A method of estimating displacement of a bridge and an electronic device for estimating displacement of a bridge

Abstract

In a method of estimating displacement of a bridge, a first displacement including a low frequency component and a first high frequency component is generated based on strains measured by a plurality of pairs of strain gauges installed in the bridge at a plurality of locations along a first direction from a reference point; a second displacement including a second high frequency component is generated based on accelerations measured by an accelerometer installed at a first location spaced apart from the reference point by a first distance along the first direction in the bridge; and a final displacement of the bridge is generated based on unknown parameters associated with the displacement, the low frequency component, and the second high frequency component. The unknown parameters are generated by applying a recursive least squares algorithm to the first high frequency component and the second high frequency component.

Description

Technical Field

[0001] The implementation relates to displacement estimation, and more specifically to a method for estimating bridge displacement based on bridge strain and acceleration, and an electronic device for performing the method. Background Technology

[0002] The durability of civil engineering structures, especially bridges, can be reduced by loads from vehicles or wind. In concrete bridges, this reduction in durability leads to cracking, making early detection crucial. However, visually detecting cracks requires significant time and manpower, and assessing crack depth and impact is challenging. When cracks appear in a bridge, its neutral point changes. The neutral point of a bridge represents the location in its cross-section where strain is zero.

[0003] Typically, since the superstructure of a bridge is subjected to compression and the substructure to tension, strain gauges are installed on the upper and lower surfaces of the bridge to estimate the bridge's neutral point.

[0004] In addition, estimating unknown parameters by converting the strain measured by the strain gauge to the frequency domain will introduce errors from the perspective of the frequency domain. Summary of the Invention

[0005] The example implementation provides a method for estimating bridge displacement that can improve accuracy.

[0006] An example implementation provides an electronic device for estimating the displacement of a bridge, which can improve accuracy.

[0007] According to an example implementation, in a method for estimating bridge displacement, a first displacement, including a low-frequency component and a first high-frequency component, is generated based on strain measured by multiple pairs of strain gauges installed at multiple locations along a first direction from a reference point on the bridge. A second displacement, including a second high-frequency component, is generated based on acceleration measured by an accelerometer installed at a first location, spaced a first distance from the reference point along the first direction on the bridge. The final displacement of the bridge is generated based on unknown parameters associated with the displacement, the low-frequency component of the first displacement, and the second high-frequency component of the second displacement. The unknown parameters are generated by applying a recursive least squares (RLS) algorithm to the first high-frequency component of the first displacement and the second high-frequency component of the second displacement.

[0008] To generate the first displacement, sub-strain is measured by the multiple pairs of strain gauges, the measured sub-strain is converted into sub-displacement, the first displacement is generated based on the sub-displacement, the low-frequency component of the first displacement is obtained by applying a low-pass filter to the first displacement, and the first high-frequency component of the first displacement is obtained by extracting the low-frequency component from the first displacement.

[0009] To generate the second displacement, the acceleration is measured by the accelerometer, the measured acceleration is double-integrated, and a high-pass filter is applied to the double-integrated acceleration to obtain the second high-frequency component of the second displacement.

[0010] To generate the final displacement, 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. The unknown parameters are estimated based on the result of the RLS algorithm. The final displacement is then provided by performing calculations based on the low-frequency component of the first displacement, the unknown parameters, and the second high-frequency component of the second displacement.

[0011] According to an example implementation, in a method for estimating bridge displacement, sub-strain is measured using multiple strain gauges installed at multiple locations along a first direction from a reference point on the bridge. The sub-strain is converted into sub-displacement. A low-pass filter is applied to the first displacement to obtain a low-frequency component of the first displacement. A first high-frequency component of the first displacement is obtained by extracting the low-frequency component from the first displacement. Acceleration is measured using an accelerometer installed at a first location spaced a first distance from the reference point along the first direction on the bridge. The measured acceleration is double-integrated. A high-pass filter is applied to the double-integrated acceleration to obtain a second high-frequency component of the second displacement. 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. Based on the result of the RLS algorithm, unknown parameters associated with the displacement are estimated. Calculations are performed based on the low-frequency component of the first displacement, the unknown parameters, and the second high-frequency component of the second displacement to generate the final displacement of the bridge.

[0012] According to an example embodiment, an electronic device for estimating the displacement of a bridge includes a communication circuit, a control circuit, and a display. The communication circuit communicates with a multi-pair strain gauge and an accelerometer, and receives strain measured by the multi-pair strain gauge and acceleration measured by the accelerometer. The multi-pair strain gauge is mounted at multiple locations in the bridge along a first direction from a reference point, and the accelerometer is mounted at a first location spaced a first distance from the reference point along the first direction in the bridge. The control circuit receives the strain and acceleration from the communication circuit and estimates a final displacement of the bridge based on the strain and acceleration. The display receives the estimated final displacement from the control circuit and displays the estimated final displacement. The control circuit generates a first displacement including a low-frequency component and a first high-frequency component based on the strain, generates a second displacement including a second high-frequency component based on the acceleration, generates unknown parameters associated with the displacement by applying the recursive least squares (RLS) algorithm to the first high-frequency component of the first displacement and the second high-frequency component of the second displacement, and generates the final displacement of the bridge based on the unknown parameters, the low-frequency component of the first displacement and the second high-frequency component of the second displacement.

[0013] Therefore, the method and electronic device for estimating bridge displacement according to the example embodiment can estimate bridge displacement more accurately because the scaling factor is used in the time domain rather than the frequency domain.

[0014] The RLS algorithm estimates the displacement, and the estimated displacement and the estimated scale factor are not affected by the accuracy of the inherent frequency. Attached Figure Description

[0015] The above and other features of this disclosure will become more apparent from the detailed description of its embodiments with reference to the accompanying drawings.

[0016] Figure 1 The illustration shows that, according to an example implementation, multiple pairs of strain gauges and accelerometers are installed in a bridge based on a method for estimating the bridge's displacement.

[0017] Figure 2 A flowchart illustrating a method for estimating bridge displacement according to an example implementation.

[0018] Figure 3 The diagram shows the axial and vertical loads experienced by real bridges with different cross-sections.

[0019] Figure 4 Showing the installation by Figure 3 The strain measured by one of multiple strain gauges in a bridge.

[0020] Figure 5To illustrate the estimation according to the example implementation Figure 2 A flowchart of a method for measuring bridge displacement.

[0021] Figure 6A shows a sample bridge using the method for estimating bridge displacement according to an example embodiment, and Figure 6B shows the cross-sectional dimensions of the sample bridge.

[0022] Figure 7 The ground motion signal applied to the sample bridge in Figure 6A is shown.

[0023] Figures 8A to 8C show when Figure 7 Examples of ground motion signals in the figure are applied to the estimated displacements of the sample bridge in Figure 6A.

[0024] Figure 9 An example of a sample bridge with a varying cross-section is shown, to which the method for estimating bridge displacement according to an example embodiment is applied.

[0025] Figure 10 This illustrates when the method for estimating bridge displacement according to the example embodiment is applied. Figure 9 The difference between the actual mode shape and the estimated mode shape when considering the first sample bridge.

[0026] Figure 11 The method for estimating bridge displacement according to the example implementation is shown to be applied to a real bridge.

[0027] Figure 12 This is a block diagram illustrating an example of an electronic device for performing a method for estimating the displacement of a bridge, according to an exemplary embodiment. Detailed Implementation

[0028] It should be understood that although the terms first, second, third, etc., may be used herein to describe various elements, components, and / or parts, these elements, components, and / or parts should not be limited by these terms. These terms are used only to distinguish one element, component, or part from another. Therefore, without departing from the teachings of the exemplary embodiments, the first element, component, or part discussed below may be referred to as the second element, component, or part.

[0029] It should be understood that when an element or layer is referred to as "connected to" or "coupled to" another element, it may be directly located, connected to, or coupled to the other element, or there may be intermediate components or layers. Conversely, when an element is referred to as "directly in," "directly connected to," or "directly coupled to" another element, there are no intermediate elements. Similar or analogous reference numerals always refer to similar or analogous elements. As used herein, the term "and / or" includes any and all combinations of one or more associated listed items.

[0030] The terminology used herein is for the purpose of describing particular exemplary embodiments only and is not intended to limit the invention. As used herein, the singular forms “a,” “an,” and “described” are also intended to include the plural forms unless the context clearly indicates otherwise. It will be further understood that, when used in this specification, the terms “comprising,” “including,” and “including” designate the stated features, integers, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0031] Unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It will be further understood that terms, such as those defined in common dictionaries, should be interpreted as consistent with their meaning in the context of the relevant art and not in an idealized or overly formal sense, unless expressly defined herein.

[0032] Example implementations will be described more fully below with reference to the accompanying drawings, which illustrate various implementations.

[0033] Figure 1 The illustration shows that, according to an example implementation, multiple pairs of strain gauges and accelerometers are installed in a bridge based on a method for estimating the bridge's displacement.

[0034] Reference Figure 1 Multiple strain gauges 20a, 20b, ..., 20m are installed at multiple positions x1, x2, ..., xm along the first direction D1 from the reference point RP in the bridge 10, and an accelerometer 30 is installed at a first position in the bridge 10 along the first direction D1, separated from the reference point RP by a first distance xd.

[0035] Each of the multiple strain gauges 20a, 20b, ..., 20m may include a first strain gauge and a second strain gauge, which are located at one of multiple positions xl, x2, ..., xm and spaced apart from each other by a second distance along a second direction D2 perpendicular to the first direction D1.

[0036] The strain measured by multiple strain gauges 20a, 20b, ..., 20m can be converted into a first displacement, the acceleration measured by accelerometer 30 can be converted into a second displacement, and the displacement of bridge 10 can be estimated by combining the first and second displacements.

[0037] Figure 2 This is a flowchart illustrating a method for estimating the displacement of a bridge according to an example implementation.

[0038] Reference Figure 1 and 2 Based on the strain measured by multiple pairs of strain gauges 20a, 20b, ..., 20m installed in the bridge 10 at multiple locations x1, x2, ..., xm along the first direction D1 from the reference point RP, a first displacement (operation) including a low-frequency component and a first high-frequency component is generated (i.e., calculated).

[0039] S100).

[0040] The second displacement, which includes a second high-frequency component, is generated based on acceleration measured by an accelerometer 20, which is mounted at a first position in the bridge 10, spaced apart from the reference point RP by a first distance xd along the first direction D1 (operation S200).

[0041] The final displacement of the bridge 10 is generated based on the unknown parameters 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 parameters can be generated by applying the recursive least squares (RLS) algorithm to the first high-frequency component of the first displacement and the second high-frequency component of the second displacement.

[0042] To generate the first displacement (operation S100), sub-strain is measured by the multiple pairs of strain gauges 20a, 20b, ..., 20m (operation S110), the measured sub-strain is converted into sub-displacement (operation S120), the first displacement is generated based on the sub-displacement (operation S130), the low-frequency component (i.e., low-frequency displacement) of the first displacement is obtained by applying a low-pass filter to the first displacement (operation S140) (operation S150), and the first high-frequency component (i.e., high-frequency displacement) of the first displacement is obtained by extracting the low-frequency component from the first displacement (operation S160) (operation S170).

[0043] In order to generate the second displacement (operation S200), the acceleration is measured by the accelerometer 20 (operation S210), the measured acceleration is double-integrated (operation S220), and the second high-frequency component (i.e., high-frequency displacement) of the second displacement is obtained by applying a high-pass filter (FIR) to the double-integrated acceleration (operation S230) (operation S240).

[0044] To generate 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 S300).

[0045] S310), the unknown parameters are estimated based on the results of the RLS algorithm (operation S320), and the final (estimated) displacement is provided by performing calculations based on the low-frequency component of the first displacement, the unknown parameters, and the second high-frequency component of the second displacement (operation S330) (operation S340).

[0046] In one implementation, the final displacement can be obtained by dividing the low-frequency component of the first displacement by the estimated unknown parameter and adding the second high-frequency component of the second displacement to the result of the division operation.

[0047] In an implementation, the estimated unknown parameter may correspond to a scaling factor, which is associated with compensating for the difference between the estimated modal shape of the bridge 10 and the actual modal shape of the bridge.

[0048] Figure 3 The diagram shows the axial and vertical loads experienced by real bridges with different cross-sections.

[0049] Reference Figure 3 Bridge 10a may have different cross sections and bridge 10a may withstand axial loads and vertical loads.

[0050] Figure 4 Showing the installation by Figure 3 The strain measured by one of multiple strain gauges in a bridge.

[0051] Figure 4 Showing the installation by Figure 3 The strain measured by a strain gauge at any location in bridge 10a.

[0052] A pair of strain gauges may include a first strain gauge 21 and a second strain gauge 21 that are spaced apart from each other by a second distance h(x) along a second direction D2.

[0053] The sub-strain ε(x, y, k) measured at any location in bridge 10a can include a uniform axial sub-strain ε u (x, k) and linearly varying bending strain ε b (x, y, k).

[0054] Figure 4 In the diagram, O represents the center of the cross section of bridge 10a in the second direction D2.

[0055] The relationship between strain and displacement from the current strain is expressed by Equation 1.

[0056] [Formula 1]

[0057]

[0058] Here, u represents the displacement of bridge 10a along the second direction D2.

[0059] Reference Figure 4 As shown, when each of the multiple pairs of strain gauges includes a first strain gauge and a second strain gauge, the difference between the sub-strains measured by the first strain gauge and the second strain gauge is represented by the following Equation 2.

[0060] [Equation 2]

[0061]

[0062] Here, Δε represents the difference between the sub-strains, x represents the position in the first direction, k represents the kth time point, u(x, k) represents the first displacement, and h(x) represents the second distance.

[0063] The first displacement is represented by the following equation 3.

[0064] [Formula 3]

[0065]

[0066] here, q represents the shape of the j-th modality. j Let L represent the j-th modal response, and L represent the number of modes.

[0067] When equation 3 is substituted into equation 2, we obtain equation 4.

[0068] [Formula 4]

[0069]

[0070] Equation 4 is represented by the vector representation of Equation 5 below.

[0071] [Formula 5]

[0072] Δε(k)=HΦq(k)

[0073] Equation 5 is satisfied by the following equations 6, 7, 8 and 9.

[0074] [Formula 6]

[0075] Δε(k)=[Δε(x1,k)...Δε(x m ,k)] T 1×m

[0076] Here, m represents multiple positions.

[0077] [Formula 7]

[0078] q(k)=[q1(k)...q L (k)] T 1×L

[0079] [Formula 8]

[0080]

[0081] [Formula 9]

[0082]

[0083] The modal response q(k) is derived from Equation 5 to Equation 10.

[0084] [Formula 10]

[0085] q(k)=(Φ T Φ) -1 Φ T H -1 Δε(k)

[0086] When Equation 10 is substituted into Equation 3, the first displacement at the first position is represented by Equation 11.

[0087] [Equation 11]

[0088] u(k)=TH -1 Δε(k)

[0089] Equation 11 is satisfied by Equations 12 and 13 below.

[0090] [Equation 12]

[0091] T = Ψ(x d )[Φ T Φ] -1 Φ T

[0092] [Equation 13]

[0093]

[0094] When a scaling factor α is introduced to compensate for the difference between the estimated modal shape of the bridge and the actual modal shape of the bridge, the first displacement is represented by the following equation 14.

[0095] [Formula 14]

[0096]

[0097] Here, T a It is an approximation matrix of matrix T.

[0098] A finite response pulse is represented by the following equation 15.

[0099] [Formula 15]

[0100] u * =(Δt) 2 (L T L+λ 2 I) -1 L T L a a+λ 2 (L T L+λ 2 I) -1 u

[0101] Here, u * The vector representation of the final displacement, u represents the vector representation of the first displacement transformed from strain, a represents the vector representation of acceleration, La represents the (2N+1)th order diagonal weight matrix, and λ represents the normalization factor satisfied by the following equation 16.

[0102] [Formula 16]

[0103] λ = 46.81(2N+1) -1.95

[0104] Here, λ is satisfied by the following equation 17.

[0105] [Equation 17]

[0106]

[0107] Here, f l The first natural frequency of bridge 10a is represented.

[0108] When superposition is applied to Equation 15, Equation 18 is derived.

[0109] [Formula 18]

[0110] u * (k)=C H a+C L u

[0111] Here, C H Representative (Δt) 2 (L T L+λ 2 I) -1 L T L a The (N+1)th row corresponds to the combination of double integrator and high-pass filter, and c L Represents λ 2 (L) T L+λ 2 I) -1 The low-pass filter.

[0112] The first displacement is represented by the following equation 19.

[0113] [Formula 19]

[0114] u s ={T a H -1 Δε} T

[0115] Here, the low-frequency component and the first high-frequency component of the first displacement are represented by Equations 20 and 21.

[0116] [Formula 20]

[0117]

[0118] [Equation 21]

[0119]

[0120] The second high-frequency component of the second displacement is represented by the following equation 22.

[0121] [Equation 22]

[0122]

[0123] 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 to the first high-frequency component of the first displacement, and the second high-frequency component of the second displacement is represented by the following equation 23.

[0124] [Equation 23]

[0125]

[0126] When the scaling factor α(k) is estimated based on the RLS algorithm, the scaling factor α(k) is represented by the following equation 24.

[0127] [Equation 24]

[0128]

[0129] Here, p(k) represents the relative weights assigned to the current measurement and the previous estimate.

[0130] In Equation 24, p(k) is represented by Equation 25.

[0131] [Equation 25]

[0132]

[0133] When the estimated scaling factor α(k) is used to scale the low-frequency component of the first displacement, the estimated final displacement is represented by the following equation 26.

[0134] [Equation 26]

[0135]

[0136] Each of the multiple strain gauges 20a, 20b, ..., 20m is capable of measuring strain at a first sampling frequency, and the accelerometer 30 is capable of measuring acceleration at a second sampling frequency greater than the first sampling frequency. Cubic spline interpolation can be used to upsample the first displacement converted from strain to match the second sampling frequency. Furthermore, a low-pass Butterworth filter with the Nyquist cut-off frequency can be applied to the first high-frequency component of the first displacement and the second high-frequency component of the second displacement.

[0137] Referring to Equations 1 to 26, the method for estimating bridge displacement according to the example implementation can estimate bridge displacement more accurately because the scaling factor α(k) is estimated using the RLS algorithm in the time domain rather than in the frequency domain, and the estimated displacement and the estimated scaling factor are not affected by the inherent frequency accuracy.

[0138] Figure 5 To illustrate the estimation according to the example implementation Figure 2 A flowchart of a method for measuring bridge displacement.

[0139] Figure 5 In this diagram, the parameters measured or generated in each operation are shown together.

[0140] Reference Figure 5 When with Figure 2 Compared to the previous method, the method further includes the operation of estimating the scaling factor α(k) based on the scaling factor α(k) (S320) and the operation of scaling the low-frequency component of the first displacement (S325).

[0141] Figure 6A shows a sample bridge using the method for estimating bridge displacement according to an example embodiment, and Figure 6B shows the cross-sectional dimensions of the sample bridge.

[0142] Referring to Figure 6A, the sample bridge 50 has a length of 10m. Multiple strain gauges are installed at several locations along the first direction D1, spaced 2m, 5m, and 8m apart from the reference point, respectively. An accelerometer is installed at position 60, 5m apart from the reference point along the first direction D1. At position 60, the displacement of the sample bridge 50 is measured. In Figure 6A, label 110 indicates the ground motion signal.

[0143] Referring to Figure 6B, the cross-section of the sample bridge 50 can have a size defined by 120mm*120mm.

[0144] Figure 7 The ground motion signal applied to the sample bridge in Figure 6A is shown.

[0145] Reference Figure 7 Ground motion signals 121, 122 and 123 with different accelerations were applied to the sample bridge 50.

[0146] Figures 8A to 8C show when Figure 7 Examples of ground motion signals in the figure are used to estimate displacement when they are applied to the sample bridge in Figure 6A.

[0147] Referring to Figures 8A to 8C, the reference displacement and estimated displacement, along with conventional techniques applied to the sample bridge 50, are shown. Figure 7 The ground motion signals 121, 122 and 123 in the figure were applied to the estimated displacement of the sample bridge 50 in Figure 6A.

[0148] In Figures 8A to 8C, it is assumed that the conventional technique corresponds to the power spectral density (SPD) technique.

[0149] Referring to Figures 8A to 8C, it is noted that as the acceleration of the ground motion signal increases, the difference between the displacement and the reference value according to the method of this disclosure becomes smaller than that according to...

[0150] The difference between the displacement and the reference value in the PSD technique.

[0151] Figure 9An example of a sample bridge with a varying cross-section is shown, to which the method for estimating bridge displacement according to an example embodiment is applied.

[0152] Figure 10 This illustrates when the method for estimating bridge displacement according to the example embodiment is applied. Figure 9 The difference between the actual modal shape and the estimated modal shape when the first sample bridge is used.

[0153] Reference Figure 9 and Figure 10 When the cross section of the bridge varies as the first sample bridge I, it is noted that there is almost no difference between the true modal shape and the estimated modal shape in the first order 131 and the third order 133, and there is a difference between the true modal shape and the estimated modal shape in the second order 132.

[0154] Figure 11 The method for estimating bridge displacement according to the example implementation is shown to be applied to a real bridge.

[0155] Reference Figure 11 It is noted that there is almost no difference between the displacement and the reference value according to the method of this disclosure, and there is a difference between the displacement and the reference value according to the method of PSD technology within a timing range of 13 to 17 seconds.

[0156] Figure 12 This is a block diagram illustrating an example of an electronic device for performing a method for estimating the displacement of a bridge, according to an exemplary embodiment.

[0157] Reference Figure 1 and Figure 12 The electronic device 200 used to estimate the displacement of the bridge may include a communication circuit 210, a control circuit 220, and a display 230.

[0158] The communication circuit 210 can communicate with multiple pairs of strain gauges 20a, 20b, ..., 20m installed in the bridge 10 at multiple positions x1, x2, ..., xm along the first direction D1 from the reference point RP, and with an accelerometer 30 installed in the bridge 10 at a first position spaced from the reference point RP by a first distance xd along the first direction D1. It can receive the strain STS measured by the multiple pairs of strain gauges 20a, 20b, ..., 20m, and can also receive the acceleration ACS measured by the accelerometer 30.

[0159] The communication circuit 210 typically includes one or more modules that enable wireless communication, such as between the electronic device 200 and a wireless communication system, between the electronic device 200 and another electronic device, or between the electronic device 200 and an external server. Furthermore, the communication circuit 210 may include a broadcast receiving module, a mobile communication module, a wireless internet module, a short-range communication module, and a location information module.

[0160] The broadcast receiving module can receive broadcast signals and / or broadcast-related information from an external broadcast management entity via a broadcast channel. The broadcast channel may include a satellite channel, a terrestrial channel, or both. The broadcast management entity may use a server or system that generates and transmits broadcast signals and / or broadcast-related information, or a server that receives pre-generated broadcast signals and / or broadcast-related information and transmits these items to mobile terminals. Broadcast signals may be implemented using any of TV broadcast signals, radio broadcast signals, data broadcast signals, or combinations thereof. In some cases, the broadcast signal may also include a data broadcast signal combined with a TV or radio broadcast signal.

[0161] Examples of broadcast-related information may include information related to broadcast channels, broadcast programs, broadcast events, broadcast service providers, etc. Broadcast-related information may also be provided via mobile communication networks, and in this case, received by a mobile communication module.

[0162] A mobile communication module can send and / or receive wireless signals to or from one or more network entities. Examples of wireless signals sent and / or received via a mobile communication module include audio call signals, video (telephone) call signals, or various data formats that support text and multimedia messaging communications.

[0163] A wireless internet module facilitates wireless internet access. This module can be coupled internally or externally to electronic device 200. The wireless internet module can transmit and / or receive wireless signals via a communication network 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), etc.

[0164] Short-range communication modules can facilitate short-range communication. Suitable technologies for implementing such short-range communication include BLUETOOTH. TM. Radio Frequency Identification (RFID), Infrared Data Association (IrDA), Ultra-Wideband (UWB), ZigBee, Near Field Communication (NFC), Wireless-Fidelity (Wi-Fi), Wi-FiDirect, Wireless Universal Serial Bus, etc.

[0165] The location information module can detect, calculate, derive, or otherwise identify the location of the electronic device 200. As an example, the location information module may include a Global Positioning System (GPS) module.

[0166] Control circuit 220 can receive strain STS and acceleration from communication circuit 210.

[0167] The ACS can estimate the final displacement of the bridge based on the strain STS and acceleration ACS, and can display the estimated final displacement on the display 230.

[0168] The control circuit 220 can generate a first displacement including a low-frequency component and a first high-frequency component based on strain STS, generate a second displacement including a second high-frequency component based on acceleration ACS, generate unknown parameters associated with the displacement by applying the RLS algorithm to the first high-frequency component of the first displacement and the second high-frequency component of the second displacement, and generate the final displacement of the bridge based on the unknown parameters, the low-frequency component of the first displacement and the second high-frequency component of the second displacement.

[0169] This disclosure can be applied in various ways to methods and apparatus for measuring the displacement of bridges.

[0170] The foregoing is illustrative of exemplary embodiments and should not be construed as limiting. Although several exemplary embodiments have been described, those skilled in the art will readily understand that many modifications can be made to the exemplary embodiments without substantially departing from the novel teachings and advantages of this disclosure. Therefore, all such modifications are intended to be included within the scope of this disclosure as defined in the appended claims.

Claims

1. A method for estimating the displacement of a bridge, the method comprising: Based on the sub-strain measured by multiple pairs of strain gauges, a first displacement including a low-frequency component and a first high-frequency component is generated, wherein the multiple pairs of strain gauges are installed at multiple locations in the bridge from a reference point along a first direction. Based on the acceleration measured by an accelerometer, a second displacement including a second high-frequency component is generated, the accelerometer being mounted at a first position, the first position being spaced a first distance from the reference point along the first direction in the bridge; The scaling factor is estimated based on the first high-frequency component of the first displacement and the second high-frequency component of the second displacement. and The final displacement of the bridge is generated based on the scaling factor, the low-frequency component of the first displacement, and the second high-frequency component of the second displacement. The scaling factor is estimated in the time domain by applying a recursive least squares (RLS) algorithm to the first high-frequency component of the first displacement and the second high-frequency component of the second displacement. The multiple strain gauges measure the sub-strain at a first sampling frequency, and the accelerometer measures the acceleration at a second sampling frequency greater than the first sampling frequency.

2. The method of claim 1, wherein generating the first displacement comprises: The sub-strain is measured using the multiple pairs of strain gauges; Convert the sub-strain into sub-displacement; The first displacement is generated based on the sub-displacement; The low-frequency component of the first displacement is obtained by applying a low-pass filter to the first displacement. and The first high-frequency component of the first displacement is obtained by extracting the low-frequency component from the first displacement.

3. The method of claim 1, wherein generating the second displacement comprises: The acceleration is measured using the accelerometer; The acceleration is double-integrated; and The second high-frequency component of the second displacement is obtained by applying a high-pass filter to the double-integrated acceleration.

4. The method of claim 1, wherein generating the final displacement comprises: 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 in the time domain. The scaling factor is estimated based on the results of the RLS algorithm. and The final displacement is provided by performing calculations based on the low-frequency component of the first displacement, the scaling factor, and the second high-frequency component of the second displacement.

5. The method of claim 4, wherein the final displacement is obtained by: Divide the low-frequency component of the first displacement by the estimated scaling factor; and Add the second high-frequency component of the second displacement to the result of the division operation.

6. The method of claim 4, wherein the scaling factor is associated with compensating for the difference between the estimated modal shape of the bridge and the actual modal shape of the bridge.

7. The method of claim 1, wherein each of the plurality of strain gauges comprises a first strain gauge and a second strain gauge, the first strain gauge and the second strain gauge being spaced apart from each other by a second distance along a second direction perpendicular to the first direction at one of the plurality of locations.

8. The method of claim 7, wherein the difference between the sub-strains measured by the first strain gauge and the second strain gauge is represented by the following formula 1: [Formula 1] Where Δε represents the difference between the sub-strains, x represents the position in the first direction, k represents the kth time point, u(x, k) represents the first displacement, and h(x) represents the second distance.

9. The method according to claim 8, wherein the first displacement is represented by the following formula 2: [Equation 2] in q represents the shape of the j-th modality. j Let L represent the j-th modal response and L represent the number of modes. When equation 2 is substituted into equation 1, we get equation 3 as follows: [Formula 3] 10. The method according to claim 9, wherein equation 3 is represented by the vector representation of equation 4: [Formula 4] Δε(k)=HΦq(k), Equation 4 is satisfied by the following equations: Equations 5, 6, 7, and 8: [Formula 5] De(k)=[De(x1,k) … De(x m ,k)] T 1×m , Where m represents the plurality of positions. [Formula 6] q(k)=[q1(k) … q L (k)] T 1×L , [Formula 7] [Formula 8] The modal response q(k) is derived from Equation 4 to Equation 9: [Formula 9] q(k)=(Φ T F) -1 F T H -1 No.

11. The method of claim 10, wherein when equation 9 is substituted into equation 2, the first displacement at the first position is represented by the following equation 10: [Formula 10] u(k)=TH -1 Δε(k), Equation 10 is satisfied by the following equations 11 and 12. [Equation 11] T=Ψ(x d )[Φ T F] -1 F T , [Equation 12] When the scaling factor α, which is associated with compensating for the difference between the estimated modal shape and the actual modal shape of the bridge, is introduced, the first displacement is represented by the following equation 13: [Equation 13] in, T a It is an approximate matrix of matrix T.

12. The method of claim 11, wherein when the finite response impulse is represented by the following formula 14, [Formula 14] and * =(Δt) 2 (L T L+λ 2 I) -1 L T L a a+λ 2 (L T L+λ 2 I) -1 and, Where u * The vector representation of the final displacement, u represents the vector representation of the first displacement transformed from the sub-strain, a represents the vector representation of the acceleration, La represents the (2N+1)th order diagonal weight matrix, and λ represents the normalization factor satisfied by the following equation 15. [Formula 15] λ=46.81(2N+1) -1.95 , Where λ is satisfied by the following equation 16, [Formula 16] Where f1 represents the first natural frequency of the bridge. When superposition is applied to Equation 14, Equation 17 is derived. [Equation 17] u * (k)=C H a+C L u, in, c H Representative (Δt) 2 (L T L+2 2 I) -1 L T L a The (N+1)th row corresponds to the combination of double integrator and high-pass filter, and c L Represents λ 2 (L T L+λ 2 I) -1 The low-pass filter.

13. The method of claim 12, wherein the first displacement is represented by the following formula 18: [Formula 18] u s ={T a H -1 Δε) T , The low-frequency component and the high-frequency component of the first displacement are represented by the following equations 19 and 20: [Formula 19] [Formula 20] The second high-frequency component of the second displacement is represented by the following equation 21: [Equation 21] The final displacement is represented by the following equation 22: [Equation 22] Where α(k) represents the scaling factor.

14. The method of claim 1, wherein the final displacement corresponds to the displacement of the bridge located at the first position.

15. The method according to claim 1, The first displacement is upsampled using cubic spline interpolation.

16. A method for estimating the displacement of a bridge, the method comprising: Sub-strain is measured by multiple pairs of strain gauges, which are installed at multiple locations in the bridge from a reference point along a first direction; Convert the sub-strain into sub-displacement; A first displacement is generated based on the sub-displacement; By applying a low-pass filter to the first displacement, the low-frequency component of the first displacement is obtained. The first high-frequency component of the first displacement is obtained by extracting the low-frequency component from the first displacement. Acceleration is measured by an accelerometer, which is installed at a first position, which is spaced a first distance from the reference point along the first direction in the bridge. The measured acceleration is double-integrated; By applying a high-pass filter to the double-integrated acceleration, the second high-frequency component of the second displacement is obtained; The scaling factor is estimated based on the first high-frequency component of the first displacement and the second high-frequency component of the second displacement. and and The final displacement of the bridge is generated by calculating the low-frequency component of the first displacement, the scaling factor, and the second high-frequency component of the second displacement. The scaling factor is estimated in the time domain by applying a recursive least squares (RLS) algorithm to the first high-frequency component of the first displacement and the second high-frequency component of the second displacement. The multiple strain gauges measure the sub-strain at a first sampling frequency, and the accelerometer measures the acceleration at a second sampling frequency greater than the first sampling frequency.

17. An electronic device configured to estimate the displacement of a bridge, the electronic device comprising: A communication circuit is configured to communicate with a plurality of strain gauges and an accelerometer, and is configured to receive strain measured by the plurality of strain gauges and acceleration measured by the accelerometer, wherein the plurality of strain gauges are mounted at a plurality of locations in the bridge along a first direction from a reference point, and the accelerometer is mounted at a first location, the first location being spaced a first distance from the reference point in the bridge along the first direction. A control circuit is configured to receive the strain and the acceleration from the communication circuit, and is configured to estimate the final displacement of the bridge based on the strain and the acceleration; and A display is configured to receive the estimated final displacement from the control circuit and to display the estimated final displacement. The control circuit is configured as follows: Based on the strain, a first displacement is generated, comprising a low-frequency component and a first high-frequency component; A second displacement, including a second high-frequency component, is generated based on the acceleration. The scaling factor is estimated based on the first high-frequency component of the first displacement and the second high-frequency component of the second displacement. and The final displacement of the bridge is generated based on the scaling factor, the low-frequency component of the first displacement, and the second high-frequency component of the second displacement. The control circuit is further configured to estimate the scaling factor in the time domain by applying a recursive least squares (RLS) algorithm to the first high-frequency component of the first displacement and the second high-frequency component of the second displacement. The multiple strain gauges measure the sub-strain at a first sampling frequency, and the accelerometer measures the acceleration at a second sampling frequency greater than the first sampling frequency.

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