KR100837576B1 - Vibration controlling method of structure - Google Patents

Abstract

A method for controlling oscillation of structures is provided to apply a control force to the structure by utilizing grating typed training patterns based on CMAC(Cerebellar Model Articulation Controller). Grating typed training patterns having a status vector by displacement(u) and speed, and a control force are formed. Distances with four training patterns are obtained by using the status vector of structures on an external force and a grating probabilistic neural network. By applying a large weighted value to control force corresponding to close training patterns and a small weighted value to control force corresponding to distant training patterns, four control forces(fc) are processed. By adding control force variation amounts to the processed control force, the added force is applied to the structure.

Description

Vibration controlling method of structure

1 shows a basic conceptual diagram of a grid probability neural network composed of a state vector and a control force.

2 shows a conceptual diagram of class regions and boundaries.

3 shows a Parzen method for density function estimation.

4 shows the structure of a probabilistic neural network.

5 shows the structure of the learning layer.

6 shows a structure to be applied according to the present invention.

7 shows a grid probability neural network controller block diagram according to the present invention.

The present invention relates to a vibration control method of a structure, and more particularly, to a vibration control method of a structure for controlling vibration of an external force using a grid probability neural network obtained by introducing a basic concept of a cerebellar model articulation controller (CMAC). It is about.

In general, modern structures have been increased and enlarged due to the development of new materials and construction techniques, but the structures easily vibrate against external loads, and excessive vibrations cause serious damage to the usability and structure.

Therefore, damping against external force of the structure has become a very important technology especially in the recent building and other structures which are getting higher.

In the vibration damping method, input the 'active control method' to reduce the vibration of the structure by applying the control force corresponding to the vibration of the structure inside and outside the structure by measuring the vibration from the outside and thus the structure's vibration. There is a 'manual control method' that controls the structure by responding to the characteristics of vibration.

Existing active control methods include optimal control, fuzzy control, neural network control, etc. The present invention is an active control method using a grid probability neural network.

The technical problem to be achieved by the present invention is to provide a vibration control method that can minimize the damage and risk of the structure due to vibration.

The present invention to achieve the above technical problem,

Forming a training pattern in the form of a lattice consisting of a state vector consisting of displacement and velocity and a control force;

Using a grid probability neural network to obtain a distance from each of the four training patterns using four training patterns adjacent to the structure state vector of the structure;

Combining the four control forces by giving a large weight to the control force corresponding to the training pattern close to the distance and giving a small weight to the control force corresponding to the training pattern far from the distance;

Adding a control force change amount and the combined control force in the above step and applying it to the structure; And

Distributing a value obtained by multiplying a control force change amount and a weight to a control force corresponding to four existing training patterns to update the existing control force.

Hereinafter, the present invention will be described in more detail.

Vibration control method of the structure according to the present invention is a method that can minimize the damage and risk of the structure due to the vibration, it is to control the vibration of the structure receiving the external force using the grid probability neural network. The grid probability neural network according to the present invention applies a control force corresponding to the state vector of the structure with respect to the external force by using the training pattern of the grid shape to the structure, thereby controlling the vibration of the structure, the training pattern of the grid It can be upgraded to an optimal training pattern through learning.

In the vibration control method according to the present invention, a training pattern in the form of a lattice formed of a state vector and a control force of displacement and velocity is formed, and each distance is obtained by using four training patterns adjacent to a state vector of the structure for external force. Then, a large weight is given to a control force corresponding to a training pattern with a close distance, and a small weight is given to a control force corresponding to a training pattern with a long distance, and a weight proportional to the distance is calculated for each of these four control forces. It is determined by the control power.

The control force may be expressed as a product of the state vector of the structure and the control gain as shown in Equation 1 below:

<Equation 1>

In the formula, z denotes the state vector of the structure, G denotes the control gain, [R] denotes the weight matrix, [L _e ] denotes the position of the external force in the state space, and [S] Represents the solution of the Riccati matrix equation:

<Equation 2>

[Q] and [R] represent a weight matrix, [A] represents a system matrix, and T represents a transpose matrix.

Equation 1 representing the control force can be obtained through the following process.

[Equation 21]

에 비례하는 외력하중이며,

및

는 제어력과 외력의 작용 위치를 0과 1로 나 타내고 있는 위치행렬로 다음과 같다:Where [M], [C] and [K] are n X n mass, damping and stiffness matrices, respectively, {u (t)} is the relative displacement of the structure, {f _c (t)} is the control force vector, { f _e (t)} is the earthquake load

Is an external force proportional to

And

Is a position matrix representing the positions of control and external forces acting as 0 and 1 as follows:

는 지진시 지반가속도이며,

및

는 일구현예에서는 1층 구조물에 대한 예로 제어력과 외력의 위치가 1만 존재한다. 상기 수학식 21을 바로 사용하기는 매우 어려우므로 상기 수학식 21을 하기 수학식 22의 상태공간방정식으로 전개해야 된다. 전개 과정은 다음과 같다. From here

Is the ground acceleration during the earthquake,

And

In one embodiment, there is only one position of control force and external force as an example of a one-story structure. Since it is very difficult to directly use Equation 21, Equation 21 should be developed as the state space equation of Equation 22 below. The development process is as follows.

In Equation 21, if the inverse of the mass matrix [M] is multiplied by both sides, the following equation is obtained.

로 나타내면 상기 수학식 1은 다음과 같이 나타낼 수 있다.Displacement and velocity terms in state vector

Equation 1 can be expressed as follows.

In other words

The above equation can be expressed as a state-space equation in the form of the following determinant.

[Equation 22]

here

Where {z (t)} is a state vector, [A} is a system matrix, and [L _c ] and [L _e ] are matrices representing the positions of the control and external forces in the state space.

The state space equation can be simulated into a structure using Matlab Simulink. The training pattern of the grid probability neural network controller configures the control force corresponding to the state vector and the state vector between the maximum and minimum responses of the structure before the control in a grid form as shown in FIG. 1, and the control force is represented by Equation 1 below. It can be found as the product of the state vector of and the control gain.

<Equation 1>

The control gain [G] can be obtained from [S] which is the solution of the Riccati matrix equation of Equation 2 below.

<Equation 2>

[Q] and [R] represent the weight matrix.

The present invention introduces the basic concept of CMAC (Cerebellar Model Articulation Controller) to solve the vibration problem of the structure, develops the probabilistic neural network theory, suggests the active control algorithm and the learning method of the structure, and the state space of the structure before control. We proposed a method of constructing a training pattern in the form of a grid using the maximum and minimum values of the (state-space) vector and the control gain (G). Also, the structure is controlled by the proposed method for seismic loads, and the method of upgrading the existing training pattern is also proposed with the control of the structure as the learning method using the best descending method. The following is a basic probability neural network theory underlying the present invention.

You can use class analysis when you need to classify the data obtained from experiments or samples into several homogeneous classes (classes or clusters) according to some property. Class analysis, one of the multivariate analysis methods, is to measure the degree of similarity between N entities using the observed P variables when the P variables are measured for N entities. It is a statistical analysis method that classifies objects in order of distance, represented by distance (or quantified). A typical class analysis process is as follows.

(1) Measure by setting P variables for N individuals.

(2) Calculate the distance matrix by calculating the distance between all objects. Here, the closer the distance between individuals, the greater the similarity between them.

(3) Classify objects into classes based on distance matrices.

In general, the main measures of distance for two vectors X ₁ and X ₂ are Euclidean distance, Chebychev distance, and City-block or Manhattan distance. The larger the similarity between two individuals, the smaller the smaller.

Probabilistic Neural Network (PNN) is a classifier that determines which entity belongs to which class by combining Bayes decision theory and Parzen Window method for estimating probability density function (see FIG. 2). Probabilistic neural networks are modeled by algorithms learned from two or more training patterns, and the distance to classes for an input entity is determined to determine the class to which the entity belongs.

The classification of types is essentially the minimization of expected risk in classification, and Bayesian decision-making is one of these methods and can be applied to problems involving multiple classes. For example, suppose that θ is one of classes A and B, θ _A or θ _B. Vector of order p X = [X ₁ ... X _j … The Bayesian probability method for determining whether θ = θ _A or θ = θ _B using the measure represented by X _p ] ^T is as follows.

Where f _A (X) and f _B (X) are the Probabilistic Density Functions (PDF) for classes A and B, respectively, and _A and l _B are the loss coefficients associated with the bad decision, respectively. . If the error is an accurate decision, the loss factor is zero. H _A is the prior probability that θ = θ _A , and h _B = 1-h _A is the prior probability that θ = θ _B. When Bayesian decision theory is used, assuming that the prior probability h and the loss factor 1 are the same for all classes, the class is determined only by the probability density function.

Parzen (1962) has shown that if the sum of the probability density functions of the classes is continuous, it is asymptotic with the overall density function (see FIG. 3). As shown in FIG. 3, when the probability density functions of the variables have the same Gaussian distribution, it can be estimated as one probability density function by the Parzen window as follows.

Where X is the input pattern to classify, m is the number of all training patterns, X _Ai is the i-th training type in class θ _A , σ is the smoothing coefficient, and p is the dimension of the training vector. T is a symbol representing a transpose matrix. f _A (X) is a simple sum of Gaussian multivariate distributions, but need not necessarily be Gaussian. When a small σ (smoothing coefficient) is used, f _A (X) has a peak that is completely separated from each other at the positions of the training patterns, and as σ is used, f _A (X) is gradually flattened. . In the case of m = ∞, we approach the Gaussian distribution regardless of the probability density function f _A (X).

4 illustrates a probability neural network structure for classifying the input pattern X into two classes. The input layer is a kind of distributing layer that inputs the same input pattern to all training types, and the pattern layer is the dot product of the weight vector W _i and the input pattern X for each training pattern (Z _i = X after obtaining a · W _i), by entering the Z _i to a non-linear activation functions (activation function) performs a non-linear operation (see Fig. 5). As shown in FIG. 5, the stochastic neural network theory uses a nonlinear operator instead of the sigmoid activation function used in the back propagation neural network. Normalizing X and W _i to unit size, a nonlinear operator looks like this:

The summation layer simply sums up the results obtained by the above method for each class. The output layer selects the final class by outputting the class having the largest sum from the summing layer as 1 and the rest as 0.

의 두 개의 입력에 대하여 하나의 결과(제어력)를 출력하는 CMAC의 기본적인 개념도이며, CMAC의 기본개념은 입력 u와

에 해당하는 결과를 좌표에서 출력하는 것이다. 격자확률신경망은 훈련패턴을 등 간격으로 규정할 수 있는 경우에 보다 효율적으로 사용할 수 있어 바람직하지만, 이에 한정되는 것은 아니다.In relation to a probability neural network (PNN) (hereinafter referred to as a lattice probability neural network) incorporating a CMAC concept according to the present invention, FIG. 6 shows the displacement u and velocity of the structure.

This is a basic conceptual diagram of CMAC that outputs one result (control force) for two inputs. The basic concept of CMAC is the input u and

Outputs the result of the coordinates. The grid probability neural network can be used more efficiently when training patterns can be defined at equal intervals, but is not limited thereto.

The structure of the grid probability neural network is composed of an input layer, a learning layer, a summation layer, and an output layer, and follows the structure of the existing probability neural network, but has a difference in that the structure of the learning layer is different. In the existing learning layer, the similarity was determined using Euclidian distance for the input type and all training patterns, but in the grid probability neural network according to the present invention, only the training patterns around the displacement and velocity of the structure corresponding to the input type were used. The similarity is determined so that the calculation time can be drastically reduced. For example, in FIG. 6, the control forces to be applied to the structure when the displacement of the structure = 3.2 and the speed = 4.7 are compared with the displacements of the control forces f ₃₄ , f ₃₅ , f ₄₄ and f ₄₅ around the displacement = 3.2 and the speed = 4.7. The control force is determined by calculating the distance from the speed and calculating a weight proportional to the distance for each. In addition, the training pattern made of the control power is learned by the learning rule to be described later, the update is made to the optimal training pattern.

The distance and the weight may be obtained by the following Equations 3 and 4.

[Equation 3]

Where x is the state vector of the structure and y is the training pattern of the grid. dist means the distance representing the similarity of the four training patterns to the state vector of the structure.

[Equation 4]

Where sd is the sum of the distances from the four training patterns obtained in Equation 3, pd _i is the weighted participation rate of the i th training pattern, sp is the sum of four pd _i , and w _i is four according to the distance. It represents the weight of the training pattern.

[Equation 5]

Here, f _c is four control forces corresponding to the four training patterns, and f _{c, k} is a control force considering weights of the four control forces, and is a control force to be applied to the current structure in addition to Equation 9 below.

According to one embodiment of the present invention, the control force applied to the structure may be represented by the sum of the control force considering the weight and the control force change amount obtained by the steepest descent method described below.

[Equation 6]

Where {z} _{k + 1} is the response (state vector) of the structure at k + 1 time, {f _c } _k is the control force at k time, N _f is the final time interval, [Q] and [R ] Represents a weighting matrix having sizes 2n × 2n and m × m, respectively.

According to an embodiment of the present invention, it is preferable that learning of the training pattern is performed by a learning rule according to Equation 7 below:

[Equation 7]

Where f _{c, k + 1} represents the control force at time k + 1, f _{c, k} represents the control force obtained by Equation 5 above, and Δf _c represents the amount of change of the control force according to the learning rule as follows:

[Equation 8]

Where η represents a learning rate.

According to one embodiment of the present invention, the change amount of the control force of Equation 8 is multiplied by the weight of Equation 4 to distribute this value to the control force corresponding to the existing four training patterns to update the existing control force, The change amount of the control force may be represented by the following Equations 9 and 10 when the partial derivative of the control force and the objective function is δ.

[Equation 9]

[Equation 10]

: 단위 제어력에 대한 구조물의 응답)는 다음과 같은 민감도 계산법에 의해서 구할 수 있다. The sensitivity of the response in Equation (10)

The response of the structure to unit control forces can be obtained by the following sensitivity calculation method.

The sensitivity of the response can be easily obtained if the equation of motion of the structure is clearly defined. The state-space equation of the structure is shown in Equation 22, and when discretized, is shown in Equation 11 below.

[Equation 22]

[Equation 11]

G (n X n) and H (n X m) are as follows using zero-order-hold approximation.

If Equation 11 is differentiated with respect to the control force in k time, Equation 12 can be obtained.

[Equation 12]

As can be seen from Equation 12, the sensitivity of the response is the same as obtaining the H matrix. The condition for applying unit control force only to the i-th controller when the structure is stationary to obtain H matrix is as follows.

In this case, Equation 11 is as follows.

Where h _i is the i-th column vector of the H matrix. That is, h _i refers to the response of the structure occurring after one sample step. H matrix can be obtained by applying unit control force to each controller and measuring the response after one sample step.

According to one embodiment of the present invention, the amount of change in the control force of Equation 9 is added to the control force obtained from the lattice of Equation 5 to calculate the final control force of Equation 7 and to apply the control force to the structure.

Example

According to the above procedure according to the present invention it is possible to reduce the vibration of the structure by using the grid probability neural network, and the active control of the structure was performed with respect to FIG.

The vibration control process of the structure is shown as a block diagram of the grid probability neural network controller for the seismic load of FIG. 7, and provides control to the structure through the grid probability neural network controller. Matlab Simulink was used to simulate the control of the structure.

A detailed vibration control process of FIG. 6 receiving an earthquake load is as follows.

A training pattern in the form of a lattice consisting of a state vector consisting of displacement and velocity and a control force is made as shown in FIG. 8.

The Northridge earthquake of FIG. 9 is entered into the structure.

The displacement and velocity of the structure at time 0.152 sec are 0.0073e-3 (m) and 0.1706e-3 (m / sec), and the displacement and velocity of the grid training pattern around the displacement and velocity of the structure is 0, 0), 2 points (0, 0.01), 3 points (0.0001, 0), 4 points (0.0001, 0.01). Using Equation 3 and Equation 4, the distance between the state vector of the structure and the four points of the lattice training pattern is calculated and the weight is 0.3304, 0.176, 0.3182, and 0.1753, respectively. Multiplying this weight by the control forces 0, -9.5132, -0.0001, and -9.5133 at four points through Equation 5 yields a weighted control force of -3.3429 in the grid.

The value through Equation 10 is -3.6941, and the change in control power is -0.3694 by multiplying by the learning rate 0.1 in Equation 9.

The weighted control force of Equation 5 obtained in the above process -3.3429 and the change amount of the control force obtained in Equation 9 -0.3694 are added as in Equation 7 to be -3.7123. This force is applied to the structure, and the displacement and velocity of the structure at 0.156 seconds next time are 0.0069e-3 (m) and -0.3630e-3 (m / sec), and the displacement is 0.0073e-3 (m) It can be seen from the figure to 0.0069e-3 (m).

The change of the control force obtained from Equation 9 -0.3694 and the weights 0.3304, 0.176, 0.3182, and 0.1753 obtained above are respectively multiplied by 0, -9.5132, -0.0001, and -9.5133 to -0.1220, -0.0650, -0.1175, If you add -0.0647, the existing control is updated to -0.1220, -9.5782, -0.1176, and -9.578.

The vibration control process of the above structure shows an interval of 0.004 hours between 0.152 seconds and 0.156 seconds, and when the structure is controlled for the entire time, the control result is reduced before the displacement and the speed are controlled as shown in FIGS. 10 and 11. It can be seen.

The present invention develops the grid probability neural network by introducing the basic concept of CMAC into the theory of probability neural network, and controls the vibration of the structure under external force based on the developed theory. The grid probability neural network according to the present invention applies a control force corresponding to the structure's state vector with respect to the external force by using the training pattern of the grid shape to control the vibration of the structure. In addition, the training pattern of the grid can be upgraded to the optimal training pattern through learning.

Claims (8)

Forming a training pattern in the form of a lattice consisting of a state vector consisting of displacement and velocity and a control force; Using a grid probability neural network to obtain a distance from each of the four training patterns using four training patterns adjacent to the structure state vector of the structure; Combining these four control forces by giving a large weight to the control force corresponding to the training pattern close to the distance, and giving a small weight to the control force corresponding to the training pattern far from the distance; And And adding a control force change amount and the combined control force to the structure. The method of claim 1, Distributing the control force change amount to the four control forces in consideration of the weight; Vibration control method of a structure characterized in that it further comprises. The method of claim 1, The control force is a vibration control method of a structure, characterized in that the product of the structure state vector and the control gain as shown in Equation 1 below: <Equation 1>

Where f _c is the control force, z is the state vector of the structure, G is the control gain, [R] is the weight matrix, [L _e ] is the matrix representing the position of the external force in the state space, and [S] is The solution of the Ricati matrix equation of Equation 2: <Equation 2>

[Q] and [R] represent a weight matrix, [A] represents a system matrix, and T represents a transpose matrix. The method of claim 1, The vibration control method of the structure, characterized in that the distance between the state vector of the structure and the four training patterns adjacent to the external force is obtained by the following equation: <Equation 3>

Where x is the state vector of the structure and y is the training pattern of the grid. dist is the distance representing the similarity of the four training patterns to the state vector of the structure. The method of claim 4, wherein Vibration control method of a structure, characterized in that to calculate the weight proportional to the distance using Equation 4 below: <Equation 4>

Where dist is the distance representing the similarity of the training pattern to the state vector of the structure, sd is the sum of the distances from the four training patterns obtained in Equation 3 above, and pd _i is the weighted participation rate of the i-th training pattern, sp Denotes the sum of four pd _i , and w _i denotes the weight of four training patterns according to distance. The method of claim 1, The vibration control method of the structure, characterized in that the amount of change in the control force is obtained by the following equation: [Equation 8]

Here, η represents a learning rate, f _c and _ij are control powers obtained by a learning rule (quick descent method), and J _k , represents an objective function in k time. The method of claim 1, When the amount of change in the control force is a partial derivative with respect to the control force and the objective function is δ, the vibration control method of the structure, characterized in that obtained by the following equation (9) and (10):  [Equation 9]

[Equation 10]

In the above formula, f _c , _ij is the control power obtained by the learning rule (highest descent), η is the learning rate, z is the state vector of the structure, k is the variable of time, R is the weight matrix, f _c , _k is k time Control. The method of claim 7, wherein The control force variation of Equation 9 is multiplied by the weight of Equation 4 below to distribute this value to the control force corresponding to the existing four training patterns to update the existing control force of the structure, characterized in that Vibration Control Method: [Equation 4]

In the above equation, w is the weight of the training pattern according to the distance indicating similarity, pd _i is the weight participation rate of the i-th training pattern, sp is the sum of the four pd values, sd is the sum of the distances from the training pattern, and dist is the The distance representing the similarity of four training patterns with respect to the state vector is shown.

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