Electrode-finger skin impedance variant model and parameter estimation method thereof

Abstract

The invention discloses an electrode-finger skin impedance variant model and a parameter estimation method thereof, and belongs to the field of electric tactile feedback. The method comprises the following steps: deducing a mathematical expression of an electrode skin impedance model; response data # imgabs2 # of the stimulation frequency # imgabs0 # and the impedance model # imgabs1 # of the human finger skin in the stimulation frequency interval from Fmmin to Fmmax are measured, and a target function is established according to EFSIE model target parameters; and performing parameter estimation on the electrode-finger skin impedance variant model by adopting a badger foraging sine and cosine algorithm. According to the electrode-finger skin impedance variant model provided by the invention, the influence of impedance characteristics of nerve fibers on the model precision is fully considered, and a frequency-response mathematical expression is deduced. A sine and cosine updating strategy is introduced into a badger foraging algorithm, the original badger foraging algorithm is improved, and parameter estimation is performed on an electrode-finger skin impedance variant model by using an HBSCA algorithm.

Description

Technical Field

[0001] The present invention belongs to the technical field of electric tactile feedback, and in particular relates to an electrode-finger skin impedance variant model and a parameter estimation method thereof. Background Art

[0002] Haptic feedback technology enriches the interactive experience by simulating the sense of touch. By providing users with tactile feedback, tactile feedback improves the performance and user experience of human-computer interaction systems. Currently, there are various tactile feedback methods, including vibration feedback, tactile force feedback, electrotactile feedback, and thermal tactile feedback. Electrotactile feedback has been widely used due to its low power consumption, parameter decoupling, compact circuits, and flexible electrode pad configuration. Electrotactile devices can produce a richer sensation when stimulating areas of the human body with a high concentration of mechanoreceptors.

[0003] The electrical stimulation applied to the surface of human skin by an electrotactile device needs to overcome the human skin impedance value to activate the tactile receptors and simulate the real tactile sensation. Therefore, when using an electrotactile device to apply electrical stimulation to the finger skin, real-time skin impedance measurement is required. However, this measurement method is relatively cumbersome to implement, and there may be interference from adverse factors during the measurement process, resulting in inaccurate skin impedance values. Therefore, to ensure that electrotactile devices can easily and accurately apply electrical stimulation, it is particularly important to establish a skin impedance model that can accurately estimate the human skin impedance value.

[0004] Generally, establishing a finger skin impedance model involves two steps: (1) establishing the finger skin impedance circuit model and mathematical model; (2) estimating the parameters of the impedance mathematical model. In 2022, Uehara et al. (Uehara O, Kusuhara T, Matsuzaki K, et al. Skin electrical impedance model for evaluation of the thickness and water content of the stratum corneum [J]. Advanced Biomedical Engineering, 2022, 11: 98-108.) regarded the stratum corneum as a parallel model of resistance and capacitance and proposed a new skin model that can estimate the thickness and water content of the stratum corneum based on the parameters of the parallel resistance and capacitance. In 2022, He Yonghua (Design of electrotactile device and research on its electrode-finger skin impedance model [D]. Nanchang University, 2023) proposed a new electrode-finger skin impedance model that takes into account the electrode-skin contact model and the influence of environmental factors. In 2023, DJ Bora (Bora D J. Astudy of the characteristics of Skin Impedance Models based on the simulation of models [C]. 2023 IEEE 8th International Conference for Convergence in Technology (I2CT). IEEE, 2023: 1-5.) proposed a hybrid model that combines the biological characteristics of the skin with the physiological stratification characteristics. This model uses the CPE model and the Tregear model to describe the outer and deep layers of the skin, respectively. However, the existing skin impedance model does not fully consider the impact of the impedance characteristics of nerve fibers on the model accuracy, resulting in inaccurate models. In addition, due to the complexity of the skin impedance model, existing swarm intelligence algorithms still have shortcomings in solution speed and estimation accuracy when estimating the parameters of this impedance model, and suffer from problems such as slow convergence and easy falling into local optimality. Summary of the Invention

[0005] The present invention aims to provide an Electrode-Finger Skin Impedance Exchange (EFSIE) model and its Honey Badger Sine Cosine Algorithm (HBSCA) parameter estimation method. Taking into account the influence of the impedance characteristics of nerve fibers on model accuracy, the present invention provides an Electrode-Finger Skin Impedance Exchange (EFSIE) model for the first time. It also uses an improved Honey Badger Sine Cosine Algorithm (HBSCA) to estimate the parameters of the Electrode-Finger Skin Impedance Exchange (EFSIE) model, thereby obtaining an accurate Electrode-Finger Skin Impedance Exchange (EFSIE) model.

[0006] The present invention is achieved through the following technical solutions.

[0007] The electrode-finger skin impedance variant model and parameter estimation method thereof described in the present invention include the following steps:

[0008] Step 1: Derive the mathematical expression of the electrode skin impedance model, which is specifically expressed as follows:

[0009] (a) Setting resistance R b The expression of (f) is:

[0010] R b (f) = A + Be C / f (1)

[0011] Where A, B and C are model constants;

[0012] (b) Based on the AC analysis, the mathematical expression of the electrode-skin impedance circuit model is derived:

[0013]

[0014] Where f is the frequency of the electrical stimulation; j is the imaginary unit; R a is a constant linear resistance, C a is a constant linear capacitance, through R a and C a The parallel connection simulates the impedance value generated by the contact between the electrode and the skin; r a is a constant linear resistance used to simulate the adverse effects caused by the environment; R b is the nonlinear resistance, C a For a constant linear capacitance, use R b and C b The parallel connection of represents the impedance value of the stratum corneum in the finger epidermis; R c 、R d is a constant linear resistance, C ε is a constant linear capacitance, R c 、Rd Used to simulate the impedance value of nerve fibers.

[0015] Step 2: Measure the skin of human finger when the stimulation frequency changes from F mmin to F mmax Stimulation frequency in the interval With impedance model Response data

[0016] Step 3: The target parameters of the EFSIE model are set as (R a , A, B, C, R c 、C a 、C b 、C ε 、r a ), establish the objective function according to the parameters:

[0017]

[0018] Where X=[x1,…,x 10 ], and [x1,…,x 10 ] corresponds to the parameters that need to be estimated; are the parameters X and the stimulation frequency Substitute the estimated impedance model data into equation (2).

[0019] Step 4: Use the improved Honey Badger Sine Cosine Algorithm (HBSCA) to estimate the parameters of the electrode-finger skin impedance variant model and finally obtain the optimal solution. The specific process of parameter estimation is described as follows:

[0020] (a) Initialize the honey badger matrix of the HBSCA algorithm;

[0021] (b) Randomly initialize the position of the honey badger population according to the upper and lower bounds of the honey badger search space;

[0022] (c) Define the odor intensity as I, which indicates the concentration of prey and the distance between the prey and the honey badger. a is the scent intensity of the prey that the ath honey badger can detect. When the scent intensity I of the prey increases as the honey badger moves, the honey badger's movement speed will also increase.

[0023] (d) Update the density factor α. To ensure that the algorithm's exploration process can proceed to the development stage, the density factor α is used to control the randomness caused by time changes. The density factor α will become smaller as the number of iterations increases, thereby reducing the uncertainty of the algorithm.

[0024] (e) The algorithm enters the mining phase. Compared to the traditional honey badger algorithm (HBA), the proposed HBSCA algorithm uses a sine-cosine update strategy when updating the honey badger's location. This strategy aims to address the insufficient exploration capability of the traditional HBA algorithm, preventing the algorithm from converging to a local optimal solution rather than a global optimal solution, thereby improving the algorithm's exploration capability.

[0025] (f) The algorithm will eventually enter the honey collection stage. The honey badger will follow the honey guide bird to find the beehive and obtain honey. During the process of honey badger collecting honey, the algorithm will perform more refined processing and search, and finally obtain the optimal solution.

[0026] The advantages of the present invention are as follows: 1. The disclosed electrode-finger skin impedance variant model fully considers the influence of the impedance characteristics of nerve fibers on the model accuracy and derives its frequency-response mathematical expression; 2. The sine-cosine update strategy is introduced to improve the original sine-cosine algorithm, and the HBSCA algorithm is used to estimate the parameters of the electrode-skin impedance model. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a variant of the electrode-skin impedance model.

[0028] Figure 2 It is a flowchart of the steps of the HBSCA algorithm.

[0029] Figure 3 This is a comparison diagram between the electrode-finger skin impedance variant model after parameter estimation and the real data.

[0030] Figure 4 is the nonlinear resistance R b Resistance-frequency variation curve. DETAILED DESCRIPTION

[0031] The present invention will be further illustrated by the following examples.

[0032] The electrode-finger skin impedance variant model and parameter estimation method thereof described in this embodiment include the following steps:

[0033] Step 1: Derive the mathematical expression of the electrode skin impedance model, which is specifically expressed as follows:

[0034] (a) First, set the resistance R b The expression of (f) is:

[0035] R b (f) = A + Be C / f (1)

[0036] Where A, B and C are model constants

[0037] (b) The expression of the skin-electrode impedance in the circuit model is:

[0038]

[0039] In the above formula, ω is the angular frequency. Substituting the angular frequency formula ω = 2πf into the above formula, we can obtain:

[0040]

[0041] Similarly, the skin impedance in the circuit model can be obtained for:

[0042]

[0043] Among them, the nonlinear resistance R b (f) as above;

[0044] The dermis-subcutaneous tissue impedance in the circuit model is determined solely by R d and C ε Composition, the impedance can be derived

[0045]

[0046] The overall impedance formula is as follows:

[0047]

[0048] Will Bring in separately You can get:

[0049]

[0050] Finally, separating the real and imaginary parts yields:

[0051]

[0052] Where f is the frequency of the electrical stimulation; j is the imaginary unit; R a is a constant linear resistance, C a is a constant linear capacitance, through R a and C a The parallel connection simulates the impedance value generated by the contact between the electrode and the skin; r a is a constant linear resistance used to simulate the adverse effects caused by the environment; R b is the nonlinear resistance, C a For a constant linear capacitance, use R b and C b The parallel connection of represents the impedance value of the stratum corneum in the finger epidermis; R c 、R cis a constant linear resistance, C ε is a constant linear capacitor used to simulate the impedance of nerve fibers.

[0053] Step 2: Measure the skin of human fingers at 100 stimulation frequencies ranging from 10 Hz to 1000 Hz at room temperature of 25°C. With impedance model Response data

[0054] Step 3: The target parameters of the EFSIE model are set as (R a , A, B, C, R c 、C a 、C b 、C ε 、r a ), establish the objective function according to the parameters:

[0055]

[0056] Where X=[x1,…,x 10 ], and [x1,…,x 10 ] corresponds to the parameters that need to be estimated; When the parameter is X, the parameter X and the stimulation frequency Substitute the estimated impedance model data into formula (3). According to the actual finger impedance value measured in step 2, it can be seen that the finger skin impedance value is basically lower than 5000Ω, so the Z in the RC circuit is R Set to 0Ω≤Z R ≤10000Ω. The capacitance impedance expression is:

[0057]

[0058] Therefore, the impedance If the minimum value is not 1Ω, the maximum value of the capacitor can be estimated to be 0.1592F. α is set to a random number between [-1, 1]. The parameter A is set to the range of -10000Ω≤A≤10000Ω.

[0059] Step 4: Use the improved Honey Badger Sine Cosine Algorithm (HBSCA) to estimate the parameters of the electrode-finger skin impedance variant model. The specific process of parameter estimation is described as follows:

[0060] (a) Initialize the honey badger matrix of the HBSCA algorithm:

[0061]

[0062] Where M is a matrix composed of honey badgers, a represents the total number of honey badger populations, b represents the dimension of the target optimization problem, and m a =[m a1 m a2 …m ab ] represents the individual position of the ath honey badger.

[0063]

[0064] Where, f[·] is the fitness function, and f[m 11 m 12 …m 1b ] represents the fitness value of the honey badger individual.

[0065] Set the parameters α1 = 2-0, α2 = 2π*rand, α3 = 2*rand, α4 = rand, β = 6, and C = 2. Set the population size of the HBSCA algorithm to 100 and the maximum number of iterations to 500. To ensure the effectiveness of the finger skin impedance model, it is necessary to eliminate the randomness of the swarm intelligence algorithm. Therefore, the total number of algorithm runs was set to 30 during the experiment, and the best experimental result was used as the basis.

[0066] (b) Randomly initialize the position of the honey badger population according to the upper and lower bounds of the honey badger search space. The initialization formula is as follows:

[0067] m a =lb a +r1×(ub a -lb a ) (6)

[0068] Among them, m a Represents the individual position of the αth honey badger, ub a and lb a It represents the upper and lower bounds of the search space of the honey badger, and r1 is a random number between (0,1).

[0069] (c) Define the odor intensity I, which indicates the concentration of prey and the distance between the prey and the honey badger. a is the scent intensity of the prey that the ath honey badger can detect. When the scent intensity I of the prey increases as the honey badger moves, the honey badger's movement speed will also increase, and vice versa, it will slow down. The definition formula of scent intensity is as follows:

[0070]

[0071] Among them, r2 is a random number between [0,1], S represents the concentration of prey, d a Expressed as the distance between the honey badger and its prey.

[0072] (d) Update the density factor α. To ensure that the algorithm's exploration process can proceed to the development stage, the density factor α is used to control the randomness caused by changes over time. The density factor α will decrease as the number of iterations increases, thereby reducing the uncertainty of the algorithm. The formula is as follows:

[0073]

[0074] Where D is a constant greater than or equal to 1. According to experiments, it is generally set to 2. t represents the current number of iterations. max Indicates the maximum number of iterations set.

[0075] (e) The algorithm enters the mining phase. Compared with the traditional HBA algorithm, the HBSCA algorithm proposed in this paper adopts a sine-cosine update strategy when updating the honey badger position. This strategy aims to solve the problem of insufficient exploration capability in the traditional HBA algorithm, thereby preventing the algorithm from converging to a local optimal solution rather than a global optimal solution, and improving the algorithm's exploration capability. The specific formula is as follows:

[0076]

[0077] Among them, k and k+1 represent the current and next iterations respectively; as well as It represents the solution after k and k+1 iterations; It is the global optimal solution in the mixed population generated by comparing each update iteration after this update iteration; as the number of iterations increases, the parameter α1 will decay linearly, and the formula is as follows:

[0078]

[0079] Where β is set as a constant, t is the current number of iterations, and T is the maximum number of iterations. When β = 2, the fluctuation amplitude of α1sin(α2) and α1cos(α2), that is, the sine and cosine parameters in the above formula, will gradually decrease as the number of iterations increases.

[0080] Parameter α2 is a random number between [0, 2π] and must satisfy uniform distribution; while parameters α3 and α4 are two variables randomly generated between [0, 1]. F indicates whether the search direction has changed during the search process. The expression of F is as follows:

[0081]

[0082] Among them, r6 is a random number before (0, 1).

[0083] (f) The algorithm will eventually enter the honey collection phase. The honey badger will follow the honey guide bird to find the beehive and obtain honey. The update formula is as follows:

[0084] m new =m prey +F×r7×α×d a (13)

[0085] Among them, m new represents the location information of the honey badger after completing one step of updating, r7 is a random number between (0,1), and F and α are expressed by equations (12) and (9). During the process of collecting honey, the honey badger will perform more refined processing and search, and finally obtain the optimal solution.

[0086] The above embodiments are only used to illustrate the present invention, rather than to limit the present invention.

Claims

1. An electrode-finger skin impedance variant model and its parameter estimation method, characterized in that The steps include: Step 1: Derive the mathematical expression of the electrode skin impedance model: (a) Setting resistance R b The expression of (f) is: R b (f)=A+Be C / f (1) Where A, B and C are model constants; (b) Based on the AC analysis, the mathematical expression of the electrode-skin impedance circuit model is derived: Where f is the frequency of the electrical stimulation; j is the imaginary unit; R a is a constant linear resistance, C a is a constant linear capacitance, through R a and C a The parallel connection simulates the impedance value generated by the contact between the electrode and the skin; r a is a constant linear resistance used to simulate the adverse effects caused by the environment; R b is the nonlinear resistance, C a For a constant linear capacitance, use R b and C b The parallel connection of represents the impedance value of the stratum corneum in the finger epidermis; R c , R d is a constant linear resistance, C ε is a constant linear capacitance, R c , R d Used to simulate the impedance value of nerve fibers; Step 2: Measure the skin of human fingers when the stimulation frequency changes from F mmin To F mmax Stimulation frequency in interval With impedance model Response data Step 3: Set the model target parameter of EFSIE to R a , A, B, C, R c , C a , C b , C ε 、r a , establish the objective function according to the parameters: Where X = [x1,…,x 10 ], and [x1,…,x 10 ] corresponds to the parameters that need to be estimated; are the parameters X and the stimulation frequency Substitute the estimated impedance model data into equation (2); Step 4: Use the honey badger sine-cosine algorithm to estimate the parameters of the electrode-finger skin impedance variant model and obtain the optimal solution: (a) Initialize the honey badger matrix of the HBSCA algorithm; (b) Randomly initialize the position of the honey badger population according to the upper and lower bounds of the honey badger search time space; (c) Define the odor intensity as I, I a is the odor intensity of the prey that the ath honey badger can detect; when the odor intensity I of the prey increases as the honey badger moves, the movement speed of the honey badger increases; (d) Update the density factor α, and use the density factor α to control the randomness caused by changes over time; the density factor α will become smaller as the number of iterations increases to reduce the uncertainty of the algorithm; (e) The algorithm enters the mining phase and adopts the sine and cosine update strategy when updating the position of the honey badger; (f) Finally, the algorithm enters the honey collection stage and finally obtains the optimal solution.

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