantages of using regression models in the form of power-polynomials during adjustment and the upgrading of existing structures of the ICE, is shown. The modern guidelines in the branch of experimental design while studying the ICE processes are given, based on the progressive ideas of the branch of experimental design and the technical possibilities of collecting, processing and presenting the results of the experiment. The requirements for the development of the direction of experimental research and necessity of multifactorial analysis of processes that are complex indicators of the quality of systems are shown. As an example of the experimental design, the study of the starting qualities of the diesel engine series DA10 shows the urgent need for organizing an experiment with six-factors. The stages of the experimental design process are determined and the place of the mathematical experimental design is shown in the process of preparing the research of the ICE processes. The disadvantages of traditional methods of mathematical experimental design and the ways of their elimination are substantiated. The requirements of the further research in the branch of multi-factor experiments and the improvement of the accuracy of the analytical description and the experimental measurement of the investigated parameter are shown. The paper presents the Approximation_LSM software program by authors own design, which execute a number of requirements that have been advanced to the traditional method of processing the results of experimental studies. According to the considered solutions to the tasks are set for the mathematical experimental design, are determined the directions that require further analysis for the creation of new methods for the compilation of diluted and asymmetric plans of the experiment with a number of factors of not less than six, determination of criteria for assessing the completeness and the factors influence in terms of diluted and asymmetric plans. In addition, the proposed methods of conducting research experiments to optimize a significant parameter with the use of refinement of the experiment plans and the methodology for estimating the coefficients of the polynomial regression model for the possibility of reducing the number of the polynomial components.

Forestry wastes filled polymer composites for agricultural use

Two kinds of polymer composites were prepared using poly (vinyl alcohol) as binder and forestry or wood processing wastes as fillers. In one kind of the composites pine needle meal was used as filler while the other kind of the composites was filled with pine bark meal. Glycerol and oleic acid were used for the modification of mechanical, sorption properties and solubility of the composites. The films of the composites were fabricated and their mechanical, viscoelastic and antifungal properties as well as water absorption and solubility in water were studied. Mathematical experiment design was used to evaluate influence and importance of both glycerol and oleic acid content on of mechanical properties, solubility and water absorption of the composite films filled with pine bark meal. The second order polynomial models were developed in order to find out optimal content of both glycerol and oleic acid in compositions. Exploitation properties of the composite pots prepared from the composites were studied and vegetation tests were performed. It was shown that evaporation rate of water through the walls of the composite pots was by 45% lower and the temperature of substrate in the composite pots was by 3–4 °C higher as compared with the corresponding characteristics of peat pots. Plants cultivated in the composite pots had better developed root system relative to those cultivated in peat pots.

METHODOLOGY OF DETERMINING THE PARAMETERS OF TRACTION ELECTRIC MOTOR FAILURES WHEN OPERATING TROLLEYBUSES

Purpose. The work is aimed to study the change in parameters of traction electric motors of trolleybuses during operation and improvement of the technical state control system, using modern diagnostic methods. Methodology. Solution of the scientific problem is based on the control of technical state and change in the parameters of traction electric motors in the process of operation. For analysis of operational factors, we used the method of mathematical statistics and probability theory. Mathematical modelling and design of experiment, multifactor regression analysis provides an assessment of the reliability of the electric traction motor elements. Physical and statistical methods provide for research and detection of patterns of influence of the factors that accelerate the wear of parts. This allows us to generate models of system reliability that take into account the influence of operational factors on the reliability. Findings. As a result of the studies we obtained quantitative characteristics of the reliability of commutator and established that the failures of traction motors make up 20% of all failures of electrical equipment. We analysed the operation conditions of traction electric motors and determined the failure distribution law N{mx,sx}, which allows assessing the progression between gradual failures. We obtained a mathematical model characterizing the object operation. A generalized equation of the failure rate of elements for traction electric motor (TEM) was found. We improved the estimation methods of reliability of TEM element base that makes it possible to determine the ETM lifetime taking into account the features of each trolleybus. We established the failure rate of commutators using physical and statistical methods. Originality. For the first time, the choice of physico-statistical methods of simulation and reliability calculation was substantiated. We determined the regularities of change in parameters of the trolleybus traction electric motor elements, which makes it possible to control the processes of their wear in the operation conditions. We developed a mathematical model for estimating the traction electric motor reliability, based on a system analysis of the probabilities of failures of subsystems to be diagnosed. Practical value. Based on the results of the study, we developed practical recommendations for rational choice of diagnostic parameters of traction motors. Their implementation at the enterprises of electric transport will increase reliability of electric motors in general up to 10%. It is proposed to use the results of the work in the educational process and in the research work of students at the Department of Electric Transport of the O.M. Beketov National University of Urban Economy in Kharkiv. The developed methodology for determination of parameters of traction electric motors when operating trolleybuses allows assessing the reliability of any type of trolleybus traction motor.

Optimization of contents of two-component polydispersed filler by applying the mathematical design of experiment in forming composites for transport repairing

Optimization of contents of two-component polydispersed filler by applying the mathematical design of experiment in forming composites for transport repairing

Combined Use of Mathematical Optimization and Design of Experiments for the Maximization of Profit in a Four-Echelon Supply Chain

This paper develops a location-allocation model to optimize a four-echelon supply chain network, addressing manufacturing and distribution centers location, supplier selection and flow allocation for raw materials from suppliers to manufacturers, and finished products for end customers, while searching for system profit maximization. A fractional-factorial design of experiments is performed to analyze the effects of capacity, quality, delivery time, and interest rate on profit and system performance. The model is formulated as a mixed-integer linear programming problem and solved by using well-known commercial software. The usage of factorial experiments combined with mathematical optimization is a novel approach to address supply chain network design problems. The application of the proposed model to a case study shows that this combination of techniques yields satisfying results in terms of both its behavior and the obtained managerial insights. An ANOVA analysis is executed to quantify the effects of each factor and their interactions. In the analyzed case study, the transportation cost is the most relevant cost component, and the most relevant opportunity for profit improvement is found in the factor of quality. The proposed combination of methods can be adapted to different problems and industries.

Sorption of Rhenium from Concentration Products of Placers of Concentrate Gold by Magnetic Liquid Separation

Separation in ferromagnetic liquid (FML) is recommended for separating gold from concentration products of placers. Magnetic liquid separation is based on the appearance in FML of a ponderomotive force of a nonuniform magnetic liquid additional to the gravity buoyancy force. A horizontal component of this force in the separation medium bulk participates in the body motion along the equipotential surface across the working zone—to separation cuvette walls and towards the central plane of the pole gap, while the longitudinal component is directed along it. In order to increase process characteristics, it is recommended to limit transverse motions of bodies by vertical partitions established in the separation medium along the separator pole gap. It follows from the results of a theoretical investigation into the particle motion in a separator working zone that the influence of walls manifests itself in the appearance of the counterflow to the particle motion, which causes the rise of the hydrodynamic drag force and deceleration of the particle motion. It is shown that, in the presence of vertical walls, shortening the residence time of a light concentrate fraction in a separator working zone promotes the rise of process productivity in regards to the initial feed and productivity in regards to a heavy fraction (recovery of gold into the heavy fraction). Research tests of competitive separation methods for artificial mixtures of minerals and heavy gold-bearing concentrates are performed using methods of mathematical experiment design. It is proven that, when passing from separation in the FML volume to separation using the developed method, the apparatus productivity increases by 9%, while the recovery of gold into the heavy fraction increases from 84.34 to 91.77% due to a decrease in losses with a light fraction from 15.46 to 7.96%. The material containing gold in amounts more than 800 kg/t is acquired with a decrease in the yield of a heavy fraction by 11 rel. %.

Gravity concentration efficiency probabilistic estimate and mathematical design of extremal experiments

Gravity concentration efficiency probabilistic estimate and mathematical design of extremal experiments

Preparation of nanosized nickel powder by direct-current electrolysis combined with high-voltage spark discharge

The possibility of obtaining nanosized nickel powder by simultaneous dc electrolysis and high-voltage spark discharge has been explored. The powder has been prepared from a nickel sulfate-containing electrolyte using soluble nickel anodes at a cathodic current density in the range of 11000–19000 A/m2, a voltage on the spark gap of 12–16 kV, and a pulse repetition frequency of 0.5 Hz. The effect of various factors on the synthesis of the powder has been studied and the optimum conditions for its preparation have been found using mathematical experiment design. The size distribution of particles has been determined with a particle size analyzer. The BET specific surface area of the powder has been measured to be 11.7 ± 2.1 m2/g.

The investigation of expanded polystyrene creep behaviour

The results obtained in long-term testing under constant compressive stress of the cut from the Slabs EPS 50/100 and EPS 150 with the density ranging from 15 to 24 kg/m 3 , which were manufactured by the same manufacturer by foaming EPS solid granules (beads) in closed volume. The creep strain of the above described specimens was used as a criterion for estimating the deformability of the EPS slabs under long-term compressive stress. It was measured using special stands EN 1606, maintaining constant stress during the fixed time interval t n =122 days. Creep strains were determined by the methods described in EN 1606 for constant stress σ c =0.35σ 10% (compressive stress σ 10% was determined in accordance with EN 826:2013. The long-term compressive stress measurement error did not exceed 1 %, while the creep strain measurement error was not larger than 0,005 mm. The tests were conducted at the ambient temperature of (23±2)°С and relative humidity of (50±5) %.The long-term constant compressive load σ c =0.35σ 10% . The method of mathematical and statistical experimental design optimization models taking into account the thickness of specimens is proposed to determine the creep compliance I c ( t n ) the creep strain e c ( t n ) and predictive point estimate of creep strain e c ( T ). Graphical interpretation of the abstained models is also presented. It should be noted that the abstained equations may be used in practice for estimating the creep strains at time t n =122 days and predictive estimates of e c ( T ) for the load time of 10 years.

Создание математической модели для оценки энергоёмкости процесса обеззараживания стоков животноводства

Introduction. A perspective method of the livestock wastes disinfection is considered. The key point of the method is in complex physical and chemical impact of the variable magnetic field coupled with a chemical reagent. The device for implementing the proposed technique is an inductor. Electric energy intensity is selected as a parameter characterizing the energy efficiency of the of livestock wastes disinfection process. To increase the efficiency of investigating the livestock wastes disinfection process, it is proposed to use the mathematical experimental design theory. Materials and Methods. In the course of this research, the following techniques were used: instrument, direct and indirect methods of measurement, statistical processing technique, and mathematical experimental design theory. Research Results. The effect of technological factors on the energy efficiency of the livestock wastes disinfection process is experimentally investigated. On the basis of the data obtained, the strength effect ranking of the technology factors on the specific electrical energy capacity of the process is performed. A noncritical degree of impact of evaluating the pair-wise interaction coefficients is established. Their absence in the mathematical model suggests this. Discussion and Conclusions. A mathematical model of the livestock wastes disinfection process which allows evaluating the effect of the technology factors on the specific electrical energy intensity of the given process is developed.

Chemical-spectroscopic determination of impurity elements in concentrated salt products from pyrochemical reprocessing of spent nuclear fuel

A procedure was developed for separating fission products and impurity elements from concentrated solutions of alkali metal salts by precipitation of carbonates for their subsequent determination by atomic emission spectroscopy. Coprecipitation of Cr, Al, Pb, Fe, Ni, Mo, Cu, Ca, Mg, Eu, Sm, and Gd with various collectors (Zn, Ga, Bi, In, Sc, Sr, Y, Cd) on introducing potassium carbonate into aqueous solutions of potassium sulfate, hydrosulfate, chloride, and nitrate with the salt concentration of 25 to 250 g dm–3 was studied. The optimum composition of the coprecipitants and the precipitation conditions were determined by methods of mathematical experiment design. The procedure developed is applicable to solutions of alkali metal sulfates, chlorides, and nitrates.