I want to elaborate on my previous answer in response to one of your comment, but have too much to say to put in a single comment. As you can probably tell, I feel passionate about the subject matter; however you should feel completely free to ignore all of these ramblings if they go beyond what you are actually interested in or if your passion does not match mine.
Modern "grammatical" terminology has its ultimate roots in terms originally designed to describe classical Greek and to reflect specific traditions of Aristotelian logic and predicate logic; however, linguists, as opposed to traditional grammarians, have come to realize that that approach has many aspects that are inappropriate to describe some languages that are structurally unlike classical Greek.
Some linguistics even reject that the dichotomy of subject and predicate is fundamental to language analysis and think this idea arose from early linguists unconsciously biased by native languages that happened to be grounded in this dichotomy. Topic-comment structure is an example of one of these new realizations that is now widely accepted by modern linguists and applied to many languages.
The topic-comment structure doesn't apply only to Chinese, but is helpful in describing aspects of many languages. That structure can even describe some aspects of classical Greek despite its structure of subjects and predicates. In the case of classical and modern Chinese, however, topics-comment structure is not just helpful, but fundamental.
Consider the beginning of one version of the Tai Chi Chuan/Taijiquan Treatise of Wang Zongyue (太极拳论), one of the "Tai Chi classics." (I am using the version from Fu Zhongwen's book Mastering Yang Style Taijiquan translated by Louis Swaim:
Taiji, being born of Wuji, is the mother of yin and yang. In movement, it differentiates; in stillness it consolidates. It is
without excess or insufficiency. Follow, bend, then extend.
I would argue that there is no grammatical subject or even thematic agent stated anywhere in the Chinese; however, the particle 者 unambiguously marks 太極 ("Taji"/"Tai Chi") as the topic of the first sentence. According to the syntax of classical Chinese, 太極 ("Taji"/"Tai Chi") will continue to be the default topic of all subsequent "sentences" until replaced by something else. Other sentences, however, can also have different subtopics. How Chinese handles the identification of topics and subtopics is something linguistics have now begun to study and understand better.
To me, the structure and syntax of the Chinese is simple and clear, but utterly unlike what is necessary for English sentences.
When you translate the sentences into English, you have to add in subjects and predicates. You have to segment the text according to English syntax, which requires a more hypotactic structure than Chinese. An English sentence is actually not quite the same unit as a Chinese sentence, and so you have to make choices about how to relate the sentences to each other. Chinese is syntactically vaguer, relying on discourse relationships to make the relationships clear. You also have to make decisions about what tenses and moods to use, since again Chinese does not make such distinctions.
Because of this vast difference in syntax between the languages, you could translate the English very differently, for instance, replacing all the instances of "it" with "you" and changing all the statements to commands and vice versa. These differences would appear to change the meaning, but actually, these are just quirks of English syntax that handle discourse relationships quite differently from Chinese. In classical Chinese, specifying subjects, agents, tense, and mood is often unnecessary and often inappropriate for general statements of principle, such as this one is.
I have used this long comment to explain further why the analysis of sentences like 沛公军霸上 and 陨石于宋五 becomes very awkward if we rely only on terms like "subject" and "predicate" developed to describe languages like English. It turns out that the concepts of "topics," "agents," and "patients" are probably more fundamental to all languages, and concepts of "subjects," "predicates," and "active and passive verbs" are merely one way to grammaticalize these relationships in a particular way. Chinese remains structured around "topics" and "comments" and does not grammaticalize things like "subjects," "predicates," "moods," "voice," "tense," and other grammatical features prominent in English and similar languages.