JP7255804B2 - State quantity estimation method, state quantity estimation device, and program - Google Patents

Description

The present invention relates to a state quantity estimation method, a state quantity estimation device, and a program for estimating a current flowing from a sacrificial anode.

Sacrificial anodes are commonly used to prevent corrosion of steel structures placed in water. Metals such as aluminum, zinc, and magnesium, which have a higher electrochemical ionization tendency than steel, and their alloys are used for the sacrificial anode. to prevent Sacrificial anodes tend to wear out over time and must be periodically renewed. In order to evaluate the soundness of the sacrificial anode and to grasp the renewal time, there is a method of measuring the volume and weight of the sacrificial anode to estimate the degree of consumption of the sacrificial anode. For example, a diver measures the perimeter of a sacrificial anode in water, calculates the volume, and obtains the remaining life. However, measurement by divers not only raises concerns about safety, but also requires a large amount of labor, takes time for inspection work, and increases costs.

The applicant has already proposed means for estimating the current of the sacrificial anode and predicting the timing of renewal of the sacrificial anode (for example, Patent Document 1). According to the method described in Patent Document 1, a measuring unit having a sensor for measuring the potential around the sacrificial anode in water, a moving body to which the measuring unit is attached, and a moving body installed near the sacrificial anode. and a guide portion that slides in the vertical direction. According to this method, the electric current output from the sacrificial anode can be estimated based on the potential detected by the sensor while moving the movable body along the guide portion in the vertical direction.

JP 2019-002073 A

According to the method described in Patent Literature 1, the position of the moving body itself in the sea is known, and it is assumed that the moving body moves vertically along the guide section. However, due to the influence of various natural conditions such as swells and waves in the marine environment, the position of the measurement part, which is the premise for estimating the current output from the sacrificial anode, does not necessarily correspond to the position of the guide part, resulting in inaccurate estimation results. There was a problem that it may become.

SUMMARY OF THE INVENTION The present invention has been made in view of the above problems, and provides a state quantity estimation method, a state quantity estimation device, and a program capable of estimating a current flowing from a sacrificial anode even when the position of a moving object is unclear. for the purpose.

In order to achieve the above object, the present invention provides a state quantity estimation method for estimating an unknown state quantity representing the cathodic protection state of a metal structure protected by a sacrificial anode in an electrolyte using a state quantity estimation model. a step of obtaining a measured value of the potential in the electrolyte around the sacrificial anode when a moving body having a potential sensor is moved for a predetermined time; and using the state quantity estimation model, predicting the next state temporally updated from the previous state; repeating a filtering process of correcting the next state to a state probabilistically closest to the true value based on the measured value; and calculating an estimated value of the state quantity including the position and attitude of the moving body and the current output from the sacrificial anode.

According to the present invention, when measuring the potential around the sacrificial anode installed in water, even if the position and posture of the moving object are unstable due to the influence of waves, etc., the state quantity can be estimated by , the position and attitude of the moving body can be calculated, and the current of the sacrificial anode can also be calculated. Further, according to the present invention, the calculated position and orientation can be converted into an estimated potential value by electrostatic field analysis, and only the electric field formed by the sacrificial anode can be measured. According to the present invention, there is no need for a device such as a rail for moving the measurement unit, which reduces the measurement cost, eliminates the need for divers to perform measurements, and improves safety.

In order to achieve the above object, the state quantity estimation model calculates the state quantity that changes from time to time from the measured value containing an error, and a state equation that temporally updates the state quantity; and an observation equation that converts the state quantity into an observed value that is the same physical quantity as the measured value, and is indefinitely spaced from the sacrificial anode by the moving body having a plurality of the potential sensors whose positions are relatively fixed. a step of repeatedly acquiring n (n=A/T) measured values from the plurality of sensors at a constant sampling interval T within an observation time A in a state of unclear attitude at a position; , at time t=0, the step of generating the initial state of the state quantity, and using the state equation, at t=1, 2, . . . converting the next state quantity predicted using the observation equation into the observed value; and the filtering process of calculating the estimated value based on the observed value and the measured value. and performing.

According to the present invention, based on the measured value of the electric field formed by the sacrificial anode, the state quantity estimation is performed by repeatedly estimating the state quantity using the state equation and the observation equation, so that the corrosion protection output from the sacrificial anode Current can be estimated.

In order to achieve the above object, the state quantity estimation model is a particle filter, and when t = 0, a step of generating an initial state of a large number of particles having information on the state quantity, and using the state equation when t=1, 2, . . . A/T, predicting the next state from the previous state for each of the particles; and predicting the next state for each of the particles using the observation equation. into the observed value; and the filtering process of calculating the likelihood of the observed value and the measured value for each particle, weighting by normalization, and obtaining the estimated value by weighted average and a resampling step of extracting particles having a likelihood higher than a predetermined value from the particles and duplicating the extracted particles.

According to the present invention, in state quantity estimation using a particle filter, by filtering the estimated value of the state quantity calculated using the likelihood, the estimated value can be stochastically approximated to the true value, and the sacrificial anode can most likely estimate the protection current output from

To achieve the above object, the observation equation may include an equation representing an electric field analysis based on a discretization technique for partial differential equations.

According to the present invention, the anticorrosion current output from the sacrificial anode can be estimated using the potential measurement value by solving the observation equation according to the discretization method of the partial differential equation.

Further, the present invention is a state quantity estimating device for estimating an unknown state quantity representing the cathodic protection state of a metal structure protected by a sacrificial anode in an electrolyte using a state quantity estimating model, Using an acquisition unit that acquires a measured value of the potential in the electrolyte around the sacrificial anode when the moving body having the potential sensor is moved during time, and the state quantity estimation model, predicting the temporally updated next state, repeating filtering processing for correcting the next state to a state probabilistically closest to the true value based on the measured values, and determining the position, posture, and sacrifice of the moving body and an estimating unit that calculates an estimated value of the state quantity including the current output from the anode.

In order to achieve the above object, the moving body may be further provided, and the moving body may include a body portion and a hydrofoil provided on the body portion and formed along a vertical direction.

According to the present invention, when the mobile body moves in the water, the hydrofoil is formed in the main body, so that the movement of the main body is stabilized, the variation in the measured values is reduced, and the state quantity estimation accuracy is improved. can be improved.

In order to achieve the above object, the main body may be formed in any one of a tubular shape, a conical shape, a polyhedral shape, and a frame shape.

ADVANTAGE OF THE INVENTION According to this invention, while comprising a main-body part by a simple shape, while reducing underwater resistance, a manufacturing process can be simplified and cost can be reduced.

Further, the present invention provides a program for estimating an unknown state quantity representing the state of cathodic protection of a metal structure protected by a sacrificial anode in an electrolyte using a state quantity estimation model, wherein a computer stores a predetermined Acquire a measured value of the potential in the electrolyte around the sacrificial anode when moving the moving body having the potential sensor during time, and use the state quantity estimation model to temporally change the state from the previous state Predicting the updated next state, repeating filtering processing for correcting the next state to a state probabilistically closest to the true value based on the measured values, and determining the position and orientation of the moving body and the sacrificial anode. It is characterized in that an estimated value of the state quantity including the current to be output is calculated.

According to the present invention, when the electric potential is measured around the sacrificial anode installed in water, the state quantity estimation model can be used even if the position and posture of the moving object are unstable due to the influence of waves and the like. Therefore, it is possible to calculate the position and attitude of the moving body and also the current output from the sacrificial anode.

According to the present invention, it is possible to estimate the current output from the sacrificial anode even when the position and attitude of the moving body are unclear.

It is a figure which shows the electric potential measurement situation of the vicinity of the sacrificial anode provided in the structure. It is a block diagram which shows the structure of a state quantity estimation apparatus. FIG. 4 is a diagram showing a modeled measurement unit; 4 is a flowchart showing the flow of state quantity estimation processing; 4 is a flow chart showing the flow of processing executed in an estimating unit 30. FIG. FIG. 4 is a diagram showing parameters used for generating simulated measurement data for numerical experiments; It is a figure which shows the parameter of the equation of state and particle generation conditions which were used for the numerical experiment. It is a figure which shows the result of a numerical experiment. FIG. 4 is a diagram showing results of numerical experiments on estimated potentials; It is a perspective view which shows the structure of a mobile body. FIG. 11 is a perspective view showing another structure of the moving body; FIG. 11 is a perspective view showing another structure of the moving body; FIG. 11 is a perspective view showing another structure of the moving body; FIG. 11 is a perspective view showing another structure of the moving body; FIG. 11 is a perspective view showing another structure of the moving body; FIG. 11 is a perspective view showing another structure of the moving body;

Embodiments of the state quantity estimation method, the state quantity estimation device, and the program according to the present invention will be described below with reference to the drawings.

As shown in FIG. 1, the sacrificial anode P is attached, for example, in the vicinity of a metal structure U placed in the sea with a predetermined distance therebetween via a fixing portion Q such as a metal core. The sacrificial anode P is made of, for example, a metal such as aluminum, zinc, magnesium, or an alloy thereof. The sacrificial anode P may be provided not only in the sea but also in the ground.

Between the sacrificial anode P and the steel material, an anti-corrosion current (current I) steadily flows from the sacrificial anode P toward the structure U using seawater as an electrolyte due to a potential difference caused by a difference in ionization tendency. is galvanically protected. At this time, an electric field is formed around the sacrificial anode P by a current flowing from the sacrificial anode P to the steel material.

As shown in FIGS. 2 and 3, the state quantity estimation device 1 includes a measurement unit 2 that measures the potential around the sacrificial anode P, a moving body 10 provided in the measurement unit 2, and a terminal device 15. Prepare. The state quantity estimating device 1 measures the electric potential in the vicinity of the sacrificial anode P using the moving body 10, and based on the measurement result, an unknown electric potential representing the cathodic protection state of the metal structure U protected by the sacrificial anode P. State quantity is estimated using a state quantity estimation model. The state quantity estimation device 1 tracks the position of the moving body 10 that moves over time, and calculates the estimated value of the position of the moving body 10 and the current output from the sacrificial anode at each time.

The moving body 10 is, for example, a moving body formed so as to be lifted vertically upward from a state of being suspended in water by a wire or the like, or to be lowered. The moving body 10 may move not only in the vertical direction, but also in the horizontal direction or the oblique direction. That is, the moving direction of the moving body 10 is not limited, and the moving body 10 may move in any direction. The structure of the moving body 10 will be detailed later.

A moving body 10 is provided with a plurality of (for example, four) sensors o, a, b, and c. A plurality of sensors o, a, b, and c are potential sensors that detect potential. The plurality of sensors o, a, b, and c are set such that, for example, a sensor serving as a reference for position measurement is set to o. It is attached to the moving body 10 so as to maintain the positional relationship of . A plurality of sensors o, a, b, and c whose relative positions are fixed detect potentials and obtain measured values. The measured values are potentials, potential differences between sensors, or both.

Since the natural potential of the steel material constituting the structure U immersed in seawater varies depending on the situation, the influence of the unknown natural potential of the steel material can be canceled by using the potential difference as the measured value. Obtaining a potential difference measurement is particularly effective in real field measurements. In addition to the plurality of sensors o, a, b, and c, the moving body 10 may be provided with other sensors for measuring the position, such as a water depth gauge and a laser rangefinder. Other sensors capable of grasping these positions can improve the accuracy of estimated values based on the equation of state described later.

The mobile unit 10 and the terminal device 15 are connected by wire or wirelessly, for example. The mobile unit 10 and the terminal device 15 do not necessarily have to be connected. Alternatively, the terminal device 15 may obtain the information through data communication or the like.

The terminal device 15 is configured by, for example, a personal computer, a tablet terminal, a smart phone, or the like. For example, the terminal device 15 estimates the position of the moving body 10 and the current output from the sacrificial anode based on the acquisition unit 20 that acquires the measurement values acquired by the measurement unit 2 and the measurement values acquired by the acquisition unit 20. and a display unit 40 for displaying the calculation result of the estimation unit 30 . The acquisition unit 20 is an interface that acquires measurement data from the measurement unit 2 .

The estimating unit 30 calculates estimated values of the position of the measuring unit 2 and the current of the sacrificial anode P based on the measured values obtained from the measuring unit 2 . The estimating unit 30 calculates, for example, the self-position and orientation of the measuring unit 2 and the estimated values of the current output from the sacrificial anode P by state quantity estimation using a particle filter. A calculation method of the estimation unit 30 will be described later.

The estimation unit 30 is implemented by a processor such as a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit) executing a program (software). Some or all of these functional units may be realized by hardware such as LSI (Large Scale Integration), ASIC (Application Specific Integrated Circuit), and FPGA (Field-Programmable Gate Array), or may be realized by software. It may be realized by cooperation of hardware. The program may be stored in advance in a storage device such as a HDD (Hard Disk Drive) or flash memory, or may be stored in a removable storage medium such as a DVD or CD-ROM. It may be installed in the storage device by being attached.

A display unit 40 outputs the calculation result of the estimation unit 30 . The display unit 40 is, for example, a display device such as an LCD (Liquid Crystal Display), an organic EL (Electro Luminescence) display, an LED (Light Emitting Diode) display, or the like.

Next, state estimation processing executed by the estimation unit 30 will be described.

The estimation unit 30 estimates state quantities based on the measured values measured by the measurement unit 2 . The measured value is the potential in the vicinity of the sacrificial anode P measured by the measuring unit 2 having the moving body 10 while moving unstably under the influence of waves or the like. Therefore, the measured values are obtained by the measuring unit 2 having a plurality of sensors provided so as to maintain a relative positional relationship with the moving body 10 in an indefinite posture state at a position indefinitely separated from the sacrificial anode P. measured.

The estimation unit 30 estimates the current output from the sacrificial anode P based on the state quantity estimation method in such an observation environment. A state quantity estimation method is a method of estimating an unknown state using a state quantity estimation model. The state quantity estimation model calculates a state quantity that changes from moment to moment. The state quantity estimation model is described by a state equation (system equation) and an observation equation, and has the following processes (1) and (2). Here, the state equation is an equation for estimating a new state quantity by temporally updating the state quantity at a certain point in time. The state equation is, for example, an equation for estimating state x t+1 at time t+ ₁ by adding probabilistic noise to state x _t . An observation equation is a formula for converting a state quantity into an observed value, which is the same physical quantity as a measured value. The observation equation, for example, adds probabilistic noise based on states x _t to produce observations y _t .

(1) Prediction: Predict the state _xt at time t based on the discretized state equation, and calculate the observed value _yt based on the observation equation. (2) Filtering: A process of estimating the state x _t based on the measured values measured during the observation time _from time 1 to time t. presume.

Here, a nonlinear Kalman filter such as a particle filter, an extended Kalman filter, or an unscented Kalman filter is used for the state quantity estimation method.

FIG. 4A is a flowchart showing the processing flow of a state estimation method based on the state estimation method. A state space is constructed based on a state quantity estimation model including a state equation and an observation equation (step S1). For example, a program that causes the estimation unit 30 to execute the state equation and the observation equation is input to the terminal device 15 in advance. The moving body 10 is moved around the sacrificial anode in the electrolyte, and the measurement unit 2 acquires the measured value of potential (step S2).

The estimator 30 generates state quantities in the initial state (step S3). The initial state is given, for example, by the operator inputting arbitrary values into the terminal device 15 . The estimation unit 30 calculates an observed value based on the state quantity generated using the observation equation (step S4). Based on the measured values obtained from the measuring unit 2 and the calculated observed values, the estimating unit 30 performs filtering processing for correcting the next state to a state that is probabilistically closest to the true value. An estimated state quantity including the current output from the sacrificial anode is calculated (step S5).

The estimating unit 30 updates the estimated value to a state quantity that is temporally transitioned using the state equation (step S6). The estimating unit 30 determines in step 7 whether or not a certain end condition such as the end of the measurement period is satisfied. The estimating unit 30 terminates the repetitive processing when the termination condition is satisfied in step 7 . Through the above processing, the estimating unit 30 calculates the estimated values of the state quantities including the position and posture of the moving body 10 and the current output from the sacrificial anode so as to be closest to the true values.

State quantity estimation using a particle filter, which is known as one method of Bayesian estimation, will be described below as an example. The estimating unit 30 calculates the position and orientation of the moving body 10 and the current output from the sacrificial anode P using processing that repeats the procedure of prediction, observation, and resampling based on the particle filter.

FIG. 4B is a flow chart showing the flow of processing executed in the estimation unit 30. As shown in FIG. The estimation unit 30 constructs a state space model for the position and posture of the moving body 10 and the current output from the sacrificial anode P. FIG. N particles (N is a natural number) included in the area where the moving object 10 exists are set as means for estimation using a particle filter. The estimating unit 30 first generates an initial state by scattering a large number (N) of particles, to which position, orientation, and current value information is randomly given, in space (step S10). Next, the estimating unit 30 uses the discretized state equation to calculate the predicted value of the next state after the N particles temporally transition from the previous state (step S12).

The estimation unit 30 calculates N positions (hereinafter referred to as potential measurement positions) of the respective sensors o, a, b, and c based on the predicted values of the states including the calculated positions and orientations of the N particles. Then, the estimation unit 30 performs electrostatic field analysis using the boundary element method based on the calculated positions and current values of the sensors o, a, b, and c, and measures the potentials of the sensors o, a, b, and c. An observed value of the potential measured at the position is calculated using an observation equation for each of N particles (step S14).

Next, the estimation unit 30 obtains the likelihood of each particle from the measured potential values obtained from the sensors o, a, b, and c and the calculated estimated values of the observed values. Then, these likelihoods are weighted by normalization, and weighted averaging is performed to calculate an estimated value (step S16). That is, the estimating unit 30 performs filtering processing to stochastically obtain the potential so that the estimated value of the observed value at the position of the moving body 10 approaches the true value of the measured value.

Next, the estimating unit 30 extracts particles having a likelihood higher than a predetermined value from among the N particles, copies the extracted particles, generates new N particles, and scatters them in space. Sampling is performed (step S18). Next, in step S<b>20 , the estimating unit 30 determines whether or not a certain end condition such as the end of the measurement period is satisfied. The estimating unit 30 terminates the repetitive processing when the termination condition is satisfied in step 20 .

Next, the contents of each process of steps S10 to S20 executed in the estimation unit 30 will be described in detail.

First, the processing of step S10 will be described.

式（１）は、犠牲陽極Ｐの重心を３次元座標系の原点として、測定部２の推定すべき複数のパラメータを含む状態量を状態ベクトルＸとして表現したものである。原点は予め解析領域内(もしくは構造物上)の任意の点を設定してもよい。原点は、例えば、構造物の端部に設定してもよいし、構造物の任意の位置に設定してもよい。状態ベクトルＸは、例えば、測定部２の基準点の３次元座標のパラメータｘ，ｙ，ｚと、測定部２の姿勢を表すオイラー角のパラメータα，β，γと、電流Ｉとの７個のパラメータを含む。測定部２の姿勢は、オイラー角のみではなく、回転ベクトル、回転行列、クォータニオンなど他の表現方法が用いられてもよい。測定部２の基準点の座標は、２次元座標であってもよい。 The estimation unit 30 performs processing for generating N particles based on the following equation (1). The subscript t represents time and the superscript T represents matrix transpose. However, t depends on the observation time A and a constant sampling interval T, and ranges from 1 to A/T, where A/T is a natural number.

Equation (1) expresses a state quantity including a plurality of parameters to be estimated by the measurement unit 2 as a state vector X, with the center of gravity of the sacrificial anode P as the origin of the three-dimensional coordinate system. An arbitrary point within the analysis area (or on the structure) may be set in advance as the origin. For example, the origin may be set at the end of the structure, or may be set at any position on the structure. The state vector X is, for example, seven parameters of three-dimensional coordinate parameters x, y, and z of the reference point of the measuring unit 2, Euler angle parameters α, β, and γ representing the attitude of the measuring unit 2, and the current I. contains the parameters of The orientation of the measurement unit 2 may be represented by other representation methods such as rotation vectors, rotation matrices, quaternions, etc., in addition to Euler angles. The coordinates of the reference point of the measurement unit 2 may be two-dimensional coordinates.

The reference point is the coordinate of ? with respect to the origin. The position and rotation of the measurement unit 2 are calculated with о as a reference point. Since the measurement unit 2 rotates under the influence of various marine environments during measurement, the state vector X uses Euler angle parameters α, β, and γ to express the attitude.

A current I is a current output from the sacrificial anode P. The current I is set as a steady value during the measurement.

In the initial state (time t=0), the estimation unit 30 generates random numbers according to a normal distribution to give initial values to parameters of the state vector X, and generates N particles based on the state vector X.

Next, the processing of step S12 will be described.

The estimating unit 30 performs a process of estimating temporally transitioned states of the generated N particles based on the following equation (2). Equation (2) is a state equation for calculating the attitude, position, and current estimated values of the moving body 10 after a predetermined time (time t+1) from the previous state (time t). The previous state indicates the initial state in the case of the initial state (time t=0), and indicates the state after resampling (time t), which will be described later, in the process of repeated processing.

ここで、Ｆは非線形の関数であり、ｗ_ｔはシステムノイズを表す。ただし、システムノイズｗ_ｔは正規分布に従う。Ｆは、例えば、後述のようにランダムウォークモデルが用いられる。推定部３０は、式（２）に基づいて、前回（時刻ｔ）の状態から所定時間後（時刻ｔ＋１）に遷移したＮ個の粒子の状態を予測した予測値を算出する。

where F is the nonlinear function and _wt represents system noise. However, the system noise _wt follows a normal distribution. For F, for example, a random walk model is used as described later. Based on Equation (2), the estimation unit 30 calculates a predicted value that predicts the state of N particles that transitioned after a predetermined time (time t+1) from the previous state (time t).

Next, the processing of step S14 will be described.

The estimation unit 30 calculates an estimated value of the observed value of the potential observed at each of the positions of the sensors o, a, b, and c for each of the N particles. The parameters of the N particles calculated in step S12 are the position, orientation and current. The positions of the sensors o, a, b, and c are calculated using the predicted position and orientation parameters.

A reference point in the measuring unit 2 is set at the position of the sensor . Assuming that the position of the sensor ? given the predicted coordinates is the position of the particle, the positions of the sensors a, b, and c are always constant relative to the position of the sensor ?, since the measurement unit 2 is a rigid body.

The estimation unit 30 calculates the positions (three-dimensional coordinates) of the sensors a, b, and c based on the calculated position and orientation values. At this time, the positions of the plurality of sensors o, a, b, and c are called potential measurement positions. A specific method for calculating the potential measurement positions corresponding to the positions of the sensors a, b, and c when the three-dimensional coordinates of the sensor o serving as the reference point and the orientation of the measurement unit 2 are given is as follows. .

ただし、Ｅ^ｚαｔＥ^ｙβｔＥ^ｚγｔは回転行列であり、以下の式（４）で表される。

なお、０はゼロベクトルである。推定部３０は、式（３）、式（４）に基づいて、測定部２の位置と姿勢の値を用いて、電位測定位置ｐ（ｐ＝ｏ_ｔ，ａ_ｔ，ｂ_ｔ，ｃ_ｔ）を算出する。電位測定位置ｐ（ｐ＝ｏ_ｔ，ａ_ｔ，ｂ_ｔ，ｃ_ｔ）において観測されるのは電位の値なので、推定部３０は、電位と電位測定位置ｐとの関係を算出する。 Relative position vectors between the potential measurement position o _t serving as a reference point and the potential measurement positions _at , b _t , and c _t are expressed as constant vectors a, b, and c (see FIG. 3). The relationship between the potential measurement position o _t serving as the reference point and each potential measurement position at _, b _t , c _t conforms to Equation (3).

However, E ^zαt E ^yβt E ^zγt is a rotation matrix and is represented by the following equation (4).

Note that 0 is the zero vector. The estimating unit 30 calculates the potential measurement position p (p=o _t , a _t , b _t , c _t ) using the position and orientation values of the measuring unit 2 based on Equations (3) and (4). Calculate Since what is observed at the potential measurement position p (p=o _t , _at , b _t , c _t ) is the potential value, the estimator 30 calculates the relationship between the potential and the potential measurement position p.

Next, the estimating unit 30 measures the potential when the current I output from the sacrificial anode P is applied, based on the calculated potential measurement position p (p=o _t , _at , b _t , c _t ). A potential φ _p (φ _p =φ _ot φ _at φ _bt φ _ct ) at the position is calculated by electrostatic field analysis. An observation equation using the nonlinear function H can be modeled as shown in Equation (5) below. _Yt is an observation vector that summarizes observed values, H is a nonlinear function, and _vt is observation noise.

The electrostatic field analysis will be described below. Consider a region Ω surrounded by electrolyte (seawater) and assume that no ion loss or gain occurs within the region. The potential φ in the region Ω satisfies the Laplace equation of the following equation (6). In this embodiment, the potential φ is the potential of seawater with respect to metal. Therefore, the sign of the potential of the metal with respect to the solution normally used in electrochemistry is reversed.

式(６)より通常の境界要素法の定式化に従い、境界積分方程式(７)を導く。ただし、Γは境界、iは電流密度を表す。

定電位、定電流密度の条件下では式（７）は式（８）のように変形できる。

From the equation (6), the boundary integral equation (7) is derived according to the usual formulation of the boundary element method. However, Γ represents the boundary and i represents the current density.

Under conditions of constant potential and constant current density, equation (7) can be transformed into equation (8).

ｓは犠牲陽極Ｐの表面積を、κは電気伝導度を表す。ここでφ^＊（ｑ，ｐ）は３次元ラプラス方程式の基本解であり、次式（９）で表される。

上式において、ｒは境界上の点ｑから領域内部の点ｐまでのベクトルｒの大きさを表す。式（８）を離散化することで、電位測定位置ｐにおける電位推定値を数値的に解くことができる。

s represents the surface area of the sacrificial anode P, and κ represents the electrical conductivity. Here, φ ^* (q, p) is the basic solution of the three-dimensional Laplace's equation and is represented by the following equation (9).

In the above equation, r represents the magnitude of vector r from point q on the boundary to point p inside the region. By discretizing equation (8), the potential estimated value at the potential measurement position p can be numerically solved.

Next, the processing of step S16 will be described.

Since _Yt can also be obtained as a measured potential value of each sensor o, a, b, and c, the estimator 30 compares the estimated value of the observed value with the measured potential value to obtain the estimated value of the observed value. Calculate the likelihood of the corresponding N particles.

The estimation unit 30 acquires measured values of potentials from the sensors o, a, b, and c via the acquisition unit 20 . Let the potential measurement positions at time t be o _t , a _t , b _t , and c _t , and the potential measurement values at the respective measurement positions be denoted as φ _ot , φ _at , φ _bt , and φ _ct . A noise component is included in the potential measurement value measured at the potential measurement position p.

Next, how to obtain the likelihood and the weighted average will be described.

このノイズεが平均０、標準偏差Ｒのガウス分布に従うとすると、尤度Ｐは式（１１）により算出できる。

ただし、ｘは各粒子の情報から求めた電位の観測値である。 The measured potential φ' can be separated into the true value of the potential φ and the noise ε as shown in equation (10).

Assuming that this noise ε follows a Gaussian distribution with an average of 0 and a standard deviation of R, the likelihood P can be calculated by equation (11).

However, x is the observed value of the potential obtained from the information of each particle.

The estimating unit 30 evaluates that the information possessed by the particle is plausible when the likelihood is large, and that the information possessed by the particle is reliable, and is not very reliable when the likelihood is small. In this embodiment, since the potential is measured at four points of the sensors o, a, b, and c, there are four types of measured values. Therefore, four types of likelihoods are also calculated (P _o , P _a , P _b , P _c ). In order to perform evaluation using likelihoods as described above, it is necessary to combine the likelihoods into one. Therefore, the estimation unit 30 uses Equation (12) to unify the likelihoods. Likelihoods can be handled in the same way as probabilities, and since the four types of likelihoods have a relationship of "Po _and Pa _{and Pb} and _Pc ", they are combined into one by the product.

続いて推定部３０は、得られた尤度を、式(１３)を用いて正規化し、重みとして処理する。

ただしＮは粒子数であり、ｉは粒子に割り振ったＩＤである。推定部３０は、式（１４）を用いてこの重みを使って加重平均を行い、推定値を算出する。

加重平均を行うことにより、推定値に対する信頼のできる粒子(尤度の大きな粒子)の寄与を大きくすることができる。

Subsequently, the estimation unit 30 normalizes the obtained likelihood using equation (13) and processes it as a weight.

where N is the number of particles and i is the ID assigned to the particles. The estimator 30 performs weighted averaging using this weight using Equation (14) to calculate an estimated value.

Weighted averaging makes it possible to increase the contribution of reliable particles (particles with high likelihood) to the estimated value.

Next, the processing of step S18 will be described.

The estimating unit 30 performs resampling to extract particles having a likelihood higher than a predetermined value from among the N particles. The estimation unit 30 duplicates the extracted particles to generate N particles and scatter them in space. The newly dispersed N particles are dispersed in an area closer to the true value of the position of the moving body 10 than in the area where the N particles in the previous state exist. The estimation unit 30 changes the time and repeats the process from step S12. That is, the estimating unit 30 repeats filtering processing for correcting the next state so that the calculated N particles indicating the next state probabilistically approach the true value.

The estimation unit 30 repeats the above process A/T times within the time measured by the moving body 10, for example. As a result, the estimator 30 can estimate the position and posture of the moving body 10 and the current output from the sacrificial anode at each time, and update the estimated value of the potential.

As described above, the estimating unit 30 calculates the potential measurement position p when given the seven types of parameters shown in equation (1), calculates the potential at the potential measurement position p, and calculates the calculation result The current I output from the sacrificial anode P can be calculated based on.

The effectiveness of the processing executed by the estimating unit 30 will be verified by numerical experiments below. Specifically, a boundary element method calculation simulating an actual environment is performed to calculate the potential at a preset potential measurement position, and an error generated by a random number is added to obtain simulated measurement data. Then, this method is applied to the simulated measurement data to estimate the current of the sacrificial anode P and the position and orientation of the moving body 10 itself. In this numerical experiment, the problem of obtaining an estimated value from the electric field formed by one sacrificial anode P was dealt with.

FIG. 5 shows parameters used to generate simulated measurement data for numerical experiments. In the experiment, a right-handed coordinate system with the center of gravity of the sacrificial anode P as the origin was used. The sacrificial anode was a cuboid of 0.05W×0.05D×0.5Hm, and the output current was 1A. The measurement line was a vertical line 0.2 m away from the origin, and potentials were calculated at 31 points on the measurement line. Each potential measurement position can be expressed as follows using _ot as a reference point. That is, a _t , b _t , and c _t are positions +0.25 m in the x-axis direction, +0.25 m in the y-axis direction, and +0.25 m in the z-axis direction from the reference point.

Assuming the measurement position as described above, the measurement position at each time is calculated in advance. However, it is assumed that the Euler angles α, β, γ and the z coordinate in the depth direction are +0.2 degrees, −0.3 degrees, 0 degrees, and −0.05 m, respectively. Then, the potential at the four measurement positions at each time was calculated. Random numbers following a normal distribution N (0, 0.001) were added to these potentials to obtain simulated measurement data. Each component in parentheses is the average value and standard deviation of normal distribution, and the electrical conductivity was set to 4.5 S/m.

ｂは入力ベクトルであり、一定時間後の移動体１０の移動量を表す。 In the experiment, the equation of state was assumed to follow the random walk model shown in Equation (15).

b is an input vector representing the amount of movement of the moving body 10 after a certain period of time.

FIG. 6 shows the equation of state and the parameters of the particle generation conditions used in the numerical experiment. Ave and SD in the figure represent the average value and standard deviation of the normal distribution, respectively. Also, the particle generation conditions are conditions for generating particles at the initial time step. The calculation time step Δt was 1 s, the number of steps was 31, and the number of particles was 3,000.

As shown in FIGS. 7A and 7C, it was confirmed that the estimated values of the x and z coordinates were able to reproduce the correct values with sufficient accuracy. As shown in FIG. 7(b), different coordinates were estimated at the initial time step of the y-coordinate, and it was observed that the y-coordinate converged to the correct value as time passed. Such different coordinates were estimated because the conditions during particle generation have ambiguous parameters that differ from the correct values. From the above, it was confirmed that the state quantity can be estimated even when the initial particle generation conditions are unknown.

As shown in FIGS. 7(d), (e), and (f), in estimating each Euler angle, it was inferred that the state equation could not model the actual posture of the measurement unit. That is, the input vector at each Euler angle is a parameter different from the simulated measurement data, and the system noise is an ambiguous parameter with a large standard deviation. In this numerical experiment, random numbers following a normal distribution of 0 degree for the input vector and N(0, 2) for the system noise were used as the parameters described above.

From the graph of the estimation results, it was confirmed that the estimated values were able to reproduce the correct values with sufficient accuracy. This is because system noise with a large standard deviation was used. From the above results, it was confirmed that the state quantity can be estimated with sufficient accuracy even when the state equation cannot reflect the actual state. From FIG. 7(g), the estimated value of the anode output current was able to be estimated with sufficient accuracy with an error of about 3% compared to the correct value.

FIG. 8 shows the estimation result of the potential measurement value at the reference point o. In the correct value, it was observed that the potential became base in the vicinity of t=16s. This is the effect of the measurement error added to the simulated measurement data. Since the moving body 10 passed near the sacrificial anode, the potential becomes noble near t=16s, and a potential peak appears. The estimated values were able to reproduce the correct values, including the vicinity of the sacrificial anode, which is greatly affected by the positional error during measurement.

As described above, according to the state quantity estimating device 1, the generalized state estimation problem of estimating the position of the moving body 10 itself and the anode output current from the measured potential value is solved by using a particle filter, so that the moving body Even under the condition that the position and orientation of 10 itself are unknown, the anode output current can be evaluated appropriately. According to the state quantity estimating device 1, a device such as a rail installed in water for moving the measuring unit 2 in the measurement of the sacrificial anode P becomes unnecessary, which reduces the measurement cost and eliminates the need for divers to measure. Safety can be improved.

Next, the structure of the moving body 10 will be described. The moving body 10 that moves in water may be formed in various shapes. As described above, the moving body 10 is an object suspended by a wire (not shown) or the like and moving in any direction in water. The moving body 10 is made of resin or the like so as not to be subjected to electromagnetic induction by the electric field generated by the sacrificial anode P. As shown in FIG. The moving body 10 may be made of metal coated with insulation, ceramic-coated, FRP, wood, or other materials. The moving body 10 may be made of any material as long as it is not subject to electromagnetic induction.

As shown in FIG. 9, the moving body 10 includes a body portion 11 formed in a circular tubular shape. A plurality of sensors o, a, b, and c for measuring electric potential are provided so as to maintain relative positional relationship with the main body 11 . The plurality of sensors o, a, b, and c may be attached at any position as long as the relative positional relationship is maintained. A plurality of sensors o, a, b, and c are attached inside the main body 11 to reduce resistance when the moving body 10 moves and prevent cables from being caught. The moving body 10 may be provided with at least a plurality of potential sensors, but in order to improve accuracy, a device such as a water depth gauge or a laser rangefinder for acquiring position information of the moving body 10 may be further provided. may have been

A plurality of hydrofoils 12 are formed along the pipe axis L direction on an inner wall surface 11A of the body portion 11 . For example, three hydrofoils 12 are provided at equal intervals in the circumferential direction of the wall surface 11A. The hydrofoil 12 is formed so as to protrude toward the center of the main body 11 when viewed from the pipe axis L direction. The number of hydrofoils 12 may be increased or decreased. The hydrofoil 12 may be provided on the side surface of the main body 11 . By forming the hydrofoil 12, when the movable body 10 moves in the vertical direction, the main body 11 is suppressed from moving in the horizontal direction and rotating around the pipe axis L, thereby improving stability. .

As shown in FIG. 10, the moving body 10 includes a tubular main body 11 having a triangular cross section. The body portion 11 is formed by contacting the long sides of three rectangular plate-like bodies 11a, 11b, and 11c. Plate-like bodies 11a, 11b, and 11c function as hydrofoils. A plurality of sensors o, a, b, and c for measuring electric potential are provided so as to maintain relative positional relationship with the main body 11 . A plurality of sensors o, a, b, and c are attached inside the main body 11 to reduce resistance when the moving body 10 moves and prevent cables from being caught.

The plates 11a, 11b, and 11c simplify the structure of the moving body 10 and function as hydrofoils, so that the main body 11 moves horizontally when the moving body 10 moves vertically. Also, the rotation around the tube axis L is suppressed, and the stability is improved.

As shown in FIG. 11, the moving body 10 may be formed by combining three circular pipes 11B, 11C, and 11D with the body portion 11 thereof. The circular tubes 11B, 11C, and 11D function as hydrofoils. A plurality of sensors o, a, b, and c for measuring electric potential are provided so as to maintain relative positional relationship with the main body 11 . A plurality of sensors o, a, b, and c are attached inside the main body 11 to reduce resistance when the moving body 10 moves and prevent cables from being caught.

The circular tubes 11B, 11C, and 11D simplify the configuration of the moving body 10, and function as hydrofoils, so that when the moving body 10 moves vertically, the main body 11 moves horizontally. , the rotation around the tube axis L is suppressed, and the stability is improved.

As shown in FIG. 12, moving body 10 in which main body 11 is formed by combining three circular pipes 11B, 11C, and 11D has a portion where three internal circular pipes 11B, 11C, and 11D are in contact with each other. may be cut off and formed only by the side surfaces of the circular tubes 11B, 11C, and 11D. By forming the moving body 10 in this way, resistance during underwater movement is reduced, and the circular tubes 11B, 11C, and 11D function as hydrofoils. Therefore, when the moving body 10 moves in the vertical direction, the main body 11 is prevented from moving in the horizontal direction and rotating around the tube axis L, thereby improving the stability.

As shown in FIG. 13, the moving body 10 may have a main body 11 formed of a rectangular frame. The moving body 10 is provided in the body part 11 so that the relative positional relationship between the plurality of sensors o, a, and c is maintained so as to measure the electric potential two-dimensionally. A plurality of sensors o, a, and c are provided outside the body portion 11 . The body portion 11 may be provided with hydrofoils for stabilizing movement. The structure can be simplified by the moving body 10 formed in a frame shape.

As shown in FIG. 14, a moving body 10 having a main body 11 formed of a rectangular frame has an arm-shaped projecting portion 13 formed at the lower portion of the main body 11 so as to measure potential in three dimensions. there is A plurality of sensors o, a, b, and c for measuring electric potential are provided so as to maintain relative positional relationship with the main body 11 . A plurality of sensors o, a, b, and c are provided outside the body portion 11 . The body portion 11 may be provided with hydrofoils for stabilizing movement. The structure can be simplified by the moving body 10 formed in a frame shape.

The body portion 11 may be formed not only by a rectangular frame but also by a triangular or polygonal frame. Further, the main body portion 11 may be provided with one or more arm-shaped protrusions to enable measurement in the depth direction.

As shown in FIG. 15, the moving body 10 may have a main body 11 formed in a triangular pyramid shape. The body portion 11 is formed by combining four triangular plate-like bodies 11E, 11F, 11G, and 11H. A plurality of sensors o, a, b, and c for measuring electric potential are provided so as to maintain relative positional relationship with the main body 11 . A plurality of sensors o, a, b, and c are attached to the outside of the body portion 11 .

For example, when the moving body 10 is caused to sink vertically downward, the streamlines of the fluid concentrate in the direction of the sensor c, the generation of a wake is suppressed, and the underwater resistance is reduced. Alternatively, the two main bodies 11 may be connected vertically opposite to each other and moved vertically to reduce water resistance. Further, the body portion 11 may be provided with hydrofoils for stabilizing movement. The main body part 11 may be formed in a pyramid shape other than a triangular pyramid, such as a cone, a square pyramid, or the like. The body portion 11 may also have a polyhedral shape such as a columnar body, a pyramidal body, or a bipyramidal body.

Although each moving body 10 described above does not necessarily need to be equipped with a water level gauge, the estimation accuracy of the state quantity estimating device 1 may be improved using the information of the water level gauge by attaching the water level gauge. The arrangement of the sensors on the moving body 10 may be two-dimensional or three-dimensional. However, in order to improve the estimation accuracy of the state quantity estimation device 1, it is desirable to arrange the sensors three-dimensionally. A weight may be suspended from each moving body 10 described above to improve stability.

Although one embodiment of the present invention has been described above, the present invention is not limited to the above-described embodiment, and can be modified as appropriate without departing from the scope of the invention. For example, in the above-described embodiment, a particle filter is used for state quantity estimation, but other state quantity estimation methods such as an extended Kalman filter and an unscented Kalman filter may be used. Further, the orientation of the measurement unit 10 may use a rotation vector, a rotation matrix, a quaternion, or the like, in addition to the Euler angles. Besides the boundary element method, the finite element method, the finite volume method, the finite difference method, etc. may be used as the discretization method of the partial differential equation used for the electrostatic field analysis. In addition, the anti-corrosion current estimation method may be used not only for the current output from the sacrificial anode P, but also for evaluation of corrosion occurring in structures and evaluation of current measurement of electrical equipment and devices.

1 State quantity estimation device 2 Measurement unit 10 Moving body 11 Main unit 11a, 11b, 11c, 11E, 11F, 11G, 11H Plate-like object 11A Wall surface 11B, 11C, 11D Circular pipe 12 Hydrofoil 13 Protrusion 15 Terminal device 20 Acquisition Unit 30 Estimation unit 40 Display unit a, b, c, o Sensor

Claims (8)

A state quantity estimation method for estimating an unknown state quantity representing the cathodic protection state of a metal structure protected by a sacrificial anode in an electrolyte using a state quantity estimation model,
obtaining a measurement of the potential in the electrolyte surrounding the sacrificial anode when moving a moving body having a potential sensor for a predetermined time;
predicting the next state temporally updated from the previous state using the state quantity estimation model;
Repeating a filtering process for correcting the next state to a state probabilistically closest to the true value based on the measured value;
and calculating an estimated value of the state quantity including the position and orientation of the moving body and the current output from the sacrificial anode.
State quantity estimation method. The state quantity estimating model calculates the state quantity that changes from time to time from the measured value that includes an error, and includes a state equation that temporally updates the state quantity and the state quantity as the measured value. and an observation equation that transforms the same physical quantity into an observed value,
In a state of indefinite posture at a position indefinitely separated from the sacrificial anode by the moving body having a plurality of the potential sensors whose positions are relatively fixed, n samples are collected at a constant sampling interval T within the observation time A. repeatedly obtaining (n=A/T) measurements from the plurality of sensors;
generating an initial state of the state quantity at time t=0 using the state equation;
a step of predicting the next state quantity from the previous state quantity when t=1, 2, . . . A/T using the state equation;
converting the next state quantity predicted using the observation equation into the observed value;
and performing the filtering process of calculating the estimated value based on the observed value and the measured value.
The state quantity estimation method according to claim 1. The state quantity estimation model is a particle filter,
generating an initial state of a number of particles having information of the state quantity when t=0;
predicting the next state from the previous state for each of the particles when t=1, 2, . . . A/T using the equation of state;
converting the predicted next state for each particle into the observed value using the observation equation;
calculating the likelihood of the observed value and the measured value for each of the particles, performing weighting by normalization, and performing the filtering process to obtain the estimated value by a weighted average;
a resampling step of extracting particles with a likelihood higher than a predetermined value from the particles and duplicating the extracted particles;
The state quantity estimation method according to claim 2. The observation equation includes an equation representing an electric field analysis based on a partial differential equation discretization technique,
The state quantity estimation method according to claim 2. A state quantity estimating device for estimating an unknown state quantity representing the state of cathodic protection of a metal structure protected by a sacrificial anode in an electrolyte using a state quantity estimating model,
an acquisition unit that acquires a measured value of the potential in the electrolyte around the sacrificial anode when the moving body having the potential sensor is moved for a predetermined time;
Filtering processing for predicting the next state temporally updated from the previous state using the state quantity estimation model, and correcting the next state to a state probabilistically closest to the true value based on the measured value. and an estimating unit that calculates an estimated value of the state quantity including the position and orientation of the moving body and the current output from the sacrificial anode,
State quantity estimator. further comprising the moving body;
The moving body includes a main body,
a hydrofoil provided in the main body and formed along a vertical direction;
comprising a
The state quantity estimation device according to claim 5 . The main body is formed in any one of tubular, conical, polyhedral, and frame shapes,
The state quantity estimating device according to claim 6. A program for estimating an unknown state quantity representing the cathodic protection state of a metal structure protected by a sacrificial anode in an electrolyte using a state quantity estimation model,
to the computer,
Acquiring a measured value of the potential in the electrolyte around the sacrificial anode when a moving body having a potential sensor is moved for a predetermined period of time;
Using the state quantity estimation model, predict the next state temporally updated from the previous state,
repeating the filtering process of correcting the next state to a state probabilistically closest to the true value based on the measured value;
calculating an estimated value of the state quantity including the position and orientation of the moving body and the current output from the sacrificial anode;
program.

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