A quantitative assessment method for crack state of box girders

Abstract

This invention provides a method for quantitatively assessing the crack state of box girders, belonging to the field of bridge health monitoring. The method includes the following steps: constructing a cluster of state characteristic quantities based on the harmonic vibration response of the box girder during crack development; calculating the three-dimensional probability density function of the cluster of state characteristic quantities during crack development; establishing confidence regions corresponding to different crack states based on the distribution of the three-dimensional probability density function in a reference space; calculating a confidence index based on the three-dimensional probability density function, and using the confidence index to reflect the probability ratio of box girder cracks in each confidence region to quantitatively assess the crack state. This invention can construct a cluster of state characteristic quantities through the harmonic vibration response of box girders, calculate the three-dimensional probability density function during crack development, calculate a confidence index using the three-dimensional probability density function, and use the confidence index to reflect the probability ratio of box girder cracks in each confidence region, thereby achieving a quantitative assessment of the crack state of box girders.

Description

Technical Field

[0001] This invention belongs to the field of bridge health monitoring, specifically relating to a quantitative assessment method for the crack state of box girders. Background Technology

[0002] Under vehicle loads and other variable loads, bridge box girders experience repeated stress changes. Combined with residual stress, stress concentration occurs at welded areas and locations with abrupt changes in cross-section, making them highly susceptible to fatigue cracks. Late-stage crack development significantly impacts the box girder's load-bearing capacity, posing a threat to bridge safety and even potentially leading to collapse. Therefore, quantitatively assessing the crack state of box girders is crucial for timely repair and reinforcement, ensuring the health of bridges.

[0003] Existing technologies use singular spectrum analysis of the structural harmonic vibration response to obtain state characteristic quantities under different damage states, and distinguish damage states based on the different distributions of state characteristic quantity clusters. However, the state characteristic quantity clusters corresponding to several damage states often have significant overlap, making it difficult to quantitatively describe the damage states corresponding to state characteristic quantities in the overlap, thus limiting the quantitative assessment of box girder cracks using existing technologies. Summary of the Invention

[0004] To overcome the shortcomings of the existing technology, the present invention provides a quantitative assessment method for the crack state of box girders.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A quantitative assessment method for the crack state of a box girder includes the following steps:

[0007] A cluster of state characteristic quantities is constructed based on the harmonic dynamic response of the box girder during crack development;

[0008] The three-dimensional probability density function of the state characteristic cluster during crack propagation is calculated, and the formula for the three-dimensional probability density function is as follows:

[0009]

[0010] In the formula, f1 M* (D1), f2 M* (D2) and f3 M* (D3) represents the normalized kernel density function of the crack state M in the three dimensions;

[0011] Based on the distribution of the three-dimensional probability density function in the reference space, a confidence region Ω corresponding to different crack states is established. M ;

[0012] The confidence index is calculated based on the three-dimensional probability density function. The confidence index reflects the probability ratio of box girder cracks in the confidence domain, thereby quantitatively assessing the crack state.

[0013] Preferably, the method for constructing the state feature cluster includes the following steps:

[0014] Based on the harmonic vibration response X of the box girder under healthy conditions 0 (t) Construct its Hankel matrix Regarding the Perform singular value decomposition Let U be The corresponding reference space;

[0015] Data set X of harmonic dynamic response of box girder under the same crack state during crack propagation. i For each t (i = 1, 2, 3, ...), calculate its corresponding Hankel matrix. Projecting onto reference space U yields Calculate A i First three principal component vectors 2-norm Set, by Set constructs a cluster of state features in Indicates by X 0 The second norm obtained from (t).

[0016] Preferably, the normalized kernel density function formula is:

[0017]

[0018] In the formula, It is a Gaussian function. n is the number of signals, and σ is the standard deviation.

[0019] Preferably, the box girder specimen is subjected to simple harmonic excitation by an electromagnetic vibrator, and the harmonic vibration response of the box girder is measured by a laser vibration meter.

[0020] Preferably, the electromagnetic exciter is a 4890 modal exciter manufactured by B&K GmbH in Denmark; and the laser vibration meter is a PSV-400 laser scanning vibration meter manufactured by Polytec GmbH in Germany.

[0021] Preferably, the confidence index β is:

[0022]

[0023] In the formula, Ⅰ, Ⅱ, M... represent different crack states, F, F, ... F MThis represents the three-dimensional probability density function corresponding to different crack states.

[0024] The quantitative assessment method for box girder crack state provided by this invention has the following beneficial effects:

[0025] This invention can construct a cluster of state characteristic quantities through the harmonic vibration response of a box girder, and calculate the three-dimensional probability density function of the cluster of state characteristic quantities during crack development. The distribution of the three-dimensional probability density function in the reference space can establish the confidence region corresponding to different crack states. Then, the confidence index is calculated based on the three-dimensional probability density function. The confidence index reflects the probability ratio of box girder cracks in each confidence region, thereby realizing a quantitative assessment of the crack state of the box girder. Attached Figure Description

[0026] To more clearly illustrate the embodiments and design schemes of the present invention, the accompanying drawings required for this embodiment will be briefly described below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a flowchart illustrating the quantitative assessment method for box girder crack state according to an embodiment of the present invention.

[0028] Figure 2 This is a schematic diagram of a steel box girder model in an embodiment of the present invention;

[0029] Figure 3 This is a cluster diagram of state characteristic quantities under different crack states in the embodiments of the present invention;

[0030] Figure 4 These are confidence region diagrams for different crack states in embodiments of the present invention;

[0031] Figure 5 This is a confidence index diagram of different crack states in the embodiments of the present invention. Detailed Implementation

[0032] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0033] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the technical solution of this invention and 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 this invention.

[0034] Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance. In the description of this invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "connected" or "linked" 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. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances. In the description of this invention, unless otherwise stated, "a plurality of" means two or more, which will not be elaborated further here.

[0035] Example

[0036] This invention provides a method for quantitatively assessing the crack state of box girders, comprising the following steps (e.g. Figure 1 As shown):

[0037] Step 1: Construct a cluster of state characteristic quantities based on the harmonic vibration response of the box girder during crack development.

[0038] The method for constructing a cluster of state feature quantities includes the following steps:

[0039] Based on the harmonic vibration response X of the box girder under healthy conditions 0 (t) Construct its Hankel matrix right Perform singular value decomposition Let U be The corresponding reference space;

[0040] Data set X of harmonic dynamic response of box girder under the same crack state during crack propagation. i For each t (i = 1, 2, 3, ...), calculate its corresponding Hankel matrix. Projecting onto reference space U yields Calculate A i First three principal component vectors 2-norm Set, by Set constructs a cluster of state features in Indicates by X 0 The second norm obtained from (t).

[0041] Step 2: Calculate the three-dimensional probability density function of the state characteristic cluster during crack propagation. The formula for the three-dimensional probability density function is:

[0042]

[0043] In the formula, f1 M* (D1), f2 M* (D2) and f3 M* (D3) represents the normalized kernel density function of crack state M in three dimensions. The formula for the normalized kernel density function is:

[0044]

[0045] In the formula, It is a Gaussian function. n is the number of signals, and σ is the standard deviation.

[0046] Step 3: Establish the confidence region Ω corresponding to different crack states based on the distribution of the three-dimensional probability density function in the reference space. M ;

[0047] Step 4: Calculate the confidence index based on the three-dimensional probability density function. The confidence index reflects the probability ratio of a crack in the box girder within the confidence region, thus quantitatively assessing the crack state. Here, I, II, M… represent different crack states, and F, F, ... F… M This represents the three-dimensional probability density function corresponding to different crack states.

[0048] Example:

[0049] A steel box girder model was selected as the specimen for the embodiment. The girder was 400mm long, 10mm wide, and 20mm high. A V-shaped notch was prefabricated on the upper surface of the box girder at a distance of 92mm from the fixed end on the left side. Figure 2 As shown, fatigue cracks were induced at the tip of the specimen through fatigue loading and gradually propagated. Six crack states (labeled as S1, S2, S3, S4, S5, and S6) with crack depths of 0.5 mm, 1 mm, 1.5 mm, 2 mm, 2.5 mm, and 3 mm were selected. The specimen was subjected to simple harmonic excitation using an electromagnetic vibrator, and the transverse velocity harmonic response of the upper surface of the right end of the box girder was measured using a laser vibrometer. The electromagnetic vibrator was a 4890 modal vibrator manufactured by B&K GmbH in Denmark, and the laser vibrometer was a PSV-400 laser scanning vibrometer manufactured by Polytec GmbH in Germany.

[0050] Based on step 1 above, a cluster of state characteristic quantities is constructed from the harmonic vibration response of the box girder. The specific process is as follows:

[0051] Based on the dynamic response X of the steel box girder specimen under healthy conditions mentioned above 0 (t) Construct its Hankel matrix right Perform singular value decomposition Let U be The corresponding reference space.

[0052] The dynamic response dataset X of the steel box girder specimen under the same crack state during crack development was measured. i For each t (i = 1, 2, 3, ...), calculate its corresponding Hankel matrix. Projecting onto reference space U yields Calculate A i First three principal component vectors 2-norm Set, by Set constructs a cluster of state features like Figure 3 As shown.

[0053] Calculate the three-dimensional probability density function of the characteristic clusters of each state during crack propagation. Where f1 M* f2 M* and f3 M* These are the normalized kernel density functions in the three dimensions of the crack state M.

[0054] According to F M Establish the confidence region Ω corresponding to states S1-S6 in the reference space. M ,like Figure 4 As shown, from Figure 4 As can be seen, the clusters of state characteristic quantities corresponding to several crack states have obvious overlap, making it difficult to quantitatively describe the crack states corresponding to the state characteristic quantities in the overlap. Therefore, we calculate the confidence index according to step 4 above, and then use the confidence index to reflect the probability ratio of the box girder crack in the confidence domain to quantitatively evaluate the crack state. The specific process is as follows: First, select three sets of beam velocity harmonic response signals with unknown crack states (labeled as T1, T2, and T3), and calculate their state characteristic quantities (D1, D2, D3), which are (6.311, 3.546, 2.010), (7.500, 5.656, 3.499), and (8.464, 6.254, 4.777), respectively; Second, calculate the confidence index corresponding to the state characteristic quantities in states T1, T2, and T3, such as... Figure 5As shown, the values ​​are (0,0,1,0.2478,0,0), (0,0,0.0657,1,0.3321,0), and (0,0,0,0,1,0.3725), respectively. It can be seen that crack state T1 belongs to state S3 or S4 with a probability ratio of 1:0.2478; crack state T2 belongs to state S3, S4, or S5 with a probability ratio of 0.0657:1:0.3321; and crack state T3 belongs to state S5 or S6 with a probability ratio of 1:0.3725. This reflects the probability ratio of crack states belonging to states S1-S6, thus completing the quantitative assessment of crack states.

[0055] As described above, this invention can construct a cluster of state characteristics through the harmonic vibration response of a box girder, and calculate the three-dimensional probability density function of the cluster of state characteristics during crack development. The distribution of the three-dimensional probability density function in the reference space can establish the confidence region corresponding to different crack states. Then, the confidence index is calculated based on the cluster of state characteristics. The confidence index reflects the probability ratio of box girder cracks in each confidence region, thereby realizing a quantitative assessment of the crack state of the box girder.

[0056] The above-described embodiments are merely preferred embodiments of the present invention, and the scope of protection of the present invention is not limited thereto. Any simple changes or equivalent substitutions of the technical solutions that can be obviously obtained by those skilled in the art within the scope of the technology disclosed in the present invention shall fall within the scope of protection of the present invention.

Claims

1. A method for quantitatively assessing the crack state of a box girder, characterized in that, Includes the following steps: A cluster of state characteristic quantities is constructed based on the harmonic dynamic response of the box girder during crack development; The three-dimensional probability density function of the state characteristic cluster during crack propagation is calculated, and the formula for the three-dimensional probability density function is as follows: Among them, f1 M* (D1) and f3 M* (D3) represents the normalized kernel density function of the crack state M in the three dimensions; Based on the distribution of the three-dimensional probability density function in the reference space, a confidence region Ω corresponding to different crack states is established. M ; The confidence index is calculated based on the three-dimensional probability density function. The confidence index reflects the probability ratio of box girder cracks in the confidence region to quantitatively assess the crack state. The method for constructing the state feature cluster includes the following steps: Based on the harmonic vibration response X of the box girder under healthy conditions 0 (t) Construct its Hankel matrix Regarding the Perform singular value decomposition Let U be The corresponding reference space; Data set X of harmonic dynamic response of box girder under the same crack state during crack propagation. i For each t (i = 1, 2, 3, ...), calculate its corresponding Hankel matrix. Projecting onto reference space U yields Calculate A i First three principal component vectors L2 norm Set, by Set constructs a cluster of state features in Indicates by X 0 The second norm obtained from (t).

2. The quantitative assessment method for box girder crack state according to claim 1, characterized in that, The formula for the normalized kernel density function is: In the formula, It is a Gaussian function. n is the number of signals, and σ is the standard deviation.

3. The quantitative assessment method for box girder crack state according to claim 1, characterized in that, The box girder specimen was subjected to simple harmonic excitation by an electromagnetic vibrator, and the harmonic vibration response of the box girder was measured by a laser vibration meter.

4. The quantitative assessment method for box girder crack state according to claim 3, characterized in that, The electromagnetic exciter is a 4890 modal exciter; the laser vibration meter is a PSV-400 laser scanning vibration meter.

5. The quantitative assessment method for box girder crack state according to claim 1, characterized in that, The confidence index β is: In the formula, Ⅰ, Ⅱ, M... represent different crack states, and F Ι ,F II ,...F M This represents the three-dimensional probability density function corresponding to different crack states.

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