helper method to obtain a fragment cache key depending on the currently selected page on the refinery menu

_header.html.erb

.......
.......
<% cache menu_cache_key, expire_in: 1.day do %>
  <%= render(:partial => "/refinery/menu", :locals => {
   :css => 'submenu'
 }) %>
<% end %>
.......
.......

application_helper.rb

def menu_cache_key

  # We get the current page: @page or the first page which is
  current_cache_page = @page

  if @page.nil?
    path = request.path.sub("//", "/")
    path = path.force_encoding('utf-8') if path.respond_to?(:force_encoding)

    # Ensure we match the path without the locale, if present.
    if ::Refinery.i18n_enabled? and path =~ %r{^/#{::I18n.locale}/}
      path = path.split(%r{^/#{::I18n.locale}}).last
      path = "/" if path.blank?
    end

    current_cache_page = Refinery::Page.with_translations(::I18n::locale).where("menu_match IS NOT NULL AND menu_match != ''").detect{ |p| path =~ Regexp.new(p.menu_match) }
  end

  cache_key = "-#{current_cache_page.id}" unless current_cache_page.nil?
  cache_key = "refinery-menu-#{I18n.locale}#{cache_key}"

end

Added also a condition to check for non blank menu matches