The study introduced a finite element model of DQ75t-28m bridge crane metal structure and made finite element static analysis to obtain the stress response of the dangerous point of metal structure in the most extreme condition. The simulated samples of the random variable and the stress of the dangerous point were successfully obtained through the orthogonal design. Then, we utilized BP neural network nonlinear mapping function trains to get the explicit expression of stress in response to the random variable. Combined with random perturbation theory and first-order second-moment (FOSM) method, the study analyzed the reliability and its sensitivity of metal structure. In conclusion, we established a novel method for accurately quantitative analysis and design of bridge crane metal structure.
Bridge crane metal structure is significant in the bridge crane to host, tract, walk, and brake, which is the most critical part of the performance to determine its safety. As the stability and reliability of metal structure is the guarantee of the entire system, its corresponding analysis, therefore, is crucial before the application [
The study introduced a finite element model of bridge crane metal structure and then applied finite element simulation and orthogonal experimental design to obtain the dangerous parts and stress response in the most extreme condition. We utilized BP neural network fitting technology to get an explicit expression of the stress on the design variables. Besides, random perturbation theory and FOSM method were used for the reliability analysis. The matrix differential technology further contributed to deduce the influence degree of various random parameters on the reliability of the bridge crane metal structure.
ANSYS parametric design language (APDL) was used to establish the finite element model of bridge crane metal structure (Figure
Finite element model of bridge crane metal structure.
We applied finite element analysis software ANSYS to simulate and analyze the metal structure of bridge crane. The stress response in the most severe operating conditions was obtained (Figure
Stress nephogram of metal structure under full-load condition.
Since the metal structure of bridge machine is an extremely complex box structure, the function of stress and random design variables is a highly nonlinear and implicit. Therefore, we utilized the orthogonal experimental design method and finite element simulation to get sample data. Then, we combined the BP neural network technology to map the relationship between structure design variables and stress values in dangerous parts, fitting to acquire their explicit expression [
The study applied orthogonal experimental design method to establish the reasonable quantity and distribution of neural network training samples to accurately express the mapping relationship of neural network model. According to the reliability theory, we selected the simulated full-load condition as the object and obtained the data of random variable as well as the stress response (Table
Random variable and its statistical properties of bridge crane metal structure.
Random variable (factors) | Meaning | Average | Standard deviation |
---|---|---|---|
|
Lifting load | 250 | 20 |
|
Main beam height | 8155 | 366 |
|
Main beam width | 4108 | 207 |
|
Elastic modulus | 206 | 10 |
|
Upper and lower flange plate thickness | 14 | 4.2 |
|
Main, vice web thickness | 12 | 2.5 |
The output samples of stress response of dangerous parts could be gained through the experimental design. It would be further used as the training samples of BP neural network to eventually fit required explicit expressions:
Training samples of the neural network model was obtained by using the orthogonal table
Orthogonal factors and the level.
Level |
|
|
|
|
|
|
---|---|---|---|---|---|---|
1 | 230 | 8000 | 3800 | 196 | 11 | 6 |
2 | 240 | 8100 | 3900 | 201 | 12 | 7 |
3 | 250 | 8200 | 4000 | 206 | 13 | 8 |
4 | 260 | 8300 | 4100 | 211 | 14 | 9 |
5 | 270 | 8400 | 4200 | 216 | 15 | 10 |
For the 6 random variables of bridge crane metal structure system, BP neural network input layer had 6 neurons and the hidden layer had 15 neurons. Each neuron of the output layer was described as the stress response of the bridge crane metal structure.
To get the stress response neural network model of the global significance, each random variable in its feasible region took 5 discrete values (horizontal) and generated 25 design samples as the training set by the combination of orthogonal test. Then, finite element simulation experiments were carried out on all samples by ANSYS software.
After the model structure of BP neural network was determined, the toolbox (NNET Toolbox) of MATLB was used in training the network using the input sample set and the output sample set to achieve a given input-output mapping relationship and further correct the thresholds and weights of the network [
Some neurons reached saturation due to the large difference in the magnitude of each variable in the original sample. As a result, the input samples should be normalized first and then selected the neurons pass for hidden layer and output layer as tansig() and purelin(), respectively [
Typically, the training patterns included in the training set are only part of the source data set. Even if the network was trained by all the patterns within the training set, it also could not guarantee that the test by another mode could give satisfactory results. Therefore, the generalization ability of fitting functions of 25 new samples, as a test set, is still needed to be examined after the network learning. From the result of test error (Figure
Relative error of BP neural network fitted model.
In addition, the convergence of the neural network training was demonstrated (Figure
Grid training convergence curve.
A set of basic random variables
when
Based on the perturbation theory,
Based on the FOSM method and matrix differential, the mean and variance sensitivity of the metal structure reliability to each random variable are expressed as follows:
According to formula (
Variance sensitivity is as follows:
It can be drawn from the sensitivity matrix of
The study applied the neural network technology and orthogonal experimental design method to solve the reliability calculation with the implicit limit state function and to obtain the explicit expression of the random variable and the stress response of bridge crane metal structure. The integrated use of orthogonal experimental design method and finite element simulation test in the reliability analysis engineering can significantly reduce the design costs and markedly shorten the cycle. Based on the theory of reliability design and sensitivity, we made a derivation analysis of the reliability and its sensitivity and then established a basis for accurately quantitative analysis of the reliability of bridge crane metal structure.
The project is supported by the Natural Science Foundation Committee (51075289); National Natural Science Foundation International Cooperation and Exchanges Project (51110105011); 2012 Higher School Specialized Research Fund for the Doctoral Program Joint Funding Issues (20121415110004); Research Foundation for Returning Scholar in 2009 of Shanxi province (20091074); International Scientific and Technological Cooperation Projects in 2010 of Shanxi province (2010081039); Shanxi Natural Science Foundation (2011011019-3); 2010 Scientific Star Project in Taiyuan city (2010011605); 2009 Shanxi province Graduates’ Excellent and Innovative Project (20093099); Shanxi province 2011 UIT Item, TYUST 2010 UIT Item (201008X); Doctor Start up Item and Characteristics & Leading Academic Discipline Project of Universities of Shanxi Province.