The model uses quantitative analysis. Quantitative chart analysis

This type of analysis is based on the calculation of a number of quantitative indicators for the constructed model. It is necessary to take into account that these assessments are largely subjective, since the assessment is carried out directly using graphical models, and their complexity and level of detail are determined by many factors.

Complexity. This indicator characterizes how hierarchically complex the process model is. The numerical value is determined by the complexity coefficient k sl .

k sl = ? ur /? ekz

Where? ur -- number of decomposition levels,

Ekz -- number of process instances.

The complexity of the model under consideration is equal to:

At k sl<= 0,25 процесс считается сложным. При k sl =>0.66 is not considered as such. The process under consideration is 0.25, which does not exceed the complexity threshold.

Processivity. This indicator characterizes whether the constructed process model can be considered essential (describes the structure of the subject area in the form of a set of its main objects, concepts and connections) or process (all instances of the model processes are connected by cause-and-effect relationships). In other words, this indicator reflects how well the constructed model of a certain situation in the company corresponds to the definition of the process. The numerical value is determined by the process coefficient k pr

k pr = ? raz/? kep

Where? raz -- the number of “gaps” (lack of cause-and-effect relationships) between instances of business processes,

Processivity is equal to

Controllability. This indicator characterizes how effectively process owners manage processes. The numerical value is determined by the controllability coefficient k kon

k kon = ? s/? kep

Where? s -- number of owners,

Kep -- the number of instances in one diagram.

Controllability is equal to

When k kon = 1 the process is considered controlled.

Resource intensity. This indicator characterizes the efficiency of resource use for the process in question. The numerical value is determined by the resource intensity coefficient k r

k r = ? r/? out

Where? r -- the number of resources involved in the process,

Out -- number of outputs.

Resource intensity is equal to

The lower the coefficient value, the higher the efficiency of resource use in the business process.

At k r< 1 ресурсоемкость считается низкой.

Adjustability. This indicator characterizes how strongly the process is regulated. The numerical value is determined by the adjustability coefficient k reg

where D is the number of available regulatory documentation,

Kep -- number of instances in one diagram

Adjustability is equal to

At k reg< 1 регулируемость считается низкой.

Parameters and values of quantitative indicators are presented in table. 7.

Table 7. Quantitative indicators

For a general assessment of the analyzed process, calculate the sum of the calculated indicators

K = k sl + k pr + k kon + k r + k reg

The sum of the indicators is equal to

K = 0.1875 + 0.25 + 0.9375 + 0.273 + 0.937 = 2.585

The calculated value satisfies the condition K > 1. When K > 2.86, the process is considered obviously ineffective. At 1< K < 2,86 процесс частично эффективен.

The abstraction stage in the study of certain physical phenomena or technical objects consists of identifying their most essential properties and features, presenting these properties and features in such a simplified form that is necessary for subsequent theoretical and experimental research. Such a simplified representation of a real object or phenomenon is called model.

When using models, some data and properties inherent in a real object are deliberately abandoned in order to easily obtain a solution to a problem, if these simplifications only have an insignificant effect on the results.

Depending on the purpose of the research, various models can be used for the same technical device: physical, mathematical, simulation.

A model of a complex system can be represented as a block structure, that is, as a connection of links, each of which performs a specific technical function ( functional diagram ). As an example, we can consider the generalized model of the transmission system shown in Figure 1.2.

Figure 1.2 – Generalized model of an information transmission system

Here, a transmitter is understood as a device that converts a message from source A into signals S that best correspond to the characteristics of a given channel. Operations performed by the transmitter may include primary signal conditioning, modulation, encoding, data compression, etc. The receiver processes the signals X(t) = S(t) + x(t) at the channel output (taking into account the influence of additive and multiplicative noise x) in order to best reproduce (restore) the transmitted message A at the receiving end. A channel (in the narrow sense) is a medium used to transmit signals from a transmitter to a receiver.

Another example of a complex system model is a phase-locked loop (PLL), used to stabilize the intermediate frequency (IF) in radio receivers (Figure 1.3).

Figure 1.3 – PLL system model

The system is designed to stabilize the inverter f f = f c - f g by correspondingly changing the frequency of the tunable oscillator (heterodyne) f g when the signal frequency changes f with. Frequency f g in turn, will change with the help of a controlled element in proportion to the output voltage of the phase discriminator, depending on the phase difference of the output frequency f fc and reference oscillator frequencies f 0 .

These models make it possible to obtain a qualitative description of processes, highlight the features of the functioning and performance of the system as a whole, and formulate research objectives. But for a technical specialist, this data is usually not enough. It is necessary to find out exactly (preferably in figures and graphs) how well the system or device works, identify quantitative indicators for assessing effectiveness, and compare the proposed technical solutions with existing analogues in order to make an informed decision.

For theoretical research, obtaining not only qualitative but also quantitative indicators and characteristics, it is necessary to perform a mathematical description of the system, that is, to create its mathematical model.

Mathematical models can be represented by various mathematical means: graphs, matrices, differential or difference equations, transfer functions, graphical connection of elementary dynamic links or elements, probabilistic characteristics, etc.

Thus, the first main question that arises in the quantitative analysis and calculation of electronic devices is the compilation, with the required degree of approximation, of a mathematical model that describes changes in the state of the system over time.

A graphical representation of a system in the form of a connection of various links, where each link is associated with a mathematical operation (differential equation, transfer function, complex transfer coefficient), is called block diagram . In this case, the main role is played not by the physical structure of the link, but by the nature of the connection between the input and output variables. Thus, different systems can be dynamically equivalent, and after replacing the functional diagram with a structural one, general methods of systems analysis can be applied, regardless of the scope of application, physical implementation and operating principle of the system under study.

Contradictory requirements are placed on a mathematical model: on the one hand, it must reflect the properties of the original as fully as possible, and on the other, it must be as simple as possible so as not to complicate the study. Strictly speaking, every technical system (or device) is nonlinear and nonstationary, containing both lumped and distributed parameters. Obviously, an accurate mathematical description of such systems is very difficult and is not associated with practical necessity. The success of system analysis depends on how correctly the degree of idealization or simplification is chosen when choosing their mathematical model.

For example, any active resistance ( R) may depend on temperature and have reactive properties at high frequencies. At high currents and operating temperatures, its characteristics become significantly nonlinear. At the same time, at normal temperatures, at low frequencies, in the small-signal mode, these properties can be ignored and the resistance can be considered an inertia-free linear element.

Thus, in a number of cases, with a limited range of parameter changes, it is possible to significantly simplify the model, neglect the nonlinearity of the characteristics and nonstationarity of the parameter values of the device under study, which will allow, for example, its analysis using a well-developed mathematical apparatus for linear systems with constant parameters.

As an example, Figure 1.4 shows a block diagram (graphical representation of the mathematical model) of the PLL system. If the frequency instability of the input signal is slight, the nonlinearity of the characteristics of the phase discriminator and the controlled element can be neglected. In this case, mathematical models of the functional elements indicated in Figure 1.3 can be represented in the form of linear links described by corresponding transfer functions.

Figure 1.4 – Block diagram (graphical representation of the mathematical model) of the PLL system

Designing electronic circuits using analysis and optimization programs on a computer, as noted above, has a number of advantages over the traditional method of designing “by hand” with subsequent finishing on a breadboard. Firstly, with the help of computer analysis programs it is much easier to observe the effect of varying circuit parameters than with the help of experimental studies. Secondly, it is possible to analyze the critical operating modes of a circuit without physically destroying its components. Thirdly, analysis programs make it possible to evaluate the operation of a circuit under the worst combination of parameters, which is difficult and not always possible to carry out experimentally. Fourthly, the programs make it possible to carry out measurements on a model of an electronic circuit that are difficult to perform experimentally in the laboratory.

The use of a computer does not exclude experimental research (and even involves subsequent testing on a prototype), but it puts in the hands of the designer a powerful tool that can significantly reduce the time spent on design and reduce the cost of development. A computer has a particularly significant effect when designing complex devices (for example, integrated circuits), when it is necessary to take into account a large number of factors affecting the operation of the circuit, and experimental rework is too expensive and time-consuming.

Despite the obvious advantages, the use of computers has given rise to great difficulties: it is necessary to develop mathematical models of components of electronic circuits and create a library of their parameters, improve mathematical methods for analyzing the diverse operating modes of various devices and systems, develop high-performance computer systems, etc. In addition, many tasks turned out to be beyond the control of computers. For most devices, their structure and circuit diagram largely depend on the field of application and initial design data, which creates great difficulties in synthesizing circuit diagrams using a computer. In this case, the initial version of the circuit is compiled by an engineer “manually”, followed by modeling and optimization on a computer. The greatest achievements in the construction of programs for structural synthesis and synthesis of circuit diagrams are in the field of designing matching circuits, analog and digital filters, and devices based on programmable logic matrices (PLM).

When developing a mathematical model, a complex system is divided into subsystems, and for a number of subsystems, mathematical models can be unified and concentrated in appropriate libraries. Thus, when studying electronic devices using computer modeling programs, a schematic or block diagram is a graphical representation of components, each of which is associated with a selected mathematical model.

To study circuit diagrams, models of typical independent sources, transistors, passive components, integrated circuits, and logic elements are used.

To study systems defined by structural diagrams, it is important to indicate the relationship between input and output variables. In this case, the output of any structural component is represented as a dependent source. Typically, this relationship is specified by either a polynomial function or a fractional rational transfer function using the Laplace operator. Taking into account the selected function coefficients, it is possible to obtain models of such structural components as an adder, subtractor, multiplier, integrator, differentiator, filter, amplifier and others.

Modern computer modeling programs contain dozens of types of libraries of various models, and each library contains dozens and hundreds of models of modern transistors and microcircuits produced by leading manufacturers. These libraries often make up the bulk of the software. At the same time, during the modeling process it is possible to quickly correct the parameters of existing models or create new ones.

To conduct a quantitative analysis of the models, we will use the following indicators:

1. The number of blocks on the diagram is N;

2. Decomposition level of the diagram – L;

3. Balance of the diagram – B;

4. The number of arrows connecting to the block is A.

This set of indicators applies to each diagram in the model, then using the coefficients (formula 1, 2), by which the quantitative characteristics of the model as a whole can be determined. To increase the understandability of the model, it is necessary to strive to ensure that the number of blocks (N) in the diagrams of lower levels is less than the number of blocks in the parent diagrams, that is, with an increase in the level of decomposition (L), the decomposition coefficient d decreases: d = N / L

Thus, a decrease in this coefficient indicates that as the model is decomposed, the functions should be simplified, therefore, the number of blocks should decrease.

Diagrams must be balanced. This means that the number of arrows entering and leaving the block should be equally distributed, that is, the number of arrows should not vary greatly. It should be noted that this recommendation may not be followed for processes that involve obtaining a finished product from a large number of components (production of a machine unit, production of a food product, etc.). The diagram's balance coefficient is calculated using the following formula:

It is desirable that the balance coefficient be minimal for the diagram and be constant in the model

In addition to assessing the quality of the diagrams in the model and the model itself in general based on the coefficients of balance and decomposition, it is possible to analyze and optimize the described processes. The physical meaning of the balance coefficient is determined by the number of arrows connected to the block, and accordingly it can be interpreted as an evaluation coefficient for the amount of information processed and received. Thus, on the graphs of the dependence of the balance coefficient on the level of decomposition, the existing peaks relative to the average value show the overload and underload of the information system subsystems in the enterprise, since different levels of decomposition describe the activities of various subsystems. Accordingly, if there are peaks in the graphs, then a number of recommendations can be made for optimizing the described processes automated by the information system.

Analysis of the context diagram “A-0 Information system of a construction organization”

Number of blocks: 1

Chart decomposition level: 3

Balance factor: 3

Number of arrows connecting to the block: 11

Analysis of process details “A2 Module “Suppliers”

Number of blocks: 4

Analysis of process detail “A3 Module “Objects”

Number of blocks: 3

Chart decomposition level: 2

Balance factor: 5.75

Analysis of process detail “A1 Module “Workers”

Number of blocks: 3

Chart decomposition level: 2

Balance factor: 5.75

Analysis of process details “A 4.1 Module “Reports”

Number of blocks: 3

Chart decomposition level: 2

Balance factor: 5.75

Analysis of process detail “A 5 Module “Contractors”

Number of blocks: 3

Chart decomposition level: 2

Balance factor: 5.75

The balance coefficient at the child levels of decomposition for the child levels of the process The store information system indicates that the diagram is balanced. Because the balance coefficient is not equal to zero, then it is possible to carry out further decomposition of some levels, after which it is possible to analyze the names of the activities of this model.

When conducting a quantitative analysis of the model, a graph of the decomposition coefficient was constructed, in which we see that as the level of decomposition increases, the decomposition coefficient decreases. Thus, a decrease in this coefficient indicates that as the model is decomposed, the functions are simplified, therefore, the number of blocks decreases. The decomposition coefficient graph is shown in Figure 10.

Figure 10 – Decomposition coefficient graph

On the graph of the dependence of the balance coefficient on the level of decomposition, the existing peaks relative to the average value indicate the congestion of the information system subsystems of the enterprise; the balance coefficient for the diagram is maximum. The balance coefficient graph is shown in Figure 11.

Figure 11 - Balance coefficient graph

Quantitative (mathematical and statistical) analysis- a set of procedures, methods for describing and transforming research data based on the use of mathematical and static apparatus.

Quantitative Analysis implies the ability to treat results as numbers - the use of calculation methods.

Deciding to quantitative analysis, we can immediately turn to the help of parametric statistics or first carry out primary and secondary data processing.

At the stage of primary processing are being decided two main tasks: introduce obtained data in a visual form convenient for preliminary qualitative analysis in the form of ordered series, tables and histograms And prepare data for application of specific methods secondary processing.

Arranging(arranging numbers in descending or ascending order) allows you to highlight the maximum and minimum quantitative value of the results, evaluate which results occur especially often, etc. A set of indicators of various psychodiagnostic methods obtained for the group is presented in the form of a table, the rows of which contain the examination data of one subject, and the columns contain the distribution of the values of one indicator across the sample. bar chart is the frequency distribution of the results over the range of values.

At the stage secondary processing The characteristics of the research subject are calculated. Analysis of results secondary processing allows us to prefer the set of quantitative characteristics that will be most informative. Purpose of the stage secondary processing consists not only in obtaining information, but also in preparing data for possible assessment of the reliability of information. In the latter case, we turn to help parametric statistics.

Types of mathematical-static analysis methods:

Descriptive statistics methods are aimed at describing the characteristics of the phenomenon under study: distribution, communication features, etc.

Static inference methods are used to establish the statistical significance of data obtained from experiments.

Data transformation techniques focus on transforming data to optimize its presentation and analysis.

Towards quantitative methods of analysis and interpretation (transformation) of data include the following:

Primary processing of “raw” estimates to create the possibility of using nonparametric statistics, it is performed using two methods: classification(dividing objects into classes according to some criterion) and systematization(ordering objects within classes, classes among themselves, and sets of classes with other sets of classes).

By clicking on the "Download archive" button, you will download the file you need completely free of charge.
Before downloading this file, think about those good essays, tests, term papers, dissertations, articles and other documents that are lying unclaimed on your computer. This is your work, it should participate in the development of society and benefit people. Find these works and submit them to the knowledge base.
We and all students, graduate students, young scientists who use the knowledge base in their studies and work will be very grateful to you.

To download an archive with a document, enter a five-digit number in the field below and click the "Download archive" button