Method for evaluating earthquake loss

Abstract

To evaluate the earthquake loss of a building on the basis of output of a sensor.SOLUTION: A method for evaluating an earthquake loss has an earthquake loss evaluation step of evaluating the earthquake loss of a building, using sensor information that the sensor set in the building acquired when an earthquake happened.SELECTED DRAWING: Figure 2

Description

Technical Field

[0001] The present invention relates to a method for evaluating earthquake losses.

Background Art

[0002] In Patent Document 1, based on the output of sensors installed in a building, the maximum response value of the building is obtained, and the analytical damage degree of the building is calculated. Next, the building is surveyed to obtain the surveyed damage degree, and the integrated damage degree is calculated in combination with the analytical damage degree.

[0003] Also, in Patent Document 2, for a building having a plurality of floors, the earthquake risk is evaluated by PML (Probable Maximum Loss rate).

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0005] In the case of Patent Document 1, for the purpose of ensuring the safety of people in the building immediately after an earthquake, the damage degree of the building is calculated based on the output of sensors installed in the building, but the earthquake loss of the building cannot be evaluated. In the case of Patent Document 2, the loss distribution of the building is calculated with respect to earthquake motion (such as the maximum ground surface velocity). Therefore, based on the output of sensors installed in the building, the loss distribution of the building cannot be evaluated.

[0006] The present invention has been made in view of such problems, and an object thereof is to evaluate the earthquake loss of a building based on the output of sensors.

Means for Solving the Problems

[0007] The main invention for achieving the above object is an earthquake loss evaluation method characterized by having an earthquake loss evaluation step of evaluating the earthquake loss of the building using sensor information acquired by a sensor installed in the building during an earthquake.

[0008] Other features of the present invention will be clarified by the description in this specification and the attached drawings.

Effects of the Invention

[0009] According to the present invention, the earthquake loss of a building can be evaluated based on the output of a sensor.

Brief Description of the Drawings

[0010]

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Mode for Carrying Out the Invention

[0011] The following matters at least will become clear from the description of this specification and the attached drawings.

[0012] (Aspect 1) An earthquake loss evaluation method, comprising an earthquake loss evaluation step of evaluating the earthquake loss of the building by using sensor information acquired by a sensor installed in the building during an earthquake.

[0013] According to the earthquake loss evaluation method of Aspect 1, based on the output of the sensor during an earthquake, the earthquake loss of the building can be evaluated immediately (immediately after the earthquake).

[0014] (Aspect 2) The earthquake loss evaluation method according to Aspect 1, preferably further comprising a preparation step of assuming and preparing for the earthquake loss of the building corresponding to the sensor information before the earthquake loss evaluation step.

[0015] According to the earthquake loss evaluation method of Aspect 2, the earthquake loss of the building can be predicted from sensor information (for example, acceleration).

[0016] (Aspect 3) The earthquake loss evaluation method according to Aspect 2, wherein the preparation step preferably includes an earthquake loss curve creation step of creating an earthquake loss curve obtained by calculating the earthquake loss of the building according to the installation mode of the sensor in the building, and a sensor installation step of installing the sensor of the installation mode in the building.

[0017] According to the earthquake loss evaluation method of Aspect 3, the earthquake loss of the building can be assumed before the earthquake.

[0018] (Aspect 4) The earthquake loss evaluation method according to Aspect 3, wherein the earthquake loss curve is preferably a curve showing the relationship between the sensor response value, which is the response value of the sensor, and the earthquake loss of the building.

[0019] According to the earthquake loss evaluation method of Aspect 4, the earthquake loss (loss rate, loss amount, etc.) of the building corresponding to the sensor response value can be evaluated.

[0020] (Aspect 5) The earthquake loss evaluation method described in Aspect 4, wherein based on the sensor information, a calculated value of the index at the time of the earthquake corresponding to a predetermined index of the sensor response value is calculated, which is desirable.

[0021] According to the earthquake loss evaluation method of Aspect 5, based on the sensor information, a calculated value of a predetermined index (maximum relative displacement, maximum acceleration, seismic intensity, etc.) can be obtained.

[0022] (Aspect 6) The earthquake loss evaluation method described in Aspect 5, wherein the earthquake loss of the building corresponding to the sensor response value of the earthquake loss curve is estimated and evaluated as the earthquake loss of the building corresponding to the calculated value, which is desirable.

[0023] According to the earthquake loss evaluation method of Aspect 6, the earthquake loss of the building can be evaluated immediately.

[0024] (Aspect 7) The earthquake loss evaluation method described in Aspect 4, wherein according to the installation mode, a plurality of analysis values analyzed before the earthquake for each predetermined index of the sensor are regressed to obtain a relational expression between the sensor response value and each floor response value which is the response value of each floor of the building, which is desirable.

[0025] According to the earthquake loss evaluation method of Aspect 7, a relational expression between the sensor response value and each floor response value of the building can be obtained according to the installation mode of the sensor.

[0026] (Aspect 8) The earthquake loss evaluation method described in Aspect 7, wherein from the relational expression and the limit value (disaster degree) of each floor of the building, a damage probability function of each floor of the building is obtained, which is desirable.

[0027] According to the earthquake loss evaluation method of Aspect 8, it is possible to evaluate the damage probability function of each floor of a building using the sensor response value.

[0028] (Aspect 9) The earthquake loss evaluation method described in Aspect 8, wherein it is desirable to obtain the earthquake loss curve from the damage probability function of each floor of the building and the restoration cost of the building.

[0029] According to the earthquake loss evaluation method of Aspect 9, it is possible to evaluate the earthquake loss curve of a building using the sensor response value.

[0030] ===Embodiment=== <<Regarding the system configuration>> FIG. 1 is a schematic diagram showing an example of the system configuration for earthquake loss evaluation.

[0031] The system shown in FIG. 1 includes a building 10, sensors 20, a computer 30, and a LAN cable 40.

[0032] The building 10 is a structure to be evaluated for earthquake loss in this embodiment and has a plurality of floors. The building 10 in the figure has 4 floors, but it is not limited to 4 floors and may be less than 4 floors or 5 floors or more. Also, the building 10 in this embodiment is made of reinforced concrete (RC structure), but it is not limited to this and may be, for example, a steel-reinforced concrete structure (SRC structure), a steel structure (S structure), etc.

[0033] In this embodiment, the sensor 20 is an acceleration sensor capable of measuring the acceleration waveform. The acceleration data measured (acquired) by the sensor 20 corresponds to the sensor information. Note that it is possible to obtain the velocity waveform and displacement waveform from the acceleration waveform by calculation (such as time integration). As shown in FIG. 1, two sensors 20 are installed in the building 10. However, the number of sensors 20 is not limited to two and may be, for example, one or three or more.

[0034] The computer 30 is installed inside the building 10. The computer 30 includes a storage unit that stores various data, programs, etc., an arithmetic processing unit that executes programs to perform various arithmetic operations, a display unit such as a liquid crystal display, an input unit such as a keyboard and a mouse, and a communication unit that communicates with the sensor 20. In addition, the storage unit of the computer 30 stores earthquake wave data, a building design model, a building earthquake loss curve (described later), etc.

[0035] The LAN cable 40 communicably connects each sensor 20 to each other and the sensor 20 to the computer 30.

[0036] With the above configuration, during an earthquake, the acceleration waveforms measured by each sensor 20 are sent (aggregated to) the computer 30 via the LAN cable 40. Then, as described later, the computer 30 immediately (immediately after the earthquake) evaluates the earthquake loss of the building based on the acceleration waveforms.

[0037] Note that the system configuration for earthquake loss evaluation is not limited to the above-described one. For example, the number of installed sensors 20 and the installation floors may be changed.

[0038] Also, in FIG. 1, the computer 30 is connected to the router 60 via the LAN cable 40 and the hub 50, and the earthquake loss evaluated by the computer 30 is transmitted outside the building 10 and can be viewed on a portable terminal (such as a tablet). Also, the sensor 20 may be a wireless sensor that does not require the LAN cable 40. Alternatively, the computer 30 may be installed outside the building 10 and the evaluation may be performed by a cloud (a computer connected to a network such as the Internet).

[0039] <<Regarding the earthquake loss evaluation method>> <Overview of earthquake loss evaluation> FIG. 2 is a schematic flowchart of the earthquake loss evaluation method in the present embodiment form. Also, FIG. 3 is a schematic explanatory diagram of the earthquake loss evaluation method. Note that FIG. 3 represents the content of FIG. 2 in a diagram.

[0040] Although not shown in FIG. 2, before an earthquake, the installation mode (such as the number of installations and the installation floor) of the sensors 20 in the building 10 is determined, and the sensors 20 are installed in the building 10. Further, the computer 30 creates an earthquake loss curve of the building using sensor response values (such as maximum relative displacement, maximum acceleration, measured seismic intensity, etc.) according to the installation mode (such as the number of installations and the installation floor) of the sensors 20 (S1: Details will be described later). Note that the step of installing the sensors 20 in the building 10 and the step of creating an earthquake loss curve of the building using the sensor response values (S1) correspond to the preparation step.

[0041] During an earthquake, each sensor 20 measures the acceleration waveform and outputs it to the computer 30 (S2). The computer 30 calculates sensor observation values (such as maximum relative displacement, maximum acceleration, measured seismic intensity, etc.) corresponding to the indices of the sensor response values using the acceleration waveform (S3). Then, the computer 30 evaluates the earthquake loss (such as average loss rate, 90% non-exceeding loss rate, etc.) of the building immediately after the earthquake by inputting the sensor observation values into the "earthquake loss curve of the building using sensor response values" created before the earthquake (S4).

[0042] Thereby, not only the damage degree of the building 10 but also the earthquake loss of the building 10 can be evaluated immediately after the earthquake using the sensor observation values (that is, based on the output of the sensors 20). For example, in a production facility, it is important to quickly determine the resumption of production including building restoration after an earthquake, so information on the earthquake loss of the building is required as soon as possible after the earthquake. The earthquake loss of the building using sensor observation values can be widely used not only in production facilities but also in BCP (Business Continuity Plan) during a disaster.

[0043] <Evaluation of Earthquake Loss Curve of Building Using Sensor Response Values> FIG. 4 is a flowchart showing an example of a method for evaluating the earthquake loss curve of the building 10 performed before an earthquake. Note that the main entity of the operations in the following evaluation is mainly the computer 30.

[0044] Here, the number of floors of the building 10 is n, the number of installed sensors 20 is two, and the installed floors of the sensors 20 are the i-th floor and the j-th floor (where i < j). Also, in this embodiment, the index of the response value of each floor of the building is the maximum inter-story displacement, and the index of the sensor response value is the maximum relative displacement (corresponding to a predetermined index). However, the index is not limited to displacement, and for example, acceleration, seismic intensity, etc. may also be used.

[0045] <Evaluation of the relational expression between the sensor response value and the response value of each floor of the building> First, using the structural calculation document (such as the relationship diagram between the weight of each floor of the building, the inter-story deformation angle, and the story shear force), a design model (such as a lumped mass model) of the building 10 is created (S11).

[0046] Also, for a plurality of seismic waves (such as past observed waves, simulated waves, etc.), a seismic wave DB composed of a total of M seismic waves is created by parametrically changing the maximum acceleration of the seismic waves (S12).

[0047] Next, seismic response analysis is performed on the design model for the seismic wave m (S13), and the sensor analysis value (maximum relative displacement) d Aji,m between the i-th floor and the j-th floor, and the analysis value (maximum inter-story displacement) Δ Ak,m of the k-th floor are calculated as shown in FIG. 5 (S14 and S15). Note that FIG. 5 is a diagram showing the relationship between the sensor response value (maximum relative displacement) and the response value of each floor of the building (maximum inter-story displacement).

[0048] At this time, regression analysis is performed using the analysis values d Aji,m and Δ Ak,m (m = 1 to M) (S16), and the relational expression f Aji between the sensor response value d k and the response value of the k-th floor Aji is evaluated (S17). TIFF2025113817000002.tif7150

[0049] The regression coefficients a k and b k in equation (1) are obtained by the following equations. TIFF2025113817000003.tif6150 TIFF2025113817000004.tif9150

[0050] (2) The E[ln(Δ Ak )] and E[ln(d Aji )] in equation (2) are the average values of ln(Δ Ak ) and ln(d Aji ) respectively, and the coefficients q k and r k are calculated by the following equations (4) to (7). TIFF2025113817000005.tif13150 TIFF2025113817000006.tif13150 TIFF2025113817000007.tif13150 TIFF2025113817000008.tif13150

[0051] The response value (maximum relative displacement) d Aji of the k-th layer with respect to the sensor response value (maximum relative displacement) between the i-th and j-th floors is evaluated using the relational expression f AK of the response value of the k-th layer k (d Aji ). TIFF2025113817000009.tif12150 Here, h k : Floor height of the k-th layer

[0052] Also, the response value (maximum inter-story deformation angle) δ Oji of the k-th layer with respect to the sensor observation value (maximum relative displacement) d K between the i-th and j-th floors during an earthquake is evaluated by inputting the sensor observation value d Oji into the relational expression f k (d Aji ) of the response value of the k-th layer. TIFF2025113817000010.tif12150

[0053] <Correction factor for the response value of each floor of the building> The response value obtained by inputting the sensor observation value during an earthquake into the relational expression of the response value may deviate from the observed value of the actual building due to factors such as the number of sensors installed and the installation floor, the difference between the observed wave and the earthquake wave DB, and the variation of the design model. Therefore, in this embodiment, a virtual model is used to calculate the virtual observation value and the virtual response value of each floor of the building, and the ratio of the virtual observation value to the virtual response value is obtained. The uncertainty when evaluating the response value is evaluated by modeling this ratio as the correction coefficient for each floor of the building.

[0054] Note that the evaluation of the correction coefficient of the response value for each floor of the building described below (S18 in FIG. 4) does not necessarily have to be performed (it may be omitted). However, performing the evaluation of the correction coefficient can further improve the accuracy of the evaluation of the earthquake loss.

[0055] FIG. 6 is a flowchart showing an example of a method for evaluating the correction coefficient of the response value for each floor of the building.

[0056] First, a virtual model is created using the design model (S181). The virtual model is a model for calculating the sensor virtual observation value that simulates the observed value of the actual building and the virtual observation value of each floor of the building, and is created by multiplying the design model (such as a mass point system model) by a redundancy factor of the bearing capacity.

[0057] Also, an earthquake wave DB (correction coefficient) composed of a total of S earthquake waves (past observed waves, simulated waves, etc.) is created under the condition of excluding the earthquake wave used when creating the relational expression (S17 in FIG. 4) of the above-described sensor response value and the response value of each floor of the building (S182).

[0058] Next, seismic response analysis is performed on the virtual model with respect to the earthquake wave s (S183), and the sensor virtual observation value (maximum relative displacement) d OVji,s and the virtual observation value (maximum inter-story drift angle) δ OVk,s of the k-th floor are calculated (S184, S187). The same seismic response analysis is performed for a total of S earthquake waves, and d OVji,s and δ OVk,s (s = 1 to S) are calculated. The sensor virtual observation value d OVji,s is substituted into the relational expression f k(d Aji ) is substituted (S185), and the virtual response value (maximum inter-story displacement) Δ Vk,s of the k-th layer is calculated (S186). TIFF2025113817000011.tif6150

[0059] The virtual response value (maximum inter-story deformation angle) δ Vk,s of the k-th layer is calculated using equation (9). TIFF2025113817000012.tif10150

[0060] The correction coefficient γ k,s of the response value of the k-th layer Vk,s is defined as the ratio of the virtual observed value δ OVk,s to the virtual response value δ TIFF2025113817000013.tif11150

[0061] The same calculation is performed for S seismic waves to obtain the correction coefficient γ k,s (s = 1 to S). The coefficient of variation V[γ k is calculated from the following equation. TIFF2025113817000014.tif14150 TIFF2025113817000015.tif18150 TIFF2025113817000016.tif10150

[0062] The corrected response value (maximum inter-story deformation angle) δ Hk of the k-th layer is evaluated by multiplying the correction coefficient γ k (S18 in Figure 4) of the response value of the k-th layer by the relational expression f Aji between the sensor response value d k and the response value of the k-th layer (S17 in Figure 4). Aji (d TIFF2025113817000017.tif12150Here, h k : Floor height of the k-th layer

[0063] In this way, the relational expression between the sensor response value and the corrected response value of each floor of the building is obtained (S19 in Figure 4)

[0064] <Limit values for each floor of the building> Set the structural type of Building 10 as RC construction, and evaluate the limit values for each floor of the building as follows (S20 in Figure 4). The limit values for each floor of the building are set for each damage level (such as minor damage, moderate damage, etc.).

[0065] First, set the ultimate story drift angle δ Uk for the k-th floor. The ultimate story drift angle δ Uk is the story drift angle when the story collapses, and is determined based on the ductility index (F value) in the seismic diagnosis standard (Japan Building Disaster Prevention Association: Revised Edition 2017, Seismic Diagnosis Standard for Existing Reinforced Concrete Buildings and Explanation, July 2017).

[0066] When the maximum story drift angle of the k-th floor is δ k , the seismic performance survival rate g k (δ k ) is as shown in Figure 7 according to the damage level classification criteria (Japan Building Disaster Prevention Association: Damage Level Classification Criteria and Restoration Technology Guidelines for Earthquake-Damaged Buildings, Revised Edition 2015, 2016). Note that Figure 7 is an explanatory diagram of the seismic performance survival rate. The horizontal axis of Figure 7 is the story drift angle δ k , and the vertical axis is the story shear force Q k .

[0067] Set the ultimate story drift angle δ Uk and calculate the energy absorption amount P Uk up to the ultimate story drift angle. Then, the seismic performance survival rate g k (δ k ) is obtained as the ratio of the remaining energy absorption capacity P Uk (δ Rk ) to P k . Here, P DK (δ k ) is the energy consumption when the maximum story drift angle of the k-th floor is δ k . TIFF2025113817000018.tif10150 TIFF2025113817000019.tif6150

[0068] The energy absorption amount P up to the ultimate story drift angleUk and the residual energy absorption capacity P Rk (δ k ) is determined based on the restoring force characteristics of the layer.

[0069] For example, when the restoring force characteristics of the layer are the Takeda model shown in FIG. 8, P Rk (δ Sk ) is calculated as follows. The energy absorption amount P up to the ultimate interlayer deformation angle δ of the k-th layer Uk is calculated from the following equation. Note that FIG. 8 is a diagram showing the seismic performance survival rate (Takeda model), and the vertical axis and the horizontal axis are the same as those in FIG. 7. Uk In the above equation, η is the stiffness degradation index during unloading, and η = 0.4 is generally used. Next, the residual energy absorption capacity P TIFF2025113817000020.tif22150 Here, TIFF2025113817000021.tif12150

[0070] In the above equation, η is the stiffness degradation index during unloading, and η = 0.4 is generally used. Next, the residual energy absorption capacity P Rk (δ k ) is calculated from the following equation. TIFF2025113817000022.tif6150

[0071] In the above equation, the energy consumption P DK (δ k ) is calculated from the following equation according to the maximum interlayer deformation angle δ k .

[0072] (δ k < δ Ck ) (when TIFF2025113817000023.tif6150

[0073] (δ Ck ≦ δ k < δ yk ) (when TIFF2025113817000024.tif11150 TIFF2025113817000025.tif11150 TIFF2025113817000026.tif10150

[0074] (δ yk ≤δ k in the case of) TIFF2025113817000027.tif22150 TIFF2025113817000028.tif11150 TIFF2025113817000029.tif12150

[0075] The limit value (maximum inter-story drift angle) δ of the damage level w (minor damage, moderate damage, etc.) of the k-th floor Rwk is evaluated based on the threshold value g of the seismic performance survival rate in the above-described damage level classification criteria Rw The seismic performance survival rate g of the k-th floor k (δ k ) is calculated from equation (17), so the limit value δ of the damage level w of the k-th floor Rwk and the threshold value g of the seismic performance survival rate Rw have the following relationship TIFF2025113817000030.tif10150

[0076] The limit value δ of the damage level w of the k-th floor Rwk is evaluated by solving the above equation for δ Rwk Here, P TIFF2025113817000031.tif6150 Here, P Rk -1 (·): P Rk The inverse function of P(·)

[0077] The threshold value g of the seismic performance survival rate corresponding to the damage level w Rw is set within a threshold range in the damage level classification criteria. Therefore, the uncertainty of the limit value is modeled using the upper and lower limit values of the threshold value g of the seismic performance survival rate Rw <Function of damage probability for each floor of the building using sensor response values>

[0078] The damage of the k-th floor with damage level w occurs when the corrected response value δ Hk exceeds the limit value δ Rwk . Therefore, the limit state function Z of the k-th floor wk ​is the limit value δ Rwk and the corrected response value δ Hk is calculated using the difference between them. TIFF2025113817000032.tif6150 Here, Z wk <0: Damage occurrence

[0079] The corrected response value δ Hk and the limit value δ Rwk When the probability distribution shapes of are modeled by a lognormal distribution, the reliability index β of the damage degree w of the k-th layer wk is calculated using the limit state function Z of equation (31) wk as follows. TIFF2025113817000033.tif15150 Here, λ Hk : Logarithmic mean value of the corrected response value of the k-th layer ζ HK : Logarithmic standard deviation of the corrected response value of the k-th layer λ Rwk : Logarithmic mean value of the limit value of the damage degree w of the k-th layer ζ Rwk : Logarithmic standard deviation of the limit value of the damage degree w of the k-th layer

[0080] The corrected response value δ of the k-th layer Hk is calculated from equation (16) using the sensor response value d Aji Taking the natural logarithm of both sides of equation (16) gives the following equation. TIFF2025113817000034.tif6150

[0081] Here, when the probability distribution shape of the correction coefficient γ of the response value k is modeled by a lognormal distribution, the logarithmic mean value λ of the corrected response value Hk and the logarithmic standard deviation ζ HK are obtained from the following equation. TIFF2025113817000035.tif6150 TIFF2025113817000036.tif6150 Here, λ γk : Logarithmic mean value of the correction coefficient of the k-th layer ζ γk : Logarithmic standard deviation of the correction coefficient of the k-th layer

[0082] Logarithmic mean value λ of equation (34) Hk and logarithmic standard deviation ζ of equation (35) HK are substituted into equation (32), and the reliability index β of the damage degree w of the k-th floor wk (d Aji ) is given by the following equation. TIFF2025113817000037.tif16150

[0083] At this time, the probability of damage function P Aji of the damage degree w of the k-th floor using the sensor response value d wk (d Aji ) is evaluated using the reliability index β wk (d Aji ). TIFF2025113817000038.tif19150Here, Φ[·]: standard normal distribution function with mean 0 and standard deviation 1

[0084] As described above, the probability of damage function P Aji of the damage degree w of the k-th floor using the sensor response value d wk (d Aji ) is evaluated (S21 in FIG. 4). In this embodiment, the response values of each floor of the building are corrected. However, as described above, the correction may not be performed. In that case, the probability of damage function of each floor of the building may be evaluated in the same manner from the relational expression between the sensor response value and the response value of each floor of the building (S17 in FIG. 4) and the limit value of each floor of the building (S20 in FIG. 4).

[0085] <Probability Distribution of Seismic Loss of Building Using Sensor Response Value> Let the sum of the damage degrees w of the k-th floor be n wk , the probability of damage be P wk (d Aji ), and the recovery cost be C wk . At this time, the mean value μ wk (d Aji ) and standard deviation σ wk (d Aji ) of the seismic loss of the k-th floor are obtained from the following equations. TIFF2025113817000039.tif14150 TIFF2025113817000040.tif18150

[0086] Here, ΔP wk (d Aji ) is obtained from the following equation according to the damage degree w. TIFF2025113817000041.tif6150 TIFF2025113817000042.tif6150

[0087] The seismic loss of a building is the sum of the seismic losses of each floor. At this time, the average value μ of the seismic loss of the building C (d Aji ) and the standard deviation σ C (d Aji ) are calculated from the following equation. TIFF2025113817000043.tif14150 TIFF2025113817000044.tif18150 Here, n: the number of building floors n wk : the sum of the damage degrees w of the kth floor In the above equation, ρ wk,vl is the correlation coefficient of the occurrence of losses between the damage degree w of the kth floor and the damage degree v of the lth floor.

[0088] The probability density function f(c|d Aji ) of the seismic loss of the building in the sensor response value d Aji ) is modeled using a beta distribution where the value range of the loss c is 0 ≦ c ≦ C B . TIFF2025113817000045.tif13150 Here, C B : the new construction cost B[q(d Aji ),r(d Aji )]: the beta function in the sensor response value d Aji

[0089] The beta function B[q(d Aji ),r(d Aji )] is calculated using the gamma function Γ[·]. TIFF2025113817000046.tif12150

[0090] Here, for example, the gamma function Γ[q(dAji )] is calculated from the following equation. TIFF2025113817000047.tif11150

[0091] Also, in Equation (45), the sensor response value d Aji parameters q(d Aji ) and r(d Aji ) are calculated from the following equation. TIFF2025113817000048.tif13150 TIFF2025113817000049.tif13150 Here, μ C (d Aji ): The average value of the seismic loss of the building calculated from Equation (42) σ C (d Aji ): The standard deviation of the seismic loss of the building calculated from Equation (43)

[0092] The probability distribution function F(c|d Aji ) of the building using the sensor response value d is calculated from the following equation. Aji ) is calculated from the following equation. TIFF2025113817000050.tif12150 TIFF2025113817000051.tif11150

[0093] Here, the normalization variable u in the above equation is calculated from the following equation. TIFF2025113817000052.tif9150

[0094] <Seismic Loss Curve of Building Using Sensor Response Value> (Seismic Loss Curve of Building (Average Loss Rate)) The seismic loss curve (average loss rate) SLER(d Aji ) of the building using the sensor response value d is calculated from the following equation using Equation (42). Aji ) is calculated from the following equation. TIFF2025113817000053.tif11150

[0095] (Seismic Loss Curve of Building (Average Loss Amount)) The sensor response value dAji Seismic loss curve (average loss amount) SLE(d Aji ) of the building using is calculated from Equation (42). TIFF2025113817000054.tif6150

[0096] (Seismic loss curve of the building (90% non - exceedance loss rate)) Sensor response value d Aji Seismic loss curve (90% non - exceedance loss rate) SLMR(d Aji ) of the building using is the standardized variable (u Aji |d Aji ) in the probability distribution function F(c|d TIFF2025113817000055.tif12150 that satisfies is obtained by inverse - calculating 0.9 |d Aji ). TIFF2025113817000056.tif6150

[0097] (Seismic loss curve of the building (90% non - exceedance loss amount)) Sensor response value d Aji Seismic loss curve (90% non - exceedance loss amount) SLM(d Aji ) of the building using is obtained from the following equation using Equation (55). TIFF2025113817000057.tif6150

[0098] Thus, based on the restoration cost C wk (S22 in Figure 4) of each floor of the building set for each damage level and the damage probability function P wk (d Aji ) (S21 in Figure 4) of the building using the sensor response value, a seismic loss curve of the building using the sensor response value is created (S1 in Figures 2 and 4).

[0099] <Sensor observation value> Next, the measurement of sensor observation values during an earthquake (S3 in Figure 2) will be described. The acceleration waveforms (S2 in Figure 2) measured by the sensors 20 installed on the i - th floor and the j - th floor are time - integrated to obtain the sensor observation value (maximum relative displacement) dOji is obtained as follows.

[0100] (1) Acceleration waveform The acceleration waveform AM measured by the sensor 20 installed on the i-th floor i (t) is baseline corrected. Let the start time of the acceleration waveform for which the time average value is obtained be T f Then, the number of data points f at the start time is given by the following equation. TIFF2025113817000058.tif9150 Here, Δt: time increment of the acceleration waveform

[0101] Start time T f If the time average value of the acceleration waveform at the start time T is ΔA, the following equation holds. TIFF2025113817000059.tif14150

[0102] At this time, the baseline-corrected acceleration waveform A i (t) is obtained from the following equation. TIFF2025113817000060.tif6150 Here, T: duration of the acceleration waveform

[0103] (2) Velocity waveform The baseline-corrected acceleration waveform A i (t) is Fourier-transformed to calculate the complex Fourier coefficient C i (s). Here, s is the complex angular frequency jω (j is the imaginary unit). To remove the long-period components of the acceleration waveform, a high-pass filter is applied. As the high-pass filter, a fourth-order Butterworth filter H HC with a passband of ω H (s) and above is adopted. Then, the transfer function H H (s) and the gain G(ω) are given by the following equations. TIFF2025113817000061.tif11150 TIFF2025113817000062.tif6150

[0104] For example, if the natural frequency F Hc is set to 0.1 Hz, the natural angular frequency ωHc becomes TIFF2025113817000063.tif6150, and when calculating the gain G(ω), it becomes as shown in Fig. 9. Note that Fig. 9 shows an example of a fourth-order Butterworth filter. The horizontal axis in Fig. 9 is the frequency in Hz, and the vertical axis is the gain G.

[0105] Under the above conditions, the complex Fourier coefficient C i ´(s) after applying the high-pass filter is obtained. TIFF2025113817000064.tif6150

[0106] C i ´(s) is inverse Fourier-transformed to calculate the acceleration waveform AF i (t) after applying the high-pass filter. AF i (t) is integrated with respect to time to obtain the velocity waveform V(t). TIFF2025113817000065.tif6150 TIFF2025113817000066.tif6150

[0107] (3) Displacement waveform Velocity waveform V i (t) is corrected for the baseline, and the correction function ΔV i (t) is set. TIFF2025113817000067.tif6150 Here, a, b: correction coefficients

[0108] V i (t) and ΔV i (t) and the mean square error Δ 2 is given by the following equation. TIFF2025113817000068.tif13150 Here, N is the number of data points of the acceleration waveform. TIFF2025113817000069.tif9150

[0109] At this time, the correction coefficients a and b for which the mean square error Δ 2 is minimized are given by the following equation. TIFF2025113817000070.tif11150 TIFF2025113817000071.tif6150 TIFF2025113817000072.tif13150 TIFF2025113817000073.tif13150

[0110] At this time, the velocity waveform VB i after baseline correction becomes TIFF2025113817000074.tif6150, and the displacement waveform D i (t) is obtained by integrating the velocity waveform VB i (t) with respect to time. TIFF2025113817000075.tif6150 TIFF2025113817000076.tif6150

[0111] (4) Relative displacement waveform Using the displacement waveforms of the i-th and j-th floors, the relative displacement waveform RD ji (t) is obtained. TIFF2025113817000077.tif6150

[0112] (5) Sensor observation value The sensor observation values (maximum relative displacement) d Oji of the i-th and j-th floors are calculated from the following equation. TIFF2025113817000078.tif7150

[0113] <Immediate assessment of seismic losses of buildings> During an earthquake, the acceleration waveforms of the sensors 20 installed on the i-th and j-th floors are calculated, and the sensor observation values (maximum relative displacement) d Oji between the i-th and j-th floors are obtained.

[0114] The average loss rate CLER of the building is evaluated by inputting the sensor observation value d Oji into equation (52). TIFF2025113817000079.tif6150

[0115] Similarly, the average building loss amount CLE is evaluated by inputting the sensor observation value d Oji into Equation (53).

[0116] The 90% non-exceedance loss rate CLMR of the building is evaluated by inputting the sensor observation value d Oji into Equation (55). TIFF2025113817000080.tif6150

[0117] Similarly, the 90% non-exceedance loss amount CLM of the building is evaluated by inputting the sensor observation value d Oji into Equation (56). TIFF2025113817000081.tif6150

[0118] In this way, based on the pre-made (before the earthquake) seismic loss curve of the building (S1 in Figure 2) and the sensor observation values during the earthquake (S3 in Figure 2), the seismic losses of the building (such as average loss, 90% non-exceedance loss, etc.) are evaluated (S4 in Figure 2).

[0119] <<Evaluation Example>> Next, an evaluation example of the seismic loss evaluation method of this embodiment will be described. Here, the number of building floors is 10, and the building structure type is RC structure. The number of sensors installed is 2, and the sensor installation floors are the 1st floor and the 10th floor.

[0120] <Setting of Design Model and Virtual Model> Figure 10 is a diagram showing the relationship between the inter-story drift angle and the story shear force of each layer in the design model (lumped mass model). Figure 11 is a diagram showing the relationship between the inter-story drift angle and the story shear force of each layer in the virtual model. Figure 12 is a diagram showing the calculation conditions of the required holding lateral force.

[0121] The second inflection point strength Q2 in Figure 10 is the required holding lateral force calculated under the calculation conditions in Figure 12.

[0122] The first and second inflection point strengths of the virtual model in Figure 11 are set by multiplying the Q1 and Q2 of the design model by the strength increase coefficient ε.

[0123] Taking into account the statistical values of the ultimate strength formula of members in the design model (variation due to material strength, variation due to evaluation formula, variation with respect to actual structures), etc., three types of amplification factors ε for the bearing capacity in the virtual model are set to 1.1, 1.2, and 1.5.

[0124] In the design model and the virtual model, the restoring force characteristics of each layer are the Takeda model, and the stiffness degradation index η after yielding is set to 0.4.

[0125] <Seismic waves used for seismic response analysis of the design model> Figure 13 is a diagram showing the seismic waves used for seismic response analysis of the design model. Here, as shown in Figure 13, three waves are used: the announced wave (Type 2 ground) random phase, the Kobe wave NS, and the Sendai wave NS.

[0126] Also, Figure 14 is a diagram showing the acceleration response spectra (ratio to the maximum acceleration of the seismic wave) of the three seismic waves.

[0127] At this time, the maximum acceleration of the seismic wave is changed from 1 to 1000 (cm / s 2 ) and the total number of seismic waves M is set to 45.

[0128] <Setting of seismic wave DB (correction coefficient)> Figure 15 is an explanatory diagram of the seismic waves used for the seismic wave DB (correction coefficient). Here, the seismic wave DB (correction coefficient) is set using the seismic waves observed in the 10 earthquakes shown in Figure 15. The seismic wave DB (correction coefficient) is composed of a total of 50 waves by selecting 5 seismic waves from each earthquake.

[0129] Figure 16 is a diagram showing the frequency distribution of the maximum accelerations of the 50 seismic waves. The horizontal axis in Figure 16 is the maximum acceleration of the seismic wave, and the vertical axis is the number.

[0130] Also, Figure 17A is a diagram showing the acceleration response spectrum with a damping constant of 5%. The horizontal axis is the period (sec), and the vertical axis is the acceleration (cm / s 2) It is also the case that Figure 17B is a diagram showing the speed response spectrum with a decay constant of 5%, where the horizontal axis is the period (sec) and the vertical axis is the speed (cm / s).

[0131] <Setting the Limit Values for Each Floor of the Building> The ultimate inter-story drift angle of the k-th floor is the inter-story drift angle when the floor collapses, and it is determined based on the toughness index (F value) in the seismic diagnosis criteria (Japan Building Disaster Prevention Association: Revised Edition 2017, Seismic Diagnosis Criteria for Existing Reinforced Concrete Buildings, Explanation of the Same, 2017.7).

[0132] When setting the toughness index F to 3.2 for the bending column as the failure mode of the member, the ultimate deformation angle becomes 1 / 33. The restoring force characteristics of the floor are based on the Takeda model, and the relationship diagram of the inter-story drift angle and the story shear force in each floor of the design model (lumped mass model) is shown in Figure 10. When calculating the relationship between the inter-story drift angle of the k-th floor and the seismic performance survival rate using Equation (17), it becomes as shown in Figure 18. Note that Figure 18 is a diagram showing the relationship between the inter-story drift angle and the seismic performance survival rate.

[0133] The seismic performance survival rate corresponding to the damage level (minor damage to collapse) is set based on the threshold values of the damage level classification criteria (Japan Building Disaster Prevention Association: Damage Level Classification Criteria and Restoration Technology Guidelines for Earthquake-Damaged Buildings, Revised Edition 2015, 2016). Also, the threshold value of the inter-story drift angle corresponding to the damage level is calculated from Equation (30) using Figure 18. The seismic performance survival rate and the inter-story drift angle corresponding to the damage level are shown in Table 1.

[0134]

Table 1

[0135] Also, using the threshold value of the inter-story drift angle corresponding to the damage level, when calculating the average value and the coefficient of variation of the limit value (inter-story drift angle) of the damage level of the k-th floor, it becomes as shown in Figure 19. Note that Figure 19 is a diagram showing the average value and the coefficient of variation of the limit value (inter-story drift angle) corresponding to the damage level. The horizontal axis of Figure 19 is the damage level (minor damage, moderate damage, severe damage, collapse), the vertical axis (left side) is the average value of the limit value, and the vertical axis (right side) is the coefficient of variation of the limit value.

[0136] <Setting of Restoration Costs for Each Floor of the Building> The restoration costs corresponding to the damage level (from minor damage to collapse) are set based on the statistical values of the restoration costs incurred during restoration work in the southern part of Hyogo Prefecture and other areas.

[0137] Set the ratio of the restoration cost to the new construction cost for each floor of the building. An example of the ratio of the restoration cost to the new construction cost is shown in Table 2.

[0138]

Table 2

[0139] <Seismic Loss of the Building> The correlation coefficient of the occurrence of losses between the damage level w of the k-th floor and the damage level v of the l-th floor in Equation (43) is set to zero for all floors and damage levels.

[0140] <<Evaluation Results>> <Relational Expression between Sensor Response Value and Response Value of Each Floor of the Building> For the design model (lumped mass model) in Figure 10, seismic response analysis was performed for the 45 seismic waves described in <Seismic Waves Used in Seismic Response Analysis of the Design Model> mentioned above. When calculating the sensor response value (maximum relative displacement) and the response value of each floor of the building (maximum inter-story displacement), Figure 20 was obtained. Note that Figure 20 is a diagram showing the relationship between the sensor response value (maximum relative displacement) and the response value of each floor of the building. In Figure 20, the relationship between the sensor response value (horizontal axis) and the response value of each floor (vertical axis) is shown for each floor. Also, in the figure, the relational expression between the sensor response value calculated from Equation (1) and the response value of each floor of the building is shown.

[0141] <Correction Coefficient of Response Value of Each Floor of the Building> When calculating the correction coefficient of the response value of each floor of the building in Figure 6 for the seismic wave DB (correction coefficient) set in <Setting of Seismic Wave DB (Correction Coefficient)> mentioned above, it became as shown in Figure 21. Note that Figure 21 is a diagram showing the correction coefficient of the response value of each floor of the building.

[0142] The figure shows the result of modeling the probability distribution of the correction factor of the response value with a lognormal distribution. At this time, the average value and coefficient of variation of the correction factor of the response value for each floor of the building are as shown in Fig. 22. Note that Fig. 22 is a diagram showing the average value and coefficient of variation of the correction factor of the response value for each floor of the building.

[0143] <Probability function of damage for each floor of the building using sensor response values> Based on the limit values (damage levels) for each floor of the building set in the above-mentioned <Setting of limit values for each floor of the building>, when calculating the probability function of damage for each floor of the building using sensor response values, it became as shown in Fig. 23. Note that Fig. 23 is a diagram showing the probability function of damage for each floor of the building using sensor response values. In Fig. 23, the probability functions of damage for each floor of the building (from the 1st floor to the 10th floor) using sensor response values (functions for minor damage, moderate damage, major damage, and collapse) are shown for each floor. In the diagrams for each floor of Fig. 23, the horizontal axis is the sensor response value, and the vertical axis is the probability of damage.

[0144] <Seismic loss curve of the building using sensor response values> When calculating the seismic loss curve of the building using the sensor response value (maximum relative displacement) based on Eqs. (52) to (56), the seismic loss curve (average loss rate) and the seismic loss curve (90% non-exceedance loss rate) of the building became as shown in Fig. 24. Note that Fig. 24 is a diagram showing the seismic loss curve of the building using the sensor response value (maximum relative displacement). The horizontal axis of Fig. 24 is the sensor response value (cm), and the vertical axis is the loss rate (%).

[0145] <Immediate evaluation of seismic loss of the building> Assume that during an earthquake, the acceleration waveforms shown in Fig. 25 were measured at the sensors installed on the 1st floor and the 10th floor. Note that Fig. 25 is a diagram showing the acceleration waveforms observed by the sensors on the 1st floor and the 10th floor, respectively.

[0146] At this time, when calculating the relative displacement waveform using Eq. (76) etc., it became as shown in Fig. 26. Note that Fig. 26 is a diagram showing the relative displacement waveform. In this waveform, the sensor observation value (maximum relative displacement) was calculated to be 45.7 cm using Eq. (77).

[0147] When the sensor observation value of 45.7 cm is input into the seismic loss curve of the building in Fig. 24, the average loss rate and 90% non-exceedance loss rate of the building are as shown in Figs. 27 and 28. In other words, the seismic loss of the building corresponding to the sensor response value of the seismic loss curve was estimated and evaluated as the seismic loss of the building corresponding to the sensor observation value of 45.7 cm. Note that Fig. 27 is a diagram when the sensor observation value of 45.7 cm is substituted into the seismic loss curve of the building, and Fig. 28 is a diagram showing the loss rates (average loss rate and 90% non-exceedance loss rate) at the sensor observation value of 45.7 cm in a bar graph.

[0148] Thus, in this embodiment, by creating a seismic loss curve of a building using the sensor response value (maximum relative displacement) before an earthquake, the seismic loss of the building can be immediately (immediately after the earthquake) evaluated using the output of the sensor during the earthquake.

[0149] As described above, the above embodiments are for facilitating the understanding of the present invention and are not for limiting and interpreting the present invention. It goes without saying that the present invention can be changed and improved without departing from its gist, and equivalents of the present invention are included therein.

Description of Reference Numerals

[0150] 10 Building 20 Sensor 30 Computer 40 LAN Cable 50 Hub 60 Router

Claims

1. An earthquake loss evaluation step of evaluating the earthquake loss of the building by using the sensor information acquired by a sensor installed in the building during an earthquake, characterized by comprising the above.

2. The earthquake loss evaluation method according to Claim 1, wherein, prior to the earthquake loss evaluation step, a preparation step of assuming and preparing for the earthquake loss of the building corresponding to the sensor information is included. characterized by comprising the above.

3. The earthquake loss evaluation method according to Claim 2, wherein the preparation step includes an earthquake loss curve creation step of creating an earthquake loss curve obtained by calculating the earthquake loss of the building according to the installation mode of the sensor in the building, and a sensor installation step of installing the sensor of the installation mode in the building. characterized by comprising the above.

4. The earthquake loss evaluation method according to Claim 3, wherein the earthquake loss curve is a curve showing the relationship between the sensor response value which is the response value of the sensor and the earthquake loss of the building. characterized by comprising the above.

5. The earthquake loss evaluation method according to Claim 4, wherein, based on the sensor information, a calculated value of the index during the earthquake corresponding to a predetermined index of the sensor response value is calculated. characterized by comprising the above.

6. The earthquake loss evaluation method according to Claim 5, wherein the earthquake loss of the building corresponding to the sensor response value of the earthquake loss curve is estimated and evaluated as the earthquake loss of the building corresponding to the calculated value. characterized by comprising the above.

7. The earthquake loss evaluation method according to Claim 4, wherein, according to the installation mode, a plurality of analysis values analyzed before the earthquake for each predetermined index of the sensor are regressed to obtain a relational expression between the sensor response value and the response value of each layer of the building which is the response value of each layer. characterized by comprising the above.

8. The earthquake loss evaluation method according to Claim 7, wherein, from the relational expression and the limit value of each layer of the building, a damage probability function of each layer of the building is obtained. characterized by comprising the above.

9. The earthquake loss evaluation method according to Claim 8, wherein, from the damage probability function of each layer of the building and the restoration cost of the building, the earthquake loss curve is obtained. characterized by comprising the above.

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