A structure temperature effect separation method based on temperature orthogonal space
By employing a temperature-orthogonal space-based method, using cubic spline functions and orthogonal space decomposition, the problem of insufficient causal relationships in existing temperature effect separation methods is solved. This achieves effective separation of structural temperature effects and standardization of data processing, thereby improving analytical efficiency and accuracy.
Patent Information
- Application Number
- CN202311794906.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-12-22
- Publication Date
- 2026-08-25
- Estimated Expiration
- 2043-12-22
AI Technical Summary
Existing temperature effect separation methods mainly focus on the pure numerical processing of structural response signals, failing to effectively address the causal relationship between structural temperature changes and structural temperature response, resulting in an insufficient understanding of structural temperature effects in data analysis.
The temperature data of each measuring point is expressed by a cubic spline function, and an orthogonal temperature space is constructed. The temperature effect component in the overall structural response signal is extracted by the Schmidt method or singular value decomposition method, and the structural response component under live load is determined.
It achieves temperature effect separation based on causal relationships, standardizes data processing, reduces storage requirements, simplifies data volume, and improves the efficiency of understanding and analyzing structural temperature effects.
Smart Images
Figure CN117633428B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of automated monitoring data processing technology for bridge engineering, and specifically to a method for separating structural temperature effects based on orthogonal temperature space. Background Technology
[0002] Sunlight and environmental influences cause periodic changes in the internal temperature field of bridge structures, leading to corresponding changes in the stress-free length and stress-free curvature of bridge structural components. This results in structural stress and deformation, such as main girder deflection, tower top misalignment, support displacement, and changes in internal forces within components. On a temporal scale, the periodicity of environmental temperature mainly includes short-term variations such as strong storms and heavy rains, diurnal variations, and seasonal variations. On a spatial scale, different components of the bridge structure experience asynchronous temperature changes due to differences in materials, construction, orientation, and shading relationships, resulting in both local cross-sectional effects and overall structural effects. Furthermore, the structural system changes from the construction phase to the operational phase, leading to different structural effects from temperature variations. The purpose of temperature monitoring and structural temperature effect analysis is to assess the structural safety under temperature influence and to isolate the temperature effect from monitoring data of other structural response parameters, serving as a basis for further structural analysis and evaluation.
[0003] The completed state and construction process state of a bridge are affected by the changing temperature field of the structure. The assessment of each state is inseparable from the study of the structural temperature characteristics and effects, and the research methods include finite element analysis, temperature field monitoring, and data analysis. The structural temperature response can be calculated based on the monitored temperatures of each component, but this requires a large number of monitoring sections and measuring points to reflect the changing patterns of the structural temperature field. Data analysis of temperature field monitoring and structural response monitoring data to isolate the structural temperature effects is currently a commonly used method.
[0004] Various data processing methods, such as moving average, wavelet transform, and empirical mode decomposition, have been used to study the temperature effects of structural static and dynamic responses, thereby separating and predicting these temperature effects. However, these commonly used methods for separating temperature effects are purely numerical processing methods targeting the structural response signal R itself, rather than addressing the causal relationship between structural temperature changes and the structural temperature response. Therefore, they are not conducive to enhancing the understanding of structural temperature effects through data analysis. Summary of the Invention
[0005] To address the shortcomings of existing technologies, the present invention aims to provide a structural temperature effect separation method based on temperature orthogonal space. This method solves the problem that existing temperature effect separation methods are purely numerical processing methods for the structural response signal R itself, rather than starting from the causal relationship between structural temperature changes and structural temperature response, which makes it difficult to enhance the understanding of structural temperature effects through data analysis.
[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: This invention provides a method for separating structural temperature effects based on orthogonal temperature space, comprising the following steps: The daily temperature data for each measuring point is expressed using a cubic spline function. A temperature orthogonal space is constructed based on the cubic spline function of each measuring point. Based on the temperature orthogonal space, the temperature effect component in the overall structural response signal is extracted; The structural response components under live load are determined based on the overall structural response and temperature effect components.
[0007] In some alternative solutions, the expression of daily temperature data for each measuring point using a cubic spline function includes: Collect temperature data at each measuring point; The daily temperature data at each measuring point are fitted with a cubic polynomial to obtain the root mean square error of the cubic polynomial fitting at each measuring point. The nodes of the cubic spline function are determined based on the root mean square error of the daily temperature curve. The cubic spline function coefficients are obtained by fitting the function based on the determined cubic spline function nodes.
[0008] In some alternative schemes, when the temperature data of each measuring point is fitted with a cubic polynomial to obtain the daily temperature curve of each measuring point, the time is expressed in real number form, and the 0-24 hours are converted into the interval [0,1].
[0009] In some alternative schemes, the construction of an orthogonal temperature space based on cubic spline functions at each measuring point includes: Based on the sampling rate of the overall structural response measurement points, the cubic spline function of the temperature measurement points is used to regenerate the structural temperature data with the same sampling rate as the structural response measurement points; Based on the structural temperature data regenerated from each temperature measurement point, an orthogonal temperature space is constructed using the Schmidt method or singular value decomposition method.
[0010] In some alternative schemes, if the Schmidt method is used to construct the temperature orthogonal space, the constructed temperature orthogonal space is as follows:
[0011] in, Let i be the vector corresponding to the sampling point of the i-th measurement point. for The transformed orthogonal vectors are i=1…q, where q is the number of temperature measurement points and j is the vector index.
[0012] In some alternative schemes, if the singular value decomposition method is used to construct the temperature orthogonal space, the constructed temperature orthogonal space is: , v The eigenvector matrix corresponds to the eigenvalues, q is the number of temperature measurement points, and n is the total length of the regenerated structural temperature data from the temperature measurement points.
[0013] In some alternative solutions, the extraction of the temperature effect component from the overall structural response signal based on temperature orthogonal space includes: Decompose the single variable in the overall structural response in the temperature orthogonal space; Based on the decomposition coefficients of each single variable in the overall structural response on each basis vector, the temperature effect component of the overall structural response in the orthogonal temperature space is obtained.
[0014] In some alternative solutions, according to the formula Determine the projection coefficients of the structural response at the j-th measurement point in the overall structural response onto the corresponding basis vectors in the temperature orthogonal space. ,in, for transpose, , This represents the structural response at the j-th measurement point in the overall structural response. This is the margin.
[0015] In some alternative solutions, according to the formula Determine the temperature effect components of the overall structural response in the orthogonal temperature space. ,in, for The transpose of the structural response vector, the decomposition coefficients q is the number of temperature measurement points. For the overall structural response, p denoted as the number of structural response measurement points, and n as the total length of the regenerated structural temperature data from the temperature measurement points.
[0016] On the other hand, the present invention also provides a structural temperature effect separation device based on temperature orthogonal space, comprising: The cubic spline expression module is used to express the daily temperature data of each measuring point using a cubic spline function. The orthogonal space establishment module is used to construct an orthogonal temperature space based on the cubic spline function of each measuring point; The temperature effect extraction module is used to extract the temperature effect component in the overall structural response signal based on the temperature orthogonal space. The live load response separation module is used to determine the structural response components under live load based on the overall structural response and temperature effect components.
[0017] Compared with existing technologies, the advantages of this invention are as follows: This scheme expresses the daily temperature data of each measuring point using a cubic spline function; based on the cubic spline functions of each measuring point, a temperature orthogonal space is constructed; based on the temperature orthogonal space, the temperature effect component in the overall structural response signal is extracted; and based on the overall structural response and the temperature effect component, the structural response component under live load is determined. This scheme is based on the causal relationship between temperature and structural response, using structural temperature monitoring data to separate the temperature effect component in the structural response monitoring results, resulting in a clear physical concept; and decomposing all structural response vectors of the entire bridge based on a unified temperature orthogonal space facilitates the standardization of data processing. Furthermore, the method of decomposing structural temperature effects using temperature orthogonal space is beneficial for the standardization of static monitoring data, as only one temperature orthogonal space is needed to decompose all structural temperature effects for the day, while the number of decomposition coefficients that need to be stored is very small compared to the structural response data. The signal after removing the temperature effect is caused by factors such as wind and operational live load. For most highway bridges, the proportion of heavy-load vehicles that have a significant impact on structural damage is not high, therefore the amount of data to be processed is much less than the original signal. Attached Figure Description
[0018] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0019] Figure 1 This is a flowchart of a structural temperature effect separation method based on temperature orthogonal space in an embodiment of the present invention. Detailed Implementation
[0020] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0021] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.
[0022] like Figure 1 As shown, this invention provides a method for separating structural temperature effects based on orthogonal temperature space, comprising the following steps: S1: Express the daily temperature data of each measuring point using a cubic spline function.
[0023] Temperature monitoring data is obtained through digital discrete sampling, resulting in a time series, which is inconvenient for certain data processing scenarios. For example, calculating the rate of temperature change requires time differentiation, and considering factors such as sensor resolution, the smoothness of the actual time series is poor; when performing correlation analysis on multiple temperature measurement points, the sampling times of each point are not entirely consistent; when correlating temperature with structural response, their sampling frequencies are often different; and so on. If we could fit the daily temperature time series to a function, mathematical processing methods could be introduced, and these problems would be readily solved.
[0024] Under atmospheric conditions, the structural temperature time history controlled by the heat conduction equation exhibits continuity, and theoretically, its analytical solution possesses sufficient smoothness. Representing the daily temperature time history with a sine function is only suitable for coarse processing due to its limited fitting accuracy. Cubic spline functions (CSF) are commonly used fitting tools, possessing second-order continuity. Their mathematical theory and applications are well-established, and many CSF functions are available in commonly used numerical processing software, facilitating application and meeting the aforementioned requirements.
[0025] In some optional embodiments, step S1 includes: S11: Collect temperature data at each measuring point.
[0026] In this example, when collecting the daily temperature curves of each measuring point, the time is expressed in real number form, and the 0-24 hours are converted into the interval [0,1].
[0027] Specifically, in the daily temperature time history data of temperature measurement points, time can be expressed in real number form, with the integer part representing the number of days since the beginning of the Gregorian calendar and the decimal part representing the specific time of day. This representation method facilitates standardized time processing; the times of different dates differ only in their integer parts, with the decimal parts all falling within the range [0, 1]. Therefore, the structured daily temperature time history can be expressed as the following function form. T is the temperature. The structure is a daily temperature time history function. This represents the time interval for conversion to the [0,1] range. Note that the raw temperature data obtained through sampling is expressed discretely, that is, it is represented as a series of temperature data at specific sampling time points.
[0028] S12: The daily temperature data of each measuring point are fitted with a cubic polynomial. The root mean square error of the fitted data represents the degree of daily temperature fluctuation at the measuring point.
[0029] The principle of using CSF (Constant Squared Error) to fit daily temperatures is to approximate the daily temperature curve with as few intermediate nodes as possible, keeping the error within an acceptable range. Fewer intermediate nodes mean reduced computation time and storage space requirements. Steel structures and cables exhibit large temperature variations, while concrete temperatures vary less, especially at deeper measuring points where temperature fluctuations are minimal. Therefore, measuring points with large daily temperature fluctuations use more CSF intermediate nodes, while measuring points with small fluctuations use fewer CSF intermediate nodes, still achieving a precise approximation of the original temperature curve. Thus, the number of intermediate nodes can be correlated with the degree of daily temperature curve fluctuation. One indicator for measuring the degree of fluctuation of the original temperature curve is the root mean square error (RMSE) of the daily temperature curve fitted using a cubic polynomial. Therefore, the RMSE of the cubic polynomial fitting at each measuring point is obtained by first fitting the temperature data of each measuring point using the cubic polynomial.
[0030] S13: Determine the nodes of the cubic spline function based on the root mean square error of the daily temperature curve.
[0031] In this example, the larger the root mean square error of the daily temperature curve, the greater the temperature fluctuation. To obtain the accuracy of the cubic spline function representation, the node spacing of the selected cubic spline function should be as small as possible. (Cuboid spline function node spacing) step The relationship between the root mean square error of the daily temperature curve and the error of the daily temperature curve is expressed as a piecewise function as follows:
[0032] In the formula, The root mean square error is calculated in the interval [0,1]. Set intermediate nodes. If there are s intermediate nodes, the interval [0,1] is divided into s+1 smaller intervals.
[0033] Traverse all s+1 intervals to find the maximum and minimum temperature nodes within a day. Sort all node coordinates by time, remove duplicate nodes, and obtain all nodes required for cubic spline fitting. Additionally, for intervals containing times 0 and 1, calculate the first derivatives of these two times as boundary conditions for the cubic spline end nodes. ), ( ).
[0034] S14: Fit the cubic spline function based on the determined cubic spline function nodes to obtain the cubic spline function coefficients.
[0035] The coefficient equations of a cubic spline function can be solved using the chasing method.
[0036] The CSF parameters are obtained by fitting the fitting function provided by the numerical processing software. The results are stored in a cell array. Only one cell array is needed to store the CSF parameters of all temperature measurement points of the full bridge. One row represents one day and one column represents one temperature measurement point.
[0037] After the above processing, the cubic spline function fitting result of the temperature time history data of each structural temperature measuring point is obtained, denoted as { , i =1…q}, where q is the total number of temperature measurement points on the structure. The cubic spline function is a continuous function of time, which facilitates mathematical processing.
[0038] S2: Construct an orthogonal temperature space based on the cubic spline function of each measuring point.
[0039] In some optional embodiments, step S2 includes: S21: Resampling of structural temperature data: Based on the sampling rate of the overall structural response measurement points, the structural temperature data with the same sampling rate as the structural response measurement points is regenerated using the cubic spline function of the temperature measurement points.
[0040] S22: Based on the resampled data of all temperature measurement points, construct an orthogonal temperature space using the Schmidt method or singular value decomposition method.
[0041] Regarding the temperature set matrix of the sampling points obtained above { , i =1…q}, constructing a temperature orthogonal space as In mathematics, there are many methods for constructing orthogonal spaces. This invention uses the Schmidt method or the singular value decomposition method.
[0042] ① If the Schmidt method is used to construct the temperature orthogonal space, then the constructed temperature orthogonal space is:
[0043] in, Let i be the vector corresponding to the sampling point of the i-th measurement point. for The transformed orthogonal vectors, i=1…q, where q is the number of measurement points and j is the vector index.
[0044] As can be seen, this method continuously eliminates non-orthogonal projections to form an orthogonal vector space, and the generated orthogonal space is related to the order of the vectors involved in the calculation. For structural temperature, it is advisable to place measuring points with large temperature variations, such as those for steel box girders and stay cables, earlier, and measuring points with smaller variations, such as those for concrete, later. Because the temperature changes at different measuring points have inconsistent phases, as the number of temperature measuring points increases, the amplitude of subsequent orthogonal vectors will become smaller and the fluctuations will become faster, resulting in a fluctuating curve near the zero value after normalization.
[0045] ②If the singular value decomposition method is used to construct the temperature orthogonal space, then the constructed temperature orthogonal space is: , v The eigenvector matrix corresponds to the eigenvalues, q is the number of measurement points, and n is the total length of the data after the structural temperature is resampled in step S2, and the total length of the structural temperature data regenerated from the temperature measurement points.
[0046] Specifically, the temperature matrix is constructed from the regenerated structural temperature data of the temperature measurement points after resampling. T autocorrelation matrix ( ) Singular value decomposition yields orthogonal matrices, which is the calculation method used in principal component analysis.
[0047]
[0048] In the formula, This indicates the eigenvalue solution. This is a diagonal matrix of eigenvalues of the autocorrelation matrix, arranged in descending order of value; The eigenvector matrix corresponds to the eigenvalues. Each column represents the set matrix of temperature samples. T The combination coefficients of a linear combination are such that the larger the eigenvalues, the greater the variance of the combination vector, and from the perspective of principal component analysis, the more information it contains. According to... The orthogonal temperature space can be solved directly, as shown in the following equation:
[0049] In the formula, Let be the generated temperature orthogonal space, where n is the vector length and q is the number of temperature vectors.
[0050] S3: Based on the temperature orthogonal space, extract the temperature effect component in the overall structural response signal.
[0051] In some optional embodiments, step S3 includes: S31: Decompose the single variable in the overall structural response in the temperature orthogonal space. Specifically, according to the formula... Determine the projection coefficients of the structural response at the j-th measurement point in the overall structural response onto the basis vector corresponding to the sampling point at the i-th measurement point in the temperature orthogonal space. ,in, for transpose, , Let j be the structural response at the j-th measurement point in the overall structural response, i.e., the j-th single variable in the overall structural response. This is the margin.
[0052] For example: single variables in the overall structural response In temperature orthogonal space The decomposition of is shown in the following formula. This is the remaining amount after decomposition. The projections onto each basis vector are all 0.
[0053]
[0054] The decomposition coefficients are:
[0055] In the formula, express The transpose of . Let ,Right now If the space is orthonormal, then:
[0056] In the formula, for Projection coefficients on each basis vector. S32: Based on the decomposition coefficients of each single variable in the overall structural response on each basis vector, obtain the temperature effect component of the overall structural response in the orthogonal temperature space.
[0057] Multi-vector decomposition can be performed simultaneously. Let the number of sampling points be... n ,have p One structural response measurement point q For each temperature measurement point, the decomposition coefficients of the structural response vector are... K for:
[0058] First, calculate the decomposition coefficients according to the above formula. K , representing the structural response R in the temperature orthogonal space The decomposition coefficients in the equation.
[0059] The structural response R in the temperature orthogonal space has now been obtained. Decomposition coefficients in K .
[0060] Based on the decomposition coefficients and the temperature orthogonal space matrix, the structural temperature response components can also be directly obtained. , ; That is, structural response R In temperature orthogonal space The decomposition result in the equation is the temperature effect component of the overall structural response in the orthogonal temperature space.
[0061] Number of sampling points n Typically much larger than the number of measuring points. p , q Therefore, the number of orthogonal temperature space bases is very small relative to the matrix length.
[0062] S4: Determine the structural response components under live load based on the overall structural response and temperature effect components.
[0063] In this example, removing the temperature effect component from the overall structural response yields the structural response component under live load.
[0064] In summary, the present invention provides a structural temperature effect separation device based on temperature orthogonal space, comprising: a cubic spline expression module, an orthogonal space establishment module, a temperature effect extraction module, and a live load response separation module.
[0065] The cubic spline expression module is used to express the daily temperature data of each measuring point using a cubic spline function; the orthogonal space establishment module is used to construct a temperature orthogonal space based on the cubic spline functions of each measuring point; the temperature effect extraction module is used to extract the temperature effect component in the overall structural response signal based on the temperature orthogonal space; and the live load response separation module is used to determine the structural response component under live load based on the overall structural response and the temperature effect component.
[0066] This scheme is based on the causal relationship between temperature and structural response. It uses structural temperature monitoring data to separate the temperature effect component from the structural response monitoring results, providing a clear physical concept. It decomposes all structural response vectors of the entire bridge using a unified temperature orthogonal space, facilitating data standardization. Furthermore, the temperature orthogonal space decomposition method is beneficial for standardizing static monitoring data, as it decomposes all structural temperature effects for the day using only one temperature orthogonal space, requiring very few decomposition coefficients compared to the structural response data. For example, at a 1Hz sampling rate, 86,400 structural response records are made daily, but storing coefficients from fewer than 40 nodes is sufficient to well fit the temperature effect. The signal after removing the temperature effect is caused by factors such as wind and operational live loads. For most highway bridges, the proportion of heavy-load vehicles that significantly impact structural damage is not high, therefore the amount of data to be processed is much less than the original signal.
[0067] In the description of this application, it should be noted that the terms "upper," "lower," etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application 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, and therefore should not be construed as a limitation of this application. Unless otherwise expressly specified and limited, the terms "installed," "connected," and "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; they can refer to the internal communication between two elements. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.
[0068] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0069] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.
Claims
1. A method for separating structural temperature effects based on orthogonal temperature space, characterized in that, Includes the following steps: The daily temperature data for each measuring point is expressed using a cubic spline function. Based on the cubic spline functions of each measuring point, an orthogonal temperature space is constructed, including: Based on the sampling rate of the overall structural response measurement points, the cubic spline function of the temperature measurement points is used to regenerate the structural temperature data with the same sampling rate as the structural response measurement points; Based on the structural temperature data regenerated from each temperature measurement point, a temperature orthogonal space is constructed using the singular value decomposition method. If the singular value decomposition method is used to construct the temperature orthogonal space, then the constructed temperature orthogonal space is: , v The eigenvector matrix corresponds to the eigenvalues, where q is the number of temperature measurement points and n is the total length of the regenerated structural temperature data from the temperature measurement points. Based on the temperature orthogonal space, the temperature effect component in the overall structural response signal is extracted, including: Decompose the single variable in the overall structural response in the temperature orthogonal space; Based on the decomposition coefficients of each single variable in the overall structural response on each basis vector, the temperature effect component of the overall structural response in the orthogonal temperature space is obtained. The structural response components under live load are determined based on the overall structural response and temperature effect components.
2. The structural temperature effect separation method based on orthogonal temperature space as described in claim 1, characterized in that, The method of expressing daily temperature data for each measuring point using a cubic spline function includes: Collect temperature data at each measuring point; The daily temperature data at each measuring point are fitted with a cubic polynomial to obtain the root mean square error of the cubic polynomial fitting at each measuring point. The nodes of the cubic spline function are determined based on the root mean square error of the daily temperature curve. The cubic spline function coefficients are obtained by fitting the function based on the determined cubic spline function nodes.
3. The structural temperature effect separation method based on temperature orthogonal space as described in claim 2, characterized in that, When the temperature data of each measuring point is fitted with a cubic polynomial to obtain the daily temperature curve of each measuring point, the time is expressed in real number form, and the 0-24 hours are converted into the interval [0,1].
4. The structural temperature effect separation method based on temperature orthogonal space as described in claim 1, characterized in that, If the Schmidt method is used to construct the temperature orthogonal space, the constructed temperature orthogonal space is: in, Let i be the vector corresponding to the sampling point of the i-th measurement point. for The transformed orthogonal vectors are i=1…q, where q is the number of temperature measurement points and j is the vector index.
5. The structural temperature effect separation method based on orthogonal temperature space as described in claim 1, characterized in that, According to the formula Determine the structural response at the j-th measurement point in the overall structural response. The corresponding basis vectors in the temperature orthogonal space Projection coefficients on ,in, for transpose, , This represents the structural response at the j-th measurement point in the overall structural response. This is the margin.
6. The structural temperature effect separation method based on temperature orthogonal space as described in claim 5, characterized in that, According to the formula Determine the temperature effect components of the overall structural response in the orthogonal temperature space. ,in, for The transpose of the structural response vector, the decomposition coefficients q is the number of temperature measurement points. For the overall structural response, p denoted as the number of structural response measurement points, and n as the total length of the regenerated structural temperature data from the temperature measurement points.
7. A structural temperature effect separation device based on orthogonal temperature space, characterized in that, include: The cubic spline expression module is used to express the daily temperature data of each measuring point using a cubic spline function. The orthogonal space construction module is used to construct an orthogonal temperature space based on the cubic spline function of each measuring point, including: Based on the sampling rate of the overall structural response measurement points, the cubic spline function of the temperature measurement points is used to regenerate the structural temperature data with the same sampling rate as the structural response measurement points; Based on the structural temperature data regenerated from each temperature measurement point, a temperature orthogonal space is constructed using the singular value decomposition method. If the singular value decomposition method is used to construct the temperature orthogonal space, then the constructed temperature orthogonal space is: , v The eigenvector matrix corresponds to the eigenvalues, where q is the number of temperature measurement points and n is the total length of the regenerated structural temperature data from the temperature measurement points. A temperature effect extraction module, used to extract the temperature effect component from the overall structural response signal based on a temperature orthogonal space, includes: Decompose the single variable in the overall structural response in the temperature orthogonal space; Based on the decomposition coefficients of each single variable in the overall structural response on each basis vector, the temperature effect component of the overall structural response in the orthogonal temperature space is obtained. The live load response separation module is used to determine the structural response components under live load based on the overall structural response and temperature effect components.