“广义否定结构”的说法好像是柯林斯系列辞书的专用术语。我在《柯林斯高级英语用法词典》上找到了“广义否定词”的相关描述，引用如下（英汉对照）：

Broad negatives广义否定词

A broad negative is one of a small group of words which are used to make a statement almost negative. 

广义否定词（broad negatives）指使陈述句变成几乎是否定句的一小组词。

We were scarcely able to move.  我们几乎不能移动。

Fathers and sons very seldom now go together to football matches.  = 现在，父亲和儿子很少一起参加橄榄球赛了。

The five broad negatives are: barely, hardly, rarely, scarcely, seldom 

五个广义否定词：barely, hardly, rarely, scarcely, seldom

If you want to say that there is very little of something, you can use a broad negative with “any” or with a word which begins with “any-”. 

表示“几乎没有一点”，可以用一个广义否定词加上有any或开头带有any-的词。

There is rarely any difficulty in finding enough food.  要找到足够的食物几乎没什么困难。

Hardly anybody came.  简直没什么人来。

Instead of using a broad negative, you can use “almost” followed by a negative word such as “no” or “never”. For example, “There was almost no food left” means the same as “There was hardly any food left”. 

可以用almost加上no或never这样的否定词来代替广义否定词。例如：There was almost no food left. 和 There was hardly any food left.的意思是一样的。

They’ve almost no money for anything.  他们几乎没有钱买东西了。

Men almost never begin conversations.  男人们几乎从来不开始交谈。

If you make a tag question out of a statement that contains a broad negative, the tag at the end of the statement is normally positive, as it is with other negatives. 

在包含广义否定词的陈述句后，反意疑问句一般是肯定的。

She’s hardly the right person for the job, is she?  她不是这项工作的合适人选，对吗？

You seldom see that sort of thing these days, do you?  这些天你很少能见到那种东西了，是吗？