66 results about "Nonlinear kinetics" patented technology

The invention discloses an attention mechanism and LSTM fused industrial bearing vibration time sequence signal fault prediction method and system. The method comprises the following steps: collecting a bearing vibration signal and carrying out filtering, noise reduction and normalization preprocessing; constructing a deep learning model combining the bidirectional BiLSTM and a coordinate attention mechanism to extract bidirectional time sequence features and enhance key fault features; carrying out model training by adopting a multi-target composite loss function and an Adam optimizer, and introducing an early stop mechanism to prevent overfitting; performing fault type identification and degree evaluation on the real-time vibration signal by using the trained model, and performing quantitative analysis by fusing multi-scale spectrum kurtosis features and nonlinear kinetic parameters; and finally, outputting a fault diagnosis report, and triggering multi-stage early warning based on an adaptive threshold. The method can realize high-precision and high-reliability bearing fault prediction and health state evaluation, and is suitable for intelligent operation and maintenance of industrial equipment.

The invention provides an intelligent anesthesia depth monitoring method and system. A plurality of physiological parameter sensors are used for synchronously collecting composite physiological signals of a patient, and meanwhile brain wave signals of the patient in the anesthesia process are obtained; analyzing and processing the anesthesia state by fusing an electroencephalogram spectrum analysis algorithm and a nonlinear kinetic model to obtain a consciousness state map of anesthesia depth and consciousness edge fluctuation; performing real-time evaluation on the current anesthesia depth by using an adaptive threshold algorithm in combination with a Bayesian reasoning framework, and performing prediction processing on the trend change of the anesthesia depth in a future short time by using a long-short term memory neural network to obtain an evaluation result and a prediction trend; the anesthetic infusion rate is automatically adjusted so as to maintain the ideal anesthesia depth, meanwhile, potential risks are subjected to intelligent grading early warning processing, and an anesthesia management strategy is generated. According to the technical scheme provided by the invention, the safety and personalized management level of the anesthesia process are improved.

The invention belongs to the technical field of diving state monitoring, and relates to a diver state monitoring method based on biofeedback, and the method comprises the steps: aligning a sign signal with environment data through a timestamp, extracting motion features through acceleration data, constructing a motion noise model, and removing signal artifacts in real time; in the aspect of EEG signal purification, a db4 wavelet basis is adopted for carrying out wavelet packet decomposition, water pressure related frequency band characteristics are extracted, low-frequency drift is removed, meanwhile, heart rate signals are analyzed through nonlinear dynamics, a Lyapunov index is extracted to evaluate HRV changes, breathing and EEG # imgabs0 # wave coupling are analyzed through wavelet transformation, and the risk evaluation precision is further enhanced; in the aspect of environment compensation, through compensation of a depth and SpO2 relational expression and water temperature on respiratory frequency, in combination with SLTM network extraction time sequence features and a deep causal convolutional layer, risk trend prediction is performed, a diver risk level and a prediction curve are output in real time, a comprehensive risk index is finally calculated, the health state and potential risk of the diver are comprehensively evaluated, and safety is improved.

The invention discloses a micro-cantilever geometric structure parameter inversion system, method and device, and belongs to the technical field of micro-electro-mechanical systems. According to the system, a dynamic model containing geometry, material and electromechanical coupling nonlinearity is constructed, a PINNs network fused with physical constraints is designed, a staged training optimization strategy is adopted, and efficient inversion of micro-cantilever geometric parameters is achieved. The core of the method is that a nonlinear kinetic equation is used as a constraint to be embedded into a neural network for training, experimental data and physical residual errors are combined to construct a composite loss function, and the problems that a traditional method neglects a nonlinear effect, depends on finite element simulation and is low in inversion precision are solved. The average relative error of inversion of the system is lower than 1%, which is obviously superior to that of a traditional method, and the method can be widely applied to MEMS device design, online detection and closed-loop control scenes.

The invention relates to the technical field of deep learning, in particular to a parameterized nonlinear system identification method based on a dynamic embedded GAN. The method comprises the following steps: forming a dynamic condition generative adversarial network by adopting a deep learning method and combining a dynamical generator and a discriminator, fusing system physical parameters and response data, realizing extrapolation of nonlinear system dynamic response of a parameterized system under variable parameters, and remarkably enhancing generalization ability; meanwhile, according to the method, under the condition that initial conditions and system parameters are given, long-time-period prediction of parameterized nonlinear system dynamic response is achieved, the dependency relation of response data on system physical parameters is recognized from the response data, and recognition and prediction of any nonlinear dynamic system are achieved.

The invention relates to the field of nonlinear system modeling, and particularly provides a global linear modeling method and system for a nonlinear system based on Lie derivative and sparse recognition, a terminal and a medium, and the method comprises the steps: obtaining an explicit nonlinear kinetic equation of a target system, calculating the Lie derivative of a state variable or an output variable of the system based on the kinetic equation, constructing a candidate observation function library directly associated with the physical mechanism of the system; performing screening and dimension reduction on the candidate observation function library by adopting a sparse recognition method to obtain a low-dimensional observation function set; and on the basis of the screened observation function and system operation data, a finite-dimensional global linear model of the target system in the dimension raising observation space is obtained through identification by using a data driving algorithm. According to the method, the online solving efficiency and the control real-time performance are improved, and efficient and reliable multi-target collaborative optimization control of systems such as a wind driven generator is realized.

The present invention relates to a data fusion processing method and system for an MEMS-based intelligent sensor, including the following steps: decomposing the multi-modal physiological parameter time series data stream to obtain a key vital sign feature sequence; calculating the phase coupling degree of the key vital sign feature sequence to obtain an organ-interfunction association strength matrix; performing high-dimensional feature space projection on the critically ill patient based on the organ-interfunction association strength matrix to obtain a patient pathological state feature map; performing non-linear dynamics analysis on the patient pathological state feature map to obtain a disease progression dynamic trajectory; and performing clinical decision support reasoning based on the disease progression dynamic trajectory to obtain personalized treatment recommendations, solving the technical problem that existing analysis methods are often limited to the observation of a single physiological parameter or simple statistical analysis and lack the ability to understand the disease mechanism from an overall perspective.

The invention discloses a consistency control method and system for second-order multi-agent iterative learning and a medium. The method comprises the steps that a second-order nonlinear CMANSs kinetic equation which is composed of N follower bodies and a leader body and has uncertainty disturbance is constructed; constructing a double-layer adaptive iterative learning control input model; controlling an input model based on the double-layer adaptive iterative learning so as to enable the tracking consistency error of the iterative learning of the second-order nonlinear CMANSs kinetic equation within a preset time range to be within a preset range; and on the basis of a Lyapunov function, the tracking consistency error of iterative learning in a preset time range is demonstrated in a preset range. Therefore, the method can control the input model through double-layer adaptive iterative learning, and ensures that the second-order nonlinear CMANSs can still realize robust tracking in an uncertain environment, thereby realizing tracking consistency of the second-order nonlinear CMANSs with uncertain disturbance in finite time.

According to the fault-tolerant control method for the actuator fault in the urban sewage treatment process, stable control over the dissolved oxygen concentration and the nitrate nitrogen concentration in the urban sewage treatment process under the influence of the actuator fault is achieved. Firstly, a nonlinear observer is designed to accurately estimate an actuator fault; secondly, constructing a radial basis function neural network to accurately characterize the time-varying nonlinear dynamic characteristics of the sewage treatment process; a fault-tolerant controller based on self-adaptive dynamic programming is designed, and the problem that the dissolved oxygen concentration and the nitrate nitrogen concentration deviate from set values due to actuator faults is solved jointly by constructing an evaluation network and an execution network, training a neural network by adopting a strategy iterative algorithm, solving an approximate optimal control law and fusing a prior classical controller. Experimental results show that the method can realize fault-tolerant control of the dissolved oxygen concentration and the nitrate nitrogen concentration, and ensures stable operation of the urban sewage treatment process.

The invention discloses an intelligent self-healing power grid metrological verification control method, system and device and a medium, and the method comprises the steps: carrying out the phase-space reconstruction based on the fused time sequence data, judging whether the time sequence has a nonlinear dynamic characteristic or not, and outputting a predicted value and a residual feature of a system state; performing anomaly identification on the operation state of the metering device by adopting an improved anomaly detection algorithm, and outputting an anomaly type, a confidence coefficient and a risk level; dynamically generating a verification task priority list and a resource scheduling scheme in combination with a historical verification record of the equipment and a current resource state; and a self-adaptive self-healing control mechanism is triggered, corresponding self-healing operation is executed, an optimized control strategy is fed back to all the links, and closed-loop self-recovery and continuous optimization of the system are achieved. The reliability, the self-adaptability and the intelligent level of the verification system are remarkably improved.

The present application relates to the technical field of nonlinear dynamics experimental equipment, in particular to a V-shaped spring oscillator programmable excitation device and method based on reference frame transformation. The device comprises a V-shaped spring structure, a driving module, a control module and a measurement module. The V-shaped spring structure comprises two springs, one end of each spring is connected to a movable suspension point, and the other end is connected to a mass. The driving module is used to drive the two movable suspension points to move synchronously. The control module is used to generate a control signal according to a target external force waveform to control the motion trajectory of the movable suspension points. The measurement module is used to collect the motion data of the mass. By transforming the reference frame to a non-inertial reference frame with the movable suspension point as the origin, the mass is subjected to an equivalent inertial force in the non-inertial reference frame, which is the programmable external force applied to the mass.

The application discloses a kind of fusion attention mechanism and the industrial bearing vibration time series signal fault prediction method and system of LSTM.This method includes: collecting bearing vibration signal and carrying out filtering, noise reduction and normalization preprocessing;BiLSTM and coordinate attention mechanism combined deep learning model is constructed to extract bidirectional time series features and enhance key fault features;Multi-objective composite loss function and Adam optimizer are used for model training, and early stopping mechanism is introduced to prevent overfitting;Real-time vibration signal is used to identify fault type and degree evaluation using the trained model, and multi-scale spectral kurtosis features and nonlinear dynamics parameters are used for quantitative analysis;Finally, output fault diagnosis report, and trigger multi-level early warning based on adaptive threshold value.The application can realize high-precision, high-reliability bearing fault prediction and health state evaluation, and is suitable for industrial equipment intelligent operation and maintenance.

The invention discloses a liquid level indication anti-leakage tray based on a weight sensor. The liquid level indication anti-leakage tray is characterized in that the weight sensor detects weight signals of chemicals in a liquid medicine barrel; the signal processing module converts signals detected by the weight sensor into liquid level height, the liquid level height is converted into liquid level percentage, the liquid pumping rate of a liquid medicine pump is calibrated online in real time through RLS, the reference pump speed is input into an EKF algorithm, the liquid level height is fused through the EKF algorithm, a nonlinear kinetic model is constructed to predict the liquid level track, and the liquid level return time is calculated. Calculating safety trigger time according to the liquid level return-to-zero time, designing a dynamic calculation interval function based on the remaining time, and adaptively adjusting the execution frequency of a prediction algorithm according to the liquid level height and the liquid level change rate; and the signal output module sends a shutdown control signal to the liquid medicine pump according to the time point of the safety triggering time. The liquid level monitoring function of converting the weight into the liquid level is achieved, and when the liquid level of liquid medicine is about to be zero, the liquid medicine pump is automatically stopped working.

The invention discloses a method for determining a pulse electrochemical machining non-linear dynamic characteristic parameter mapping relation, which comprises the following steps: acquiring a current density time sequence of a workpiece in a pulse electrochemical machining process and surface topography data of the workpiece after the pulse electrochemical machining is completed, performing non-linear dynamic analysis on the surface topography data, and determining a pulse electrochemical machining non-linear dynamic characteristic parameter mapping relation. Obtaining a first workpiece surface space heterogeneous recursive entropy; performing nonlinear kinetic analysis on the current density time sequence to obtain a first current density heterogeneous recursive entropy; and establishing a linear regression relationship according to the first current density heterogeneous recursive entropy and the first workpiece surface space heterogeneous recursive entropy, and obtaining a corresponding relationship between the current density and the workpiece surface microstructure. Based on this, a linear regression relationship is established between the current density and the surface topography data, the surface quality of the workpiece after machining under the current parameters can be predicted in real time only according to the current density signal, and off-line measurement does not need to be carried out after machining is completed.

The invention relates to the technical field of thermal data processing, and discloses a thermodynamic behavior analysis method and system for high-temperature synthesis of a kiln, and the method comprises the steps: collecting kiln operation data through a kiln sensor, building a nonlinear thermodynamic model, and describing the dynamic change of the thermodynamic behavior in the kiln; constructing a thermodynamic behavior map by using the kiln operation data, and predicting thermodynamic behaviors under different operation conditions; adjusting control parameters of a nonlinear kinetic model based on the thermodynamic behavior result; and performing joint iteration on the nonlinear thermodynamic model and the thermodynamic behavior map to realize optimization of kiln operation. The temperature control precision, the energy efficiency and the stability of the kiln are remarkably improved, the energy consumption is reduced, the quality of finished products is improved, and the limitation of a traditional method in the aspects of dynamic adjustment and real-time optimization is overcome.

The invention relates to the technical field of battery management, in particular to a novel self-adaptive control and synchronization method for nonlinear dynamic behaviors of a sodium-ion battery, which comprises the following steps: designing a controller by combining a self-adaptive inversion technology, and constructing a strategy by adopting a multi-step Lyapunov function; in order to ensure that a system state error and a parameter estimation error can be converged to zero within free intention time pre-specified by a user, a self-adaptive parameter adjustment rate is designed to ensure the continuity and the bounded property of a control signal, and in order to cope with parameter uncertainty caused by battery aging and environment change, a self-adaptive parameter adjustment rate is designed. The method further introduces a real-time monitoring and dynamic adjusting mechanism. According to the method, the control capability of a highly-uncertain and highly-nonlinear system is remarkably enhanced, the control flexibility is improved through setting of free intention time, the global stability is enhanced through multi-step inversion design, the control precision and robustness are remarkably improved, and the method can be widely applied to various scenes such as fixed energy storage and electric automobiles and is prominent in practical value.

The present invention discloses a nonlinear dynamic analysis method for a projectile charge partition structure. According to the characteristics of the projectile segmented charge, a typical projectile charge partition structure is extracted as a research object, and a mass-spring-damper system model reflecting the connection characteristics of the charge, shell, and partition is given; a two-degree-of-freedom system nonlinear dynamic theoretical analysis model considering gap and connection characteristics is established; the analysis model is subjected to time expansion and contraction transformation and dimensionless processing except for displacement, and is discretized using numerical integration to calculate the dynamic response under a given time-history load, and the nonlinear response law of the charge structure is analyzed from the perspective of structural dynamics; the normalized motion equation expressed in displacement variables obtained by dimensionless processing of mass, stiffness, load, etc. is convenient for comparing the influence of changes in each dimensionless parameter on the response of the structure, can better reflect the multi-body interaction effects caused by structural collisions, gaps, etc., and can be used to guide projectile structure design.

The utility model relates to a non-linear dynamic test bench, which comprises a non-linear dynamic test assembly, a surrounding frame and an experiment table, and is characterized in that a motor is started through the arranged experiment table, the output end of the motor drives a linkage rod to steer under rotation, a push-pull arm pushes a door plate, and the door plate swings and folds on the rear end face of a surrounding plate; the rear end face of the peripheral plate is in an opening state, personnel can directly enter the interior of the peripheral plate through the opened opening to overhaul algorithm hardware, after overhaul is completed, the convenient opening and closing structure is made to operate reversely, and after the door plate is closed, the heat dissipation body is started, and the front end of the heat dissipation body is made to rotate at a high speed; according to the utility model, hot gas generated in the peripheral plate can be accelerated and dissipated conveniently, gas cooling is realized, meanwhile, the plate body is provided with a plurality of through holes, the hot gas can be discharged outwards through the through holes conveniently, and thus the test bed is ensured to have excellent heat dissipation performance.

The invention discloses a beneficial disturbance perception-oriented pneumatic artificial muscle manipulator control method and system, and belongs to the technical field of pneumatic system control, and the method comprises the following steps: constructing a nonlinear kinetic model of a pneumatic artificial muscle manipulator system according to a three-element model of pneumatic artificial muscle and a kinetic equation of a manipulator, defining an angle error and an angular velocity error when the manipulator moves; a nonlinear controller based on beneficial disturbance perception is constructed by taking the control targets that the motion angle of the manipulator reaches an expected position and the tracking angle error converges to 0 and considering unknown dynamic state and external disturbance in the system; and according to the angle, obtained through actual measurement, of the manipulator during movement, the constructed nonlinear controller is used for determining the input air pressure of the pneumatic artificial muscle so as to drive the manipulator to move. Accurate and efficient angle tracking control of the manipulator under external disturbance can be achieved, and stable and efficient operation of the system is guaranteed.

The present invention provides a method for analyzing the stability of heterogeneous systems based on a simplified nonlinear dynamics model, comprising the following steps: establishing a simplified model topology based on the heterogeneous system and obtaining a phase angle difference, where the phase angle difference is the difference between the phase angle of a first node and the phase angle of a second node; obtaining a simplified nonlinear dynamics model based on the heterogeneous system and the phase angle difference based on the simplified model topology; solving the nonlinear dynamics model using an averaging method to obtain an analytical solution, where the analytical solution is an expression of the square of the system amplitude; differentiating the analytical solution with respect to time to obtain a third first-order derivative; obtaining a stability criterion when the third first-order derivative is zero; and determining the stability of the heterogeneous system based on the stability criterion. The method for analyzing the stability of heterogeneous systems based on a simplified nonlinear dynamics model provided by the present invention is simple and efficient, has a low model order, retains the nonlinear characteristics of the system, performs an analytical solution based on a generalized averaging method, proposes a system stability criterion, and facilitates stability analysis.

The application discloses a gear box fault diagnosis method and system based on scatter recurrence analysis, and belongs to the technical field of wind turbine fault diagnosis, and comprises the following steps: collecting vibration signals of a wind turbine gear box under different health states; utilizing scatter recurrence analysis to represent sensitive fault features in the gear box vibration signals from multiple dimensions; proportionally dividing the multi-dimensional features into a training set and a test set; inputting the training set to train an intelligent fault diagnosis model based on a support vector machine; and finally inputting the test set data into the trained SVM to obtain a gear box fault diagnosis result. The application combines nonlinear dynamics and machine learning to provide a diagnosis method and system capable of accurately identifying various faults of a wind turbine gear box, provides a reference for realizing efficient operation and maintenance of the wind turbine, and guarantees reliable and stable operation of the wind turbine.

The present invention discloses a method for evaluating children's object control ability based on nonlinear dynamics. First, the Kinect sensor is used to collect the spatial position information of the motion skeleton points of the tester's hand, elbow and shoulder, and the inertial sensor is used to collect the motion biomechanical signals of the tester's hand; then the time-frequency domain features and sample entropy features of human motion are extracted from the spatial position information of the skeleton points and the motion biomechanical signals; the principal component analysis method is used to fuse the time-frequency domain features and sample entropy features; finally, an RF-based evaluation model for children's object control ability is constructed to realize the classification of children's object control ability. The present invention solves the problems of identifying children's object control ability and low recognition accuracy caused by the inability to quantify the target in the prior art, and realizes the hierarchical evaluation of children's object control ability.

The invention discloses a mechanism and deep learning fused machine tool precision out-of-tolerance fault diagnosis method, and belongs to the technical field of precision numerical control machine tool health management. Comprising the following steps: S10, constructing a tool nose nonlinear dynamic model of a nonlinear stiffness item K (x) considering thermal deformation influence; s20, the inherent frequency, damping and Taylor empirical formula coefficients of the whole machine are obtained in combination with the hammering excitation test and the cutting test; s30, the displacement change of a tool nose is obtained; s40, constructing an out-of-tolerance recognition library; and S50, calculating a precision index of the X (t) obtained under different working conditions, comparing the precision index with a threshold value to generate a qualified / out-of-tolerance label, and carrying out fault prediction based on a 1D-CNN-BiLSTM fusion network training classification model. And finally verifying the precision out-of-tolerance problem of the machining process in combination with field experimental data. The method can solve the problems that the traditional diagnosis technology is difficult to capture in real time, the precision is out-of-tolerance, and generalization is insufficient due to separation of a physical model and a data driving method.

The invention discloses a nonlinear coupling control method and device for piezoelectric dispensing and a medium, and relates to the technical field of precise dispensing and motion control. The method comprises the following steps: acquiring structural parameters of the dispensing system, and establishing a nonlinear kinetic model of the dispensing system; performing parameter scanning and sensitivity index calculation on the structure parameters through a nonlinear kinetic model to obtain key parameters of which the response to the dispensing system is greater than a preset threshold value; constructing a multi-objective optimization function taking the maximum displacement, the maximum speed and the vibration amplitude of the firing pin as performance objectives; building a joint simulation platform, and importing the key parameters into the joint simulation platform to obtain real-time response energy of the firing pin; adjusting a weight coefficient of the multi-objective optimization function; and performing iterative simulation and iterative adjustment through an optimization algorithm to obtain an optimal parameter combination of the key parameters. According to the method, the platform is optimized by fusing nonlinear dynamic modeling and joint simulation, and the movement performance of the firing pin and the overall stability of the dispensing system are improved.

The invention belongs to the technical field of non-linear dynamic numerical calculation and rigid differential equation solution, and discloses a non-matrix rigid self-adaptive non-linear dynamic numerical calculation method and a non-matrix rigid self-adaptive non-linear dynamic numerical calculation system. According to the method, equivalent product calculation of the Jacobian matrix and the vector is realized based on the directional derivative through a matrix-free calculation framework, and a complete Jacobian matrix does not need to be stored; high-efficiency and high-precision estimation of the spectral radius is realized through quantum annealing driven Krofft power iteration; constructing an adaptive mixing precision calculation engine based on a spectral radius result to reduce memory occupation; and realizing stable solution of the extreme rigid system through rigid self-adaptive step length control. According to the method, the solution convergence rate and the calculation efficiency of the extreme rigid nonlinear system can be effectively improved, the memory occupation and the long-term integral error are greatly reduced, and the method can be widely applied to the fields of aerospace, mechanical engineering, intelligent equipment, chemical reaction kinetics and the like.

The application discloses an angular acceleration estimation method based on accelerometer correction, which comprises the following steps: S1, establishing a process model of an estimated signal, including a state equation and an observation equation; S2, performing first prediction based on a nonlinear dynamic model, obtaining a first k+1 prior state estimation matrix and a prior estimation error covariance matrix; S3, performing first correction, establishing an observation equation, calculating a Kalman gain K, and updating a posteriori estimation matrix and a posteriori estimation error covariance matrix P; S4, performing second prediction; S5, performing second correction; setting the posteriori estimation matrix after the first Kalman filtering as the initial value of the second correction process, performing second correction, and completing correction; and S6, returning to step S2 and performing iterative estimation. The application has the characteristics of further reducing time delay and more accurately and effectively estimating the angular acceleration under interference.

The invention discloses a multi-scale phase space correlation dimension analysis method for a jet reactor under a negative pressure condition, and systematic research is carried out on nonlinear dynamic characteristics of an internal flow field of a jet impinging reactor by introducing a phase space reconstruction and attractor analysis method, namely a correlation dimension method. According to the phase space reconstruction technology, time sequence data are reconstructed into a track in a high-dimensional phase space through a delay embedding method, so that internal dynamic behaviors of the system are revealed. The attractors serve as geometric structures in the phase space and reflect the long-term dynamic characteristics of the system, and the shapes and distribution of the attractors can provide important clues for understanding the complexity of the flow field. Chaotic behaviors, fractal features and geometric structures of attractors in a flow field can be recognized through phase-space reconstruction attractor analysis, and then theoretical support is provided for optimization of reactor design and operation conditions.

This application belongs to the technical field of diving state monitoring, and relates to a diver state monitoring method based on biofeedback. By aligning the physiological signs signal and environmental data through timestamps, and using acceleration data to extract motion features, a motion noise model is constructed to remove signal artifacts in real time; in terms of EEG signal purification, db4 wavelet basis is used for wavelet packet decomposition, features of water pressure-related frequency bands are extracted and low-frequency drift is removed. At the same time, the heart rate signal is analyzed by nonlinear dynamics, Lyapunov exponents are extracted to evaluate HRV changes, and wavelet transform is used to analyze the coupling between respiration and EEG #imgabs0# waves to further enhance the accuracy of risk assessment; in terms of environmental compensation, through the relationship between depth and SpO2 and the compensation of water temperature for respiratory rate, combined with the SLTM network to extract temporal features, and a deep causal convolution layer is used for risk trend prediction, the diver risk level and prediction curve are output in real time, and finally the comprehensive risk index is calculated to comprehensively evaluate the diver's health status and potential risks and improve safety.

The invention relates to a transient dynamic response calculation method and system for a high-dimensional complex nonlinear rotor system, and the method is characterized in that the method comprises the following steps: 1, obtaining a nonlinear dynamic equation of the rotor system, and carrying out the discretization of the nonlinear dynamic equation; 2, acquiring an algebraic equation which takes displacement response of a rotor system at a to-be-solved moment as a unique unknown quantity by utilizing two basic assumptions of a Newmak method, acquiring an accurate jacobian matrix J of the algebraic equation by utilizing an automatic differential function jacrev in PyTorch, and constructing a Newton-Raphson iterative format to perform iterative calculation; step 3, utilizing two basic assumptions of the Newmak method to further obtain the acceleration and the speed response of the rotor system at the moment to be solved; and step 4, repeating the step 2 to the step 3 to obtain the dynamic response of the rotor system at each moment until the set time is reached, and completing the calculation. According to the method, the problems of low efficiency and difficult solution of obtaining the transient dynamic response of the high-dimensional complex nonlinear rotor system at present are solved, the method can be widely applied to calculation of the transient dynamic response of the high-dimensional complex nonlinear rotor system, and the method has the characteristics of universality and modularization.

The application discloses a design method of an alternating current stimulation Hodgkin-Huxley cardiac Purkinje fiber model, and the dynamic characteristics of the model under different alternating current parameters and different initial conditions are observed through a phase plane orbit, a waveform, a bifurcation diagram and a Lyapunov exponent spectrum, and multiple coexisting membrane action potential modes are revealed, corresponding to the same or different periodic coexisting attractors in a phase diagram. The model experiences period, quasi-period and forward or reverse period-doubling bifurcation with the change of an amplitude A or a frequency f, and it is proved that the cardiac Purkinje fiber model with alternating current injection has complex nonlinear characteristics. By changing a current I m , a sodium ion equilibrium potential E Na and a potassium ion equilibrium potential E K , heartbeat frequency rules are observed, and state conversion of the cardiac Purkinje fiber between normal, abnormal and sudden cardiac arrest is found. The application provides a reference for exploring the evolution rules of nonlinear dynamics in the HH CPF model, protecting life and heart health.