The advent of equipment condition evaluation at the edge, facilitated by the Internet of Things (IoT), has led to significant reduction in data transmission and improvement in diagnostic efficiency. Nevertheless, the multiscale components and noise interferences will seriously affect the quality of end-side sensed signals. Additionally, the mismatch between edge-side rigid models and time-varying nature of data features can lead to the failure of edge evaluation. To overcome these issues, this study introduces an IoT-based adaptive multiplication-convolution sparse denoising (AMCSD) method for the accurate equipment edge condition evaluation. Initially, from the perspective of signal processing synergized with deep learning, a lightweight signal denoising network is proposed with an array of multiplication filtering kernels (MFKs). Guiding by fault signal modulation mechanism, the learned MFKs sparse filters can adaptively extracted the fault-related frequency features with irrelevant components suppressed from the time-series differential information distributed in the degeneration process. Subsequently, an end-edge collaborative mechanism framework is designed and deployed on end-edge hardware unit. A compact end-side processing node (EPN) prototype can achieve efficient edge denoising effect with data adaptive compressing. Concurrently, the edge-side device named AlxBoard can implement the model adaptive dynamic updating. This means that adaptive signal denoising employed in the end-side focuses on the improvement of signal quality and sparse filter learning encompassed in the edge-side aims to solve the model mismatch. These advancements are anticipated to provide a monotonic but sensitive evaluation of degradation at the edge, surpassing the capability of conventional approaches.