CN115563545B - Neuron discharge abnormality detection system based on definite learning - Google Patents
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Abstract
The invention discloses a neuron discharge abnormality detection system based on definite learning, which relates to the technical field of neuron discharge abnormality detection, and comprises: the acquisition module is used for acquiring unknown dynamics information of a system to be identified of the nonlinear system; the identification model construction module is used for constructing a system identification model of the nonlinear system; the identification module is used for locally approaching the unknown dynamics information of the system to be identified through the system identification model so as to obtain the unknown dynamics information of the identified system; the training learning module is used for constructing a dynamic training mode and a dynamic training mode database according to the unknown dynamics information of the identified system; the construction module is used for constructing a dynamic similarity measurement model of the dynamic mode to be identified and the dynamic training mode; and the dynamic residual error constructing module is used for constructing a dynamic residual error estimator according to the dynamic pattern recognition system and the dynamic similarity measurement model. The invention has the advantage of accurately detecting abnormal discharge of the neuron.
Description
Technical Field
The invention relates to the technical field of neuron discharge abnormality detection, in particular to a neuron discharge abnormality detection system based on definite learning.
Background
Neuroscience is an emerging discipline integrating multiple disciplines, biology being the basis of neuroscience research. The development and research of neurobiology provide scientific principles and possible ways for human beings to overcome various nerve and mental diseases, create conditions for developing and utilizing human intelligence, and simultaneously promote the development of artificial neural networks, artificial intelligence science and information industry. In the nervous system, neurons are the smallest nonlinear units forming the nervous system, are the basis of physiological activities of human bodies, and have rich discharge characteristics. For various change information of the environment inside and outside the organism, the neuron encodes, transmits and decodes the information in different discharge modes (whether the action potential exists, frequency, peak value and the like). Different external stimuli cause different discharge modes of nerve fibers, and the physiological effects of organisms are different.
The Hindmarsh-Rose (HR) neuron model is a mathematical representation of the firing activity of neurons. When internal parameters or external excitation is changed, the membrane potential of the neuron presents a resting-dispensing-resting discharge mode and has rich dynamic activity, wherein the discharge mode comprises a single period, a double period and a chaotic state discharge mode, and different discharge modes have different dynamic characteristics and biological significance. Bifurcation is a kinetic mechanism of neuronal firing, whereas qualitative behavior of a bifurcation is a phenomenon in which qualitative behavior of a nonlinear system changes with a parameter. The bifurcation research can not only reveal the connection and conversion between different states of the system, but also is one of important ways to research the mechanism and condition of instability and chaos generation.
For many biological and engineering systems, bifurcation is a dynamically changing process that can lead to system failure with serious consequences. Aiming at the detection problem of abnormal neuron discharge or bifurcation under external stimulus, the existing mode is to study the state identification of an HR neuron model, and the method mainly aims at the static system condition: one is to calculate the characteristic root and balance point according to the model equation to judge whether the neuron discharge system is stable. Through a mathematical calculation principle, indexes such as a Liapunov index, a bifurcation diagram and the like are calculated, and the discharge state of the neuron is identified. The Hamiltonian energy function is calculated for the discharge of the neurons, and different discharge states have obvious differences from the target energy function, so that the discharge state identification is realized. However, these recognition methods are still in the processing of static model data, and have the disadvantages of large calculation amount, high complexity, strict requirements on the data model and easy external interference. In reality, moreover, neuronal networks are highly nonlinear and complex, and the parameters or topology of most real world networks are virtually unknown, and it is also difficult to accurately identify or detect neuronal firing anomalies in the manner described above.
Disclosure of Invention
The invention aims to solve the technical problem of providing a neuron discharge abnormality detection system based on definite learning, which can accurately detect the problem of neuron discharge abnormality.
The detection of abnormal neuron discharge can be essentially regarded as a problem of identification and recognition of dynamic patterns, which is one of the difficulties in the field of pattern recognition. Based on the study of the continuous excitation characteristics of Radial Basis Function (RBF) neural networks, C.Wang et al propose a definite learning theory, which includes identification, expression and rapid recognition methods of dynamic modes generated by a nonlinear dynamic system, namely, by definite learning to obtain locally accurate neural network modeling of system dynamics in the dynamic modes, the dynamic modes changing with time are effectively expressed in a time-invariant and spatially distributed manner, and further similarity definition between the dynamic modes is given by utilizing the inherent dynamic topological similarity of the dynamic modes, and a new set of methods for rapidly recognizing the dynamic modes are provided.
The invention applies the definite learning theory to the nonlinear discharging dynamics of the neurons to carry out local accurate modeling and identification, the learned dynamics knowledge of the discharging of the neurons is stored in the form of constant neural network weights, and the differences of the different dynamic modes or the discharging modes on the system dynamics are utilized to classify so as to detect abnormal discharging of the neurons.
In order to solve the above technical problems, the present invention provides a neuron discharge abnormality detection system based on deterministic learning, comprising: the acquisition module is used for acquiring unknown dynamics information of a system to be identified of the nonlinear system; the identification model construction module is used for constructing a system identification model of the nonlinear system through the RBF neural network according to the determined learning theory; the identification module is used for locally approaching the unknown dynamics information of the system to be identified through the system identification model so as to obtain the unknown dynamics information of the identified system; the training learning module is used for constructing a dynamic training mode according to the unknown dynamics information of the identified system and establishing a dynamic training mode database; the construction module is used for constructing a dynamic similarity measurement model of a dynamic to-be-identified mode and a dynamic training mode of unknown dynamic information of the to-be-identified system; the dynamic residual error construction module is used for constructing a dynamic residual error estimator according to the dynamic pattern recognition system and the dynamic similarity measurement model; and the dynamic residual error estimator is used for carrying out dynamic similarity measurement on the dynamic to-be-identified mode and the dynamic training mode in the dynamic training mode database so as to obtain the minimum dynamic error between the dynamic to-be-identified mode and the dynamic training mode and predict the bifurcation phenomenon of the dynamic to-be-identified mode, thereby detecting the abnormal discharge phenomenon of the neuron.
As an improvement of the above-described aspect, the acquisition module includes an acquisition unit configured to:
obtaining unknown dynamics information of a system to be identified of a nonlinear system;
wherein x= [ x ] 1 ,…，x n ] T ∈R n For the state vector of the system to be identified, p E R m As a vector of the parameters,
f（x;p）=[f 1 （x;p）,…,f n （x;p）] T is a continuous smooth nonlinear function vector.
As an improvement of the above-described solution, the identification model construction module includes an identification model construction unit for constructing the identification model according to the formula:to construct a system identification model of the nonlinear system;
wherein ,for the state vector of the system identification model, x= [ x ] 1 ,…，x n ] T ∈R n A is a state vector of a system to be identified i >0 is an adjustable gain parameter, ">Is RBF god
The method is used for approaching unknown kinetic information of the system to be identified through a network.
As an improvement of the above-described scheme, the identification model construction unit includes an RBF neural network updating subunit;
the RBF neural network updating subunit is configured to, according to the formula:to determine an update rate of network weights of the RBF neural network;
wherein ,，/>is ideal weight +.>Estimated value of ∈10->Error for state estimation +.>Is an adjustable parameter variable.
As an improvement of the above-described scheme, the identification module includes an identification initializing unit and an identification unit;
an identification initialization unit for returning the unknown dynamics information of the system to be identifiedFrom the initial condition x 0 =x(t 0 ) E.OMEGA, the initial weight value of the neural network is +.>Starting;
regression trajectory of unknown dynamics information located in system to be identifiedNeural network weights in local neighborhood of (c)Will converge to a small neighborhood of the ideal value, far from the regression trajectory +.>Is hardly excited, the corresponding weight will remain zero;
an identification unit for identifying the following formula:accurately identifying unknown dynamic information of a system to be identified under unknown system parameters through a local RBF neural network, and fixing weight neural network +.>Storing and expressing unknown dynamics information of the identified system in a form;
wherein ,is->Representing the corresponding time period after the convergence of the weights, < -> and />To approach +.>Is a approximation error of (a).
As an improvement of the above-described scheme, the training learning module includes a dynamic training learning unit and a database construction unit;
a dynamic training learning unit for determining different dynamic modes X as dynamic training modes X according to the different dynamic modes X generated by the unknown dynamics information of the identified system and having the values of the parameters u at the transition stage, wherein the values of the parameters u are orderly selected at predetermined intervals k For the kth dynamic training pattern X k ：
Where k represents the kth pattern in the dynamic training pattern database, u k Is the corresponding parameter for all dynamic training patterns X with different unknown system parameters k All can be realized by using a constant RBF neural networkTo realize dynamic training mode X k Is an approximate approximation of the system dynamics:
wherein ,Ωζ Along a regression pathIs defined by a central region of the substrate;
is omega ζ Approximation errors of the system dynamics within;
a database construction unit for obtaining a constant RBF neural network by the aboveAnd constructing a dynamic training pattern database under parameter disturbance.
As an improvement of the scheme, the construction module comprises an acquisition unit to be identified, a dynamic unit to be identified, a system dynamics difference calculation unit and a dynamics similarity measurement construction unit;
the to-be-identified acquisition unit is used for carrying out the following formula:to obtain unknown dynamics information of the system to be identified:
wherein ,x∈Rn Is a variable vector, u d ∈R p Is the parameter vector of the system to be identified, f d :R n+p →R m Is C k Spatially smooth but unknown nonlinear functions, k is greater than or equal to 1;
a dynamic to-be-identified unit for representing the dynamic mode generated by the to-be-identified system with unknown dynamic information as a dynamic to-be-identified mode X d For different parameter values u d Dynamic pattern X to be identified d Will exhibit different qualitative behavior and steady state;
a system dynamics difference calculation unit for calculating the dynamic pattern X d State stay in dynamic training mode X k Regression trace of (a)When in the neighborhood region, then the dynamic pattern to be identified X d Represented as and dynamic training pattern X k Similarly, and along dynamic training pattern X k According to the formula:
to obtain the dynamic pattern X to be identified d And dynamic training mode X k A model of the differences between the system dynamics of (a);
wherein ,is a dynamic pattern X to be identified d Regression trace of->Is a dynamic pattern X to be identified d And dynamic training pattern X k A similarity measure between;
a dynamic similarity measure construction unit for constructing a dynamic pattern X to be identified d And dynamic training mode X k A kinetic similarity metric model is constructed from a model of the differences between the system dynamics of (a).
As an improvement of the above-described scheme, the dynamic similarity measure construction unit includes a dynamic similarity measure construction subunit;
kinetic similarity measure construction subunit usingBased on the dynamic pattern X to be identified d And dynamic training mode X k Is built along a dynamic training pattern X k Dynamic pattern X to be identified of trajectories of (2) d And dynamic training pattern X k A model of kinetic similarity measure between:
wherein ,is in accordance with dynamic training pattern X k And a dynamic pattern to be identified X d Normal number corresponding to similarity error between +.>Is a dynamic training pattern X k Based on constant RBF neural network +.>Is a approximation error of (a).
As an improvement of the above-described scheme, the dynamic residual error constructing module includes a dynamic estimator constructing unit and an identification error processing unit;
a dynamic estimator building unit for building a dynamic training pattern X according to the kth k Dynamic training pattern X in dynamic training pattern database k To be used forForm store of (c) and construct a dynamic estimator as:
wherein ,is the kth dynamic training pattern X k Dynamic estimator of->Is a dynamic pattern X to be identified d State input of b i >0 is a positive adjustable constant parameter;
an identification error processing unit for identifying the pattern X according to the dynamic state d And a dynamic estimator to obtain an identification error system:
wherein ,is the estimation error of the state system.
As an improvement of the above scheme, the dynamic residual error construction module further comprises a difference measurement unit and a bifurcation judgment unit;
a difference measurement unit for measuring the residual error based on L1 norm according to the dynamic similarity measurement modelThe differences between the measurement system dynamics are:
wherein T >0, continuously adjustable;
a bifurcation judging unit for determining that there is a finite time t for all integers r E {1, …, K }/{ K }, based on the dynamic pattern recognition system k So that at t E [ t ] k ,t k +T]Within a period of (a) of；
When the dynamic pattern to be identified is X d With the kth stable or normal dynamic training pattern X in the dynamic training pattern database k When the power error is minimum, the dynamic mode X to be identified d And its corresponding nonlinear system is identified as stable or normal, i.e., normal firing of neurons;
when the dynamic pattern to be identified is X d Dynamic training pattern X with the kth anomaly or instability in the dynamic training pattern database k When the power error is minimum, the dynamic mode X to be identified d And the corresponding nonlinear system is identified as abnormal or unstable, namely bifurcation phenomenon occurs, and neuron discharge is abnormal.
The implementation of the invention has the following beneficial effects:
according to the neuron discharge abnormality detection system based on the determination learning, under the condition that the determination parameters are known, the determination learning theory is utilized, dynamic modeling is carried out on various discharge modes of an HR neuron model through an RBF neural network, and modeling results are built into a dynamic training mode database. And constructing a dynamic residual error estimator according to the dynamic similarity measurement model and the dynamic pattern recognition system, and carrying out dynamic similarity measurement on the dynamic pattern to be recognized and the dynamic training pattern in the dynamic training pattern database through the dynamic residual error estimator so as to obtain the minimum dynamic error between the dynamic pattern to be recognized and the dynamic training pattern and predict the bifurcation phenomenon of the dynamic pattern to be recognized, thereby detecting the abnormal discharge phenomenon of neurons. The invention provides assistance for human brain disease monitoring and treatment, and has certain significance for exploring the nerve activity rule and human health.
Drawings
FIG. 1 is a functional block diagram of a neuron discharge abnormality detection system based on deterministic learning in accordance with the present invention;
FIG. 2 is a functional block diagram of an acquisition module of the present invention;
FIG. 3 is a schematic block diagram of an identification model building block of the present invention;
FIG. 4 is a functional block diagram of an identification module of the present invention;
FIG. 5 is a schematic block diagram of a training learning module of the present invention;
FIG. 6 is a schematic block diagram of a building block of the present invention;
FIG. 7 is a functional block diagram of a dynamic residual construction module of the present invention;
FIG. 8 is a graph of peak-to-peak interval bifurcation of the HR neuron model according to the present invention under a change in bifurcation parameter I;
FIG. 9 is a graph of a state trace of membrane voltage at an I parameter of 1.5 in the HR neuron model according to the present invention;
FIG. 10 is a graph of a state trace of membrane voltage at an I parameter of 1.9 in the HR neuron model according to the present invention;
FIG. 11 is a graph of a state trace of membrane voltage at an I parameter of 3 in the HR neuron model according to the present invention;
FIG. 12 is a timing diagram of neuron firing according to the present invention;
fig. 13 is an error diagram of two dynamic residual estimators of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings, for the purpose of making the objects, technical solutions and advantages of the present invention more apparent. It is only stated that the terms of orientation such as up, down, left, right, front, back, inner, outer, etc. used in this document or the imminent present invention, are used only with reference to the drawings of the present invention, and are not meant to be limiting in any way.
As shown in fig. 1, the present invention provides a neuron discharge abnormality detection system based on determination learning, comprising:
the acquisition module 1 is used for acquiring unknown dynamics information of a system to be identified of a nonlinear system;
the identification model construction module 2 is used for constructing a system identification model of the nonlinear system through the RBF neural network according to the determined learning theory;
the identification module 3 is used for locally approaching the unknown dynamics information of the system to be identified through the system identification model so as to obtain the unknown dynamics information of the identified system;
the training learning module 4 is used for constructing a dynamic training mode according to the unknown dynamics information of the identified system and establishing a dynamic training mode database;
the construction module 5 is used for constructing a dynamic similarity measurement model of a dynamic to-be-identified mode and a dynamic training mode of unknown dynamic information of the to-be-identified system;
a dynamic residual error constructing module 6, configured to construct a dynamic residual error estimator 7 according to the dynamic pattern recognition system and the dynamic similarity measurement model;
and the dynamic residual estimator 7 is used for carrying out dynamic similarity measurement on the dynamic to-be-identified mode and the dynamic training mode in the dynamic training mode database so as to obtain the minimum dynamic error between the dynamic to-be-identified mode and the dynamic training mode and predict the bifurcation phenomenon of the dynamic to-be-identified mode, thereby detecting the abnormal discharge phenomenon of the neuron.
It should be noted that, under different parameter values, nonlinear dynamics recognition is performed by using a definite learning theory, and a system recognition model of a nonlinear system is constructed through an RBF neural network, where the system recognition model is used for locally approximating unknown dynamics information of a system to be recognized. Locally approximating the unknown dynamics information of the system to be identified through the system identification model to obtain the unknown dynamics information of the identified system; and determining different dynamic modes generated according to the unknown dynamics information of the identified system as corresponding dynamic training modes so as to complete the learning training of the discharging mode of the neuron, and constructing a learning training result as a dynamic training mode database.
And constructing a dynamic residual error estimator 7 according to the dynamic similarity measurement model and the dynamic pattern recognition system, and measuring the dynamic similarity between the dynamic pattern to be recognized and the dynamic training pattern in the dynamic training pattern database through the dynamic residual error estimator 7 so as to obtain the minimum dynamic error between the dynamic pattern to be recognized and the dynamic training pattern and predict the bifurcation phenomenon of the dynamic pattern to be recognized, thereby detecting the abnormal discharge phenomenon of neurons. The invention provides assistance for human brain disease monitoring and treatment, and has certain significance for exploring the nerve activity rule and human health.
As shown in fig. 2, the acquisition module 1 comprises an acquisition unit 11, the acquisition unit 11 being configured to:
obtaining unknown dynamics information of a system to be identified of a nonlinear system;
wherein x= [ x ] 1 ,…，x n ] T ∈R n For the state vector of the system to be identified, p E R m As a vector of the parameters,
different values of p will yield different system dynamics behavior, f (x; p) = [ f 1 （x;p）,…,f n （x;p）] T Is a continuous smooth nonlinear function vector.
It should be noted that the state x remains consistently bounded, i.e., x satisfies: x (t) ∈Ω ⊂ R n ,∀t≥t 0 Where Ω is a tight set. In addition, regression trajectories of the systemTo->The points are initial points and have regression or quasi-regression characteristics.
In addition, regression trajectoriesRepresenting a series of trajectories generated by a nonlinear system, including not only periodic trajectories, but also quasi-periodic, quasi-periodic and even chaotic trajectories. In particular, many practical systems, such as vibration systems, rotating machinery, electronic systems, electric systems, communication networks, etc., exhibit the property of such a regression trajectory.
As shown in fig. 3, the recognition model construction module 2 includes a recognition model construction unit 21, the recognition model construction unit 21 being configured to:to construct a system identification model of the nonlinear system;
wherein ,for the state vector of the system identification model, x= [ x ] 1 ,…，x n ] T ∈R n A is a state vector of a system to be identified i >0 is an adjustable gain parameter, ">The RBF neural network is used for approximating unknown kinetic information of the system to be identified.
Specifically, the recognition model construction unit 21 includes an RBF neural network updating subunit 211;
the RBF neural network updating subunit 211 is configured to:to determine an update rate of network weights of the RBF neural network;
wherein ,，/>is ideal weight +.>Estimated value of ∈10->Error for state estimation +.>Is an adjustable parameter variable.
As shown in fig. 4, the recognition module 3 includes a recognition initializing unit 31 and a recognition unit 32;
an identification initializing unit 31 for returning the unknown dynamics information of the system to be identified to the regression pathFrom the initial condition x 0 =x(t 0 ) E.OMEGA, the initial weight value of the neural network is +.>Starting;
regression trajectory of unknown dynamics information located in system to be identifiedThe neural network weights in the local neighborhood of (2) will convergeA small neighborhood to the ideal value, far from the regression trace +.>Is hardly excited, the corresponding weight will remain zero;
an identification unit 32 for identifying the following formula:accurately identifying unknown dynamic information of a system to be identified under unknown system parameters through a local RBF neural network, and fixing weight neural network +.>Storing and expressing unknown dynamics information of the identified system in a form;
wherein ,is->Representing the corresponding time period after the convergence of the weights, < -> and />To approach +.>Is a approximation error of (a).
It should be noted that, by properly selecting the number of the neural network points and adjusting the neural network parameters, the corresponding system track is finally obtainedThe accurate identification of the local dynamics information of the identified system is realized by expressing or acquiring the unknown dynamics information of the identified system through a constant RBF neural network, so that the unknown dynamics information f (x; p) of the identified system is realized along the corresponding system trackIs a locally accurate approximation of (a).
As shown in fig. 5, the training learning module 4 includes a dynamic training learning unit 41 and a database construction unit 42;
a dynamic training learning unit 41 for determining different dynamic modes X as dynamic training modes X according to the different dynamic modes X generated by the unknown dynamics information of the identified system and having the values of the parameters u at the transition stage, wherein the values of the parameters u are sequentially selected at predetermined intervals k For the kth dynamic training pattern X k ：
Where k represents the kth pattern in the dynamic training pattern database, u k Is the corresponding parameter for all dynamic training patterns X with different unknown system parameters k All can be realized by using a constant RBF neural networkTo realize dynamic training mode X k Is an approximate approximation of the system dynamics:
wherein ,Ωζ Along a regression pathIs defined by a central region of the substrate;
is omega ζ Approximation errors of the system dynamics within;
a database construction unit 42 for passing the obtained constant RBF neural networkThe dynamic training mode database under the disturbance of the parameters is constructed. Namely, finish the mindTraining through learning of discharge patterns of elements. Wherein, for the system identification model, the dynamic training mode X which needs to be identified k Unknown parameters to the recognition system, but actual dynamic training pattern X k The determination parameters are known.
It should be noted that the features of each dynamic pattern, presented in the dynamic recognition mechanism determining learning (Deterministic learning, DL), may be stored and weighted with constant networkIs expressed in terms of (a). The kth pattern in the dynamic training pattern database is denoted +.>While the entire dynamic training pattern database is denoted as X k ={X k |k=1,…，M}。
By using the constant neural weights obtained aboveThe dynamic mode can express the space information in a time-invariant form or the trained dynamic mode can express the dynamic information in a time-invariant form. That is, in the experience trace +.>Is defined by the local area omega of (2) ζ In (a) positive constants d and +.>The corresponding expression is:
wherein ,is a pattern to be identified and a dynamic training pattern X k At Ω ζ Approximation errors of the system dynamics within.
As shown in fig. 6, the construction module 5 includes an acquisition unit 51 to be identified, a dynamic unit 52 to be identified, a system dynamics difference calculation unit 53, and a dynamics similarity metric construction unit 54;
an acquisition unit 51 to be identified, configured to:to obtain unknown dynamics information of the system to be identified:
wherein ,x∈Rn Is a variable vector, u d ∈R p Is the parameter vector of the system to be identified, f d :R n+p →R m Is C k Spatially smooth but unknown nonlinear functions, k is greater than or equal to 1;
a dynamic recognition unit 52 for representing the dynamic pattern generated by the recognition system with unknown dynamic information as a dynamic recognition pattern X d For different parameter values u d Dynamic pattern X to be identified d Will exhibit different qualitative behavior and steady state;
a system dynamics difference calculation unit 53 for calculating a dynamic pattern X d State stay in dynamic training mode X k Regression trace of (a)When in the neighborhood region, then the dynamic pattern to be identified X d Represented as and dynamic training pattern X k Similarly, and along dynamic training pattern X k According to the formula:
to obtain the dynamic pattern X to be identified d And dynamic training mode X k A model of the differences between the system dynamics of (a);
wherein ,is a dynamic pattern X to be identified d Regression trace of->Is a dynamic pattern X to be identified d And dynamic training pattern X k Similarity measure between.
A dynamic similarity measure construction unit 54 for constructing a pattern X according to the dynamic pattern to be identified d And dynamic training mode X k A kinetic similarity metric model is constructed from a model of the differences between the system dynamics of (a).
It should be noted that, in the above manner, when the pattern X is to be dynamically identified d State X in dynamic training mode X k Is defined by the local area of (a)In the inner case, it is possible to use a constant RBF neural network +.>To measure the dynamic differences of the system.
Specifically, the dynamic similarity measure construction unit 54 includes a dynamic similarity measure construction subunit 541;
a dynamic similarity measure construction subunit 541 for constructing a dynamic pattern X according to the dynamic pattern X d And dynamic training mode X k Is built along a dynamic training pattern X k Dynamic pattern X to be identified of trajectories of (2) d And dynamic training pattern X k A model of kinetic similarity measure between:
wherein ,is in accordance with dynamic training pattern X k And a dynamic pattern to be identified X d Normal number corresponding to similarity error between +.>Is a dynamic training pattern X k Based on constant RBF neural network +.>Is a approximation error of (a). When the dynamic pattern to be identified is X d Is maintained in dynamic training mode X k In any neighborhood region of the state trace of (2) and the similarity error between the two dynamic modes +.>Is infinitesimal, then the dynamic pattern to be identified X d Identified as and dynamic training pattern X k Similarly.
It should be noted that, in the definition of the dynamic similarity measurement model, the similarity error between the different modes is measured according to the states and the dynamic differences of the different modes. They are based on dynamic training pattern X k System dynamics of (2)And a dynamic pattern to be identified X d F of (2) d Naturally including information of system states and system parameters. Thus, this definition provides a reasonable way to measure the similarity between different kinetic modes generated by a nonlinear system at different parameter values.
As shown in fig. 7, the dynamic residual constructing module 6 includes a dynamic estimator constructing unit 61 and an identification error processing unit 62;
a dynamic estimator build unit 61 for generating a dynamic training pattern X according to the kth dynamic training pattern X k Dynamic training pattern X in dynamic training pattern database k To be used forForm store of (c) and construct a dynamic estimator as:
wherein ,is the kth dynamic training pattern X k Is a dynamic estimator of the (c) in the (c),/>is a dynamic pattern X to be identified d State input of b i >0 is a positive adjustable constant parameter, b i The values will remain the same for all dynamic training patterns.
It should be noted that, in the embodiment of the present invention, the specific value range of bi is preferably 5>b i >0, but is not limited thereto.
An identification error processing unit 62 for processing the identification error according to the dynamic pattern X to be identified d And the dynamic estimator obtains an identification error system:
wherein ,is the estimation error of the state system.
Specifically, the dynamic residual constructing module 6 further includes a difference measuring unit 63 and a bifurcation judging unit 64;
a difference measurement unit 63 for knowing that the state error between the two dynamic modes is proportional to the dynamic difference thereof by the similarity definition of the dynamic similarity measurement model, based on the residual measurement of L1 norm, byThe differences between the system dynamics were measured explicitly as:
wherein T >0, continuously adjustable.
A bifurcation judging unit 64 for providing a finite time t for all integers r E {1, …, K }/{ K }, based on the dynamic pattern recognition system k So that at t E [ t ] k ,t k +T]Within a period of (a) of；
When the dynamic pattern to be identified is X d With the kth stable or normal dynamic training pattern X in the dynamic training pattern database k The dynamic error between the two modes is minimum, and the mode X to be identified is dynamically determined d And its corresponding nonlinear system is identified as stable or normal, i.e., normal firing of neurons;
when the dynamic pattern to be identified is X d Dynamic training pattern X with the kth anomaly or instability in the dynamic training pattern database k The dynamic error between the two modes is minimum, and the mode X to be identified is dynamically determined d And the corresponding nonlinear system is identified as abnormal or unstable, namely bifurcation phenomenon occurs, and neuron discharge is abnormal.
By the dynamic residual error constructing module 6, a dynamic residual error estimator 7 is constructed, and the dynamic residual error estimator 7 is used for identifying the dynamic pattern X to be identified d With dynamic training pattern X in dynamic training pattern database k Performing dynamic similarity measurement to obtain a dynamic pattern X to be identified d And dynamic training pattern X k Minimum power error between and predicting dynamic pattern X to be identified d Thereby detecting abnormal discharge of neurons.
It should be noted that the dynamic pattern recognition system utilized in the present invention is provided by the prior art document "topology recognition and dynamic pattern recognition based on deterministic learning Hindmarsh-Rose neuron model" disclosed by Danfeng Chen, junsheng Li, wei Zeng and Jun He et al. This prior document is published in a SCI center two-area article of Cognitive Neurodynamics journal under Spring (schpringer) publishers. See Spring website (https:// link. Spring. Com/arm/10.1007/s 11571-022-09812-3) for details.
The following description is made by introducing an HR neuron model in the embodiment of the present invention, where the HR neuron model is:
wherein x= [ x ] 1 ,x 2 ,x 3 ] T Is a system state vector, x 1 Representing the membrane potential of neurons; x is x 2 Is a recovery variable, x, related to the internal current 3 Representing a slow-varying regulated current; a, b, c, d, s, X 0 Are all constants; i represents external direct current excitation; x is X 0 For regulating the resting state. r is related to the concentration of calcium ions, and can control the slow-changing regulating current x 3 Is a variable rate of change of (c).
In the embodiment of the invention, r is fixed, and the neuron model parameter is set to be r=0.013; a=1.0; b=3.0; c=1.0; d=5.0; s=4.0; x is X 0 -1.56. The external stimulus current I is used as a system variable I epsilon (1, 4), and the system presents different dynamic behaviors along with different values of the parameter I.
As shown in fig. 8, fig. 8 is a peak-to-peak interval bifurcation diagram of HR neuron model under variation of bifurcation parameter I, which is obtained by numerical analysis by fourth-order longgnus-Kutta method range-Kutta; wherein the order is an integer order q=1. Based on a Runge-Kutta numerical analysis method of a fourth-order Dragon-Gregorian tower method, the state track of the corresponding system under different I values is obtainedDifferent dynamic modes such as single period, double period and chaos are correspondingly generated. Here, the initial state x (0) = [ x ] is selected 1 (0),x 2 ( 0),x 3 (0)] T =[0.3,1,3] T 。
Specifically, when 1.2<I<1.7, dynamic mode 1-The mode having a single periodic character
Regression trajectories; when I increases to 1.7, the stable monocycle track loses its stability and diverges into another track whose length is exactly twice that of the original track, which is the so-called double cycle bifurcation (PDB)
Phenomenon. When i=3, a dynamic mode 3-The pattern has a regression trace of the chaotic characteristics. The three modes described above represent three different topologies and thus have different dynamic behaviors.
As shown in fig. 9-11, fig. 9-11 are three state trajectory models of membrane voltage at different values of I parameters in the HR neuron model. Wherein, fig. 3 is a state trace of membrane voltage at an I parameter of 1.5 in HR neuron model; FIG. 4 is a trace of the state of membrane voltage at an I parameter of 1.9 in the HR neuron model; fig. 5 is a trace of the state of membrane voltage at an I parameter of 3 in HR neuron model.
From the above, when the applied stimulation current I increases to 1.7, the stable monocycle trajectory loses its stability and diverges into a double cycle trajectory, i.e., a double cycle bifurcation (PDB) phenomenon occurs. As shown in fig. 6, with the slow increase of the applied stimulation current I, the discharge rate of the neurons is also increased continuously, when reaching the specified amplitude (I > 1.7), the corresponding neurons are branched at the position of 990ms, and the discharging of the neurons is changed from a single-period discharging mode to a multiple-period discharging mode; this also means that the variation in abnormal discharge rate is increased by a plurality of branches.
It should be noted that the HR neuron model is the system to be identified under definite parameters, HR neuron
The model has complex discharge behavior under the influence of different parameters.
Wherein the dynamic training modeThe u parameter in (a) is the parameter I. The embodiment of the invention mainly aims at bifurcation prediction of single-cycle and double-cycle discharging, namely neuron discharging abnormality detection, and if bifurcation occurs, the neuron discharging abnormality is generated. In the embodiment of the invention, by orderly selecting the parameter u (i.e. the parameter I) at a preset interval, as the occurrence of abnormal or bifurcation of the neuron discharge approximately occurs in the range interval of I=1.7, the embodiment of the invention takes the externally applied stimulation current I as bifurcation parameter, the interval is 0.05, and respectively learns and trains a normal monocycle dynamic mode (1.7-0.05 x N) and a fault or abnormal multiple cycle dynamic mode (1.7+0.05 x)N) is the selected number, and the specific value of N can be determined according to actual requirements.
The embodiment of the invention carries out the discharge mode learning training of the neurons by selecting the plurality of single-period dynamic modes and the plurality of double-period dynamic modes so as to construct a dynamic training mode database. And constructing a dynamic residual estimator 7 according to the similarity measurement between the dynamic modes and the dynamic mode recognition system, wherein the dynamic residual estimator 7 predicts the bifurcation phenomenon of the dynamic mode to be recognized through the minimum power error between the dynamic mode to be recognized and the dynamic training mode, thereby accurately detecting the abnormal discharge problem of the neuron.
As shown in fig. 12, in the neuron discharge timing chart, the system neuron discharges into a single-cycle discharge state before t <990ms, and into a double-cycle discharge state after t >990 ms. Taking the neuron discharge timing chart in fig. 12 as an example, the abnormal phenomenon of neuron discharge can be detected by performing bifurcation prediction by the dynamic residual estimator 7. As shown in fig. 13, the discharge pattern of HR neurons is detected by two sets of dynamic residual estimators 7. One group of dynamic residual estimators 7 is a single-period discharging training mode estimator in a normal state, and the other group of dynamic residual estimators 7 is a double-period discharging training mode estimator in an abnormal state. To facilitate the effect presentation, fig. 13 only shows two sets of data as examples. Before 990ms, the state of the neuron system can be rapidly identified to be in a single-period discharging state by selecting the minimum residual error from residual error values of the two groups of dynamic residual error estimators 7; when t=990 ms, the residual values of the two groups of dynamic residual estimators 7 change, and the minimum residual is switched from a single-period discharging mode to a double-period discharging mode, namely, the state of the neuron system is switched to double-period discharging at the moment, so that bifurcation prediction is realized, and the abnormal discharge of the HR neurons is accurately detected. The method provides reference ideas for human brain disease monitoring and treatment, and has certain significance for exploring the nerve activity rule and human health.
The foregoing disclosure is merely illustrative of the preferred embodiments of the present invention and is not intended to limit the scope of the claims herein, as equivalent changes may be made in the claims herein without departing from the scope of the invention.
Claims (9)
1. A neuron discharge abnormality detection system based on deterministic learning, comprising:
the acquisition module is used for acquiring unknown dynamics information of a system to be identified of the nonlinear system;
the identification model construction module is used for constructing a system identification model of the nonlinear system through the RBF neural network according to the determined learning theory;
the identification module is used for locally approaching the unknown dynamics information of the system to be identified through the system identification model so as to obtain the unknown dynamics information of the identified system;
the training learning module is used for constructing a dynamic training mode according to the unknown dynamics information of the identified system and establishing a dynamic training mode database;
the training learning module comprises a dynamic training learning unit and a database construction unit;
the dynamic training learning unit is used for determining different dynamic modes X as the dynamic training modes X according to the different dynamic modes X generated by the unknown dynamics information of the identified system, wherein the parameter u values are sequentially selected at preset intervals k For the kth said dynamic training pattern X k ：
Where k represents the kth pattern in the dynamic training pattern database, u k Is the corresponding parameter for all the dynamic training patterns X with different unknown system parameters k All can be realized by using a constant RBF neural networkTo realize the dynamic training mode X k Is an approximate approximation of the system dynamics:
wherein ,Ωζ Along a regression pathIs defined by a central region of the substrate;
is omega ζ Approximation errors of the system dynamics within;
the database construction unit is used for obtaining the constant RBF neural network through the aboveConstructing a dynamic training pattern database under parameter disturbance;
the construction module is used for constructing a dynamic similarity measurement model of a dynamic to-be-identified mode of unknown dynamic information of the system to be identified and the dynamic training mode;
the dynamic residual error constructing module is used for constructing a dynamic residual error estimator according to the dynamic pattern recognition system and the dynamic similarity measurement model;
the dynamic residual estimator is used for carrying out dynamic similarity measurement on the dynamic to-be-identified mode and the dynamic training mode in the dynamic training mode database so as to obtain the minimum power error between the dynamic to-be-identified mode and the dynamic training mode and predict the bifurcation phenomenon of the dynamic to-be-identified mode, thereby detecting the abnormal discharge phenomenon of neurons.
2. The neuron discharge abnormality detection system based on determination learning according to claim 1, wherein the acquisition module includes an acquisition unit for, according to the formula:
obtaining unknown dynamics information of a system to be identified of the nonlinear system;
wherein x= [ x ] 1 ,…，x n ] T ∈R n For the state vector of the system to be identified, p E R m As a vector of the parameters,
f（x;p）=[f 1 （x;p）,…,f n （x;p）] T is a continuous smooth nonlinear function vector, x (t 0 ) At t 0 System state of time, x 0 At t 0 The initial state of the system at the moment.
3. The neuron discharge abnormality detection system based on the deterministic learning according to claim 2, wherein the recognition model construction module includes a recognition model construction unit for constructing a recognition model according to the formula:to construct a system identification model of the nonlinear system;
wherein ,for the state vector of the system identification model, x= [ x ] 1 ,…，x n ] T ∈R n A is the state vector of the system to be identified i >0 is an adjustable gain parameter, ">And the RBF neural network is used for approximating the unknown dynamics information of the system to be identified.
4. The system for detecting abnormal firing of neurons based on deterministic learning according to claim 3, wherein the recognition model constructing unit comprises an RBF neural network updating subunit,
the RBF neural network updating subunit is configured to, according to the formula:to determine an update rate of network weights of the RBF neural network;
wherein ,，/>is ideal weight +.>Estimated value of ∈10->For the purpose of the state estimation error,is an adjustable parameter variable.
5. The neuron discharge abnormality detection system based on determination learning according to claim 4, wherein the recognition module includes a recognition initializing unit and a recognition unit;
the identification initialization unit is used for returning the unknown dynamics information of the system to be identified to the regression trackFrom the initial condition x 0 =x(t 0 ) E.OMEGA, the initial weight value of the neural network is +.>Starting;
the regression track of the unknown dynamics information of the system to be identifiedThe neural network weights in the local neighborhood of (2) will converge to a small neighborhood of ideal values, far from the regression trajectory +.>Is hardly excited, the corresponding weight will remain zero;
the identification unit is used for according to the formula:accurately identifying unknown dynamic information of the system to be identified under unknown system parameters through the RBF neural network, and adding the fixed weight neural network>Storing and expressing unknown kinetic information of the identified system in a form;
wherein ,is->Representing the corresponding time period after the convergence of the weights, < -> and />To approach +.>Is a approximation error of (a).
6. The neuron discharge abnormality detection system based on the determination learning according to claim 5, wherein the construction module includes an acquisition unit to be recognized, a dynamic unit to be recognized, a system dynamics difference calculation unit, and a dynamics similarity metric construction unit;
the to-be-identified acquiring unit is configured to, according to the formula:to obtain unknown dynamics information of the system to be identified:
wherein ,x∈Rn Is a variable vector, u d ∈R p Is the parameter vector of the system to be identified, f d :R n+p →R m Is C k Spatially smooth but unknown nonlinear functions, k is greater than or equal to 1;
the dynamic to-be-identified unit is used for representing a dynamic mode generated by a to-be-identified system with unknown dynamic information as the dynamic to-be-identified mode X d For different parameter values u d The dynamic pattern to be identified X d Will exhibit different qualitative behavior and steady state;
the system dynamics difference calculation unit is used for calculating the dynamic pattern X to be identified d Stay in the dynamic training mode X k Regression trace of (a)When the dynamic pattern to be identified is in the neighborhood region of (2), then the dynamic pattern to be identified is X d Is represented as being in accordance with the dynamic training pattern X k Similarly, and along the dynamic training pattern X k According to the formula:
to obtain the dynamic pattern to be identified X d And the dynamic training pattern X k A model of the differences between the system dynamics of (a);
wherein ,is the dynamic pattern to be identified X d Regression trace of->Is the dynamic pattern to be identified X d And the dynamic training mode X k A similarity measure between;
the dynamics are similarA measurement construction unit for constructing a dynamic pattern X according to the dynamic pattern d And the dynamic training pattern X k The dynamic similarity measure model is constructed by a difference model between the system dynamics.
7. The neural firing anomaly detection system based on deterministic learning of claim 6, wherein the kinetic similarity metric construction unit comprises a kinetic similarity metric construction subunit;
the dynamics similarity measure is used for constructing a subunit according to the dynamic pattern X to be identified d And the dynamic training pattern X k Is built along one of said dynamic training patterns X k The dynamic pattern X to be identified of the trajectory of (2) d And the dynamic training mode X k The dynamic similarity metric model between:
wherein ,is in accordance with the dynamic training pattern X k And the dynamic pattern to be identified X d Normal number corresponding to similarity error between +.>Is the dynamic training pattern X k Based on constant RBF neural network +.>Is a approximation error of (a).
8. The neuron discharge abnormality detection system based on determination learning according to claim 7, wherein the dynamic residual construction module includes a dynamic estimator construction unit and an identification error processing unit;
the dynamic estimator building unit is used for building a dynamic training mode X according to the kth dynamic training mode k The dynamic training pattern X in the dynamic training pattern database is processed k To be used forForm store of (c) and construct a dynamic estimator as:
wherein ,is the kth dynamic training pattern X k Dynamic estimator of->Is a dynamic pattern X to be identified d State input of b i >0 is a positive adjustable constant parameter;
the recognition error processing unit is used for processing the dynamic pattern X to be recognized according to the dynamic pattern X d And said dynamic estimator to obtain an identification error system:
wherein ,is the estimation error of the state system.
9. The neuron discharge abnormality detection system based on the determination learning according to claim 8, wherein the dynamic residual construction module further includes a difference measurement unit and a bifurcation judgment unit;
the difference measurement unit is used for measuring the residual error based on the L1 norm according to the dynamic similarity measurement modelThe differences between the measurement system dynamics are:
wherein T >0, continuously adjustable;
the bifurcation judging unit is used for determining that a finite time t exists for all integers of r E {1, …, K }/{ K }, according to the dynamic pattern recognition system k So that at t E [ t ] k ,t k +T]Within a period of (a) of；
When the dynamic pattern to be identified is X d The dynamic training pattern X which is stable or normal with the kth in the dynamic training pattern database k When the power error between the dynamic pattern X and the pattern X to be identified is minimum d And its corresponding nonlinear system is identified as stable or normal, i.e., the neuron discharges normally;
when the dynamic pattern to be identified is X d The dynamic training pattern X being abnormal or unstable with the kth in the dynamic training pattern database k When the power error between the dynamic pattern X and the pattern X to be identified is minimum d And its corresponding nonlinear system is identified as abnormal or unstable, i.e., a bifurcation phenomenon occurs, with abnormal firing of the neurons.
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