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Indirect, online tool wear monitoring is one of the most difficult tasks in the context of process monitoring for metal-cutting machining processes. Based on a continuous acquisition of certain process parameters (signals such as cutting forces or acoustic emission) with multi-sensor systems, it is possible to estimate or to classify certain wear parameters. However, despite of intensive scientific research during the past decades, the development of reliable and flexible tool wear monitoring systems is an ongoing attempt. This article introduces a new, hybrid technique for tool wear monitoring in turning which fuses a physical process model (hard computing) with a neural network model (soft computing). The physical model describes the influence of cutting conditions (such as tool geometry or work material) on measured force signals and it is used to normalize these force signals. The neural model establishes a relationship between the normalized force signals and the wear state of the tool. The advantages of this approach are demonstrated by means of experimental results. Moreover, it is shown that the consideration of process parameters, cutting conditions, and wear in one model (either physical or neural) is extremely difficult and that existing hybrid approaches are not adequate. The ideas presented in this article can be transferred to many other process monitoring tasks.