Note that the dimension of the high-dimensional space may be arbitrarily large and can even be infinite, which ensures strong nonlinear mapping ability. Among these parameters, the range of the kernel parameter was a symmetrical expansion of the parameter value selected by the formula in [ 30 ]. The extracted component may not be the true environmental effect of dam response variables. All input variables are mapped to be in the high-dimensional space. Stop when , with being the selected number of latent variables.

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The phenomenon was also reflected when increasing the FDI. A multivariate fusion diagnosis method of the safety monitoring model is presented in Section 3.

## Translation of “KPls” in Russian

Multivariate fusion diagnosis of radial displacements in the test period. KPLS obtains the complex nonlinear relationship by a nonlinear mappingtwo linear mappingsand a linear regressionshown in Figure 1. Their corresponding measuring point positions are adjacent and there are strong correlations among the multiple response variables. From Figure 14we can speculate that there may be behavior adjustments in dam foundation and middle elevations of the super-high arch dam.

Then, OKPLS is used to establish a strongly nonlinear multivariate safety monitoring model to identify the abnormal behavior of a super-high dam via model multivariate fusion diagnosis.

The differences from the cross-validation selecting kernel parameters are as follows: In total, monitoring data samples were obtained by the pendulums from July 1,to December 31,as shown in Figure 9.

# #kpls hashtag on Instagram • Photos and Videos

In fact, cross-validation only gives an index evaluating the expected risk of one model, for example, the above-described PRESS. KPLS is equivalent kppls constructing a linear PLS regression model between andwhich can be expressed as where is a matrix of the regression coefficients; is a matrix of residuals.

Calculate the matrix of the regression coefficients using the modified KPLS algorithm. Therefore, the algorithm design of the outer and inner loops can reduce the computational cost of selecting the optimal KPLS parameters.

Furthermore, the optimization selection of the kernel parameters and the number of latent variables ensure that OKPLS correctly obtains the complex nonlinear relationship.

In addition, thanks are due to Professor Chongshi Gu for giving great help in writing this paper. The selection method of the kpld is not of general applicability and may not be optimal.

Establishing dam safety monitoring models involves obtaining the determined relationship between the environmental variables and the dam response variables according to the dam monitoring data without abnormalities. There are 5 crest overflow surface holes, 6 flood discharge middle holes, 2 escape bottom holes, 4 diversion middle holes, and 2 diversion bottom holes in the dam body. Therefore, it is urgent to research strongly nonlinear multivariate safety monitoring models appropriate for super-high dams.

When the fusion diagnosis index FDI is identified as being abnormal, great attention should be given. The corresponding monitoring control charts of the diagnosis method are shown in Kpld 4.

Hence, the obtained useful environmental and response components can best explain the behavior of a super-high dam. The outer loop optimizes the kernel parameters via a genetic algorithm. Currently, 51 super-high dams kkpls heights greater than meters exist worldwide, and another 31 super-high dams are under construction or are proposed for construction.

Dam safety monitoring is the process of identifying abnormal dam behavior according to inputs and outputs of the dam system.

## SITE SAFETY

Next, OKPLS is used to establish a strongly nonlinear multivariate safety monitoring model to monitor a super-high dam to ensure its safety. Because the kernel function and the number of latent variables in KPLS have strong influence on KPLS generalization performance, the universal unified optimization algorithm is designed to select the KPLS parameters and obtain the optimal kernel partial least squares.

Moreover, KPLS can handle a wide range of nonlinearities by using different types of kernel functions. The models forecast future dam response values according to the new values of the environmental variables and identify abnormal dam behavior by comparing the predicted values and the observed values. Super-high arch dam structure and the layout of the pendulum monitoring points. Among these points, 52 pendulum monitoring points are used to monitor the horizontal deformation of the dam body and the dam foundation, as shown in Figure 7.

Additionally, according to the principle of minor probability accident, the FDI probability distribution is first estimated, and then some control limits are set based on the probability distribution. Model diagnosis of dam behavior involves identifying the abnormal dam behavior by comparing the observed value and the predicted value of the safety monitoring model. During the same period, the observed values of the reservoir water level are also shown in Figure 9.

The excluded block is used for testing, and an individual predicted error sum of squares PRESS is calculated.