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The phrase "according to established principles" is correct and usable in written English.
You can use it when referencing widely accepted rules or guidelines in a particular field or context.
Example: "According to established principles, all experiments must be conducted under controlled conditions to ensure valid results."
Alternatives: "in line with accepted standards" or "following recognized guidelines".
Exact(2)
The design of insulin analogues has emphasized stabilization or destabilization of structural elements according to established principles of protein folding.
Those findings were not valid, Dr. Sloan said, because the researchers had failed to analyze their data according to established principles of statistics.
Similar(58)
From that meager beginning, Giazotto fleshed out a complete composition according to established Baroque principles of composition, creating something generally in the style of a chaconne, in which a set of repeated pitches underlies an evolving melody.
Guidelines have also been developed in Sweden according to established ethical principles about withdrawing or withholding life-supporting treatment[ 18].
Let me discuss the many problems and injustices associated with the existence of the CMUs....the conduct of legal proceedings according to established rules and principles for the protection and enforcement of private rights, including notice and the right to hearing before a tribunal [my emphasis] with the power to decide the case.
In the end, scholars said, the real impact of the new provision — defining "principles of Shariah" according to established Sunni Muslim thought — would be to move the battle over the application of Islamic law further into the terrain of religious scholarship.
The subjects were classified according to established criteria.
According to established procedures, the smaller groups were to stay behind to provide fire cover.
The conflict had at this time, according to established definitions, reached the threshold of civil war.
Cases and controls were classified according to established FEBSTAT protocols.
Data were analyzed according to established standards of descriptive statistics.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com