Patent ID: 12209935

DETAILED DESCRIPTION OF THE EMBODIMENTS

It will be understood that, although the terms first, second, third etc. may be used herein to describe various elements, components, and/or sections, these elements, components, and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, or section from another element, component, or section. Thus, a first element, component, or section discussed below could be termed a second element, component, or section without departing from the teachings of example embodiments.

It will be understood that when an element or layer is referred to as being “connected to” or “coupled to” another element, it can be directly on, connected or coupled to the other element or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly connected to” or “directly coupled to” another element, there are no intervening elements present. Like or similar reference numerals refer to like or similar elements throughout. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items.

The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a,” “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises”, “includes”, “including”, and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.

Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

Example embodiments will be described more fully hereinafter with reference to the accompanying drawings, in which various embodiments are shown.

FIG.1illustrates that a plurality of pairs of strain gauges and an accelerometer are installed in a bridge according to a method of estimating a displacement of a bridge according to example embodiments.

Referring toFIG.1, a plurality of pairs of strain gauges20a,20b, . . . ,20mare installed at a plurality of positions x1, x2, . . . , xm in a first direction D1 from a reference point RP in a bridge10and an accelerometer30is installed at a first position spaced apart from the reference point RP by a first distance xd in the first direction D1 in the bridge10.

Each of the plurality of pairs of strain gauges20a,20b, . . . ,20mmay include a first strain gauge and a second strain gauge that are spaced apart from each other at one of the plurality positions x1, x2, . . . , xm by a second distance in a second direction D2 perpendicular to the first direction D1.

Strain that is measured by plurality of pairs of strain gauges20a,20b, . . . ,20mmay be transformed into a first displacement, an acceleration that is measured by the accelerometer30may be transformed a second displacement and a displacement of the bridge10may be estimated by combining the first displacement and the second displacement.

FIG.2is a flow chart illustrating a method of estimating displacement of a bridge according to example embodiments.

Referring toFIGS.1and2, a first displacement including a low frequency component and a first high frequency component is generated (i.e., calculated) based on a strain that is measured by a plurality of pairs of strain gauges20a,20b, . . . ,20minstalled at a plurality of positions x1, x2, . . . , xm in a first direction D1 from a reference point RP, in the bridge10(operation S100).

A second displacement including a second high frequency component is generated based on an acceleration that is measured by an accelerometer20installed at a first position spaced apart from the reference point RP by a first distance xd in the first direction D1 in the bridge10(operation S200).

A final displacement of the bridge10is generated based on an unknown parameter associated with the displacement, the low frequency component of the first displacement and the second high frequency component of the second displacement (operation S300). The unknown parameter may be generated by applying a recursive least square (RLS) algorithm to the first high frequency component of the first displacement and the second high frequency component of the second displacement.

For generating the first displacement (operation S100), sub strains are measured by the plurality of pairs of strain gauges20a,20b, . . . ,20m(operation S110), the measured sub strains are transformed into sub displacements (operation S120), the first displacement is generated based on the sub displacements (operation S130), the low frequency component of the first displacement (i.e., low frequency displacement) is obtained (operation S150) by applying a low-pass filter to the first displacement (operation S140), and the first high frequency component of the first displacement (i.e., high frequency displacement) is obtained (operation S170) by extracting the low frequency component from the first displacement (operation S160).

For generating the second displacement (operation S200), the acceleration is measured by the accelerometer20(operation S210), the measured acceleration is double-integrated (operation S220) and the second high frequency component of the second displacement (i.e., high frequency displacement) is obtained (operation S240) by applying a high-pass (FIR) filter to the double-integrated acceleration (operation S230).

For generating the final displacement (operation S300), the RLS algorithm is applied to the first high frequency component of the first displacement and the second high frequency component of the second displacement (operation S310), the unknown parameter is estimated based on a result of the RLS algorithm (operation S320), and the final (estimated) displacement is provided (operation S340) by performing an operation based on the low frequency component of the first displacement, the unknown parameter and the second high frequency component of the second displacement (operation S330).

In embodiments, the final displacement may be obtained by dividing the low frequency component of the first displacement by the estimated unknown parameter and by summing the second high frequency component of the second displacement to a result of the dividing.

In embodiments, the estimated unknown parameter may correspond to a scaling factor associated with compensating for a difference between an estimated mode shape of the bridge and a real mode shape of the bridge10.

FIG.3illustrates axial loading and vertical loading that a real bridge having a varying cross-section experiences.

Referring toFIG.3, a bridge10amay have a varying cross-section and the bridge10amay experience axial loading and vertical loading.

FIG.4illustrates a strain that is measured by one of a plurality of pairs of strain gauges installed in a bridge ofFIG.3.

FIG.4illustrates a strain that is measured by a strain gauge installed at an arbitrary position in the bridge10aofFIG.3.

A pair of strain gauge may include a first strain gauge21and a second strain gauge21that is spaced apart from each other by a second distance h(x) in the second direction D2.

A sub strain ε(x, y, k) measured at an arbitrary position in the bridge10amay include an axial sub strain εu(x, k) that is uniform and a bending sub strain εb(x, y, k) that varies linearly.

InFIG.4, O denotes a center of a cross-section of the bridge10ain the second direction D2.

A relationship between a strain and a displacement from the being strain is expressed by following Equation 1.

εb(x,y,k)=y⁢d2⁢u⁡(x,k)dx2[Equation⁢1]

Here, u denotes a displacement of the bridge10ain the second direction D2.

When each of the plurality of pairs of strain gauges includes a first strain gauge and a second strain gauge as illustrated with reference toFIG.4, a difference between sub strains measured by the first strain gauge and the second strain gauge is expressed by following Equation 2.

Δ⁢ε⁡(x,k)=h⁡(x)⁢d2⁢u⁡(x,k)dx2[Equation⁢2]

Here, Δε denotes a difference between sub strains, x denote a position in the first direction, k denotes k-th timing, u(x, k) denotes the first displacement and h(x) denotes the second distance.

The first displacement is expressed by following Equation 3.

u⁡(x,k)=∑j=1Lφj(x)⁢qj(k)[Equation⁢3]

Here, φjdenotes a j-th mode shape, qjdenotes a j-th modal response and L denotes a number of modes.

When Equation 3 is input to Equation 2, following Equation 4 is obtained.

Δ⁢ε⁢(x,k)=h⁡(x)⁢∑j=1Ld2⁢φj(x)dx2⁢qj(k)[Equation⁢4]

Equation 4 is represented by vector representation by following Equation 5.
Δε(k)=HΦq(k)  [Equation 5]

Equation 5 is satisfied by following Equation 6, Equation 7, Equation 8 and Equation 9.
Δε(k)=[Δε(x1k) . . . Δε(xm,k)]T1×m[Equation 6]

Here, m denote the plurality of positions.

q⁡(k)=[q1(k)⁢…⁢qL(k)]1×LT[Equation⁢7]Φ=[d2⁢φ1(x1)dx2…d2⁢φL(x1)dx2⋮⋱⋮d2⁢φ1(xm)dx2…d2⁢φL(xm)dx2]m×L[Equation⁢8]H=[h⁢(x1)…0⋮⋱⋮0…h⁢(xm)]m×m[Equation⁢9]

The modal response q(k) is deduced to following Equation 10 from Equation 5.
q(k)=(ΦTΦ)−1ΦTH−1Δε  [Equation 10]

When Equation 10 is input to Equation 3, the first displacement at the first position is expressed by following Equation 11.
u(k)=TH−1Δε(k)  [Equation 11]

Equation 11 is satisfied by following Equation 12 and Equation 13.
T=Ψ(xd)[ΦTΦ]−1ΦT[Equation 12]
Ψ=[φ1(xd) . . . φL(xd)]1×L[Equation 13]

When a scaling factor α associated with compensating for a difference between an estimated mode shape of the bridge and a real mode shape of the bridge is introduced, the first displacement is expressed by following Equation 14.

u⁡(k)=1α⁡(k)⁢Ta⁢H-1⁢Δ⁢ε⁡(k)[Equation⁢14]

Here, Tais an approximation matrix of a matrix T.

A finite response pulse is expressed by a following Equation 15.
u*=(Δt)2(LTL+λ2I)−1LTLaa+λ2(LTL+λ2I)−1u[Equation 15]

Here, denotes u*vector representation of the final displacement, u denotes a vector representation of the first displacement transformed from the strain, a denotes a vector representation of the acceleration, La denotes (2N+1)-th order diagonal weight matrix, and λ denotes a normalizing factor that is satisfied by a following Equation 16.
λ=46.81(2N+1)−1.95[Equation 16]

Here, λ satisfied by a following Equation 17.

λ=2⁢N+1=2.68f1⁢Δ⁢t[Equation⁢17]

Here, f1denotes a first natural frequency of the bridge10a.

When a superposition is applied to Equation 15, following Equation 18 is deduced
u*(k)=CHa+CLu[Equation 18]

Here, CHdenotes a (N+1)-th row of (Δt)2(LTL+λ2I)−1LTLaand corresponds to a combination of a double integration and a high-pass filter and CLdenotes a low-pass filter of λ2(LTL+λ2I)−1.

The first displacement is expressed by a following Equation 19.
us={TaH−1Δε}T[Equation 19]

Here, the low frequency component and the first high frequency component of the first displacement is expressed by following Equation 20 and Equation 21.
uzl(k)=CLus[Equation 20]
uah(k)=CHα  [Equation 21]

The second high frequency component of the second displacement is expressed by a following Equation 22.
ush(k)=uz(k)−uzl(k)  [Equation 22]

When the scaling factor α(k) is applied to the first high frequency component of the first displacement, the second high frequency component of the second displacement is similar with the first high frequency component of the first displacement and the second high frequency component of the second displacement is expressed by a following Equation 23.

uah(k)≈1α⁡(k)⁢ush(k)[Equation⁢23]

When the scaling factor α(k) is estimated based on RLS algorithm, the scaling factor α(k) is expressed by a following Equation 24.
α(k)=α(k−1)+p(k)uah(k)[ush(k)−uah(k)α(k−1)]  [Equation 24]

Here, p(k) denotes relative weights assigned to a current measured value and a previous estimated value.

In Equation 24, p(k) is expressed by a following Equation 25.

p⁡(k)=p⁡(k-1)1+p⁡(k-1)[uah(k)]2[Equation⁢25]

When the estimated scaling factor α(k) is used for scaling the low frequency component of the first displacement, the estimated final displacement is expressed by a following Equation 26.

u*⁢(k)=1α⁡(k)⁢usl⁢(k)+uah⁢(k)=1α⁡(k)⁢CL⁢{Ta⁢H-1⁢Δ⁢ε}T+CH⁢a[Equation⁢26]

Each of the plurality of pairs of strain gauges20a,20b, . . . ,20mmay measure the strain with a first sampling frequency and the accelerometer30may measure the acceleration with a second sampling frequency greater than the first sampling frequency. The first displacement transformed from the strain may be up-sampled using a cubic spline interpolation for matching the second sampling frequency. In addition, a low-pass Butterworth filter having a Nyquist cut-off frequency may be applied to the first high frequency component of the first displacement and the second high frequency component of the second displacement.

Referring to Equation 1 through Equation 26, the method of estimating displacement of a bridge according to example embodiments may estimate a displacement of a bridge more accurately because the scaling factor α(k) is estimated in a time domain instead of a frequency domain with using RLS algorithm in estimating a displacement and the estimated displacement and the estimated scaling factor are not affected by an accuracy of a natural frequency.

FIG.5is a flow chart illustrating a method of estimating displacement of a bridge ofFIG.2in detain according to example embodiments.

InFIG.5, parameters measured or generated in each of operations are illustrated together.

Referring toFIG.5, an operation (S320) of estimating the scaling factor α(k) and an operation (S325) of scaling the low frequency component of the first displacement based on the scaling factor α(k) are further included when compared with the method ofFIG.2.

FIG.6Aillustrates a sample bridge to which a method of estimating displacement of a bridge according to example embodiments is applied andFIG.6Billustrates a size of a cross-section of the sample bridge.

Referring toFIG.6A, a sample bridge50has a length of 10 m, a plurality of pairs of strain gauges are installed at a plurality of positions spaced apart from a reference point by distances of 2 m, 5 m and 8 m, respectively, in the first direction D1 and an accelerometer is installed at a position60spaced apart from the reference point by a distance of 5 m in the first direction D1. At the position60, a displacement of the sample bridge50is measured. InFIG.6A, a reference numeral110indicates a ground motion signal.

Referring toFIG.6B, the cross-section of the sample bridge50may have a size defined by 120 mm*120 mm.

FIG.7illustrates ground motion signals applied to the sample bridge ofFIG.6A.

Referring toFIG.7, ground motion signals121,122and123having different accelerations are applied to the sample bridge50.

FIGS.8A to8Cillustrate examples of estimated displacements when the ground motion signals inFIG.7are applied to the sample bridge ofFIG.6A, respectively.

Referring toFIGS.8A to8C, estimated displacement is illustrated when the ground motion signals121,122and123inFIG.7are applied to the sample bridge50ofFIG.6A, respectively, along with a reference displacement Reference and an estimated displacement when a conventional technique is applied to the sample bridge50.

InFIGS.8A to8C, it is assumed that the convention technique corresponds to a power spectral density (SPD) technique.

Referring toFIGS.8A to8C, it is noted that a difference between a displacement according to a method of the present disclosure and the reference value Reference becomes smaller than a difference between a displacement according to a method of the PSD technique and the reference value Reference as a change of the acceleration of the ground motion signal increases.

FIG.9illustrates examples of a sample bridge having a varying cross-section, to which a method of estimating displacement of a bridge according to example embodiments is applied.

FIG.10illustrates a difference between a real mode shape and an estimated mode shape when a method of estimating displacement of a bridge according to example embodiments is applied to a first sample bridge inFIG.9.

Referring toFIGS.9and10, when a cross-section of a bridge varies as a first sample bridge I, it is noted that there is little difference between a real mode shape and an estimated mode shape in a first order131and a third order133and their there is a difference between the real mode shape and an estimated mode shape in a second order132.

FIG.11illustrates that a method of estimating displacement of a bridge according to example embodiments is applied to a real bridge.

Referring toFIG.11, it is noted that there is little difference between a displacement according to a method of the present disclosure and the reference value Reference and there is a difference between a displacement according to a method of the PSD technique and the reference value Reference in timing ranges from 13 second to 17 second.

FIG.12is a block diagram illustrating an example of an electronic device to perform a method of estimating displacement of a bridge according to example embodiments.

Referring toFIGS.1and12, an electronic device200to estimate displacement of a bridge may include a communication circuit210, a control circuit220and a display230.

The communication circuit210may communicate with a plurality of pairs of strain gauges20a,20b, . . . ,20mthat are installed at a plurality of positions x1, x2, xm in a first direction D1 from a reference point RP in a bridge10and an accelerometer30that is installed at a first position spaced apart from the reference point RP by a first distance xd in the first direction D1 in the bridge10, may receive a strain STS that is measured by the plurality of pairs of strain gauges20a,20b, . . . ,20mand may receive and an acceleration ACS that is measured by the accelerometer30.

The communication circuit210may typically include one or more modules which permit communications such as wireless communications between the electronic device200and a wireless communication system, communications between the electronic device200and another electronic device, communications between the electronic device200and an external server. Further, the communication circuit210may include a broadcast receiving module, a mobile communication module, a wireless Internet module, a short-range communication module, and a location information module.

The broadcast receiving module may receive a broadcast signal and/or broadcast associated information from an external broadcast managing entity via a broadcast channel. The broadcast channel may include a satellite channel, a terrestrial channel, or both. The broadcast managing entity may be implemented using a server or system which generates and transmits a broadcast signal and/or broadcast associated information, or a server which receives a pre-generated broadcast signal and/or broadcast associated information, and sends such items to the mobile terminal. The broadcast signal may be implemented using any of a TV broadcast signal, a radio broadcast signal, a data broadcast signal, and combinations thereof, among others. The broadcast signal in some cases may further include a data broadcast signal combined with a TV or radio broadcast signal.

Examples of broadcast associated information may include information associated with a broadcast channel, a broadcast program, a broadcast event, a broadcast service provider, or the like. The broadcast associated information may also be provided via a mobile communication network, and in this case, received by the mobile communication module.

The mobile communication module may transmit and/or receive wireless signals to and from one or more network entities. Examples of wireless signals transmitted and/or received via the mobile communication module include audio call signals, video (telephony) call signals, or various formats of data to support communication of text and multimedia messages.

The wireless Internet module may facilitate wireless Internet access. This module may be internally or externally coupled to the electronic device200. The wireless Internet module may transmit and/or receive wireless signals via communication networks according to wireless Internet technologies. Examples of such wireless Internet access include Wireless LAN (WLAN), Wireless Fidelity (Wi-Fi), Wireless Broadband (WiBro), Worldwide Interoperability for Microwave Access (WiMAX), High Speed Downlink Packet Access (HSDPA), and the like.

The short-range communication module may facilitate short-range communications. Suitable technologies for implementing such short-range communications include BLUETOOTH™, Radio Frequency IDentification (RFID), Infrared Data Association (IrDA), Ultra-WideBand (UWB), ZigBee, Near Field Communication (NFC), Wireless-Fidelity (Wi-Fi), Wi-Fi Direct, Wireless USB (Wireless Universal Serial Bus), and the like.

The location information module may detect, calculate, derive or otherwise identify a position of the electronic device200. As an example, the location information module may include a Global Position System (GPS) module.

The control circuit220may receive the strain STS and the acceleration ACS from the communication circuit210, may estimate a final displacement of the bridge based on the strain STS and the acceleration ACS according to a method of estimating displacement of a bridge and may display an estimated final displacement in the display230.

The control circuit220may generate a first displacement including a low frequency component and a first high frequency component based on the strain STS, may generate a second displacement including a second high frequency component based on the acceleration ACS, may generate an unknown parameter associated with the displacement by applying a RLS algorithm to the first high frequency component of the first displacement and the second high frequency component of the second displacement and may generate the final displacement of the bride based on the unknown parameter, the low frequency component of the first displacement and the second high frequency component of the second displacement.

The present disclosure may be applicable to a method and a device to measure displacement of a bridge, variously.

The foregoing is illustrative of example embodiments and is not to be construed as limiting thereof. Although a few example embodiments have been described, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from the novel teachings and advantages of the present disclosure. Accordingly, all such modifications are intended to be included within the scope of the present disclosure as defined in the appended claims.