Crane girder non-probability reliability assessment method based on convex set model

Abstract

The invention discloses a crane main beam non-probability reliability assessment method based on a convex set model, and the method comprises the steps: collecting the working condition and key section multi-source data of a crane, and carrying out the time alignment, missing measurement compensation and time-frequency feature extraction; selecting a parameter vector influencing the safety of the main beam, and constructing a combined convex set uncertain domain consisting of an interval box, an ellipsoid set and polyhedron linear constraints; based on a finite element and radial basis function substitution model, main beam key section response mapping is established, the proportion of equivalent stress and deflection relative to an allowable value is obtained, and an overall limit criterion is formed; executing worst case search in the uncertain domain, and calculating an opposite number of a maximum value of a limit criterion as a non-probability reliability index; and reliability indexes are further calculated and summarized at the section layer and the main beam layer, and the reliable state grading of the main beam is realized according to a preset threshold value. The method does not need to depend on probability distribution hypothesis, and rapid assessment of the safety of the crane girder can be realized under small sample and multi-source uncertain conditions.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of crane safety, and particularly relates to a crane girder non-probabilistic reliability evaluation method and system based on a convex set model. BACKGROUND

[0002] As large hoisting and carrying equipment, the girder of a crane is a key force component for bearing and transferring load, and the structural safety thereof is directly related to the operation reliability and work safety of the whole crane. The girder is subjected to the combined influence of dynamic load impact, side wind disturbance, temperature gradient and other factors during long-term service, and the stress state thereof has significant uncertainty. Traditional structural reliability evaluation is mostly based on probability statistics, and the probability distribution of material parameters, load or geometric size is taken as input, and the failure probability is calculated by means of Monte Carlo or FORM / SORM. However, in actual engineering, sufficient sample data are often lacking to support the statistical modeling of parameter distribution, especially under the long-term operation condition of the crane, the environmental and load conditions change dramatically, which makes it difficult for the probability model to accurately describe the uncertainty of the system.

[0003] In order to solve the above problems, in recent years, the non-probabilistic reliability theory has been proposed, which describes the uncertain parameters in the form of convex set through set theory, so that the safety evaluation can be carried out without relying on the probability distribution. This kind of method can still maintain the conservatism and robustness of the evaluation results in the engineering scene of "small sample and strong uncertainty". The existing non-probabilistic method has been applied to bridges, pressure vessels, blades and other structures, but its application in the field of cranes is still insufficient. In particular, for the crane girder, the load is complex and the working condition is significantly coupled.

[0004] Based on this, the application provides a crane girder non-probabilistic reliability evaluation method based on a convex set model, so as to realize accurate evaluation of the safety state of the crane girder. SUMMARY

[0005] In order to solve the above problems, the application provides a crane girder non-probabilistic reliability evaluation method based on a convex set model, so as to realize accurate evaluation of the safety state of the crane girder.

[0006] In order to achieve the above technical purposes, the application adopts the following technical solutions: In a first aspect, the application provides a crane girder non-probabilistic reliability evaluation method based on a convex set model, comprising: S1: Obtain the working condition data of the crane and the multi-source sensor data arranged at the key sections of the main girder, time-align, compensate for missing data, and extract time-frequency features at a uniform time step to obtain normalized state feature sequences for evaluation; S2: Select a parameter vector that affects the safety of the main girder, and model the uncertainty of the parameter vector as a combined convex set uncertainty domain, which is composed of the intersection of the following three types of constraints: one is an interval box constraint, which indicates that the parameter values are located between the preset upper and lower limits; the second is an ellipsoid set constraint, which is used to reflect the correlation between parameters and is determined by a mean vector, a covariance matrix, and a radius parameter; the third is a polyhedral linear constraint, which is used to express the linear inequality relationship between the working condition and the load coupling and the mechanical consistency; S3: Based on the finite element method and combined with the surrogate model, construct the response mapping of the key section set of the main girder to obtain the proportions of the equivalent stress and deflection with respect to their respective allowable values, and take the larger one of the two proportions at any key section as the limit criterion for the section, and take the most unfavorable criterion among all key sections as the overall limit criterion; S4: Search for the worst case of the overall limit criterion in the combined convex set uncertainty domain, obtain the maximum value of the criterion in the uncertainty domain as the worst case value, and define the inverse of the worst case value as the non-probabilistic reliability index; S5: Calculate the non-probabilistic reliability index at the section level and the main girder level respectively, wherein the main girder level index takes the minimum value of the key section index, and classifies the main girder reliability state according to a preset threshold, and outputs the evaluation results including the reliability index, the most dangerous parameter combination, the weakest section position, and the disposal suggestion.

[0007] As a possible implementation, further, step S1 includes the following steps: S1.1: At a sampling period , collect the PLC working condition data of the crane to obtain discrete sequences of hoisting height , walking speed , trolley speed , actual load , and braking state ; S1.2: Arrange strain gauges, accelerometers, displacement meters, and thermometers at the key sections of the main girder to obtain multi-source high-frequency sensor signals at a sampling frequency , ; wherein, is the original observation value of the i-th sensor at the n-th sampling point, is the total number of sensor channels, is the number of sampling points; S1.3: Define a main time grid , , is the number of PLC data points; high frequency signals are mapped to aligned data by linear interpolation , is the signal value of the i-th channel at time after interpolation; S1.4: Kalman filter is adopted to compensate missing data and smooth noise, and the filtered reconstructed signal is obtained; ; S1.5: Short-time Fourier transform is performed on the reconstructed signal in a sliding window of length L, and the amplitude spectrum statistics are extracted in the frequency band to form the time-frequency feature vector ; S1.6: All time-frequency features are spliced with low-frequency operating quantities to form the feature vector , and Z-score method is used to perform normalization to obtain , the expression is as follows: ; wherein, and are the historical mean and standard deviation of the j-th feature, and d is the dimension of the feature vector.

[0008] As a possible implementation, further, step S2 comprises the following steps: S2.1: Construct a parameter vector affecting the reliability of the main beam : ; wherein, Q is the actual load, is the dynamic load coefficient; is the wind load factor of the main beam, ; E is the elastic modulus of the material; is the yield strength of the material; is the thickness of the i-th plate, a total of m plates; is the temperature gradient of the main beam cross section; is the measurement bias of the i-th channel sensor, ; S2.2: Construct interval box uncertainty set wherein, l and are the lower limit vector and the upper limit vector of each parameter, respectively; S2.3: Construct ellipsoid uncertainty set wherein, wherein is a parameter mean vector, is a covariance matrix, is a Mahalanobis distance radius; S2.4: Constructing a polyhedral linear constraint set

[0009] where A is a coefficient matrix and d is an upper bound vector; the at least includes the following linear constraints: i) Load-amplitude coupling constraint

[0010] where, , is an empirical coefficient for adjusting the weight of load and amplitude; is an envelope upper limit, which is set according to the structural limit state; ii) Temperature-elastic modulus correction constraint

[0011] where, is the nominal elastic modulus at the reference temperature; is the cross-section temperature gradient; is the temperature sensitivity coefficient; iii) Wind load-amplitude coupling constraint

[0012] where, is the coupling coefficient; is the maximum deflection of the main girder under the action of wind load; is the wind load-structural deformation safety limit value; iv) Sensor bias coupling constraint

[0013] where, is the maximum allowed value of the bias sum.

[0014] S2.5: Combination of convex sets Take the intersection of the three types of constraints to obtain the final uncertainty domain , .

[0015] As a possible implementation, further, step S3 includes the following steps: S3.1: Determine a set of main girder key section sets at key positions ; the key positions include the midspan of the main girder, the vicinity of the load action point, the vicinity of the lifting point, and the vicinity of the support, etc. S3.2: Calculate the equivalent stress and deflection of each section based on the sample points , and train the surrogate model to obtain and , and evaluate the maximum absolute prediction error of the two surrogate models using leave-one-out cross-validation , and ensure that for any , any section has , ; S3.3: Define the normalized hyper-limit for each section :

[0016] where is the allowable stress of the section, is the allowable deflection of the section; and are the surrogate model predicted stress and deflection of the section , respectively; S3.4: Take the most unfavorable one from all section criteria to form: ; where, when , it is determined that the specification limit is met.

[0017] As a possible implementation, further, step S3.2 specifically includes the following steps: S3.21: Use Latin hypercube design to generate K sets of training samples in the parameter vector space , where , is the dimension of the parameter vector; S3.22: For each sample point , use the finite element model of the main beam to solve the equivalent stress and deflection response of each section under different input parameters,

[0018] S3.23: Construct a stress radial basis function surrogate model: where is the weight coefficient determined by least squares, is the input parameter of the current solution point, Represents training sample points, The kernel width hyperparameter of the stress model; S3.24: Deflection Radial Basis Function Alternative Model: in, The weighting coefficients are determined using the least squares method. The input parameters for the current solution point. Represents training sample points, The kernel width hyperparameter of the deflection model; S3.25: Use leave-one-out cross-validation to evaluate the maximum absolute prediction error of the two alternative models, and calculate them respectively: Guarantee for any Arbitrary cross-section All , .

[0019] As one possible implementation, step S3.4 is further detailed as follows: The global limit function is defined as the supremum of all cross-sectional exceedances:

[0020] when When, it is determined that the main beam is in the parameter combination The following meets the specification requirements; when If so, it is determined that there is a risk of exceeding the limit.

[0021] As one possible implementation, step S4 further includes the following steps: S4.1: At the nominal parameter point Limit function of the whole By performing piecewise linear external approximation, we obtain: ;in, Section The set of indices of the tangent plane; For sampling points The calculated gradient vector; The intercept; S4.2: The limit function after external approximation is uniformly expressed as And introduce an auxiliary variable t to construct a convex optimization problem: maximize This satisfies the following for all tangent planes. ;at the same time Satisfying the uncertainty region Constraints; S4.3: Solve the optimization problem to obtain the optimal value. and define the non-probabilistic reliability index is the opposite number of , which means that there is still a safety margin in the whole uncertainty domain; , which means that it is on the limit boundary; , which means that there is an over-limit risk, and its absolute value represents the over-limit degree of the worst case.

[0022] As a possible implementation, further, step S4 further comprises: S4.4: updating the nominal point to the worst parameter combination obtained in this round of optimization, and then repeating the outer approximation and solving process until the optimal value t* converges.

[0023] As a possible implementation, further, step S5 comprises the following steps: S5.1: for each critical section , find the parameter combination that maximizes the normalized over-limit degree in the uncertainty domain , and take the opposite number of the maximum over-limit degree as the non-probabilistic reliability index of the section; S5.2: take the minimum value of all section-level non-probabilistic reliability indexes as the overall non-probabilistic reliability index of the main beam, to reflect the safety margin of the weakest section; S5.3: preset two threshold values , where ; when , it is determined to be a safe level; when , it is determined to be a level of attention; when , it is determined to be a warning level; and when , it is determined to be an over-limit level; S5.4: output the overall non-probabilistic reliability index of the main beam, the position of the weakest section, the parameter combination that leads to the most unfavorable criterion, and the corresponding treatment suggestion; the treatment suggestion includes load limiting, amplitude limiting, re-measuring, maintenance and reinforcement, etc.

[0024] In a second aspect, the present application also provides a computer-readable storage medium, wherein the storage medium stores at least one instruction, at least one program, a code set or an instruction set, which are loaded and executed by a processor to realize the above-mentioned non-probabilistic reliability evaluation method for the main beam of a crane based on a convex set model.

[0025] Compared with the existing main girder reliability evaluation method based on a probability model or a single uncertain parameter, the crane main girder non-probabilistic reliability evaluation method based on the convex set model has the following remarkable beneficial effects: 1. The convex set theory is used for non-probabilistic modeling of multiple source uncertain parameters such as load, material and environment, and the method does not rely on the probability distribution assumption in traditional reliability analysis, and can accurately evaluate the safety margin of the main girder in the case of lack of large sample statistical data, and effectively solve the problem of sparse data and unknown distribution in the crane field operation condition.

[0026] 2. The intersection of the interval box, ellipsoid set and polyhedron constraint three types of convex sets is used to comprehensively describe the linear and nonlinear coupling relationship between the multiple source uncertain factors such as dynamic load coefficient, main girder wind load factor, temperature gradient and sensor bias, so as to ensure the mechanical consistency and physical rationality of the working condition constraint, and avoid the evaluation deviation caused by the independent processing of a single factor in the past.

[0027] 3. The radial basis function surrogate model is introduced on the basis of finite element calculation to quickly predict the equivalent stress and deflection response of the key section, and the upper bound of the model error is determined through leave-one-out cross validation, so that the calculation cost is significantly reduced while ensuring the physical consistency, and the worst case search can be completed within seconds.

[0028] 4. The global most unfavorable point of the structure response can be obtained by converting the overall limit criterion into a worst case optimization problem in the form of a second-order cone programming in the combined convex set uncertainty domain. The optimization model has strict mathematical convexity and solvability, ensures that the solution result is stable and has physical conservativeness, and can be directly used for online monitoring and risk prediction.

[0029] 5. The double-layer reliability index calculation mechanism of the section level and the main girder level is proposed, the minimum value of the non-probabilistic reliability index of each section is taken as the overall index of the main girder, and the safety level, attention level, warning level and overrun level are divided according to the preset threshold, so that the grading evaluation and early warning from local damage to overall safety state are realized. And the evaluation result not only includes the numerical reliability index, but also synchronously outputs the most dangerous parameter combination, the weakest (dangerous) section position and the corresponding disposal suggestion, so as to facilitate the maintenance personnel to quickly locate the risk source and take targeted maintenance measures. BRIEF DESCRIPTION OF DRAWINGS

[0030] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creating any inventive labor.

[0031] Figure 1 A schematic diagram of a brief implementation process of a crane girder non-probabilistic reliability evaluation method based on a convex set model is shown in the figure. Figure 2 A schematic diagram of a computer readable storage medium provided in the embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0032] The present application will be further described in conjunction with the accompanying drawings and embodiments. It is particularly pointed out that the following embodiments are only used to illustrate the present application, but do not limit the scope of the present application. Similarly, the following embodiments are only part of the embodiments of the present application, but not all embodiments. All other embodiments obtained by those of ordinary skill in the art without creative labor are within the scope of the present application.

[0033] Embodiment 1 Referring to the accompanying drawings, Figure 1 the present embodiment provides a crane girder non-probabilistic reliability evaluation method based on a convex set model, comprising the following steps: S1: Obtain the working condition data of the crane and the multi-source sensor data arranged at the key section of the girder, and perform time alignment, missing data compensation and time-frequency feature extraction under a unified time step to obtain a normalized state feature sequence for evaluation; specifically comprising the following steps: S1.1: Collect PLC working condition data of the crane at a sampling period to obtain discrete sequences of lifting height , walking speed , trolley speed , actual load and braking state ; S1.2: Arrange strain gauges, accelerometers, displacement meters and thermometers at the key section of the girder to obtain multi-source high-frequency sensor signals at a sampling frequency , ; wherein, is the original observation value of the i-th sensor at the n-th sampling point, is the total number of sensor channels, is the number of sampling points; S1.3: Define a main time grid , , is the number of PLC data points; map the high-frequency signals to aligned data by linear interpolation , wherein is the signal value of the i-th after interpolation at time S1.4: Perform signal The Kalman filter is used for missing data compensation and noise smoothing to obtain a filtered reconstructed signal ; S1.5: The reconstructed signal is subjected to a short-time Fourier transform within a sliding window of length L, and the amplitude spectrum statistics are extracted within the frequency band to form a time-frequency feature vector ; By simultaneously capturing the instantaneous changes in the time domain signal and the spectral characteristics, it is possible to sensitively identify the high-order harmonics, impacts, and post-impact residual vibrations in the dynamic response of the main girder, and other precursors of failure.

[0034] S1.6: All time-frequency features are concatenated with low-frequency operating quantities to form a feature vector , and the Z-score method is used to perform normalization to obtain , which is expressed as follows: ; where and are the historical mean and standard deviation of the jth feature, respectively, and d is the dimension of the feature vector.

[0035] S2: Select the parameter vector that affects the safety of the main girder, and model its uncertainty as a combined convex set uncertainty domain, which is composed of the intersection of the following three types of constraints: first, interval box constraints, which indicate that the values of each parameter are within the preset upper and lower limits; second, ellipsoid set constraints, which are used to reflect the correlation between parameters and are determined by the mean vector, covariance matrix, and radius parameter; and third, polyhedral linear constraints, which are used to express the linear inequality relationship between the operating conditions and the loads and the mechanical consistency; the specific steps are as follows: S2.1: Construct the parameter vector that affects the reliability of the main girder :

[0036] where Q is the actual load, is the dynamic load coefficient; is the wind load factor of the main girder, ; E is the material elastic modulus; is the material yield strength; is the thickness of the ith plate (or web), considering the manufacturing deviation and corrosion effect, a total of m plates; is the temperature gradient of the main girder cross section; is the measurement bias of the ith sensor, ; S2.2: Construct the interval box uncertainty set

[0037] where, l and are the lower bound vector and upper bound vector of each parameter, respectively; S2.3: Constructing the ellipsoid uncertainty set where, where is the parameter mean vector, is the covariance matrix, is the Mahalanobis distance radius; S2.4: Constructing the polyhedral linear constraint set where, A is the coefficient matrix, d is the upper bound vector. Wherein, at least includes the following linear constraints; i) Load-amplitude coupling constraint In high load working conditions, in order to avoid the simultaneous occurrence of extreme amplitude and rated load, a linear envelope can be set: where, , is an empirical coefficient, used to adjust the weight of load and amplitude; is the envelope upper limit, which is set according to the structural limit state. This constraint can prevent the use of too high dynamic load amplification at high load, and ensure that the combination in the evaluation domain meets the structural bearing safety logic.

[0038] ii) Temperature-elastic modulus correction constraint The material elastic modulus E changes with the temperature gradient , which can be linearly corrected as follows: where, is the nominal elastic modulus at the reference temperature; is the cross-section temperature gradient; is the temperature sensitivity coefficient. In high temperature difference environment, the upper limit of elastic modulus is automatically tightened to avoid the risk of high stress caused by ignoring the temperature softening effect.

[0039] iii) Wind load-amplitude coupling constraint The wind load factor of the main beam and the deflection amplitude of the main beam A linear constraint is set between them: where, is the coupling coefficient; is the maximum deflection of the main beam under wind load (obtained by alternative model prediction); is the wind load safety threshold of structure deformation. The above constraint can prevent the extreme combination of large wind and large deflection from occurring at the same time, and enhance the conservatism of reliability evaluation under wind load.

[0040] iv) Sensor bias coupling constraint For multi-channel sensors, limit the sum of their biases to avoid the maximum bias from occurring simultaneously in multiple measurements: where, is the maximum allowed value of the bias sum. The above constraint can ensure that the measurement deviation of multiple channels will not be amplified at the same time, avoiding misjudgment of the worst case.

[0041] In this embodiment, the above linear inequalities are summarized to form a matrix form ; where, ; .

[0042] S2.5: Combination of convex sets Take the intersection of the three types of constraints to get the final uncertainty domain , .

[0043] Uncertainty domain The combined convex set takes into account the upper and lower limits of the parameters, statistical correlation and physical coupling, forming a reliable evaluation domain that is both conservative and flexible, which is beneficial for subsequent analysis of the worst case.

[0044] S3: Based on the finite element method and combined with the surrogate model, construct the response mapping of the key section set of the main beam, get the equivalent stress and deflection ratio with respect to the respective allowed values, take the larger one of the two ratios at any key section as the limit criterion for that section, and take the most unfavorable criterion among all key sections as the overall limit criterion; Specifically includes the following steps: S3.1: Determine a set of key sections of the main beam at key positions ; Key positions include midspan, load application point, suspension point and support point, etc.; Cover the most sensitive areas of the main beam to ensure that reliability evaluation can find the weakest point.

[0045] S3.2: Calculate the equivalent stress and deflection of each section under the parameter vector , and get and based on the sample points trained surrogate model, and use leave-one-out cross-validation to evaluate the maximum absolute prediction error , and guarantee that for any , any cross-section has , ; specifically including: S3.21: Utilize Latin hypercube design to generate K groups of training samples in the parameter vector space , where , , is the dimension of the parameter vector; S3.22: For each sample point , utilize the finite element model of the girder to solve the equivalent stress and deflection responses at each cross-section under different input parameter conditions,

[0046] S3.23: Construct stress radial basis function surrogate model: where is the weight coefficient determined by least squares method, is the input parameter of the current solving point, represents the training sample point, is the kernel width hyperparameter of the stress model; S3.24: Deflection radial basis function surrogate model:

[0047] where is the weight coefficient determined by least squares method, is the input parameter of the current solving point, represents the training sample point, is the kernel width hyperparameter of the deflection model; S3.25: Use leave-one-out cross-validation (LOOCV) to evaluate the maximum absolute prediction error of the two surrogate models, respectively calculating:

[0048] and guarantee that for any , any cross-section has , .

[0049] By constructing independent radial basis surrogate models for stress and deflection respectively, and determining the maximum error of each through leave-one-out cross-validation, not only does this significantly reduce the computational overhead of repeated solving of physical models, but also ensures the conservatism of surrogate model prediction and the consistency of reliability assessment.

[0050] S3.3: For each section Define the normalized over-limit as: where, is the allowable stress of the section, is the allowable deflection of the section; and are the stress and deflection predicted by the surrogate model of the section respectively. S3.4: Take the most unfavorable one among all section criteria to form: ; where, if , it is determined that the specification limit is satisfied.

[0051] In this embodiment, step S3.4 is specifically as follows: The global limit function is defined as the supremum of all section over-limits:

[0052] If , it is determined that the main beam satisfies the specification requirement under the parameter combination ; if , it is determined that there is an over-limit risk. Since is a convex function for , the global limit function is also a convex function, which guarantees the global optimality solvability of the subsequent worst-case optimization problem. By uniformly converting the dual restrictions of stress and deflection into a single numerical index, it is convenient for subsequent worst-case analysis.

[0053] S4: Worst-case search is performed on the global limit criterion in the combined convex set uncertainty domain, the maximum value of the criterion in the uncertainty domain is obtained as the worst-case value, and the opposite of the worst-case value is defined as the non-probabilistic reliability index; specifically including the following steps: S4.1: Perform piecewise linear outer approximation on the global limit function at the nominal parameter point , to obtain: ; wherein, is the tangent plane index set of the section ; is the gradient vector calculated at the sampling point ; is the intercept; by converting the complex nonlinear limit function into a convex cone outer approximation of multiple facets, it is convenient to embed convex optimization, and the conservativeness to the worst case is maintained.

[0054] S4.2: The limit function after outer approximation is uniformly expressed as and introduce an auxiliary variable t to construct a convex optimization problem: maximize subject to for all tangent planes; meanwhile satisfy the constraints of the uncertainty domain . The resulting optimization problem is a second-order cone programming, which can be solved by general convex optimization solvers, ensuring global optimality and reproducibility.

[0055] S4.3: Solve the optimization problem to obtain the optimal value and define the non-probabilistic reliability index as the negative of ; where indicates that there is still a safety margin within the entire uncertainty domain; indicates that it is at the limit boundary; indicates that there is an overrun risk, and its absolute value represents the overrun degree of the worst case. By measuring the global worst safety margin with a single scalar, the structural reliability is intuitively reflected, facilitating threshold classification and decision-making.

[0056] S4.4: Update the nominal point to the worst parameter combination obtained in this round of optimization (i.e., u when t reaches the optimal value), and then repeat the outer approximation and solving process (i.e., steps S4.1~S4.3) until the optimal value t* converges, ensuring that the evaluation result is closer to the true worst case while keeping the computational load controllable.

[0057] S5: Calculate the non-probabilistic reliability index at the section layer and the main beam layer respectively, where the main beam layer index takes the minimum value of each key section index, and the main beam reliability state is classified according to the preset threshold, outputting the evaluation results including reliability index, most dangerous parameter combination, weakest section position, and disposal suggestions; specific steps include: S5.1: For each key section , find the parameter combination that maximizes the normalized overrun degree within the uncertainty domain , and take the negative of this maximum overrun degree as the non-probabilistic reliability index of the section; S5.2: Take the minimum value of all section-level non-probabilistic reliability indexes as the overall non-probabilistic reliability index of the main beam, reflecting the safety margin of the weakest section; S5.3: Predefine two thresholds , where ; when , it is determined to be safe; when , it is determined to be attention level; when When the result is greater than 1, it is determined as the alert level; when the result is greater than 2, it is determined as the overrun level. When the result is greater than 1, it is determined as the alert level; when the result is greater than 2, it is determined as the overrun level. S5.4: outputting the main beam overall non-probabilistic reliability index, the weakest section position (i.e. the section position corresponding to the minimum section level non-probabilistic reliability index , the parameter combination leading to the most unfavorable criterion (i.e. the most dangerous parameter combination) and the corresponding treatment suggestion; the treatment suggestion includes load limiting, amplitude limiting, retesting, maintenance reinforcement, etc.

[0058] In summary, by introducing the convex set non-probabilistic modeling, alternative model prediction and convex optimization solving and other technical means, the present application realizes the rapid and graded safety evaluation of the crane main beam in the case of lacking statistical distribution information, and has strong engineering applicability and popularization value.

[0059] Embodiment 2 Referring to the accompanying drawings Figure 2 Based on the same inventive concept, the present embodiment provides a computer readable storage medium, which stores computer instructions, and when the computer instructions run on a computer, the computer executes the crane main beam non-probabilistic reliability evaluation method based on the convex set model as in embodiment 1.

[0060] In the specific implementation process, the computer readable storage medium includes: a universal serial bus flash drive (USB), a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk and various storage media that can store program codes.

[0061] The device embodiments described above are only schematic, wherein the units / modules illustrated as separate components can or can not be physically separated, and the components illustrated as units / modules can or can not be physical units / modules, i.e. can be located in one place or distributed on multiple network units / modules. Part or all of the modules can be selected to achieve the purpose of the present embodiment scheme according to actual needs. Those skilled in the art can understand and implement it without creative labor.

[0062] Those skilled in the art can clearly understand the implementation of the various embodiments by means of software and necessary general hardware platforms through the description of the above embodiments, and of course, the various embodiments can also be implemented by hardware. Based on such understanding, the above technical solutions can be embodied in the form of a software product, and the computer software product can be stored in a computer readable storage medium, such as a ROM / RAM, a magnetic disk, an optical disk, etc., and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods of the various embodiments or some parts of the embodiments.

[0063] The above only describes some embodiments of the present application, and does not limit the protection scope of the present application, and any equivalent device or equivalent process transformation made by using the content of the present application specification and drawings, or directly or indirectly applied to other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A method for evaluating non-probabilistic reliability of a crane girder based on a convex set model, characterized in that, Comprise: S1: Obtain the working condition data of the crane and the multi-source sensor data arranged at the key sections of the main girder, time align, compensate for missing data and extract time-frequency features at a uniform time step to obtain normalized state feature sequences for evaluation; S2: Select a parameter vector that affects the safety of the main girder, and model the uncertainty of the parameter vector as a combined convex set uncertainty domain, which is composed of the intersection of the following three types of constraints: one is an interval box constraint, which means that the value of each parameter is located between the preset upper and lower limits; the second is an ellipsoid set constraint, which is used to reflect the correlation between parameters and is determined by the mean vector, the covariance matrix and the radius parameter; the third is a polyhedral linear constraint, which is used to express the linear inequality relationship between the working condition and the load coupling and the mechanical consistency; S3: Based on the finite element method and combined with the surrogate model, a response mapping of the key section set of the main girder is constructed, the equivalent stress and deflection are obtained with respect to the respective allowable values, and the larger one of the two proportions is taken as the limit criterion for any key section, and the most unfavorable criterion among all key sections is taken as the overall limit criterion; S4: Search for the worst case of the overall limit criterion in the combined convex set uncertainty domain, obtain the maximum value of the criterion in the uncertainty domain as the worst case value, and define the inverse of the worst case value as the non-probabilistic reliability index; S5: Calculate the non-probabilistic reliability index at the section layer and the main girder layer respectively, wherein the main girder layer index takes the minimum value of each key section index, and the main girder reliability state is classified according to a preset threshold, and the evaluation results including the reliability index, the most dangerous parameter combination, the weakest section position and the disposal suggestion are output.

2. The convex set model based crane girder non-probabilistic reliability assessment method according to claim 1, characterized in that, Step S1 comprises the following steps: S1.1: Based on sampling period Collect PLC operating data of the crane to obtain the lifting height. Walking speed Car speed Actual load and braking state Discrete sequences; S1.2: Strain gauges, accelerometers, displacement meters and thermometers are arranged at key sections of the main girder with a sampling frequency of Obtaining multi-source high-frequency sensor signals , ; wherein, is the original observation value of the i-th sensor at the n-th sampling point, is the total number of sensor channels, is the number of sampling points; S1.3: Define master time grid , , is the number of PLC data points; map high frequency signal to aligned data by linear interpolation , is the signal value of the i-th interpolated path at time ; S1.4: to the aligned signal The missing data is compensated and the noise is smoothed by Kalman filter to obtain the filtered reconstructed signal ; S1.5: on the reconstructed signal The short-time Fourier transform is performed over a sliding window of length L and the amplitude spectrum statistics are extracted over a frequency band forming a time-frequency feature vector ; S1.6: Concatenate all time-frequency features with low frequency operating quantities to form feature vectors and perform normalization using Z-score method to get The expression is as follows: ； wherein, with are the historical mean and standard deviation of the jth feature, respectively, and d is the dimension of the feature vector.

3. The convex set model based crane girder non-probabilistic reliability assessment method according to claim 1, characterized in that, Step S2 comprises the following steps: S2.1: Constructing the parameter vector influencing the reliability of the main girder : ； wherein Q is the actual load, is the dynamic load coefficient; is the main girder wind load factor, ; E is the material elastic modulus; is the material yield strength; is the thickness of the i-th plate, a total of m plates; is the main girder cross-section temperature gradient; is the i-th road sensor measurement bias, ; S2.2: Construct an interval box uncertainty set ； wherein l and are lower and upper limit vectors for each parameter, respectively; S2.3: Construct an ellipsoid uncertainty set ； wherein, wherein is a parameter mean vector, is a covariance matrix, is a Mahalanobis distance radius; S2.4: Construct a polyhedral linear constraint set ； where A is a coefficient matrix and d is an upper bound vector; the at least includes the following linear constraints; i) Load-amplitude coupling constraint ； wherein, , is an empirical coefficient used to adjust the weight of the load and the amplitude; is an upper limit of the envelope, set according to the structural limit state; ii) Temperature-elastic modulus correction constraint ； wherein, E0is the nominal elastic modulus at reference temperature; G0is the temperature gradient of the cross section; β is the temperature sensitivity coefficient; iii) Wind load-amplitude coupling constraint ； wherein, is the coupling coefficient; is the maximum deflection of the main girder under wind load; is the wind load-structure deformation safety limit value; iv) Sensor bias coupling constraint ； wherein is the maximum allowed value of the bias sum; S2.5: Combined convex set construction The intersection of the three types of constraints is taken to obtain the final uncertainty region , .

4. The convex set model based crane girder non-probabilistic reliability assessment method according to claim 1, characterized in that, Step S3 comprises the following steps: S3.1: Determine a set of main girder critical section set at critical locations ; the critical locations include mid-span of main girder, near load action point, near lifting point and near support S3.2: Train surrogate models for equivalent stress and deflection of each section based on the parameter vector The equivalent stress and deflection of each section are calculated and based on the sample points, surrogate models are trained to obtain and The maximum absolute prediction error of the two surrogate models is evaluated using leave-one-out cross-validation , and it is guaranteed that for any , any section has , ; S3.3: For each section Define the normalized upper limit: ； wherein, is the allowable stress for the cross section, is the allowable deflection for the cross section; and are the stress and deflection, respectively, predicted by the alternative model for the cross section . S3.4: Take the most unfavorable one of all section criteria to form: ； wherein, when the specification limit is satisfied.

5. The convex set model based crane girder non-probabilistic reliability assessment method according to claim 4, characterized in that, Step S3.2 specifically comprises the following steps: S3.21: Utilizing a Latin hypercube design, K sets of training samples are generated in the parameter vector space where , is the dimension of the parameter vector.​ S3.22: For each sample point , the finite element model of the girder is used to solve the equivalent stress and deflection responses at each cross section of the structure under different input parameters, S3.23: Construct a stress radial basis function surrogate model: ； wherein, is a weight coefficient determined by the least square method, is an input parameter of the current solving point, denotes a training sample point, is a kernel width hyperparameter of the stress model; S3.24: Deflection radial basis function surrogate model: ； wherein, is a weight coefficient determined by the least square method, is an input parameter of the current solution point, denotes a training sample point, is a kernel width hyperparameter of the deflection model; S3.25: Evaluate the maximum absolute prediction error of the two surrogate models using leave-one-out cross-validation, and calculate: ； ； to ensure that for any , any cross section has , .

6. The convex set model based crane girder non-probabilistic reliability assessment method according to claim 4, characterized in that, Step S3.4 is specifically as follows: The global limit function is defined as the upper bound of all cross section excesses: when When, it is determined that the main beam is in the parameter combination The following meets the specification requirements; when If so, it is determined that there is a risk of exceeding the limit.

7. The convex set model based crane girder non-probabilistic reliability assessment method according to claim 1, characterized in that, Step S4 comprises the following steps: S4.1: At the nominal parameter point Limit function of the whole By performing piecewise linear external approximation, we obtain: ;in, Section The set of tangent plane indices; For sampling points The calculated gradient vector; The intercept; S4.2: The limit function after the outer approximation is uniformly expressed as and introduce an auxiliary variable t to construct a convex optimization problem: maximize such that for all tangent planes ; while satisfying the constraints of the uncertainty region ​ S4.3: solving the optimization problem to obtain the optimal value and define a non-probabilistic reliability index as the reciprocal of indicates that there is still safety margin within the entire uncertainty domain; indicates that it is on the limit boundary; indicates that there is an overrun risk, and its absolute value represents the overrun degree of the worst case.

8. The convex set model based crane girder non-probabilistic reliability assessment method according to claim 7, characterized in that, Step S4 further comprises: S4.4: Update the nominal point to the worst parameter combination obtained by the current optimization, and then repeat the outer approximation and solution process until the optimal value t* converges.

9. The convex set model based crane girder non-probabilistic reliability assessment method according to claim 1, characterized in that, Step S5 comprises the following steps: S5.1: For each critical section , find the maximum parameter combination in the uncertain domain that normalizes the section beyond the limit , and take the inverse of the maximum excess as the non-probabilistic reliability index of the section ; S5.2: Take the minimum value of all section-level non-probabilistic reliability indices as the overall non-probabilistic reliability index of the main beam Take the minimum value as the overall non-probabilistic reliability index of the main beam to reflect the safety margin of the weakest section; S5.3: preset two thresholds wherein when a safety level is determined; when a concern level is determined; when a warning level is determined; and when an out-of-limit level is determined. S5.4: Output the main girder overall non-probabilistic reliability index, the weakest section position, the parameter combination leading to the most unfavorable criterion and the corresponding disposal suggestion; the disposal suggestion includes load limiting, amplitude limiting, retesting, maintenance and reinforcement.

10. A computer readable storage medium characterized by: The storage medium stores at least one instruction, at least one program, a code set or an instruction set, and the at least one instruction, the at least one program, the code set or the instruction set are loaded and executed by the processor to realize the crane girder non-probabilistic reliability evaluation method based on the convex set model.

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