JP6536384B2 - State estimation method, level control method, program and state estimation device - Google Patents

Description

  The present invention relates to a state estimation method for estimating a state of a molten metal level fluctuation in a mold of a continuous casting machine, a molten metal level control method based on an estimation result of the state estimation method, and a program for causing a computer to execute the state estimation method. , And a state estimation device for estimating the state of fluctuation of the level in the mold of the continuous casting machine.

  In continuous casting of steel, the level of molten metal in mold is measured with a level gauge for operation stabilization and quality improvement, and the level of molten metal is controlled by opening and closing the nozzle to maintain the measured value at the target value Control is being performed. That is, control is performed to suppress the overall vertical movement of the surface of the molten metal (that is, the volume fluctuation of the molten steel in the mold).

  In the present specification, the surface level at a specific point in the width direction in the mold is the surface level, and the distribution in the width direction of the surface level in the mold is defined as the surface level distribution. Further, the distribution of the surface level at the position in the mold width direction based on the case where the surface is horizontal is referred to as the surface shape, and the temporal variation of the surface shape is referred to as the surface shape variation. In addition, temporal variation including the vertical movement of the surface of the molten metal (variation in the level of molten metal) uniformly generated in the entire mold in the width direction due to molten steel balance difference in molten metal shape variation (that is, in the mold width direction) Temporal fluctuation of the surface level in the whole) is called surface fluctuation.

  Here, in the measurement value of the surface level meter, not only the vertical movement of the surface of the molten metal to be suppressed, but also the standing wave due to the wave surface of the surface, bulging of the surface due to the molten steel flow, measurement error, etc. The disturbance component due to is superimposed. Therefore, the measurement value of one level meter does not necessarily accurately represent the entire vertical movement of the surface. Therefore, even if the opening and closing operation of the nozzle is performed based on the measurement value of the hot water level meter, it is difficult to appropriately suppress the overall vertical movement of the hot water surface.

  Therefore, various techniques have been proposed for extracting the entire vertical movement component from the measurement value of a single level meter and controlling the injection amount of molten steel based on this. For example, Patent Document 1 describes a method of separating the whole vertical movement component and the standing wave component of the surface of the molten metal in real time from the time series data of a single level meter. More specifically, Patent Document 1 describes the coefficient (amplitude) when describing the standing wave component of the melt level fluctuation at a predetermined position using a sine function and a cosine function at a frequency calculated from the mold width. A technique is described that estimates from the measurements of the level meter.

  Further, in Patent Document 2, a model of hot water level fluctuation due to standing waves is expressed by a secondary vibration system, and the measurement value of the hot water level measured with a single hot water level meter determines the first to third order A technique is described that achieves high precision surface level control by extracting only bulging level fluctuation to be originally controlled by extracting and removing existing wave components and using it for surface level control. There is.

JP, 2009-241150, A JP 2012-170999 A

  However, as described above, the components other than the total vertical movement component included in the measurement value of the surface level meter are not only the standing wave component, but in addition to the measurement value, molten steel flow in the mold It includes disturbance components such as rise of the surface of the molten metal and measurement error due to the influence of On the other hand, in the techniques described in Patent Documents 1 and 2, such disturbance components are not taken into consideration. Therefore, in the techniques described in Patent Documents 1 and 2 above, for example, in the case where variation in molten metal level occurs due to another disturbance component at a cycle different from that of the standing wave, the measurement value of the molten metal level meter It is not possible to remove the influence of such disturbance components, and it may not be possible to realize appropriate level control.

  Therefore, the present invention has been made in view of the above problems, and an object of the present invention is to be able to more accurately estimate the surface level distribution in a mold in a continuous casting machine. A new and improved state estimation method, a level control method, a program and a state estimation device.

  In order to solve the above problems, according to one aspect of the present invention, there is provided a state estimation method for estimating the distribution of the surface height in the mold in the mold in the mold of the continuous casting machine with respect to the mold width direction position. Obtaining the measurement value of the surface level in the mold at at least two different measurement points in the above, the surface level at any time and any position in the width direction of the mold, an overall vertical movement component, and A wavelength of 2 W / n (where W is the width of the mold, n is an integer of 1 or more) in which both ends of the mold become antinodes of waves is expressed by a linear equation obtained by superposition of sine wave wavelength components The component coefficient is represented by a standing wave component and a disturbance component, and the step represented by a state space model and the condition represented by the state space model are estimated by treating the disturbance component as system noise Expanding the state space model using a frequency weighting function for giving a frequency weight to an evaluation function of a Kalman filter for the purpose of expanding the state space model and expanding the state space model. Applying a Kalman filter using the measured value of the surface level as an observed value to sequentially estimate the coefficients of the overall vertical movement component and the wavelength component.

  In the state estimation method, a first-order low-pass filter may be used as the frequency weighting function.

  Moreover, in the said state estimation method, the frequency weighting function corresponding to the frequency characteristic of the said disturbance component analyzed based on the measured value of the said pouring level may be used as said frequency weighting function.

  Further, the state estimation method may further include a step of estimating the hot water level at the arbitrary time and the arbitrary position using the estimated whole vertical movement component and the coefficient of the wavelength component. .

  Further, in order to solve the above-mentioned problems, according to another aspect of the present invention, using the coefficients of the whole vertical movement component and the wavelength component, the surface level of the molten metal at the arbitrary time and the arbitrary position And deviding into the overall vertical movement component and the wavelength component, and controlling the molten steel injection amount to the mold or the billet withdrawal speed from the mold based on the total vertical movement component. A level control method is provided, further comprising the steps of:

  Further, in order to solve the above problems, according to another aspect of the present invention, a computer is caused to execute a state estimation method for estimating the distribution of the surface height in the mold of the continuous casting machine with respect to the mold width direction position. A program, wherein the state estimation method comprises: obtaining measured values of the surface level in the mold at at least two different measurement points in the width direction of the mold; arbitrary time and the mold width direction The elevation of the surface at any position, the total vertical movement component, and the wavelength of a sine wave of wavelength 2 W / n (where W is the width of the mold and n is an integer of 1 or more) where both ends of the mold become antinodes of waves. A state space model represented by a linear equation obtained by superposition of the components, wherein the coefficients of the wavelength components are represented by a standing wave component and a disturbance component; Expanding the state space model using a frequency weighting function for giving a frequency weight to an evaluation function of a Kalman filter for estimating the state to be treated by treating the disturbance component as system noise, and the state space A step of sequentially estimating the coefficients of the overall vertical motion component and the wavelength component by applying a Kalman filter to the magnified state space model obtained by magnifying the model using the measured value of the surface level as an observed value And a program is provided.

  Further, in order to solve the above problems, according to another aspect of the present invention, there is provided a state estimation device for estimating the distribution of the surface height in the mold in the mold of the continuous casting machine with respect to the mold width direction position. A measurement value acquiring unit for acquiring measurement values of the surface level of the mold in the mold at at least two different measurement points in the width direction of the surface, and the surface level of the surface at any time and any position in the width direction of the mold; According to the linear equation obtained by superposing the whole vertical motion component and the wavelength component of the sine wave of 2 W / n (where W is the width of the mold and n is an integer of 1 or more) at which both ends of the mold become antinodes of waves. By expressing the coefficients of the wavelength component represented by the standing wave component and the disturbance component and expressing the state space model as a system noise, by expressing the condition represented by the state space model as the system noise Estimate The state space model is expanded using the frequency weighting function for giving frequency weighting to the evaluation function of the Kalman filter, and the hot water is compared to the expanded state space model obtained by expanding the state space model. There is provided a state estimation device comprising: an arithmetic unit that sequentially estimates the coefficients of the entire vertical movement component and the wavelength component by applying a Kalman filter using a measured value of a surface height as an observed value.

  As described above, according to the present invention, in a continuous casting machine, it becomes possible to more accurately estimate the surface level distribution in the mold.

It is a figure showing an example of composition of a system concerning this embodiment. It is a figure for demonstrating the example of arrangement | positioning of the surface level meter in the system shown in FIG. It is a block diagram which shows the flow of the signal from noise vector (zeta) (k) to presumed error vector e (k) in state estimation by a general Kalman filter. It is a block diagram which shows the flow of the signal from noise vector eta (k) to presumed error vector e (k) in the state estimation by the Kalman filter which concerns on this embodiment which considered frequency weighting function W (z). It is a figure for demonstrating the structure of the algorithm of the presumed process of the pouring level distribution by a state estimation apparatus. It is a figure for demonstrating the structure of the algorithm of the estimation process of the pouring surface level distribution by a state estimation apparatus including the real machine process. It is a flow figure showing the processing procedure of the presumed processing of the pouring level distribution by a state estimating device. It is a block diagram showing functional composition of a state estimating device concerning this embodiment. It is a block diagram which shows an example of the hardware constitutions of the state estimation apparatus which concerns on this embodiment. It is a graph which shows the result of a 2nd Example.

  The present invention will now be described more fully with reference to the accompanying drawings, in which exemplary embodiments of the invention are shown. In the present specification and the drawings, components having substantially the same functional configuration will be assigned the same reference numerals and redundant description will be omitted.

(1. System configuration)
The configuration of a system according to an embodiment of the present invention will be described with reference to FIG. FIG. 1 is a view showing an example of the configuration of a system according to the present embodiment. Referring to FIG. 1, a system 1 according to the present embodiment includes a level gauge 3 disposed in a mold 2 of a continuous casting machine, a state estimation device 4, a display / printing device 5, and a continuous casting control device 6. And.

  The surface level meter 3 is, for example, an eddy current level meter, and measures the surface level of the mold 2 at a predetermined position. As will be described later, in the present embodiment, a plurality of level gauges 3 are installed.

  The state estimation device 4 estimates the surface level distribution in the mold 2 based on the measurement value of the surface level meter 3. Specifically, when estimating the hot water level distribution, the state estimation device 4 separates the entire vertical movement component of the hot water surface from the other components (that is, the components corresponding to the hot water surface shape fluctuation) Can be estimated. In addition, the state estimation device 4 can estimate the surface level distribution in real time during continuous casting. The estimation result of the surface level distribution is sent to the display / printing device 5 or the continuous casting control device 6.

  The display / print device 5 outputs the estimation result of the hot water level distribution by the state estimation device 4 in real time, for example, by display on a display or printing on a paper medium. For example, the display / printer 5 displays the estimated hot water surface shape as a graph on a display or the like. In this case, the display / printing device 5 may express the surface shape by superposing the actual measurement value by the surface level meter 3 and the estimation value by the state estimation device 4 as illustrated.

  Here, according to the conventional knowledge, it is known that in continuous casting, a large number of slab defects are generated at a position where the temporal fluctuation of the surface level is particularly large. Therefore, the hot-water surface shape estimated as described above is output in real time by the display / printing device 5, so that the hot-water surface shape fluctuation can be grasped, and the casting is completed based on the hot-water surface shape fluctuation. It becomes possible to grasp the distribution of slab defects in the slab width direction before. By this, speeding up of slab quality control can be achieved.

  The continuous casting control device 6 performs the surface level control to maintain the in-mold surface level at the target value based on the estimation result by the state estimation device 4. Specifically, since the vertical movement of the entire surface of the molten metal occurs due to the molten steel balance difference in the mold, the continuous casting control device 6 is based on the estimation result of the general vertical movement of the surface of the molten metal by the state estimation device 4 The opening / closing control of the immersion nozzle 8 for injecting the molten steel into the mold 2 and the rotational speed control of the pinch roll for pulling out the slab from below the mold 2 are executed so as to suppress the overall vertical movement. The surface level control by the continuous casting control device 6 may be performed in real time during continuous casting.

  FIG. 2 is a view for explaining an arrangement example of the level meter 3 in the system 1 shown in FIG. In FIG. 2, a widthwise cross section of the mold 2 is shown. In the present embodiment, two sets of surface level meters 3a and 3b can be installed at both widthwise end portions of the mold 2, that is, both short sides in the cross section of the mold 2. Here, it is preferable that the installation position of the level meter 3 be close to the antinode of the wavelength component to be detected. As will be described later, both end portions in the width direction of the mold 2 are positions that become antinodes of the respective wavelength components, and thus are suitable as the installation positions of the surface level meter 3. The meaning of the wavelength component will be described later.

  However, the installation position of the hot water level meter 3 in the present embodiment is not limited to such an example. For example, one mold level meter is generally installed in the mold 2 for level control. From the viewpoint of operation maintainability and maintenance cost, it is desirable that the number of hot surface level meters added for use in this embodiment be as small as possible. Therefore, when a level gauge for control is already used, it is desirable that the level gauge for control is one of the level gauges 3 used in the present embodiment.

  The level gauge installed for control is usually mounted at a position away from the center of the mold, avoiding the immersion nozzle. For example, a level gauge for control is attached at 1/4 of the mold width. When a second level meter is installed in addition to the level level meter for control, for example, the second end section in the width direction of the mold 2 which is the position of the antinode for all wavelength components It is desirable that a level gauge be attached.

  If the level meter for control is not installed or if it is installed but not used, two level meters on both ends in the width direction of the mold 2 You may install newly.

  In order to further increase the estimation accuracy, three or more hot surface level meters 3 may be installed. It is desirable that the third level meter 3 also be installed at a position close to the antinode of the wavelength component to be detected. As in the example above, a new level gauge was installed at one end of the mold 2 in the width direction using a level gauge for control that is attached to a position such as 1⁄4 of the mold width. In this case, it is desirable that the third level meter be attached to the widthwise end of the mold 2 opposite to the second level meter. In addition, when the first and second surface level meters have already been installed at both ends in the width direction of the mold 2, there is no position where all wavelength components become antinodes other than the both ends in the width direction of the mold 2 Therefore, the wavelength component to be detected may be specified, and the third level meter 3 may be installed at the position where the wavelength component is located at the antinode. For example, since the longer wavelength component is generally observed, the third surface is located near the antinode of the longer wavelength component such as 2 W, W, 2 W / 3, etc. with respect to the width W of the mold 2 A level meter 3 may be installed. Also, in this case, if it is difficult to install the first and second hot metal level meters 3 at both ends in the width direction of the mold 2 for some reason, the wavelength components to be detected otherwise. The first and second level gauges 3 may be installed near the belly.

(2. Estimation of Hot Surface Height Distribution)
Subsequently, the estimation processing of the molten metal level distribution performed by the state estimation device 4 of the above-described system 1 will be further described.

(2-1. Modeling of hot water level distribution)
Continuing with reference to FIG. 2, the wavelength components that make up the surface shape will be described. FIG. 2 shows the waveforms of _{first to third} wavelength components S _{1 to} S ₃ constituting the surface shape of the molten metal in the mold 2 (for the sake of explanation, the amplitude of each wavelength component is equal ). Wavelength lambda ₁ of the first-order wave component _{S 1} is a lambda ₁ = 2W, the wavelength lambda ₂ of the second wavelength component _{S 2} is a lambda ₂ = W, the wavelength lambda ₃ of third-order wave component _{S 3} is λ ₃ = 2 W / 3 (W is the mold width).

  Here, since the height of the mold 2 is sufficiently larger than the width, deep water wave approximation can be used in modeling of the surface shape of the molten metal. Further, since the width of the mold 2 is sufficiently larger than the thickness, it is possible to consider only the variation in the width direction without considering the variation of the surface level in the thickness direction in modeling.

Since the horizontal velocity of molten steel = 0 always holds at the boundary of the mold short sides of the surface of the melt, the height of the melt surface y (x, t) at an arbitrary time t and an arbitrary position x in the width direction in the mold 2 , And a linear model in which a sine wave shape of a wavelength λ _n = 2 W / n (template width W, n = 1, 2,...) Is a basis function f _n (x). As a result, the surface shape at any given time is represented by the superposition of basis functions f _n (x) with both ends in the width direction of the mold 2 as antinodes. In the present embodiment, the basis function f _n (x) is also referred to as an n-order wavelength component. The waveforms of the first to third wavelength components S _{1 to} S ₃ shown in FIG. 2 described above correspond to the first to third basis functions f ₁ (x) to f ₃ (x).

Specifically, the n-order wavelength component, that is, the basis function f _n (x) is expressed as follows.
n: even f _n (x) = cos (2πnx / 2W)
n: odd number f _n (x) = sin (2πnx / 2W)

  When the wavelength component is defined as described above, the surface height of the molten metal at an arbitrary time t and an arbitrary position x in the width direction in the mold 2 considering the wavelength components up to the Nth order (n = 1, 2,..., N) Y (x, t) can be expressed by a linear equation such as the following equation (1).

Here, a ₀ (t) indicates the entire vertical movement component included in the surface level of the hot water. Further, f _n (x) is the basis function and represents the sine / cosine function portion of the nth wavelength component included in the surface level, and a _n (t) represents the coefficient of the nth wavelength component.

Since the wavelength of each wavelength component is obtained from the width W of the mold 2, f _n (x) can be calculated at any time. Therefore, if the coefficients a ₁ (t), a ₂ (t),..., A _N (t) of the n-order wavelength component and the overall vertical motion component a ₀ (t) are obtained, the surface of the molten metal at any time The height y (x, t) can be estimated. Also, at that time, any of the coefficients a ₁ (t), a ₂ (t),..., A _N (t) of the n-order wavelength component and the overall vertical motion component a ₀ (t) obtained The hot water surface shape at the time of and the overall vertical movement of the hot water surface can also be estimated simultaneously.

Here, assuming that molten steel is a non-vortex, non-viscous, non-compressive complete fluid, the coefficient a _n (t) of the n-order wavelength component generated as a standing wave is a natural angular frequency ω according to the basic equation of surface waves. _It can be expressed as superposition of n-order wavelength component fluctuations that are single-oscillating at n. In this case, the coefficient a _n (t) of the nth-order wavelength component satisfies the following formula (2).

If it is assumed that the fluctuation of the surface contains only the whole vertical movement component and the standing wave component, if the coefficient a _n (t) of the n-order wavelength component can be calculated by the above equation (2), the surface fluctuation can be explained. it can. However, not only the vertical movement component and the standing wave component but also the disturbance component other than the standing wave such as the rising of the molten metal surface under the influence of the molten steel flow in the mold 2 includes the fluctuation of the molten metal surface. Therefore, in the present embodiment, the coefficients a _n (t) of each wavelength component are driven by disturbance due to molten steel flow in the mold to be time-changed, and the disturbance variation is regarded as a stochastic noise component as a single vibration model. Capture to Specifically, the time variation followed by the coefficients a _n (t) of the respective wavelength components can be expressed as the following equation (3).

Here, d _n (t) is a disturbance that drives the nth-order wavelength component. The disturbance d _n (t) corresponds to system noise in the state space model.

  When the above equation (3), which is a forced vibration model of each n-order wavelength component, is discretized (.DELTA.t: sampling time) by an exact solution (0th-order hold), the following equation (4) is obtained. The following equation (4) corresponds to the system equation in the state space model.

On the other hand, the surface level of the molten metal measured at the sampling time k by the ith surface level meter 3 (i = 1, 2,..., L) installed at the width direction position x _i (measurement point) of the mold 2 When y (x _i , k) is described using the above equation (1), the following equation (5) is obtained. Here, w _i (k) is a time-varying measurement error in each level level meter 3 and corresponds to observation noise in the state space model. The following equation (5) corresponds to the observation equation in the state space model.

The equation (4), (5), the state-space model of the coefficient of each wavelength component _a n (k) is represented by the following equation (6) can be expressed as (7).

(2-2. Estimation of molten metal level distribution by Kalman filter)
In this embodiment, in the state space model generated as described above, a Kalman filter is applied as a method of sequentially estimating a state variable inside the model (that is, the above x (k)). The Kalman filter is a method of sequentially estimating state variables in the model from information of limited observation points when the dynamics of the target process conform to a linear state space model. Since the state space model of the water level fluctuation in the present embodiment is linear, a Kalman filter can be applied.

  Here, let a vector consisting of the system noise d (k) and the observation noise w (k) in the above equations (6) and (7) be a noise vector ξ (k) (ie, ξ (k) = (d ( t), w (k)) At this time, in the state estimation by a general Kalman filter, the signal flow from the noise vector ξ (k) to the estimation error vector e (k) is a block diagram as shown in FIG. 3 is a block diagram showing a flow of signals from a noise vector ξ (k) to an estimation error vector e (k) in state estimation by a general Kalman filter.

In the block diagram shown in FIG. 3, the discrete transfer function from the noise vector xi] (k) to the estimated error vector e (k) and _{T eξ} (z) _{(i.e., e (k) = T eξ} (z) ξ ( k)). At this time, it is known that the stationary Kalman filter minimizes the H 2 norm of T _{e ξ} (z) shown in the following equation (8) (for example, “T. Katayama,“ Applied Kalman Filter ”, Asakura Shoten, 2000 See February). That is, it can be said that the H2 norm of the transfer function T _{e ξ} (z) is an evaluation function of the Kalman filter.

  However, in the system shown in FIG. 3, the noise vector ξ (k) (ie, the system noise d (k) and the observation noise w (k)) is regarded as white noise. On the other hand, the actual system noise d (k) and the observation noise w (k) are not necessarily white noise but colored noise having a non-flat spectral distribution. In the system shown in FIG. 3, if the noise vector ξ (k) is not white noise but colored noise, bias may occur in the Kalman filter estimated value, and the estimation accuracy may be degraded.

In order to prevent this, in the present embodiment, the above-described transfer function T _{e ξ} (z) has a frequency weight. Specifically, it is considered to introduce the frequency weighting function W (z) and minimize the H2 norm of _{Te ξ} (z) W (z) shown in the following equation (9).

  Thus, even when the noise vector ξ (k) is a colored noise, the wavelength component coefficients can be obtained by appropriately selecting the frequency weighting function W (z) according to the frequency characteristics of the noise vector ξ (k). It is possible to suppress deterioration in estimation accuracy when estimating. For example, when the low frequency component of the noise vector ξ (k) is relatively strong, the frequency weighting function W (z) may have low-pass filter characteristics to reduce the estimation accuracy of the low frequency component in the estimation of the wavelength component coefficient. It is possible to suppress the deterioration.

Here, considering the frequency weighting function W (z) with respect to the transfer function T _{e ξ} (z) is because, in the block diagram shown in FIG. 3, the noise vector ξ (k) which is the input and the estimation error which is the output This corresponds to adding a block corresponding to the frequency weighting function W (z) between the vector e (k). A block diagram considering such a frequency weighting function W (z) is shown in FIG. FIG. 4 is a block diagram showing the flow of signals from the noise vector η (k) to the estimation error vector e (k) in the state estimation by the Kalman filter according to the present embodiment in consideration of the frequency weighting function W (z). is there.

  As shown in FIG. 4, in consideration of the frequency weighting function W (z), the noise vector ξ (k) which is colored noise and the noise vector η (k) which is white noise have a transfer function W (z). It corresponds to assuming that it is generated by passing. That is, to minimize the H2 norm shown in the above equation (9) is a normal system for the system obtained by expanding the state space model shown in the above equations (6) and (7) to include the dynamics of colored noise. It is nothing but applying a Kalman filter.

Accordingly, in the present embodiment, the dynamics of colored noise formulated, the equation by using the (6), of an enlarged view of a state-space model shown in (7), the coefficient a _{n (k)} of each wavelength component It is a state space model. Then, by estimating the state variables of this expanded state space model (hereinafter referred to as the expanded state space model) using a Kalman filter, the overall vertical motion component a ₀ (k) and the coefficients a _{n of} each wavelength component Estimate (k) and estimate the surface level distribution.

(2-3. Extended state space model)
Derivation of the expanded state space model is specifically described. First, a noise vector ξ (k) which is colored noise is expressed by a discrete-time state space model. In the present embodiment, the system noise d (k) is considered to be colored, and d (k) is represented by a state space model.

Here, as an example, the case where the frequency weighting function W (z) is a first-order low-pass filter will be described. In this case, the state space model of W (z) is expressed by the following equations (10) and (11). Here, v _n (k) is white Gaussian noise.

The equation (10), (11), the coefficient ^{_{A n (d), B n}} (d), C n (d), D n (d) is determined according to a frequency weighting function W (z) . Specifically, the transfer function G (z) in the equations (10) and (11) can be written as the following equation (12).

On the other hand, since the frequency weighting function W (z) is a first-order low-pass filter, the first-order low-pass filter 1 / (1 + T _L s) (time constant T _L ) is a bilinear transformation s = Assuming that the transfer function is discretized using (2 / T) ((1−z ⁻¹ ) / (1 + z ⁻¹ )) (sampling time T), W (z) is expressed by the following equation (13) It can be expressed as

From the above equations (12) and (13), the coefficients _An ^(d) , B _n ^(d) , and so on are satisfied so that G (z) = W (z), that is, the following equation (14) is satisfied. C _n ^(d) and D _n ^(d) may be determined.

For example, the coefficient ^{_{A n (d), B n}} (d), C n (d), D n (d) is determined as following equation (15) to (18). However, the values shown in the following equations (15) to (18) are examples of the coefficients _An ^(d) , B _n ^(d) , C _n ^(d) and D _n ^(d) , and the above equation (14) The coefficients A _n ^(d) , B _n ^(d) , C _n ^(d) and D _n ^(d) may have other values as long as

The above equation (4), the equation (10), extending with (11), the dynamics of the coefficients of each of the wavelength components _a n (t) can be expressed as following equation (19).

  As a result, the state space model according to the present embodiment can be expressed by the following equation by extending the state space model shown in the equations (6) and (7) using the equations (10) and (11). It is expressed as (20) and (21).

In the present embodiment, the state estimation device 4 shown in FIG. 1 selects the frequency weighting function W (z), and uses the selected frequency weighting function W (z) according to the above-described procedure according to the procedure described above. And 21) to generate an expanded state space model. Then, the state estimation device 4 estimates the overall vertical motion component a ₀ (k) and the coefficients a _n (k) of the respective wavelength components by applying a Kalman filter to the expanded state space model. Specifically, the state estimation device 4 estimates the molten metal level y _est (x _i , k) at the level gauge position x _i and the measured value y _obs (x _{i of the} molten metal level meter at each sampling time. , K), correct the overall vertical motion component a ₀ (k) and the time-variant coefficients a _n (k) (n = 1, 2,... N) of each wavelength component, Use to estimate sequentially. Then, the state estimation device 4 can estimate the hot water level distribution for each sampling time by substituting the estimated a ₀ (k) and a _n (k) into the equation (1). Incidentally, the equation (20), the estimation of (21) a ₀ in the expanded state space model shown in _(k), a n _(k) is commonly used as a technique for state estimation method using a Kalman filter Various techniques may be used. Therefore, detailed description of the estimation method is omitted here.

  In the above description, although the case where the frequency weighting function W (z) is a first-order low-pass filter has been described, the present embodiment is not limited to such an example. As the frequency weighting function W (z), for example, a band pass filter, a second-order low pass filter, or the like corresponding to various frequency characteristics may be used. When the forms of the frequency weighting function W (z) are different, specific forms of the state space model shown in the above equations (10) and (11) and the frequency weighting function W (z) shown in the equation (13) Although it changes, it is possible to construct an extended state space model by performing the same process as the process described above.

As described above, in the present embodiment, by introducing the weight frequency function W (z) into the estimation mechanism by the Kalman filter, when the system noise is colored noise, the estimation accuracy by the Kalman filter can be improved. . Therefore, it becomes possible to estimate the surface elevation distribution in the mold 2 with higher accuracy. Here, according to the present embodiment, when estimating the hot-water level distribution, the entire vertical movement component of the hot-water surface (ie, a ₀ (k)) and the fluctuation component of each wavelength component (ie, a ₁ (K),..., A _N (k)) can be estimated separately. That is, it is possible to separate and obtain the whole vertical movement component which is the control object of the molten metal level control with high accuracy. Therefore, the accuracy of the surface level control can be improved by performing the surface level control using the estimated total vertical movement component.

  Further, as described above, it is known from the conventional knowledge that in a continuous casting machine, a large number of slab defects are generated at a position where the temporal fluctuation of the surface level of the molten metal in the mold 2 is particularly large. According to this embodiment, since it becomes possible to estimate the hot-water surface shape with high accuracy, for example, by combining the hot-water surface shape fluctuation and the distribution of the subsurface subcutaneous defect in the slab, it is possible to realize high quality slab production. It is possible to understand proper operating conditions. At this time, by performing the estimation of the surface shape in real time based on the measurement value of the surface level meter 3, the distribution of the slab defect in the slab width direction based on the estimation result before the completion of casting Since it can be grasped, it becomes possible to carry out slab quality control quickly.

  As described above, according to the present embodiment, since the molten metal surface height distribution can be estimated with high accuracy, the cast slab quality can be significantly improved, and the yield improvement and the reduction of the manufacturing cost can be obtained. be able to.

FIG. 5 is a diagram for explaining the configuration of an algorithm of the process of estimating the molten metal level distribution by the state estimation device 4. In the figure, the estimation process 30 corresponds to the estimation process of the molten metal level distribution by the state estimation device 4. As shown, the state estimation device 4 calculates an estimated value y _est (x _i , k) of the surface level at the installation position x _i of the surface level meter 3 according to the estimation process of the estimation process 30. Then, the state estimation device 4 measures the error between the measured value of the surface level of molten metal y _obs (x _i , k) by the surface level meter 3 and the estimated value of the surface of molten metal level y _est (x _i , k) Calculate (output prediction error). The state estimation device 4 updates the Kalman gain _Kaug so that the output prediction error becomes smaller, and recalculates the estimated value y _est (x _i , k + 1) of the surface level at the next sampling time k + 1. . By repeating such a step of successive estimation, it becomes possible to estimate the molten metal level distribution with high accuracy.

The state estimation device 4 executes the above calculation for each installation position x _i of the surface level meter 3. Accordingly, the estimated value y _est (x _i , k) of the surface level at the installation position x _i of the surface level meter 3 is calculated for each position x _i .

In the figure, the state variable estimated value x _{B | A} represents a predicted value of the state quantity x _aug at time B at time A. The state estimation device 4 calculates the estimated value y _est (x _i , k) of the surface level from x _{k | k} obtained in the process of calculating the overall vertical motion component a ₀ (k) and the coefficient a of each wavelength component Extract ₁ (k), ..., a _N (k). Then, the state estimation device 4 substitutes the extracted a ₀ (k), a ₁ (k),..., A _N (k) into the equation (1) to obtain the surface height distribution y We can find x, k).

  An outline of an algorithm of the estimation processing of the hot water level distribution by the state estimation device 4 including the actual machine process is shown in FIG. FIG. 6 is a diagram for describing a configuration of an algorithm of a process of estimating the hot water level distribution by the state estimation device 4 including the actual machine process.

  In FIG. 6, the actual machine process 20 represents the state change of the surface of the molten metal occurring in the mold 2 of the actual continuous casting machine. As illustrated, the real machine process 20 can be expressed by the state space model shown in the above equations (6) and (7). The configuration of the estimation process 30 is the same as that shown in FIG.

In the algorithm, the state estimation device 4 executes the calculation process shown in the estimation process 30, and estimates the estimated value y _est (x _i , k) of the surface level at the installation position x _i of the surface level meter 3 Calculated by simulation. Then, the state estimation device 4 reduces the output prediction error which is the difference between the calculated y _est (x _i , k) and the measured value of the surface level y _obs (x _i , k) by the surface level meter 3. As described above, by repeating the sequential steps of the Kalman filter, by performing the process in the estimation process 30, it is possible to estimate the molten metal level distribution y (x, k) with high accuracy.

  FIG. 7 is a flowchart showing the procedure of the process of estimating the molten metal level distribution by the state estimation device 4. As shown in FIG. 7, in the estimation process according to the present embodiment, first, the frequency weighting function W (z) is selected (Step 1). The frequency weighting function W (z) can be determined, for example, according to the frequency characteristic of the disturbance component included in the fluctuation of the surface actually occurring in the mold 2 of the continuous casting machine. For example, when the low frequency component is relatively strong in the disturbance component, a low pass filter may be selected as the frequency weighting function W (z).

  The frequency characteristic of the disturbance component can be estimated, for example, by frequency analysis of the measured value of the surface level meter 3. Specifically, as a result of the frequency analysis, when the frequency distribution of the measurement value of the surface level meter 3 includes a periodic component different from the natural frequency of the wavelength component, the periodic component is disturbed by the disturbance. It can be regarded as representing the frequency characteristic of Alternatively, if the frequency characteristics of the disturbance component can be predicted from past actual values according to the operating conditions at the time of continuous casting, the frequency weighting function W (z) may be selected according to the prediction result. .

  However, in practice, the disturbance components included in the fluctuation of the surface of the mold 2 in the mold 2 are mixed in a complex manner due to various factors. Therefore, it may be difficult to estimate the frequency characteristic of the disturbance component from frequency analysis as described above or to predict the frequency characteristic of the disturbance component from operation conditions. Therefore, as the frequency weighting function W (z), it is preferable to select one that exerts a certain effect on disturbances having any frequency characteristics. As a result of experiments by the present inventors, by using a first-order low-pass filter as the frequency weighting function W (z), relatively high-accuracy estimation can be performed even for disturbances having any frequency characteristics. It turned out (for details, see Examples 1 and 2 below). From the experimental results, when it is difficult to estimate or predict the frequency characteristics of the disturbance component, a first-order low-pass filter may be suitably selected as the frequency weighting function W (z). However, even if the result of the frequency analysis of the disturbance component is not available, it is not necessary to use a first-order low-pass filter as the frequency weighting function W (z). For example, when it is known that the frequency characteristic of the disturbance component empirically has a second-order low-pass characteristic, the frequency weighting function W (z) may be appropriately selected, such as using a second-order low-pass filter.

  Once the frequency weighting function W (z) is selected, next, using the selected frequency weighting function W (z), the expanded state space model shown in the above equations (20) and (21) is constructed ( Step 2).

Next, by applying a Kalman filter to the constructed expanded state space model, a ₀ (k), a ₁ (k),..., A _n (k) are estimated (Step 3).

And, by substituting the estimated a ₀ (k), a ₁ (k),..., A _n (k) into the equation (1), the surface level distribution is estimated (Step 4) . The processes shown in Step 3 and Step 4 are executed according to the algorithm shown in FIG.

(3. Functional configuration of state estimation device)
The functional configuration of the state estimation device 4 that executes the processing described above will be described with reference to FIG. FIG. 8 is a block diagram showing a functional configuration of the state estimation device 4 according to the present embodiment. Referring to FIG. 8, the state estimation device 4 according to the present embodiment has a measurement value acquisition unit 41, an operation unit 42, an output unit 43, and a storage unit 44 as its function. The functions of each part will be described below.

  The measured value acquisition unit 41 is realized by a communication device that receives the measured value from the surface level meter 3. As described above, in the present embodiment, since the plurality of hot water level meters 3 (for example, the hot water level meters 3a and 3b shown in FIG. 2) are installed, the measurement value acquisition unit 41 Measured values are obtained from each of the three. The measurement value acquisition unit 41 provides the acquired measurement value to the calculation unit 42.

  The calculation unit 42 is realized by a processor such as a central processing unit (CPU) or a digital signal processor (DSP). In the calculation unit 42, the processor constituting the calculation unit 42 operates in accordance with a predetermined program, whereby the processing in Step 1 to Step 4 in FIG. 7 is executed, and the molten metal level distribution is estimated. Since the details of these processes have already been described, the description thereof is omitted here.

Arithmetic unit 42 provides output unit 43 with the estimation result of the molten metal level distribution. Alternatively, the calculation unit 42 may store the estimation result of the surface level distribution in the storage unit 44. In addition, the calculation unit 42 also calculates various information (for example, the overall vertical movement component a ₀ (k), the coefficient a _n (k) of each wavelength component, etc.) obtained in the process of estimation processing of the surface level distribution. , Or may be stored in the storage unit 44.

  The output unit 43 is realized by a processor such as a CPU and a communication device that transmits a signal to an external device. For example, the output unit 43 outputs the estimation result of the molten metal level distribution by the calculation unit 42 to the display / print device 5 shown in FIG. The display / printer 5 displays the estimation result of the surface level distribution on a display or the like. In addition, the output unit 43 may output the estimation result of the molten metal level distribution by the calculation unit 42 to the continuous casting control device 6 illustrated in FIG. 1. The continuous casting control device 6 controls, for example, the injection amount of molten steel into the mold 2 and / or the billet drawing speed from the mold 2 based on the estimated total vertical movement component so as to suppress the general vertical movement of the molten metal surface. Control.

  The storage unit 44 is implemented by, for example, a memory such as a read only memory (ROM) or a random access memory (RAM), and various storage devices such as a hard disk drive (HDD). The storage unit 44 stores, for example, various types of parameters used for estimation processing of the molten metal level distribution by the calculation unit 42, and various types of data such as the progress of the estimation processing. In addition, in the storage unit 44, the estimation result of the molten metal level distribution by the operation unit 42 may be temporarily or permanently stored. The estimation result may be output by the output unit 43 to the display / printing device 5 and / or the continuous casting control device 6 shown in FIG.

  In the above, an example of a function of state estimating device 4 concerning this embodiment was explained. Each component described above may be configured using a general-purpose member or circuit, or may be configured by hardware specialized for the function of each component. Also, the functions of a plurality of components may be realized collectively by the CPU. In addition, the structure for implementing the state estimation apparatus 4 can be suitably changed according to the technical level of occasions to implement.

  Moreover, it is possible to create a computer program for realizing each function of the state estimation device 4 according to the present embodiment as described above, and to implement the computer program on a personal computer or the like. It is also possible to provide a computer readable recording medium in which such a computer program is stored. The recording medium may be, for example, a magnetic disk, an optical disk, a magneto-optical disk, a flash memory or the like. Also, the above computer program may be distributed via, for example, a network without using a recording medium.

(4. Hardware configuration)
FIG. 9 is a block diagram showing an example of the hardware configuration of the state estimation device 4 according to the present embodiment. Referring to FIG. 9, the state estimation device 4 includes a CPU 901, a ROM 903, and a RAM 905. The state estimation device 4 further includes a bus 907, an input device 909, an output device 911, a storage device 913, a drive 915, a connection port 917, and a communication device 919.

  The CPU 901 functions as an arithmetic processing unit and a control unit, and controls the entire operation in the state estimation device 4 or a part of the operation according to various programs recorded in the ROM 903, the RAM 905, the storage device 913, or the removable recording medium 921. The ROM 903 stores programs used by the CPU 901, calculation parameters, and the like. The RAM 905 primarily stores programs used by the CPU 901, parameters that appropriately change in the execution of the programs, and the like. These are mutually connected by a bus 907 constituted by an internal bus such as a CPU bus. The CPU 901 can configure the arithmetic unit 42 and the output unit 43 illustrated in FIG. 8. In addition, the ROM 903 and the RAM 905 can constitute the storage unit 44 shown in FIG.

  The bus 907 is connected to an external bus such as a peripheral component interconnect / interface (PCI) bus via a bridge.

  The input device 909 is, for example, an operation unit operated by the user, such as a mouse, a keyboard, a touch panel, a button, a switch, and a lever. Further, the input device 909 may be, for example, a remote controller using infrared rays, radio waves, or the like, or may be an externally connected device 923 such as a tablet terminal having an operation function of the state estimation device 4. Furthermore, the input device 909 is configured of, for example, an input control circuit that generates an input signal based on the information input by the user using the above-described operation means, and outputs the generated input signal to the CPU 901. The user of the state estimation device 4 can input various data to the state estimation device 4 and instruct processing operations by operating the input device 909.

  The output device 911 is configured of a device capable of visually or aurally notifying the user of the acquired information. Examples of such a device include a display using a liquid crystal or CRT, an indicator such as a lamp, an audio output device such as a speaker or a headphone, or a printer. The output device 911 outputs, for example, results obtained by various processes performed by the state estimation device 4. For example, the display displays the results obtained by the various processes performed by the state estimation device 4 on the screen as text or an image. Also, for example, the voice output device voice-outputs the result obtained by the various processes performed by the state estimation device 4 as an alarm or a dialog. As described with reference to FIG. 1, the system 1 according to the present embodiment includes the display / printer 5 as means for presenting information to the user. Since the display / print device 5 has the same function as the output device 911, when the display / print device 5 can substitute the function of the output device 911, the state estimation device 4 outputs the output device 911. May not necessarily be provided.

  The storage device 913 is a device for data storage configured as an example of a storage unit of the state estimation device 4. The storage device 913 is configured of, for example, a magnetic storage device such as an HDD, a semiconductor storage device, an optical storage device, or a magneto-optical storage device. The storage device 913 stores programs executed by the CPU 901, various data, various data acquired from the outside, and the like. The storage device 913 can constitute the storage unit 44 shown in FIG.

  The drive 915 is a reader / writer for a recording medium, and is built in or externally attached to the state estimation device 4. The drive 915 reads out information recorded in a removable recording medium 921 such as a mounted magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory, and outputs the information to the RAM 905. The drive 915 can also write a record on a removable recording medium 921 such as a mounted magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory.

  The connection port 917 is a port for directly connecting the device to the state estimation device 4. Examples of the connection port 917 include a universal serial bus (USB) port, an IEEE 1394 port, a small computer system interface (SCSI) port, and an RS-232C port. By connecting the external connection device 923 to the connection port 917, the state estimation device 4 acquires various data directly from the external connection device 923 or provides various data to the external connection device 923.

  The communication device 919 is, for example, a communication interface configured of a communication device or the like for connecting to the communication network 925. The communication device 919 may include, for example, a communication card for LAN (Local Area Network). The communication device 919 may also include a router or a modem for various wired communication. The communication device 919 can transmit and receive signals and the like according to a predetermined protocol such as TCP / IP, for example, with the Internet or another communication device. Further, the communication network 925 connected to the communication device 919 is configured by a network or the like connected by wire or wireless, and may include, for example, the Internet, a LAN, and the like. The communication device 919 can constitute the output unit 43 shown in FIG.

  In the above, an example of the hardware configuration which can implement | achieve the function of the state estimation apparatus 4 which concerns on this embodiment was shown. Each component described above may be configured using a general-purpose member, or may be configured by hardware specialized to the function of each component. Therefore, it is possible to change the hardware configuration to be used as appropriate according to the technical level of the time of carrying out the present embodiment.

  A first embodiment of the present invention will be described. In the first embodiment, disturbance is numerically generated on a computer to generate data of virtual fluctuation of the metal surface. And with respect to the data of the produced | generated melt surface fluctuation, the melt surface height distribution estimation method which concerns on this embodiment shown in FIG. 7 mentioned above was performed, and the estimation precision was evaluated.

  As disturbances, those having frequency characteristics of the following six types ((A) to (F)) were prepared. (A) to (E) are colored disturbances, and (F) is a white disturbance prepared for comparison.

(Type of disturbance)
(A): 2 nd order band pass filter (center frequency 0.1 Hz)
(B): Second-order low-pass filter (cut-off frequency 0.6 Hz)
(C): 2 nd order low pass filter (cutoff frequency 0.3 Hz)
(D): 1st order low pass filter (cutoff frequency 0.6 Hz)
(E): 1st order low pass filter (cutoff frequency 0.3 Hz)
(F): White noise

  In addition, the colored disturbance in (A)-(E) produced | generated the white noise by passing the transfer function corresponding to each disturbance. The transfer function G (s) of the disturbance dynamics is shown in the following equations (22) to (24). However, when implemented in a computer, the transfer functions shown in the following equations (22) to (24) are time-discretized using a bilinear transformation.

  In addition, the following six types ((a) to (f)) are taken into consideration as the frequency weighting function W (z) of the Kalman filter estimation mechanism, and a Kalman filter that provides a robust estimation result against variations in frequency characteristics of disturbances The frequency weights of the evaluation function were investigated.

(Type of frequency weighting function)
(A): Second-order band pass filter (center frequency 0.1 Hz)
(B): Second-order low-pass filter (cut-off frequency 0.6 Hz)
(C): Second-order low pass filter (cutoff frequency 0.3 Hz)
(D): 1st order low pass filter (cutoff frequency 0.6 Hz)
(E): 1st order low pass filter (cutoff frequency 0.3 Hz)
(F): No frequency weighting

  The specific form of the frequency weighting function W (z) is the same as the transfer function G (s) of the disturbance dynamics described above. That is, W (z) in (a) is the time discretization of the above equation (24) using bilinear transformation, and W (z) in (b) and (c) is the above equation (23) Is time-discretized using bilinear transformation, and W (z) in (d) and (e) is time-discretized using the above-mentioned equation (22) using bilinear transformation.

Other detailed conditions of the simulation are as follows.
-Mold width 1.63 m.
-Three level meters shall be installed, and the measurement position was at both ends and 1/4 width position.
・ Measurement is performed for 20480 seconds at 0.1 sec pitch.
-The number of wavelength components is considered up to the fifth order.
・ We assume step-like disturbance about whole up-and-down motion.
The frequency weighting function is the same for each wavelength component coefficient.
• The system noise variance value of each wavelength component coefficient is the same.
• The observation noise variance was fixed in each case.

  The simulation is executed under the above conditions, and each frequency weighting function W (z) ((a) to (f)) is applied to the data on the surface fluctuation corresponding to each disturbance (A) to (F). The molten metal level distribution estimation method according to the present embodiment was respectively executed to estimate the molten metal level distribution. Then, in order to quantitatively evaluate the estimation accuracy of each case, a root mean square error (RMSE: Root Mean Square Error) defined by the following equation (25) was calculated.

here,
T is the number of sampling points in the time direction,
Δt is the sampling interval,
P is the number of sampling points in the mold width direction,
Y _sim (p, kΔt) is the surface level at the widthwise position p at the sampling time t = kΔt in the surface level fluctuation to be analyzed generated on the computer
Y _est (p, kΔt) is the surface level at the widthwise position p at the sampling time t = kΔt in the surface level fluctuation estimated by the surface level estimation method according to the present embodiment.

  The results are shown in Table 1 below. In Table 1, for each of the disturbances (A) to (F), the RMSE in the case where the estimation accuracy is the best (that is, when the RMSE is minimum) is normalized as 1, and the RMSE in each case is displayed There is. Moreover, in Table 1, the addition value of RMSE for every frequency weighting function W (z) ((a)-(f)) is also collectively described (refer rightmost column).

  From Table 1 above, when the disturbance is a colored disturbance (cases (A) to (E)) and the hot water level distribution is estimated without frequency weighting ((f)), the disturbance is a white disturbance. It can be seen that the estimation error is larger than in the case (case (F)). That is, it can be said that it is difficult to accurately estimate the surface level distribution in the actual mold by a method in which the disturbance is assumed to be a white disturbance and no frequency weight is considered.

  Also, in the case where the disturbance is generated through the second order band pass filter and the second order low pass filter (cases of (A), (B) and (C)), the surface height distribution without frequency weighting ((f)) Estimation makes the estimation accuracy worse. Conversely, when the disturbance is white noise ((F)), if the second-order low-pass filter is selected as the frequency weighting function W (z) ((b), (c)) and the hot-water level distribution is estimated , The estimation accuracy is degraded.

  In addition, referring to the addition value of RMSE for each frequency weighting function W (z) ((a) to (f)), a first-order low-pass filter (cutoff frequency 0.6 Hz, 0) as the frequency weighting function W (z) When .3 Hz is selected ((d), (e)), it can be seen that the added value is smaller than in the other cases. This is because, by selecting a first-order low-pass filter as the frequency weighting function W (z), an average good estimation result can be obtained for various disturbances as shown in (A) to (F). It shows what can be done. Thus, when selecting the frequency weighting function W (z), for example, for each frequency weighting function, estimation processing is performed on hot water surface fluctuation including each of a plurality of types of assumed disturbances, and from the estimation result It is preferable to calculate the addition value of RMSE and select the frequency weighting function W (z) that minimizes it. Here, as an example, the validity of the frequency weighting function W (z) is determined using the addition value, but instead of the addition value, each frequency weighting function W (z) ((a) to (f)) An average value of RMSE of

  Alternatively, RMSE corresponding to each disturbance ((A) to (F)) is calculated for each of the frequency weighting functions W (z) ((a) to (f)), and the frequency weighting function W (z) ((a) The maximum value may be obtained for each of (f) to (f), and the frequency weighting function W (z) having the smallest maximum value may be selected. By selecting the frequency weighting function W (z) in this way, it is possible to obtain highly robust estimation results.

  A second embodiment of the present invention will be described. In the second embodiment, a water model experiment of molten steel flow was conducted to confirm the effectiveness of the present invention. In addition, a water model experiment is an experiment which simulates the fluctuation | variation of a molten-steel surface by making a model of a full size large mold using a transparent acrylic resin board, and filling water instead of molten steel. Water is often used as the liquid that fills the mold because water has similar hydrodynamic characteristics to molten steel.

  Specifically, by analyzing the water surface shooting video at the time of water model experiment, fluctuation data of water surface height was acquired. And the value of the water surface height in the position corresponding to a water surface level meter installation position among the fluctuation data of the said water surface height is regarded as the measured value in a water surface level meter, and the water according to this embodiment The surface height distribution estimation method was implemented.

  In the second embodiment, a first-order low-pass filter is applied as the frequency weighting function W (z) on the basis of the result of the first embodiment. However, in order to confirm the influence of the cut-off frequency on the estimation accuracy, the cut-off frequency of the first-order low-pass filter is changed in the range of 0.1 Hz to 1.0 Hz, and the surface height for each cut-off frequency The distribution was estimated.

  In addition, in the case where the frequency weighting function W (z) was not taken into consideration, for the sake of comparison, the hot water level fluctuation was similarly estimated.

Other detailed conditions of the simulation are as follows.
・ Mold width 1.63 m, casting speed 1.6 m / m equivalent.
-The level meter shall be installed at 3 points, and the measurement position was at both ends and 1/4 width position.
Measured for 150 seconds at 0.1 second pitch.
-The number of wavelength components is considered up to the fifth order.
・ We assume step-like disturbance about whole up-and-down motion.
• The system noise and frequency weighting function are the same for each wavelength component coefficient.
• The observation noise variance was fixed in each case.
· The system noise dispersion value of the wavelength component coefficient uses the value obtained by numerical optimization (dispersion value at which the RMSE of the metal surface shape estimation error is minimized).

  The simulation is performed under the above conditions, and a first-order low-pass filter (cutoff frequency: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, as a frequency weighting function W (z) In the case of applying 0.7, 0.8, 0.9, 1.0 Hz)) and in the case of not applying the frequency weighting function W (z), the method of estimating the surface height distribution according to this embodiment Was performed, and the RMSE with the water surface height obtained as a result of the video analysis was calculated for the estimation results in each case. The definition of RMSE is the same as in the first embodiment.

  The results are shown in Table 2 below and FIG. FIG. 10 is a graph showing the results of the second embodiment. FIG. 10 is a graph of the contents of Table 2 below.

  As shown in Table 2 and FIG. 10, when the frequency weighting function W (z) was not applied, the RMSE was 0.908 mm. On the other hand, when the first-order low-pass filter was selected as the frequency weighting function W (z), the RMSE had a value between about 0.850 and 0.860 mm. In particular, when a first-order low-pass filter having a cutoff frequency of 0.3 Hz is selected as the frequency weighting function W (z), the RMSE is minimized, and its value is 0.853 mm.

  From the result, regardless of the cutoff frequency, by applying a first-order low-pass filter as the frequency weighting function W (z), the estimation accuracy can be improved compared to the case where the frequency weighting function W (z) is not used It could be confirmed. Further, in this example, it was found that the estimation accuracy is the highest when the first-order low-pass filter having a cutoff frequency of 0.3 Hz is selected as the frequency weighting function W (z).

(5. supplement)
Although the preferred embodiments of the present invention have been described in detail with reference to the accompanying drawings, the present invention is not limited to such examples. It is obvious that those skilled in the art to which the present invention belongs can conceive of various changes or modifications within the scope of the technical idea described in the claims. Of course, it is understood that these also fall within the technical scope of the present invention.

Reference Signs List 1 system 2 mold 3 surface level meter 4 state estimation device 41 measured value acquiring unit 42 computing unit 43 output unit 44 storage unit 5 display / printing device 6 continuous casting control device 8 immersion nozzle

Claims (7)

A state estimation method for estimating the distribution of the surface elevation in the mold width direction in the mold of the continuous casting machine with respect to the position in the mold width direction,
Obtaining a measurement value of the surface level in the mold at at least two different measurement points in the width direction of the mold;
The height of the surface of the molten metal at any time and any position in the mold width direction, the total vertical movement component, and the wavelength 2 W / n (where W is the width of the mold and n is 1 or more) Representing by a linear equation obtained by superposition of wavelength components of sine waves of integers) and expressing the coefficients of the wavelength components by a standing wave component and a disturbance component, representing by a state space model;
The state space model is expanded using a frequency weighting function for giving a frequency weight to an evaluation function of a Kalman filter for estimating the state represented by the state space model by treating the disturbance component as system noise. Step and
By applying a Kalman filter to the expanded state space model obtained by expanding the state space model using the measured value of the surface level as an observed value, the coefficients of the overall vertical motion component and the wavelength component are sequentially Estimating steps;
including,
State estimation method. A first order low pass filter is used as the frequency weighting function.
The state estimation method according to claim 1. As the frequency weighting function, a frequency weighting function corresponding to the frequency characteristic of the disturbance component to be analyzed based on the measurement value of the surface level is used.
The state estimation method according to claim 1.   The method according to any one of claims 1 to 3, further comprising the step of estimating the hot water level at the arbitrary time and the arbitrary position using the estimated total vertical movement component and the coefficient of the wavelength component. The state estimation method described in Item. The state estimation method according to any one of claims 1 to 4, wherein the hot water level at the arbitrary time and the arbitrary position is determined using the coefficients of the whole vertical movement component and the wavelength component. Further including the step of separating and describing an overall vertical movement component and the wavelength component,
Controlling the injection amount of molten steel into the mold or the billet withdrawal speed from the mold based on the total vertical movement component.
Hot water level control method. A program that causes a computer to execute a state estimation method for estimating the distribution of the surface level in the mold in the mold width direction in the mold of the continuous casting machine,
The state estimation method is
Obtaining a measurement value of the surface level in the mold at at least two different measurement points in the width direction of the mold;
The height of the surface of the molten metal at any time and any position in the mold width direction, the total vertical movement component, and the wavelength 2 W / n (where W is the width of the mold and n is 1 or more) Representing by a linear equation obtained by superposition of wavelength components of sine waves of integers) and expressing the coefficients of the wavelength components by a standing wave component and a disturbance component, representing by a state space model;
The state space model is expanded using a frequency weighting function for giving a frequency weight to an evaluation function of a Kalman filter for estimating the state represented by the state space model by treating the disturbance component as system noise. Step and
By applying a Kalman filter to the expanded state space model obtained by expanding the state space model using the measured value of the surface level as an observed value, the coefficients of the overall vertical motion component and the wavelength component are sequentially Estimating steps;
including,
program. A state estimation device for estimating the distribution of the surface elevation in the mold width direction in the mold of the continuous casting machine with respect to the mold width direction,
A measurement value acquisition unit for acquiring measurement values of the surface level in the mold at at least two different measurement points in the width direction of the mold;
The height of the surface of the molten metal at any time and any position in the mold width direction, the total vertical movement component, and the wavelength 2 W / n (where W is the width of the mold and n is 1 or more) Expressed by a linear equation obtained by superposition of wavelength components of sine waves of integers) and by a state space model in which the coefficients of the wavelength components are expressed by a standing wave component and a disturbance component,
The state space model is expanded using a frequency weighting function for giving a frequency weight to an evaluation function of a Kalman filter for estimating the state represented by the state space model by treating the disturbance component as system noise. ,
By applying a Kalman filter to the expanded state space model obtained by expanding the state space model using the measured value of the surface level as an observed value, the coefficients of the overall vertical motion component and the wavelength component are sequentially An operation unit to estimate
Equipped with
State estimation device.

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