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Local model networks approximate a nonlinear system through multiple local models fitted within a partition space. The main advantage of this approach is that the identification of complex nonlinear processes is alleviated by the integration of structured knowledge about the process. This paper extends these concepts by the integration of quantitative process knowledge into the identification procedure. Quantitative knowledge describes explicit dependences between inputs and outputs and is integrated in the parameter estimation process by means of equality constraints. For this purpose, a constrained generalized total least squares algorithm for local parameter estimation is presented. Furthermore, the problem of proper integration of constraints in the partitioning process is treated where an expectation-maximization procedure is combined with constrained parameter estimation. The benefits and the applicability of the proposed concepts are demonstrated by means of two illustrative examples and a practical application using real measurement data.