Received date: June 11, 2018; Accepted date: June 27, 2018; Published date: July 02, 2018.
For solving the problems of study, analysis and quality management of the environment there is necessary operatively to treat great amount of measuring information on physical, chemical and biological parameters characteristic for them. To do it in a proper way is possible only by wide use of modern mathematical methods and computers. For this purpose, it is necessary to develop automated systems and universal program packages with modern mathematical methods consisting of self-learning algorithms requiring minimal a prior information and having capability of adaptation to the most unexpected changes of the character of the investigated objects. Among the most topical problems of monitoring of a natural water environment it is necessary to develop: the automated water quality control systems for operative control and management of water pollution level; simulation of pollutants transferring in water objects; methods of making decisions about condition of controlled objects and processes taking place in them; identification of sources of emergency pollution. These problems are especially urgent in urban conditions because their great number of sources of pollution exist. Their solution is of great ecological and economical significance which makes possible to investigate the effect of different sources of pollution on ecological object separately from each other, as well as jointly, to predict outcomes of such an impact and consequences of the nature protection measures against the sources of pollution. They are also actual for large plants and factories having biochemical clearing of sewages, on their design and ecological safe operation.
: Environmental Water; Pollution Control; Systems Analysis; Mathematical Methods; Software.
Technical progress brought the civilization to the arising of numerous artificial factors, the influence of which on the environment becomes in all perceptible. This implies the quantitative and qualitative change of the environment. In this connection, there arises the actual problem of studying and analyzing the existing situation with the aim to elaborate the principles and facilities of saving the life-friendly environment.
It is essential to have the adequate information about the quality of the environment for its study, analysis and management. The environment is characterized by an enormous number of physical, chemical and biological parameters. A lot of measurements are necessary for the permanent control of these parameters. Therefore, the solution of the problems of control and management of the quality of the environment can be realized only by using automated, continuously functioning analyzers of environmental pollution and automated systems of supervision and control of the environment. The designation of such systems consists in operative reduction of environment pollution based on the continuous control, forecasting and regulation of the pollutants in unfavorable situations by operative organizational-technical measures and optimal planning of long-term environment protection measures by rational distribution of existing means for each object when their quantity is limited. Designing of the systems of this kind is associated with the solution of complex problems of development of new methods and facilities for the control and management of the quality of the environment based on the methodology of the systems approach with a wide use of the modern methods of mathematics, cybernetics, modeling, information-measurement and computer instrumentation. Effective application of new methods and facilities for designing of control and management systems is hindered by the lack of systematic materials in the area of applied research of the processes of control, estimation, forecasting and regulation of their conditions.
When solving the practical problems of environment protection, to the fore come the issues associated with the measurement and control of physical quantities that are characterizing the state of this environment, as well as of the improvement of the authenticity of the information obtained by using the environment quality analyzers. The measurement information (MI) of automated measurement devices of control of the environment quality is with “noise”. It contains incorrect information along with useful information. This distorts the identity of the decision about the state of the environment. The appropriate processing of this information is necessary for filtration of MI and making an optimal decision concerning the current and perspective state of the environment. Elaboration of common methodology of the development of different aspects of automated environment control systems such as: systems, technical, informational, metrological, program, mathematical is a quite topical problem.
Automated control systems are used for operative environmental control and making decisions about the state of controlled objects. The theory of decision making is one of the most developed ones in modern mathematical statistics. However, despite the deep study of the problems of decision making in general, the development of new methods taking into account the specificity of the information-measurement systems of environmental control remains problematic.
The theory of mathematical modeling formed as an independent branch in the modern applied mathematics in the fifties of the last century. Its possibilities for the solution of complex scientific-technical problems increased practically unbounded with the development of computer technologies. The development of practical models of the environment pollution processes, with the possibility of their use in automated systems, for the solution of systems, environment protection, technical and metrological problems is very topical. Modeling opens wide possibilities for designing the analytical measurement means. It allows us to automate this process. Therefore, the work containing the general principles of modeling, working models of analytical measurement devices and their practical applications is very topical too .
Actual problems of application of mathematical methods and computer technique to the problem of pollution control of the water environment
The basic problems of environmental control and management are to acquire adequate information about the state of the environment and to make competent decisions based on this information. This can be achieved by improving the quality of MI, i.e. by improving the accuracy of measurement results and by processing these results properly, which will allow us to make an objective estimation of the existing situation, to forecast its possible development and to make a reliable decision for improving the quality of the environment. The possible ways for solving these problems are briefly considered below.
Basic sources and characteristics of the pollution of water objects
The problem of study and analysis of the environment pollution level with the purpose of making the means for saving the life-friendly environment is very topical. Kinds of pollution are diverse, including pollution of the environmental air, water, soil, noise, vibration, radiation, radio and electromagnetic fields and so on. Of these problems, the problem of the pollution of the water environment, its control and conservation in ecological equilibrium occupies the leading position.
The growth of cities and the expansion of manufacture cause the increase in the pollution level of the rivers, gulfs and seas. The pollutants spread in the limited water environment, the unpolluted volume of which has its limits. Water pools serve as collectors of retirements, and at the same time they are the sources of water and fishing, which makes the problem of water protection even more important.
Under the term of the water environment pollution we mean the change in its structure and properties under human influence that causes the deterioration of the water quality. There are three basic sources of the pollution of the environmental water: 1) economic-social sewage; 2) industrial sewage and 3) sewage from agricultural fields. The number of pollutants entering the environmental water from these sources is huge. It can reach up to 106, whereas their concentrations, in most cases, are very low and vary over the interval from 10-1 to 10-9 mg/l . For defining objectively, the state of a water object, on the one hand, we need the measurements of these parameters and, on the other hand, the criteria for making a decision about the pollution with these parameters. In many countries of the world, such criteria are maximum allowable concentrations (MACs). The maximum allowed concentration is the maximum concentration of an impurity, averaged over some interval of time, that periodically or during a full period of its life does not affect harmfully people or the environment. For controlling the environment, it is necessary to solve three problematic tasks: what to control, how to control and by what to control. Without solution of any of these problems, effective control of the environment is impossible.
All over the world, they work on the determination of the most important pollution factors and on designing of high-quality devices for measuring their concentrations in the monitored environment, and for definition of MACs for relevant substances as well. Unfortunately, MACs exist for a much less number of substances that can be measured.
The total number and the composition of parameters included in the list of important pollution substances differ significantly in different countries. Their choice is substantiated not by purely scientific thoughts, but by existing traditions, and economical, technical and other factors . In many works, the following parameters are considered as the basic indicators of water pollution: temperature, relative acidity, pH, electro-conduction, dissolved oxygen, chlorides, general alkaline, weighed substances, general content of organic carbon, chemical oxygen demand, biological oxygen consumption, etc.
Furthermore, the content of the following substances in water have decisive values concerning the natural processes in water: heavy metals, ions of different elements, oil products, pesticides, turbidity and so on .
As mentioned above, it is impossible to control the content of all pollution substances in the water for different reasons: their number is huge, they cannot be measured, there are no appropriate MACs, creation of a huge control system stipulates a set of problems of systematic character and so on. Development of a group of indicators (for example, organic carbon, chemical oxygen demand, biological oxygen consumption, etc.) and finding of the correlation relations among them and between individual indicators are offered as a way out from the existing situation in .
At present, the water quality control systems measuring a small number of water parameters (up to several tens) are developed. In the world, they continue working on the development of more modern systems which will be capable to control automatically a big number of the parameters, as well the development of the set of such systems for complex monitoring of whole regions.
Problems and facilities of quality increasing of analytical measurement information and control and regulation of water objects
Measurement errors are caused by a number of factors. There are methodological, instrumental and random errors. The methodological errors are associated with a number of factors: fixing of a transducer reading until the end of the process; linearization of the device scale; errors of dosage and dilution; wear and tear of the parts facilities and so on. Instrumental errors are caused by inaccuracy in the manufacture of elements and units of measuring devices. Random errors are determined both by the fluctuations of the environment and by the performance of the measuring system on the whole, in particular, the random errors in measurement channels, heterogeneity of the measurement environment and so on.
Due to the significant difference among the factors of distortion of measurement results, the methods and means for its elimination or mitigation can be different. In particular, to reduce the methodological errors of measurement: the methods of improving the dynamic characteristics of measurement devices, structural methods of correction of errors of measurement results, calibration and verification of measuring devices, mathematical and simulation modeling of measurement devices, complexes and systems with the purpose of automation of their design and of metrological analysis.
To reduce the instrumental errors, it is necessary to use widely the methods of automated design of measuring devices, to increase the qualification of instrument makers, to use high-quality materials and modern means of production, to use modern manipulators and robot technology in the production process with the aim of its complete automation.
To eliminate the errors caused by random fluctuations, the methods of mathematical statistics are widely used. In particular, the methods of filtration, design of optimal experiment, regression analysis, correlation and dispersion analyses, processing of time series and so on. The proper use of these methods allows us to reduce the impact of random fluctuations on the measurement results to a practically acceptable level.
The controlled water environment is a rapidly changeable dynamic object, the control of which by non-automated methods is difficult and not justified economically. According to , if the measurement is carried out more than 3-4 times for twenty-four hours, it is economically justified to use the automated systems. With application of the automated systems for environmental water control, the price of information is several (2-6) times lower than with the use of laboratory methods. Moreover, the use of the automated systems open wide opportunities for applying the modern mathematical methods of the theory of systems, of management and planning, system and applied programming for solving the problems of hydrology, hydro-chemistry, hydro-biology with the purpose to enhance the reliability, efficiency of the decisions made and to study more deeply the processes originated in the controlled water environment.
The work on the development of automated systems of environmental water quality control (ASEWQC) started in the late seventies of the last century. These systems are designed for decreasing the level of environmental water pollution based on observation, control, prediction and management of the discharge of pollutant into water. Technical requirements imposed on ASEWQC are determined by a set of tasks they should accomplish. The major problems to be resolved by using these systems are the following:
- automated observation and registration of the concentrations of pollution;
- analysis of the obtained information with the purpose of determination of the real state of the environment;
- implementation of emergency measures for environment protection;
- forecast of pollution tendencies;
- working-out of perspective recommendations for improvement of the environmental water state.
From the listed problems to be resolved by using ASEWQC, it is obvious that they must contain the following functional blocks:
- automated measurement stations (AMS), which allow to collect the data over a wide range of the values of monitored parameters of the water environment;
- data transfer devices (DTD) for transferring the information from AMS to the information collection and processing center (ICPC);
- information collection and processing centers where there is realized automated collection of information, the AMS call, synchronization of their performance, transfer of commands and service of the inquiries of AMS, receiving and collection of the information from AMS for its storage and processing with the purpose of assessment of the state of the water environment, forecast of its state and working out of the recommendations for improving the environmental quality, as well as for transferring the relevant information to ICPC of higher hierarchy.
When designing ASEWQC, it is necessary to solve a set of organizational, scientific-technical and economic problems. The definition of the place and status of the considered system in the existing organization of water environment monitoring, the degree and order of expected changes in this organization are considered under organizational problems.
The solution of scientific-technical problems implies the choice and justification of the structure of the system, the complex of technical means (CTM) based on the volume and complexity of the functional problems and requirements to the efficiency of decisions made, condition of the compatibility of the given system with other existing ones of different hierarchy. The choice and justification of the methods of solution of functional problems are necessary. The accepted organizational and scientific-technical solutions must be substantiated by economical calculations.
The automated system of environmental water quality control (ASEWQC) is a component of monitoring systems. Monitoring is a complex system of observation, estimation and forecasting of the state of the environment with the purpose of its protection against an anthropogenic impact. According to the monitored territory, the frequency of control, the volume and functional purpose of the problem to be solved, there are distinguished the following types of monitoring systems: local (executive), regional (operational) and global (suppertime). The characteristics of these monitoring systems are given in the Table 1 below . Designing of state and interstate environmental monitoring systems is expected in the near future. A number of developed countries already have the experience of designing of such systems.
Table 1: The types of monitoring and their parameters.
The type of a monitoring system
The area enclosed by a system, km2
up to 105-107
Distance between the sampling points, km
up to 3x103-5x103
Periodicity of the study
Tens of years - centuries
Frequency of observations
Minutes - hours
Ten-days – months
2 – 6 times in the year
The number of observed components
3 – 30
120 – 1,500
103 - 106
Fraction of MAC
up to 30%
Tenths of a percent
Frequency of the release of information
In real time
In 1-3 months after sampling
Years after sampling
Basic ways of improving the quality of analytical measurement devices
The measurement devices have two types of basic characteristics: dynamic and static. The improvement of static characteristics provides for the authenticity of information. The improvement of dynamic characteristics provides for the efficiency of obtained information when measuring stationary values, while, with measuring non-stationary values (for example, with continuous control of a certain ingredient in a range), the measuring process is restored. To provide the latest only on the basis of inertial measurement devices, without correction methods of the exit signals, is impossible in principle.
The measurement data of measuring devices are generally distorted. Distortion is due to both deterministic and random factors. The deterministic factor of distortion in general is caused by deviation of the parameters of measuring devices from normal values depending on the fluctuations in the measurement environment due to its heterogeneity and imperfectness of measuring devices.
At the modern level of development of science and technology, the requirements to the authenticity of MI constantly increase. There are two ways of improving the metrological characteristics of measuring devices: perfection of the devices by using new measurement principles and development of mathematical methods of MI processing, realized in measuring devices by means of modern computing hardware. The necessity in additional scientific research concerning the development of new principles, materials, production technologies, and the organization of production facilities restricts the possibilities of the first direction, making the second direction more preferable.
All over of the world there are developed a great arsenal of the methods and means of improving the quality of MI with the purpose of their use in different areas, including the environment protection. Unfortunately, generally, this problem was not adequately considered from the standpoint of the systems analysis, which remains quite actual for today.
Some Modern Software Related to the Problem
Different problems solved by the author of this work in accordance with the abovementioned strategy and realized as modern software, ready for application, are presented below. The mathematical methods, algorithms and their standard program realizations which were used at development of the considered below program packages are given in [3,4].
Application package of realization of mathematical models of pollutants transport in rivers (MMPT)
The development of the scientifically substantiated program of long-term planned measures, aimed at reducing the discharge of pollutants from different sources, estimating the ecological safety of different technologies, developing the control methods and means, forecasting and managing the quality of the environment, etc. is connected with mathematical modeling of the processes of transport and diffusion of harmful impurities. To overcome these and many other problems, the following mathematical models of formation of the river water quality under the influence of pollution sources are used in the considered program package: one-, two- and three-dimensional advection-diffusion models with the following initial and boundary conditions [5-7]: a) advective-diffusion equation with a non-local boundary condition at the end of the controlled section with an allowance for the coefficient of natural self-purification of the river; b) advective-diffusion equation with a boundary condition of full mixing at the end of the controlled section; c) advective-diffusion equation ignoring the vertical advection with a non-local boundary condition at the end of the controlled section with an allowance for the coefficient of natural self-purification of the river; d) advective-diffusion equation ignoring the vertical advection with a boundary condition of full mixing at the end of the controlled section; e) diffusion equation with a non-local boundary condition at the end of the controlled section with an allowance for the coefficient of natural self-purification of the river; f) diffusion equation with a boundary condition of full mixing at the end of the river controlled section.
The program system for numerical realization of the problems of pollutants transfer in water courses consist of three main parts: 1) the programs realizing one-dimensional problems; 2) the programs realizing two-dimensional problems; 3) the programs realizing three-dimensional problems.
The programs are mainly developed on the base of finite-difference algorithms. For some problems of specific character, the analytical method is used.
The main program modules used in all the parts are: 1) the program realizing the run method – the factorization method; 2) the program for solution of two- and three- dimensional implicit finite difference equation; this program is based on Gaussian-Zeidel iterative method.
Testing of the program system was carried out on specially selected tests problems and on the real data of some small and medium rivers of Georgia. Numerical experiments were carried out in order to: detect mechanical errors made during algorithmic presentation or programming; test the robustness against initial data, the accuracy of the results obtained, the calculating time; compare different algorithms, etc.
Particular attention was given to carrying out computational experiments in case of pollution sources of special type (an instantaneous point source, gaps in initial data, etc.).
The numerical experiments showed the high properties of elaborated algorithms and programs, the exploitation convenience, the received results accuracy and small time for calculation with high accuracy.
Input information for the developed programs is: the number and spatial coordinates of pollution sources; names and concentrations of pollutants discharged by pollution sources; special features of the river and the waste water discharge conditions (see Figure 1).
Besides of above mentioned, the program package runs service functions of initial data input-output, editing, graphic presentation of received results. There is a standard access to each package program (detailed description is given in the User Manual in Help).
The package workability has been tested in polar modes; the obtained results (see Figure 2) verify algorithms stability and reliability as well as high accuracy of the values computed.
The program package is developed for IBM-compatible personal computers in operational system WINDOWS.
Application of this software for modeling and simulation of pollutants transport in some rivers of western Georgia are given in [8,9].
Automatic Detection of River Water Excessive Pollution Sources (ADrweps)
One of the urgent problems of environmental monitoring is the problem of identification of emergency discharge sources in order to take measures to eliminate them. This problem is espe-cially urgent for city conditions where the large number of pollution sources do not allow to control of them all. Solution of this problem has not only an ecological effect, but a considerable economic effect that can be achieved by minimization of technical facilities, in particular, measurement equipment needed for separate control of each pollution source. This problem is also urgent for large factories and plants with biochemical waste-water purification, in order to identify those sections or shops that are guilty of waste-water pollution over the norm.
In spite of its urgency, this problem remained unsolved until the following works [10,11]. Simple algorithms, based on a cluster-analysis method and using the simplest model that only takes into account transfer and dilution of pollutants into wastewater, were developed and implemented in the automated waste water control system at the plant at the port of Odessa, in order to detect those shops, among five shops of the plant, which were guilty of the plant waste water emergency pollution .
The considered software is intended for automated identification of emergency discharge sources in rivers between two controlled ranges. It is developed for IBM-compatible personal computers in operational systems MS DOS and WINDOWS. Procedures, methods for solution of main problems, algorithms and programs realized in this work are original, belong to the authors and have no analogues. In particular, identification algorithms are developed that are based on methods of cluster-analysis and decision theory and are used according to the volume of a-priori available information. Increasing volumes of which require more complicated decision-making procedures, providing greater accuracy. For the last case, i.e. when the sufficient a-priori information is available, optimal (iterative) and quasi-optimal (analytical) algorithms for iden-tification of emergency pollution sources of river water are developed. Mathematical models of pollutants transfer in rivers that take into account special features of rivers, pollution sources and processes are developed. In particular, one-, two- and three- dimensional diffusion models of pollutants transport, at different initial and boundary conditions, according to special character of watercourse quality formation, were developed. Quantitative assessments allowing one to determine the limits of validity of these models, depending on special features of the watercourse, the pollutants and the type of their discharge, were obtained.
Input information for the developed programs is: the number and spatial coordinates of pollution sources; spatial coordinates and a list of parameters measured by automated stations by means of which the river is controlled; names and concentrations of pollutants discharged by pollution sources in normal and possible emergency modes of operation; special features of the river and the waste water discharge conditions (Figure 3,4).
Besides of above mentioned, the program package runs service functions of initial data input-output, editing, graphic presentation of received results. There is a standard access to each package program (detailed description is given in the User Manual in Help).
The package workability has been tested in polar modes; the obtained results verify algorithms stability and reliability as well as high accuracy of the values computed.
Automated water quality control system
The automated environmental water quality control systems open wide opportunities for objective control and management of the pollution level of their water environment, which increases the possibility of improving and making the environment life friendly. Such systems are under development in many countries of the world, and these activities become more and more intensive.
The considered automated water quality control system operates within data processing center. It is realized on the basis of IBM compatible computer with the use of commuted dropped off communication lines and gets measurement information on the concentration of parameters monitored from the automated water quality analyzers via the data transmission unit of MODEM type. Information software as well as mathematical software is realized as a system of application programs. The automated water quality control system can include very much (practically any number) of analyzers, each of them measuring up to 20 various ingredients.
The main features of the system are: operative processing of measurement information, validity of the results obtained, rapid adaptation to changes of controlled objects parameters without human intervention, simplicity of maintenance, flexibility when using the system for monitoring and analysis, visual presentation of the results obtained.
The information software realizes the following tasks:
- Automatic interrogation of water quality analyzers included into the system;
- Reception, deciphering and recording of the measurement information coming from the automated analyzers onto the carriers;
- Control of analyzers operating modes (start of the analyzer, inquiry for an additional measurement, change in step of analyzers operation, arbitrary sampling, inquiry for information recovery after the troubleshooting in case there has been a break in analyzers connection to the data processing center);
- Display of the current and retrospective measurements on the video terminal screen, support of communication between the operator at data processing center and data base (generation, updating and liquidation of system's directory and files), control of timely reception of measurement results from the analyzers, information output in accepted forms according to the user's order (24-hourly printout per analyzer; printing of master reports per analyzer for a day, a decade, a month; printing of reports on the violation of hydrological regimes), data archiving, processing of information coming from sanitary or mobile hydro chemical laboratories as well as stationary hydro chemical laboratories within surface water control system and printing of reports for 24-hours, a decade, a month, a quarter and a year; display of information on the video terminal by dispatcher's order.
A special attention is paid to displaying of information which includes graphical displaying of change in parameters controlled with time, visual interpretation of the states of water body controlled and of water quality control system, statistic processing of measurement results per each parameter and presentation of results of this processing in easy-to-use form, etc.
The mathematical software of the system realizes the following tasks:
- Preliminary statistic processing of the measurement results (calculation of the minimum, maximum and mean values of the ingredients measured in a given period of time);
- Calculation of trends for the temporal series;
- Calculation of automatic and inter-correlation functions for the temporal series;
- Classification of the state of the tests media in a discrete moment of time and evaluation of adequacy of the control (printing of alarm warnings; alarms in case of natural environment contamination);
- Calculation of the predicted values of the ingredients controlled with a given lead value;
- Classification according to the predicted values and calculation of adequacy of the decisions mode;
- Detection of trends of change in the state of media controlled; selection of optimum step for the discrete control of water quality; analysis of the ingredients measured for "anomaly" (i.e. abrupt change in the concentration of given ingredient);
- Search for a contaminer;
- Calculation of the maximum permissible discharge.
Communication with the information software and use of the information accumulated in the system for drawing up reports, carrying out hydrological, hydro biological, hydro chemical and other studies by methods of applied mathematics as well as visual presentation of the results obtained is carried out on the basis of the given menu on the computer display: system adjustment, operation with a database, reports, research, forecasting, mobile hydro chemical laboratories. In each menu respective submenus are realized. In particular, system adjustment - start, commands, initialization; operation with the database - generation of a file directory, file generation, file preparation, file nullification, communication with the information base, file annulment, maintenance of standardized information; reports-information display, operational paper, 24-hour report, master report over a decade, master report over a month, master report over a quarter of the year, master report over six months, annual master report; research - plots of the parameters measured, statistical study of the parameters measured, regression analysis of the parameters measured, correlation analysis of the parameters measured, forecasting of the values for the parameter measured; forecasting - routine, short-term I, short-term II, comparison. The following possibilities are realized in the submenu "commands": change in the measurement step, extra measurement, arbitrary sampling, regeneration of the information; "Generation of the file directory" offers the following: formation, abridgment, broadening and annulment of the directory. "Regression analysis" enables the regeneration of auto- and inter-regression between the parameters measured. Results of each task are presented in the form of a text, table or plot, which can be output to the computer monitor, printer or plotter, if any.
The system may include water quality analyzers together with air monitoring analyzers. It may be adapted to user's specific conditions.
Application package for experimental data processing (SDpro)
Computation of the metrological characteristics of measuring devices is complicated by the complexity of computation and the necessity of processing of a huge quantity of information. In some cases, it is impossible in principle to make such computation without suitable software because of the complexity of the computation algorithms. Therefore, the development of special software for making such computations is very urgent and important. One of such software packages, which subsequently became the universal software for experimental data analysis, is offered below.
All over the world there is a set of applied software package of processing of experimental data. For example, the wide propagation was received the statistical program packages: SPSS, SAS, STATGRAPHICS, STATISTICA, STADIA, SYSTAT, Evrista, MINILAB, Statistical Package for the Social Sciences, STATPACK2, MANOVA, PSTAT, SASGLM, GLIM, GENSTAT etc. In former of USSR were elaborated software packages of the statistical programs: a software of EU Computers, packages developed in Central Economical Mathematical Institute of Science Academy of USSR under a management of prof. S.A. Aivazian, applied program package SAFRA, developed in M.V. Keldish Institute of applied mathematics of Science Academy of USSR under the direction of the academician A.A. Samarski etc. These packages differ from each other by purpose and in the result by set of soluble tasks. Therefore no one of these packages no include the basic tasks that are included in offered package. The offered package is continuation of works on development of program packages processing of experimental results and essentially expands a circle of tasks solved by these packages.
The package is intended for processing results of various experiments and scientific investiga-tions by applied statistics and computational mathematics methods in metrology, instrumentation manufacturing, ecology, medicine, physics, biology, chemistry, economics, sociology and others .
The package is designed for a user unfamiliar with special sections of mathematics, applied statistics and programming. It is used for IBM PC compatible personal computers.
The merits of the package are: statistical efficiency, user friendliness. The package control is high automated. The result presentation is most suitable for the user (tables, plots, comments).
The contents and aspects of problems solve by package are treated as a result of expert questioning with due regard for the features of the unprecedented problems raised.
Programs contained in the package treat problems, which can be confined to eight aspects.
1. Computation of statistical numerical values includes:
• the graphical representation of initial data and analysis of “rude mistakes”;
• computation of main numerical values of the phenomenon under study;
• computation of confidence intervals of main numerical values (the classical method, a new method);
• checking of dispersion tolerance of variance estimation in several observation groups;
• checking of dispersion tolerance of arithmetic means by Fisher method;
• checking of dispersion tolerance of groups arithmetic means at different intra-group variance;
• identification of two empirical distributions by using of Chi – square and Kolmogoroff – Smirnoff tests (generalization of the classical case when a number and sizes of the intervals of giving of random values no coincide);
• calculation of probability distribution laws quantiles.
2. Computation of dynamic characteristics includes:
• identification of the first and second order equations of transient processes under different initial conditions;
• computation of pulse, transmission, transient and amplitude-phase- frequency characteristics.
3. Identification of functional dependences (include the possibility to calculate the prognostic values for arbitrary value of independent variable from its domain of definition) includes the restoration of auto – , inter – and multi-regression dependences of following view:
• y = a⋅xb (geometrical);
• y = a⋅ebx (exponential);
• y = a⋅ln(b⋅x) (logarithmic);
• y = a⋅xb⋅ecx (geometric-exponential);
• y = a⋅ (1 ⋅ e⋅bx) (inverse-exponential);
• y = a + b⋅xc (geometrical with a free term);
• y = a + b⋅ecx (exponential with a free term);
• y = (a+b⋅x)⋅ecx (linear-exponential);
• y = h + (a+b⋅x)⋅ecx (linear-exponential with a free term);
• y = a⋅xc⋅ (1 ⋅ bx)d (product of geometrical);
• y = a⋅xc + b⋅xd (sum of geometrical);
• y = a⋅ecx + b⋅edx (sum of exponential);
• y = h + a⋅xc + b⋅xd (sum of geometrical with a free term);
• y = h + a⋅ecx + b⋅edx (sum of exponential with a free term);
• y = ecx⋅ (a⋅cos(ωx) + b⋅sin(ωx)) (exponential-sine);
• y = h + ecx⋅ (a⋅cos(ωx) + b⋅sin(ωx)) (exponential-sine with a free term);
• Restoration of functional dependence by polynomial or trigonometrical splines.
These algorithms have been developed with regard to non-stationary variance within the observation range considering non-linearity factor. There are realized of regression analysis algorithms. There is the possibility to calculate the values of restored functional dependences in any points from their definition areas.
4. Identification of probability distribution densities includes:
• estimation of unknown parameters of probability distribution densities: normal, uniform, triangular, trapezoidal, antimodal I, antimodal II, truncated Raileigh, chi-square, Student, binomial, Poisson;
• identification of the above-mentioned probability distribution densities by chi-square test;
• identification of the above-mentioned probability distribution functions by the Kolmogoroff-Smirnoff and omega-square tests except for Poisson and Bernoulli distribution functions;
• testing of distribution normality at N<50 by V and D tests.
The chosen power of these tests are ensured at using estimations of unknown parameters of probability distributions defined by given sample at identifying a distribution function by Kolmogoroff-Smirnoff and omega-square tests.
5. Decision making application tasks include:
• computation of density functions of suspended particle sizes in liquid medium during dynamic sedimentation process at preset theoretical and empirical distributions;
• identification of two empirical distribution densities at different number of random variables representation intervals;
• identification of M-dimensional objects;
• detection of intensity variation of the Poisson flow;
• detection of intensity “rejection” of the Poisson flow;
• testing many simple hypotheses by using of unconstrained, constrained and quasi-optimal Bayesian decision making rules.
6. Non-parametrical methods:
• hypotheses testing by Mann-Whitney criterion;
• hypotheses testing by Wilcoxon criterion;
• sing test for one sample;
• sing test for the analysis of paired observations;
• Wilcoxon singed-rank sum test;
• One-factor analysis
- Kruskal-Wallis test;
- Jonckheere test;
- one-factor analysis of variance;
• Two-factor analysis
- Friedman test;
- Page test;
- two-way analysis of variance;
• Causation of indications measured in the scale of order
- Spearman’s rank correlation;
- Kendell’s correlation coefficient.
7. Time series processing includes:
• calculation of multidimensional time series trends and centred random series;
• calculation of forecasting values of time series;
• calculation of one-dimensional distribution law of momentary values of truncated realization of standardized random series;
• calculation of auto- and inter-covariance (correlation) functions and fulfillment of total cor-relation analysis; the latter includes in the following tasks: correlation coefficient, correlation coefficients homogeneity, correlation index, partial correlation coefficient, multiplicity correlation coefficient;
• calculation of auto- and inter-spectral power densities;
• testing stationary state by trend of centered random series;
• testing stationary state of centered random series according to the second moments;
• testing stationary state of centered random series using covariance matrix calculation errors.
8. Generating of pseudo-random numbers and processes includes:
• generating pseudo-random numbers distributed according to normal, uniform, triangular, trapezoidal, antimodal I, antimodal II, truncated Raileigh, chi-square, Student, binomial, Poisson distribution laws;
• generating the Poisson flow;
• generating normally distributed random vectors;
• generating multidimensional normal Markoff processes with calculation of made absolute errors;
There is a standard access to each package program (detailed description is given in the User Manual) and the user can insert each of them as a subroutine into him own package.
The package workability has been tested in polar modes; the obtained results verify algorithms stability and reliability as well as high accuracy of the values computed. Figure 5,6.
Language options are provided for communication with the package in all the software considered above. There are the possibilities to choose the working language from the set of languages that are realized in the packages. Moreover, the user can include himself the new language in package without any problems. In the Help is given very simple, suitable instruction.
It is necessary especially to emphasize, that the offered packages are completely original, as all algorithms, programs, texts, diagrams, figures, tables, design etc. realized in the given package, are original, belonging to the authors, and have no analogues.
Kachiashvili KJ (2017) EDITORIAL: Some Ways of Resolution of Current Environmental Problems. MOJ Ecology & Environmental Science 2: 00049.
Primak AV, Kafarov VV, Kachiashvili KJ (1991) System Analysis of Control and Management of Air and Water Quality. Naukova Dumka, Kiev, 360 p. (Science and technical progress)
Kachiashvili KJ, Melikdzhanian DI, Prangishvili AI (2015a) Computing Algorithms for Solutions of Problems in Applied Mathematics and Their Standard Program Realization. Part 1-Deterministic Mathematics. Nova Science Publishers, Inc., New York, 372 p.
Kachiashvili KJ, Melikdzhanian DI, Prangishvili AI (2015b) Computing Algorithms for Solutions of Problems in Applied Mathematics and Their Standard Program Realization. Part 2- Stochastic Mathematics. Nova Science Publishers, Inc., New York, 358 p.
Kachiashvili KJ, Melikdzhanian DI (2006a) Parameter optimization algorithms of difference calculation schemes for improving the solution accuracy of diffusion equations describing the pollutants transport in rivers. International Journal Applied Mathematics and Computation 183: 787-803.
Kachiashvili KJ, Melikdzhanian DI (2009) Software Realization Problems of Mathematical Models of Pollutants Transport in Rivers. International Journal Advances in Engineering Software 40: 1063-1073.
Kachiashvili KJ, Melikdzhanian DI (2012) Advanced Modeling and Computer Technologies for Fluvial Water Quality Research and Control. Nova Science Publishers, Inc., New York, 348 p
Kachiashvili KJ, Gordeziani DG, Melikdzhanian DI, Nakani DV (2006) River pollution components mean annual values estimation by computer modeling. Applied Mathematics and Informatics (AMIM) 11: 20-30.
Kachiashvili KJ, Gordeziani DG, Lazarov RG, Melikdzhanian DI (2007) Modeling and simulation of pollutants transport in rivers. International Journal of Applied Mathematical Modelling (AMM) 31: 1371-1396.
Kachiashvili KJ (1984) Identification of pollution sources by means of automatic stations of river water quality control. In the book: Regulation of the qualities of the environmental waters. Scientific Proceedings of VNIIVO, Kharkov, 114-119.
Kachiashvili KJ, Melikdzhanian DI (2006b) Identification of River Water Excessive Pollu-tion Sources. International Journal of Information Technology & Decision Making, World Scientific Publishing Company 5: 397-417.
Kachiashvili KJ, Melikdzhanian DI (2010) SDpro – The Software Package for Statistical Processing of Experimental Information. International Journal Information Technology & Decision Making (IJITDM) 9: 115-144.