How tot search Elasticsearch-rails with associtaion model conditions?

I'm trying to search Doc model has_and_belongs_to_many projects which belongs to specific project.

models/doc.rb require 'elasticsearch/model'

class Doc < ActiveRecord::Base
  include Elasticsearch::Model
  include Elasticsearch::Model::Callbacks

  settings index: {
    analysis: {
      tokenizer: {
        ngram_tokenizer: {
          type: "nGram",
          min_gram: "2",
          max_gram: "3",
          token_chars: [
            "letter",
            "digit",
            "punctuation"
          ]
        }
      },
      analyzer: {
        ngram_analyzer: {
          tokenizer: "ngram_tokenizer"
        }
      },
    },
  } do
      mappings do
        indexes :sourcedb, type: 'string', analyzer: 'ngram_analyzer'
        indexes :sourceid, type: 'string', analyzer: 'ngram_analyzer'
        indexes :body, type: 'string', analyzer: 'ngram_analyzer'
        indexes :docs_projects do
          indexes :doc_id
          indexes :project_id
          indexes :projects do
            indexes :id, index: :not_analyzed
          end
        end
      end
  end

  def as_indexed_json(options={})
    as_json(
      only: [:id, :sourcedb, :sourceid, :body],
      include: { projects: {only: :id} }  
    )
  end
end

search method is below

  search_docs = docs.search(
    query: {
      bool:{
        must: [
          {match: {
              'projects.id' => project_id
            }
          }
        ]
      }
    },
    size: 5000,
  ).records.order('sourcedb ASC, sourceid ASC').paginate(page:params[:page], per_page: 10)

This search method finishes without errors but nothing returned.

  Doc Load (4.6ms)  SELECT "docs".* FROM "docs" INNER JOIN "docs_projects" ON "docs"."id" = "docs_projects"."doc_id" WHERE "docs_projects"."project_id" = 56
   (0.4ms)  SELECT COUNT(*) FROM "docs" WHERE 1=0
  Doc Load (0.3ms)  SELECT "docs".* FROM "docs" WHERE 1=0 ORDER BY sourcedb ASC, sourceid ASC LIMIT 10 OFFSET 0
  CACHE (0.0ms)  SELECT COUNT(*) FROM "docs" WHERE 1=0

I've tried to search with where([projects.id IN (?)], project_ids), but it cannot search docs belongs to project with max size.
How to search by match with associations?
Thanks in advance.