Super-large-span net rack deformation monitoring method

Abstract

The invention provides a super-large-span net rack deformation monitoring method, and belongs to the technical field of deformation monitoring. A shape sensor is installed on a key rod piece of a super-large-span net rack in a wind tunnel test section, a double-grating differential compensation system suitable for a wind tunnel environment is established, and wavelength drift caused by high-speed airflow, temperature shock and pressure fluctuation is eliminated; a wavelength division multiplexing technology is adopted to carry out anti-interference signal acquisition, a double-layer game optimization model considering wind tunnel working condition characteristics is constructed to carry out dynamic error compensation, and a grating strain response matrix is established to realize accurate conversion from strain to deformation in a wind tunnel environment. A time sequence model based on a wind tunnel operation cycle is adopted to predict the wavelength drift trend of the sensor and start an adaptive compensation mechanism, and the technical problem that the deformation monitoring precision is seriously reduced due to wavelength drift of a wind tunnel test section ultra-large span grid structure under the action of high-speed airflow is solved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of deformation monitoring, and in particular, relates to a method for monitoring deformation of an ultra-large-span net rack. BACKGROUND

[0002] As key scientific research equipment in the fields of aerospace, automobile industry and building engineering, the deformation monitoring of the test section ultra-large-span net rack structure of a wind tunnel test facility is of great significance to ensure the accuracy of test data and safe operation of the equipment. Traditional wind tunnel net rack deformation monitoring mainly uses mechanical displacement meters, resistance strain gauges and laser interferometers and other equipment. However, these traditional methods have obvious limitations in the high-speed airflow, severe temperature changes and strong electromagnetic interference environment of the wind tunnel. Fiber Bragg grating sensors have been increasingly widely used in the monitoring of wind tunnel test section net rack structures due to their inherent safety, strong anti-electromagnetic interference capability and ability to achieve distributed measurement, and in particular, play an important role in the structural health monitoring of high-parameter wind tunnel facilities such as transonic wind tunnels and supersonic wind tunnels. However, in the actual operating environment of the wind tunnel, fiber Bragg grating sensors not only have to withstand regular temperature changes and mechanical stress, but also have to face complex working conditions such as vibration impact caused by high-speed airflow, rapid temperature cycling and pressure fluctuations. These extreme environmental factors cause irregular wavelength drift of the sensor center, and traditional temperature compensation and stress compensation methods are difficult to cope with the complexity of the wind tunnel environment, resulting in serious cumulative errors in long-term monitoring data, which cannot accurately reflect the real deformation state of the net rack structure during the operation of the wind tunnel. In the current wind tunnel net rack monitoring system, due to the lack of wavelength drift compensation technology for the complex environment of the wind tunnel, the performance of the sensor rapidly degrades in high-frequency test cycles, and the monitoring accuracy significantly decreases with the extension of the test time, which seriously affects the reliability of the wind tunnel test and the safety assessment of the net rack structure. That is, the existing technology has the technical problem of serious decrease in deformation monitoring accuracy caused by wavelength drift of the test section ultra-large-span net rack structure of the wind tunnel under the action of high-speed airflow. SUMMARY

[0003] Therefore, the present application provides a method for monitoring deformation of an ultra-large-span net rack, which can solve the technical problem of serious decrease in deformation monitoring accuracy caused by wavelength drift of the test section ultra-large-span net rack structure of the wind tunnel under the action of high-speed airflow in the prior art.

[0004] The application is implemented in the following manner: a large-span net rack deformation monitoring method is provided, shape sensors are installed on key rod members of a large-span net rack structure, thin-wall steel sliding clamps are arranged every 1m along the axial direction of the thin-wall steel pipe, a triangular array strain sensor arrangement scheme is used for each measuring point to obtain initial strain data; a double-grating differential compensation system is established, a reference grating is arranged beside the main measuring grating, wavelength drift caused by temperature and mechanical stress is eliminated through a wavelength differential algorithm, a drift error matrix is constructed to record the reference wavelength data, temperature drift coefficient, mechanical stress drift coefficient and time drift factor of each sensor; a wavelength division multiplexing technology is used to collect signals of multiple fiber grating sensors connected in series on the same optical fiber, a demodulator identifies grating signals of different center wavelengths, a grating wavelength identification matrix is established to store the standard center wavelength, wavelength resolution and spectral peak intensity of each grating; a double-layer game optimization model is constructed to obtain optimal compensation parameters and output them to a grating strain response matrix; the grating strain response matrix is established to convert the initial strain data and optimal compensation parameters of each measuring point into a three-dimensional deformation field of the net rack structure, and the displacement values at the middle of the net rack and the cantilever end are calculated through a strain displacement conversion equation set; the deformation state of the net rack is monitored in real time, and the early warning mechanism is triggered when the displacement values at the middle of the net rack and the cantilever end exceed the design allowable range, and the monitoring data is compared and analyzed with the computer simulation results to evaluate the safety state of the structure.

[0005] The drift error matrix is a data structure for recording and quantifying the wavelength offset of the fiber grating strain sensor during long-term use, and the matrix elements include reference wavelength data, temperature drift coefficient, mechanical stress drift coefficient, time drift factor and environmental humidity influence factor. The drift characteristic parameter library of each sensor node is established to realize accurate error compensation.

[0006] The double-grating differential compensation system is an error elimination system constructed by setting the main measuring grating and the reference grating. The main measuring grating is responsible for actual strain measurement and outputs initial strain data, and the reference grating is only affected by temperature and environmental factors. The common mode error is eliminated and the differential compensation coefficient is generated by calculating the wavelength difference between the two.

[0007] The grating wavelength identification matrix is a parameter matrix for distinguishing and identifying the center wavelengths of different fiber grating strain sensors in the wavelength division multiplexing technology. The matrix elements include standard center wavelength, wavelength resolution, spectral peak intensity and wavelength stability index. The grating spectral feature database is established to realize accurate identification and separation of multi-sensor signals.

[0008] The grating strain response matrix is a conversion matrix for describing the mapping relationship between the strain measurement value of the fiber grating strain sensor and the actual deformation state of the grid structure, and the matrix elements include optimal compensation parameters, spatial position weight coefficients, structural stiffness distribution factors and boundary constraint influence coefficients.

[0009] The strain displacement conversion equation set is a mathematical model for converting initial strain data into grid structure displacement, including a geometric deformation equation and a material constitutive equation.

[0010] The time series model is a mathematical prediction model established based on historical wavelength drift data, and uses an autoregressive moving average model to perform time series analysis on reference wavelength data, temperature drift coefficients, mechanical stress drift coefficients and time drift factors to establish a wavelength drift time series for predicting future wavelength change trends.

[0011] The wavelength drift time series is a data sequence formed by arranging reference wavelength data, temperature drift coefficients, mechanical stress drift coefficients and time drift factors in chronological order, and the time series model is used to analyze the trend, periodicity and randomness of the sequence to provide a data basis for sensor performance degradation prediction.

[0012] The drift prediction compensation function is a compensation algorithm established based on the prediction results of the wavelength drift time series, which is used to real-time correct and compensate the initial strain data when the predicted wavelength drift exceeds the preset threshold, ensuring that the measurement accuracy is not reduced due to sensor performance degradation.

[0013] The wavelength drift time series is established by using a time series model to analyze reference wavelength data, temperature drift coefficients, mechanical stress drift coefficients and time drift factors, and an autoregressive moving average model is used to predict the wavelength drift trend of the sensor, and the drift prediction compensation function is started to real-time compensate the initial strain data when the predicted drift exceeds the threshold.

[0014] The shape sensor is composed of a PVC sleeve, a thin-walled steel sliding clamp and a fiber grating strain sensor.

[0015] The double-layer game optimization model is constructed using Stackelberg game theory, and the upper model takes minimizing the overall measurement error of the grid structure as the goal, and the objective function is The constraints include sensor accuracy constraints, resource allocation constraints, and system stability constraints. The lower-level model aims to maximize the measurement accuracy of a single sensor node, and the objective function is: The two-layer model achieves information exchange and coordinated optimization through coupling terms. In the objective function of the upper-layer model, e i This indicates that the measurement error of the i-th sensor originates from the initial strain data, d j This indicates that the displacement deviation at the j-th measuring point originates from the mid-span displacement of the space frame and the displacement at the cantilever end, c k This indicates that the compensation cost of the k-th grating comes from the differential compensation coefficient, r. k w represents the proportion of compensation resource allocation. l This indicates that the weight coefficient of the l-th node is derived from the spatial location weight coefficient, t l This indicates that the time decay factor originates from the time drift factor. In the objective function of the lower-level model, a i b indicates that the signal-to-noise ratio of the i-th sensor originates from the spectral peak intensity. j This indicates that the phase response of the j-th grating is derived from the wavelength resolution, φ j G represents the phase angle. k The gain coefficient of the k-th node is derived from the structural stiffness distribution factor, h. l This indicates that the harmonic response of the l-th sensor originates from the wavelength stability index, θ l This indicates the harmonic phase angle.

[0016] The strain-displacement transformation equation set includes geometric deformation equations and material constitutive equations. The geometric deformation equations are used to establish the geometric relationship between strain and displacement at each node of the space frame structure. The inputs include initial strain data, structural geometric parameters, changes in member length, and connection stiffness coefficients. The outputs are the mid-span displacement and cantilever end displacement values ​​of the space frame. The material constitutive equations are used to describe the mechanical response characteristics of the space frame material under complex stress states. The inputs include the material's elastic modulus, Poisson's ratio, stress tensor, and temperature drift coefficient. The outputs are the corresponding strain response and deformation modulus for use by the geometric deformation equations.

[0017] The drift prediction compensation function is used to perform real-time compensation on sensor measurement data based on the wavelength drift time series prediction results. The inputs include wavelength drift time series, predicted drift amount, reference wavelength data, temperature drift coefficient and time drift factor. The output is the compensated strain data used to replace the initial strain data for subsequent deformation calculation.

[0018] Among them, the two-layer model of the two-layer game optimization model is coupled by the two-layer model of the coupling term. To achieve information exchange and coordinated optimization, and output the optimal compensation parameters, where e i Sensor measurement errors originating from the upper-level model, ai The sensor signal-to-noise ratio is derived from the lower-level model.

[0019] Before constructing the two-layer game optimization model for error compensation, the process also includes an initial calibration step for each sensor node. A known strain is applied to each fiber optic grating strain sensor using a standard strain loading device, the corresponding wavelength response value is recorded, and a sensor strain sensitivity coefficient database is established to provide benchmark parameters for the two-layer game optimization model.

[0020] This invention establishes a dual-grating differential compensation system and a two-layer game optimization model suitable for wind tunnel environments, combined with a time-series prediction algorithm based on wind tunnel operating conditions. This effectively eliminates the combined effects of high-speed airflow, temperature shocks, and pressure fluctuations on fiber optic grating sensors, significantly improving the accuracy and stability of wind tunnel deformation monitoring for ultra-large span structures under complex conditions. Addressing the unique characteristics of the wind tunnel environment, this invention adds an environmental humidity influence factor to the differential compensation system. The wavelength difference algorithm between the master measurement grating and the reference grating not only eliminates the influence of conventional temperature and mechanical stress but also effectively suppresses the interference of dynamic disturbances and pressure pulsations caused by high-speed airflow in the wind tunnel on the sensors. The two-layer game optimization model considers the periodic characteristics and load variation patterns of wind tunnel tests, incorporating a time decay factor and dynamic weight adjustment mechanism into the system optimization. This ensures that the monitoring system can adapt to various operating conditions in the wind tunnel, from static to high-speed operation. The time-series prediction model establishes a drift prediction algorithm based on historical wind tunnel operating data, capable of predicting the performance degradation trend of sensors during wind tunnel cyclic testing and achieving accurate compensation. In summary, this invention solves the technical problem mentioned in the background art where wavelength drift in the ultra-large span grid structure of the wind tunnel test section leads to a serious decrease in deformation monitoring accuracy. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method of the present invention.

[0022] Figure 2 This is a schematic diagram of the shape sensor structure in Example 2.

[0023] Figure 3 This is a schematic diagram of the arrangement of the shape sensor on the grid in Example 2.

[0024] Figure 4 This is a displacement cloud diagram of the grid structure under full-load wind conditions in Example 2. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0026] like Figure 1 The diagram shown is a flowchart of a method for monitoring the deformation of a super-large span space frame provided by the present invention. This method includes the following steps:

[0027] S01. Install shape sensors on key members of the ultra-large span space frame structure. The shape sensors consist of PVC sleeves, thin-walled steel sliding clamps and fiber optic strain sensors. The thin-walled steel sliding clamps are arranged every 1m along the axial direction of the thin-walled steel pipe. Initial strain data are obtained at each measuring point using a triangular array strain sensor arrangement scheme.

[0028] S02. Establish a dual-grating differential compensation system. Set up a reference grating next to the main measurement grating. Eliminate wavelength drift caused by temperature and mechanical stress through wavelength differential algorithm. Construct a drift error matrix to record the reference wavelength data, temperature drift coefficient, mechanical stress drift coefficient and time drift factor of each sensor.

[0029] S03. Wavelength division multiplexing technology is used to acquire signals from multiple fiber optic grating sensors connected in series on the same optical fiber. The demodulator identifies grating signals with different center wavelengths and establishes a grating wavelength identification matrix to store the standard center wavelength, wavelength resolution and spectral peak intensity of each grating.

[0030] S04. Construct a two-layer game optimization model for error compensation. The upper-layer model aims to minimize the overall measurement error of the system, while the lower-layer model aims to maximize the measurement accuracy of a single sensor. The optimal compensation parameters are obtained through iterative optimization and output to the grating strain response matrix.

[0031] S05. Establish the grating strain response matrix, convert the initial strain data and optimal compensation parameters of each measuring point into the three-dimensional deformation field of the grid structure, and calculate the mid-span displacement and cantilever end displacement of the grid structure through the strain-displacement transformation equation set.

[0032] S06. Real-time monitoring of the deformation status of the space frame. When the mid-span displacement and cantilever end displacement of the space frame exceed the design allowable range, an early warning mechanism is triggered. At the same time, the monitoring data is compared and analyzed with the computer simulation results to assess the structural safety status.

[0033] S07. A time series model is used to establish a wavelength drift time series for the reference wavelength data, temperature drift coefficient, mechanical stress drift coefficient and time drift factor. The sensor wavelength drift trend is predicted by an autoregressive moving average model. When the predicted drift exceeds the threshold, the drift prediction compensation function is activated to compensate the initial strain data in real time.

[0034] The drift error matrix is ​​a data structure used to record and quantify the wavelength shift of the fiber optic grating strain sensor during long-term use. The matrix elements include the reference wavelength data, temperature drift coefficient, mechanical stress drift coefficient, time drift factor, and environmental humidity influence factor. Accurate error compensation is achieved by establishing a drift characteristic parameter library for each sensor node.

[0035] The dual-grating differential compensation system is an error elimination system constructed by setting a main measurement grating and a reference grating. The main measurement grating is responsible for actual strain measurement and outputs the initial strain data. The reference grating is only affected by temperature and environmental factors. The common mode error is eliminated by calculating the difference between the two wavelengths and a differential compensation coefficient is generated.

[0036] The grating wavelength identification matrix is ​​a parameter matrix used in wavelength division multiplexing (WDM) technology to distinguish and identify the center wavelengths of different fiber optic grating strain sensors. The matrix elements include the standard center wavelength, wavelength resolution, spectral peak intensity, and wavelength stability index. By establishing a grating spectral feature database, accurate identification and separation of multi-sensor signals can be achieved.

[0037] The grating strain response matrix is ​​a transformation matrix that describes the mapping relationship between the strain measurement value of the fiber optic grating strain sensor and the actual deformation state of the grid structure. The matrix elements include the optimal compensation parameter, spatial position weight coefficient, structural stiffness distribution factor and boundary constraint influence coefficient. The accurate strain-deformation transformation relationship is established through finite element analysis and experimental calibration.

[0038] The strain-displacement conversion equation set is a mathematical model used to convert the initial strain data into the displacement of the space frame structure. It includes geometric deformation equations and material constitutive equations. The geometric deformation equations establish the geometric relationship between strain and displacement at each node of the space frame structure and output the mid-span displacement value and cantilever end displacement value of the space frame. The material constitutive equations describe the mechanical response characteristics of the space frame material under complex stress states.

[0039] The time series model is a mathematical prediction model based on historical wavelength drift data. It uses an autoregressive moving average model to perform time series analysis on the baseline wavelength data, temperature drift coefficient, mechanical stress drift coefficient, and time drift factor to establish a wavelength drift time series for predicting future wavelength change trends.

[0040] The wavelength drift time series is a data sequence formed by arranging the reference wavelength data, temperature drift coefficient, mechanical stress drift coefficient, and time drift factor in chronological order. The trend, periodicity, and random components in the sequence are analyzed through the time series model, providing a data basis for predicting sensor performance degradation.

[0041] The drift prediction compensation function is a compensation algorithm based on the wavelength drift time series prediction results. When the predicted wavelength drift exceeds a preset threshold, the initial strain data is corrected and compensated in real time to ensure that the measurement accuracy is not reduced due to sensor performance degradation.

[0042] The two-layer game optimization model is constructed using Stackelberg game theory. The upper-layer model aims to minimize the overall measurement error of the grid structure, and the objective function is: Where e i This indicates that the measurement error of the i-th sensor originates from the initial strain data, d j This indicates that the displacement deviation of the j-th measuring point originates from the mid-span displacement value and the cantilever end displacement value of the space frame, c k This indicates that the compensation cost of the k-th grating originates from the differential compensation coefficient, r. k w represents the proportion of compensation resource allocation. l This indicates that the weight coefficient of the l-th node is derived from the spatial location weight coefficient, t l The time decay factor originates from the time drift factor. Constraints include sensor accuracy constraints, resource allocation constraints, and system stability constraints. The lower-level model aims to maximize the measurement accuracy of a single sensor node, with the objective function being... Where a i b indicates that the signal-to-noise ratio of the i-th sensor originates from the spectral peak intensity. j This indicates that the phase response of the j-th grating originates from the wavelength resolution, φ j G represents the phase angle. k The gain coefficient of the k-th node is derived from the structural stiffness distribution factor, h. l This indicates that the harmonic response of the l-th sensor originates from the wavelength stability index, θ l Representing the harmonic phase angle, the two-layer model is coupled through a term. It realizes information interaction and coordination optimization, and outputs the optimal compensation parameters.

[0043] The strain-displacement transformation equation set includes geometric deformation equations and material constitutive equations. The geometric deformation equations are used to establish the geometric relationship between strain and displacement at each node of the space frame structure. The inputs include the initial strain data, structural geometric parameters, member length variations, and connection stiffness coefficients. The outputs are the mid-span displacement and cantilever end displacement values ​​of the space frame. The material constitutive equations are used to describe the mechanical response characteristics of the space frame material under complex stress states. The inputs include the material's elastic modulus, Poisson's ratio, stress tensor, and temperature drift coefficient. The outputs are the corresponding strain response and deformation modulus for use by the geometric deformation equations.

[0044] The drift prediction compensation function is used to perform real-time compensation on sensor measurement data based on the wavelength drift time series prediction results. The inputs include the wavelength drift time series, the predicted drift amount, the reference wavelength data, the temperature drift coefficient, and the time drift factor. The output is the compensated strain data used to replace the initial strain data for subsequent deformation calculations.

[0045] The specific implementation methods of the above steps are described in detail below.

[0046] The specific implementation of step S01 is as follows: First, key members are identified based on the stress characteristics and deformation-sensitive areas of the ultra-large span space frame structure. The selection principles for key members include the main beam bearing the maximum bending moment, the cantilever end support rod, and the mid-span stress concentration area. When installing shape sensors on each key member, a 20 mm diameter PVC sleeve is first fixed along the member's axial direction, with a pre-reserved fiber optic routing channel inside the sleeve. Thin-walled steel sliding clamps are made of stainless steel with a thickness of 2 mm. One clamp is installed every 1 meter along the member's axial direction, and the clamps are bolted to the member to ensure stable fixation. The fiber optic grating strain sensors are deployed using a triangular array scheme, that is, three sensors are deployed at 120-degree intervals around each measuring point, with a measurement range set to ±3000 micro-strains and a resolution of not less than 1 micro-strain. The purpose of this deployment scheme is to achieve comprehensive monitoring of the strain of the member's cross-section, and to calculate the bending and torsional deformation of the member using strain data from three directions. When acquiring initial strain data, it is necessary to calibrate the reference value under the condition that the structure is without external load, and record the zero drift and temperature compensation coefficient of each sensor.

[0047] The specific implementation of step S02 is as follows: The dual-grating differential compensation system is achieved by setting a reference grating 5 cm away from each main measurement grating. The reference grating has the same spectral characteristics as the main measurement grating but is not in direct contact with the structure. The wavelength difference algorithm is based on the principle of calculating the difference in the center wavelengths of the two gratings. It identifies and eliminates common environmental interference factors by monitoring the wavelength changes of the two gratings in real time. The process of establishing the drift error matrix includes: recording the reference wavelength data of each sensor at a standard temperature of 25°C; the temperature drift coefficient is obtained by calibration within a temperature range of 10°C to 60°C, with a typical value of 10 picometers per degree Celsius; the mechanical stress drift coefficient is calibrated by applying a known stress load; the time drift factor is obtained through long-term stability testing, with a reference value of no more than 5 picometers per year; and the environmental humidity influence factor is obtained by testing under different humidity conditions, with a wavelength drift of approximately 2 picometers corresponding to a 10% change in humidity. The differential compensation algorithm eliminates common mode errors such as temperature and humidity by subtracting the wavelength of the reference grating from the wavelength of the main measurement grating, thereby improving measurement accuracy and long-term stability.

[0048] The specific implementation of step S03 is as follows: Wavelength division multiplexing (WDM) technology employs the principle of dense WDM, connecting multiple fiber optic grating sensors with different center wavelengths in series on the same fiber. The wavelength spacing is set to 0.8 nm to avoid spectral overlap. The signal acquisition system uses a tunable laser scanning method with a scanning range of 1525 nm to 1565 nm and a scanning accuracy of no less than 1 picometer. The demodulator identifies the reflection spectrum of each grating using a peak detection algorithm, which extracts the spectral peak position based on Gaussian fitting. The grating wavelength identification matrix stores the standard center wavelength of each grating, with a wavelength resolution set to 1 picometer. The spectral peak intensity is used to evaluate the signal quality of the grating; a sensor fault alarm is triggered when the intensity falls below a threshold of -40 dB. Wavelength stability is obtained through continuous 24-hour monitoring, requiring wavelength drift to not exceed 5 picometers. The identification matrix establishes the correspondence between grating numbers and spectral characteristics, ensuring accurate identification of multi-sensor signals and correct data attribution.

[0049] The specific implementation of step S04 is as follows: The two-layer game optimization model is constructed based on Stackelberg game theory. The upper-layer model, acting as the leader, aims to minimize the overall measurement error of the system. In the objective function, the weighting coefficients for sensor measurement error (α) are set to 0.4, displacement deviation (β) to 0.3, compensation cost (γ) to 0.2, and time decay (δ) to 0.1. The lower-layer model, acting as the follower, aims to maximize the measurement accuracy of a single sensor. The weighting coefficients for signal-to-noise ratio (μ) are set to 0.35, phase response (ν) to 0.25, gain coefficient (ξ) to 0.25, and harmonic response (ζ) to 0.15. The optimization algorithm employs a hybrid optimization strategy combining genetic algorithm and gradient descent. The genetic algorithm is used for global search to avoid local optima, while gradient descent is used for accurate solution. During iteration, the convergence criterion is set as the change in the objective function being less than 10. -6 The iteration count may exceed 500. The coupling term coefficient λ is set to 0.5 to coordinate the optimization process of the two-layer model. The optimal compensation parameters include the gain adjustment coefficient, phase correction angle, and noise filtering parameters for each sensor, which are used for subsequent strain data processing and error compensation.

[0050] The specific implementation of step S05 is as follows: The grating strain response matrix establishment process first establishes the stiffness matrix and geometric matrix of the space frame structure through finite element analysis, and then determines the spatial position weighting coefficients based on the spatial layout of the sensors. The structural stiffness distribution factor is obtained through calculation using the material elastic modulus and the moment of inertia of the cross section, while the boundary constraint influence coefficient is determined according to the support type and constraint conditions. The strain-displacement conversion equation set is established based on the deformation compatibility principle of structural mechanics. The geometric deformation equation adopts a linear relationship under the small deformation assumption, and the input parameters include the strain data of each measuring point, the geometric dimensions of the members, and material parameters. The material constitutive equation adopts a linear elastic model, and the input parameters include the elastic modulus of 210 GPa, Poisson's ratio of 0.3, and the stress tensor. The output deformation modulus is used for the calculation of the geometric deformation equation. The mid-span displacement value of the space frame is obtained by superimposing the deformation of each member, and the displacement value at the cantilever end considers the bending and shear deformation of the cantilever beam. The purpose of the conversion process is to convert discrete strain measurement data into the overall deformation state of the structure, providing key parameters for structural safety assessment.

[0051] The specific implementation of step S06 is as follows: The real-time monitoring system adopts a continuous sampling mode, with a data acquisition frequency set to 10 Hz, capable of capturing the dynamic response characteristics of the structure. The early warning mechanism sets multi-level thresholds: the first-level early warning threshold is 70% of the design allowable displacement, the second-level threshold is 85%, and the third-level threshold is 95%. The allowable displacement at mid-span of the space frame is calculated as 1 / 300 of the span, and the allowable displacement at the cantilever end is calculated as 1 / 200 of the cantilever length. The comparison and analysis of monitoring data and simulation results uses the root mean square error (RMSE) evaluation method; when the deviation between the measured value and the simulated value exceeds 15%, an anomaly analysis program is triggered. The structural safety status assessment uses a fuzzy comprehensive evaluation method, with evaluation indicators including displacement, strain, frequency, and damping ratio. The safety level is divided into four levels: excellent, qualified, caution, and dangerous. The data processing system uses a sliding window filtering algorithm to eliminate measurement noise, with the window length set to 50 sampling points. Early warning information is sent to the monitoring center via audible and visual alarms and network communication, with a response time not exceeding 3 seconds.

[0052] The specific implementation of step S07 is as follows: The time series model is constructed based on an autoregressive moving average model. The model order is determined by the Akaike Information Criterion, with a typical model order being ARMA(3,2). The wavelength drift time series establishment process includes data preprocessing, trend analysis, and periodicity detection. Data preprocessing uses the three sigma criterion to remove outliers, trend analysis uses the least squares method to fit the long-term trend, and periodicity detection uses fast Fourier transform to identify periodic components. The parameter estimation of the autoregressive moving average model uses the maximum likelihood estimation method. The prediction accuracy of the model is evaluated by the mean square prediction error, requiring the prediction error to not exceed 10% of the actual drift. The drift prediction threshold is set to 0.01% of the reference wavelength. When the predicted drift exceeds this threshold, the compensation procedure is initiated. The drift prediction compensation function uses the Kalman filter principle, achieving real-time correction of the initial strain data through state estimation and prediction updates. The input parameters of the compensation algorithm include historical wavelength data, environmental factors, and sensor status. The output compensated strain data replaces the original measured values ​​for subsequent calculations. The compensation effect is verified through comparison with standard sensors, requiring a measurement accuracy improvement of more than 30% after compensation.

[0053] The dual-grating differential compensation system is one of the core technological innovations of this invention. This system constructs a differential measurement architecture by setting up a master measurement grating and a reference grating, effectively solving the technical challenge of eliminating systematic errors such as temperature drift, mechanical stress drift, and time drift in traditional single-grating systems. Compared to existing technologies that rely on software algorithms for post-processing compensation, dual-grating differential compensation achieves real-time error cancellation at the hardware level, resulting in higher compensation accuracy and faster response speed. The physical principle of this technology is based on the characteristic that two gratings produce the same drift under the same environmental conditions. By calculating the wavelength difference, common mode errors are automatically eliminated, thereby improving the measurement accuracy from the micro-strain level of traditional methods to the sub-micro-strain level.

[0054] A two-layer game theory optimization model constructs a collaborative optimization framework at the system and sensor levels, solving the balance problem of resource allocation and accuracy optimization in multi-sensor networks. Traditional methods typically employ single-objective optimization or simple weight allocation strategies, making it difficult to simultaneously consider the overall system performance and the optimal operating state of individual sensors. This invention uses Stackelberg game theory to establish upper and lower layer models. The upper-layer model comprehensively considers minimizing the overall system error, while the lower-layer model focuses on maximizing the accuracy of individual sensors, achieving a Nash equilibrium solution through an iterative game process. This game theory approach can fully exploit the measurement potential of each sensor while ensuring overall system performance, significantly improving measurement accuracy and resource utilization efficiency compared to traditional methods of average allocation or empirical parameter setting.

[0055] Time-series predictive compensation technology achieves predictive compensation for measurement errors by establishing a mathematical model of sensor performance degradation. Traditional monitoring systems typically employ passive error detection and post-hoc correction methods. By the time measurement deviations are detected, sensor performance may have already significantly degraded, affecting the continuity and reliability of monitoring. This invention establishes a wavelength drift time series based on an autoregressive moving average model. By analyzing the trend, periodic, and random components in historical data, it predicts the future performance change trend of the sensor. When performance degradation is predicted to exceed a threshold, a proactive compensation algorithm is activated to correct the measurement data in real time. This represents a technological leap from post-hoc compensation to predictive compensation, significantly improving the stability and accuracy of long-term monitoring.

[0056] Multi-sensor fusion monitoring technology achieves comprehensive, high-density monitoring of structural deformation through triangular array deployment and wavelength division multiplexing (WDM). Traditional methods typically employ single-point or limited-point monitoring, which struggles to fully reflect the complex deformation state of large-span structures. This invention utilizes triangular array strain sensors on key members, integrating multiple sensors onto a single optical fiber using WDM technology, achieving continuous spatial distribution monitoring. This deployment scheme not only monitors bending deformation but also identifies torsional deformation and localized stress concentrations, providing more comprehensive and accurate data support for structural safety assessment.

[0057] The synergistic effect of the aforementioned key technologies forms a complete intelligent monitoring system, exhibiting significant comprehensive advantages over existing technologies. Dual-grating differential compensation provides hardware support for high-precision measurement, dual-layer game theory optimization ensures rational allocation of system resources, time-series prediction compensation guarantees the reliability of long-term monitoring, and multi-sensor fusion monitoring achieves full spatial coverage. The organic combination of these four technologies overcomes the technical bottlenecks of low accuracy, poor stability, and limited coverage in traditional monitoring methods, constructing an intelligent monitoring system with adaptive, self-correcting, and predictive functions, providing reliable technical support for the safe operation of ultra-large span grid structures.

[0058] It should be noted that this invention also solves the problem of signal coupling interference between multiple sensors in a high-frequency vibration environment in a wind tunnel. During wind tunnel operation, high-speed airflow not only generates complex pressure distribution and dynamic loads on the grid structure, but also excites multiple vibration modes of the structure. These vibrations propagate to various sensor nodes through optical fibers, causing mutual coupling and interference between different sensor signals. Especially during the wind tunnel startup and shutdown phases, rapid changes in airflow velocity and pressure lead to frequent fluctuations and aliasing of sensor spectral signals, making it difficult for traditional wavelength identification methods to accurately distinguish the effective signals of each sensor. This invention establishes a grating wavelength identification matrix, which not only records the static spectral characteristic parameters of each sensor, but also considers the wavelength stability index and dynamic response characteristics under the dynamic environment of the wind tunnel. Combined with an improved wavelength division multiplexing algorithm, it can achieve accurate identification and effective separation of multi-sensor signals in complex vibration environments, ensuring that each monitoring point can provide reliable strain data, and effectively solving the signal coupling interference problem of multi-sensor systems in wind tunnel environments. The space frame structure in a wind tunnel test section exhibits complex aeroelastic responses under high-speed airflow, with a strong coupling relationship between structural deformation and aerodynamic loads. Traditional linear strain-deformation conversion models cannot accurately describe this dynamic nonlinear behavior, especially under transonic and supersonic conditions. Complex flow phenomena such as shock waves and boundary layer separation lead to unsteady loads on the space frame structure, resulting in significant spatiotemporal nonlinear characteristics in strain distribution. Simple static conversion methods produce significant errors. This invention constructs a grating strain response matrix optimized for the wind tunnel environment. The structural stiffness distribution factor in the matrix considers the dynamic influence of aeroelastic effects on structural stiffness, and the boundary constraint influence coefficient reflects the influence of the wind tunnel wall boundary layer on the space frame constraint conditions. The material constitutive equations in the strain-displacement conversion equation set include a dynamic response model considering strain rate and temperature effects, which can accurately describe the true mechanical behavior of the space frame material under complex wind tunnel loading conditions. This achieves high-precision dynamic strain-deformation conversion, significantly improving the accuracy and reliability of wind tunnel space frame structure deformation monitoring.

[0059] Specifically, the principle of this invention is as follows: The core principle that enables this invention to solve the wavelength drift problem of fiber optic grating sensors in wind tunnel environments lies in the construction of a multi-dimensional error compensation system for the complex operating conditions of wind tunnels. This system fully considers the dynamic, periodic, and extreme characteristics of the wind tunnel environment and adopts an adaptive compensation strategy to achieve accurate error elimination. The dual-grating differential compensation system is designed specifically for the wind tunnel environment. The main measuring grating is not only affected by the strain of the grid structure but also simultaneously bears the combined loads of dynamic pressure, temperature gradient, and vibration impact generated by the high-speed airflow in the wind tunnel. The reference grating, through a special installation method, is only affected by environmental factors and does not sense structural strain. The wavelength difference calculation between the two can effectively separate the pure structural deformation signal, eliminating the interference of complex environmental factors during wind tunnel operation. The environmental humidity influence factor added to the drift error matrix is ​​used to compensate for the sensor response changes caused by the wind tunnel humidity control system. The design of the two-layer game optimization model fully considers the special characteristics of wind tunnel testing. The objective function of the upper-layer model introduces a time decay factor to reflect the intermittent operation of the wind tunnel, and the weight coefficients are dynamically adjusted according to the wind tunnel operating status. The lower-layer model optimizes the response characteristics of individual sensors in the wind tunnel environment, and uses phase response and harmonic response terms to handle the nonlinear response of sensors caused by high-speed airflow. The coupled optimization of the two-layer model ensures that the monitoring system maintains optimal performance under various wind tunnel operating conditions. Based on the periodic characteristics of wind tunnel operation cycles, the time series prediction model establishes a wavelength drift prediction algorithm that considers the frequency of wind tunnel start-up and shutdown, operating time, and load changes. This algorithm can identify the trend, periodicity, and random components of sensor drift, accurately predict the sensor performance degradation trend during long-term wind tunnel operation, and achieve active compensation, thereby ensuring that the monitoring system maintains high-precision measurement capabilities in the complex operating environment of the wind tunnel.

[0060] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0061] In this embodiment, the specific implementation of step S01 is the same as described above, and will not be repeated in detail here.

[0062] The specific implementation of step S02 is as follows: The wavelength difference algorithm of the dual-grating differential compensation system is based on the principle of calculating the difference in the center wavelengths of the two gratings. The mathematical expression of its differential compensation algorithm is:

[0063] Δλ comp =λ main -λ ref -Δλ env ;

[0064] In the formula, Δλ comp The compensated wavelength change is expressed in picometers; λ mainThe center wavelength of the main measurement grating, in nanometers; λ ref The center wavelength of the reference grating, in nanometers; Δλ env This represents the wavelength shift caused by environmental factors, expressed in picometers. The drift error matrix is ​​represented using a multidimensional array structure:

[0065]

[0066] In the formula, M drift Here is the drift error matrix; λ base，i K represents the reference wavelength data for the i-th sensor, in nanometers; T，i K represents the temperature drift coefficient of the i-th sensor, typically 10 picometers per degree Celsius; M，i K represents the mechanical stress drift coefficient of the i-th sensor, in picometers per megapascal; t，i K represents the time drift factor of the i-th sensor, in picometers per year; H，i The ambient humidity influence factor for the i-th sensor is typically 0.2 picometers per percentage. The total drift is calculated using the following formula:

[0067] Δλ drift =K T ·ΔT+K M ·Δσ stress +K t ·t time +K H ·ΔH+η;

[0068] In the formula, Δλ drift Total drift, in picometers; K T K M K t K H These represent the temperature drift coefficient, mechanical stress drift coefficient, time drift factor, and humidity influence factor corresponding to specific sensors, respectively, from the drift error matrix M. drift Extract the corresponding row; ΔT is the temperature change in degrees Celsius; Δσ stress The stress change is expressed in megapascals (MPa); t time ΔH is the time variable, in years; ΔH is the humidity change, in percentage; η is the random error term, ranging from -2 to 2 picometers.

[0069] The specific implementation of step S03 is as follows: The grating wavelength identification algorithm of wavelength division multiplexing technology adopts the Gaussian fitting peak detection method, and its spectral intensity distribution function is:

[0070]

[0071] In the formula, I(λ) wave ) represents the wavelength λwave The spectral intensity at λ is expressed in decibels. wave λ represents the spectral wavelength variable, in nanometers; I0 represents the peak intensity, in decibels; c The center wavelength is expressed in nanometers; σ g The standard deviation is a Gaussian distribution, typically 0.1 nm. The mathematical expression for the grating wavelength recognition matrix is:

[0072]

[0073] In the formula, M recognition λ is the grating wavelength recognition matrix; ci The standard center wavelength of the i-th grating is in nanometers; I 0i σ represents the peak spectral intensity of the i-th grating, in decibels; gi S represents the wavelength resolution of the i-th grating, in picometers; i is the wavelength stability index for the i-th grating, in picometers.

[0074] The specific implementation of step S04 is as follows: The two-layer game optimization model is constructed using Stackelberg game theory, and the objective function of the upper-layer model is:

[0075]

[0076] In the formula, J1 is the objective function value of the upper-level model; α is the sensor measurement error weighting coefficient, with a value of 0.4; e i Let n be the measurement error of the i-th sensor, expressed in microstrain; sensor d represents the total number of sensors; β is the displacement deviation weighting coefficient, with a value of 0.3; j The displacement deviation of the j-th measuring point is expressed in millimeters (m). point γ represents the total number of measurement points; γ is the compensation cost weighting coefficient, with a value of 0.2; c k The compensation cost for the k-th grating; r k To compensate for the resource allocation ratio, the value ranges from 0 to 1; p grating δ represents the total number of gratings; δ is the time decay weighting coefficient, with a value of 0.1; w l t represents the weight coefficient of the l-th node; decay，l q is the time decay factor, in hours; node Let be the total number of nodes. The objective function of the lower-level model is:

[0077]

[0078] In the formula, J2 is the objective function value of the lower-level model; μ is the signal-to-noise ratio weight coefficient, with a value of 0.35; a i s is the signal-to-noise ratio of the i-th sensor;sensor is the number of sensors in the lower-level model; v is the phase response weighting coefficient, with a value of 0.25; b j φ is the phase response amplitude of the j-th grating; j The phase angle is expressed in radians; t grating ξ represents the number of gratings in the lower-level model; ξ is the gain coefficient weight, with a value of 0.25; g k u is the gain coefficient of the k-th node; node ζ represents the number of nodes in the lower-level model; ζ is the harmonic response weighting coefficient, with a value of 0.15; h l θ represents the harmonic response amplitude of the l-th sensor; l This is the harmonic phase angle, in radians; v sensor This represents the number of sensors in the lower-level model. The two models exchange information through coupling terms:

[0079]

[0080] In the formula, C coupling For coupling terms; λ couple Here, n is the coupling coefficient, with a value of 0.5; n is required to be... sensor =s sensor Ensure consistency of corresponding sensors in the upper and lower layer models.

[0081] The specific implementation of step S05 is as follows: During the establishment of the grating strain response matrix, the geometric deformation equation for strain-displacement transformation is expressed as:

[0082] {u}=[N] -1 {ε}·[L]·[K s ];

[0083] In the formula, {u} is the displacement vector, containing the mid-span displacement and cantilever end displacement of the space frame, in millimeters; [N] is the node coordinate matrix; {ε} is the strain vector, composed of the initial strain data of each measuring point, in microstrain; [L] is the length matrix, containing the geometric dimensions of the members, in meters; [K] is the length matrix. s [ ] represents the structural stiffness distribution matrix. The material constitutive equation adopts a linear elastic model:

[0084] {σ mech}=[D]{ε}+[T]ΔT;

[0085] In the formula, {σ mech} represents the mechanical stress vector, in megapascals (MPA); [D] is the elasticity matrix; [T] is the temperature stress coefficient matrix; ΔT represents the temperature change, in degrees Celsius. The specific form of the elasticity matrix is:

[0086]

[0087] In the formula, E is the elastic modulus, with a value of 210 GPa; v is Poisson's ratio, with a value of 0.3. The grating strain response matrix is ​​expressed as:

[0088]

[0089] In the formula, [R] is the grating strain response matrix; P i The optimal compensation parameters for the i-th sensor are derived from the output of the two-layer game optimization model; W i The spatial position weighting coefficient is determined by the geometric position of the sensor within the space frame structure; K si B is the structural stiffness distribution factor, expressed in Newtons per meter. i This is the boundary constraint influence coefficient, which is determined based on the support type and constraint conditions.

[0090] The specific implementation method of step S06 is as follows: The formula for calculating the early warning threshold of real-time monitoring is:

[0091]

[0092] In the formula, D threshold The warning threshold is in millimeters; D allow To determine the allowable displacement values, the allowable displacement at mid-span of the space frame is L / 300, and the allowable displacement at the cantilever end is L. c / 200, where L is the span. c The length is the cantilever length, and all units are millimeters. The root mean square error calculation formula for the comparison and analysis of monitoring data and simulation results is as follows:

[0093]

[0094] In the formula, RMSE is the root mean square error, in millimeters; D measured，i D represents the measured displacement value of the i-th measuring point, in millimeters; simulated，i n represents the simulated displacement value of the i-th measuring point, in millimeters; measure This represents the number of displacement measurement points.

[0095] The specific implementation of step S07 is as follows: The time series model adopts an autoregressive moving average model, the mathematical expression of which is:

[0096]

[0097] In the formula, X t φ is the wavelength drift observation at time t, in picometers; i p is the i-th order autoregressive coefficient; arma θ is the autoregressive order, typically 3; j q is the coefficient of the j-th moving average; armaThis is the order of the moving average, typically 2; ∈ t The white noise error term at time t follows a normal distribution. Where σ noise Let be the noise standard deviation. The prediction formula for wavelength drift time series is:

[0098]

[0099] In the formula, Here, represents the predicted value h steps forward, in picometers; h is the prediction step size. The drift prediction compensation function is constructed based on the Kalman filter algorithm:

[0100]

[0101] In the formula, ε compensated，t For post-compensation strain data, the unit is microstrain; ε initial，t These are initial strain data, in microstrain units; K kalman，t Let be the Kalman gain at time t; To predict drift, the unit is picometer; X reference This is a reference wavelength value, measured in picometers.

[0102] It should be noted that the objective functions J1 and J2 of the two-layer game optimization model are based on multi-objective optimization theory. By balancing the overall system performance and the accuracy of a single sensor, the model achieves global minimization of measurement error. Compared with traditional single-layer optimization methods, this model can optimize the overall system performance while ensuring high accuracy of a single sensor, thereby improving the reliability and stability of the monitoring system.

[0103] Wavelength difference algorithm Δλ comp By eliminating common mode errors, the influence of temperature and environmental factors on measurement accuracy is effectively suppressed, resulting in an accuracy improvement of over 30% compared to traditional single-grating measurement methods. The formula for calculating the differential compensation coefficient is as follows:

[0104]

[0105] In the formula, α comp This is the differential compensation coefficient, with units of microstrain per picometer.

[0106] Drift error matrix M drift A quantitative evaluation mechanism for sensor performance degradation was established, and accurate compensation for drift error was achieved through multi-dimensional parameter recording. Compared with traditional single error compensation methods, this matrix considers the coupled effects of multiple factors such as temperature, mechanical stress, time, and humidity, improving the compensation accuracy by more than 25%.

[0107] The strain-displacement transformation equations establish precise geometric deformation and material constitutive relations, enabling accurate conversion of discrete strain data into a continuous displacement field, thus providing a reliable data foundation for structural safety assessment. The complete form of the elastic matrix [D] considers the material response characteristics under three-dimensional stress, improving computational accuracy by more than 20% compared to the simplified one-dimensional model.

[0108] Autoregressive moving average model X t Time series analysis can be used to predict sensor performance degradation trends. The formula for constructing the wavelength drift time series is:

[0109] S drift (t)=[λ base (t), K T (t), K M (t), K t (t), K H (t)] T ;

[0110] In the formula, S drift (t) is the wavelength drift time series vector at time t, which contains 5 time-varying parameters; λ base (t) represents the reference wavelength data at time t, in nanometers; K T (t) represents the temperature drift coefficient at time t, measured in picometers per degree Celsius; K M (t) represents the mechanical stress drift coefficient at time t, in picometers per megapascal; K t (t) represents the time drift factor at time t, in picometers per year; K H (t) represents the humidity influence factor at time t, in picometers per percentage; the superscript T indicates vector transpose.

[0111] Combined with Kalman filter compensation function ε compensated，t This enables real-time correction of measurement data, ensuring the accuracy and stability of long-term monitoring. Compared to traditional fixed compensation methods, this compensation algorithm can adaptively adjust according to the actual degradation state of the sensor, improving long-term stability by more than 40%.

[0112] Grating wavelength recognition matrix M recognition An accurate identification mechanism for multi-sensor signals was established, solving the signal crosstalk problem in wavelength division multiplexing (WDM) systems and improving the system's integration and reliability. This identification algorithm, based on Gaussian fitting peak detection, improves identification accuracy by over 35% and reduces the false positive rate by over 50% compared to traditional threshold detection methods.

[0113] To better understand and implement this invention, the following is a specific application scenario of the invention, Example 2: In the construction of the tunnel, one of the space frame structures used is an orthogonal square pyramidal space frame with a height of 8m and a cantilever length of 15m, mainly bearing the roof load and wind load. The space frame is made of Q345 steel, the members are φ159×6mm steel pipes, and the nodes are connected by welded balls.

[0114] The technical team first conducted a stress analysis on the space frame structure, identifying 12 key members, including 4 mid-span main beams, 4 cantilever end support members, and 4 web members at stress concentration points. Based on the deformation cloud map analysis of the space frame structure during the lifting and operation phases, locations with significant deformation were identified, and sensor placement points were determined for focused monitoring. Figure 2 As shown, the shape sensor consists of a PVC sleeve, a thin-walled steel sliding clamp, and a fiber optic strain gauge sensor. It boasts several technological advantages: the sensor's measurement results are less affected by temperature; it utilizes a self-developed enhanced-sensitivity FBG sensor, resulting in high sensitivity; the sensor is welded to the steel pipe surface via a fixed support, avoiding the use of adhesives; the sensor is internally located on the steel pipe surface, allowing for timely replacement if damaged; and it enables the measurement of dynamic structural deformation fields with millimeter-level accuracy. Figure 3 A schematic diagram of the arrangement of shape sensors on the grid is given.

[0115] The PVC sleeve has an outer diameter of 70mm and an inner diameter of 60mm. It has four grooves, each 1.5mm deep, perpendicular to each other in its cross-section. The thin-walled steel pipe has an outer diameter of 27mm and a thickness of 1.5mm. Sliding clamps are installed at regular intervals along its axial direction. These clamps are mounted on the outer surface of the thin-walled steel pipe by tightening the top nut. Four ball-head plungers are installed at the ends of the clamps, their positions matching the grooves in the PVC sleeve, ensuring free sliding of the thin-walled steel pipe within the sleeve. Two strain measurement points are set between two adjacent sliding clamps. Each measurement point uses a triangular array strain sensor layout, with one clamp-type FBG strain sensor placed every 120° circumferentially. The FBG sensors have fixed supports welded to the outer surface of the thin-walled steel pipe at both ends, and the sensors are mechanically connected to the fixed supports. The sensors are installed using fixed supports. First, the sensors are unrolled from the coil and straightened along the selected component axis. Then, a fixed support is installed approximately every 0.5m to pre-fix the sensors, ensuring they are taut along the component axis. Finally, they are welded in place. The measurement range is set to ±3000με, the resolution to 1με, and the minimum distance between two measuring points can reach 1m. The entire monitoring system consists of 144 strain measuring points and 432 fiber optic strain sensors.

[0116] The shape sensor uses a thin-walled steel tube with FBG strain gauges embedded on its surface as the sensing element. Different measurement requirements can be met by adjusting the position and number of sliding clamps. An external PVC sleeve not only protects the internal strain gauges but also allows the internal steel tube to be easily removed and replaced if the gauges are damaged. Utilizing wavelength division multiplexing (WDM) technology, the demodulator can independently identify fiber gratings with different center wavelengths connected in series on the same optical fiber, reducing the number of demodulator channels required for multi-sensor signal acquisition and facilitating internal wiring within the shape sensor. Fiber optic transmission offers strong anti-interference capabilities, enabling long-distance transmission of optical signals and facilitating remote monitoring.

[0117] When establishing the dual-grating differential compensation system, the technical team placed a reference grating 5 cm away from each main measurement grating. The reference grating has the same spectral characteristics as the main measurement grating but is not in direct contact with the structure; it is used only for environmental compensation. The reference wavelength data for each sensor were determined through calibration experiments, as shown in Table 1.

[0118] Table 1. Typical sensor reference wavelength calibration data

[0119]

[0120] The wavelength division multiplexing (WDM) system employs dense WDM technology, cascading 36 fiber optic grating sensors with different center wavelengths onto a single fiber, with a wavelength spacing of 0.8 nm. The signal acquisition system uses a tunable laser with a scanning range of 1525–1565 nm and a scanning accuracy of 1 pm. The demodulator uses a peak detection algorithm to identify the reflection spectrum of each grating, with the spectral peak intensity threshold set at -40 dB.

[0121] When constructing a two-layer game optimization model for error compensation, the weight coefficients of the objective function of the upper-layer model are set as follows:

[0122] α = 0.4, β = 0.3, γ = 0.2, δ = 0.1. The weight coefficients of the objective function in the lower-level model are set as follows: μ = 0.35, ν = 0.25, ξ = 0.25, ζ = 0.15. A hybrid optimization strategy combining genetic algorithm and gradient descent is adopted, with a population size of 50, a crossover probability of 0.8, a mutation probability of 0.1, and an iteration convergence criterion of less than 10 for the change in the objective function. -6 The optimal compensation parameters were obtained after 326 iterations. The optimized compensation parameters for various sensors are shown in Table 2.

[0123] Table 2 Sensor Optimization Compensation Parameters

[0124]

[0125]

[0126] When establishing the grating strain response matrix, the technical team determined the stiffness characteristics of the space frame structure through finite element analysis. The material's elastic modulus was taken as 210 GPa, Poisson's ratio as 0.3, and density as 7.85 × 10⁻⁶. 3 kg / m 3 The strain-displacement transformation equations take into account the geometric nonlinear characteristics of the space frame structure. The allowable displacement at the mid-span of the space frame is calculated as 1 / 300 of the span, i.e., 400 mm, and the allowable displacement at the cantilever end is calculated as 1 / 200 of the cantilever length, i.e., 75 mm.

[0127] The real-time monitoring system uses a continuous sampling frequency of 10Hz and sets three warning thresholds: Level 1 warning is 70% of the design allowable displacement (280mm at mid-span, 52.5mm at the cantilever end), Level 2 warning is 85% (340mm at mid-span, 63.8mm at the cantilever end), and Level 3 warning is 95% (380mm at mid-span, 71.3mm at the cantilever end). The monitoring data is compared and analyzed with the finite element simulation results. The displacement monitoring results under typical working conditions are shown in Table 3.

[0128] Table 3 Deformation monitoring data of the space frame under typical working conditions

[0129] Monitoring point locations Measured displacement / mm Simulated displacement / mm Relative error / % Safety rating Midspan A 185.2 178.6 3.7 Excellent Midspan B 192.8 186.4 3.4 Excellent Cantilever end C 38.5 36.2 6.3 Excellent Cantilever end D 41.3 39.7 4.0 Excellent 1 / 4 span E 96.7 92.8 4.2 Excellent

[0130] The time series model uses the ARMA(3,2) model to predict wavelength drift, and the model parameters are determined using the maximum likelihood estimation method. Historical data shows that the sensor wavelength drift exhibits significant temperature and time correlations, with a long-term drift trend of 3–6 pm per year. A compensation procedure is initiated when the predicted drift exceeds 0.01% (approximately 150 pm) of the reference wavelength. The drift prediction and compensation effects are shown in Table 4.

[0131] Table 4 Comparison of Wavelength Drift Prediction Compensation Effects

[0132]

[0133] Figure 4 The displacement contour plot of the space frame structure under full-load wind conditions is displayed, clearly showing the distribution pattern of structural deformation: the deformation is greatest in the mid-span region, gradually decreasing towards the supports, and the cantilever ends exhibit obvious downward deflection. The deformation pattern is in high agreement with the finite element analysis results, verifying the accuracy of the monitoring system.

[0134] Compared to traditional leveling and total station monitoring methods, this technical solution represents a significant improvement in several aspects. Measurement accuracy has increased from ±5mm to ±2mm, an improvement of approximately 15%. Monitoring efficiency has been greatly enhanced; traditional methods require 3-4 hours to complete a full measurement, while the fiber optic sensing system enables continuous real-time monitoring, increasing the data update frequency from once per day to 10 times per second. In adverse weather conditions, traditional measurement methods often fail to operate normally, while the fiber optic sensing system is unaffected by weather and can provide 24-hour uninterrupted monitoring. The system's long-term stability is also significantly better than traditional methods. During a 6-month monitoring period, sensor drift is controlled within 5pm, equivalent to a strain error of 2.5με, while the annual drift of traditional strain gauges typically reaches 50-100με. Furthermore, the fiber optic sensing system has strong resistance to electromagnetic interference, maintaining stable operation even in strong electromagnetic environments, while traditional resistance strain gauges are easily affected by electromagnetic interference. Automated data processing and early warning functions improve monitoring efficiency by approximately 18%, reducing the need for manual intervention and lowering monitoring costs. The overall performance of the system is significantly improved in terms of accuracy, efficiency and reliability compared with traditional monitoring methods, providing a more advanced technical solution for the safety monitoring of ultra-large span grid structures.

[0135] It should be noted that the variables involved in this invention are explained in detail in Tables 5 and 6.

[0136] Table 5. Variable Explanation Table (Part 1)

[0137]

[0138] Table 6. Variable Explanation Table (Part Two)

[0139]

[0140]

[0141] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for monitoring the deformation of ultra-large span space frames, characterized in that, Shape sensors are installed on key members of the ultra-large span space frame structure. Thin-walled steel sliding clamps are arranged every 1m along the axial direction of the thin-walled steel pipe. Initial strain data is obtained at each measuring point using a triangular array strain sensor layout. A dual-grating differential compensation system is established, with a reference grating set next to the main measuring grating. Wavelength drift caused by temperature and mechanical stress is eliminated through wavelength differential algorithm. A drift error matrix is ​​constructed to record the reference wavelength data, temperature drift coefficient, mechanical stress drift coefficient, and time drift factor of each sensor. Wavelength division multiplexing technology is used to acquire signals from multiple fiber optic grating sensors connected in series on the same optical fiber. The demodulator identifies grating signals with different center wavelengths. A grating wavelength identification matrix is ​​established to store the standard center wavelength, wavelength resolution, and spectral peak intensity of each grating. A two-layer game optimization model is constructed to perform error compensation, obtain the optimal compensation parameters, and output them to the grating strain response matrix. A grating strain response matrix is ​​established to convert the initial strain data and optimal compensation parameters of each measuring point into a three-dimensional deformation field of the space frame structure. The mid-span displacement and cantilever end displacement of the space frame are calculated through a set of strain-displacement conversion equations. The deformation status of the space frame is monitored in real time. When the mid-span displacement and cantilever end displacement exceed the design allowable range, an early warning mechanism is triggered. At the same time, the monitoring data is compared and analyzed with the computer simulation results to assess the structural safety status.

2. The method for monitoring deformation of ultra-large span space frames according to claim 1, characterized in that, The drift error matrix is ​​a data structure used to record and quantify the wavelength shift of the fiber optic grating strain sensor during long-term use. The matrix elements include reference wavelength data, temperature drift coefficient, mechanical stress drift coefficient, time drift factor, and environmental humidity influence factor. Accurate error compensation is achieved by establishing a drift characteristic parameter library for each sensor node.

3. The method for monitoring deformation of ultra-large span space frames according to claim 2, characterized in that, The dual-grating differential compensation system is specifically an error elimination system constructed by setting up a main measurement grating and a reference grating. The main measurement grating is responsible for the actual strain measurement and outputs the initial strain data, while the reference grating is only affected by temperature and environmental factors. The common mode error is eliminated by calculating the wavelength difference between the two and generating a differential compensation coefficient.

4. The method for monitoring deformation of ultra-large span space frames according to claim 3, characterized in that, The grating wavelength identification matrix is ​​specifically a parameter matrix used in wavelength division multiplexing (WDM) technology to distinguish and identify the center wavelengths of different fiber optic grating strain sensors. The matrix elements include standard center wavelength, wavelength resolution, spectral peak intensity, and wavelength stability index.

5. The method for monitoring deformation of ultra-large span space frames according to claim 4, characterized in that, The grating strain response matrix is ​​specifically a transformation matrix that describes the mapping relationship between the strain measurement value of the fiber optic grating strain sensor and the actual deformation state of the grid structure. The matrix elements include the optimal compensation parameter, spatial position weight coefficient, structural stiffness distribution factor, and boundary constraint influence coefficient.

6. The method for monitoring deformation of ultra-large span space frames according to claim 5, characterized in that, The strain-displacement conversion equation set is specifically used to convert initial strain data into a mathematical model of space frame structure displacement. It includes geometric deformation equations and material constitutive equations. The geometric deformation equations establish the geometric relationship between strain and displacement at each node of the space frame structure and output the mid-span displacement value and cantilever end displacement value of the space frame. The material constitutive equations describe the mechanical response characteristics of the space frame material under complex stress states.

7. The method for monitoring deformation of ultra-large span space frames according to claim 6, characterized in that, The time series model is specifically a mathematical prediction model based on historical wavelength drift data. It uses an autoregressive moving average model to perform time series analysis on the baseline wavelength data, temperature drift coefficient, mechanical stress drift coefficient, and time drift factor to establish a wavelength drift time series for predicting future wavelength change trends.

8. The method for monitoring deformation of ultra-large span space frames according to claim 7, characterized in that, The wavelength drift time series is specifically a data sequence formed by arranging the reference wavelength data, temperature drift coefficient, mechanical stress drift coefficient, and time drift factor in chronological order.

9. The method for monitoring deformation of ultra-large span space frames according to claim 8, characterized in that, The drift prediction compensation function is specifically a compensation algorithm based on the wavelength drift time series prediction results. When the predicted wavelength drift exceeds a preset threshold, the initial strain data is corrected and compensated in real time.

10. The method for monitoring the deformation of ultra-large span space frames according to claim 9, characterized in that, It also includes using a time series model to establish a wavelength drift time series based on the reference wavelength data, temperature drift coefficient, mechanical stress drift coefficient and time drift factor, predicting the sensor wavelength drift trend through an autoregressive moving average model, and activating a drift prediction compensation function to compensate the initial strain data in real time when the predicted drift exceeds a threshold.

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