KR20130141226A - Method and system for estimating unknown heat - Google Patents

Abstract

A method and system for estimating an unknown heat source are provided. According to an embodiment of the present invention, the method for estimating, from measured temperature data, an unknown heat source of which the temperature changes according to the passage of time comprises the step of: obtaining the measurement data of temperatures measured by temperature sensors; obtaining, based on the measurement data, operation data of temperatures operated according to the location of the unknown heat source and the passage of time; setting an objective function for the unknown heat source based on the measurement and operation data; and producing the optimal solution of the objective function by a distributed particle swarm optimization - quantum infusion (DPSO-QI) scheme. [Reference numerals] (AA) Start;(BB) End;(S110) Obtain the measurement data of temperatures measured by temperature sensors;(S120) Obtain the operation data of temperatures operated according to the location of the unknown heat source and the passage of time on the basis of the measurement data;(S130) Set an objective function for the unknown heat source based on the measurement and operation data;(S140) Produce the optimal solution of the objective function by a DPSO-QI scheme

Description

[0001] The present invention relates to a method and system for estimating an unknown heat source,

The present invention relates to an unknown heat source estimation method and system, and more particularly, to a method and system for estimating an unknown heat source in an inverse problem through a DPSO-QI (Distributed Particle Swarm Optimization-Quantum Infusion) And a system and method for estimating an unknown heat source.

Recently, inverse heat conduction technique has been widely applied to various fields. In practice, it is difficult to install a temperature sensor at a desired position in a system, so that a desired temperature can be predicted through an inverse thermal conduction analysis method. For example, if the heat flux or temperature history at the solid surface is known as a time function, the temperature distribution inside can be inferred using inverse thermal conduction techniques.

This inverse thermal conduction technique can be classified into finding the boundary conditions of the surface, finding the shape of an object whose part of the boundary is unknown, finding the unknown heat source through the temperature distribution measured at a specific position in the object, Many techniques have been proposed to solve the inverse problem of finding an unknown heat source.

In contrast to estimating the temperature of a specific location where a known heat source is known through a governing equation or the like, the heat conduction station problem is a reverse process of estimating unknown heat source information through temperature information at a specific location measured using a sensor or the like . This heat conduction problem is an ill-posed problem in which the stability of the solution is not guaranteed. That is, the information of the heat source is not unique or difficult to accurately estimate.

Recently, various studies have been made to solve the heat conduction problem effectively, but it is required to develop a technique for estimating the unknown heat source more efficiently and precisely.

DISCLOSURE OF THE INVENTION The present invention has been made to solve the above problems and it is an object of the present invention to provide a DPSO-QI (Distributed Particle Swarm Optimization-Quantum Infusion) technique capable of more accurately and accurately estimating an unknown heat source in an inverse problem A method and system for estimating an unknown heat source.

The problem to be solved by the present invention is to solve the ill-posed problem in which the stability of the solution is not guaranteed in the inverse problem through the normalization technique, so that the unknown heat source can be estimated more quickly and accurately A method and system for estimating an unknown heat source.

Problems to be solved by the present invention are not limited to the above-mentioned problems, and other problems not mentioned will be clearly understood by those skilled in the art from the following description.

According to an aspect of the present invention, there is provided an unknown heat source estimating method for estimating an unknown heat source whose temperature varies with time from measured temperature data, Obtaining measurement data of the measured temperature; Obtaining calculation data of a temperature at which the temperature of the unknown heat source is calculated based on the measurement data; Setting an objective function for the unknown heat source based on the measurement and calculation data; And a DPSO-QI (Distributed Particle Swarm Optimization-Quantum Infusion) technique to calculate an optimal solution of the objective function.

According to another aspect of the present invention, there is provided an unknown heat source estimation system for estimating an unknown heat source whose temperature varies with time from measured temperature data, A temperature sensor for acquiring a temperature of the fuel cell; A temperature calculator for calculating the temperature and the temperature of the unknown heat source based on the measurement data to obtain calculation data; An objective function setting unit for setting an objective function for the unknown heat source based on the measurement and calculation data; And a DPSO-QI unit for calculating an optimal solution of the objective function through a DPSO-QI (Distributed Particle Swarm Optimization-Quantum Infusion) technique.

Other specific details of the invention are included in the detailed description and drawings.

According to the present invention, an ill-posed problem in which the stability of a solution is not guaranteed in a heat conduction inverse problem can be solved through a normalization technique.

In addition, the DPSO (Distributed Particle Swarm Optimization - Quantum Infusion) technique can estimate the unknown heat source more efficiently and precisely than the unknown heat source in the inverse problem.

1 is a flowchart of an unknown heat source estimation method according to an embodiment of the present invention.
2 is a sectional view of the one-dimensional heat conductive rod.
3 and 4 are graphs for explaining the PSO algorithm.
5 is a graph showing the result of applying the PSO algorithm.
FIGS. 6 and 7 are diagrams for explaining the difference between the PSO algorithm and the method using the DPSO-QI algorithm used in the embodiments of the present invention.
8 is a detailed flowchart of an unknown heat source estimation method applying the DPSO-QI algorithm used in the embodiments of the present invention.
FIG. 9 is a diagram for explaining a function of performing a constraint condition. FIG.
10 is a graph showing the results of applying the PSO algorithm and the DPSO-QI algorithm.
FIG. 11A is a graph showing a result of applying the PSO algorithm when the heat source is located at the first position in the one-dimensional bar of FIG. 2, and FIG. 11B is a graph illustrating the result of applying the DPSO-QI algorithm.
FIG. 12A is a graph showing a result of applying the PSO algorithm when the heat source is located at the second position in the one-dimensional bar of FIG. 2, and FIG. 12B is a graph showing the result of applying the DPSO-QI algorithm.
13 is a configuration diagram of an unknown heat source estimation system according to an embodiment of the present invention.
14 is a configuration diagram of a DPSO-QI unit according to an embodiment of the present invention.
15A and 15B are graphs showing the results according to the normalization coefficient when various algorithms are applied to the one-dimensional bar of FIG.

Advantages and features of the present invention and methods for achieving them will be apparent with reference to the embodiments described below in detail with the accompanying drawings. The present invention may, however, be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Is provided to fully convey the scope of the invention to those skilled in the art, and the invention is only defined by the scope of the claims. Like reference numerals refer to like elements throughout.

Although the first, second, etc. are used to describe various elements, components and / or sections, it is needless to say that these elements, components and / or sections are not limited by these terms. These terms are only used to distinguish one element, element or section from another element, element or section. Therefore, it goes without saying that the first element, the first element or the first section mentioned below may be the second element, the second element or the second section within the technical spirit of the present invention.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. In the present specification, the singular form includes plural forms unless otherwise specified in the specification. As used herein, the terms "comprises" and / or "made of" means that a component, step, operation, and / or element may be embodied in one or more other components, steps, operations, and / And does not exclude the presence or addition thereof.

Unless otherwise defined, all terms (including technical and scientific terms) used in the present specification may be used in a sense that can be commonly understood by those skilled in the art. Also, commonly used predefined terms are not ideally or excessively interpreted unless explicitly defined otherwise.

Hereinafter, the present invention will be described in more detail with reference to the accompanying drawings.

1 is a flowchart of an unknown heat source estimation method according to an embodiment of the present invention.

The unknown heat source estimation method estimates an unknown heat source whose temperature varies with time from the measured temperature data, and obtains measurement data of the temperature measured by the temperature sensor (S110), and based on the measurement data, (S120), and sets an objective function for the unknown heat source on the basis of the measurement and calculation data (S130). Then, the DPSO-QI (Distributed Particle Swarm Optimization - Quantum Infusion) technique, the optimal solution of the objective function is calculated (S140).

Specifically, a method of estimating an unknown heat source will be described with respect to one-dimensional heat conduction. 2 is a sectional view of the one-dimensional heat conductive rod.

에서 변하는 열원(heat source)

가 있으며, 막대의 양 끝단은 단열 상태이다. 도 2에 도시한 1차원 막대의 경우에 1차원 열전도 지배 방정식을 다음의 수학식 1과 같다.In Fig. 2, the length of the rod is L and has a constant thermal conductivity. Specific location

A heat source that varies in the < RTI ID = 0.0 >

And both ends of the rod are insulated. In the case of the one-dimensional bar shown in FIG. 2, the one-dimensional heat conduction governance equation is expressed by Equation 1 below.

Here, the boundary condition (e.g., adiabatic condition) and the initial temperature condition are expressed by the following equations (2) and (3), respectively.

는 밀도, C는 비열, K는 전도 계수이고,

인 디락 델타 함수(Dirac delta function)이다.Here, T (x, t) means the temperature at position x at time t,

Is the density, C is the specific heat, K is the conduction coefficient,

Which is a Dirac delta function.

Equation (1) can be represented by the following Equation (4) by discretizing Crank-Nicolson by an implicit finite difference equation.

는 j번째 시간에서 i번째 격자 간격의 위치에서의 온도이고(i=1,2,...,Nx, Nx는 위치 격자의 수; j=1,2,...,Nt, Nt는 위치 격자의 수),

는 증가 시간의 크기이며,

는 거리 간격이다. 또한,

는 G(t)의 j번째의 값을 의미한다. 따라서, G(t)의 개수는

와 같다.From here,

..., Nt, Nt is the temperature at the position of the ith grid interval at the jth time (i = 1, 2, ..., Nx, Nx is the number of position grids; Number of gratings),

Is the magnitude of the increase time,

Is the distance interval. Also,

Denotes the j-th value of G (t). Therefore, the number of G (t) is

Same as

Accordingly, the calculated temperature T for the desired position and time can be obtained by Equation (4). That is, it is possible to obtain the calculated temperature T at the position where the sensor is attached through the estimated temperature G (t). If the estimated unknown heat source G (T) is equal to the actual heat source, The calculated temperature Y and the calculated temperature T will become equal.

Thus, an optimization problem of finding an unknown heat source G (T) that reduces the difference between the temperature Y measured through the sensor and the calculated temperature T can be derived. The derivation of this optimization problem is to set the objective function for the unknown heat source using the measured temperature Y and the calculated temperature T. [ To set the objective function, Least Square Method can be used. Therefore, the objective function for the unknown heat source can be set based on the measured temperature Y and the calculated temperature T using Least Square Method. The objective function set in this manner is expressed by Equation (5).

는 측정 종료 시간이며, 상기 Y는 측정 온도, 상기 T는 연산 온도, 상기 G는 미지의 열원의 추정 온도이다.Here, x is a measurement position, t is a measurement time, n is a number of temperature sensors,

Y is the measurement temperature, T is the calculation temperature, and G is the estimated temperature of the unknown heat source.

On the other hand, there may arise a case where an inaccurate result is derived due to a measurement noise and an error of a mathematical calculation. Regularization techniques can be introduced to solve and stabilize such ill-posed problems.

Therefore, the normalization term can be added to the objective function set by the Least Square Method through the Tikhonov regulation method. Accordingly, Equation (5) can be replaced with Equation (6).

이며,

는 정규화 계수, m은 정규화 차수, L은 1차원 막대의 길이이다. 그리고, 상기 x는 측정 위치, 상기 t는 측정 시간, 상기 n은 온도 센서의 개수, 상기

는 측정 종료 시간이고, 상기 Y는 측정 온도, 상기 T는 연산 온도, 상기 G는 미지의 열원의 추정 온도를 의미한다.From here,

Lt;

Is the normalization coefficient, m is the normalized order, and L is the length of the one-dimensional bar. X is the measurement position, t is the measurement time, n is the number of temperature sensors,

Y is the measurement temperature, T is the calculation temperature, and G is the estimated temperature of the unknown heat source.

In general, the normalized order m is assigned as 0 or 1 in Equation (6). If m is assigned as 0, the normalization term is an objective function that reduces the norm of a given function vector. Also, when m is assigned to 1, the normalization term is an objective function to reduce the vibration characteristics of a given function.

는 정규화 매개 변수로서

의 영향에 따라 안정화 정도가 달라진다. 만일

가 0에 가까워지면 정규화 항의 영향은 사라져 진동의 영향과 불안정한 해가 도출될 것이고,

가 커진다면 해는 감쇠되고 정확한 해로부터 벗어나게 될 수 있다.In Equation (6) above,

As a normalization parameter

The degree of stabilization varies depending on the influence of the influence. if

Is close to zero, the influence of the normalization term disappears and the influence of the vibration and the unstable solution will be obtained,

If it is large, the solution is attenuated and can be deviated from the exact year.

In order to solve the optimization problem of Equation (6), a PSO (Particle Swarm Optimization) technique can be used. For example, in the literature, the PSO algorithm is applied to a number of conventional evolutionary computation algorithms, such as the " Inverse < RTI ID = 0.0 > Heat Conduction & It can be used as a more effective and precise solution to the heat conduction problem for the unknown heat source estimation.

However, if the application time of the heat source increases or the sampling time of the temperature measurement decreases, the number of Gs to be estimated increases sharply. Therefore, if the dimension of the inverse problem solution increases in the heat transfer problem solution using the PSO technique, the possibility of finding the correct solution may be drastically lowered. Accordingly, the optimal solution of Equation (6), which is an objective function, can be derived through the DPSO-QI (Distributed Particle Swarm Optimization-Quantum Infusion) technique.

Hereinafter, the DPSO-QI technique will be described in comparison with the PSO technique.

In the PSO system, each particle is connected in a social environment and is a candidate in the multi-dimensional search domain of the optimization problem. The PSO algorithm is an algorithm designed by Kennedy and Eberhart. The position of each particle is shared with each other, and at this time, the velocity of each other is determined by sharing the information of the particles in the optimum position.

FIGS. 3 and 4 are graphs for explaining the PSO algorithm, and FIG. 5 is a graph showing the results of applying the PSO algorithm.

A schematic feature of the PSO algorithm is that a large number of particles move by mutual interaction and seek the optimal solution of the objective function. In the PSO algorithm, the particles are updated in accordance with Equations (7) and (8) below.

은 inertia factor,

은 cognitive scaling factor,

는 social scaling factor로서 각각 사전 설정된 값이고,

및

은 0과 1 사이에서 균일하게 분산된 난수(random number)이다.Here, i denotes the number of each particle, and k denotes the number of iterations. x is the position of each particle, and v is the velocity of each particle.

The inertia factor,

Cognitive scaling factor,

Is a social scaling factor,

And

Is a random number uniformly distributed between zero and one.

는 현재 k에서 군집 입자들 중 가장 최적의 입자 위치를 의미하고,

는 각 입자들의 개인적인 최적 위치를 의미한다. 즉, 지베스트(gbest)는 모든 입자들중 목적 함수를 최소로 하는 위치의 입자이며, 피베스트(pbest)는 하나의 입자가 그전 반복 실행시에 경험한 목적 함수를 최소로하는 위치이다.To describe the movement of particles in the PSO algorithm, five particles are used as shown in Figs. 3 and 4 as an example. In Equation 8

Represents the most optimal particle position among the cluster particles at present k,

Means the individual optimal position of each particle. That is, the gbest is a particle having a position that minimizes the objective function among all the particles, and the pbest is a position where one particle minimizes the objective function experienced in the previous iteration.

와

는 다음의 수학식 9 및 10을 따른다.Such

Wow

Lt; RTI ID = 0.0 > (9) < / RTI >

와

를 이용하여 단순한 벡터 연산에 따라 각 입자는 다음 위치로 이동하게 된다. 이러한 방식으로 다른 입자들도 각각 이동을 하게 되고, 결과적으로 글로벌 최적(global optimum)에 수렴하게 된다. like this,

Wow

, Each particle moves to the next position according to a simple vector operation. In this way, each of the other particles is also moved, resulting in global optimum convergence.

However, when 50 experiments were performed by applying the PSO algorithm to Equation (11) with constraint conditions as shown in Equation (12) below, the results of the experiment are as shown in FIG.

As shown in FIG. 5, it can be seen that the experimental result is not always a constant value, but the deviation is very severe. This phenomenon is called premature convergence, which has been pointed out as a fatal weakness in the PSO algorithm.

FIGS. 6 and 7 are diagrams for explaining the difference between the PSO algorithm and the method using the DPSO-QI algorithm used in the embodiments of the present invention.

를 사용하는 반면에, DPSO-QI 알고리즘에서는 도 8에 도시하였듯이

라는 텀(term)을 사용한다는 것이다. The DPSO-QI algorithm to be applied in the embodiments of the present invention is based on the characteristics of the distributed particle community optimization (DPSO) algorithm and a mechanism called Quantum Infusion. The DPSO-QI algorithm and the PSO algorithm The major difference is that in the PSO algorithm, as shown in FIG. 6

Whereas in the DPSO-QI algorithm, as shown in FIG. 8,

Term is used.

That is, unlike the PSO algorithm, the particles in the DPSO-QI algorithm update their positions according to the following equations (13) and (14).

8 is a detailed flowchart of an unknown heat source estimation method applying the DPSO-QI algorithm used in the embodiments of the present invention.

를

로 대체한다. 그리고,

의 도출을 위해

와

을 산출한다.Referring to FIG. 8, in step S140,

To

. And,

For the derivation of

Wow

.

를 산출하며(S142), QI(Quantum Infusion) 기법을 통해, 임의의 입자를 선택하여 생성되는 새로운 입자의 위치인

을 산출하고(S144), 상기

및

를 기초로

를 산출하여(S146), 상기

를 기초로 목적 함수의 최적해를 연산하게 된다(S148).Specifically, a plurality of neighboring particles are selected in a cluster composed of a plurality of particles through a DPSO (Distributed Particle Swarm Optimization) technique, and a plurality of neighboring particles are selected from a plurality of groups formed by the neighboring particles,

(S142). Then, through the QI (Quantum Infusion) technique, the position of a new particle generated by selecting an arbitrary particle

(S144). Then,

And

On the basis of

(S146). Then,

The optimal solution of the objective function is calculated (S148).

Here, the concept of neighborhood is newly introduced to determine the number of neighbor particles in order to select a tbest.

For example, when the number of neighboring particles is two, each neighboring particle forms two groups, and the most optimal position among the formed groups becomes tbest. Then, offspring particles, which are offspring particles, are newly generated in each group. Then, if the generated off-spring is more optimal than the tee vest, the te vest is replaced by the off spring and is selected as the sbest, and in the opposite case the te vest is moved to the sbest ). The particles are moved through the sbest defined above.

는 다음의 수학식 15에 의해 산출된다.In step S142,

Is calculated by the following equation (15).

는 목적 함수,

는 이웃 입자의 개수이다.From here,

Is the objective function,

Is the number of neighboring particles.

는 임의의 그룹 내에서 가장 최적의 값을 갖는 위치를 의미한다.Referring to Equation 15,

Means a position having the most optimum value in an arbitrary group.

은 다음의 수학식 16에 의해 산출된다.In step S144,

Is calculated by the following expression (16).

는 임의로 선택된 이웃 입자,

및

은 0과 1 사이에서 균일하게 분산된 난수(random number),

,

은 creativity coefficient로서 사전 설정된 값이고,

는 각 입자를 k번 이동시키는 과정에서의 목적 함수의 값을 최소화시킨 각 입자의 최적 위치,

는 입자들의 평균 최적 위치이다.From here,

Lt; RTI ID = 0.0 > selected < / RTI &

And

Is a random number uniformly distributed between 0 and 1,

,

Is a preset value as the creativity coefficient,

The optimal position of each particle minimizing the value of the objective function in the process of moving each particle k times,

Is the average optimal position of the particles.

은 각 그룹 내에서 새롭게 생성되는 위치를 의미한다.Referring to Equation 16,

Quot; means a position newly generated in each group.

및

는 각각 다음의 수학식 17 및 18에 의해 정의된다.In Equation 16,

And

Are defined by the following equations (17) and (18), respectively.

는 다음의 수학식 19에 의해 산출된다.In step S146,

Is calculated by the following equation (19).

이

보다 최적 위치인 경우에는

을

로 선정하며, 반대의 경우에는

를

로 선정함을 알 수 있다. 이 때 새롭게 생성된

은 PSO 알고리즘에서 탐색(search)의 다양성을 개선시키는 효과가 있다.Referring to Equation 19,

this

In a more optimal position

of

, And in the opposite case

To

As shown in Fig. At this time,

Has the effect of improving the diversity of the search in the PSO algorithm.

를

로 대체하여 최종적으로 목적 함수의 최적해를 산출하게 되며, 전술한 수학식 13 및 14에 따라 입자가 움직이게 된다.In step S148,

To

To finally calculate the optimal solution of the objective function, and the particles move according to the above-described equations (13) and (14).

FIG. 9 is a diagram for explaining a function of performing a constraint condition. FIG.

Meanwhile, the DPSO-QI algorithm introduces the concept of a virtual objective function to deal with various constrained conditions, which allows the value of the objective function to be transformed according to equations (20) to (22).

은 여러 구속 조건을 의미한다.Where

Means several constraints.

In Equation (22), the value obtained by subtracting? / 2 from the objective function f (x) after the arctan operation is taken as a virtual objective function, but this virtual objective function is not limited to Equation (22) If it is a monotone function, it can take various forms as needed. Here, Equation (20) means to calculate the optimum value of the design parameter after preferentially removing at least one constraint.

As shown in FIG. 9, if a certain particle is in an infeasible region, it comes into a feasible region by a mechanism such as Equation (20), and after that, The optimum position is searched in the possible area.

10 is a graph showing the results of applying the PSO algorithm and the DPSO-QI algorithm.

10, the results of applying the PSO algorithm and the DPSO-QI algorithm to Equations (11) and (12), respectively, are shown. That is, it is the result of the experiment when 50 experiments are applied to the problem of Equation (11) having constraint conditions as shown in Equation (12). Blue is the result of applying the PSO algorithm, and red is the result of applying the DPSO-QI algorithm. The application result of the PSO algorithm shown in FIG. 10 is the same as the result shown in FIG.

Referring to FIG. 10, it can be seen that the result converged to different values in the PSO algorithm converges to 50 in the DPSO-QI algorithm, which indicates the excellentness of the proposed DPSO-QI algorithm. That is, in the case of the DPSO-QI algorithm, it can be seen that the results of 50 experiments converge to the same optimum value, which shows that the stability is greatly improved.

This DPSO-QI algorithm will be applied to the one-dimensional heat conduction problem of FIG.

FIG. 11A is a graph showing a result of applying the PSO algorithm when the heat source is located at the first position in the one-dimensional bar of FIG. 2, and FIG. 11B is a graph illustrating the result of applying the DPSO-QI algorithm. Here, the first position is that the heat source is located at the center of the rod.

는 다음의 수학식 23으로 정의한다.Heat source

Is defined by the following equation (23).

는 1, 시간 간격

는 0.02, 거리 간격

는 0.05이다. 그러므로, 입자들은

에 해당하는 차원의 탐색 영역(search domain)에서 최적해를 찾게 된다.Here, the measurement end time

1, time interval

0.02, distance interval

Is 0.05. Therefore,

The optimal solution is found in the search domain of the dimension corresponding to the dimension.

는 4000번, 입자의 개수

은 2000개,

, 주변 입자

는 20으로 설정한다.Also,

4000 times, the number of particles

2000,

, Peripheral particles

Lt; / RTI >

는 0.05로 설정한다.Then, the normalization coefficient

Is set to 0.05.

However, it is assumed that the heat source is located in the middle of the bar. That is, if the length of the bar L = 1, the heat source is located at 0.5.

In this case, the particle moves in a space corresponding to 50 dimensions and finds an optimal solution. The results of applying the PSO algorithm and the results of applying the DPSO-QI algorithm are shown in FIGS. 11A and 11B.

In FIG. 11A, the result of applying the PSO algorithm does not match the mathematical theoretical value, but shows a sloping appearance. On the other hand, in FIG. 11B, the result of applying the DPSO-QI algorithm almost agrees with the mathematical theoretical value. Therefore, it can be seen that the optimal solution of the objective function is obtained more accurately and stably than the PSO algorithm when the DPSO-QI algorithm is applied.

Alternatively, if the length of the bar L = 1, it is assumed that the heat source is located at 0.7 rather than the middle of the bar. FIG. 12A is a graph showing a result of applying the PSO algorithm when the heat source is located at the second position in the one-dimensional bar of FIG. 2, and FIG. 12B is a graph showing the result of applying the DPSO-QI algorithm. That is, the second position means that the heat source is located at 0.7 from the origin of the rod when the length L = 1 of the rod.

12A, the result of applying the PSO algorithm does not match the mathematical theoretical value, but shows a loose appearance. On the contrary, in FIG. 12B, the result of applying the DPSO-QI algorithm is a mathematical theory And the value of " Thus, it can be seen that the optimal solution of the objective function is obtained more accurately and stably than the PSO algorithm when the DPSO-QI algorithm is applied.

Therefore, it is possible to increase the diversity of the particles by allowing the particles to exchange only local information by using the DPSO technique corresponding to the Neighborhood topology. By using the QI technique based on the quantum behavior mechanism, offspring particles It is possible to improve the search more precisely. In other words, the search ability of the PSO algorithm can be improved by combining the mechanism of the Neighborhood topology and the quantum behavior.

FIG. 13 is a configuration diagram of an unknown heat source estimation system according to an embodiment of the present invention, and FIG. 14 is a configuration diagram of a DPSO-QI unit according to an embodiment of the present invention.

The unknown heat source estimation system 100 according to an embodiment of the present invention may include a temperature sensor unit 110, a temperature calculation unit 120, an objective function setting unit 130, and a DPSO-QI unit 140 have. However, since the DPSO-OI algorithm applied to the unknown heat source estimation system 100 is the same as the unknown heat source estimation method according to the embodiment of the present invention described above, a detailed description will be omitted.

The temperature sensor unit 110 measures the temperature at a specific position to acquire measurement data. A thermistor , a platinum, a nickel, a thermocouple, or the like can be used as a detecting element of a temperature sensor that converts the detected temperature into an electric signal and transmits the electric signal.

The temperature calculation unit 120 calculates the temperature and temperature of the unknown heat source based on the temperature data measured by the temperature sensor unit 110 to obtain calculation data. Particularly, the temperature calculator 120 can obtain computational data by discretizing the heat transfer governing equations for the unknown heat source whose temperature changes with time at a specific position into a finite difference equation of Crank-Nicolson. Here, the above Equation (1) is transformed into Equation (4) through the finite difference equation of Crank-Nicolson as described above, so the detailed contents will be omitted.

The objective function setting unit 130 sets an objective function for the unknown heat source based on the measurement data of the temperature sensor unit 110 and the calculation data of the temperature calculation unit 120. [ Here, the objective function can be set by Least Square Method. The objective function set by the least squares method can be expressed by Equation (5). In addition, the objective function setting unit 130 may add the normalization term to the objective function set by the least squares method through the Tikhonov regulation method. A concrete procedure for this can be performed by Equation (6), and a detailed description thereof will be omitted since it is as described above.

The DPSO-QI unit 140 calculates the optimal solution of the objective function through the DPSO-QI (Distributed Particle Swarm Optimization-Quantum Infusion) technique. To this end, the DPSO-QI section 140 includes a tbest calculation module 142, an offspring calculation module 144, a sbest calculation module 146 and an optimal solution calculation module 148, As shown in FIG.

를 산출한다.

의 산출 시 상기 수학식 15가 이용될 수 있다.The tbest calculation module 142 selects a plurality of neighbor particles in a cluster composed of a plurality of particles through DPSO (Distributed Particle Swarm Optimization) Lt; RTI ID = 0.0 >

.

The above equation (15) can be used.

을 산출한다.

산출 시 상기 수학식 16이 이용될 수 있다.The offspring output module 144 uses the QI (Quantum Infusion) technique to calculate the position of a new particle generated by selecting an arbitrary particle

.

The above equation (16) can be used in calculation.

및

를 기초로

를 산출한다.

산출 시 상기 수학식 19가 이용될 수 있다.The sbest module 146 calculates

And

On the basis of

.

The above equation (19) can be used in calculation.

를 기초로 목적 함수의 최적해를 연산한다. 이를 위해, 상기 수학식 13 및 14가 사용되며, 입자들은 상기 수학식 13 및 14에 따라 위치를 갱신하게 된다.The optimal solution calculation module 148

The optimal solution of the objective function is calculated. To this end, equations 13 and 14 above are used and the particles are updated in accordance with Equations 13 and 14 above.

15A and 15B are graphs showing the results according to the normalization coefficient when various algorithms are applied to the one-dimensional bar of FIG.

의 값이 0.05이나, 도 15b의 경우에는 정규화 계수

의 값이 0이다. 도 15a 및 도 15b에 도시된 바와 같이,

의 값이 0인 경우보다

의 값이 0.05인 경우에 동일한 알고리즘을 적용하더라도 그 움직임이 보다 안정화된 것을 확인할 수 있다. 그러므로, 적절한 정규화 계수

의 값을 설정하는 것이 중요하다.In the case of Figs. 15A and 15B, the heat source function and various conditions are the same as Figs. 11A and 11B. However, in the case of Fig. 15A,

Is 0.05, and in the case of Fig. 15B, the normalization coefficient

Is zero. As shown in Figs. 15A and 15B,

Is less than 0

Is 0.05, it can be confirmed that the motion is stabilized even if the same algorithm is applied. Therefore, an appropriate normalization coefficient

It is important to set the value of.

In the case of applying the DPSO-QI algorithm, it is possible to find the optimal solution of a given objective function with very high precision even if there is no information about the input heat source in estimating an unknown heat source. Therefore, It is possible to estimate the unknown heat source more efficiently and precisely.

Meanwhile, the unknown heat source estimation method of the present invention and each component of the unknown heat source estimation system can be implemented as one module by software and hardware, and the above-described embodiments of the present invention can be implemented by a computer- And can be implemented in a general-purpose computer that operates the program using a computer-readable recording medium. The computer-readable recording medium is implemented in the form of a carrier wave such as a ROM, a floppy disk, a magnetic medium such as a hard disk, an optical medium such as a CD or a DVD, and a transmission through the Internet. In addition, the computer-readable recording medium may be distributed to a network-connected computer system so that computer-readable codes may be stored and executed in a distributed manner.

While the present invention has been described in connection with what is presently considered to be practical exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, You will understand. It is therefore to be understood that the above-described embodiments are illustrative in all aspects and not restrictive.

100: unknown heat source estimation system
110: temperature sensor unit 120: temperature calculation unit
130: Object function setting unit 140: DPSO-QI unit

Claims (23)

An unknown heat source estimation method for estimating an unknown heat source whose temperature varies with time from measured temperature data,
Obtaining measurement data of the temperature measured by the temperature sensor;
Obtaining calculation data of a temperature at which the temperature of the unknown heat source is calculated based on the measurement data;
Setting an objective function for the unknown heat source based on the measurement and calculation data; And
A method for estimating an unknown heat source, comprising calculating an optimal solution of the objective function through a DPSO-QI (Distributed Particle Swarm Optimization-Quantum Infusion) technique. The method of claim 1,
The step of setting the objective function comprises:
Wherein the objective function is set by a Least Square Method. ≪ Desc / Clms Page number 20 > 3. The method of claim 2,
By the least squares method,

Lt; / RTI >
Here, x is a measurement position, t is a measurement time, n is a number of temperature sensors,

Wherein Y is the measurement temperature, T is the calculation temperature, and G is the estimated temperature of the unknown heat source. 3. The method of claim 2,
The step of setting the objective function comprises:
Further comprising the step of adding a normalization term to the objective function set by the least squares method through a Tikhonov regulation method. 5. The method of claim 4,
By the least squares method and the Tihonov normalization technique,

Lt; / RTI >
From here,

Lambda is a normalization coefficient, m is a normalized order, L is the length of a one-dimensional bar,
X is the measurement position, t is the measurement time, n is the number of temperature sensors,

Wherein Y is the measurement temperature, T is the calculation temperature, and G is the estimated temperature of the unknown heat source. The method of claim 1,
The step of calculating an optimal solution of the objective function may include:
A plurality of neighboring particles are selected in a cluster composed of a plurality of particles through a DPSO (Distributed Particle Swarm Optimization) technique, and a plurality of neighboring particles are selected from a plurality of groups formed by the neighboring particles,

;
Through the Quantum Infusion (QI) technique, the position of new particles generated by selecting arbitrary particles

;
remind

And

On the basis of

; And
remind

And calculating an optimal solution of the objective function based on the unknown heat source. The method according to claim 6,
remind

Quot;

Lt; / RTI >
From here,

Is the objective function,

Is the number of neighboring particles. The method according to claim 6,
remind

silver,

Lt; / RTI >
From here,

Lt; RTI ID = 0.0 > selected < / RTI &

And

Is a random number uniformly distributed between 0 and 1,

,

Is a preset value as the creativity coefficient,

The optimal position of each particle minimizing the value of the objective function in the process of moving each particle k times,

Is an average optimal location of the particles. The method of claim 8,
remind

Quot;

Lt; / RTI >
remind

Quot;

Is calculated by the following equation. The method according to claim 6,
remind

The step of calculating,
remind

In this case,

If the position is more optimal,

Gt;

And in the opposite case,

Gt;

The method further comprising the step of: The method according to claim 6,
The optimal solution of the objective function may be expressed as:

And

Lt; / RTI >
Where

An inertia factor,

Cognitive scaling factor,

Is a predetermined value as a social scaling factor,

And

Is a random number that is uniformly distributed between zero and one. An unknown heat source estimation system for estimating an unknown heat source whose temperature varies with time from measured temperature data,
A temperature sensor unit for obtaining temperature measurement data;
A temperature calculator for calculating the temperature and the temperature of the unknown heat source based on the measurement data to obtain calculation data;
An objective function setting unit for setting an objective function for the unknown heat source based on the measurement and calculation data; And
An unknown heat source estimation system comprising a DPSO-QI unit for calculating an optimal solution of the objective function through a DPSO-QI (Distributed Particle Swarm Optimization-Quantum Infusion) technique. 13. The method of claim 12,
Wherein the temperature calculator obtains the computed data by discretizing a heat transfer governing equation for the unknown heat source whose temperature changes with time at a specific position into a Crank-Nicolson finite difference equation. 13. The method of claim 12,
Wherein the objective function setting unit sets the objective function by a least squares method. The method of claim 14,
By the least squares method,

Lt; / RTI >
Here, x is a measurement position, t is a measurement time, n is a number of temperature sensors,

Where Y is the measured temperature, T is the computed temperature, and G is the estimated temperature of the unknown heat source. The method of claim 14,
Wherein the objective function setting unit adds the normalization term to the objective function set by the least squares method through a Tikhonov regulation method. 17. The method of claim 16,
By the least squares method and the Tihonov normalization technique,

Lt; / RTI >
From here,

Lambda is a normalization coefficient, m is a normalized order, L is the length of a one-dimensional bar,
X is the measurement position, t is the measurement time, n is the number of temperature sensors,

Is the measurement end time, Y is the measurement temperature, T is the computation temperature, and G is the estimated temperature of the unknown heat source. 13. The method of claim 12,
The DPSO-
A plurality of neighboring particles are selected in a cluster composed of a plurality of particles through a DPSO (Distributed Particle Swarm Optimization) technique, and a plurality of neighboring particles are selected from a plurality of groups formed by the neighboring particles,

A tbest calculation module that calculates a tester;
Through the Quantum Infusion (QI) technique, the position of new particles generated by selecting arbitrary particles

An offspring (off-spring) output module to calculate
remind

And

On the basis of

A sbest module to calculate the best estimate; And
remind

And an optimal solution calculating module for calculating an optimal solution of the objective function based on the unknown heat source. 19. The method of claim 18,
The " tbest "

Lt; / RTI &

Lt; / RTI >
From here,

Is the objective function,

Is the number of neighboring particles. 19. The method of claim 18,
The offspring (off-spring)

Lt; / RTI &

Lt; / RTI >
From here,

Lt; RTI ID = 0.0 > selected < / RTI &

And

Is a random number uniformly distributed between 0 and 1,

,

Is a preset value as the creativity coefficient,

The optimal position of each particle minimizing the value of the objective function in the process of moving each particle k times,

Is an average optimal location of particles. The method of claim 20,
The offspring (off-spring)

Lt; / RTI &

Lt; / RTI >

Lt; / RTI &

Of the unknown heat source. 19. The method of claim 18,
The sbest module may include:

Lt; / RTI &

Of the unknown heat source. 19. The method of claim 18,
Wherein the optimal solution calculation module comprises:

And

To calculate the optimal solution,
Where

An inertia factor,

Cognitive scaling factor,

Is a predetermined value as a social scaling factor,

And

Is a random number that is uniformly distributed between zero and one.

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