Pandas 如何基于多个条件子字符串搜索语句创建新的dataframe值列？

我有一个包含许多产品描述的数据框架。我想做的是创建多个条件语句来搜索产品描述，并用结构化详细信息标记一个新列。有什么好办法吗？将有许多条件语句

这将是起始表

df = pd.DataFrame({"product_description": ['nike running shoes','nike football cleats','nike baseball mitt','adidas run shoes','brooks sprint spikes'], "brand": ['Nike','Nike','nike','adidas','brooks']})

在本例中，我的条件将搜索部分字符串（不区分大小写）-请原谅非实际代码：

if ('run' | 'sprint' ) & ('shoes' | 'cleats' | 'spikes') are found in df['product_description'], then write to df['subproduct'] = "running shoes"  
if ('football' ) & ('shoes' | 'cleats' | 'spikes') are found in df['product_description'], then write to df['subproduct'] = "football shoes"  

因此，生成的表将是

product_description    brand   subproduct
nike running shoes     Nike    running shoes
nike football cleats   Nike    football shoes
nike baseball mitt     nike    
adidas run shoes       adidas  running shoes
brooks sprint spikes   brooks  running shoes