## 1 Introduction
The construction of the surrogate model can be divided into two stages, namely the initial modelling and subsequent update. In the first phase, the initial sample can be generated via Latin hypercube sampling or other methods, supporting the modelling. Afterwards, samples of great significance will be gradually added to the initial sample referring to the principle of different points, accomplishing the update of the surrogate model. Regarding the traditional Kriging model, it possesses advantages compared with other surrogate models, such as quadratic polynomials, in several cases. However, the analysis result might be worse than that if the calculation of weight coefficient is imprecise, that is, the accurate calculation of the weight coefficient is crucial for the reliability analysis within Kriging model. Furthermore, its computational efficiency is inherently constrained by the iterative process that discards all sample points, limiting further enhancement. In contrast, the single-step approach to agent model construction, which involves selecting the training set from the input variable space in a single instance, intuitively suggests an improvement in model accuracy with an increased number of sample points. However, empirical findings indicate that for low-dimensional scenarios, once the training point count reaches a threshold, further augmentation of sample points does not significantly enhance the constructed agent model. To overcome the mentioned issue, the adaptive surrogate model method comes into being. It adaptively screens training sample points via learning functions and convergence criteria, and then improves model accuracy through a multi-step iteration strategy. Common learning functions comprise U [35] and H [36], EFF [37], EGO [38], CCL [39], etc. Motivated by pulling the aforementioned gaps, this paper devises a multi-performance reliability evaluation approach for complicated mechanical systems based on the surrogate model with cluster mixing weight, which produces several contributions in practical engineering, the surrogate model and performance-based reliability analysis, summarized as follows:  
* Devising a multi-performance reliability analysis algorithm appropriate for complicated mechanical assets with various failure modes;* Promoting efficiency in balancing the calculation cost and accuracy of the proposed cluster surrogate model to a great extent;
* Generating a mixing weight channel to investigate the different contributions to overall reliability corresponding to diverse practical engineering scenarios. In detail, the particle swarm algorithm is employed to optimize relevant parameters, avoiding the local optimality. This method avoids redundant information via preserving existing high-value test points through sample inheritance, which utilizes a cluster-based active learning strategy in selecting multiple high-value test points in each iteration to expand the test point set, achieving rapid convergence. Then, the convergent surrogate model is combined with the importance sampling method to calculate the reliability, and the weight importance sampling function is constructed to predict the failure probability. This paper utilizes a surrogate model based on the Kriging method to fit implicit reliability issues, which could greatly improve computing efficiency and reduce computing costs. The remainder of the paper is organized as follows. Section 2 introduces the learning function definition and convergence criteria in the surrogate model construction. A brief introduction of mixing weight importance sampling is presented in Section 3. The proposed algorithm and application of reliability approaches are elaborated in Section 4. A numerical example as well as two engineering experiments are studied in Section 5 to demonstrate the applicability of the proposed approach. The conclusion is summarized in Section 6.