## 1 Introduction  
In the last stage of the LP steam turbine, rotor blades can vibrate with higher amplitudes as a result of flutter or changes in condenser pressure [1]. This paper considers rotor blade amplitudes and frequencies using the tip-timing method. Measurements of steam turbine last stage LP rotor blade vibrations were presented by [PERSON] and [PERSON] [2], using a noise sensor mounted in the casing to find the excessive blade vibration caused by flutter in high condenser pressure. [PERSON] et al. [3] used the tip-timing method with an optical sensor mounted in the casing to find blade vibration in an LP last stage. The experimental and numerical results of the last-stage low-pressure rotor blade flutter were presented by [PERSON] et al. [4]. The dynamic behavior of blades was numerically investigated, and the grouping of blades in packs was optimized to avoid resonances. This led to the design of new blades, which were mounted in the turbine, and the measured results showed an improvement in the turbine's dynamic behavior. [PERSON] and [PERSON] [5] used tip-timing to show an increase in the vibration amplitude of a cracked blade in a 1000 MW turbine LP last stage. [PERSON] [6] used tip timing to analyze synchronous and nonsynchronous vibrations of a steam turbine LP last stage rotor blade. This showed how the pressure in the condenser influences rotor blade vibration in a nominal state. This paper analyzes blade amplitudes and frequencies by varying the condenser pressure and power to non-nominal conditions in the steam turbine LP last stage, which is a new approach. The condenser pressure is regulated by a valve breaking the vacuum in the exhaust hood. The nonlinear least-squares Levenberg-Marquardt tip-timing method is used to identify multimode blade vibrations. A literature review of tip-timing methods was presented at ASME Turbo-Expo 2012, Copenhagen [7; 8; 9; 10; 11; 12], and by [PERSON] et al. [13]. Several processing techniques have been proposed for the blade tip-timing method, using various numbers of probes and probe configurations. Some tip-timing studies have assumed that each blade vibrates with a single frequency mode [14; 15; 16]. An auto-based blade tip-timing (BTT) analysis method for blades vibrating with two simultaneous resonances was used by [PERSON] et al. [17]. A method of analyzing multimode blade vibration signals involving groups of regularly spaced optical sensors was used by [PERSON] and [PERSON] [18]. Blade multi modes in a rotating stall were identified using the non-uniform Fourier transform by [PERSON] and [PERSON] [19]. Most of the eigenmodes in the rotating stall were excited as the result of repeated, strong impacts on the blade. Eight optical probes were used. [PERSON] et al. [20] used the non-uniform Fourier transform (NUDFT), the minimum variance spectrum estimator approach, a multichannel technique with in-between samples interpolation, the Lomb-Scargle periodogram and an iterative variable threshold procedure to analyze synchronous engine order resonance, rotating stall and limit-cycle oscillations. The synchronous analysis required a higher number of sensors. NUDFT methods estimated the first three nonsynchronous blade modes of a steam turbine for vibration. Sparse reconstruction of the blade tip-timing signal for multimode blade vibrations was proposed by [PERSON] et al. [21]. Four sensors were sufficient to reconstruct the vibration signal for a numerical simulation of rotor blade vibration with three modes. In the experimental set-up, three optical sensors were mounted in the casing, and an additional optical fiber once-per-revolution sensor was also used. One-frequency blade vibrations were detected. The number of sensors depended on the sparseness of the blade vibration signal. In the worst case, the number of sensors was twice the number of dominant vibration frequencies. The influence of measurement uncertainties was not considered.