CN113158746A - Weak signal sensing method based on neuron small-world network stochastic resonance - Google Patents

Weak signal sensing method based on neuron small-world network stochastic resonance Download PDF

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CN113158746A
CN113158746A CN202110143648.4A CN202110143648A CN113158746A CN 113158746 A CN113158746 A CN 113158746A CN 202110143648 A CN202110143648 A CN 202110143648A CN 113158746 A CN113158746 A CN 113158746A
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蔡哲飞
范影乐
房涛
武薇
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Abstract

The invention discloses a weak signal sensing method based on neuron worldlet network stochastic resonance. The improved parameter setting method can enhance the potential function potential barrier of the film, thereby improving the transition probability among potential wells; then, constructing an FHN neuron calculation model containing weak signal input and background noise, setting the FHN neuron calculation model as a small-world network node, and giving and realizing a dynamic synapse interconnection rule representing the relationship among all nodes; for the output of each node of the small-world network, a mean value fusion method based on cross correlation coefficients is adopted to screen and fuse information of the output of each node of the network so as to improve the performance and robustness of the system and further obtain the weak signal perception effect in the sense of the small-world network system.

Description

Weak signal sensing method based on neuron small-world network stochastic resonance
Technical Field
The invention belongs to the field of application of a neural computation model, and particularly relates to a weak signal sensing method based on neuron small-world network stochastic resonance.
Background
Visual nerve physiological experiments and computational simulation show that a stochastic resonance mechanism exists in a nervous system, namely part of background noise energy of the nervous system is converted into weak signal energy by utilizing the nonlinear characteristics of neural coding and dynamic synaptic connection, so that the perception of the weak signal is realized. At present, many researches apply a stochastic resonance mechanism to a weak signal processing process, but most of the selected nonlinear systems are ideal physical systems represented by bistable states or simplified nervous systems represented by single neuron calculation models, but characteristics, nonlinear fitting and anti-interference capability of neuron clusters are ignored, so that the intrinsic stochastic resonance mechanism in the neural visual and auditory perception process is not fully exploited and applied. In addition, with the continuous development of computing power and algorithms in recent years, a complex network has become one of the research hotspots of computational nerves, and more neurophysiological experimental results show that the characteristic of a small-world network of a nervous system plays an important role in maintaining the normal physiological function of the nervous system.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a weak signal sensing method based on neuron small-world network stochastic resonance.
The method firstly improves the parameter setting of the FHN neuron calculation model, and changes the traditional situation that the membrane potential and the recovery variable characteristic time are set to be the same value in the consideration of simple calculation. The improved parameter setting method can enhance the potential function potential barrier of the film, thereby improving the transition probability among potential wells; then, constructing an FHN neuron calculation model containing weak signal input and background noise, setting the FHN neuron calculation model as a small-world network node, and giving and realizing a dynamic synapse interconnection rule representing the relationship among all nodes; for the output of each node of the small-world network, a mean value fusion method based on cross correlation coefficients is adopted to screen and fuse information of the output of each node of the network so as to improve the performance and robustness of the system and further obtain the weak signal perception effect in the sense of the small-world network system.
The method comprises the following steps:
step 1, constructing a small-world network based on probability random connection. The nodes in the small world network are distributed according to a ring rule, and each node in the network corresponds to a unique mark l, l belongs to [1, N ∈ respectively]And N is the total number of nodes of the small-world network. The labels are sequentially increased in a clockwise direction according to the positions of the nodes in the network, and are connected end to finally form a closed annular structure. Defining the distance d between two small world network nodes labeled i and ji，jAs shown in formula (1), where | represents an absolute value function.
di，j＝min(|j-i|，|N-j+i|)，i，j∈[1，N]，i≠j (1)
For a node labeled i, i ∈ [1, N)]With probability p between it and the node numbered ji，jMaking a random connection, pi，jThe setting is performed according to the following rule.
ifj＝＝mod((i+1)，N)
pi，j＝1；
else
pi，j＝p；
Where mod is a remainder taking function, p is a random number, and p is [0, 1 ].
And 2, constructing an FHN neuron calculation model which is used as a basic node of the small-world network. Wherein only one node of the small world network receives external input stimulation, the node label is marked as in, in belongs to [1, N ], and the FHN neuron calculation model adopted by the node is shown as a formula (2).
Figure BDA0002929104460000021
In the formula, epsilonv、εwRepresenting the characteristic times of the membrane potential and of the recovery variable, respectively, the invention changes the conventional idea of setting the two characteristic times to the same value, epsilonv、εwCan be independently arranged, thereby flexibly changing the potential function of the membranePotential barriers to improve transition probability between potential wells; v. ofinAnd ωinRespectively representing a node output signal and a recovery variable marked as in; b represents a dimensionless positive number; i issigRepresenting an external input stimulus, corresponding to a periodic weak signal to be sensed, IsigHas a period of Tsig(ii) a ζ represents white gaussian noise having a mean value of 0 and a noise intensity σ; i issigZeta, and
Figure BDA0002929104460000022
the sum of which corresponds to the node input signal labeled in, denoted SinI.e. by
Figure BDA0002929104460000023
Wherein
Figure BDA0002929104460000024
The calculation process is shown as formula (3) for the coupling term of the node dynamic synapse interconnection pattern with the label in.
Figure BDA0002929104460000025
In the formula, wherein Lin，jThe connection between two small world network nodes denoted by the reference numerals in and j, Lin，j1 or 0 indicates the presence or absence of a synaptic connection between the two nodes, respectively. Alpha is alphain，jThe strength of the connection between two nodes of the small world network denoted by the reference numerals in and j, and the distance d between themin，jInversely proportional, as shown in formula (4).
Figure BDA0002929104460000026
For nodes marked with i in the small-world network, i belongs to [1, N ], i is not equal to in, the nodes do not receive external input stimulation, and the FHN neuron calculation model is shown as a formula (5).
Figure BDA0002929104460000031
In the formula, vi、ωiAnd
Figure BDA0002929104460000032
respectively representing the node output signal, the recovery variable and the coupling item of the dynamic synapse interconnection mode which are marked as i; the node input signal labeled i is denoted SiI.e. by
Figure BDA0002929104460000033
Wherein
Figure BDA0002929104460000034
The calculation is performed with reference to equation (3).
Step 3, calculating the cross-correlation coefficient of the small world network nodes
Figure BDA0002929104460000035
And
Figure BDA0002929104460000036
computing output v of a small world network node according to equations (2) and (5)inAnd vi. Wherein (M +1) possible noise intensities σ are set for the Gaussian white noise ζ in the equation (2)z0.01z, 0, 1, M, default M takes 50. For a certain specific σzAnd calculating the cross-correlation coefficient of all nodes of the small-world network based on the correlation between the input signal and the output signal.
For the in node, the cross correlation coefficient is calculated as shown in equation (6).
Figure BDA0002929104460000037
In the formula (I), the compound is shown in the specification,
Figure BDA0002929104460000038
node denoted by reference number in is at TsigTime input signal SinThe mean value of (a);
Figure BDA0002929104460000039
node denoted by reference number in is at TsigOutput signal v over timeinIs measured.
For a node labeled i in a small-world network, i belongs to [1, N ], i is not equal to in, and the cross-correlation coefficient calculation is shown as a formula (7).
Figure BDA00029291044600000310
In the formula (I), the compound is shown in the specification,
Figure BDA00029291044600000311
node denoted by i is at TsigTime input signal SiIs measured.
Figure BDA00029291044600000312
Node denoted by i is at TsigOutput signal v over timeiIs measured.
And 4, determining the zeta noise intensity sigma corresponding to the optimal cross-correlation coefficient. And (3) on the basis of the step (3), solving the cross-correlation coefficient of each node in the small-world network under different Gaussian white noise intensities, summing and taking the maximum value, wherein the maximum value is shown as a formula (8).
Figure BDA00029291044600000313
Obtaining CsumThe maximum value corresponds to a parameter z, and thus the noise intensity σ of ζ is determined to be 0.01 z.
Step 5, obtaining the optimized output v 'of the small world network node'inAnd v'iWhere i ∈ [1, N ]]I ≠ in. On the basis of the sigma calculated in the step 4, discarding abnormal node output information with an excessively low cross-correlation coefficient to obtain an optimized output v'inAnd v'iWhere i ∈ [1, N ]]I ≠ in. The calculation process is shown in equations (9) and (10).
Figure BDA00029291044600000314
Figure BDA00029291044600000315
In the formula, Threshold represents an adaptive Threshold value, and the median of the cross-correlation coefficients of all nodes of the small-world network is taken as a default.
Step 6, determining the output of the whole small-world network, namely the weak signal sensing result vout. In order to improve the robustness of the weak signal enhancement performance, the output signals of all nodes of the small-world network are subjected to mean value fusion to obtain a final weak signal sensing result voutSpecifically, the formula is shown in formula (11).
Figure BDA0002929104460000041
In the formula, kin、kiAnd is used for indicating whether the output of the small world network node in and the rest nodes i of the small world network are effective or not, and is specifically shown as formulas (12) and (13).
Figure BDA0002929104460000042
Figure BDA0002929104460000043
The invention has the beneficial effects that:
the invention constructs a small-world network which takes FHN neurons as nodes and is based on probability random reconnection, fully utilizes the random resonance characteristic, can realize effective reduction and enhancement of periodic weak signals and non-periodic signals with noise, can keep the consistency of periodic signal frequency spectrums, can enable original weak signals and system output signals to achieve higher cross correlation coefficients, and meets the actual requirements; the defect that a nonlinear system model is over-ideal in the traditional random resonance research is overcome, and the performance of a system for sensing weak signals is effectively improved.
Drawings
Fig. 1(a) shows a schematic diagram of a small-world network structure when a reconnection probability p between neuron nodes is 0;
fig. 1(b) shows a schematic diagram of a worldlet network structure when the reconnection probability p between neuron nodes is 0.2.
Detailed Description
A weak signal sensing method based on neuron small-world network stochastic resonance specifically comprises the following steps:
step 1, constructing a small-world network based on probability random connection.
The nodes in the small world network are distributed according to a ring rule, and each node in the network corresponds to a unique mark l, l belongs to [1, N ∈ respectively]N is the total number of nodes of the small-world network, and is a schematic diagram of the structure of the small-world network when N is 20, as shown in fig. 1 (a). The labels are sequentially increased in a clockwise direction according to the positions of the nodes in the network, and are connected end to finally form a closed annular structure. Defining the distance d between two small world network nodes labeled i and ji，jAs shown in formula (1), where | represents an absolute value function.
di，j＝min(|j-i|，|N-j+i|)，i，j∈[1，N]，i≠j (1)
For a node labeled i, i ∈ [1, N)]With probability p between it and the node numbered ji，jMaking a random connection, pi，jThe setting is performed according to the following rule.
if j＝＝mod((i+1)，N)
pi，j＝1；
else
pi，j＝p；
Where mod is a remainder taking function, p is a random number, and p is [0, 1 ].
As shown in fig. 1(a), that is, it means that the probability p of reconnection between neuron nodes is 0; graph (b) shows that the probability of reconnection p between neuron nodes is 0.2.
And 2, constructing an FHN neuron calculation model which is used as a basic node of the small-world network. Wherein only one node of the small world network receives external input stimulation, the node label is marked as in, in belongs to [1, N ], and the FHN neuron calculation model adopted by the node is shown as a formula (2).
Figure BDA0002929104460000051
In the formula, epsilonv、εwRepresenting the characteristic times of the membrane potential and of the recovery variable, respectively, the invention changes the conventional idea of setting the two characteristic times to the same value, epsilonv、εwCan be independently arranged, thereby flexibly changing the potential function potential barrier of the membrane potential to improve the transition probability among potential wells; v. ofinAnd ωinRespectively representing a node output signal and a recovery variable marked as in; b represents a dimensionless positive number; i issigRepresenting an external input stimulus, corresponding to a periodic weak signal to be sensed, IsigHas a period of Tsig(ii) a ζ represents white gaussian noise having a mean value of 0 and a noise intensity σ; i issigZeta, and
Figure BDA0002929104460000052
the sum of which corresponds to the node input signal labeled in, denoted SinI.e. by
Figure BDA0002929104460000053
Wherein
Figure BDA0002929104460000054
The calculation process is shown as formula (3) for the coupling term of the node dynamic synapse interconnection pattern with the label in.
Figure BDA0002929104460000055
In the formula, wherein Lin，jThe connection between two small world network nodes denoted by the reference numerals in and j, Lin，j1 or 0 minRespectively, the existence or non-existence of synaptic connections between the two nodes. Alpha is alphain，jThe strength of the connection between two nodes of the small world network denoted by the reference numerals in and j, and the distance d between themin，jInversely proportional, as shown in formula (4).
Figure BDA0002929104460000056
For nodes marked with i in the small-world network, i belongs to [1, N ], i is not equal to in, the nodes do not receive external input stimulation, and the FHN neuron calculation model is shown as a formula (5).
Figure BDA0002929104460000057
In the formula, vi、ωiAnd
Figure BDA0002929104460000061
respectively representing the node output signal, the recovery variable and the coupling item of the dynamic synapse interconnection mode which are marked as i; the node input signal labeled i is denoted SiI.e. by
Figure BDA0002929104460000062
Wherein
Figure BDA0002929104460000063
The calculation is performed with reference to equation (3).
Step 3, calculating the cross-correlation coefficient of the small world network nodes
Figure BDA0002929104460000064
And
Figure BDA0002929104460000065
computing output v of a small world network node according to equations (2) and (5)inAnd vi. Wherein (M +1) possible noise intensities σ are set for the Gaussian white noise ζ in the equation (2)z0.01z, 0, 1, M, default M takes 50.For a certain specific σzAnd calculating the cross-correlation coefficient of all nodes of the small-world network based on the correlation between the input signal and the output signal.
For the in node, the cross correlation coefficient is calculated as shown in equation (6).
Figure BDA0002929104460000066
In the formula (I), the compound is shown in the specification,
Figure BDA0002929104460000067
node denoted by reference number in is at TsigTime input signal SinThe mean value of (a);
Figure BDA0002929104460000068
node denoted by reference number in is at TsigOutput signal v over timeinIs measured.
For a node labeled i in a small-world network, i belongs to [1, N ], i is not equal to in, and the cross-correlation coefficient calculation is shown as a formula (7).
Figure BDA0002929104460000069
In the formula (I), the compound is shown in the specification,
Figure BDA00029291044600000610
node denoted by i is at TsigTime input signal SiIs measured.
Figure BDA00029291044600000611
Node denoted by i is at TsigOutput signal v over timeiIs measured.
And 4, determining the zeta noise intensity sigma corresponding to the optimal cross-correlation coefficient. And (3) on the basis of the step (3), solving the cross-correlation coefficient of each node in the small-world network under different Gaussian white noise intensities, summing and taking the maximum value, wherein the maximum value is shown as a formula (8).
Figure BDA00029291044600000612
Obtaining CsumThe maximum value corresponds to a parameter z, and thus the noise intensity σ of ζ is determined to be 0.01 z.
Step 5, obtaining the optimized output v 'of the small world network node'inAnd v'iWhere i ∈ [1, N ]]I ≠ in. On the basis of the sigma calculated in the step 4, discarding abnormal node output information with an excessively low cross-correlation coefficient to obtain an optimized output v'inAnd v'iWhere i ∈ [1, N ]]I ≠ in. The calculation process is shown in equations (9) and (10).
Figure BDA00029291044600000613
Figure BDA00029291044600000614
In the formula, Threshold represents an adaptive Threshold value, and the median of the cross-correlation coefficients of all nodes of the small-world network is taken as a default.
Step 6, determining the output of the whole small-world network, namely the weak signal sensing result vout. In order to improve the robustness of the weak signal enhancement performance, the output signals of all nodes of the small-world network are subjected to mean value fusion to obtain a final weak signal sensing result voutSpecifically, the formula is shown in formula (11).
Figure BDA0002929104460000071
In the formula, kin、kiAnd is used for indicating whether the output of the small world network node in and the rest nodes i of the small world network are effective or not, and is specifically shown as formulas (12) and (13).
Figure BDA0002929104460000072
Figure BDA0002929104460000073

Claims (3)

1. A weak signal sensing method based on neuron small-world network stochastic resonance is characterized by comprising the following steps:
step 1, constructing a small-world network based on probability random connection;
the nodes in the small world network are distributed according to a ring rule, and each node in the network corresponds to a unique mark l, l belongs to [1, N ∈ respectively]N is the total number of nodes of the small world network; the labels are sequentially increased in a clockwise direction according to the positions of the nodes in the network, and are connected end to finally form a closed annular structure; defining the distance d between two small world network nodes labeled i and ji，jAs shown in formula (1), wherein | · | represents an absolute value function;
di，j＝min(|j-i|，|N-j+i|)，i，j∈[1，N]，i≠j (1)
for a node labeled i, i ∈ [1, N)]With probability p between it and the node numbered ji，jMaking a random connection, pi，jSetting according to the following rules;
if j＝＝mod((i+1)，N)
pi，j＝1；
else
pi，j＝p；
wherein mod is a remainder taking function, p is a random number, and p belongs to [0, 1 ];
step 2, constructing an FHN neuron calculation model which is used as a basic node of the small world network; wherein only one node of the small-world network receives external input stimulation, the node label is marked as in, in belongs to [1, N ], and the FHN neuron calculation model adopted by the node is shown as a formula (2);
Figure FDA0002929104450000011
in the formula, epsilonv、εwRespectively representing the membrane potential and the characteristic time of the recovery variable, wherev、εwThe potential barriers are independently arranged, so that the potential function potential barriers of the membrane can be flexibly changed to improve the transition probability among potential wells; v. ofinAnd ωinRespectively representing a node output signal and a recovery variable marked as in; b represents a dimensionless positive number; i issigRepresenting an external input stimulus, corresponding to a periodic weak signal to be sensed, IsigHas a period of Tsig(ii) a ζ represents white gaussian noise having a mean value of 0 and a noise intensity σ; i issigZeta, and
Figure FDA0002929104450000012
the sum of which corresponds to the node input signal labeled in, denoted SinI.e. by
Figure FDA0002929104450000013
Wherein
Figure FDA0002929104450000014
The coupling term of the node dynamic synapse interconnection mode with the label of in is shown in a formula (3);
Figure FDA0002929104450000015
in the formula, wherein Lin，jThe connection between two small world network nodes denoted by the reference numerals in and j, Lin，j1 or 0 represents the presence or absence of a synaptic connection between the two nodes, respectively; alpha is alphain，jThe strength of the connection between two nodes of the small world network denoted by the reference numerals in and j, and the distance d between themin，jIn inverse proportion, as shown in formula (4);
Figure FDA0002929104450000021
for nodes marked with i in a small-world network, i belongs to [1, N ], i is not equal to in, the nodes do not receive external input stimulation, and the FHN neuron calculation model is shown as a formula (5);
Figure FDA0002929104450000022
in the formula, vi、ωiAnd
Figure FDA0002929104450000023
respectively representing the node output signal, the recovery variable and the coupling item of the dynamic synapse interconnection mode which are marked as i; the node input signal labeled i is denoted SiI.e. by
Figure FDA0002929104450000024
Wherein
Figure FDA0002929104450000025
Calculating with reference to formula (3);
step 3, calculating the cross-correlation coefficient of the small world network nodes
Figure FDA0002929104450000026
And
Figure FDA0002929104450000027
computing output v of a small world network node according to equations (2) and (5)inAnd vi(ii) a Wherein (M +1) possible noise intensities σ are set for the Gaussian white noise ζ in the equation (2)z0.01z, z 0, 1zCalculating cross-correlation coefficients of all nodes of the small-world network based on the correlation between the input signal and the output signal;
for the in node, the cross correlation coefficient is calculated as shown in formula (6);
Figure FDA0002929104450000028
in the formula (I), the compound is shown in the specification,
Figure FDA0002929104450000029
node denoted by reference number in is at TsigTime input signal SinThe mean value of (a);
Figure FDA00029291044500000210
node denoted by reference number in is at TsigOutput signal v over timeinThe mean value of (a);
for a node marked with i in a small-world network, i belongs to [1, N ], i is not equal to in, and the cross-correlation coefficient calculation is shown as a formula (7);
Figure FDA00029291044500000211
in the formula (I), the compound is shown in the specification,
Figure FDA00029291044500000212
node denoted by i is at TsigTime input signal SiThe mean value of (a);
Figure FDA00029291044500000213
node denoted by i is at TsigOutput signal v over timeiThe mean value of (a);
step 4, determining zeta noise intensity sigma corresponding to the optimal cross correlation coefficient; on the basis of the step 3, the cross-correlation coefficient of each node in the small-world network under different Gaussian white noise intensities is calculated, the sum is carried out, and the maximum value is taken, specifically shown as a formula (8);
Figure FDA00029291044500000214
obtaining CsumThe parameter z corresponds to the maximum value, so that the noise intensity sigma of zeta is determined to be 0.01 z;
step 5, obtaining the optimized output v 'of the small world network node'inAnd v'iWhere i ∈ [1, N ]]I is not equal to in; on the basis of the sigma calculated in the step 4, discarding abnormal node output information with an excessively low cross-correlation coefficient to obtain an optimized output v'inAnd v'iWhere i ∈ [1, N ]]I is not equal to in; the calculation process is shown in formulas (9) and (10);
Figure FDA0002929104450000031
Figure FDA0002929104450000032
wherein Threshold represents an adaptive Threshold;
step 6, determining the output of the whole small-world network, namely the weak signal sensing result vout(ii) a In order to improve the robustness of the weak signal enhancement performance, the output signals of all nodes of the small-world network are subjected to mean value fusion to obtain a final weak signal sensing result voutSpecifically, as shown in formula (11);
Figure FDA0002929104450000033
in the formula, kin、kiThe node I is used for representing whether the output of the small world network node in and the rest nodes i of the small world network are effective or not, and is specifically shown as formulas (12) and (13);
Figure FDA0002929104450000034
Figure FDA0002929104450000035
2. the weak signal perception method based on neuron small-world network stochastic resonance as claimed in claim 1, wherein the weak signal perception method comprises the following steps: the Threshold is the median of the cross-correlation coefficients of all nodes of the small-world network.
3. The weak signal perception method based on neuron small-world network stochastic resonance as claimed in claim 1, wherein the weak signal perception method comprises the following steps: and M is taken as 50.
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