## 2 Materials and Methods  
In recent times, machine learning algorithms, including support vector machines and deep learning, have become prominent in capability evaluation problems [25]. Typically, machine learning models employ the loss function as the optimization objective for training model parameters [26; 27]. For capability evaluation, the cross-entropy loss function is predominantly used, as represented in (1).  
\[L_{CE}(p_{i},y_{i})=-{y_{i}}^{T}\text{log}(p_{i}) \tag{1}\]  
In this Equation, \(y_{i}\) represents the actual ability level of the \(i\)th sample, and \(p_{i}\) represents the predicted probability distribution generated by the competency evaluation model for the competency level of the \(i\)th sample.  
Before we delve into the details of the Weighted Adaptive Focus Loss (WAFL) function, it is essential to define the terms \"simple\", \"difficult\", and \"anomalous\" samples.  
**Definition 1**.: _Suppose that the capability characteristics of the \(i\)th sample are denoted by xi, and the true value of the capability level is represented by \(y_{i}\). The capability levels of the construction weather disaster emergency agency are categorized into five levels: AAA (very good capability), AA (good capability), A (better capability), BBB (average capability), and CCC (poor capability), respectively._\(y_{i}\) belongs to the set {AAA, AA, A, BBB, CCC}. For each \(y_{i}\), a One-Hot encoding method is used, utilizing a 5-bit status register to represent the 5 ability levels. Each level has its own independent register bit, and only one bit is valid at any given moment. The representation in One-Hot encoding is as follows:  
\[y_{i}\in\left\{[1,0,0,0,0]^{T},[0,1,0,0,0]^{T},[0,0,1,0,0]^{T},[0,0,0,1,0]^{T},[ 0,0,0,0,1]^{T}\right\}\]  
The predicted probability distribution of the ability levels is denoted by \(p_{i}\), given by:  
\[p_{i}=[P(y_{i}=[1,0,0,0,0]^{T}),P(y_{i}=[0,1,0,0,0]^{T}),P(y_{i}=[0,0,1,0,0]^{T }),P(y_{i}=[0,0,0,1,0]^{T}),P(y_{i}=[0,0,0,0,1]^{T})]^{T}.\]  
Assuming that the capability characteristics of the first sample are denoted by \(x_{i}\), the true value of the capability level is denoted by \(y_{i}\), and the predicted value of the capability level is denoted by \(p_{i}\), we define the following types of samples:  
1. Simple sample: a sample whose ability level can be easily discerned by the model, i.e., the sample whose predicted label value closely matches the true value. The closer the error \(|y_{i}-p_{i}|\) is to zero, the simpler the sample is.
2. Difficult samples: samples for which the model finds it hard to correctly determine the ability level, i.e., samples with predicted label values significantly differing from the true values. The larger the error \(|y_{i}-p_{i}|\), the more challenging the sample is.
3. Anomalous samples: extreme cases within the difficult samples, deviating significantly from the normal distribution, such that not even the optimal model can classify them correctly.  
The sample types are defined in Definition 1 based on the error in determining the ability levels. As illustrated, difficult samples vary significantly from both simple and abnormal samples. The existing loss function of the model is not tailored to address this subset of samples, resulting in a substantial classification error for them. If the loss function, as depicted in Equation (1), leads to a total loss dominated by a majority of high-ability-level samples, the ability evaluation model may find it challenging to distinguish between samples with lower ability levels. To address this, enhancing the loss function coupled with specific sampling techniques can facilitate the generation of simple samples from difficult ones, highlighting that difficult samples are not synonymous with abnormal samples.