The working principle of the fabric spreading machine

Because complete probability information is generally impossible to obtain in industrial applications, the joint cumulative distribution function or the conditional cumulative distribution function can be approximated by using transformations. This analysis method is intuitive, simple, and convenient for calculation and application. However, since the spreading machine approximates near the design point, the accuracy of this method completely depends on the degree of approximation of the line function, so the precision is difficult to guarantee. The limitations of its application include: the variance or variation interval of the uncertain variable cannot be too large, and the nonlinearity degree of the system model cannot be too high; otherwise, the calculation accuracy will be greatly affected. Although there are the above deficiencies, considering the calculation of complex sum solution comprehensively, this method is still a practical and feasible one and has been widely applied in uncertain analysis. In specific engineering applications, high-order terms in Taylor expansion can be considered for introduction according to actual needs, thereby improving the accuracy of the distribution at the tail end of the prediction function.。

      The possible point method is different from the local expansion method. Although the possible point method also approximates through order or second-order Taylor expansion, it does not expand and approximate at the design point but at the possible point, which improves the accuracy of the probability distribution at the end of the function. It is mainly used based on reliable design. The concept of possible points was initially proposed in structural reliability, which are points with probability density on the finite state function. When conducting reliability and failure probability estimation, the possible point is a very important design point. In structural reliability, the system output is also called the finite state function. The failure surface or limit state is defined as, which is also the boundary between the region in the random variable space and the failure region. At that time, the structure was; At that time, the structure will fail. The solution of the multivariate integral in the above formula is very difficult, and the placing machine is usually not feasible in practice. The concept of possible points was proposed for approximating this multivariate integral. Possible points are defined in the vertical standard normal space. Input random variables, the original design space, and convert the space to the standard normal space. The commonly used conversion is the transformation, where is the inverse function of the normal cumulative distribution function. The above formula indicates that during the transformation, the values of the space and the corresponding cumulative probability distribution of the space are guaranteed to be equal. See. The solution to a minor problem is called a possible point. It can be seen from this that the probability value of the finite state function in the standard normal space exists. Short-distance β is also called exponential in reliable analysis. Thus, the feasibility of probability constraints is obtained by comparing the relationship between the reliability index √ and the target reliability index.