A METHOD FOR EXAMINING AND ANALYSING THE ENTITY AND ENTITY PROPERTIES OF AN OBJECT

Abstract

The method refers to information- and interdisciplinary research and analysis techniques in disciplines that make extensive use of mathematical models and hardware-software-based object design tools. Comparative causal analysis methods and similarity properties of the object and its components were applied. The purpose of the method is the indirect, component-based determination of the entity's structure, behavior, and properties by examining the influence of each component on its presence in entity-like objects from various disciplines. The technical result of applying the method is the ability to arrive at a systematic judgment about the causes of object properties, the analysis and mathematical description of the composition of components, and the properties of the entity.The method is accompanied by an example from the component of harmonic oscillations for two objects.

Description

[0001] The invention relates to information methods for the study and design of objects in disciplines where mathematical and logical methods, models, software and hardware, databases, and computer-aided object design are widely used. The method refers to indirect methods, applies comparative essential cause-effect analysis, and similarity properties of objects and their entities.

[0002] The purpose of the proposed method is to indirectly determine the structure, behavior, and properties of entity components by responding to their embodiment and implementation into objects of the same entity in different disciplines.

[0003] Comparative essence-causal analysis is subject to both the properties of the objects and the analytical expressions that describe them.

[0004] All experimental methods for studying material objects and methods of cause-and-effect analysis can be considered analogues of the proposed method. However, they are all applicable to material objects, while the essence is an abstract object and can therefore only be studied indirectly. This became reliably possible only after the mathematical and functional properties of the similarity of objects that share a mathematical model of the entity became known. They were published in the method of complex entity construction, "Type of Object Construction" (DE 10 2021 784 A1 2022.10.13). The basic concepts of "object" and "entity"—regardless of the design method and programming language—and the connection between them from this method are also fundamental here.The application of the properties of essence similarity in cause-and-effect analysis has further modified the analysis into an essence and comparative analysis and a mathematical analysis. The proposed method is intended, among other things, to provide the necessary data for creating mathematical models of the essences of the designed objects and their components for the method of comprehensive entity design. Therefore, this method is selected as the closest prototype method.

[0005] Technical results that can be achieved with this method: - The possibility of investigation; analysis and analytical description of the behavior and properties of the components of the entity itself in different domains and different boundary conditions. - The ability to investigate the structural composition and interaction of the components of an entity. - Providing source material for the mathematical modeling of the individual components and the entire entity. - The possibility of applying the method to the study of abstract objects of a single entity, in particular a program. - The ability to examine the entity properties of objects in all subject areas. - The possibility of using the method of comparative causal analysis of entities for universal purposes.

[0006] Known methods and analogues could not achieve this: - Ignorance of the essential properties of the entity first described in the prototype method; - the lack of a general systematic approach to the study of the properties of entities ; - the lack of an essential approach to the study of the properties of objects; - the absence of a comparative cause-effect analysis based on the nature of the case; - limited basic concepts of the disciplines.

[0007] A common disadvantage of known similar methods for studying objects is their lack of reliability: they are not designed for the study and analysis of both abstract and material objects.

[0008] The proposed method involves examining an object with an unknown structural (component) composition, unknown properties, unknown behavior, and unknown interaction of the components in parts, for each of the components. However, since the entity and all its components are abstract objects that we do not perceive, this is done indirectly. In fact, it is not the property of the essential component itself that is available for research and cognition, but rather the effect of its presence in the object under study on the properties of that object. And this becomes possible and practically convincing through the discovery of the properties of an entity – using a prototypical method. There is no other proof that the conclusions about what we do not perceive are correct.

[0009] Experimental and analytical data on the essential properties of material objects are the actual "rock" from which the properties of the essence and its components are derived. This is done through the analysis of cause and effect and the important property of objects of the same entity – confirming their mathematical similarity to the consequence (the property itself) of comparable objects.

[0010] The analysis uses the combined principle of similarity and difference to determine the relationships between cause and effect.

[0011] If two or more events are similar only in one circumstance and one or more events differ only in the absence of that circumstance, then that circumstance is the cause of the event

[0012] There are two circumstances that might justify an investigation using the proposed method:. - The mathematical similarity (e.g. mechanics and electrical engineering), but belonging to the same domain of knowledge (e.g. vibrations). - Known cause and effect of a property in one of these objects and unknown in the other.

[0013] Before research and analysis, available data on the nature of the topic under study and the component to which the objects being compared belong are examined. Furthermore, a sketch of an adapted working version of the entity is created from its main components and the structure of the component under study. Priority is given to mathematical and semantic similarities over technical differences in the properties. The structural diagrams adapted based on the results of the studies of the various components should ultimately form the basis for the structure of the entity itself.

[0014] In research and comparative analysis, two additional theses of content similarity are used: - The Whose or component is the principal determining cause, and the essential properties of the objects are the consequence of the subject interpretations of that property by each of the objects. - The general essence or its component is the main thing for the mathematical similarity of objects from different disciplines, as well as for the types of similarity (geometric, physical, chemical) within the basic laws of their disciplines.

[0015] Comparative causal analysis of experimental and analytical data of properties is performed for objects of the same component entity. And let objects A and B from different disciplines with a similar common property be analyzed. In this case, object A has the cause (entity) of this property (consequence), and object B has the cause as the sought-after entity. Analysis is performed by comparing the concepts of these causes in the disciplines to which objects A and B belong. If the causal concept can be adapted to suit other objects with the same component property, then the causes and effects of comparable objects A and B are considered to be essentially similar. The essence of this component property is the general concept of reason object property.

[0016] The results of the analysis are then coordinated with experts in the field under investigation, and the formulation of the property concepts and their nature, as well as a working version of the component structure, are adjusted as needed. The final version of this structure should form the basis for a mathematical model of the component.

[0017] A new realm essential features of the proposed process are : - Evaluation and analysis of the properties of an entity through its individual components using material objects. - The investigation and analysis of the essential properties of objects in various disciplines and peripheral operations. - Using a modified application of similarity and comparison of a data set through the methodology of cause and effect analysis of the properties of objects and their analytical representations. - Use of universal concepts common to different disciplines for common essential properties of objects. - Use of the results of the work as raw material for structural and mathematical models of the components of the entity itself.

[0018] The new combination of these features makes the proposed method a systematic, universal and common method for different disciplines for the investigation and analysis of properties of abstract and material objects of common essence.

[0019] The feasibility and effectiveness of the method is confirmed by an example of its application.

[0020] The research area is "Free Harmonic Inference" within the field of "Oscillations." The two objects being studied, essentially compared and annotated, belong to different branches (and laws) of physics and are examined and described in great detail. Object A, in the general case, is a damped mechanical pendulum. We consider the oscillations of a vertically suspended weight on a spring due to its elasticity.

[0021] Object B is a series resonant circuit (RLC). The damped free oscillations of both objects are investigated: for object A, the oscillation deviation, and for object B, the voltage level. In contrast to the familiar investigations of the properties of objects, here we are also interested in the nature of processes and properties, as well as their possible similarities, the essential causes of the properties of objects.

[0022] First, based on the materials studied on the subject of study, a sketch of the structure of the subject (entity) "vibrations" and, in more detail, the section "harmonic vibrations" (component) will be created. We will also use the most general definition of the term "vibrations": A fluctuation is a deviation of one or more parameters of an object from an equilibrium or rest state.

[0023] The structural composition of the entity under investigation can be easily represented using the following data.

[0024] The type of oscillation is divided into 2 types: - linear (including harmonic); - others (non-linear, relaxation).

[0025] Linear oscillations are divided into , depending on their periodicity: - periodic, quasi-periodic, aperiodic, antiperiodic. Interaction with the environment: - free vibrations under the influence of internal forces or a single external action (for objects A and B); - forced vibrations under the influence of external forces or the phenomenon of resonance; - Other (parametric, natural vibrations). Parameters that characterize vibrations: - The deviation x(t) is the instantaneous value of the movement relative to the equilibrium value. - The amplitude X m is the maximum deflection. - The period T=1f is the duration of the total oscillation. - Frequency f=1T - Number of oscillations per unit of time. - Angular frequency ω=2πf=2πT. - Phase φ=ωt+φ0. - Initial phase φ0 is the phase value at t=0 (the beginning of the oscillation).

[0026] In the field of: Mechanics, electrical engineering, optics, biology, economics, quantum mechanics, chemistry, information and computer technology, mathematics, climatology, finance.

[0027] The “Harmonic Vibrations” component has the following properties: - all oscillations are deflections with variable velocity v(t), whose maximum values ​​are observed at the equilibrium point. - Oscillations are carried out by objects that are capable of undergoing mutual deflection when energy is supplied to them. - The damped oscillations occur with decreasing amplitude. - Harmonic oscillations can be represented as a projection of the deflections in a circular motion, which results in a sinusoidal pattern in the coordinates x - t in the diagram. - The instantaneous velocity v(t) of an oscillating object is always the vertical component of its velocity. - The instantaneous acceleration a(t) is always equal to the vertical component of the centripetal acceleration. The acceleration is always directed toward the equilibrium position, directly opposite to the displacement. - the instantaneous speed and acceleration are always directed in opposite directions: the speed is equal to the vertical component of the circular motion, and the acceleration is opposite to the displacement (and the speed) - to the position of the weight. - Harmonic oscillations are characterized by a linear force law: the mutual force of the reaction is directly proportional in magnitude and opposite in direction to the deflection.

[0028] The above-mentioned properties of harmonic oscillations apply not only to mechanics, but also to similar parameters of similar processes in other disciplines.

[0029] The example is accompanied by six figures, a table and a "Technical Justification" as an appendix to the application form. Fig. shows “spring pendulum” with a)initial state, b)compression, c)tension. Fig. shows “harmonically damped oscillations of a mechanical pendulum”. Fig. shows an “RLC circuit” in which electromagnetic oscillations occur when the key is switched from position 1 to position 2. Fig. shows “Harmonic damped current oscillations in the RLC circuit”. Fig. shows the "graphs of the oscillation states" for the duration of an oscillation period T in each of its four quadrants", where a) the oscillating states of the spring pendulum, b) the graphs of current i and voltage u R , and L , and C on the elements of the RLC circuit, c) the graphs of the states of the RLC circuit in the different quadrants of the period. Fig. shows the “Structure Components-Harmonic Oscillations” according to the results of research and analysis.

[0030] The table shows the materials of comparative analysis of the study of objects, their elements, process parameters and their mathematical properties.

[0031] The “Technical Justification” shows the physical and mathematical justification of the example.

[0032] Since the conclusions of research and analysis must do justice not only to the material objects studied but also to the abstract objects (especially programs), the most general terms must be used.

[0033] Harmonic oscillations are due to periodic deviations of one or more parameters of the object from the rest state.

[0034] The table below summarizes the results of a study of a mechanical spring pendulum (object A) and an RLC loop (object B) subjected to a single impact on each object. In the mechanical pendulum, the weight on the spring is briefly pulled and then released. And the RLC loop, which was previously connected to a DC voltage source, is disconnected from the source and shorted to itself.

[0035] A comparative analysis of the objects must answer the question “what” is the cause (essence) of the harmonic vibrations (effect) in object B, but also “why this something” (consequently which general subject property) is the cause.

[0036] The analysis of the table and diagrams in Fig. shows: 1.The parameters of the studied objects and processes are similar. The mathematical descriptions and analytical characteristics of the processes are also similar. 2. In a mechanical pendulum, free oscillations are initiated by a single external oscillation. Damped harmonic oscillations in the form of periodic stretching and compression of a pendulum spring occur due to the spring's elasticity as action-counteraction, accompanied by concomitant conversions of kinetic energy into potential energy and vice versa. Table Mechanical pendulum RLC circuit Object - Elements metal spring Reactive resistances L, C Weight of a load m Voltage source U Resistance from the external environment β Resistance R Process parameters Deflection of the pendulum x(t) Capacitor charge q(t) Speed ​​of the load v=ẋ=dx / dt Current in the circuit i(t)=dq / dt mass m Inductance L Elasticity coefficient k elasticity 1 / C Kinetic energy mv 2 / 2 Magnetic energy THAT 2 / 2 Potential energy mx 2 / 2 Electrical energy q 2 / 2C Physical and mathematical properties of processes Damping factor b21Km R2CW Damping frequency ω1 ω01−14(βmω0)2 ω01−14Q2 differential equation mẍ+βẋ+kx=0 Lq̈+Rq̇+q / C=0

[0037] Damping occurs through friction losses, losses in the external environment, and the use of additional damping devices.

[0038] 3- In an RLC circuit, free oscillations are also induced by a single action: the closing of the RLC circuit by the capacitance C charged from an external source. Here, too, due to the reactance properties of the elements L and C, harmonic damping oscillations of current and voltage occur across the circuit components. This process is accompanied by the generation of wave oscillations and oscillations of electrical and magnetic energy as the capacitance is recharged and the magnitude and direction of the magnetic flux in the inductance changes. This, along with the losses in the resistance R, results in losses in the circuit.

[0039] 4. From an electrical and physical point of view, the current and voltage fluctuations in an RLC circuit are explained by physical peculiarities in AC circuits, which are the same in each case: XL=ωL=2πfL, Xc=−1ωC=−12πf.

[0040] 5. Mathematically, the nature of the reactances L and C for alternating current is represented by positive and negative imaginary quantities for inductance and capacitance, respectively. This is the reason why the phase of the voltage across an ideal capacitor C (with infinite resistance) is ahead of the current in the circuit by π / 2 radians, and for an ideal inductance L (with zero resistance) is ahead of the current by π / 2 radians, so that their complex resistances are ZL=ωLejπ2=jωL=jXL, Zc=1ωCe−jπ2=−j1ωC=jXc, j=−1.

[0041] For a capacitive circuit element, the sinusoidal voltage u C the current l̇ by the angle π / 2, with an inductance the voltage u follows L the current by the angle π / 2 ( Fig. ,b). In an RLC circuit, the elements L and C alternately absorb energy during oscillation and return it to the circuit.

[0042] 6. The reactive properties of the RLC elements are the intrinsic properties of the elements L and C to resist external disturbances of the resting state.

[0043] The elastic resistance—the resistance of a mechanical pendulum spring—is essentially similar to the reactive resistances in the circuit, as it leads to a similar result in both pendulums. However, in different material objects, this similarity has its own characteristics: electromagnetic or mechanical.

[0044] Therefore, the reactance properties L and C can be referred to as "electromagnetic elastic resistances" in the elasticity categories. For capacitance, C is the "lagging resistance," while for inductance, L is the "leading elastic resistance."

[0045] 7. If this is true, then the cause of harmonics in an RLC circuit on an alternating basis is the elasticity of the reactances L and C.

[0046] 8. The fact that the RLC circuit is used as a more convenient experimental tool than a physical model for modeling and investigating the processes in a spring pendulum can confirm the possibility of such a conclusion. In this simulation, the change in elasticity is simulated, and the active resistance values ​​simulate the damping.

[0047] 9. As a general intrinsic property of objects, elastic resistance can also be referred to as “elastic resistance”.

[0048] The elastic counteraction is an internal property (reaction) of objects to an external disturbance, which is opposite to the disturbance in order to bring the object back to a state of rest.

[0049] Action and reaction lead to a process of periodic dominance of the energies that generate them, resulting in periodic harmonic processes, deviation of object parameters, fluctuations of springs and environment.

[0050] 10. The common property of harmonic oscillations of material objects under the influence of elastic counteraction is the periodic transformations and oscillations of subject energies (potential - kinetic, electric - magnetic), and the difference is the absence of the generation of waves and fields in mechanical oscillations.

[0051] The invention has the following advantages over the known methods: 1. It provides an indirect means of examining and analyzing objects with a degree of certainty due to the essential properties of similarity transcribed in the prototypical method. 2. The prototype method and the proposed method together form a technical tool for the comprehensive essential synthesis (design and embodiment) and analysis (proposed method) of material, mixed and software objects. 3. A modified causal methodology of comparative analysis of objects using the properties of essential similarity is proposed to analyze the properties of objects and their analytical data. 4. The research and analysis data form the basis for creating mathematical models of entities, their components and other data for entity databases required for entity design of objects. 5. The invention is not only an information technology, but also a general technical method of indirect investigation and analysis of entities.

[0052] The method does not require new research tools and equipment; it is sufficient to use what is available in the specialist disciplines. QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited patent literature

[0000] DE 10 2021 784 A1

[0004]

Claims

[] A method for investigating and analyzing the entity and entity properties of an object uses both disciplines methods for investigating objects, determining their properties, mathematical and analytical description, characterizing similarities in different disciplines as well as common properties of essential mathematical and functional similarities, to methods of cause-effect analysis, which differs in that the entity is investigated component-wise, the effects of each property determine a component indirectly - according to its behavior, its properties and mathematical descriptions in different objects, - additionally uses two theses of essential similarity which state that the entity or its component is the most important determining cause,and essential properties of objects are the consequences of the subjective interpretations of this property by each of the objects, and that the general essence or its component is the main thing for the mathematical similarity of objects both from different subject areas and in the types of similarity themselves - geometric, physical, chemical - within the validity of the basic laws of their disciplines. In addition, before the analysis, based on the available information, a sketch of the working, corrected version of the structure of an entity from its main components and the structure of the component under study are created, preferring these mathematical and semantic similarities over object differences. They conduct a comparative causal analysis of objects A and B from different disciplines common property (consequence) of a component,of which one - object A - a known concept of the cause can be adapted so that it is common for other objects of the component with this property, then causes and effects in comparable objects A and B are considered to be essentially similar, and the general concept of cause of the property is the essence of this property of the component, after which the results of the analysis are agreed with the experts of the disciplines studied, adjusted if necessary, as well as the working version of the component structure, the final version of which should be the basis for creating the mathematical model.

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