mongodb update多层嵌套数组

This is more or less my current schema:

{ "_id" : 1
"user_id": 1,
"message" : "Yes"
"translations" : [
{
"destination" : "fr",
"text": "Oui",
"rating" : [
{ "user_id" : 1,
"rating" : 1
},
{ "user_id" : 2,
"rating" : 1
}
]
}
]
}

db.getCollection('message').update({
'_id': 1,
'translations.destination': 'fr',
'translations.rating.user_id':'1'
},
{
'$set': {
"translations.$.rating.$.rating": 5
}
}

{ "_id" : 1
"user_id": 1,
"message" : "Yes"
"translations" : {
"fr": {
"destination" : "fr",
"text": "Oui",
"rating" : [
{ "user_id" : 1,
"rating" : 1
},
{ "user_id" : 2,
"rating" : 1
}
}
},
"en": {...}
]
}

“translations.fr.rating.$.rating”: 5