CN107678543B - Method for estimating parameters of human hand skin-electrode bio-impedance model based on electric touch equipment - Google Patents

Method for estimating parameters of human hand skin-electrode bio-impedance model based on electric touch equipment Download PDF

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CN107678543B
CN107678543B CN201710871845.1A CN201710871845A CN107678543B CN 107678543 B CN107678543 B CN 107678543B CN 201710871845 A CN201710871845 A CN 201710871845A CN 107678543 B CN107678543 B CN 107678543B
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李春泉
林凡超
罗族
张�浩
索婧雯
熊辉
杨峰
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Lattice Power Jiangxi Corp
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Abstract

A method for estimating parameters of a human hand skin-electrode bio-impedance model based on an electric tactile device. The method adopts a recursion algorithm containing a forgetting factor, weights data by a preset forgetting factor, enables new data to occupy larger weight in parameter estimation, improves estimation accuracy by using new input and output data continuously provided by an electric touch device, modifies an estimation value when parameters are changed, realizes parameter online real-time estimation, simultaneously adopts an augmentation model, completely and reasonably assumes that the error between the electric stimulation quantity output by the model and the actual finger electric stimulation quantity is colored noise instead of white noise in an ideal state, is more suitable for actual conditions, and can adapt to parameter estimation under different noise conditions. The method avoids the reduction of parameter correction capability and the interference of single noise model to parameter estimation after the number of recursion steps is too long, and improves the real-time performance and the accuracy of the finger skin impedance parameter estimation. The invention has detailed consideration, simple and reasonable design, easy realization and strong adaptability.

Description

Method for estimating parameters of human hand skin-electrode bio-impedance model based on electric touch equipment
Technical Field
The invention relates to an impedance parameter estimation method used in a human hand epidermis-dermis-subcutaneous tissue electrical impedance model in electrotactile equipment, in particular to an impedance parameter estimation method in the epidermis-dermis-subcutaneous tissue electrical impedance model based on a recurrence and augmentation least square method containing a forgetting factor.
Background
Haptic rendering refers to stimulating haptic information of a remote environment or a virtual environment to a corresponding sensory part of a human by means of a local haptic device so that the human can feel various kinds of force haptic information (pressure, vibration, tremor, skin deformation, spatial resolution, sliding sensation, texture, material properties, spatial sensation, object stretching) in the remote environment or the virtual environment. Developed countries and regions such as the united states, japan, and the european union have long recognized the importance of haptic interactive feedback devices, and have been invested in a great deal of human, material, and financial research. The research in this aspect in China starts late, and at present, no manufacturers of man-machine interaction tactile feedback equipment exist in China. All domestic commercial human-computer interaction tactile devices completely depend on imports, key technologies of the devices in hardware and software are monopolized abroad, and only simple use interfaces are opened for users. Therefore, the development of an electrotactile feedback device with independent intellectual property rights is of great significance for breaking the monopoly of foreign technologies, and promoting the independent innovation and technological development of the electrotactile feedback technology and the related robot field.
In order to achieve a realistic reproduction of a remote environment or a virtual environment, the development of haptic feedback devices has become a current research hotspot and development trend. Compared with other types of touch equipment, the electric touch equipment has the advantages of lightness, convenience, simplicity, practicability, high stimulation resolution, high energy conversion efficiency, easiness in integration with various types of force feedback equipment, suitability for various microprocessors for control and the like. However, the accuracy and estimation algorithm of the hand skin-electrode bio-impedance model of the existing electrotactile device are still to be further improved. For example, professor Zhang Zhumao and Chaxinyu of Shanghai university of transportation studied electrotactile devices for blind reading (see in detail: Zhang Zhumao, Liujie, Zhao Yu, Yu autumn, Chaxinyu. design and implementation of finger-based tactile sense alternative vision system [ J ]. Chinese medical physics journal. 2009,4: 1293-1298.). Xufei of shanghai transportation university and zhangdingnational professor designed an electrotactile device for use in a haptic alternative vision system (see: zhanmao. development of finger-based haptic alternative vision system [ D ]. shanghai transportation university master academic paper, 2009). Jiang Liang and Zhou Qi professor of Chongqing university designed electrotactile and carried out the research of tactile sensation-visual substitution (see Jiang Ling. research of tactile sensation-visual substitution system based on skin electrostimulation [ D ]. Chongqing university Master academic thesis, 2013.). However, none of the above studies fully considers that the human hand-skin impedance model is a time varying system, because the impedance parameters of human finger skin vary with the amplitude and frequency of the current, and are also affected by the diameter of the electrode and the contact area of the finger. Furthermore, Yantao Shen et al, which simplifies the skin-electrode bio-impedance model of the electrotactile device human hand into a first-order model, estimated the finger skin-electrode impedance model (see YantaoShen, John group, Ning xi. Simulation Current Control for Load-aware electric characterization: Modeling and Simulation [ J ]. Robotics and analysis Systems,2014,62: 81-89.), but do not fully consider the model parameters between the finger epidermis and the electrodes.
Disclosure of Invention
The invention aims to provide a method for estimating parameters of a human hand skin-electrode bioimpedance model based on electrotactile equipment, which aims at the human hand skin-electrode bioimpedance model in the electrotactile equipment and time-varying characteristics thereof and adopts a recursive augmented least square method containing forgetting factors to estimate the parameters of the bioimpedance model in real time. The invention fully considers the biological relation between the human finger skin and the electrode impedance in the electric tactile device and the requirement on the real-time impedance estimation in the electric tactile device, establishes the finger skin-electrode bio-impedance model of the electric stimulation-based tactile device, and obtains each impedance parameter value in the model in real time by using a recursive augmented least square method.
The invention is realized by the following technical scheme.
The invention relates to a method for estimating parameters of a human hand skin-electrode bio-impedance model based on electrotactile equipment, which comprises the following steps:
(1) modeling of human hand skin-electrode bioimpedance
The laplace transform can be obtained from the epidermal-dermal-subcutaneous tissue electrical impedance model:
X(S)=Y(S)V(R1,R2,R3,C1,C2,S)
wherein X (S), Y (S) respectively represent Laplace transform formula of input voltage and output current, and V (R)1,R2,R3,C1,C2S) represents the laplace transform of the epidermal-dermal-subcutaneous tissue electrical impedance model, which is abbreviated as v (S). Therefore, x(s) ═ y(s) v(s), given the laplace transform and Z transform relationship:
X(Z)=Y(Z)V(R1,R2,R3,C1,C2,Z)
wherein X (Z), Y (Z) are Z transformation formulas of X (S), Y (S), V (R)1,R2,R3,C1,C2Z) is a Z transformation of the epidermal-dermal-subcutaneous tissue electrical impedance model, which is abbreviated as V (Z). Therefore, x (Z) ═ y (Z) v (Z), which was subjected to inverse Z transformation, was used to obtain an electrical impedance model of epidermal-dermal-subcutaneous tissue:
y(n)=-f1y(n-1)-f2y(n-2)+f3x(n)+f4x(n-1)+f5X(n-2)
wherein f is1,f2,f3,f4,f5Are all variable R1,R2,R3,C1,C2X (n), y (n) respectively represent the input voltage and the output current value obtained by the nth sampling.
The least squares parameter estimation model, which is derived from the order of this expression, is:
y(k)=-a1y(k-1)-a2y(k-2)+b0x(k)+b1x(k-1)+b2x (k-2) + e (k), wherein e (k) is system noise. Let this model be H (k), which isThe model constructed by the input-output relation sets the actual finger skin-electrode bio-impedance model as W (k), and the preset model H (k) can approach the actual model W (k) through a parameter estimation algorithm. Impedance parameter R1,R2,R3,C1,C2Coefficient a in W (k) which can be estimated by an algorithm1,a2,b0,b1,b2And (4) showing.
(2) And (3) augmented parameter estimation:
(a) the noise e (k) is not white noise but colored noise, so that the method can be more suitable for parameter estimation and system modeling under different noise conditions. Take e (k) ═ ε (k) + c1 ε (k-1) + c2 ε (k-2) where ε (k) is white noise with constant variance, and may be 0.1.
(b) The system model is written as:
y(k)=-a1y(k-1)-a2y(k-2)+b0x(k)+b1x(k-1)+ b2X(k-2)+ε(k)+c1ε(k-1)+c2ε(k-2)
let the actual parameter matrix be [ a ═ a1,a2,b0,b1,b2,c1,c2]T
Noting the parameter estimate matrix as
Figure BDA0001417260850000031
The initial value of the matrix is set to 0.
(3) Based on recursive least square online parameter estimation containing a forgetting factor u:
(a) and adopting a recurrence algorithm to realize online parameter identification by continuously adding new input and output data x (k) and y (k) to update the estimation parameters. If L groups of data are obtained, setting a transmission value matrix
Figure BDA0001417260850000032
T denotes transposing the matrix, where:
Figure BDA0001417260850000033
will be provided with
Figure BDA0001417260850000034
Record as
Figure BDA0001417260850000035
Initial value
Figure BDA0001417260850000036
Setting matrix
Figure BDA0001417260850000037
Taking the initial value P (0) ═ CI, where C is a sufficiently large constant, e.g. 106I is a 7 × 7 identity matrix, order
Figure BDA0001417260850000038
Figure BDA0001417260850000039
Obtaining a parameter estimate matrix
Figure BDA00014172608500000310
(see (b) of step (3)) is
Figure BDA00014172608500000311
(b) Introducing a forgetting factor u, so that
Figure BDA00014172608500000312
Become into
Figure BDA00014172608500000313
The parameter correction capability of the identification process is improved by applying a time-varying weighting coefficient to the data, and the value u is a constant close to 1, and can be 0.95<u<1. K (k) is changed to
Figure BDA00014172608500000314
Figure BDA00014172608500000315
P (k) is changed to
Figure BDA00014172608500000316
Figure BDA00014172608500000317
The matrix recursion is still estimated for the parameters.
(4) After the data obtained by the parameter matrix is converged, substituting the parameters in the obtained parameter matrix into a preset model
y(k)=-a1y(k-1)-a2y(k-2)+b0x(k)+b1x(k-1)+b2x(k-2)+ε(k) +c1ε(k-1)+c2ε(k-2)
Mathematical expression of electrical impedance model of epidermis-dermis-subcutaneous tissue
y(n)=-f1y(n-1)-f2y(n-2)+f3x(n)+f4x(n-1)+f5X(n-2)
Comparing the coefficients to obtain an equation set, and solving to obtain the parameter R1,R2,R3,C1,C2
The invention has the advantages that: the real-time requirement of the electrotactile device on impedance parameter estimation is fully considered, a recursion algorithm containing forgetting factors is adopted, new input and output data continuously provided by the electrotactile device are used for improving the estimation precision, the estimated value is modified when the parameter is changed, the online real-time estimation of the parameter is realized, and the reduction of the parameter correction capability after the recursion step number is too long is avoided; meanwhile, an augmentation model is adopted, and noise is reasonably assumed to be colored noise instead of white noise in an ideal state. The method is more suitable for practical conditions, can adapt to parameter estimation under different noise conditions, and avoids the interference of a single noise model on the parameter estimation. The invention has the advantages of reasonable total design, careful consideration, simple design, easy realization and strong adaptability.
Drawings
FIG. 1 is a schematic diagram of an electrical impedance model of epidermis-dermis-subcutaneous tissue.
FIG. 2 is a least squares parameter estimation model.
Detailed Description
The invention will be further illustrated by the following examples.
Step 1: modeling of human hand skin-electrode bioimpedance.
(a) The laplace transform can be obtained from the epidermal-dermal-subcutaneous tissue electrical impedance model:
Figure BDA0001417260850000041
wherein,
Figure BDA0001417260850000042
laplace transform form as impedance model
(b) Relationship between Laplace transform and Z transform (Z ═ e)And τ is the sampling period) to obtain:
Figure BDA0001417260850000043
wherein,
Figure BDA0001417260850000044
as Z-transformed form of an impedance model
(c) Item shifting is carried out:
Figure BDA0001417260850000045
(d) carrying out inverse Z transformation to obtain:
Figure BDA0001417260850000046
it is rewritten as:
Figure BDA0001417260850000047
(e) the order of the finger skin-electrode bioimpedance model (namely the least square parameter estimation model) can be preset according to the order of the formula (4), and the preset human hand skin-electrode bioimpedance model is written into a least square form:
Figure BDA0001417260850000048
Figure BDA0001417260850000051
in the formula,
Figure BDA0001417260850000052
for input and output data vectors, T denotes transposing the matrix, θ ═ a1,a2,b0,b1,b2]TFor the actual parameter vector, e (k) is the system noise.
Step 2: recursive least square online parameter estimation based on forgetting factor u
Let the estimated parameter vector be
Figure BDA0001417260850000053
The k-th estimated output corresponding to the L groups of data is
Figure BDA0001417260850000054
In the formula,
Figure BDA0001417260850000055
the difference between the actual output and the estimated output of the object, i.e. the residual epsilon (k), is
Figure BDA0001417260850000056
For L observations, the performance index is taken as follows:
Figure BDA0001417260850000057
the forgetting factor u (0) is introduced into the formula<u<1) That is, a time-varying weighting coefficient is applied to the data, the newest data is weighted by 1, and the previous k-th data is weighted by uL-kAnd (4) weighting. In a slow time-varying parameter system such as a finger-skin impedance model, a common recursive least square method has the phenomenon of data saturation along with the increase of data, namely as k increases, P (k) and K (k) become smaller and smaller, so that the pair
Figure BDA00014172608500000511
The correction capability of the parameter estimation method is weakened, so that the updating effect of newly added data on the parameter estimation value is small, and after a forgetting factor is introduced, the parameter updating mainly depends on the latest data, and the real-time performance and the accuracy of parameter estimation are greatly enhanced.
Least squares estimation of the required parameters, i.e. parameters which minimize the objective function (6)
Figure BDA0001417260850000058
For this purpose, the value of J is calculated
Figure BDA0001417260850000059
And let the derivative value be 0:
Figure BDA00014172608500000510
obtaining by solution:
Figure BDA0001417260850000061
in the formula
Y=[y(1),y(2),…,y(L)]T
Figure BDA0001417260850000062
And is
Figure BDA0001417260850000063
Therefore, the formula (7) is satisfied
Figure BDA0001417260850000064
J can be minimized.
Will be provided with
Figure BDA0001417260850000065
Record as
Figure BDA0001417260850000066
Wherein
Figure BDA0001417260850000067
For historical input and output data matrices weighted by forgetting factors,
Figure BDA0001417260850000068
for the current input-output data, Y is noted
Figure BDA0001417260850000069
Order to
Figure BDA00014172608500000610
Then
Figure BDA00014172608500000611
Obtained from (7):
Figure BDA00014172608500000612
obtained from (9) and (10):
Figure BDA00014172608500000613
the least squares estimate for time k can be expressed as:
Figure BDA00014172608500000614
in the formula,
Figure BDA00014172608500000618
matrix inversion theorem: let A, (A + BC) and (I + CA)-1B) Are all nonsingular square matrices, then
(A+BC)-1=A-1-A-1B(I+CA-1B)CA-1
Substituting the lemma into (8) to order
Figure BDA00014172608500000616
Obtaining:
Figure BDA00014172608500000617
substituting (14) into (13) to obtain:
Figure BDA0001417260850000071
obtained from (14), (15):
Figure BDA0001417260850000072
from (12), (15), (16):
the least square parameter estimation recurrence formula containing the forgetting factor is as follows:
Figure BDA0001417260850000073
and step 3: augmented parameter estimation
Introducing colored noise, i.e. taking noise e (k) ═ epsilon (k) + c1ε(k-1)+c2ε (k-2) (where ε (k) is white noise whose variance is constant, and may be 0.1) is substituted into (5) to obtain:
y(k)=-a1y(k-1)-a2y(k-2)+b0x(k)+b1x(k-1)+b2x(k-2)+ε(k) +c1ε(k-1)+c2ε(k-2) (18)
feeding back L groups of data with time sequence relation by the electric tactile feedback equipment, and inputting the data of input voltage x (k) and output current y (k) which correspond to each other one by one into a transmission value matrix
Figure BDA0001417260850000074
Wherein,
Figure BDA0001417260850000075
due to the fact that
Figure BDA0001417260850000076
Since epsilon (k) in (A) is not measurable, its estimated value is used
Figure BDA0001417260850000077
Instead of, i.e.
Figure BDA0001417260850000078
In the formula:
Figure BDA0001417260850000079
Figure BDA00014172608500000710
the matrix is evaluated for the new parameters.
By using
Figure BDA0001417260850000081
Instead of the former
Figure BDA0001417260850000082
Substituting (17) to obtain a recursive and augmented least square parameter estimation formula containing a forgetting factor
Is composed of
Figure BDA0001417260850000083
Setting an initial value
Figure BDA0001417260850000084
(
Figure BDA0001417260850000085
A 1 × 7 zero matrix), P (0) ═ 10^6 × I (I is an identity matrix of 7 × 7), a value transfer matrix is constructed:
Figure BDA0001417260850000086
let k<When 0, y (k) is 0, x (k) is 0, and epsilon (k) is 0, and each acquired input data is assigned tox (k), assigning output data to y (k), wherein epsilon (k) can be white noise with variance of 0.1, forgetting factor u can be 0.95, and each group of data can obtain parameter estimation value by formula (20)
Figure BDA0001417260850000087
Since the initial value of the estimation is set to 0, initially
Figure BDA0001417260850000088
The fluctuation of the value of (a) is large, and when the amount of data taken increases,
Figure BDA0001417260850000089
converge to a fixed value, i.e. obtain an estimated parameter value
Figure BDA00014172608500000810
Respectively correspond to a in the formula (18)1,a2,b0,b1,b2,c1,c2
And 4, step 4: calculating a value of a model impedance parameter
Substituting the estimated parameter values into equation (18): y (k) ═ a1y(k-1)-a2y(k-2)+b0x(k)+b1x(k- 1)+b2x(k-2)+ε(k)+c1ε(k-1)+c2ε (k-2) and
Figure BDA00014172608500000811
the formula compares the coefficients to obtain:
Figure BDA0001417260850000091
taking tau as 1, obtaining:
Figure BDA0001417260850000092
Figure BDA0001417260850000093
Figure BDA0001417260850000094
Figure BDA0001417260850000095
Figure BDA0001417260850000096
Figure BDA0001417260850000097
and obtaining corresponding impedance parameters of the human hand epidermis-dermis-subcutaneous tissue electrical impedance model.
In practical application, after a human finger is contacted with an electrode array of the electric touch equipment, a small electric stimulation is input from a constant voltage source to stimulate the finger through an electrode, the output current of the output end of the electrode is measured, then the amplitude of the input electric stimulation is continuously changed in a small range to obtain a group of data of input voltage x (k) and output current y (k), the data are substituted into a preset model, and an algorithm calculates a least square parameter a of a human hand skin-electrode bioimpedance model based on the group of data1,a2,b0,b1,b2Further, the impedance parameter R with physical significance in the model is obtained1,R2,R3,C1,C2. Because the finger skin-electrode bio-impedance model is a slow time-varying system, and the resistance and capacitance parameters change slowly, the input voltage can be adjusted based on the impedance parameters after the impedance parameters are measured, so that the output current with the characteristics of expected amplitude, frequency, pulse width and the like is obtained, and the purpose of realizing touch simulation by the electric touch equipment is achieved. In addition, because a recursion augmentation least square method based on forgetting factors is adopted, the model error correction method has better correction capability, has stronger tracking capability on slow change of parameters, and can enable the touch simulation to have better real-time performance. When the impedance parameter changes, the corresponding input/output data and input/output switchThe algorithm dynamically adjusts the impedance parameter R according to the newly added data1,R2,R3,C1,C2An estimate of (d). If it is desired to maintain the tactile sensation constant as the impedance parameter changes, the system may adjust the input stimulus in real time based on the real-time updated impedance parameter estimate to maintain the characteristics of the output current constant to stabilize the tactile sensation.

Claims (1)

1. A method for estimating parameters of a human hand skin-electrode bio-impedance model based on an electric tactile device is characterized by comprising the following steps:
(1) modeling of human hand skin-electrode bioimpedance
The laplace transform can be obtained from the epidermal-dermal-subcutaneous tissue electrical impedance model:
X(S)=Y(S)V(R1,R2,R3,C1,C2,S)
wherein X (S), Y (S) respectively represent Laplace transform formula of input voltage and output current, and V (R)1,R2,R3,C1,C2S) represents the Laplace transform of the epidermis-dermis-subcutaneous tissue electrical impedance model, which is abbreviated as V (S); x(s) ═ y(s) v(s), given by the laplace transform and Z transform relationship:
X(Z)=Y(Z)V(R1,R2,R3,C1,C2,Z)
wherein X (Z), Y (Z) are Z transformation formulas of X (S), Y (S), V (R)1,R2,R3,C1,C2Z) is a Z transformation formula of the epidermis-dermis-subcutaneous tissue electrical impedance model, which is abbreviated as V (Z); x (Z) ═ y (Z) v (Z), and the impedance model of epidermis-dermis-subcutaneous tissue is obtained by inverse Z transformation:
y(n)=-f1y(n-1)-f2y(n-2)+f3x(n)+f4x(n-1)+f5x(n-2)
wherein f is1,f2,f3,f4,f5Are all variable R1,R2,R3,C1,C2X (n), y (n) respectively represent the input voltage and the output current value obtained by the nth sampling;
the least squares parameter estimation model derived from the order of this expression is:
y(k)=-a1y(k-1)-a2y(k-2)+b0x(k)+b1x(k-1)+b2x (k-2) + e (k) wherein e (k) is system noise; setting the model as H (k), setting the actual finger skin-electrode bio-impedance model as W (k), and enabling the preset model H (k) to approach the actual model W (k) through a parameter estimation algorithm; impedance parameter R1,R2,R3,C1,C2Coefficient a in W (k) estimated by algorithm1,a2,b0,b1,b2Represents;
(2) and (3) augmented parameter estimation:
(a) noise e (k) is taken as colored noise, e (k) is taken as ∈ (k) + c1 ∈ (k-1) + c2 ∈ (k-2), where ∈ (k) is white noise with constant variance, which may be 0.1;
(b) the system model is written as:
y(k)=-a1y(k-1)-a2y(k-2)+b0x(k)+b1x(k-1)+b2x(k-2)+ε(k)+c1ε(k-1)+c2ε(k-2)
let the actual parameter matrix be [ a ═ a1,a2,b0,b1,b2,c1,c2]T
Noting the parameter estimate matrix as
Figure FDA0002371646550000011
Setting the initial value of the matrix as 0;
(3) based on recursive least square online parameter estimation containing a forgetting factor u:
(a) continuously adding new input and output data x (k) and y (k) to update estimation parameters by adopting a recurrence algorithm to realize online parameter identification; obtaining L groups of data, setting up a transmission value matrix
Figure FDA0002371646550000012
T denotes transposing the matrix, where:
Figure FDA0002371646550000013
will be provided with
Figure FDA0002371646550000014
Record as
Figure FDA0002371646550000015
Initial value
Figure FDA0002371646550000016
Setting matrix
Figure FDA0002371646550000017
Taking an initial value P (0) ═ CI, where C is a sufficiently large constant and I is a 7 × 7 identity matrix, let
Figure FDA0002371646550000018
Figure FDA0002371646550000021
Obtaining a parameter estimate matrix
Figure FDA0002371646550000022
Is composed of
Figure FDA0002371646550000023
Figure FDA0002371646550000024
(b) Introducing a forgetting factor u, so that
Figure FDA0002371646550000025
Become into
Figure FDA0002371646550000026
The parameter correction capability in the identification process is improved by applying a time-varying weighting coefficient to the data, the value u is a constant close to 1, and u is more than 0.95 and less than 1; k (k) is changed to
Figure FDA0002371646550000027
Figure FDA0002371646550000028
P (k) is changed to
Figure FDA0002371646550000029
Figure FDA00023716465500000210
Still parameter estimation matrix recursion;
(4) after the data obtained by the parameter matrix is converged, substituting the parameters in the obtained parameter matrix into a preset model
y(k)=-a1y(k-1)-a2y(k-2)+b0x(k)+b1x(k-1)+b2x(k-2)+ε(k)+c1ε(k-1)+c2ε(k-2)
Mathematical expression of electrical impedance model of epidermis-dermis-subcutaneous tissue
y(n)=-f1y(n-1)-f2y(n-2)+f3x(n)+f4x(n-1)+f5(n-2)
Comparing the coefficients to obtain an equation set, and solving to obtain the parameter R1,R2,R3,C1,C2
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