Methods and apparatus for diagnosing unobserved operational parameters

A method comprising:

• obtaining a plurality of causal relationships between pairs of observable parameters of a machine or apparatus, wherein each pair comprises a cause parameter and an effect parameter;
• determining, for at least some of the parameters, a decomposition of a parameter of the at least some parameters into a plurality of information components based on the obtained causal relationships between the parameters, wherein the decomposition comprises a synergistic information component comprising information obtained from a combination of at least two causal relationships having the parameter as effect parameter;
• determining whether a certain parameter comprises a negative synergistic information component;
• diagnosing, based on whether the negative synergistic information component exists, whether an unobserved operational parameter exists that provides a cause for the certain parameter comprising the negative synergistic information component;
• and
• performing control and/or validation of a system design for the machine or apparatus, based on whether an unobserved parameter is diagnosed, wherein the diagnosis that no unobserved operational parameter exists is used as validation of the system design.