Digital modeling. Introduction

9. Digital Video Surveillance So far, most of the topics discussed in this book have related to analog video signals. Most modern video surveillance systems still use analogue cameras, although a growing number of manufacturers offer

2.2. Non-algorithmic methods

digital modeling.

The speed of solving a number of complex problems using a program-algorithmic method on a general-purpose digital computer is insufficient and does not satisfy the needs of computer-aided design (CAD) engineering systems. One of these classes of problems, widely used in engineering practice when studying dynamics (transient processes) complex systems automation are systems of nonlinear differential equations of high orders in ordinary derivatives. To speed up the solution of these problems, CAD software and hardware systems can include, in addition to the main (leading) general-purpose digital computer, GVMs that are problem-oriented for solving nonlinear differential equations. They are organized on the basis of digital mathematical modeling non-algorithmic method. The latter allows you to increase the productivity of CAD due to the inherent parallelism of the computing process, and the discrete (digital) method of representing mathematical quantities allows you to achieve processing accuracy no worse than in a digital computer. These GVMs use two digital modeling methods:

1. Finite-difference modeling;

2. Discharge modeling.

The first method used in GVMs such as digital differential analyzers (DDAs) and digital integrating machines (DIMs) is the well-known method of approximate (step-by-step) finite difference calculations. Digital operating units of the GVM, built on digital circuitry, process fairly small discrete increments of mathematical quantities transmitted along communication lines between operating units. Input and output mathematical quantities are represented, stored and accumulated from increments in digital n-bit codes in reverse counters or accumulating adder registers.

Increments of all quantities are usually coded in one low-order unit: D:=1ml. R. This corresponds to quantization by level of all processed quantities with at a constant pace quantization D=1. Consequently, the rate of increase of all machine quantities is limited: |dS/dx|£1.

Signs of single-bit increments are encoded using the sign coding method on two-wire communication lines between operating units:

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where DSi=yiDx – increment of the integral in i-th step integration, and the i-th ordinate of the integrand function y(x) – yi is calculated by accumulating its increments:

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with the introduction of a constant normalizing coefficient kn = 2-n, increments at the outputs of the integrators are formed sequentially and processed in the following integrators also sequentially. An exception is the integration of the sum of several integrand functions

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Then, along several m input lines lth increments can act synchronously at some jth step. For sequential addition, they are spaced within a step using delay lines, increasing the clock frequency of the input accumulating adder by m times. Therefore, the number of summable integrand functions is usually limited to two: m=2.

The structural organization of the digital integrator-adder is very simple. It is constructed in the form of a serial connection of the following functional units:

· 2OR circuit with delay line tз=0.5t at one of the inputs

· input accumulating adder of increments of integrand functions, which accumulates their n-bit ordinates according to input increments:

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When Dх:=(10) the code yk is transmitted without changes, and when Dх:=(01) the output forms a code inverse to the input code yk.

· integral output increment generator: DSi:= overflow unit Si, converting the overflow sign into a bipolar increment code (it is most simply implemented if the negative accumulated numbers Si are represented in a modified code: direct, inverse or complementary). The corresponding block diagram of the digital integrator is shown in Fig. 9.14 (p.260) of the textbook. In digital model circuits, the following symbol for a digital adder-integrator is used:

"Zn." indicates the inversion flag (-) if it is required. An important advantage of this method of finite-difference digital modeling is that the same digital integrator, without changing its circuits, is used to perform the linear and nonlinear operations necessary to solve ordinary differential equations. This is explained by the fact that when programming the CDA and CIM, the original equations in derivatives are converted to equations in differentials. Let's look at the simplest digital model programs:

1. multiplying the variable x by the constant k:

Moving on to the differentials dS=кdx, we will make sure that this operation is performed by one integrator with its corresponding initial setting:

3. Multiplication S=xy, or in differentials dS=xdy+ydx.

4.2. trigonometric functions, for example y=sinx, which is a solution to a second order differential equation (since ), or in differentials

Considering that the creation of these problem-oriented computers requires significant additional costs, when building technical means CAD often uses a simpler way to organize them by combining mass-produced general-purpose digital computers and electronic analog computers (AVMs) built on operational amplifiers into a computing complex. The digital computer and the digital computer are combined using a standard conversion and interface device (CTD), consisting mainly of an ADC and a DAC. A complex problem to be solved is rationally divided into 2 parts between analog and digital processors when programming the complex. Moreover, the analog part is most often problem-oriented at solving differential equations and is used in the general computing process as a fast subroutine.

2.3 Architecture of hybrid computing systems (HCC).

2.3.1. structure of the analog-digital computing complex (ADCC)

GVK or ATsVK is a computing complex consisting of a digital computer and a general-purpose automatic computer, combined using a UPS, and containing in the digital part additional software for automating the programming of the analog part, managing the exchange of information between the analog and digital parts, monitoring and testing the analog part, automation of input-output procedures.

Let's consider the block diagram of an ADCC with the simplest UPS, built on single-channel switched ADCs and DACs. To create the prerequisites for automating AVM programming under the control of a digital computer, the following additional blocks are introduced as part of the AVM hardware:

1. Manually adjustable variable resistances (potentiometers) at the inputs of operational amplifiers in a set of operating units (NOB), known to you from laboratory work on TAU, are replaced with digitally controlled resistances (DCR), which are used as DAC integrated circuits;

3. Automatic connection of operating units in accordance with the analog model circuit drawn up in the digital computer (clause 2.1) is carried out by an automatic switching circuit (ASC) using the binary switching vector of the SAC keys, formed in the digital computer and stored during the solution of the problem in the configuration information register (RN) in UPS.

AVM operating modes: preparation, start-up, stop, return to the initial state, output of results to analog peripheral devices (chart recorders, two-coordinate tablet recording devices - DRP) are set from the computer side through the UPS control unit (UPS BU).

The UPS control unit also carries out mutual synchronization of the operation of the digital computer and automatic computer: it transmits external interrupt signals from the analog model to the digital programs of the digital computer, under the control of digital part programs it synchronizes the polling of points in the analog model, the conversion of voltages at these points into digital codes and the transmission of the latter through the BSK and the channel input-output into the RAM of the digital computer; or similarly, the reverse conversion of digital codes into electrical voltages and the supply of the latter to the required points at the inputs of the operating units of the analog model. This principle functional organization The interaction of the digital and analog parts is supported in hardware by UPS blocks: ADC and DAC, AM and ADM - analog multiplexer and demultiplexer, ML - input and output analog memory blocks, built on a variety of similar storage sampling circuits (SSC). The inputs of the input SVX (on the left) are connected to the required points of the analog model circuit (outputs of the corresponding operating blocks). At the necessary discrete moments of time, under the control of a digital computer, individual sample ordinates of analog signals (electrical voltages) are taken from the analog model and stored in the temporary storage system. Then the outputs of the SVR are polled by the AM multiplexer and their output voltages are converted by the ADC into digital codes, which in the direct access mode as a block of numbers (linear array) are written to the OP of the digital computer.

During inverse conversion, the SVX outputs of the second group of the ML output analog memory (on the right) are connected, under the control of the digital computer, to the required inputs of the operating units of the analog model, and the SVX inputs are connected to the outputs of the analog demultiplexer, the input of which is supplied with the output voltage of the DAC. In the direct access mode, a block of numbers is read from the OP of the digital computer. Each of the numbers is converted to the DAC in electrical voltage, which, under the control of a digital computer with the help of a running ADM, is recorded for storage in one of the temporary storage warehouses. The resulting set of several voltages is stored in several temporary storage systems for a time interval specified by the digital computer program (for example, while solving a problem in the analog part) and is processed by analog operating units.

2.3.2. Methods of organizing analogue -

digital computing.

The principle of alternating operating modes of digital computers and automated computers, reducing the complexity of the control system.

ATsVK are used for analogue-digital modeling of complex automation systems containing control digital computers, as well as for accelerating the solution of complex mathematical problems that require excessive consumption of memory resources and computer computer time. In the first case, control algorithms are programmatically simulated on a digital computer, and an analog mathematical model of the control object is programmed in the automatic computer, and the ACVK is used as a complex for debugging and verifying control algorithms, taking into account the nonlinearity and dynamics of the control object, which are very difficult to take into account when developing algorithms, if do not constantly solve the differential equations of the object to determine its response to each new control action.

In the second case, for example, when solving differential equations, the general cumbersome problem of approximate calculations is divided into two parts, usually placing computationally intensive calculations in the analog part for which an error of 0.1...1% is permissible.

According to the principle of the above-mentioned division of the task into two parts and the method of organizing the interaction between the AVM and the digital computer, modern digital computers are divided into 4 classes of analog-digital computing

Classes 1,2,3 can be implemented on the basis of the considered structural organization of the ADCC with a simplified UPS built on single-channel ADCs and DACs.

Class 1 is the simplest in terms of organizing the interaction between the AVM and the digital computer. The digital and analog parts operate at different times, and therefore there are no high demands on the synchronization of the operation of the AVM and the digital computer and the speed of the digital computer and the UPS.

Class 2 requires a special organization of alternating operating modes of AVM, DVM and UPS in each cycle of calculations and interaction

Since the AC and CC do not operate simultaneously, there are no problems with their synchronization and no high demands are placed on the speed of the UPS and digital computer. Classes of problems to be solved: optimization of analog model parameters, parametric identification, modeling of random processes using the Monte Carlo method, analog-digital modeling of automatic control systems not in real time, integral equations.

Class 3 requires a different organization of alternating operating modes of AVM, TsVM and UPS.

In phase A, 2 partial tasks of one are simultaneously performed in the AC and CC difficult task compatible in time. In the CC in phase B, discrete values ​​of function arguments are most often received from the AC and stored, then in phase A the ordinates are calculated from them and prepared for the AC complex functions, which in the next phase B are transferred to the AC, where they are stored in analog storage (SVH), and then used in the next phase A in analog calculations, etc. Classes of problems to be solved: iterative calculations, solving ordinary difurs with given boundary conditions, dynamic problems with pure delay of arguments, integral equations, partial differential equations. In class 3, there are no high demands on the speed of the digital computer and digital computer, but precise synchronization of the operation of digital computer and digital computer in phase B is required, since due to the stop of the digital processor, asynchronous control of data transfer is impossible, and synchronous transmission of data blocks is carried out under the control of the direct access controller into memory (KPDP) through the digital computer input/output channel.

Class 4 is most often analog-digital modeling of digital automatic control systems in real time for checking and debugging control digital computer programs in dynamics. It is the most complex in terms of organizing the interaction and synchronization of the operation of the AVM and the digital computer, since here phases A and B are combined, there is a constant mutual exchange of data during the calculation process, and therefore the use of a digital computer and UPS of maximum speed is required.

The structural organization of the UPS, given above and suitable for classes 1,2,3, is not applicable in class 4. The latter class requires a multi-channel organization of ADC and DAC without multiplexing with the additional inclusion of parallel buffer registers at the input and output of the BSC file, exchanging with the OP of the digital computer in direct access mode. The contents of each register are either converted by separate parallel-connected DACs when transmitting data to the AVM, or generated by separate parallel-connected ADCs when transferring data from the AVM to the digital computer.

2.3.3 Features of the ACVK software.

To automate AVM programming using a digital computer and fully automate the analog-digital computing process, traditional general-purpose digital computer software (see Fig. 13.2 p. 398 in the textbook) is supplemented with the following software modules:

1. The processing programs include additional translators with special languages analogue-digital modeling, for example Fortran-IV, supplemented by subroutines in extended assembler containing special analogue-digital commands, for example, for controlling the analogue part using a digital computer program, organizing data transfer between the DF and AC, processing interrupts of DF programs initialized by the analogue part; an analog-digital compiling system is created;

2. The working, debugging and maintenance programs include an inter-machine exchange driver for controlling the analog part as a peripheral processor, graphic display programs, recording and analyzing results;

3. The library of applied programs includes programs for calculating functions and standard mathematical analog-digital programs;

4. Included in diagnostic programs Maintenance introduce UPS tests, AVM operating unit tests;

5. A whole range of additional control modules is introduced into the OS control programs:

Automation system for analog programming (SAAP), consisting of lexical analyzer; parser(checking the compliance of the analog program entered in the algorithmic language with the rules of recording syntax); block diagram generators(composition and coding of circuits of analog models using the order reduction method and implicit functions the same as in paragraph 2.1); block of calculation programs(scaling the analog model as in clause 2.1, digital software modeling of the analog part on a digital computer with a single calculation to calculate the expected maximum values ​​of variables and clarify the scaling of the analog model, as well as creating a file for static and dynamic control of the analog part after its programming); output presentation programs(display and plotter of the synthesized structure of the analog model, control printout of analog program codes, scale factors, static and dynamic control files);

· Service for synchronization and interaction of automated computers and digital computers (implementation of alternating operating modes);

· Service for processing interrupts initialized by the analog part;

· Program for managing data exchange between AVM and digital computer;

· Program for managing the loading of analog model circuit codes into the SAC (in the RN);

· Program for controlling the static and dynamic control mode (debugging the analog program loaded into the AVM).

Based on the results of automation of analog-digital programming on the magnetic disk of the host digital computer, in addition to traditional digital files, the following additional data files are created, used by the above-mentioned additional modules of the ACVK software: analog block file, switching file (for SAC), static control file, dynamic control file , preparation file for analog functional converters, library of plug-in standard analog-to-digital programs.

2.3.4. Languages ​​of analog-digital modeling.

The considered architecture of the digital computer allows you to describe and enter analog-digital programs only into the host digital computer in high-level algorithmic languages. For this purpose, traditional digital programming languages ​​are supplemented with special object description operators analog modeling, organizing data transfer between the AC and the DC, controlling the analog part using the digital computer program, processing interruptions from the analog part, setting the parameters of the analog model, monitoring the analog part, tasks official information and so on.

Universal languages ​​are used, translated by compilation (Fortran IV) or interpretation (BASIC, Gibas, Focal, HOI), supplemented by special subroutines in Assembly, usually called by the Call... operator indicating the identifier of the desired subroutine.

In order to increase the speed of operation of the CAAP, it is usually described and uses specialized analog-digital modeling languages ​​at the input: CSSL, HLS, SL – 1, APSE, and for internal interpretation the Poliz language (reverse Polish notation).

The following analog-digital macro instructions can be entered into universal compiled languages:

1. SPOT AA x– set the potentiometer (DCC) in the analog part with address AA to the position (resistance value) corresponding to the digital code value stored in the digital computer OP at address x;

2. MLWJ AA x– read the analog value at the output of the operating unit in the AC with address AA, subject it to analog-to-digital conversion, and write the resulting digital code into the digital computer OP at address x. The interaction between the analog part and the digital part can be described as a procedure call:

Call JSDA AA x, where JSDA is the corresponding identifier of a plug-in subroutine in Assembly language, for example, an installation procedure - set the value x from the DAC output to address AA in the analog part.

Therefore, it is very important to understand how the type of parallelism of the problem being solved affects the way a parallel computer is organized.

3.1.1 Natural parallelism

independent tasks.

It is observed if there is a flow of unrelated tasks in the aircraft. In this case, increasing productivity is relatively easily achieved by introducing into the “coarse-grained” BC ensemble independently functioning processors connected to the interfaces of the multi-module OP and initialization of input/output processors (I/O).

The number of OP modules is m>n+p in order to ensure the possibility of parallel access to memory of all processing processors and all PVVs and to increase the fault tolerance of the computer. Backup (m-n-p) OP modules are necessary for quick recovery in the event of a working module failure and for storing in them the SSP of processors and processes at program checkpoints required for restart in the event of a processor or OP module failure.

An opportunity is created for each of the tasks to be solved to temporarily combine the pair: Pi+OPj as an autonomously functioning computer. Previously, the same OP module worked in pairs: PVVk + OPj, and in OPj the program and data were entered into the input buffer. At the end of processing, an output buffer is organized and filled in OPj, and then the OPj module is inserted into the OPj+PVVr pair for exchange with the peripheral device.

The main task of organizing computing processes, solved by the “dispatcher” system program, is the optimal distribution of tasks between parallel processors according to the criterion of maximizing their load, or minimizing their downtime. In this sense, it is optimal asynchronous the principle of loading tasks into processors without waiting for tasks to be processed in other busy processors.

If a package of input tasks accumulated over a certain time interval is stored in the VRAM, the problem of optimal asynchronous scheduling comes down to creating an optimal schedule for when tasks are launched on different processors. The main input data required for this is a set of known expected computational processing times for all tasks of the accumulated batch, which are usually indicated in the control cards of their tasks.

Despite the independent nature of the tasks in the totality of their asynchronous computing processes, conflicts between them for shared computer resources are possible:

1) Services of a common multi-system OS, for example, processing I/O interrupts, or calls to a common reliability OS during failures and restarts;

(О–) – ®О-Д – change of sign of D.

With an operation in layer I, two operations each in layers II and III could be performed in parallel if the ALU had a corresponding excess of operating blocks.

The parallelism of operations discussed above in solving differential equations and when processing matrices belongs to the regular class, since the same operation is repeated many times over different data. Last example quadratic equation has irregular parallelism of operations, when simultaneous execution is possible on different data different types operations.

As shown above, for using regular parallelism of operations while improving performance, it is suitable matrix organization Aircraft with general control.

IN general case irregular parallelism of operations more in a suitable way productivity gains are considered streaming organization Computers and aircraft. In streaming computers, instead of the traditional von Neumann program control of the computing process in accordance with the order of commands determined by the algorithm, the reverse principle of program control is used according to the degree of readiness of the operands, or the data flow (operand flow), determined not by the algorithm, but by the operand graph (data transfer graph ).

If there is a sufficient excess of processing devices in a parallel processor, or an ensemble of redundant microprocessors in a computer system, then naturally and automatically (without special scheduling and launch scheduling) those parallel operations whose operands were prepared by previous calculations will be simultaneously executed.

The computational process begins with those operations whose operands are the original data, for example, in the first layer of the GPA of a quadratic equation, three operations are simultaneously performed, and then it develops as the operands are ready. After this, the multiplication command is called, then the subtraction and check of the logical condition, then the macrooperator (Ö) and only after that - two commands at the same time: addition and subtraction, and after them - two identical division commands.

The technical implementation of the flow organization of aircraft is possible in three ways:

1) The creation of special streaming microprocessors, which belong to the class of specialized ones and will be discussed in the next semester;

2) Special organization of the computing process and modification of machine language low level in multi-microprocessor ensemble computers built on standard von Neumann microprocessors;

3) The creation of processors with an excess of the same type of operating units and the addition of operating systems using a stream method for organizing the computing process (implemented in the domestic stream processor EC2703 and the Elbrus-2 supercomputer).

There is digital modeling in Russia: proven in NEOLANT

The NEOLANT company, based on many years of experience in information modeling in Russia, has developed its own typology of digital object models industrial enterprise. The classification is based on the key task for which the model is implemented and used, from centralizing engineering data for an object to process monitoring, modeling physical and technological processes, and personnel training.

In accordance with the NEOLANT typology, six types of information models are distinguished (Fig. 1).

The most common today are the first two types: the “Decoration” 3D model and the engineering 3D model. Moreover, they are often used at the planning and design stage of facilities, although they can also be effectively used to solve operational problems.

The NEOLANT company offers you examples real projects, presented in the form of videos that clearly demonstrate the capabilities of certain types of information models.

Type:

Example: 3D monuments of Moscow (Fig. 2).

Information 3D models of about 40 historical objects of the capital help the Department cultural heritage of the city of Moscow in the formation and implementation of state policy in the field state protection, preservation, use and popularization of cultural heritage sites (historical and cultural monuments) of the peoples of the Russian Federation. The information system created by NEOLANT solves the following problems:

• collection, accumulation, storage, maintenance of spatial and attribute information about objects of the historical and cultural reference plan of the city of Moscow;
• providing convenient access to information about objects of the historical and cultural basic plan of the city of Moscow, including the history of changes in their status;
• implementation of the ability to view 3D models of objects of the historical and cultural basic plan of the city of Moscow;
• generation of documents based on data from the historical and cultural basic plan of the city of Moscow.

Type: 3D information model “Directory”.

Example: information models of all ten Russian nuclear power plants (Fig. 3).

The information model of a nuclear power plant allows you to organize instant access to a huge unified repository of data and documentation using visual 3D models of objects. Moreover, for each power unit there are 2.5 thousand volumes of documentation, and each model of the facility contains approximately 300-400 thousand graphic elements.

Type: applied information 3D model.

Example: information system for ensuring the decommissioning of power units of the Kursk NPP (Fig. 4).

The system is based on 3D information models of objects, to which attribute information, design documentation, technological diagrams, etc. are attached.

The system allows you to solve the following applied problems:

• collection and visualization of radiation monitoring data;
• development of work plans;
• simulation modeling of hazardous work;
• calculation of the volumes of dismantling, decontamination and generated radioactive waste; etc.

Type: applied information model.

Example: modeling the progress of construction and installation work at the plant (Fig. 5).

Integration of 3D models of plant facilities with calendar and resource planning systems allows you to optimize the progress of construction and installation work, monitor the condition of objects under construction and compliance with the schedule, control construction subcontractors, and receive technical and contractual documentation directly from the 3D model. In addition, such an applied information model is convenient for holding meetings and planning sessions - visual access to information about the progress of construction eliminates the need for meeting participants to analyze reports and documents.

Type: simulation model.

Example: modeling of emergency situations at the NPP site (Fig. 6).

The modeling of potential emergency situations at nuclear power plants carried out by NEOLANT is necessary to ensure a high level of operational safety of these facilities. The project was implemented by order of the Institute for Safe Development Problems nuclear energy(IBRAE) RAS.

Type: simulation model/virtual simulator.

Example: modeling dismantling technology, training robotics operators in technological operations (Fig. 7).

To dismantle the AMB-100 reactor unit at the Beloyarsk NPP, it is planned to use “unmanned” technology, that is, only robotics will work at the site. Simulation modeling made it possible to carry out preliminary testing of the technology, identify a number of problems and develop proposals for solving them. The created simulation model will also be used to train robot operators, and in the future it will ensure the safety of work on decommissioning the power unit.

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Based on materials from the NEOLANT company

Digital modeling

a method of studying real phenomena, processes, devices, systems, etc., based on the study of their mathematical models (See Mathematical model) (mathematical descriptions) using a digital computer. The program executed by the digital computer is also a kind of Model of the object under study. In digital modeling, special problem-oriented modeling languages ​​are used; One of the most widely used languages ​​in modeling is the CSMP language, developed in the 60s. in USA. Digital mathematics is distinguished by its clarity and is characterized by a high degree of automation of the process of studying real objects.