38 results about "Systems theory" patented technology

The invention discloses an optical performance-oriented key geometric error identification method for a large aspheric element multi-axis numerical control machine tool. According to the method, a tool setting point is used as a key node to establish a surface shape error model, geometric errors and surface shape errors of a machine tool are accurately associated, multi-error coupling analysis is simplified, and targeted compensation, online monitoring and real-time correction are achieved. On the basis, a machine tool space error model is constructed in combination with a multi-body system theory, a mapping relation between a surface shape error and wavefront aberration is established by utilizing a ray tracing theory, the wavefront aberration is fitted through a Zernike polynomial, and the contribution degree of each geometric error to the aberration is quantified by means of principal component analysis, so that a key geometric error is identified and compensation is implemented. According to the method, the machining error and the final optical performance are directly associated, and the machining precision and the performance quality of the large aspheric element can be improved. The method is suitable for the manufacturing field of large complex optical elements machined by a multi-axis numerical control machine tool.

The invention discloses a predetermined time expansion state observer generation method and an observation error convergence method, which are applied to the technical field of aerospace, and comprise the following steps: constructing a controller for a second-order nonlinear system according to an all-drive system theory; converting the second-order nonlinear system according to the controller to obtain an all-drive system based on the main controller; wherein the main controller is a controller for controlling the all-wheel-drive system; designing a predetermined time expansion state observer based on the total disturbance and observation error of the all-wheel-drive system; wherein the predetermined time expansion state observer is an observer which limits the upper bound of convergence time of the observer based on a predetermined time parameter. Compared with most existing extended state observers which can only ensure asymptotic convergence and finite time or fixed time convergence, the observer generated based on the predetermined time extended state observer generation method can ensure that the observation error converges within the predetermined time, so that the converged predetermined time is more stable; and the user experience is improved.

The invention provides a smoke analysis AI system based on a quantum field theory tensor network, the algorithm is provided with a multi-camera fusion module, a quantum state coding module, a dynamic Hamiltonian construction module, a tensor network evolution module and a chaos detection module, and by monitoring a smoke diffusion Lyapunov index in real time, the sudden change from smoke to fire behavior is warned in advance; according to the algorithm, a quantum multi-body system theory and computer vision are combined, smoke diffusion is modeled into a phase change process of a quantum spin chain, high-dimensional quantum state information is compressed by using a tensor network, and a mutation behavior of a chaotic edge is detected in combination with a Lyapunov exponent. The method solves the problem of early fire hazard false alarm under the complex operation condition of the transformer substation in a traditional method, improves the initiative and accuracy of monitoring and prevention of the extremely early smoke fire hazard of the transformer substation, provides more reliable guarantee for the safe operation of the transformer substation, and has wide application prospects and important practical significance.

The embodiment of the invention discloses a GBIC-based multi-electric aircraft starting power generation system DBN model lightweight method, and relates to the technical field of reliability design and modeling of an equipment complex system.The GBIC-based multi-electric aircraft starting power generation system DBN model lightweight method comprises the steps that a DBN model of a starting power generation system is established, nodes in the DBN model correspond to key components and working states of the starting power generation system, and the nodes in the DBN model correspond to the key components and the working states of the starting power generation system; directed edges in the DBN model are used for describing the mutual relation between the nodes, a redundant structure in the DBN model is recognized, lightweight processing is carried out, and the fault state of the starting power generation system is recognized through the DBN model subjected to the lightweight processing. Aiming at the problems of complex reasoning calculation and low efficiency in the use process of the dynamic Bayesian analysis method of the equipment complex polymorphic system, the grey system theory and the Bayesian information criterion are introduced, the lightweight of the dynamic Bayesian network of the complex polymorphic system is realized, the redundant structure is eliminated, and the accuracy of the result is ensured.

The invention provides an urban carbon emission optimization model algorithm aiming at the urgent demand of green and low-carbon transformation of an urban industrial structure. According to the algorithm, a multi-agent model comprising a public management mechanism agent and an enterprise agent is constructed based on a complex adaptive system theory. The core lies in that an evolution path of urban carbon emission and industrial upgrading is dynamically deduced by simulating an adjacent learning effect between enterprises and a regulation and control mechanism of a public management mechanism based on a pre-decision. The enterprise agent decides the output value speed increase and the carbon emission intensity change rate according to the self state, the surrounding enterprise state and the public management mechanism predetermined target; and the government agent formulates and adjusts industry and emission reduction policies according to the overall goal of the city and enterprise pre-decision. According to the invention, through dynamic coupling of the microscopic enterprise decision and the macroscopic city system, low-cost and high-efficiency simulation and optimization of the city carbon emission path under different target scenes are realized, and a scientific quantitative analysis tool is provided for city carbon emission.

The invention relates to a method for determining a theoretical deflection angle of a single umbrella in a group umbrella system, which comprises the following steps of: calculating and analyzing the theoretical deflection angle of the axis of the single umbrella relative to the central line of a group umbrella bundle in the group umbrella system consisting of circumferentially and uniformly distributed and adjacently tangent single umbrellas according to a primary design principle of maximizing the resistance performance and the stability performance of the group umbrella system; the method can quantitatively reflect the influence of the number of umbrellas in the group umbrella system and the related design parameters of the single umbrellas on the theoretical deflection angle of the single umbrellas and the comprehensive performance of the system, and can preliminarily lay foundation for formation and gradual improvement of the theoretical design method of the group umbrella system.

The invention discloses a stay cable analysis digital twinborn model construction method, which comprises the following steps of: constructing a stay cable space three-dimensional vibration motion partial differential equation based on a material linear elasticity hypothesis and a double-coordinate system theory, and setting boundary conditions and initial conditions of the stay cable space three-dimensional vibration motion partial differential equation; a Galerkin multi-mode truncation method is adopted to obtain a displacement function of superposition of an end displacement excitation item and a vibration mode item; deducing a three-way strong coupling ordinary differential equation set through symbolic operation, and solving by using a step-variable Runge-Kutta algorithm to obtain a stay cable analysis digital twin model with stable parameters; structural response data are obtained through the sensor network and calculated, and when the obtained cable force, flexural rigidity and damping ratio exceed threshold values, a model updating mechanism is triggered for updating; and then the updated stay cable analysis digital twin model is obtained. According to the method, the real dynamic characteristics of the stay cable can be restored with high precision, and effective support is provided for structural state evaluation and early warning.

The invention discloses an equivalent calculation method for quantitative evaluation of the residual life of an existing pavement and a storage medium, and the method comprises the steps: firstly, determining a bearing threshold value of a lossless pavement structure based on a dual-modulus elastic layered system theory; secondly, a reduction coefficient of typical diseases to the structural strength is quantified through finite element simulation; thirdly, establishing a mathematical relationship model of the maximum effective stress and the fatigue life; then, actual disease information is accurately obtained by combining nondestructive testing technologies such as ground penetrating radar and three-dimensional laser scanning; then, correcting the maximum allowable equivalent stress in a lossless state according to the disease data; and finally, fusing the theoretical model and the traffic load history, and calculating the remaining service life. According to the method, three-dimensional and quantitative analysis on the influence of the diseases is realized through a mechanical response equivalence principle, the accuracy, objectivity and engineering application efficiency of residual life evaluation are remarkably improved, and a reliable basis is provided for scientifically making a road maintenance decision.

The application provides a kind of invariant set control and guaranteed cost control method and system of multiple equilibrium point switching generalized system, belongs to the field of hybrid system control. In order to solve the problem that traditional switching generalized system is difficult to directly apply to different equilibrium points of actual engineering application, and the traditional guaranteed cost control method is invalid due to the switching characteristics of multiple equilibrium points. The application considers the more general case of multiple equilibrium points, and studies the invariant set control strategy method of multiple equilibrium point switching generalized system, so as to realize more accurate control of the behavior of complex switching system. On the other hand, for the guaranteed cost control problem in practical application, the application designs a multiple equilibrium point switching generalized guaranteed cost controller to ensure that the cost of the system can have an upper bound. This innovation provides strong technical support for the practical application of switching generalized system theory.

The invention provides a gantry dual-drive control method and system based on an all-drive system theory, and relates to the technical field of control, and the method comprises the steps: obtaining system state data, reference input data and control performance index data of an all-drive system model; based on the control performance index data, determining control parameters by solving a Silverster matrix equation; and executing control operation based on the control parameters, the all-wheel-drive system model, the system state data and the reference input data to obtain target control data for controlling a target system so as to improve the control performance and the motion precision of the control system under various uncertainties and disturbance effects.

The invention provides a power system load frequency control method based on a high-order all-drive system theory, and relates to the technical field of power system load frequency control. Comprising the following steps: collecting physical parameters of a power system, and establishing a power system state space equation mathematical model according to the physical parameters of the power system; verifying the controllability of the power system according to the state-space equation model, and obtaining a system controllability matrix; based on the controllability matrix, converting a state-space equation model of the power system into a high-order all-drive system model; providing a power system state observer and a spoofing attack observer according to the high-order all-drive system model; and providing a power system load frequency controller based on a high-order all-drive system theory according to the high-order all-drive system model and the observer. According to the method, the linear dynamic model of the electric power system more conforming to actual working conditions is constructed. Based on the high-order all-drive method, the design complexity of the power system controller can be reduced, and the stability of the power system is ensured.

The invention relates to the field of zero-carbon energy, and discloses a zero-carbon integrated energy system and an optimization method of the zero-carbon integrated energy system.The optimization method of the zero-carbon integrated energy system comprises the steps that a historical dependency relationship is accurately captured by constructing a multi-scale prediction model fusing fractional calculus and a grey system theory; decomposing the system into multi-scale optimization sub-problems by adopting wavelet transform, and establishing a collaborative optimization objective function system; performing global optimization solution by using a fractional gradient descent algorithm to ensure stable operation of the system; and a complete closed-loop management system is formed through an efficiency verification system and a parameter adaptive correction mechanism. According to the invention, autonomous optimization and continuous improvement of the system are realized, and the operation efficiency and stability of the zero-carbon comprehensive energy system are improved.

The invention, which belongs to the technical field of image processing and artificial intelligence, discloses a multi-level image intelligent damage assessment and prediction system for highway infrastructures, comprising a multi-scale feature level extraction module, a damage type intelligent identification module, a time sequence damage evolution prediction module and an adaptive maintenance decision module. Multi-scale geometric invariance features are extracted through topological manifold learning, robust damage identification is realized based on a Lie group transformation theory, a damage evolution prediction model is established by using a power system theory, a maintenance decision is optimized by using a game theory framework, and a closed-loop adaptive optimization system is formed. According to the invention, comprehensive assessment, accurate prediction and intelligent decision-making of damage are realized, and the intelligent level and preventive maintenance capability of health monitoring of highway infrastructures are significantly improved.

The present application relates to the field of desulfurization control, and discloses a desulfurization intelligent control system based on a machine learning algorithm, comprising a collection module, an analysis module, a prediction module and a decision module, wherein a multi-physical field parameter in a desulfurization tower is collected through multi-sensor fusion to generate a multi-physical field state tensor; the dynamics behavior of an intelligent feature extraction analysis system is utilized to generate a characteristic parameter tensor; a state space model is constructed based on a dynamic system theory to generate a multi-target intelligent prediction result. The present application establishes a closed-loop control system from holographic perception to intelligent decision-making, solves the problems of perception limitations and single targets existing in traditional desulfurization systems, and improves desulfurization efficiency and reduces energy consumption.

The invention relates to the technical field of deformation monitoring, in particular to a space-time self-learning early warning system for foundation settlement risks in the highway construction process, and the system comprises an information processing module, a weight construction module, a tensor analysis module, a risk calculation module and an early warning release module. According to the method, the distribution density is evaluated through the spatial position vector and the Gaussian kernel function, the coverage weight is generated, local deviation caused by uneven network distribution is eliminated, balanced expression of regional settlement characteristics is ensured, a lagging interval is deduced through the soil consolidation theory, and deformation direction consistency screening is executed. Environmental noise is eliminated to lock effective cumulative settlement caused by a specific process, a prediction model with self-adaptive capability is constructed in combination with a grey system theory, the dynamic growth rate of a settlement cumulative value is tracked in real time, conversion from static management and control to dynamic trend early warning is realized, the sensitivity of foundation instability precursor capture is improved, and the stability of a foundation is improved. And a scientific basis is provided for construction procedure adjustment.

The invention provides a false data injection attack method for a multi-elastic-joint robot system, and belongs to the technical field of multi-agent network attacks based on computer data processing. Firstly, a multi-elastic joint robot nonlinear dynamic mathematical model is constructed and converted into a high-order all-drive quasi-linear multi-robot system dynamic model based on an all-drive system theory; and then designing a distributed consistency controller containing a linearization item and a neighbor error related item, establishing closed-loop global dynamics and deducing a state analytical solution in combination with equivalent conversion of the model. Designing a false data injection attack strategy, and constructing an attacked system dynamic model; a closed-loop terminal state error in the presence or absence of attacks is taken as a target function, an attack optimization problem is converted into a combinatorial optimization problem, a greedy algorithm is designed by applying a sub-module optimization theory, and a suboptimal solution in polynomial time is obtained and is taken as an optimal scheme of false data injection attacks of the system. According to the method, the applicability of the complex nonlinear multi-agent system is improved, and the calculation complexity is reduced.

This invention discloses a multi-level image-based intelligent damage assessment and prediction system for highway infrastructure, belonging to the fields of image processing and artificial intelligence technology. The system includes a multi-scale feature extraction module, a damage type intelligent identification module, a temporal damage evolution prediction module, and an adaptive maintenance decision module. It extracts multi-scale geometrically invariant features through topological manifold learning, achieves robust damage identification based on Lie group transformation theory, establishes a damage evolution prediction model using dynamical system theory, optimizes maintenance decisions using a game theory framework, and forms a closed-loop adaptive optimization system. This invention achieves comprehensive damage assessment, accurate prediction, and intelligent decision-making, significantly improving the intelligent level of highway infrastructure health monitoring and preventive maintenance capabilities.

This invention discloses a fault-tolerant game-theoretic control method for quadrotor helicopter swarm formations. It designs a quadrotor helicopter swarm formation mode, constructs an information interaction topology graph of the helicopter swarm, and establishes fault models for the rotating and translational subsystems. An adaptive fault diagnosis observer is designed to estimate actuator faults. Using the translational subsystem as the leader and the rotating subsystem as the follower, an inner and outer loop fault-tolerant game framework based on an incentive-based Steinberg differential graph game is constructed. Through full-drive system theory, fault-tolerant game controllers for the rotating and translational subsystems are designed separately, and a linear closed-loop system of the quadrotor helicopters is constructed. Performance indices for the rotating and translational subsystems are designed, and an optimal fault-tolerant game-theoretic control strategy is designed based on differential game theory. This invention enables stable formation control of quadrotor helicopter swarms, effectively improves the fault tolerance of helicopter swarms, and enhances the stability and intelligence of the helicopter swarm system.

The invention discloses a process modeling and fault detection method and system for machine learning guided by a control theory, and the method comprises the steps: obtaining historical operation data of an industrial process, and extracting an operation dynamic state in the historical operation data through a neural network, approximation is carried out on an observer gain part of the kernel representation model to realize complete kernel representation model design; building an adjoint system of the nuclear representation model by using a Hamilton system theory, and performing guided optimization on the learning and training process of the nuclear representation model and the adjoint system thereof by using nondestructive constraint to realize the design of a regularized nuclear representation model; and a detection statistic is constructed by using the residual error of the kernel representation model and the regularization kernel representation model, and the maximum value of the detection statistic during normal operation of the industrial process is set as a fault detection threshold, so that fault detection of the industrial process is realized, and the safety of the industrial process is guaranteed. In addition, by designing an online fine tuning strategy, generalization and applicability of the model are improved, and the method has high practical value.

The application discloses a kind of four-rotor hanging transport control methods based on double time-varying interference estimator, comprising the following steps: S1, the dynamics model of four-rotor unmanned aerial vehicle and hanging load is established;S2, the model is simplified using feedback linearization technique, and the nonlinear coupling system is decoupled into two subsystems of anti-swing and trajectory tracking;S3, according to the swing model of the goods being hung, time-varying uncertainty and interference estimator are constructed in the anti-swing controller, and time-varying interference is dynamically aggregated to eliminate the swing of heavy object;S4, according to the kinematics model of four-rotor, time-varying uncertainty and interference estimator are constructed in the trajectory tracking controller, to realize the accurate trajectory tracking of four-rotor unmanned aerial vehicle;S5, the stability of estimation error system is proved using linear time-varying system theory, and the interference estimation performance is optimized by adjusting auxiliary parameter;S6, the stability of anti-swing subsystem and trajectory tracking subsystem is proved, and the interference estimation performance is optimized by adjusting auxiliary parameter.

This invention discloses a method for determining the optimal control input trajectory in a multi-layered complex network. For a cyber-physical system characterized as a multi-layered complex network model, under the condition of minimizing control energy, a method for calculating the control input trajectory by inputting control signals into the shallow layer to control layers that cannot be directly accessed is proposed. First, for a cyber-physical system, it is modeled as a mathematical model of a multi-layered complex network. Based on this, a linear system theory framework is applied. Given the initial state, final state, control time, and sampling duration of the system, the control input trajectory is calculated under the constraint of minimizing control energy. In the calculation of the control trajectory, there is no need to calculate the complex coupling relationships between the eigenvalues ​​of the system's adjacency matrix. In the system, when the condition that there is a connection between any two layers is met, the surface layer can be controlled to achieve a given target state in inaccessible deeper layers.

The present application relates to the technical field of deformation monitoring, in particular to a time-space self-learning early warning system for foundation settlement risk in highway construction process, which comprises an information processing module, a weight construction module, a tensor analysis module, a risk calculation module and an early warning release module. In the present application, the spatial position vector and the Gaussian kernel function are used to evaluate the distribution density and generate the coverage weight, which eliminates the local deviation caused by uneven distribution and ensures the balanced expression of regional settlement characteristics. The lag interval is deduced by using the soil consolidation theory and the deformation direction consistency is screened, the environmental noise is eliminated to lock the effective cumulative settlement caused by specific process, the prediction model with self-adaptive ability is constructed by combining the grey system theory, the dynamic growth rate of the settlement cumulative value is tracked in real time, the change from static control to dynamic trend warning is realized, and the sensitivity of capturing the precursor of foundation instability is improved, which provides a scientific basis for construction process adjustment.

The invention discloses an inertial navigation system error observability quantitative analysis method and system. According to the method, aiming at the problem of observability analysis of error parameters of the composite optical fiber inertial navigation system in a dynamic environment, a complete error model is established, and a time-varying system is converted into a piecewise linear steady system by adopting a piecewise steady system theory; and constructing a segmented observability matrix and calculating an observability quantitative index of each error parameter through singular value decomposition. According to the method, the observability degree of each error parameter in a high-dimensional state can be accurately evaluated, a scientific basis is provided for calibration track optimization and filter parameter configuration, and the calibration efficiency and precision of the inertial navigation system are remarkably improved. Experimental results show that under the seven-position uniform acceleration scheme, the condition number of the observability matrix of the system is reduced from 105 magnitude to 103 magnitude, the calibration time is shortened by 75%, the precision is improved by 30%, and reliable technical support is provided for long-endurance high-precision navigation of the inertial navigation system in a satellite denial environment.

The invention discloses a large-aperture space telescope fixed time sliding mode anti-interference control method and related equipment. The method comprises the following steps: establishing a double-inertia system dynamic model containing motor end and load end dynamic parameters and total disturbance; constructing a fixed time expansion state observer based on the model, and estimating the total disturbance of the motor end; converting the model into a generalized all-wheel-drive system model through an all-wheel-drive system theory, designing an expected closed-loop system model, and identifying the expected closed-loop system model by using a neural network to obtain a preset performance function; a motor end angle position tracking error is obtained, and a speed ring reference speed instruction is generated after preset performance function constraint transformation; defining an angular velocity tracking error based on the instruction, constructing a fixed time terminal integral sliding mode control surface and designing a sliding mode reaching law; and finally, synthesizing a motor control law and applying the motor control law to a driving motor to complete anti-interference control. The problems that a traditional preset performance function is single in form, an observer cannot converge at fixed time, and a traditional control mode is difficult to suppress vibration, high in cost and limited are solved.

The application discloses a kind of system theory process analysis quantification method and system of aviation power system, belong to the field of civil aviation safety analysis, unsafe control behavior of influencing aviation power system is as final leaf node, cause scene is as intermediate leaf node, cause factor information is as root node, establishes aviation power system bayesian network model;Expert scoring is carried out to the occurrence probability of root node unsafe problem;Weight distribution is carried out to each expert score result, and the weight of the weight of each comparison data column after correction of modified reference data column is obtained, and then the modified expert scoring result is obtained;The root node of the modified expert scoring result is fused, and the occurrence probability of the fused root node is obtained and substituted into aviation power system bayesian network model, to obtain the posterior probability of each final leaf node, and then the system theory process analysis quantification result is obtained.The method can reduce the subjective influence of researchers on data processing process.

The application provides a kind of coastal zone ecological resilience intelligent evaluation and zoned optimization method, it is related to geographic information technology field, including: based on social-ecological system theory, from ecological resistance, ecological resilience and ecological stability three dimensions, the index system of coastal zone ecological resilience evaluation is constructed, the pre-processing and standardization of the obtained multi-source data are carried out;Based on the index system and the data after standardization, the ecological resilience index of each evaluation unit in the research area is calculated by using comprehensive weighting and approximation ideal solution sorting method, and the spatial distribution pattern of ecological resilience is analyzed;With the ecological resilience index as the target variable, the social, economic and environmental factors as the characteristic variables, a machine learning regression model is constructed, and the non-linear influence and interaction of each characteristic variable on the ecological resilience index are analyzed using the interpretable artificial intelligence framework to identify the key driving factors and thresholds;Based on the analysis results, the zoned ecological resilience optimization control strategy is developed.

The application discloses a remote fault diagnosis method for an aircraft system based on a hybrid observer and belongs to the technical field of fault diagnosis.The application fully considers the sparse available measurement values caused by a transmission network, makes up for the shortage of an existing estimation method designed based on continuous measurement values, fully utilizes a new generation of information technology, and effectively improves the reliability of an information physical system operation of an aircraft; the information physical system framework is introduced into the field of remote fault diagnosis of the aircraft system, a remote fault diagnosis scheme is established through system modeling, simulation verification and hybrid system theory, and the development of the health management technology of the aircraft system is promoted to a certain extent.

The application discloses a meta-universe-based management simulation system and method for dealing with chemical industrial park explosion, and belongs to the technical field of chemical emergency management. The system solves the problems of existing exercise system script rigidity and weak cooperation. The system comprises a virtual real-time monitoring and prevention module and a virtual interactive exercise disposal module. The former builds a digital twin model of the chemical industrial park through AR real scene scanning, and fuses accident cause analysis and dynamic Bayesian network of system theory to perform real-time probability reasoning, interpretable attribution and early warning on the explosion risk coupled with multiple factors. The latter adopts an event-driven deduction engine to decompose the exercise process into an atomic event directed probability graph, to drive real-time adaptive deduction of non-fixed scripts by user decision, and to realize decision timeliness monitoring, conflict detection and resolution through meta-decision agents. The application realizes real-time dynamic assessment and interpretable early warning of the explosion risk of the chemical industrial park, supports immersive collaborative exercise with thousands of faces, and significantly improves the pertinence, authenticity and fluency of emergency training.

The application discloses a large-aperture space telescope flexible load vibration suppression method and device based on preset performance control, comprising: establishing a three-inertia system dynamics model for describing a large-aperture space telescope; converting the three-inertia system dynamics model into a three-inertia system state space equation; converting the three-inertia system state space equation into a three-inertia generalized full drive system model by using a full drive system theory; improving the amplitude margin and the phase angle margin of the three-inertia generalized full drive system model by using a pole placement method; fitting the response output of the three-inertia generalized full drive system model with improved amplitude margin and phase angle margin by using a BP neural network, and designing a preset performance function of the three-inertia system; using the preset performance function as a tracking error boundary of the three-inertia system, and using a proportional differential as a nonlinear controller of the preset performance control, to realize closed-loop control of the three-inertia system, and then indirectly realize flexible load vibration suppression of the large-aperture space telescope.

The application discloses a city green land homogenization evaluation method and system based on plant landscape culture coupling, relates to the field of city planning and landscape ecology evaluation, constructs a multi-gradient observation field, selects representative cities with climate differences, and sets standard quadrats along a "central urban area-suburb-natural area" gradient in each city to collect plant community data; a plant diversity evaluation model is constructed, and the application overcomes the limitations of the prior art which only focuses on single-dimensional plant diversity analysis or pure subjective landscape aesthetic evaluation. Through the construction of a "plant-landscape-culture" three-dimensional coupling evaluation model, the quantitative correlation of ecological indexes, visual landscape patterns and regional culture perception factors is realized for the first time, and the internal driving mechanism of city green land homogenization can be revealed in depth from the perspective of system theory.