Bridge response information space-time checking and reproducing method

Abstract

This invention proposes a method for spatiotemporal verification and reproduction of bridge response information, comprising the following steps: Based on the spatial completeness of the structural response data obtained from bridge inspection, the correlation between data at each measuring point is obtained; the static response of the bridge structure at the current moment under only constant load and temperature is determined; the baseline trend of the data at the measuring points between the current and previous inspections is obtained; based on the temporal completeness of the structural response data obtained from bridge monitoring, response time-series data is obtained; the baseline trend of the monitoring measuring points between the current and previous inspection times is obtained; baseline anomaly trend verification of the monitoring data is performed; monitoring baseline verification is conducted; the baseline-corrected monitoring data is obtained; and the spatiotemporal reproduction of data at each measuring point is performed. This method aims to solve the technical problems of temporal incompleteness in inspection data and spatial incompleteness in monitoring data, maximizing the utilization of limited bridge operation and maintenance data to perceive the response information of the bridge structure with maximum efficiency, thereby enhancing infrastructure maintenance capabilities.

Description

Technical Field

[0001] This invention relates to the technical field of intelligent bridge detection and monitoring, and in particular to a method for spatiotemporal verification and reproduction of bridge response information. Background Technology

[0002] Bridge inspection and bridge health monitoring are two methods for obtaining information on the structural response of bridges. Bridge inspection involves a more comprehensive range of measurement points for observing the structural response, resulting in good spatial completeness of the obtained structural response. However, the inspections are conducted at different times with long intervals, and there are temporal gaps in the data between two inspections, meaning that the inspection data is temporally incomplete.

[0003] Bridge monitoring involves installing sensors and data storage systems at response measurement points to continuously collect structural response information. However, bridge monitoring requires consideration of hardware costs and data storage scale, resulting in a limited number of monitoring points. The monitoring data is difficult to reflect the spatial characteristics of the structural response, meaning that the detection data has spatial incompleteness. Furthermore, the monitoring data may be subject to abnormal changes in long-term trends due to various factors, causing data errors.

[0004] Clearly, only by coupling and processing the detection data with the monitoring data can we achieve a complete spatiotemporal reproduction of the bridge structure's response and effectively grasp the bridge's service status. Therefore, two issues must be addressed:

[0005] (1) Use detection data to correct for possible long-term abnormal trends in monitoring data;

[0006] (2) Using the spatial correlation principle of bridge response, the discontinuous time data of different measuring points are reproduced in a coherent time sequence. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for spatiotemporal verification and reproduction of bridge response information. It aims to solve the technical problems in the prior art where the detection data needs to be corrected relative to the detection data and different measurement points cannot be reproduced in a coherent manner.

[0008] To achieve the above objectives, this invention proposes a method for spatiotemporal verification and reproduction of bridge response information, comprising the following steps:

[0009] S1: The structural response data obtained from bridge inspection has spatial completeness, thus yielding the correlation coefficient of data at each measuring point;

[0010] S2: Determine the static response of the bridge structure at this moment when it is subjected to dead load and temperature only without other loads; obtain the static response of the bridge structure in the previous test when it was subjected to dead load and temperature only without other loads.

[0011] S3: Obtain the baseline of the data trend between the current detection and the previous detection of the detection point in step S2;

[0012] S4: Based on the structural response data obtained from bridge monitoring, which has temporal completeness, obtain the temporal continuity of the response time series data at a certain structural measuring point;

[0013] S5: Obtain the baseline of the data trend between the current detection and the previous detection of the monitoring point;

[0014] S6: Baseline anomaly trend verification of monitoring data. If the monitoring baseline shows a long-term abnormal change trend, it is necessary to determine whether the monitoring trend baseline needs to be verified based on the detection trend baseline.

[0015] S7: Perform baseline verification and obtain the corrected monitoring response data under constant load and temperature and the monitoring response data under constant load and temperature from the previous test.

[0016] S8: Obtain baseline-corrected monitoring data;

[0017] S9: Using the structural response data of a certain monitoring point and the response correlation coefficient between each measuring point, the spatiotemporal reproduction of each detection measuring point is carried out.

[0018] As a preferred option, the bridge inspection measurement points in S1 are relatively complete, typically covering all measurement points in the monitoring system, and can express the spatial regularity of the bridge cross-section. Load experiments in bridge inspection can obtain spatially complete response information from each measurement point. By selecting a specific overlapping measurement point A, regression analysis is performed on the data from other measurement points. The measurement points show a proportional correlation, yielding the correlation coefficient vector [A1, A2, A3, ..., A...] between the response data of the other n measurement points and the response data of this measurement point. n-1 A n ].

[0019] Preferably, in S2 and S3, the static response of the bridge structure under no other loads and only constant load and temperature is measured, and the static response C at this moment is calculated. b The static response C measured during the previous test s By establishing a straight line connection, a data baseline is obtained between the two detection periods. Data points are constructed on the detection data baseline according to the sampling interval of the bridge health monitoring system. If the constructed points are added to the two endpoints C... s and C b There are m data points in total, denoted as C. s Let C1 be the denoted C. b C m Then the baseline detection data vector C=[C1, C2, C3, ..., C m-1 C m ].

[0020] Preferably, in S4 and S5, the monitoring data vector M = [M1, M2, M3, ..., M...] is the data vector between the current detection and the previous detection. m-1 M m The constant load-temperature response, formed by the constant load and temperature data from the monitoring data during this period, is extracted using digital signal processing algorithms and given as H = [H1, H2, H3, ..., H]. m-1 H m The static response H at this moment will be monitored. m A straight line is drawn between the static response H1 from the previous detection to obtain the monitoring data baseline for this period. Data points are constructed on the monitoring data baseline according to the sampling interval of the bridge health monitoring system. If the constructed points are combined with the two endpoints H1 and H2... m There are m data points in total. Let H1 be J1, and H be... m For J m Then the data vector for monitoring the baseline is J=[J1, J2, J3, ..., J m-1 J m ].

[0021] As a preferred option, in S6, the detection baseline C is taken as the actual value and the monitoring baseline J is taken as the value to be evaluated. The relative average error E between the two is calculated. If the relative average error does not exceed x%, it means that the monitoring baseline does not need to be checked. If the relative average error exceeds x%, it means that it needs to be checked.

[0022] As a preferred option, the static response C detected at this moment will be included in S7. b A straight line is drawn between the static response H1 from the previous detection to obtain the corrected baseline of the monitoring data for this period. Data points are constructed on the monitoring data baseline according to the sampling interval of the bridge health monitoring system. If the constructed points are combined with the two endpoints H1 and C... b There are m data points in total. Let H1 be X1, and C be... b For X m The corrected monitoring baseline data vector is then X=[X1, X2, X3, ..., X... m-1 , X m ].

[0023] As a preferred method, in S8, the constant load-temperature response H from the monitoring data before verification is first subtracted from the original monitoring data vector M to obtain the zero-mean fluctuation data vector B=MH=[M1-H1, M2-H2, M3-H3, ..., M m-1 -H m-1 M m -H m ]=[B1,B2, B3, ..., Bm-1 B m Then, subtract the baseline J before correction from the constant load-temperature response H to obtain the baseline-free static response Q = HJ = [H1-J1, H2-J2, H3-J3, ..., H m-1 -J m-1 H m -J m ]=[Q1, Q2, Q3, ..., Q m-1 Q m Finally, B, Q, and the corrected baseline X are superimposed to obtain the corrected monitoring data h=[h1, h2, h3, ..., h m-1 , h m ].

[0024] As a preferred embodiment, in S9, if the monitoring data of the overlapping monitoring point A is h=[h1, h2, h3, ..., h m-1 ,h m If the data for the remaining detection points are h and [A1, A2, A3, ..., A], then the data for the remaining detection points are h and [A1, A2, A3, ..., A]. n-1 A n The coefficients are multiplied together, i.e., A1h, A2h, A3h, ..., A n-1 h, A n h.

[0025] As a preferred option, the formula for calculating the relative average error E is:

[0026] .

[0027] Compared with existing technologies, the beneficial effects of the spatiotemporal verification and reproduction method for bridge response information provided by this invention are as follows:

[0028] (1) The spatiotemporal characteristics of bridge response are reproduced: By combining the spatial completeness of bridge detection data and the temporal continuity of monitoring data, this invention can reconstruct spatiotemporally complete bridge response data, which can more comprehensively reflect the working status of the bridge and is the key to intelligent bridge maintenance based on detection and monitoring data.

[0029] (2) Good technical applicability: This invention is not limited to specific regression methods, interpolation methods or signal processing methods. It can adapt to the differential response related laws caused by differences in bridge structure, materials, environment and other factors. The corresponding sub-method can be flexibly selected according to specific needs, and it has a wide range of applicability.

[0030] (3) Information multiplication of limited measuring point information: This invention can diffuse the temporal continuity of the response information of a limited number of monitoring points to the entire spatial cross section, filling in the missing temporal continuity data of the detection data, and maximizing the utilization efficiency of bridge operation and maintenance information based on the fusion of monitoring data.

[0031] The features and advantages of the present invention will be described in detail through embodiments and in conjunction with the accompanying drawings. Attached Figure Description

[0032] Figure 1 This is a flowchart of the algorithm of the method of the present invention.

[0033] Figure 2 The example uses detection and monitoring points to acquire bridge structural response information.

[0034] Figure 3 This diagram illustrates the data correlation between two detection points and one overlapping detection and monitoring point.

[0035] Figure 4 The detection baseline and monitoring baseline are for the same measuring point.

[0036] Figure 5 The monitoring data for overlapping monitoring points includes data from the previous monitoring time.

[0037] Figure 6 The monitoring data for overlapping monitoring points includes the monitoring data at the current monitoring time.

[0038] Figure 7 This refers to the monitoring data of overlapping measurement points between two detection times.

[0039] Figure 8 This is time-series data for another measurement point, supplemented based on the data from overlapping measurement points and the correlation between measurement points.

[0040] Figure 9 This is time-series data for another measurement point, supplemented by data from overlapping measurement points and the correlation between measurement points. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. However, it should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0042] In the description of this invention, it should be noted that when an element is referred to as being "fixed to" or "set on" another element, it can be directly on or indirectly on the other element. When an element is referred to as being "connected to" another element, it can be directly connected to or indirectly connected to the other element.

[0043] In the description of this invention, it should be noted that the terms "center," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of this invention is in use. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified. "Several" means one or more, unless otherwise explicitly specified.

[0044] In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0045] See Figures 1-9 The technical solution of the present invention will be described in detail below.

[0046] This invention relates to a method for spatiotemporal verification and reproduction of bridge response information based on the coupling of detection and monitoring data. The method specifically includes the following steps:

[0047] Step 1: Obtain the correlation coefficients between the data from each measuring point. Bridge inspection measuring points are relatively complete, typically covering all points in the monitoring system, and can express the spatial characteristics of the bridge cross-section. Load experiments in bridge inspection can obtain spatially complete response information from each measuring point. Select a specific overlapping measuring point A, and perform regression analysis on the data from other measuring points to obtain the correlation coefficient vector [A1, A2, A3, ..., A...]. n-1 A n ].

[0048] In step 1, regression analysis is not limited to a certain regression formula or regression method. Step 1 only uses the example of a proportional correlation between measurement points. The correlation parameters between different measurement points will be treated specifically for different bridges and different regression modeling methods in actual work.

[0049] Step 2: Obtain the baseline data trend between the current and previous measurements at the test points. Measure the static response of the bridge structure under no other loads, only constant load and temperature, and calculate the static response C at the current moment. b The static response C measured during the previous test s By establishing a straight line connection, a data baseline is obtained between the two detection periods. Data points are constructed on the detection data baseline according to the sampling interval of the bridge health monitoring system. If the constructed points are added to the two endpoints C... s and C b There are m data points in total, denoted as C. s Let C1 be the denoted C. b C m Then the baseline detection data vector C=[C1, C2, C3, ..., C m-1 C m ].

[0050] In step 2, linear interpolation is used to reconstruct the data points, so that the data baseline is not distorted due to the interpolation function.

[0051] Step 3: Obtain the baseline data trend between the current monitoring point and the previous monitoring point. The monitoring data vector for this period is M = [M1, M2, M3, ..., M...]. m-1 M m The constant load-temperature response (static response) formed by the constant load and temperature of the monitoring data during this period is extracted using digital signal processing algorithms and is given as H=[H1, H2, H3,..., H...]. m-1 H m The static response H at this moment will be monitored. mA straight line is drawn between the static response H1 from the previous detection to obtain the monitoring data baseline for this period. Data points are constructed on the monitoring data baseline according to the sampling interval of the bridge health monitoring system. If the constructed points are combined with the two endpoints H1 and H2... m There are m data points in total. Let H1 be J1, and H be... m For J m Then the data vector for monitoring the baseline is J=[J1, J2, J3, ..., J m-1 J m ].

[0052] In step 3, linear interpolation is used for data point reconstruction to avoid distortion of the data baseline due to the interpolation function. The method for extracting the static response of the monitoring data is not limited to a specific signal processing method; wavelet, EMD, or other methods can be used.

[0053] Step 4: Baseline anomaly trend verification of monitoring data. The monitoring baseline may exhibit long-term abnormal change trends. It is necessary to determine whether the monitoring baseline needs to be verified based on the detection baseline. Using the detection baseline C as the actual value and the monitoring baseline J as the value to be evaluated, calculate the relative average error E between the two. If the relative average error does not exceed x%, it means that the monitoring baseline does not need to be verified. If the relative average error exceeds x%, it means that verification is required.

[0054] In step 4, the formula for calculating the relative average error E is:

[0055] ,

[0056] Step 5: Perform baseline verification (i.e., the monitoring data needs to be corrected). The static response C detected at this moment... b A straight line is drawn between the static response H1 from the previous detection to obtain the corrected baseline of the monitoring data for this period. Data points are constructed on the monitoring data baseline according to the sampling interval of the bridge health monitoring system. If the constructed points are combined with the two endpoints H1 and C... b There are m data points in total. Let H1 be X1, and C be... b For X m The corrected monitoring baseline data vector is then X=[X1, X2, X3,..., X... m-1 , X m ].

[0057] In step 5, linear interpolation is used to reconstruct the data points, so that the data baseline is not distorted due to the interpolation function.

[0058] Step 6: Obtain the baseline-corrected monitoring data. First, subtract the constant load-temperature response H from the pre-verification monitoring data from the original monitoring data vector M to obtain the zero-mean fluctuation data vector B=MH=[M1-H1, M2-H2, M3-H3, ...,M m-1 -H m-1 M m -H m ]=[B1, B2, B3, ..., B m-1 B m Then, subtract the baseline J before correction from the constant load-temperature response H to obtain the baseline-free static response Q = HJ = [H1-J1, H2-J2, H3-J3, ..., H m-1 -J m-1 H m -J m ]=[Q1, Q2, Q3, ...,Q m-1 Q m Finally, B and Q are superimposed with the corrected baseline X to obtain the corrected monitoring data h=[h1, h2, h3, ..., h m-1 , h m ].

[0059] Step 7: Reproduce the data space of each detection point. If the monitoring data of the overlapping detection point A is h=[h1, h2, h3, ..., h m-1 , h m If the data for the remaining detection points are h and [A1, A2, A3, ..., A], then the data for the remaining detection points are h and [A1, A2, A3, ..., A]. n-1 A n The coefficients are multiplied together, i.e., A1h, A2h, A3h, ..., A n-1 h, A n h.

[0060] In step 7, the recovery results of the detection points are only examples, and the final calculation results shall be based on the actual correlation.

[0061] The above methods are then applied in specific ways:

[0062] Taking the strain monitoring data of the mid-span section of the main span of a large-span continuous beam bridge in Guangdong Province and the strain monitoring data of the mid-span section of the main span obtained from two tests as examples, the specific implementation process of the present invention is explained.

[0063] like Figure 2This diagram illustrates the layout of the testing and monitoring points at the mid-span section of the main span of the bridge. There are 12 strain testing points, named C1 to C12, distributed on the upper and lower surfaces of the top slab, the left and right webs, and the bottom surface of the bottom slab; and 2 strain monitoring points, named J1 to J2. C3 and J1 are overlapping nodes, and C11 and J2 are overlapping monitoring points. The strain response time series data of C2 and C11 are reproduced using the correlation between C3 and C2 and C11, as well as the monitoring data of the J1 monitoring point which overlaps with C3. The steps are as follows:

[0064] (1) A load test was conducted during one inspection. After the convoy passed, if Figure 3 The correlation between the strain data at measuring point C3 and C2, and between the strain data at measuring point C3 and C11, is shown. If the data at measuring point C3 (which is also the data at measuring point J1) is x, and the data at the other two measuring points are y, then the relationship between the C3 (J1) data and the C2 data is y = 1.104x + 22.946, and the relationship between the C3 (J1) data and the C11 data is y = 1.229x + 56.673. These two relationships can be considered as the "correlation coefficients" described in this patent.

[0065] (2) For measuring point C3, during the last test, its static strain was measured to be -15 microstrain at a certain moment. During this test, its static strain was measured to be -26 microstrain at a certain moment. What is the baseline during this period? Figure 4 As shown, the linear interpolation function of the baseline is y = -11x - 4.

[0066] (3) For measuring point J1, during the last test, the static strain caused by constant load and temperature in the monitoring data was extracted using the wavelet method. The monitoring system data curve is as follows: Figure 5 At the same time as the static strain was measured, the monitoring system detected a static strain of -14.5 microstrain. During this test, the static strain caused by constant load and temperature was extracted from the monitoring data using wavelet methods. The monitoring system data curve is shown below. Figure 6 At the same moment that the static strain was measured, the monitoring system detected a static strain of -27 microstrain. Then, the baseline during this period is as follows: Figure 4 As shown, the linear interpolation function of the baseline is y = -12.5x - 2.

[0067] (4) The error between the detection baseline and the monitoring baseline that need to be monitored is set to 5%. The calculated error is 3.2%, which is less than 5%, so no baseline correction is required.

[0068] (5) The monitoring data of the J1 measuring point between the two detection times is as follows: Figure 7As shown, according to the relationships y=1.104x+22.946 and y=1.229x+56.673, Figure 7 The obtained monitoring data is substituted into two relational expressions as x, and the output y of the relational expressions is the time series reproduction data of measuring points C3 and C11, as shown below. Figure 8 and Figure 9 As shown.

[0069] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions or improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for spatiotemporal verification and reproduction of bridge response information, characterized in that, Includes the following steps: S1: Based on the spatial completeness of the structural response data obtained from bridge inspection, a certain overlapping monitoring point A is selected, and regression analysis is performed on the data from other monitoring points. The monitoring points show a proportional correlation, yielding the correlation coefficient vector [A1, A2, A3, ..., A] between the response data from the other n monitoring points and the response data from this monitoring point. n-1 A n ]; S2: Determine the static response of the bridge structure at this moment when it is subjected to dead load and temperature only without other loads; obtain the static response of the bridge structure in the previous test when it was subjected to dead load and temperature only without other loads. S3: Obtain the baseline of the data trend between the current detection and the previous detection of the detection point in step S2; S4: Based on the temporal completeness of the structural response data obtained from bridge monitoring, obtain temporally continuous response time-series data at a certain structural measuring point; the monitoring data vector M=[M1, M2, M3,..., M...] between the current detection and the previous detection. m-1 M m ]; S5: Using digital signal processing algorithms, the load-temperature response formed by the combined load and temperature data from the monitoring data during this period is extracted as H=[H1, H2, H3, ..., H...]. m-1 H m The static response H at this moment will be monitored. m Connect the static response H1 from the previous test with a straight line to obtain the monitoring data baseline for this period. Construct data points on the monitoring data baseline according to the sampling interval of the bridge health monitoring system. If the constructed points are combined with the two endpoints H1 and H2... m There are m data points in total. Let H1 be J1, and H be... m For J m Then, the baseline data vector of the data trend between the current detection and the previous detection at the monitoring point is J=[J1, J2, J3, ..., J...]. m-1 J m ]; S6: Determine whether it is necessary to verify the monitoring trend baseline based on the detection trend baseline; S7: Perform baseline verification of the monitoring trend and obtain the corrected monitoring baseline data vector X; S8: First, subtract the constant load-temperature response H from the monitoring data before verification from the original monitoring data vector M to obtain the zero-mean fluctuation data vector B=MH=[M1-H1, M2-H2, M3-H3, ..., M m-1 -H m-1 M m -H m ]=[B1, B2, B3, ..., B m-1 B m Then, subtract the baseline J before correction from the constant load-temperature response H to obtain the baseline-free static response Q = HJ = [H1-J1, H2-J2, H3-J3, ..., H m-1 -J m-1 H m -J m ]=[Q1, Q2, Q3, ..., Q m-1 Q m Finally, B, Q, and the corrected baseline data vector X are superimposed to obtain the corrected monitoring data h=[h1, h2, h3, ..., h m-1 , h m ]; S9: Using the structural response data of a certain monitoring point and the response correlation coefficient between each measuring point, the spatiotemporal reproduction of each detection measuring point is carried out.

2. The method for spatiotemporal verification and reproduction of bridge response information as described in claim 1, characterized in that, S3 measures the static response of a bridge structure under conditions of no other loads but only dead load and temperature. The static response C at this moment is then measured. b The static response C measured during the previous test s By establishing a straight line connection, a baseline for the detection data between the two detection periods is obtained. Data points are constructed on this baseline according to the sampling interval of the bridge health monitoring system. If the constructed points are combined with the two endpoints C... s and C b There are m data points in total, denoted as C. s Let C1 be the denoted C. b C m Then the baseline data vector for detecting the trend is C=[C1, C2, C3,..., C...]. m-1 C m ].

3. The method for spatiotemporal verification and reproduction of bridge response information as described in claim 2, characterized in that, In S6, the detection trend baseline data vector C is taken as the actual value, and the monitoring trend baseline data vector J is taken as the value to be evaluated. The relative average error E between the two is calculated. If the relative average error does not exceed x%, it means that the monitoring trend baseline does not need to be checked. If the relative average error exceeds x%, it means that it needs to be checked.

4. The method for spatiotemporal verification and reproduction of bridge response information as described in claim 3, characterized in that, S7 will detect the static response C at this moment. b A straight line is drawn between the static response H1 from the previous detection to obtain the corrected baseline of the monitoring data for this period. Data points are constructed on the monitoring data baseline according to the sampling interval of the bridge health monitoring system. If the constructed points are combined with the two endpoints H1 and C... b There are m data points in total. Let H1 be X1, and C be... b For X m The corrected monitoring baseline data vector is then X=[X1, X2, X3, ..., X... m-1 X m ].

5. The method for spatiotemporal verification and reproduction of bridge response information as described in claim 1, characterized in that, In S9, if the monitoring data of the overlapping monitoring point A is h=[h1, h2, h3, ..., h m-1 , h m If the data for the remaining detection points are h and [A1, A2, A3, ..., A], then the data for the remaining detection points are h and [A1, A2, A3, ..., A]. n-1 A n The coefficients are multiplied together, i.e., A1h, A2h, A3h, ..., A n-1 h, A n h.

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