Method for realizing dichotomy consistency of second-order nonlinear multi-agent system

Abstract

The invention discloses a bipartite consistency implementation method for a second-order nonlinear multi-agent system, and relates to the technical field of dynamic testing, comprising the following steps: S1, constructing a second-order nonlinear multi-agent test model; s2, constructing dichotomy coupling strength, and embedding the dichotomy coupling strength into a kinetic equation; s3, analyzing the evolution trajectory to obtain a bipartite consistency error index; s4, obtaining a dynamic sensitivity factor; s5, obtaining an realizability boundary index, and judging whether the bipartite consistency of the multi-agent system is in a structure reachable region or not; and S6, designing a bipartite consistency stable interval, and giving a test judgment conclusion. According to the invention, the non-intrusive test of the bipartite consistency capability of the tested object is realized; by constructing a bipartite consistency error index, a dynamic sensitivity factor and an realizability boundary index, the method disclosed by the invention can reveal the real mode separation capability and dynamic characteristic difference of the structure on the premise of not changing the running state of a measured object and not applying any control signal.

Description

Technical Field

[0001] This invention relates to the field of dynamic testing technology, specifically to a method for achieving binary consensus in a second-order nonlinear multi-agent system. Background Technology

[0002] Consistency behavior analysis of multi-agent systems is an important method in modern dynamics testing, structural state identification, and complex network performance evaluation. Bipartite consensus, as a method capable of characterizing the cooperative properties of symmetric modes under symbolic partitioning, has attracted attention in various fields such as structural dynamics testing, cooperative vibration analysis, and electrical equipment response mode identification. Traditional consensus analysis is mainly based on first-order linear models, performing simple weighted calculations on the differences between system nodes. Its computational structure relies too heavily on linear assumptions, making it difficult to effectively characterize phenomena commonly found in real structures, such as nonlinear damping, nonlinear stiffness, modal coupling, and response nonuniformity. When the system exhibits significant nonlinear characteristics, traditional first-order consensus models often fail to characterize the dynamic offset trends between nodes, making it difficult to accurately identify the bipartite structure.

[0003] Furthermore, most existing technologies directly use fixed coupling strength for consistency judgment, lacking an adaptive coupling mapping mechanism that matches the actual excitation state of the tested object. This makes the test sensitivity significantly unrobustible to changes in operating conditions. More importantly, existing consistency research is mostly used in the fields of control or network collaboration. Its methods rely on control input or real-time adjustment, and cannot evaluate the feasibility of binary consistency by building a virtual model based solely on test data when the equipment is running normally without applying control disturbances. Therefore, it is difficult to meet the needs of non-intrusive testing and state assessment in practical engineering. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for achieving binary consensus in second-order nonlinear multi-agent systems, thereby solving the problems mentioned in the background section.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] In a first aspect, the present invention provides a method for achieving binary consensus in a second-order nonlinear multi-agent system, comprising the following steps:

[0007] S1. Construct a second-order nonlinear multi-agent test model based on the tested object to obtain the incentive equilibrium index;

[0008] S2. Based on the excitation equilibrium index, construct the binary coupling strength and embed it into the second-order nonlinear multi-agent dynamic equation;

[0009] S3. Analyze the evolution trajectory of the agent's state to obtain the binary consistency error index;

[0010] S4. Based on the binary coupling strength and binary consistency error index, the dynamic sensitivity factor is obtained;

[0011] S5. Based on the dynamic sensitivity factor, obtain the realizability boundary index and determine whether the binary consistency of the multi-agent system is in the structurally reachable region.

[0012] S6. Based on the realizability boundary index, design a binary consistency stable interval and give the test judgment conclusion.

[0013] To further optimize this technical solution, in step S1, response measurement points are arranged at key locations in the object under test. Each measurement point is abstracted as an intelligent agent node in this method, and finally the whole constitutes a multi-agent system with N nodes formed by the object under test.

[0014] The second-order nonlinear multi-agent test model obtains the excitation equilibrium index by integrating and averaging the responses of each node in the multi-agent system within the observation window.

[0015] To further optimize this technical solution, the second-order nonlinear multi-agent test model is as follows:

[0016]

[0017] in,

[0018] The number of nodes in a multi-agent system is equal to the number of response measurement points deployed.

[0019] It is a dimensionless time variable, obtained by dividing the actual time by the reference time constant;

[0020] The selected observation window length is dimensionless.

[0021] For the i-th measurement point in time variable Dynamic response under the following conditions Corresponding to the i-th measurement point;

[0022] The incentive equilibrium index represents the time-space average of the response amplitude of each node within the observation window.

[0023] This model condenses dynamic information, which was originally scattered across different sensors and physical locations, into an excitation equilibrium index. This parameter directly reflects the overall response level of the tested object under the current operating conditions.

[0024] To further optimize this technical solution, in step S2, the constructed binary coupling strength is the core scalar parameter of the binary consensus protocol, which is used to make the binary consensus process adapt to the current excitation level of the tested object.

[0025] The nonlinear mapping model of the bipartite coupling strength is shown below:

[0026]

[0027] in,

[0028] It is a scalar for the binary coupling strength, used to adjust the binary interaction strength between nodes in a multi-agent system;

[0029] and These are design coefficients, adjusted through offline simulation or pre-experimentation. Controlling the coupling strength in the linear response region, Controlling the nonlinear enhancement effect in the high excitation region.

[0030] To further optimize this technical solution, the scalar of the binary coupling strength... Embedded into the second-order nonlinear multi-agent dynamics equations, corresponding to each measurement point i, the equations are as follows:

[0031]

[0032] in,

[0033] The dimensionless displacement state of the i-th intelligent agent system is obtained through numerical integration;

[0034] The dimensionless displacement state of the j-th intelligent agent system is obtained through numerical integration;

[0035] , Each is a time variable The first and second derivatives;

[0036] , These are the nonlinear damping and stiffness coefficients, both taken as positive values, used to enhance finite-time convergence characteristics;

[0037] The elements of the adjacency matrix represent the topological connection relationship between the i-th and j-th intelligent agent system nodes in the test scenario;

[0038] The partition symbols for the nodes to which the i-th and j-th intelligent agents belong are given in advance based on the structural symmetry, mode shape, or engineering experience of the tested object, and are used to construct the bipartite consistency target;

[0039] The equation is solved numerically in a multi-agent space to observe whether the system can converge to a state that satisfies the binary consistency constraint in a finite time.

[0040] To further optimize this technical solution, in step S3, the binary consistency error index is used to evaluate whether the system achieves binary consistency within a finite time under a given excitation level and coupling strength.

[0041] The calculation model for the binary consistency error index is as follows:

[0042]

[0043] in,

[0044] This is the consistency error index for binary search;

[0045] To evaluate window length, and Take the same values ​​to cover the convergence process of the intelligent agent system;

[0046] For the time variable The sign-weighted average state.

[0047] Through observation The size and its different stimulus levels The changing trend is used to determine whether the tested object has the ability to achieve binary consistency within a limited time under the current topology and partition configuration.

[0048] To further optimize this technical solution, the dynamic sensitivity factor in step S4 is calculated as follows:

[0049]

[0050] in,

[0051] This is the dynamic sensitivity factor;

[0052] It is a small constant used to avoid the case where the denominator is zero;

[0053] Based on dynamic sensitivity factor The test system identifies whether the identification error is due to insufficient coupling or structural characteristics.

[0054] To further optimize this technical solution, in step S5, the dynamic sensitivity factor is used as the output to construct a nonlinear boundary model and obtain an achievability boundary index. The closer the value is to 1, the easier it is to achieve binary consistency; the closer it is to 0, the more difficult it is.

[0055] To further optimize this technical solution, in step S6, an interval model is constructed, and the realizability boundary index is used as the output of the model to obtain the bipartite consistent stable interval. , representing the stable range of binary search consistency performance under the current incentive level.

[0056] To further optimize this technical solution, the binary consistency error index obtained in step S3... Mapped to the binary consistent stable interval In the process, the following judgments are made:

[0057] like Then it is believed that "under the current incentive and structure, the multi-agent system corresponding to the tested object can achieve binary consistency";

[0058] like This indicates that "the binary consistency achievement capability of the tested object under the current structure or excitation condition is insufficient".

[0059] In a second aspect, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, wherein the computer program instructions, when executed by the processor, implement the steps of a binary consensus implementation method for a second-order nonlinear multi-agent system as described in the first aspect of the present invention.

[0060] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program instructions are executed by a processor, they implement the steps of a binary consensus implementation method for a second-order nonlinear multi-agent system as described in the first aspect of the present invention.

[0061] Compared with existing technologies, this invention provides a method for achieving binary consensus in second-order nonlinear multi-agent systems, which has the following beneficial effects:

[0062] This method for achieving binary consistency in a second-order nonlinear multi-agent system maps the actual test response to an excitation equilibrium index, constructs the binary coupling strength from this index, and further establishes a second-order nonlinear multi-agent dynamic equation operating only in a virtual space. This enables non-invasive testing of the binary consistency capability of the tested object. By constructing a binary consistency error index, a dynamic sensitivity factor, and a realizability boundary index, this method can reveal the true pattern separation capability and dynamic characteristic differences of the structure without changing the operating state of the tested object or applying any control signals. Compared with traditional linear consistency models and fixed coupling testing methods, this method can more accurately reflect the nonlinear dynamic behavior of complex structures, has higher sensitivity and robustness, and can automatically provide the stability interval for consistency achievement under different excitation conditions, thus significantly improving the applicability and engineering practical value of the test. Attached Figure Description

[0063] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 This is a flowchart illustrating the binary consensus implementation method for a second-order nonlinear multi-agent system proposed in this invention. Detailed Implementation

[0065] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0066] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0067] Secondly, the term "an embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places throughout this specification does not necessarily refer to the same embodiment, nor is it a single embodiment or an embodiment selectively excluded from other embodiments.

[0068] Example 1:

[0069] Reference Figure 1This is the first embodiment of the present invention, which provides a method for achieving binary consensus in a second-order nonlinear multi-agent system, including the following steps:

[0070] S1. Construct a second-order nonlinear multi-agent test model based on the tested object to obtain the incentive equilibrium index.

[0071] For the mechanical structure, power device or other dynamic system under test, response measurement points are arranged at key locations in the object under test. Each measurement point is abstracted as an intelligent agent node in this method, and the whole system is finally formed into a multi-agent system with N nodes.

[0072] The second-order nonlinear multi-agent test model obtains the excitation equilibrium index by integrating and averaging the responses of each node in the multi-agent system within the observation window, thereby quantifying the overall excitation level and its distribution among nodes.

[0073] The second-order nonlinear multi-agent test model is shown below:

[0074]

[0075] in,

[0076] The number of nodes in a multi-agent system is equal to the number of response test points deployed, which is directly determined through test plan design.

[0077] It is a dimensionless time variable, obtained by dividing the actual time by the reference time constant;

[0078] The selected observation window length is dimensionless, for example, corresponding to several vibration cycles in a real experiment, and is a fixed value is used in the design.

[0079] For the i-th measurement point in time variable Dynamic response under the following conditions The corresponding measurement point i is obtained by sampling the acceleration, displacement or strain signals of the measured object and then normalizing them.

[0080] The incentive equilibrium index represents the time-space average of the response amplitude of each node within the observation window.

[0081] This model condenses dynamic information, which was originally scattered across different sensors and physical locations, into an excitation equilibrium index. This parameter directly reflects the overall response level of the tested object under the current operating conditions.

[0082] S2. Based on the excitation equilibrium index, a binary coupling strength is constructed and embedded in the second-order nonlinear multi-agent dynamic equation to establish a virtual multi-agent evolution process for testing and verification.

[0083] The constructed binary coupling strength is the core scalar parameter of the binary consensus protocol, which is used to make the binary consensus process adapt to the current excitation level of the object under test: when the response of the object under test is weak, the binary coupling strength is appropriately reduced to avoid amplifying measurement noise; when the response is strong, the coupling strength is appropriately increased so as to more obviously expose the dynamic characteristics of the structure under binary consensus within a finite time.

[0084] The nonlinear mapping model of the bipartite coupling strength is shown below:

[0085]

[0086] in,

[0087] It is a scalar for the binary coupling strength, used to adjust the binary interaction strength between nodes in a multi-agent system;

[0088] and These are design coefficients, adjusted through offline simulation or pre-experimentation. Controlling the coupling strength in the linear response region, To control the nonlinear enhancement effect in the high excitation region, a set of basic values ​​can be pre-selected according to the type of the object under test (such as bridges, rotors, converter valve structures, etc.), and then fine-tuned through a small number of calibration tests to ensure that the binary consistency convergence time and test sensitivity meet engineering requirements.

[0089] The scalar of the bipartite coupling strength Embedded into the second-order nonlinear multi-agent dynamics equations, it is used to construct a virtual evolutionary process solely for testing and evaluation, without directly acting on the measured object itself. Specifically, for each measurement point i, the equation is as follows:

[0090]

[0091] in,

[0092] Let be the dimensionless displacement state of the i-th intelligent agent system, obtained through numerical integration.

[0093] Let be the dimensionless displacement state of the j-th intelligent agent system, obtained through numerical integration.

[0094] , Each is a time variable The first and second derivatives.

[0095] , These are the nonlinear damping and stiffness coefficients, both taken as positive values, used to enhance finite-time convergence characteristics. This coefficient is obtained through prior experiments or fitting historical data to the response decay characteristics of the tested object. A positive value is taken to ensure the numerical stability of the virtual system, and the range is between 0.05 and 0.5. A larger value indicates a faster velocity decay in the virtual system, used to simulate the response characteristics of highly damped structures. This coefficient is obtained by fitting the amplitude dependence characteristics of the response of the tested object, for example, by extracting the nonlinear trend through statistical curves under multiple different excitation intensities. This coefficient must be positive to enhance finite-time convergence, and is typically between 0.1 and 1.0, used to simulate the nonlinear behavior of the softening or hardening effect of the structure in the virtual system.

[0096] The elements of the adjacency matrix represent the topological connection relationship between the i-th and j-th intelligent agent system nodes in the test scenario. They are automatically generated by reading the sensor layout diagram, the actual geometric connection relationship of the structure under test, or the preset region division.

[0097] The node partition symbols for the i-th and j-th intelligent agent systems are pre-defined based on the structural symmetry, mode shapes, or engineering experience of the tested object, and are used to construct the bipartite consistency target. The node partitions are obtained by judging the positive and negative distribution of mode shapes, structural symmetry, or engineering expert experience. Their values ​​are fixed at +1 or -1, and are used to construct the bipartite consistency target partitions in the virtual model.

[0098] The equation is solved numerically in a multi-agent space to observe whether the system can converge to a state that satisfies the bipartite consistency constraint in a finite time, thereby testing and evaluating the dynamic separability and robustness of the tested object under this stimulus level.

[0099] S3. Analyze the evolution trajectory of the agent's state to obtain the binary consistency error index.

[0100] The binary consistency error index is used to evaluate whether the system can achieve binary consistency in a finite time under a given excitation level and coupling strength, thereby completing the test of the test object's ability to achieve binary consistency under this working condition;

[0101] The calculation model for the binary consistency error index is as follows:

[0102]

[0103] in,

[0104] This is the consistency error index for binary search;

[0105] To evaluate window length, and Take the same or slightly larger value to cover the convergence process of the intelligent agent system;

[0106] For the time variable The sign-weighted average state under the following conditions, that is, during the numerical integration process, for each time step... Calculate all nodes via symbols The weighted average value naturally characterizes the target structure of binary consistency.

[0107] Through observation The size and its different stimulus levels The changing trend is used to determine whether the tested object, under the current topology and partition configuration, has the ability to achieve binary consistency within a finite time. For example, when In the given When the value is less than a preset threshold, it can be determined that the binary search consistency has been "successfully achieved" under the current operating condition; when... If the value is consistently greater than the threshold, it indicates that adjustment is needed. and Or reconfigure Topology, etc.

[0108] S4. Based on the binary coupling strength and binary consistency error index, a dynamic sensitivity factor is obtained to reveal the trend of error sensitivity with the coupling strength.

[0109] The dynamic sensitivity factor is calculated as follows:

[0110]

[0111] in,

[0112] This is the dynamic sensitivity factor;

[0113] It is a small constant used to avoid the case where the denominator is zero;

[0114] Traditional multi-agent consensus tests typically only assess the magnitude of the error, while this step... For coupling strength Normalization is performed to obtain the dynamic sensitivity factor. This allows the testing system to identify whether the error is due to insufficient coupling or structural characteristics. In smaller A rapid decrease indicates that the system is sensitive to coupling strength; if even Increase If the value is still high, it indicates that the structure itself has a binary consistency difficulty that cannot be overcome by coupling strength.

[0115] S5. Based on the dynamic sensitivity factor, obtain the realizability boundary index and determine whether the binary consistency of the multi-agent system is in the structurally reachable region.

[0116] The dynamic sensitivity factor is used as the output to construct a nonlinear boundary model and obtain an actuality boundary index. The closer the value is to 1, the easier it is to achieve binary consistency, and the closer it is to 0, the more difficult it is.

[0117] The nonlinear boundary model is shown below:

[0118]

[0119] This is a feasibility boundary indicator.

[0120] when When the error is small (low sensitivity to error), A rapid approach to 1 indicates high feasibility; when When the coupling strength is large (the system is not very sensitive to coupling strength), The rapid approach to 0 indicates that the system is unlikely to achieve binary consistency under the current structure and excitation conditions.

[0121] S6. Based on the realizability boundary index, design a binary consistency stable interval and give the test judgment conclusion.

[0122] Construct an interval model, using the realizability boundary index as the model output, to obtain the bipartite consistent stable interval. , representing the stable range of binary search consistency performance under the current incentive level.

[0123] The interval model is shown below:

[0124]

[0125] The dimensionless stability margin is typically taken between 0.05 and 0.15, obtained through historical samples or engineering experience.

[0126] The bipartite consistency error index obtained in step S3 Mapped to the binary consistent stable interval In the process, the following judgments are made:

[0127] like Then it is believed that "under the current incentive and structure, the multi-agent system corresponding to the tested object can achieve binary consistency";

[0128] like This indicates that "the binary consistency achievement capability of the tested object under the current structure or excitation condition is insufficient".

[0129] Example 2:

[0130] The binary consensus implementation method for the second-order nonlinear multi-agent system described in Example 1 was tested in practice.

[0131] In actual testing, multiple measuring points are first set up at key locations on the structure or equipment under test. Dynamic responses at each point are continuously obtained using sensors such as accelerometers, displacement sensors, or strain sensors. To facilitate subsequent quantitative analysis of consistency capabilities, the raw curves collected from different measuring points need to be processed uniformly to form a response sequence. Testers will select a reference time based on the typical operating cycle of the equipment or external stimuli, and normalize all response data to this time. The response at each measurement point is then normalized using a selected reference amplitude to obtain the dynamic response. After normalization, the testing system automatically performs a time-space average of the responses at all measurement points within a set observation window to obtain the excitation equilibrium index. During engineering use, technicians will... The magnitude of the load can be used to determine whether the object under test is under light, medium or heavy load excitation.

[0132] In obtaining the incentive equilibrium index After that, with Automatically calculate the bipartite coupling strength based on the input. Throughout the entire testing process, technicians did not need to manually set the coupling parameters; instead, they allowed... It automatically adjusts to changes in actual excitation. For example, when the structure under test is under strong excitation, This will increase accordingly, making the dynamic response of the virtual multi-agent system more sensitive; however, under conditions of weak excitation or high noise, It will automatically reduce this to avoid over-amplifying subtle differences. Subsequently, the system will base its decisions on this... A set of second-order nonlinear multi-agent dynamic equations is constructed, and an adjacency matrix and node symbols are generated based on the sensor arrangement topology of the measured structure. This indicates the binary grouping method of the virtual test objects. During the numerical solution process, the virtual intelligent agent... As it evolves over time, its operation process completely simulates "what dynamic behavior would occur if binary consistency were attempted under the current operating conditions".

[0133] After the multi-agent system completes the evolution calculation of the second-order nonlinear dynamics, the test system will automatically read the virtual displacement states of all nodes. And according to the pre-set binary grouping symbols Calculate its sign-weighted average. Then, by summing and averaging the deviations between the trajectory of each node and the average value, the bipartite consistency error index under the current working condition can be obtained. Engineering technicians see a line in the user interface that automatically updates according to changes in the stimulus. The curve can be quickly used to determine whether the structure under the current excitation state is more inclined to a first-order resonant response, a local mode-dominated response, or a non-uniform response distribution caused by potential damage.

[0134] In obtaining indicators Afterwards, the testing platform will automatically calculate the dynamic sensitivity factor. In the actual test interface, technicians can observe... The real-time trend of changes is used to determine the sensitivity of the tested structure to the bipartite consistency condition. If Follow If the increase significantly decreases, it indicates that the structure's dynamic response has high adjustability; if If the level remains high over a long period, it indicates that the structure itself has significant coupling insensitivity. For example, the dynamic differences between sensor placement areas may be due to material nonlinearity, loose local connections, damage, or other structural defects.

[0135] Realizability Boundary Indicators The changing trend clearly reflects the separability of the system: when When the value is close to 1, it indicates that under the current incentive and structural configuration, the virtual multi-agent system can almost easily achieve binary consensus; when... When the level drops to a lower level, it indicates that there are factors hindering the formation of bipartite consistency in the structure's dynamic characteristics, such as uneven distribution of response energy in different regions, insufficient topological connectivity, or abnormal local dynamic characteristics. Actual users observe this through the software interface. With incentive With coupling strength The dynamic relationship of these changes is used to evaluate the overall performance of the test object. For example, in a certain test... A sudden drop under high excitation may indicate that there is damage propagation in the structure or a decrease in the stiffness of local connections.

[0136] Binary consensus stable interval The upper and lower bounds will be presented graphically for technicians to determine the error indicators. Does it fall within the stable range? If fall into This indicates that the tested object exhibits good binary consistency under the current stimulus level; if If the result exceeds this range, it indicates that the corresponding virtual consistency model of the system is unlikely to converge stably, revealing that the tested object may have abnormal response patterns or structural differences. The final test conclusion will be based on... and The relationships are automatically generated, which can be used by engineers for health diagnosis, structural condition assessment or operational reliability determination.

[0137] Example 3:

[0138] This embodiment also provides a computer device applicable to a binary consensus implementation method for a second-order nonlinear multi-agent system, including a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the binary consensus implementation method for a second-order nonlinear multi-agent system as proposed in the above embodiment.

[0139] This embodiment also provides a storage medium on which a computer program is stored. When the program is executed by a processor, it implements a binary consensus implementation method for a second-order nonlinear multi-agent system as proposed in the above embodiment.

[0140] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0141] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0142] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0143] More specific examples (a non-exhaustive list) of computer-readable media include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which programs can be printed, because programs can be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0144] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0145] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for achieving second-order nonlinear multi-agent system bipartite consensus, characterized in that, The method comprises the following steps: S1, constructing a second-order nonlinear multi-agent test model based on a measured object to obtain an excitation balance index; S2, constructing a two-part coupling strength based on the excitation balance index and embedding the two-part coupling strength in a second-order nonlinear multi-agent dynamic equation; S3, analyzing the evolution trajectory of the state of the agent to obtain a two-part consistency error index; S4, obtaining a dynamic sensitivity factor based on the two-part coupling strength and the two-part consistency error index; S5, obtaining an realizability boundary index based on the dynamic sensitivity factor to determine whether the two-part consistency of the multi-agent system is in a structural reachable region; S6, designing a two-part consistency stable interval based on the realizability boundary index and giving a test determination conclusion.

2. The method of claim 1, wherein, In the step S1, response measurement points are arranged at key positions in the measured object, each measurement point is abstracted as an agent node in the method, and finally the whole forms a multi-agent system of the measured object with N nodes; The second-order nonlinear multi-agent test model obtains the excitation balance index by integrating and averaging the responses of the nodes of the multi-agent system in the observation window.

3. The method of claim 2, wherein The second-order nonlinear multi-agent test model is as follows: ； wherein, is the number of nodes of the multi-agent system, equal to the number of response measurement points arranged; is a dimensionless time variable, obtained by dividing the real time by a reference time constant; for the selected observation window length, is dimensionless; the dynamic response of the i-th measurement point at the time variable corresponding to the i-th measurement point;​ To motivate the equalization index, the time-space average of the response amplitude of each node within the observation window is denoted; The model condenses the dynamic information originally scattered in different sensors and physical locations into the excitation balance index which directly reflects the overall response level of the measured object under the current working condition.

4. The method of claim 1, wherein In the step S2, the two-part coupling strength is a core scalar parameter of the two-part consistency protocol and is used to adaptively make the two-part consistency implementation process meet the current excitation level of the measured object; The nonlinear mapping model of the two-part coupling strength is as follows: ； wherein, is a scalar for the strength of the bipartite coupling, used to adjust the strength of the bipartite interaction between nodes in the multi-agent system; and are design coefficients, adjusted by off-line simulation or pre-test, control the coupling strength of the linear response region, control the nonlinear enhancement effect of the high excitation region.

5. The method of claim 4, wherein, the scalar of the two-part coupling strength Embedded into the second-order nonlinear multi-agent dynamics equation, corresponding to each measurement point i, the equation is as follows: ； wherein, The dimensionless displacement state of the i-th agent system is obtained by numerical integration; The dimensionless displacement state for the jth agent system is obtained by numerical integration; , respectively the first and second derivative of the time variable t; , are nonlinear damping and stiffness coefficients, both of which are positive and used to enhance the finite-time convergence property; is an adjacency matrix element representing the topological connection relationship between the ith and jth agent system nodes under the test scenario; Let Pij denote the partition symbol of the ith and jth agent system, which is pre-defined by the structural symmetry of the measured object, the modal shape or engineering experience, and is used to construct the bipartite consistency objective; The equation is numerically solved in the multi-agent space to observe whether the system can converge to a state satisfying the two-part consistency constraint within a limited time.

6. The method of claim 1, wherein In the step S3, the two-part consistency error index is used to evaluate whether the system can realize the two-part consistency within a limited time under a given excitation level and coupling strength; The calculation model of the two-part consistency error index is as follows: ； wherein, is the two-part concordance error metric; To evaluate the window length, the same is taken to cover the convergence process of the agent system; The same is taken to cover the convergence process of the agent system; is the sign weighted average state of the time variable under the sign function. By observing the size of the gap and its trend of change at different levels of excitation it is determined whether the object under test has the ability to achieve a bisection consistency within a limited time under the current topology and partition configuration.

7. The method of claim 1, wherein In the step S4, the dynamic sensitivity factor is calculated in the following manner: ； wherein, is the dynamic sensitivity factor; is a small constant used to avoid division by zero; Dynamic sensitivity factor based The test system identifies whether the error is due to insufficient coupling or due to structural characteristics.

8. The method of claim 1, wherein, In the step S5, the dynamic sensitivity factor is taken as an output to construct a nonlinear boundary model and obtain the realizability boundary index, and the closer the value of the realizability boundary index to 1, the easier the two-part consistency is to be realized, and the closer the value of the realizability boundary index to 0, the more difficult the two-part consistency is to be realized.

9. The method of claim 1, wherein In the step S6, the interval model is constructed, the realizability boundary index is taken as the output of the model, and a two-part consistent stable interval is obtained , which represents the stable range of two-part consistent performance under the current incentive level.

10. The method of claim 9, wherein, the dichotomy consistency error index obtained in the step S3 mapping to the dichotomy consistency stable interval In this case, the following determination is made: If then it is considered that "the multi-agent system corresponding to the measured object can achieve two-part consistency under the current incentive and structure"; If then it indicates that the "measured object is currently not capable of achieving the one-half dichotomy consistency under the current structure or excitation conditions".

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