D-optimal Plan Research Articles

D-optimal designs for a two-dimensional polynomial model

The influence of an affine transformation of the design space on the number of support points in the D-optimal design has been studied for a two-dimensional polynomial regression model. For a full rank model of degree n, a result was obtained that determines the structure of the D-optimal plan. It is proven that for a region of design space that is symmetric about zero, the optimal plan is symmetric as well. This result allows for a significant reduction in the dimensionality of the optimization problem and forms the basis of an algorithm developed by the author for finding D-optimal plans for models of incomplete rank in nonsymmetric design regions. The D-efficiency of designs concentrated at equidistant points was investigated.

Experimental and industrial method of synthesis of optimal control of the temperature region of cupola melting

The object of research is the temperature regime of melting in a cupola. The synthesis of optimal control of such an object is associated with the presence of a problem consisting in the complexity of its mathematical description and the absence of procedures that allow one to obtain optimal control laws. These problems are due to the presence of links with a pure delay, non-additive random drift, and difficulties in controlling the process parameters, in particular, accurately determining the temperature profile along the horizons and the periphery of the working space of the cupola. The proposed conceptual solution for the synthesis of optimal temperature control allows the use of two levels of control: the level controller solves the problem of maintaining the constant height of the idle charge, and the problem of increasing the temperature of cast iron is solved by controlling the air supply to the tuyere box. It is shown that the problem of regulating the upper level of an idle charge can be solved by reducing the model of the regulation process to a typical form, followed by the use of the Pontryagin maximum principle. A procedure for the synthesis of optimal air flow control is proposed, which makes it possible to obtain the temperature regime control law on the basis of experimental industrial studies preceding the synthesis process. This takes into account the time delay between the impact on the object and its reaction, which makes it possible to predict the temperature value one step acharge, equal to the time interval during which the lower surface of the fuel charge reaches the upper surface of the level of the idle charge. A procedure for temperature profile control based on the use of D-optimal plans for selecting sensor installation points is proposed. Due to this, it becomes possible to determine the temperature profile of the cupola according to its horizons and the periphery of the working space of the cupola with maximum accuracy. The proposed synthesis method can be used in iron foundries equipped with cupolas, as it is a tool for studying a real production process, taking into account its specific conditions. This will allow developing or improving control systems for cupola melting, implementing different control modes: manual, automated or automatic

CO2 Emissions of Electric Scooters Used in Shared Mobility Systems

The development of the electric mobility market in cities is becoming more and more important every year. With this development, more and more electric scooters are appearing in cities. Currently, the restrictions that result from the upcoming trends are reducing the number of vehicles powered by combustion engines in favor of vehicles equipped with electric motors. Considering the number of electric vehicles, the dominant type is an electric scooter. The aim of this article is to determine the CO2 that is emitted into the atmosphere by using this type of vehicle. The main suppliers of this type of vehicle in cities are shared mobility systems. To recognize the research gap, consisting of the lack of CO2 emissions of an electric scooter type vehicle, studies were carried out on the energy consumption of an electric scooter and CO2 emissions, which were calculated based on the CO2 emission value needed to produce a given energy value kWh. The plan of the research performed was developed on the basis of the D-optimal plan of the experiment, thanks to which the results could be saved in the form of mathematical models based on formulas.

Determining the effective mode of operation for the system of washing the milking machine milk supply line

The application of techniques for effective cleaning of milking routes in milking machines is an important way to improve the quality of milk and increase labor productivity in dairy farming. The object of research was the system of washing the milk line of the milking machine with the upper milk line. The problem of rational use of energy resources was solved in the implementation of a routine operation – washing the milking machine. Experimental studies were carried out according to the Box-Benkin plan of the second order for 3 factors (the speed of movement of the washing solution, V; the temperature of the washing solution, T; the duration of the rinsing phase, t). In this case, a mathematical apparatus for planning a multivariate experiment according to the D-optimal plan was used. It was found that with an increase in the speed of movement of the washing solution and temperature, as well as the duration of the rinsing phase, the number of microorganisms on the surfaces of the nodes and elements of the milky line decreases. Milk lines of the milking machine made of any material are better cleaned with a hotter washing solution (40 °C) than with a cold one (20 °C). Thus, when cleaning with a solution of 40 °C of stainless steel and food aluminum, the reduction of microorganisms is 4.3 times, glass – 4 times, and rubber – 4.7. The essence of the experiment was to establish patterns when cleaning the milk line from various materials. The influence of the regime parameters (the speed of movement of the washing solution, V; its temperature, T; and the duration of the rinsing phase, t) on the energy consumption of the milking machine, E, was determined. The compromise problem of rationalizing the washing modes of the milk lines of the milking machine has been solved. Thus, rational mode parameters for the washing system were established: V=2.4 m/s, T=38.2 °C, t=3.2 minutes. With these parameters, the optimization criteria are: N=79 thousand CFU/cm3, Q=23.3 l, E=8.08 kWh

The use of technological aids in the processing of bacterially infected sugar beet

In the technology of beet sugar, technological aids play a special role, but the effectiveness of their complex application in the processing of bacterially infected sugar beets requires study. A three-factor laboratory experiment was carried out on the basis of the D-optimal Box-Behnken plan of the second order for three levels of variation of the studied factors the enzyme preparation Dextrasept 2, the antimicrobial agent Betacept and the defoamer Voltes FSS 93. The quality of 15 studied indicators of the state of intermediate products of the processes of obtaining and purification of diffusion juice, syrup was determined according to the generally accepted methods. The obtained regression equations adequately reflected the combined effect of these drugs on the state indicators. The highest variability (24.2-39.0%) was observed for the turbidity of juices and syrup, and the deposition rate; тhe chromaticity, the content of high-molecular compounds, lactic acid, and the height of the foam column were characterized by an average variation (12.7-17.8%). The sucrose content and the overall effect of purification of diffusion juice changed insignificantly (0.4-3.0%). Сontribution of the enzyme preparation to the variation of 6 indicators was more than 45%, 7 – 3942% and 2 – less than 10%. Under the influence of the antimicrobial agent, 6 indicators changed by more than 45%, 5 – 33-43% and 4 – less than 30%.

РОЗРОБКА МЕТОДИКИ ОПТИМІЗАЦІЇ ВІДНОВЛЕННЯ МОСТІВ

Abstract. The biggest part of the bridges in Ukraine requires serious restoration works. However, in the literature sources there are no recommendations for choosing effective organizational and technological solutions for the reconstruction of bridges and overpasses. Therefore, the design of methods for optimizing bridge restoration is an urgent task. The working optimization hypothesis is formulated in the article. A general research technique is developed. The algorithm of multicriteria analysis is presented to determine the most effective structural and technological solutions for the restoration of the main structural elements of the studied structures. As a result of the analysis, the most significant indicators of restoration efficiency were determined. These were the cost of restoration of m2 of the bridge and the duration of restoration of the bridge. As factors affecting performance indicators ‒ the intensity of the use of working time and the combination of construction processes, the size of the roadway and the operational condition of the bridge were selected. The planning of the experiment is based on the well-known theory of experimental planning. A 25-point D-optimal plan was selected, which will provide adequate results with significantly fewer experiments than in a full-factor experiment. For calculations is used the program software COMPEX, which is developed at the Odessa State Academy of Civil Engineering and Architecture under the direction of Professor V. Voznesensky. Modelling allows to find the dependencies between the input (intensity use of working time, combination of construction processes, size of the carriageway of the bridge, operational condition of the bridge) and output (cost of restoration of m2 of the bridge, duration of restoration of the bridge) parameters. Dependences data is described with usage of second-degree polynomials obtained by processing the results of a numerical experiment. These dependencies will allow to determine the cost and duration of the restoration of the bridge for varying degrees of damage and the size of the bridge. In addition, to change indicators by choosing the optimal production modes (combination of processes, the intensity of the use of working time). The analysis of the results of a numerical experiment will allow us to assess the influence of organizational and technological factors on the performance indicators of restoration technologies and find areas of factor space that provide optimization of organizational and technological solutions for the restoration of damaged bridges. At the last stage of the numerical experiment, limits are introduced into graphic models (by cost, duration, combination, etc.) and the optimal organizational and technological solutions are determined taking into account the introduced restrictions.

Bead formation research in TIG welding of AISI 304 steel

On the basis of the experimental results in depositing strips of molten metal onto AISI 304 steel using the D-optimal plan of the experiment and processing of the got results, regression equations were obtained describing the dependence of the bead width and the penetration depth depending on the welding speed and the value of the welding current. In parallel, a regression equation is obtained connecting the arc voltage and the welding current.

Optimal Plans of Constant-Stress Accelerated Life Tests for Extension of the Exponential Distribution

Abstract In this article, the optimal plans for a k-level constant-stress accelerated life test are presented for extension of the exponential failure data under complete sampling. According to the log-linear life-stress relationship, the optimal proportion of test units allocated to each stress level is determined under D- and C-optimality criteria. Moreover, a real data set is analyzed to illustrate the proposed procedures. Furthermore, the real data set is used to show that extension of the exponential (EE) distribution can be a better model than both Weibull distribution and generalized exponential distribution. In addition, numerical examples are used to illustrate the proposed procedures and to compare between the D-optimal plan and C-optimal plan through asymptotic variance of maximum likelihood estimators. Finally, some interesting conclusions are obtained.

Controlled-release in-situ gel forming formulation of tramadol containing chitosan-based pro-nanogels

Chronic pain is one of the most prevalent health problems worldwide. Tramadol is a synthetic semi-opioid analgesic, interacting with serotonergic, adrenergic and opioid receptors to reduce the pain but its short half-life in vivo may reduce patient compliance in case of chronic pains. To overcome this problem, novel drug delivery systems have been investigated. This study focuses on a chitosan based thermoresponsive in-situ gel forming formulation intended to subcutaneous injection. To evaluate further drug release, a reversed phase high performance liquid chromatography method was developed. Then two formulations (with and without TPP) were optimized by D-optimal plan using Design-Expert statistical software and were characterized in terms of morphology, release phenomenon, texture, swelling and stability as well as in vivo response. AFM images show approximately spherical nanocavities in the homogenous TPP containing gel structure, which explain the different patterns of drug release between the two formulations. This implies that changing TPP concentration can control formation of these cavities and hence drug release rate and kinetics. Not present in the sol state, nanostructures lead to emerge of a new concept: pro-nanogels. Finally, the formulations with proper texture qualities, stability and rapid sol-gel transition in vivo could be a candidate for controlled release of therapeutic agents following subcutaneous injection.

D-optimal 2 × 2 × s3 × s4 saturated factorial designs

In this paper, Resolution III saturated , factorial designs and specially the cases , , are studied, in order to obtain D-optimal plans.

Optimal Plans of Constant-Stress Accelerated Life Tests for the Lindley Distribution

AbstractIn this paper, the optimal plans for k-level constant-stress accelerated life test are presented for Lindley failure data under complete sampling. According to the log-linear life-stress relationship, the optimal proportion of test units allocated to each stress level is determined under D- and C-optimality criteria. Moreover, two real data sets are analyzed to illustrate the proposed procedures. Furthermore, the real data sets are used to show that the Lindley distribution can be a better model than one based on the exponential distribution. In addition, numerical examples are used to compare between the D-optimal plan, C-optimal plan, and traditional plan through asymptotic variance of maximum likelihood estimators (MLEs). Finally, some interesting conclusions are obtained.

Strength analysis of lamellar graphite cast iron in the «carbon (C) – carbon equivalent (Ceq)» factor space in the range of C = (3,425-3,563) % and Ceq = (4,214-4,372) %

The object of research is the structural lamellar graphite cast iron, where the carbon equivalent (C eq ) is in the range of (4,214-4,372) % and the carbon content (C) is in the range of (3,425-3,563) %. The aim of research is to describe the distribution of values of tensile strength of cast iron series in the factor space C–C eq at a fixed level of Cr-Ni-Cu-Ti alloyed complex in narrow ranges. To achieve this aim, there are the next objectives. 1. Build a workable analytical description of the impact of the selected input variables on the tensile strength of cast iron. 2. Study the response surface and identify the most informative point of the factor space for further detailed investigation of the microstructure in these points. It is shown that polynomial regression equation provides forecast accuracy, exceeding the accuracy using a linear regression equation in 1,23 times. An existence of a saddle point is revealed on the basis of the canonical transformation of response surface. It is an informative indicator, which suggests that the respective values of the input variables C = 3,492 %, C eq = 4,28 % when the content of alloying elements , form a microstructure that guarantees the value of cast iron tensile strength TS = 203 MPa. In view of the resulting confidence interval, this value with a probability of 95 % is in the range of TS = (193-213) MPa. Metallographic microstructure description in the saddle point is important and can be obtained by the development of modeling results. It is noted that there is a fundamental opportunity to improve accuracy and obtaining more precise description of the response surface – due to numerical building of D-optimal plan or artificial orthogonalization of full factorial experiment , inside the considered in this work

A-optimal and D-optimal censoring plans in progressively Type-II right censored order statistics

We study how the marginal distribution and Fisher information matrix of progressively Type-II right censored order statistics change when the progressive censoring plan changes. We consider the missing information and its connection with Fisher information matrix to determine the A-optimal and D-optimal plans in multiparameter case. We provide a simple expression and a simple way of determining an optimal censoring plan among a class of one-step censoring plans. Finally we give examples to illustrate results.

Influence of rigidity of the hardened parts on forming the shape accuracy during flat grinding

At present time there is not information about the influence of rigidity of hardened steel parts on the parameters of flatness deviations: EFE max , EFE a , EFE q , which are called correspondingly greatest, arithmetic average and quadratic average. To model the variable rigidity of workpieces, an arrangement with the frame structure was used. It allowed to simulate the variable compliance of parts with constant sizes in the direction of longitudinal feed of grinding machine. Searching for models of multiple dispersion analysis was carried out using the D-optimal plan of experiment. They predicted that in rough grinding all parameters of flatness deviations increase with the growth of the part rigidity. In the subsequent grinding stages, the increase of part rigidity is accompanied by the favorable decrease of the flatness deviations. The compliance of low-rigid parts in the finishing stage of grinding should be reduced using additional technological devices.

Bayesian D-optimal Accelerated Life Test plans for series systems with competing exponential causes of failure

This paper provides methods of obtaining Bayesian D-optimal Accelerated Life Test (ALT) plans for series systems with independent exponential component lives under the Type-I censoring scheme. Two different Bayesian D-optimality design criteria are considered. For both the criteria, first optimal designs for a given number of experimental points are found by solving a finite-dimensional constrained optimization problem. Next, the global optimality of such an ALT plan is ensured by applying the General Equivalence Theorem. A detailed sensitivity analysis is also carried out to investigate the effect of different planning inputs on the resulting optimal ALT plans. Furthermore, these Bayesian optimal plans are also compared with the corresponding (frequentist) locally D-optimal ALT plans.

A significant part of the experimental investigations (EI) in wind tunnels (WT) aimed at simultaneous measurement of air pressure at distributed points as in the WT, and aircraft models (AM) and in jet engines. In this regard, the actual problem is creati

A significant part of the experimental investigations (EI) in wind tunnels (WT) aimed at simultaneous measurement of air pressure at distributed points as in the WT, and aircraft models (AM) and in jet engines. In this regard, the actual problem is creation of means and methods for simultaneous measurement of pressure as discussed in the work.The first method. The holes of the selection pressure pneumatic tracks (PT) are connected to the pressure sensor (PS), which are connected to the channels of the measuring system (MS). In this MS apply precision instrumentation programmable filter, communication interface with computer and time measurement for channel ≤40ms. The cost of this MS is high, even for 16 channels measurement interval ≥640ms, which for most of the EI is not acceptable.The second method is the use of electro-mechanical pneumatic switches (EMPS). For example, in EMPS type PS-180/ 300/ 420 continuously rotating the rotor of the switching node with a phase shift connects PT to PS, synchronously with the time of establishment of pressure measurement is performed.The third method is the use of mobile pneumatic modules with interface for the transmission of real-time experimental data (ED) in MS. Such devices, for example, can be up to 16 with the number of measured channels and 256.The proposed unified information-MS (IMS), which can be implemented on different hardware and software platforms (VME, PC/104, MicroPC, etc.).Processing. Is calculated, sorted and stored value of the absolute and relative pressure pulsations of velocity head. Determine the mean value and standard error. Normal distribution was confirmed by ED Pearson criterion at the significance level . Statistical reproducibility of ED is confirmed by the criterion of Cochran, assess the homogeneity and error. Is determined by the Reynolds number based on the physical parameters in the WT. The accuracy of the ED algorithm provides operational control of IMS.The transformation function PS is defined in terms of the polynomial. In difficult cases it is necessary to use D-optimal plans experiment.The coefficients of longitudinal and normal components of aerodynamic force, the coefficient of longitudinal moment, the relative position of the center of pressure, normal and tangential components of aerodynamic forces. The problem is to compute the integral with minimum error. It is recommended to apply the Romberg method.

Predictive microbiology for cosmetics based on physicals, chemicals and concentration parameters.

Challenge test (CT) is essential to assure the efficiency of the preservative system in products. A previous study realized by our staff in 2012, carried out to evaluate the influence of three parameters (ethanol, pH and water) on the microbiological cosmetics products conservation. Following this work, a correlation between aw (based on the glycerine concentration) and the selected parameter has been demonstrated. In the present study, smaller limits of ethanol, pH and glycerine were applied to determinate CT necessity. Sixteen stables O/W cosmetics creams with different concentration of ethanol (1-19%), glycerine (3-16%) and different pH (6-11) were formulated. To evaluate the efficiency of the different formulations, CTs were performed according to the International Standard ISO 11930:2012. To determine the influence of the parameters, a D-optimal plan generated by Design Expert(®) was applied. Design of Experiments software offers to plan, estimate and control the statistics and models for factorial and no-factorial designs. Challenge tests results show that 10 formula passed criteria A, two passed criteria B and four are not conform. Mostly, an ethanol concentration higher than 16% exempts products of CT. It has been shown that an ethanol concentration between 10.5% and 16%, and an glycerine concentration >10%; or if the ethanol concentration is between 5% and 10.5%, glycerine is >6% and pH is ≥10, the CT is not required. Ethanol has a significant impact on conservation and especially when it is correlated with glycerine and pH. Finally, a glycerine concentration higher than 16% exempts products of CT. Following the analysis of the different concentration, a correlation between glycerine and ethanol that directly influence microbiological protection of cosmetics products has been established. Indeed, by controlling ethanol, pH and glycerine, many products may be exempted from the CT.

A graphical construction of the D-optimal saturated, [formula omitted] main effect, factorial design

This paper considers the incidence (bipartite) graph G , which is associated with a saturated main effect, 3 × s 2 factorial design. Some certain classes of paths are defined and it is shown that their various combinations determine the upper bound of the value of the determinant of the adjacency matrix. Therefore, a specific type of planar graphs is constructed and the main goal of this result is the production of D-optimal plans for each s ⩾ 3 .

Optimal experiments in the presence of a learning effect: a problem suggested by software production

In software engineering empirical comparisons of different ways of writing computer code are often made. This leads to the need for planned experimentation and has recently established a new area of application of DoE. This paper is motivated by an experiment on the production of multimedia services on the web, performed at the Telecom Research Centre in Turin, where two different ways of developing code, with or without a framework, were compared. As the experiment progresses, the programmer’s performance improves as he/she undergoes a learning process; this must be taken into account as it may affect the outcome of the trial. In this paper we discuss statistical models and D-optimal plans for such experiments and indicate some heuristics which allow a much speedier search for the optimum. Solutions differ according to whether we assume that the learning process depends or not on the treatments.

Prognosis of characteristics of multicomponent materials on the example of flexural strength of portland cement

In this paper we have made prognosis of flexural strengths of portland-cement after 3 and 28 days and pointed out importance of application of determined mathematical methods, which can be used for forming of mathematical models. Using of D-optimal plans and plans including “pseudocomponents”, original mathematical models are realized, which make possible, for different composition of four-component C-S-A-F system, to determine strength values of portland-cement after 3 and 28 days. For forming of corresponding mathematical models, for realization of qualitative prognosis, a polynomial of fourth order was used. Calculation of polynomial coefficients and determination of analytically form are made on calculator PDP 11/40.