Classification of hybrid systems. Big encyclopedia of oil and gas

(HV) is a car with at least two different energy converters and two different energy storage systems (in the car) to drive the car.

On the one hand, hybrids differ in their design (parallel, serial, combined or branched hybrid) and, on the other hand, in the degree of electrification (micro, soft, full hybrid).

If a car receives energy not only from fuel, but also from the mains, then it is called a plug-in hybrid (Plug-ln-Hybrid).

Classification by design

Picture. Parallel hybrid

• Fuel tank (T)
• Battery (V)
• Electric motor (E)
• ICE (V)
• Gearbox (G)

In parallel hybrids, the internal combustion engine and the electric motor together act on the transmission. Both engines can be smaller in size than if they were installed in a car and operated separately. Since the electric motor is simultaneously used as a generator, it is not possible to generate energy while the electric motor is moving.

Picture. Serial hybrid

• Fuel tank (T)
• Battery (V)
• Electric motor (E)
• ICE (V)
• Generator (Gen)

In successive hybrids, only the electric motor acts on the transmission. The internal combustion engine drives an electric generator that turns the electric motor and charges the battery. The Serial Hybrid runs in places on pure electricity with a charged battery and is thus very close to an electric vehicle.

For this reason, it is also called the Range-Extender.

Picture. Combined or branched hybrid

• Fuel tank (T)
• Battery (V)
• Electric motor (E)
• ICE (V)
• Generator (Gen)
• Inverter (L)

The hybrid hybrid combines parallel and serial hybrid under the hood. ICE by means of a generator and battery prepares energy for the electric motor or is directly connected to the drive. Switching and connecting between the two states is done automatically.

Picture. Plug-in hybrid

• Fuel tank (T)
• Battery (V)
• Electric motor (E)
• ICE (V)
• Generator (Gen)
• Rosette (S)

In plug-in hybrids, the battery is charged not only from the internal combustion engine, but also from the mains. Thus, a plug-in hybrid can travel long distances on pure electricity. The plug-in hybrid represents the next step in the evolution of electric vehicles.

Classification by degree of electrification

Microhybrid

Despite the fact that the so-called micro-hybrids with brake energy recovery and automatic start-stop are already making a significant contribution to fuel economy and emission reduction, they have no effect on the drive. Therefore, in the narrow sense of the word, they are not hybrid vehicles.

An example of a microhybrid system

Valeo's i-StARS system can stop the engine even before the vehicle comes to a complete stop, that is, as soon as the speed drops below 8 km / h (in the case of an automatic transmission) and 20 km / h (in the case of a manual transmission). This optimizes fuel consumption and makes driving easier. The regenerative brake function is activated as soon as the driver takes his foot off the accelerator pedal. The system then sends an electronic signal to the starter-generator, as a result of which the kinetic energy of the car is converted immediately into electrical energy, the charge of the battery. This achieves a significant reduction in fuel consumption.

Mild hybrid

A mild hybrid does not run on pure electricity. The electric motor only supports the internal combustion engine.

The energy for the electric motor comes from the use of braking energy, for example.

In conventional cars, driving energy - or kinetic energy - is converted to heat on the brake discs when braking. Heat is simply irretrievably discharged into the environment. In hybrid vehicles, kinetic energy is captured by the generator and stored in the high-voltage battery.

Example for a mild hybrid system: Honda IMA (Integrated Engine Assist)

The starter-generator is located between the engine and the gearbox instead of the flywheel.

One of the advantages of mild hybrid vehicles is the fact that an internal combustion engine, which essentially delivers its power in the mid to high rpm range, is combined with the advantages of an electric motor, which develops its power at low rpm. A hybrid system, therefore, can be viewed as a power and efficiency amplifier.

In general, we can say that by “reducing” the internal combustion engine, gasoline consumption is reduced, as well as emissions into the environment. However, customers are not ready to accept low power. A hybrid vehicle can use the electric motor to compensate for the lack of power, for example when accelerating or accelerating.

Picture. Honda-IMA power and torque characteristic

Picture. Mercedes S400 HYBRID system overview

1. 12V generator
2. Electric motor
3. 7-speed automatic transmission
4. Power electronics module
5. High voltage battery module
6. DC / DC Converter Module
7. 12V battery

Another example of soft hybrids

The Mercedes S 400 HYBRID has a parallel hybrid drive. With this drive concept, both the internal combustion engine and the electric motor are mechanically connected to the drive wheels (motors in parallel). The powers of both motors can be added together, as a result of which the individual motor powers can be lower. Driving with an electric motor alone is impossible.

Complete hybrid

The full hybrid is driven in places by an electric motor only. The technical basis for a complete hybrid is a branched, combined or sequential hybrid.

Picture. Audi A1 e-tron as a consistent full hybrid

Example of a car with full hybrid drive

The Audi A1 e-tron is powered by an electric motor with a maximum output of 75 kW / 102 hp. and a maximum torque of 240 Nm. Power transmission takes place using a single-stage gearbox. Power reserve A1 when working only on electricity: 50 km. If the lithium-ion battery in front of the rear axle is discharged, then the smallest Audi model is powered, like the Opel Ampera or Chevrolet Volt, with a small internal combustion engine.

Li-ion battery located in the base of the body in front of the rear axle to optimize the weight distribution and center of gravity of the A1 e-tron, weighing 1.2 t. The 150 kg lithium-ion battery has a capacity of 12 kWh.

Picture. Gearbox with two electric motors for drive

Another example

BMW X6 ActiveHybrid

The powerful electric motors (67 kW / 91 hp and 63 kW / 86 hp) are compactly housed in an active, dual mode transmission, in a body the size of a conventional automatic transmission.

Depending on the traffic situation, the drive is carried out either by means of electric motors, or by means of an internal combustion engine, or alternately by both drives.

• In mode 1 at low speed with the use of electric vehicles, first of all, a significant reduction in fuel consumption is ensured, as well as additional traction is created.
• In mode 2, on the other hand, the electrically transmitted power at high speed decreases with a simultaneous increase in ICE efficiency (due to load point correction) and fuel efficiency.

And in this mode, both electric machines work in different ways and, along with the electrical support of the drive and the function of the generator, in particular, are responsible for efficient gear shifting.

Picture. Location of components in the car

1. Transmission oil coolant heat exchanger
2. Transmission oil lines
3. Double disc flywheel
4. High voltage wires
5. Active transmission housing
6. Hybrid parking lock
7. Electro-hydraulic control module
8. Electrically / mechanically driven transmission oil pump

Ancillary drive in vehicles with full hybrid drive

The main problem is the drive of additional units, which must work when the engine stops. The components previously powered by the internal combustion engine must now only run on electricity.

Electric vacuum pump

Vacuum pump functions:

• provision of reduced pressure in the brake booster,
• maintaining the supply of reduced pressure in the start / stop mode.

Electro-hydraulic power steering

For the power steering to operate during an automatic engine stop, it is necessary to disconnect the power steering from the internal combustion engine and provide independent steering support. This support ensures that fuel consumption is optimized as needed.

Electric Air Conditioning Compressor

To ensure sufficient cooling capacity of the vehicle interior during an automatic engine stop, it is necessary to disconnect the drive of the air conditioning compressor and the internal combustion engine and provide independent air conditioning of the passenger compartment, as well as independent cooling of the high-voltage battery. This is done using an electrically driven A / C compressor. This cooling simultaneously optimizes fuel consumption. An air conditioner electric compressor is responsible for drawing in, compressing the refrigerant and pumping it through the system. The electric compressor of the air conditioner, depending on the evaporation temperature, is continuously regulated by the air conditioner control unit in the range from 800 to 9000 min ^ -1.

Typically, the main computing component of high performance computing systems, including clusters, is the central processing unit. However, starting with the Intel486DX processors, computers have appeared such an element as a coprocessor, which can be considered a hybridization at the hardware level.

The main challenge is finding ways to perform computational tasks using the GPU. Recognizing the demand for such computing, NVIDIA introduced the CUDA software and hardware platform in 2007, which allows arbitrary code to be run on the GPU. Before the advent of CUDA, programmers had to build hybrid systems from ordinary graphics cards and program them using sophisticated graphics APIs.

ATI has developed its CUDA counterparts for GPGPU applications. These are ATI Stream and Close to Metal technologies.

The new Intel Larrabee architecture was expected to support GPGPU technologies. However, in fact, a product released within the Intel MIC line, Xeon Phi only supported computing general purpose (x86_64 compatible), depriving the GPU capabilities. Subsequent versions of the Xeon Phi were implemented not only in the form of PCI Express expansion cards, but also in the form of a single central processor.

Technical features

GPU

The high computing power of the GPU is due to the peculiarities of the architecture. If modern CPUs contain multiple cores (on most modern systems from 2 to 8x, 2018, in the north there can be a maximum of 64x), the GPU was originally created as a multi-core structure in which the number of cores is measured in hundreds (for example, Nvidia 1070 has 1920 cores). The difference in architecture also determines the difference in the principles of operation. If the architecture of the CPU assumes sequential processing of information, then the GPU was historically intended to process computer graphics, therefore it is designed for massively parallel computations.

Each of these two architectures has its own merits. The CPU performs better with sequential tasks. With a large amount of processed information, the GPU has an obvious advantage. There is only one condition - parallelism should be observed in the task.

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Hybrid systems

Earlier, the idea has been repeatedly expressed that an expert system can contain more than one form of knowledge representation. Even in early systems like MYCIN (see Chapter 3), information specific to subject area, was stored in various forms - for example, in the form of generative rules and in the form of tables of medical parameters. Programs like CENTAUR (see Chapter 13) could already be considered hybrid in the sense that they combined different ways of representing knowledge, and then this knowledge was used for different purposes - to solve a problem and form explanations.

Later research systems, such as XPLAN (see Chapter 16), had a more complex architecture in which a variety of software tools and models were combined to develop and maintain expert systems. Such systems can be viewed as another step forward over the simplest shell supporting a single programming paradigm. Bulletin board-based systems (see Chapter 18) like HEARSAY and BB combined a variety of sources of knowledge that could have very different internal structures.

The systems we will look at in this chapter have marked a further advance along this path - they combine traditional problem solving programs with components of self-study and critical analysis. ODYSSEUS is capable of learning how to refine the knowledge base. To do this, two different techniques are used: one is based on analysis of precedents, and the other is based on analysis of explanations. Both techniques are relatively new and the reader will be able to briefly familiarize themselves with them in this chapter. Next, a program will be described in which case-based inference is used to handle rule exceptions, and generative rules are the main problem-solving tool. The program has the potential to teach new rules. At the end of the chapter, we will discuss the SCALIR information extraction system, which combines many conventional symbolic techniques with a network-of-connection approach.

Teaching methods in the ODYSSEUS system

The learning methods discussed in Chapter 20 (version space and IDS) are sometimes called similarity-based methods. The implementation of training based on these methods requires processing large amounts of information - positive and negative examples - from which the characteristic properties of the new concept are extracted.

An alternative to these methods are explanation-based methods, which allow you to generalize from a single training instance. This becomes possible, since in such methods the generalization process is "guided" by knowledge specific to a particular subject area. Explanatory learning is deductive or analytical, not empirical or inductive. In other words, with this technique, the description of a new concept is formed as a result of the analysis of the presented copy in the light of the available background knowledge.

The precedent inference technique discussed in Chapter 22 addresses a new problem by adapting previously obtained solutions to similar problems. The same technique can be used for training, because if a previously formed solution is adapted to a new problem, it can be added to the base of use cases for future use.

Below we will discuss in more detail the method of learning based on explanations and the possibility of using use cases for machine learning.

The term explanation-based generalization (EBG) refers to a domain-independent method of using domain-specific knowledge to control the generalization process from a single learning instance.

The EBG method assumes that the system has the following information:

· A positive copy of the training sample;

· Subject area theory;

· Defining a concept that the system should "learn".

To formalize these ideas, the language is usually used logic programming (see chapter 8). In particular, a concept is usually presented in the form of a predicate that characterizes the subset of the object space that interests us. For example, the predicate sur (X) can represent the concept of "cuphood", which is defined in the style of the PROLOG language as a vessel of small volume (small), possessing the properties of open (open), stable (stable). Recall that the expression

reads "a is true if b is true". Then:

cup (X): - small (X), stable (X), open (X).

Domain knowledge should include descriptions of the conditions that must be met in order for the object to be considered "stable", for example, it is stated that the object must have a flat bottom, the definition of the property "open" - for example, an object must have a concave shape, with the center of curvature located above the base.

As an instance of the training sample, we indicate an object with a flat concave bottom, the diameter of which does not exceed a few inches. The instance should be "accompanied" by the explanation that the specified properties are sufficient to represent the concept of "cuphood". A pattern is usually described by a number of ground literals, for example:

color (red, obj). diameter (4, obj).

flat (bottom, obj). concave (top, obj).

These literals represent a specific object, obj, red, flat bottom, concave, with the center of curvature at the top (concave top). The domain knowledge presented below makes it possible to recognize this instance as representing the concept sire:

small (X): - diameter (Y, X), Y< 5.

stable (X): - flat (bottom, X).

open (X): - concave (top, X).

Please note that the obj object is a cup logically follows from this piece of knowledge. Our explanation of why obj is a cup is actually proof. This concludes the clarification phase of the EBG.

Then the generalization phase begins - a set of sufficient conditions that existed during the explanation is developed. The main thing that needs to be done in this case is to determine the weakest conditions, which are enough to conclude, based on the available knowledge, that obj is a cup. The resulting generalization of the concept is that the cup is a flat-bottomed, concave object with a center of curvature at the top and a diameter of less than 5:

cup (X): - flat (bottom, X), concaveftop, X), diameter (Y, X), Y< 5.

Note that this generalization follows logically from the original definition of "cup" and basic knowledge of "small volume", "sustainability" and "openness". In this sense, the new generalization was already implicitly represented in the previously available knowledge. Analysis of the presented sample allowed this generalization to be made explicit. In addition, the use of a previously formed generalized definition of "cup-shaped" allowed us to completely painlessly ignore insignificant characteristics, in this case - color.

Case-based learning (CBL) is a teaching approach that is completely opposite to the EBG method. As shown in Chapter 22, the extraction of information with this approach is based mainly on the similarity of arguments, and not on their logical analysis. It is fair to say that the process of adapting a previously formulated solution to a new problem does not include generalization in the sense of logical programming. As an additional tool that ensures the use of knowledge about relationships between entities of the domain, a hierarchy of abstractions can be used, in particular in the form of a semantic network. However, the result will not be new rules involving variables, but rather new use cases formed from old constant substitutions.

Case-based reasoning is, in fact, reasoning by analogy, not a logical conclusion. If someone concludes that John, the owner of a Porsche, is a risk-averse driver, since there is a precedent that Jack who drives a Ferrari is also a risk-averse, then in fact, by analogy, the conclusion is drawn - John is like Jack, since Porsche's car has a lot in common with Ferrari. The conclusion suggests itself that when such an analogy is constructed, each use case implicitly generates a certain rule. In our example, this generalized rule is that people who drive sports cars are risk averse. But this rule is not complete. Are all sports car drivers risk averse, or only male or youth drivers? A program using case-based reasoning cannot answer such a question. She can only find a precedent that is closest to the case in question.

There are some things in common between the CBL and EBG methods. Both methods can be contrasted with the inductive methods discussed in Chapter 20, since neither method involves analyzing a large amount of data. We have already shown that the EBG method only needs one training instance, while the CBL method can do with one suitable use case to generate an analogy.

But learning is more than just the accumulation of knowledge. A case-based system must be capable of identifying inappropriate use cases that prevent a satisfactory solution to a pressing problem. Otherwise, it will accumulate precedents with erroneous decisions.

CHEF, described in Chapter 22, is able to identify the situation in which it is forming a bad recipe and attempts to correct it. To do this, the program must explain why it thinks the recipe is bad. To do this, the program needs to use certain knowledge from the subject area, which in this case should take the form of rules of causation.

For example, the extraction and modification modules might suggest pickling shrimp and then peeling them. But in this case, the shrimps will become too wet, and the "peeled shrimps" property specified in the order cannot be realized in the recipe. The program will detect this when it tries to simulate the cooking process according to the created recipe. Then another module of the system, responsible for recovery, will turn to knowledge about the types of errors in recipes, find a suitable strategy for correcting the situation and repeat the recipe stage. In the new recipe, you first need to peel the shrimp, and only then marinate them.

Even after a solution is obtained for a new case, the program will not be able to index it correctly until it understands why this solution is considered successful. If the user orders a light, low-fat dish and if the program, manipulating the previous recipes, has formed a new one, then this result can be used in the future only after the signs "light" and "low-fat" are associated with it.

ODYSSEUS and MINERVA systems

ODYSSEUS learns how to improve the knowledge base of expert systems designed to solve heuristic classification problems (see Chapters 11 and 12). It observes how the expert solves the problem, and forms an explanation of each action of the expert (for example, asking the expert why a certain attribute has been assigned a particular value). The formation of explanations is based on the knowledge of the problem area and the strategy for solving problems that the program has. If the program fails to generate an explanation, the process of correcting the knowledge base is initiated.

Shell of the MINERVA expert system

MINERVA is an expert system shell developed from EMYCIN and NEOMYCIN (see chapters 10-12). MINERVA provides ODYSSEUS with a knowledge base and problem solving method and is specifically designed to support the EBL teaching method. One of the main differences between MINERVA and EMYCIN is that it presents not only domain knowledge, but also strategic knowledge that reflects the way of thinking of a practitioner. Such knowledge can be considered as a further development of the meta-rules of the MYCIN, EMYCIN and NEOMYCIN systems.

The main component of this system is the medical knowledge base for diagnosing meningitis and other neurological diseases. MINERVA is implemented in the PROLOG language, and domain knowledge is represented in this system in the form of Horn phrases (see Chapter 8), but the content rules are similar to those used in MYCIN. For example, the following expression represents the fact that photophobia can be associated with headache:

conclude (migraine-headache, yes)

: - finding (photophobia, yes).

Knowledge about the state of the problem is recorded as expressions for facts during the operation of the system. For example, the expression

rule-applied (rulel63).

claims that rule 123 was activated during the system operation and that this information is available to the program in the future. Another simple expression

differential (migraine-headache, tension-headache).

will fix the fact that migraines and high blood pressure are the current hypotheses put forward by the program.

Obviously, such information can be presented and registered in any way, for example, by setting flags or variables, but it is most advisable to use the same representation that is accepted in the knowledge base of the subject area.

An uncomplicated meta rule can be represented in as follows: goal (findout (P)): - not (concluded (P)), ask-user (P).

This rule states that if the current goal of the system is to find the value of the parameter P, and if the system cannot come to a conclusion about the value of this parameter based on its knowledge, then it must request it from the user. Since P is a variable, the head of goal (findout (P)) is matched against an explicit system goal expression, such as goal (f indout (temperature)). Subgoals like not (concluded (P)) can be matched (successfully or not) with system data describing the current state of the computation process, such as concluded (temperature).

Such strategic knowledge is used to form a judgment about the current state of the problem and to decide whether the system has sufficient knowledge in this case. In addition, the presence of such knowledge simplifies the training program, which can refer to structures at the meta-level of the expert system.

Training in the ODYSSEUS system

The teaching method used in the ODYSSEUS system differs significantly from those discussed in Chapter 20. When developing this system, the goal was to endow it with the ability to expand the existing incomplete knowledge base, and not include new concepts in the knowledge base based on the analysis of a large training sample. The system learns by "observing" how an expert solves a problem, much like a diligent student comprehends the mysteries of the mastery of a teacher standing behind him.

The main type of actions that an expert performs in the process of solving a diagnostic problem is determining the values \u200b\u200bof various variables, i.e. patient characteristics such as temperature, etc. The program, observing the work of an expert, expands its knowledge, trying to understand why the expert needed an answer to this or that question.

Thus, the concept of the learning process in the ODYSSEUS system is very close to the formulation of explanations. In fact, in the context of the operation of this system, the meaning of the term "explanation" differs both from the generally accepted one and from what we gave it in Chapter 16. In ODYSSEUS, an explanation is a type of proof that carries information about why an expert asks a certain question on specific stage of solving the problem of diagnosis. The meaning of a particular question is related both to the current state of the problem and to the strategy used by the expert. Therefore, having "comprehended" why the question was asked, the program, as it were, comprehends the strategy of the expert's actions.

If the program has comprehensive knowledge, it is able to formulate a question (or rather, the statement that stands behind it) as a logical consequence of the current state of the problem, strategic knowledge contained in the meta-rules, knowledge of the subject area and one of the current goals.

For example, if the question is askuser (temprature), then looking back will take us to the nearest goal goal (f indout (temperature)).

But this goal, in turn, is shaped by a higher-level goal, for example, a desire to apply a certain rule or to divide hypotheses. The presence of such a high-level goal in the current situation explains why a lower-level goal was formed, and therefore why a certain question was asked. This backward chain of reasoning from subgoals to goals is performed by the usual means of the PROLOG language or even MYCIN, but note that this reasoning is performed at the meta-level, i.e. at the level that determines why the program works the way it does and not the other way. The "from behind" learning strategy used in the ODYSSEUS system includes three main phases.

· Determination of the flaw in the knowledge base. Such a flaw reveals itself when it is not possible to form explanations for the expert's actions using the reverse lookup method described above. Failure of this kind serves as a signal that it is time to start learning.

· Formation of proposals for making changes to the knowledge base. If it was not possible to form a proof (explanation in ODYSSEUS terminology), then it can be assumed that there is some flaw in the knowledge about the subject area or about the state of the problem. If this is a flaw in knowledge about the subject area, you can temporarily add a suitable phrase to the database and see if a proof will be generated after that. If there is a flaw in knowledge of the state of the problem, the program must look for other evidence.

· Making changes to the knowledge base. The method that ODYSSEUS uses to make changes to the knowledge base is called the “decision confirmation procedure”. Without going into details, it requires that the system designer form a procedure that will process the new rules, determining, for example, by how much the number of competing hypotheses will be reduced as a result of applying the rule.

The details of how these phases are implemented are beyond the scope of this book, but the basic principles are fairly obvious. In the applied technique, a training sample instance is a separate attribute-value pair, but during a training session, many such pairs can arise, as the program tries to explain why it attaches a value to each of these instances. If the explanation fails, the program attempts to modify the knowledge base.

To modify rules or add new rules to the knowledge base, the ODYSSEUS program also uses the CBL method in a primitive form. The program has a library of precedents, each of which contains the corresponding correct diagnosis. The program can use this library for testing. If during testing it turns out that an incorrect diagnosis has been formed, the program assigns something like fines to the rules used in this case.

The prerequisites of the rules that led to the erroneous conclusion are "weakened"; the area of \u200b\u200btheir “application is narrowed. If the application of the rules has confirmed the correct diagnosis made earlier, then the corresponding prerequisites are“ strengthened. ”This procedure has much in common with the method used in the Meta-DENDRAL system described in Chapter 20. Of course, this method modifying the rules does not guarantee a solution to the problem, but it can be useful for setting new rules.

Using Use Cases to Handle Exceptions

In this section, we will look at a different way of sharing rules and use cases than that used in ODYSSEUS. The role of use cases in the new approach is not to facilitate rule modification, but rather to complement the knowledge provided in the rules when handling exceptions. Thus, each component does what it does best — rules deal with domain generalizations, and use cases deal with individual atypical cases.

As has been demonstrated more than once in previous chapters (see, for example, Chapters 10-15), building a set of rules for an expert system is far from trivial. In addition to the difficulties associated with the extraction and presentation of knowledge, there is also the problem of completeness of coverage of the subject area with a set of rules. Ideally, the rule base should be correct, consistent (at least within the adopted conflict resolution strategy) and complete. But as the number of rules expands and the rules become more complex, it becomes more difficult to achieve this ideal state.

It is especially difficult to take into account all possible exceptions in the rules. Such an attempt leads to extremely complex rules. The assertion that there are no rules without exceptions has long been a commonplace. Sometimes they try to solve this problem by including in the set of many "small" rules that should be activated in such exceptional situations. But this means assigning to the rules an unusual function - to process not the general case, but the particular one.

Golding and Rosenbloom proposed the use of a hybrid architecture in expert systems, in which the method of using generative rules is combined with the method of using precedents in solving problems. The idea was that a use case engine should be used to critically analyze the results of applying rules. This is done by looking for use cases similar to the case in question, if the latter can be considered an exception to the rule. This approach requires the use case base to be indexed according to the applicable rules. The authors also proposed an appropriate measure of proximity, which allows you to assess the degree of similarity between the current case and the precedent (Fig. 23.1).

Hybrid system architecture using rules and use cases

The basic idea of \u200b\u200bthe system is very simple and elegant. First, rules are applied to solve the current problem, resulting in some kind of solution. Then the library of use cases is scanned to identify in it a previously veiled case of exceptions from the rules used. The system operation algorithm is shown below.

Cycle UNTIL a solution is received

1 . Use the rules to select the next operation.

2. Search the library for "compelling" use cases that offer the opposite choice of operation.

3. If a use case is found, use the proposed operation option. Otherwise, use the option suggested by the rules.

Note that the rules and use cases are accessed every loop. (If the program cannot find either a rule to apply or a use case, it stops.)

In order for the proposed idea to work, the use cases in the library must be indexed according to rules that they contradict. Consider, for example, the rule of insurance for vehicle drivers:

"Men under 25 pay a premium premium."

Such a rule should be associated in the library with a precedent that mentions an 18-year-old boy who successfully passed tests of increased difficulty and pays a fee at a reduced rate.

What considerations are used to decide whether a precedent is "compelling" or not? The solution proposed by Golding is as follows. When we draw an analogy between a precedent and a current case, we thereby form some kind of implicit rule hidden from prying eyes. Suppose our example is a 20-year-old male driver who has an advanced qualification, and we found a similar precedent, but it was about 1 8-year-old driver. "Men under 25 with an advanced qualification category pay an insurance premium at a reduced rate."

Suppose that in assessing the degree of intimacy that is needed to extract and then analyze the use cases, the age of the drivers is divided into ranges, say "under 25", "25 to 65" and "over 65". This measure of closeness will evaluate the case and precedent we are considering as very similar, since the age category and gender are the same.

You can test this rule on the rest of the use cases in the library and estimate what percentage of the identified use cases it covers. Any precedent with an advanced male driver who is less than 25 years old and pays a premium rate premium will be considered an exception and therefore lower the rating of the precedent. If the cases are similar enough, and the rule is accurate enough, then the analogy is considered "compelling" and the case-handling component wins. Otherwise, the applicable rule will win, and the option following from the rule will be used in the final decision.

Thus, "irresistibility" depends on three factors:

· The degree of closeness of cases, which must exceed a certain threshold;

· The accuracy of the implicit rule formulated as a result of the identified analogy; the proportion of precedents that confirm the application of this rule is taken as a measure of accuracy;

4 the reliability of the estimate of accuracy, which is determined by the size of the sample on which this estimate is formed.

The authors demonstrated the capabilities of the proposed architecture using the example of the problem of determining the pronunciation of names. The system they implemented, called ANAPRON, contains about 650 linguistic rules and 5000 precedents. The results of testing the system showed that it has a higher performance than analog systems that use either only rules or only use cases.

A hybrid symbolic approach and neural networks

This section will consider the prospect of using neural networks in expert systems. Neural networks assume a completely different model of the computational process, fundamentally different from the one traditionally used in expert systems. The SCALIR system (Symbolic and Connectionist Approach to Legal Information Retrieval) will be considered as an example.

This system helps the user find legal documents - descriptions of precedents or articles of laws - that are relevant to a particular case. Since legal practice covers all areas of life in modern society, the use of a traditional approach based on conventional knowledge bases to search and extract legal information will require the presentation in the system of a huge amount of knowledge, mostly non-trivial, representing such complex concepts as rights, permissions, duties, agreements, etc. The problem is compounded by the use of natural language when writing queries. Most search engines dealing with natural language queries that are used to search the web World wide Web are based on a statistical approach rather than knowledge bases.

The system attempts to solve this problem by combining a statistical approach to information extraction and a knowledge-based approach that takes into account the semantic relationships between documents.

Neural networks

With regard to artificial intelligence systems in general and expert systems in particular, the following criticisms can sometimes be heard.

· Such systems are too "fragile" in the sense that, when faced with a situation not intended by the developer, they either generate error messages or give incorrect results. In other words, these programs can be quite easily confused.

· They are not able to continuously self-learn, as a person does in the process of solving emerging problems.

Back in the mid-1980s, many researchers recommended using neural networks to overcome these (and other) shortcomings.

In its most simplified form, a neural network can be considered as a way of modeling in technical systems the principles of organization and mechanisms of functioning of the human brain. According to modern concepts, the human cerebral cortex is a set of interconnected simplest cells - neurons, the number of which is estimated at about 10 10. Technical systems in which an attempt is made to reproduce, albeit on a limited scale, such a structure (hardware or software), are called neural networks.

A neuron in the brain receives input signals from many other neurons, and the signals are in the form of electrical impulses. Neuron inputs are divided into two categories - excitatory and inhibitory. The signal received at the excitatory input increases the excitability of the neuron, which, when a certain threshold is reached, leads to the formation of an impulse at the output. The signal arriving at the inhibitory input, on the contrary, reduces the excitability of the neuron. Each neuron is characterized by an internal state and an excitability threshold. If the sum of signals at the excitatory and inhibitory inputs of a neuron exceeds this threshold, the neuron generates an output signal that goes to the inputs of other neurons connected to it, i.e. there is a propagation of excitation through the neural network. A typical neuron can have up to 10 J connections with other neurons.

It was found that the switching time of an individual neuron in the brain is on the order of several milliseconds, i.e. the switching process is rather slow. Therefore, the researchers concluded that the high performance of information processing in the human brain can only be explained by the parallel operation of many relatively slow neurons and a large number of mutual connections between them. This explains the widespread use of the term "massive parallelism" in the literature on neural networks.

The neural network approach is often viewed as non-symbolic, or subsymbolic, since the basic information item to be processed is not a symbol (as defined in Chapter 4), but something more primitive. For example, a symbol in a LISP program, say the LAPTOP MU, could be represented by a diagram of the activity of a number of connected neurons in a neural network. But, since neural networks are often modeled in software, the neuron itself is represented by some kind of software structure, which, in turn, can be implemented using symbols. For example, the role of a neuron can be played by a data object with suitable properties and methods and linked by pointers to other objects in the network. Thus, at the conceptual level, in a subsymbolic system implemented computer programthat contains symbols, there is nothing paradoxical.

Regardless of how it is implemented, a neural network can be thought of as a weighted directed graph of the type described in Chapter 6. Nodes in this graph correspond to neurons, and edges correspond to connections between neurons. Associated with each connection is a weight - a rational number - which represents the estimate of the excitatory or inhibitory signal transmitted over this connection to the input of the recipient neuron when the transmitter neuron is fired.

Since the neural network is clearly dynamic in nature, time is one of the main factors in its functioning. When simulating a network, the time changes discretely, and the state of the network can be viewed as a sequence of snapshots, with each new state depending only on the previous cycle of neuron firing.

To perform information processing using such a network, certain agreements must be followed. In order for the network to become active, it must receive some input signal. Therefore, some network nodes play the role of "sensors" and their activity depends on external sources of information. The excitation is then transferred from these input nodes to the internal nodes and thus propagates through the network. This is usually done by setting the activity level of the input nodes high, which is maintained for several excitation cycles, and then the activity level is reset.

Some of the hosts are used as egress, and their activity state is read at the end of the computation process. But often of interest is the state of the entire network after the computations are over, or the state of nodes with a high level of activity. In some cases, it may be interesting to observe the process of establishing a network in a stable state, and in others - recording the level of activation of certain nodes before the process of propagation of activity is completed.

In fig. 23.2 shows a fragment of a neural network consisting of four sensor nodes S 1 - S 4, the excitation from which is transmitted to other network nodes. One node, R, is the exit. If the weights of the connections in the network are unknown, then the node R will be excited when the nodes S 1 and S 4 are excited.But if the nodes S 2 and S 3 are also excited, this will lead to suppression of the excitation R even with the excited nodes 5) and S 4 ... Whether the node R will actually be excited in this state of signals at the inputs of the sensor nodes depends on the weights of the connections in the network.

The number of possible configurations for this type of network is very large. The number of ways to calculate the state of a neuron for a given sum of states at its inputs is also great. These details of the theory of neural networks are beyond the scope of this book. Next, we will follow Rose's ideas and consider a relatively simple model of a neural network, in which any node can be connected to any other node and in which the output of a node is its state of activity (i.e., no distinction is made between the activity of a neuron and a signal at its exit).

Fragment of a neural network with excitatory and inhibitory connections

For a more rigorous formulation of such a model, we introduce the following notation:

W ij is the weight of the connection from node j to node i,

· Net i \u003d Z j w ij - the state at the current time of the inputs of the node l, connected with other nodes of the network.

In any definition of a neural network, it is necessary to take into account the time factor, since the state of any neuron at some point in time depends on its previous state and on the previous state of the neurons associated with its inputs.

Definition

A connectionist network can be viewed as a weighted directed graph in which the following requirements are met for each node i:

(1) the state of activity of a node at any time moment t is a real number (we will denote it as a i (t));

(2) the weight of the link that connects node i with any other node in the network is a real number w ij,

(3) the activity of a node at time t + 1 is a function of

· Its activity at the moment of time t, a i (t);

· The weighted sum of signals at the inputs at time t, net i (f);

· Arbitrary external input signal x i (t).

A simple function for calculating the state of activity of node i satisfying requirement (3) of the above definition has the form

a i (t + 1) \u003d Sum j

This, however, is not the only possible way to determine activity. Other types of functions include the addition of terms corresponding to an increase or decrease in activity, or have the form of non-linear differential functions (see, for example,). They will not be discussed in this book.

When constructing a network, the link weights can be assigned a priori or change over time. In the latter case, the change in weights is one of the consequences of network activity. Weights can be viewed as a reflection of knowledge, and the process of adjusting and refining them as a learning process for the system. Since weights significantly affect the distribution of activity over the network, the behavior of the network largely depends on them, and therefore, by changing the weights, it is possible to change the behavior of the network in the desired direction.

As noted above, knowledge in the network of connectivity is represented implicitly, since it is impossible to single out one specific structural element of the network, which would represent a separate rule or entity of the domain. Knowledge is reflected precisely in the balanced connections between the myriads of individual elements of the network. Thus, in this case we are dealing with distributed knowledge, which cannot be represented as a simple enumeration of numeric or symbolic elements. For this reason, you can often come across the statement that subsymbolic information processing is performed in neural networks.

In connectivity networks, knowledge is not stored in a declarative form, and therefore it cannot be available for interpretation by any external processor. Knowledge access and inference can only be described in terms of network activity.

Of course, nothing prevents the network designer from associating its individual nodes with certain domain entities, as Rose did in the SCALIR system. However, such a reflection of concepts on network nodes does not contradict the previously made statement that relations between entities are implicitly represented in the form of links between nodes and usually cannot be interpreted in the form of rules. Consequently, although we have partially opened the veil of mystery that hides what is behind the network nodes, the essence of the weighted connections between them remains “subsymbolic” as before.

Even if the nodes represent the entities of the domain, the general picture of the activity of myriad nodes of the network can hide high-level concepts that unite certain aspects of the entities represented by the nodes. For example, let the nodes represent words and let the nodes "race", "car", "driver" be excited. This may represent the concept of "race car driver" or, conversely, the fact of driving a race car. In any case, such a representation can be regarded as subsymbolic, since its constituent nodes cannot be formed in the form of any syntactic structure that has an explicit meaning. Likewise, you cannot semantically analyze the state of a myriad of nodes using any external set of rules.

SCALIR - a hybrid system for extracting legal information

The nodes in the network structure of the SCALIR system represent precedents (cases previously considered by the courts), articles of legal acts and important (key) words that are found in such documents. Thus, the network is structurally divided into three parts (layers), as shown in Fig. 23.3. In this network, the precedent layer and the legislative layer are separated by a layer of nodes representing keywords (terms). The latter are associated with the documents in which they are found.

Thus, in the basic structure of the network, the link between the nodes of terms and documents forms an indexing scheme with weighted links. As a result, the array of terms is mapped both to the array of precedents and to the array of legal acts.

Rather than associating each term with each document in which it appears, SCALIR calculates the term weight for each keyword associated with the document as a function of the frequency of the term in a given document and the frequency of its occurrence throughout the body of documents. Intuitively, it seems that the term most appropriate for indexing a certain document would be one that appears frequently in this document, but rarely in all others. The resulting value is compared with a threshold value, as a result of which each document is indexed by about a dozen keywords. (I draw your attention to the fact that the SCALIR system network diagram shows bidirectional links. In fact, each of them is represented in the system by a pair of unidirectional links, and these links can have different weights. Thus, not only the term allows you to find a document, but also the term can be found.)

Connectivity network in SCAUR system ()

When designing a network in SCALIR, nodes were first organized for all selected terms, and then they were associated with document nodes, and the links were weighted depending on the significance of a particular term in the context of this document.

This type of link (in the documentation they are called C-links) is not the only one in SCALIR. There are also symbolic links (S-links), which in many ways resemble links in semantic networks, since they are marked and have constant weights. With the help of links of this type, relationships between documents are represented in the network, for example, one document quotes another, in one court decision another is criticized, one legal act refers to another, etc. Thus, S-links represent knowledge explicitly.

In total, the SCALIR system network contains about 13,000 term nodes, about 4,000 use case nodes and about 100 legislative nodes. There are approximately 75,000 links between term and use case nodes, and about 2,000 links between term and law nodes. In addition, there are about 10,000 symbolic links between use case nodes. Rose did not consider it necessary to dwell on the efforts required to create such a network, but it can be assumed that such key tasks as the extraction of terms and quoting were solved programmatically, and then, based on this information, the nodes of the network and the connections between them were automatically formed. It is necessary to take into account the fact that most of the city documents have already been previously processed by publishers, who have compiled fairly complete citation indexes and keywords.

The described network was then used as a basic information structure for retrieving documents. The system is based on the principle of spreading activation. This principle is not new - it was previously used by Quillian to work with Semantic Networks (see Chapter 6 for more on this). Using this formal apparatus makes it possible to find out whether there is any relationship between nodes in the network. To do this, the process of distributing tokens from nodes of interest is started, and it is analyzed whether there is an "intersection" of propagating tokens anywhere in the network.

The main idea behind SCALIR is that the level of activity of a given node should be proportional to its "relevance" in the context under consideration. If, as a result of processing a request, a certain number of nodes of the term layer are raised, this should lead to the activation of nodes of those documents that relate to this request, and the level of excitation depends on how a particular document corresponds to the essence of the request. Nodes that receive requests are, in fact, sensory nodes of a neural network, from which excitation is transmitted to other nodes via C-connections. In the process of propagation of excitement, S-links are also included in the case, which transfer excitations from some nodes of documents to others associated with them. Thus, symbolic links reflect the knowledge that if a certain document is related to a received request, then, most likely, another document associated with it is also related to this request. The weights of the symbolic links are fixed, since the strength of such an associative relationship can be estimated in advance.

There are two properties of the network activation function that seem highly desirable for applications requiring associative information retrieval. These properties influence the choice of the method of excitation of sensory nodes that perceive user requests, the method of assigning weights to the connections, and the form of the activation function.

(1) The amount of activity that is entered into the system should not depend on the dimension of the request.

(2) In each successive cycle of propagation, the activity should not increase.

If the first of these requirements is not met, then a single-word query will result in less network activity than a verbose one. It turns out that in response to a more limited verbose query, the system will retrieve more documents than in response to a looser one-word query, which is contrary to our intuitive expectations. If the network does not have the second of the formulated properties, then too many documents will be retrieved that have an extremely weak relation to the essence of the request, i.e. the system will generate a lot of "information junk".

In order for the system to have the first property, it is necessary to distribute a fixed amount of activity between the input nodes at the stage of preliminary processing of the request. The system will possess the second property if the sum of the weights of the output connections does not exceed one and, therefore, the value of the activation function will be less than or equal to its argument.

C-bonds use a linear reactivation function that contains a retention constant, p, as shown in the expression below. The value of this constant determines how much of the node's activity is retained in the subsequent excitation cycle, and what is propagated further along the network.

a i (t + 1) \u003d р а j (t) + (1 - p) Sum j

It is quite obvious that the reduced activation function will satisfy the formulated requirements, since a i (t +1) \u003d< a i (t) до тех пока, пока Sum j

A function of the same kind is used in work. Rose follows the ideas outlined in this paper and with regards to organizing network activity management in SCALIR.

· To select the nodes, the activity of which is sufficient to participate in the process of information extraction, the parameter O s is introduced - the significance threshold. The value of this threshold decreases as activity spreads over the network.

· To highlight the nodes, the activity of which is too weak and which therefore can be ignored in the process of information extraction, the parameter O q is introduced - the quiescence threshold. Using this threshold avoids wasting time on analyzing low-activity nodes.

These parameters are used in the SCALIR network traffic propagation algorithm, which is presented in a simplified form below. This algorithm implements the Breadth First Search method, starting with the input nodes of the query perception (QUERY-NODES) and ending with all weighted links.

Set the initial value O S.

Include nodes from the QUERY-NODES set in the ACTIVE-NODES set.

If prompted, set node activity levels to QUERY-NODES.

Include in the RESPONSE-SET all nodes from ACTIVE-NODES, whose activity exceeds O S.

Remove from the set ACTIVE-NODES all nodes whose activity is below O q.

Add to the ACTIVE-NODES set all the nodes associated with the nodes already included in the ACTIVE-NODES.

Update the activity value of all nodes of the ACTIVE-NODES set using the activation function.

Sort the nodes in the ACTIVE-NODES set by activity level. Decrease O s value.

until (O S \u003d< O q) или (ACTIVE-NODES = 0).

The simplified version does not cover the use of a parameter that limits the width of the search space. In addition, in this formulation of the algorithm, we have omitted the analysis of the maximum size of the set of output nodes. Limiting the set of output nodes stops searching after the maximum number of documents to retrieve has been allocated.

Most of the parameters used in the process of controlling network activity are determined empirically. Setting the weights of connections between nodes of the network W ij is, in fact, the process of training the system, which we will briefly consider in the next section.

training in the SCALIR system

Since the weights of C-bonds can be adjusted by the system during operation, it is thus capable of self-learning in accordance with the information entered by the user. Below we describe how this is done in the SCALIR system, omitting non-essential details.

Suppose that one of the inputs of node i is connected to the output of node j, and the connection has weight W ij. If node i represents a document related to the term represented by node j, then in the process of learning we may need to strengthen this connection. If the user considers that the document has little to do with this term, then this connection will need to be weakened. The main question that needs to be solved in this case is to what extent the weight value needs to be changed. One of simple rules calculating the value of the weight change W ij can be expressed by the formula

W i \u003d nf i a j,

where n | is the constant of the learning rate, and f i is the feedback coefficient from the user, which, for example, can take a value of +1 or -1.

However, the application of such a rule is not as obvious as it might seem at first glance, for the following reasons.

· It is not easy to determine the values \u200b\u200bof the activity level a, because the input node activated when a request occurs may decrease its activity after the request is canceled.

· The neighbors of the nodes that receive feedback should also seem to receive some feedback from the user confirming that they are submitting documents relevant to the request.

· Node i can be located at the end of the network of propagation of activity, and therefore, information from the user (feedback) must propagate through the network in the opposite direction. Thus, feedback received from the user should propagate through the network in much the same way as activity. The maximum feedback value for each node is recorded and updated during the propagation process, and these values \u200b\u200bthen play the role of the f i and a j terms in the above expression. Further, the obtained values \u200b\u200bof the weights are normalized so that their sum for each individual node is equal to 1.0. Of course, in a real SCALIR system, the self-learning process is somewhat more complicated, since there are different types of connections in it. Readers interested in the details of this process should familiarize themselves with the work, but the idea of \u200b\u200bcombining symbolic and subsymbolic methods deserves further in-depth study. The SCALIR system demonstrates a fairly pragmatic trade-off between a purely statistical approach to information extraction and a traditional expert system approach that requires a large amount of domain knowledge.

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Page 3

In hybrid systems with substitution, the main model is taken, one of the elements of which is mixed by another model, for example, a) the weights are recalculated in the backpropagation procedure using a genetic algorithm; b) the selection of membership functions in a fuzzy controller is carried out using a genetic algorithm. Interoperable hybrid systems use independent modules that exchange information and perform various functions in order to obtain a common solution. For example, if the problem being solved includes pattern recognition, inference and optimization, then these functions are taken over by neural networks, expert systems, and genetic algorithms. In polymorphic hybrid systems, one model is used to simulate the functioning of another model.

However, the existing hybrid systems for identifying fingerprints are not free from disadvantages. The method of analyzing fingerprints by the Fourier spectrum will interpret the same images that differ in the permutation of fragments. In addition, fingerprint images are structurally redundant.

In general, the hybrid ADT system is a further step in the development of analog computing.

The fifth chapter is devoted to the issues of building hybrid systems, including subsystems of evolutionary modeling, optimization blocks interacting with simulation models, expert systems and other decision support systems. Creature simulation models acts here as one of the directions of development of approaches to intelligent simulation. This chapter describes the approaches and models of multi-agent systems, various levels of intelligence and their further evolutionary form - models of artificial life. As examples of hybrid systems with evolution, modeling of the development of a population of the simplest automata and multi-model systems are presented.

It is possible to use hybrid systems that combine elements of active and passive systems.

When studying discrete and hybrid systems, there are parameters that cannot be described by functions of dependent or independent variables.

In the case of a hybrid system, the operation of the computer is limited to arithmetic operations, with the help of which the peak areas are calculated; in this case, the sensitivity of the detector can be taken into account, the content of substances can be determined based on the internal standard and a protocol can be printed in a given format.

The introduction into a hybrid system to automate the processing of data received from all holographic systems, a scanning-analysis unit controlled by a digital computer, should add to the system's ability to perform versatile functions high speed, increased accuracy and objectivity in data analysis.

Many hybrid control systems use various modifications of the Ethernet protocol based on Carrier Sense Multiple Access with Collision Detection (CSMA / CD) in accordance with the ISO 8802 - 3 / IEEE 802.3 standard. Its essence boils down to the fact that each node in the network monitors the line load and transmits only when it determines that the line is free. If a collision occurs because the other node also requires a line to transmit, then both nodes stop transmitting.

IMAN uses a hybrid database management system (DBMS) based on Oracle V8, which supports relational and object-oriented data models, controls access and changes, generates product specifications, and integrates application subsystems. Management of parallel and sequential business and design processes is assigned to the Workflow module.

The problem of optimization of linear hybrid systems with a generalized quadratic criterion is considered, when terms are added to the traditional terms - penalties on the squares of state and control deviations, which allow penalizing deviations in accordance with their sign. Optimal control problems with such preferences, i.e. when it is required that certain control components (or states) be positive or negative most of the time, it is often encountered in practice.

In the case of a hybrid automatic control and management system consisting of electrical and pneumatic devices, the conversion of the electrical signal into air pressure is required to communicate these devices with each other.

Along with these hybrid systems, hybrid models of a different type can also be used, in which passive models are joined with devices operating on the principles of electronic modeling. Such models make it possible to use the advantages of passive models (simplicity, a large number of nodes, speed, etc.) with the possibility of performing a number of logical operations necessary for solving nonlinear problems of field theory, without participating in the computational process of an electronic digital computer with multiple transformation of information from one type to another, without the equipment needed for this conversion. The cost of such systems is significantly lower than the cost of hybrid machines, including electronic computers.

In other words, a combined complex consisting of several electronic computers using different representations of quantities (digital and analog) and connected by a common control system. The hybrid
a computing system, in addition to digital and analog machines and a control system, as a rule, includes intra-system communication devices, converters for the representation of quantities and external equipment. A hybrid computing system is a computer complex; this is its main difference from a hybrid computing machine, which received this name because it is based on hybrid decision elements or using digital and analog elements.

In the literature, hybrid computing systems often refer to AVMs with multiple use of decision elements equipped with a memory device, AVM with digital program control and AVM with parallel logic. Computing machines of this kind, although they have elements used in digital computers, still retain the analog way of representing values \u200b\u200band all the specific differences and properties of the AVM. The emergence of hybrid computing systems is explained by the fact that for solving most of the new problems related to the control of moving objects, the creation of integrated simulators, the optimization and modeling of control systems, etc., the capabilities of separate digital computers and AVMs are already insufficient.

Dividing the computational process into separate operations, which are performed by a digital computer and an AVM in a complex, in the course of solving a problem, reduces the amount of computing operations performed on a digital computer, which, other things being equal, greatly increases the overall performance of hybrid computing systems.

There are balanced, digital-ro-oriented and analog-oriented hybrid computing systems.

In systems of the first type, digital computers are used as an additional external device to the AVM, which is necessary for the formation of complex nonlinear dependencies, storing the final results and for executing program control of the AVM. In systems of the second type, AVM is used as an additional external device of a digital computer, which is designed to simulate parts of real equipment, multiple implementation of small subroutines.

The invention of effective hybrid complexes requires, first of all, clarification of the main areas of their use and a thorough analysis of standard problems from these areas.

As a result, an expedient structure of the hybrid complex is established and requirements are imposed on its individual parts.

Problems that are successfully solved using hybrid computing systems can be divided into the following main groups: simulation of automatic control systems in real time, consisting of both digital and analog devices; real-time reproduction of actions that contain high-frequency components and variables that vary over a wide range; modeling of biological systems; statistical modeling; optimization of control systems; solution of partial differential equations.

The example of the problem of the first group can be the modeling of the control system of a rolling mill. The dynamics of the processes occurring in it is recreated on an analog machine, and on a universal digital computer of the middle class a specialized machine controlling the mill is simulated. Due to the short duration of transient processes in the drives of rolling mills, a general simulation of such processes in real time would require the use of ultra-high-speed digital computers. Such tasks are quite common in military control systems.
The tasks of controlling moving objects, including homing tasks, as well as tasks that arise when creating a computational element of complex simulators, are standard for the second group. For homing tasks, the formation of a trajectory of movement directly in the process of movement is characteristic. The high rate of variation of some parameters when the object approaches the target requires a high speed of the control system, which exceeds the capabilities of current digital computers, and at the same time, a large dynamic range requires high accuracy, which is difficult to achieve with an AVM. When solving such a problem on hybrid computing systems, it is advisable to assign the simulation of the equations of motion around the center of gravity to the analog part of the system, and the movement of the center of gravity itself and kinematic parameters to the digital part of the computing system.

The third group includes problems, the solution of which is formed as a result of processing many results of a random process, for example, solving multidimensional partial differential equations using the Monte Carlo method, finding the extremum of functions of several variables, and solving stochastic programming problems. Multiple repetition of a random process is entrusted to a high-speed AVM, which operates in the mode of repeated repetition of the solution, and the processing of the results, calculation of functionals, and reproduction of functions at the boundaries of the region are performed on a digital computer. In addition, the digital computer determines the moment of the end of the calculations. The use of hybrid computing systems makes it possible to reduce the time for solving problems of this kind by several orders of magnitude in comparison with using only a digital machine.

A similar effect is achieved when using hybrid computing systems to simulate the processes of propagation of exposure in biological systems.

The peculiarity of this process is that even in elementary cases it is necessary to reproduce a complex nonlinear system of partial differential equations.

The search for a solution to the problem of rational control for problems higher than the third order, as a rule, is associated with large, insurmountable obstacles. They are even more pronounced if it is necessary to find optimal control in the course of the system operation.

Hybrid computing systems greatly contribute to the elimination of such difficulties and the use of such computationally complex tools as the Pontryagin maximum principle.

The use of hybrid computing systems is also effective in solving nonlinear partial differential equations. In this case, it is possible to solve both problems of analysis, as well as problems of optimization and identification of objects. An example of an optimization problem is: selection of the nonlinearity of a heat-conducting material intended for a given temperature distribution; the distribution of the thickness of the evaporating layer, which protects spacecraft from excessive heating when entering the dense layers of the atmosphere; calculation of the geometry of aircraft to obtain the necessary aerodynamic characteristics; invention of an optimal heating system for aircraft to protect them from icing with a minimum use of energy for heating; calculation of the network of irrigation canals, determination of the optimal flow in them, etc. When solving these problems, the digital computer is combined with a grid model, which is repeatedly used in the solution process.

The development of hybrid computing systems is possible in two directions: the construction of specialized hybrid computing systems, which are designed to solve only one class of problems, and the construction of all-encompassing hybrid computing systems, which allow solving a fairly wide class of problems. The structure of such a universal hybrid complex consists of a single-action AVM, a grid model, an AVM with solution repetition, special equipment designed to solve problems of statistical modeling, communication devices between machines and peripheral equipment. In addition to the standard computer software included in the kit, in hybrid computing systems it is necessary to use special programs, which serve the communication system of machines and automate the process of setting and preparing tasks on the AVM, as well as a universal programming language for the set as a whole.

In parallel with new computing capabilities, specific features appear in hybrid computing systems, for example, errors arise that are absent in individual computers. The primary sources of errors can be the time delay of the analog-to-digital converter, digital-to-analog converter and digital computer; non-simultaneous feed error analog signals to analog-to-digital converter and non-simultaneous output digital signals to a digital-to-analog converter; rounding error in digital-to-analog and analog-to-digital converters; errors that are associated with the discrete nature of obtaining results from the digital computer output. When a digital computer operates independently with converters, the time delay does not give an error, and in hybrid computing systems it can not only give significant errors, but also disorganize the performance of the entire system.